A self-consistent tight-binding approach applied to semiconductor nanostructure is presented. This allows us to describe electronic and optical properties of nanostructured devices beyond the usual envelope function approximation. Example of applications are given for High Electron Mobility Transistors (HEMTs) and non-linear optical devices.

We present a tight-binding formalism which can properly treat various ionic füllendes. In the Hamiltonian we include the intrafullerene Coulomb repulsion energy and the Madelung energy of the ionic lattice, both of which depend on the possible charge disproportion between fullerenes. This Hamiltonian requires a self-consistent treatment, but it is applicable to much larger systems than first-principles methods. Using this formalism we have studied the electronic structure of the one-dimensional A1C60 polymer. The present generalization of the tight-binding model is found to be important for ionic füllendes and a moderate-amplitude charge-density-wave state is found to be a possible stable state.

A revisited electronic structure study of iron pyrite, FeS2, has been performed using a new Tight-Binding Linear Muffin-Tin Orbital (TB-LMTO) technique in which the radii of overlapping MT spheres are determined from a full potential construction. The interstitial spheres were chosen to provide an efficient packing of space while ensuring that the overlap between the spheres remain small. We have found that this treatment of interstitial spheres results in a dramatic improvement in the description of the electronic structure and the binding energy curves for FeS2 in comparison with a previous LMTO calculation. In particular, the energy band gap, the equilibrium lattice constant and the bulk modulus are all in much better agreement with experimental observations. Moreover, the calculated equation of state is in excellent accord with recent measured P- V data up to pressures of 15GPa with overall deviations of less than 10%. The predicted reflectivity spectrum of FeS2 as a function of pressure gives the observed behaviour of the optical edge. The bonding behaviour the orthorhombic marcasite phase of FeS2 is also discussed within this new TB-LMTO formalism.

We examine the effects of grain-boundaries on the order-parameter and critical-currents in superconductors. We use a geometrical model of the lattice structure of grain-boundaries. We solve the Bogoliubov-de Gennes equation using the Recursion Method to obtain the self-consistent BCS gap function Δ and the local density of states N(E) near the boundary. Imposing a phase difference across the boundary we calculate the supercurrent and hence obtain the critical-current, Ic, of the junction.

Four linear scaling tight binding methods (the density matrix method, bond order potentials, the global density of states method, and the Fermi operator expansion) are described and compared to show relative computational efficiency for a given accuracy. The density matrix method proves to be most efficient for systems with narrow features in their energy gaps, while recursion based moments methods prove to be most efficient for metallic systems.

We describe linear scaling methods for electronic structure calculations and quantum molecular dynamics simulations, which are based on an orbital formulation of the electronic problem. In particular, we discuss some open problems which need to be addressed to improve the performances of these methods, and briefly review some applications to carbon and silicon systems, within a Tight-Binding framework.

Carbon allotropy allows the formation of a large variety of disordered structures whose properties depend on the density and on the preparation technique. Computer simulations, based on quantum mechanics, can reproduce the essential features of these systems. We first assess the reliability of the amorphous carbon structures generated by molecular dynamics simulations based on a semi-empirical Tight Binding hamiltonian. Then we attempt to understand of the path followed by diamond to reach the amorphous phase via a direct crystalline-to-amorphous transformation. Results concern the large variety of structures which can be obtained and a general adequacy of the semi-empirical Tight Binding hamiltonian to reproduce the essential features of amorphous carbon structure. Moreover, it is shown that the process of direct transformation from the crystalline into the amorphous phase occurs continuously. The formation of three-fold coordinated sites is not followed by an immediate site re-hybridization. When this process takes place, a large strain sites associated with the mis-coordinated sites is released.

We show that a simple tight binding model with a repulsive potential describes the Peierls distortions in covalent systems and the well-known octet rule. The existence and the intensity of the Peierls distortion is mainly related to the hardness of the repulsive potential as demonstrated both by theoretical calculations and by the experimental systematic analysis of liquid structures. In particular, As is threefold coordinated and Sb is sixfold coordinated in the liquid, the qualitative difference is explained by the ratio of the distortion energy ΔE to the thermal energy kBT. The Asx Sb1-x alloys show continuously varying average coordination numbers showing: the semiconductor-metal transition is continuous with concentration.

In addition, we illustrate in the case of liquid Se that, tight binding Monte Carlo simulations are able to describe quantitatively the structure of liquid elements provided the Van der Waals potential is added.

By combining tight-binding (TB) molecular dynamics (MD) with the recently-proposed activation-relaxation technique (ART), we have constructed structural models of a-GaAs and a-Si of an unprecedented level of quality: the models are almost perfectly four-fold coordinated and, in the case of a-GaAs, exhibit a remarkably low density of homopolar bonds. In particular, the models are superior to structures obtained using melt-and-quench TB-MD or quantum MD. We find that a-Si is best described by a Polk-type model, while a-GaAs resembles closely the mechanical model proposed by Connell and Temkin, which is free of wrong bonds. In this paper, the structural, electronic, and dynamical properties of a-GaAs based on this approach will be reviewed, and compared to experiment and other structural models. Our study provides much-needed information on the intermediate-range topology of amorphous tetrahedral semiconductors; in particular, we will see that the differences between the Polk and Connell-Temkin models, while real, are difficult to extract from experiment, thus emphasising the need for realistic computer models.

We present a simple and informationally efficient approach to electronic-structure-based simulations of large material science systems. The algorithm is based on a flexible embedding scheme, in which the parameters of a model potential are fitted at run time to some precise information relevant to localised portions of the system. Such information is computed separately on small subsystems by electronic-structure “black box” subprograms, e.g. based on tight-binding and/or ab initio models. The scheme allows to enforce electronic structure precision only when and where needed, and to minimise the computed information within a desired accuracy, which can be systematically controlled. Moreover, it is inherently linear scaling, and highly suitable for modern parallel platforms, including those based on non-uniform processing. The method is demonstrated by performing computations of tight-binding accuracy on solid state systems in the ten thousand atoms size scale.

Atomistic modelling of Materials Science problems often requires the simulation of systems with an irreducibly-large unit cell, such as amorphous materials, fullerites, or systems containing extended defects, such as dislocations, cracks or grain boundaries. Large-scale simulations with the Tight-Binding approach must face the computational obstacle represented by the O(N3)-scaling of the diagonalization of the Hamiltonian matrix. This bottleneck can be overcome by parallel computing techniques and/or the introduction of faster, O(N)-scaling algorithms. We report the activities performed in the frame of a collaboration among several research groups on the porting of TBMD codes on parallel computers. In particular, we describe the porting of a O(N3) TBMD code on different MIMD computers, with either distributed or shared memory, by using appropriate software tools. Furthermore, preliminary results obtained in the porting of an O(N) TBMD code on an experimental, hybrid MIMD-SIMD computer architecture are reported. The new perspective of using specialized platforms to deal with large-scale TBMD simulation is discussed.

A method is presented that allows, in principle, the prediction of the existence and structure of (metastable) compounds. We show the results of this approach for two examples of binary and ternary ionic compounds that have not been synthesized yet, but should stand a fair chance of being kinetically stable.

We have developed a technique for treating the coupled dynamics of electrons and nuclei in a molecule which is subjected to ultrashort and ultra-intense laser pulses. This technique has been employed in quantitatively accurate simulations for . Many interesting phenomena have been observed, including photodissociation, bond softening, above-threshold dissociation, ion-population trapping, electron-population trapping, sudden electronic transitions, Rabi flopping, and harmonic generation. Some representative results are shown here.

We have further developed and applied a new non-empirical tight-binding total energy model to properties of Si, Xe, and Fe at high pressures. We have studied elasticity of various phases of each of these, demonstrating that the new model is applicable to a wide range of materials, including semiconductors, rare gases, and transition metals. We have used the particle-in-a-cell method to study the thermal equation of state of hep Fe and find excellent agreement with the shock equation of state. A molecular dynamics code has been developed based on this method, and we have studied the properties of Fe liquid at high pressures.

We apply the frozen phonon and molecular dynamics methods within the semiempirical orthogonal tight-binding framework to study the anomalous behaviour of the (0001) optical longitudinal (LO) and transverse (TO) phonons in the low temperature hep phase of Ti, and the ⅔[111]L and ½[110]T1 phonons in the high temperature bec phase. We demonstrate that, in agreement with previous findings in Zr, the anomalous thermal frequency shifts in hep Ti are related to the strong coupling of the electron density of states (DOS) to the particular lattice distortions. The distortions along the bec ⅔[111]L and ½[110]T1 phonons also significantly affect the DOS, resulting in the instability of these modes at low temperatures and triggering the bcc-hep and bcc-ω phase transformations.

Tight-binding molecular dynamics simulations of typical high-energy grain boundaries in silicon show that the atomic structure of the interface in thermodynamic equilibrium is similar to that of bulk amorphous silicon and contains coordination defects. The corresponding electronic structure is also amorphous-like, displaying extra states in the forbidden gap mainly localized around the coordination defects, where large changes in the bond-hybridization character are observed. It is proposed that such coordination defects in disordered high-energy grain boundaries are responsible for the experimentally observed gap states in polycrystalline Si.

The electronic structure of a continuous network model of tetrahedrally bonded amorphous silicon (a-Si) and of a model hydrogenated amorphous silicon (a-Si:H) that we have built from the a-Si model are calculated in the tight binding approximation. The band edges near the gap are characterized by exponential tails of localized states induced mainly by the variations in bond angles. The spatial localization of the states is compared between a-Si and a-Si:H. Valence band offset between the amorphous and the crystalline phases is calculated.

We investigated by tight-binding molecular dynamics the structure, the bulk modulus and the electronic properties of the smallest four-branched carbon schwarzites fcc-(C28)2, fcc-(C36)2 and fcc-(C40)2 having the shape of a D minimal periodic surface. They are found to have a stability comparable to that of fullerene C60 and to exhibit alternative metallic and insulating characters, with an apparent relationship to their local geometry. We also studied the coalescence of fullerenic fragments and carbon clusters by following the evolution of the topological connectivity. Though different temperature variation protocols lead to irregular structures similar to random schwarzites, their connectivity is found to stabilize at values corresponding either to tubulene or three-branched schwarzites, indicating that long time evolution at constant connectivity is potentially able to yield regular shapes. Experiments on laser-induced transformations of fullerite occasionally yield branched tubular structures with a schwarzite shape.