C.M. Goringe

TIGHT-BINDING MODELLING OF MATERIALS

The tight-binding method of modelling materials lies between the very accurate, very expensive, ab initio methods and the fast but limited empirical methods. When compared with ab initio methods, tight-binding is typically two to three orders of magnitude faster, but suffers from a reduction in transferability due to the approximations made; when compared with empirical methods, tight-binding is two to three orders of magnitude slower, but the quantum mechanical nature of bonding is retained, ensuring that the angular nature of bonding is correctly described far from equilibrium structures. Tight-binding is therefore useful for the large number of situations in which quantum mechanical effects are significant, but the system size makes ab initio calculations impractical. In this paper we review the theoretical basis of the tight-binding method, and the range of approaches used to exactly or approximately solve the tight-binding equations. We then consider a representative selection of the huge number of systems which have been studied using tight-binding, identifying the physical characteristics that favour a particular tight-binding method, with examples drawn from metallic, semiconducting and ionic systems. Looking beyond standard tight-binding methods we then review the work which has been done to improve the accuracy and transferability of tight-binding, and moving in the opposite direction we consider the relationship between tight-binding and empirical models.

A comparison of linear scaling tight-binding methods

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. Various example systems are explored: an insulator (carbon in the diamond structure), a semiconductor (silicon), a transition metal (titanium) and a molecule (benzene). 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.

Hydrogen diffusion on Si(001) studied with the local density approximation and tight binding

As computational power increases, it becomes easier to model complex reactions. It is important to understand where the limitations of different modelling methods lie, and what each can be used for. The diffusion of hydrogen on the Si(001) surface is presented, studied with the local density approximation (LDA) to density functional theory (DFT) and tight binding. A new parametrization for tight binding is presented, and its fitting described. Tight binding is found to describe the diffusion reaction well, once a correction has been applied.

Identification of the Si(001) missing dimer defect structure by low bias voltage STM and LDA modelling

Abstract A JEOL scanning tunneling microscope (STM) has been used to image the clean silicon (001) surface at low sample bias voltages (around −0.4 V). At this bias, many dimer vacancies are highlighted by a bright feature on the neighbouring dimers. On other defects, this situation is reversed; the area around the defect becomes dark at low voltages. In both cases, at higher bias voltages (around −0.8 V), this contrast disappears. For a number of proposed structures of the single dimer vacancy, ab initio calculations of charge density as a function of energy have been used to simulate STM images. These images show significant bias voltage dependence, and the low bias voltage images differ markedly between the structures modelled. On this basis, we identify the rebonded structure with the bright defect, and the non-rebonded structure with the dark defect.

Gas-source growth of group IV semiconductors: I. Si(001) nucleation mechanisms

The initial stages of gas-source growth of Si(001) using disilane have been investigated using a combination of elevated-temperature STM and atomistic modelling. The reaction pathway from the initial adsorption of disilane fragments up to the nucleation of short strings of epitaxial dimers is discussed. By the use of our STM to study disilane at the temperatures of interest, and atomistic modelling to calculate structural stability and significant activation barriers, we are able to propose a complete description of the mechanisms which underlie gas-source growth.

An ab initio study of SiH2 fragments on the Si(001) surface

Density functional theory calculations have been performed to find the minimum energy adsorption configuration for SiH2 on the Si(001) surface. Of the four sites considered, the two most stable are found to differ in adsorption energy by less than 0.01 eV. The energy of a second adsorption event on an adjacent site has been evaluated for the two favourable structures; in one case a strong repulsive interaction is found between the adsorbates, effectively preventing this structure from contributing to the growth mechanism. Recent experimental studies are assessed in the light of these results.

Gas-source growth of group IV semiconductors: II. Growth regimes and the effect of hydrogen

Abstract The crucial difference between gas-source molecular beam epitaxy (MBE) and conventional MBE is the presence of hydrogen on the growth surface. The amount and behaviour of the hydrogen are controlled by a combination of temperature and disilane flux. In situ observations under growth conditions are essential for an accurate understanding of non-equilibrium growth phenomena such as nucleation and coarsening, because once the flux has been cut off the surface material will redistribute itself. We have found that not only does surface hydrogen block silicon diffusion, but also hydrogen saturation of the substrate step edges blocks step-flow growth so that island growth predominates below 700 K, even at low fluxes. The denuded zones seen in MBE are not observed. Above 700 K, the adsorption barrier at step edges is overcome, and a transition from island growth to step-flow growth is observed as the flux is varied.

Statistical analysis of adsorbates

Abstract Now that it is possible to observe individual atoms and molecules adsorbed on a surface, a method is required to evaluate the correlation between the occupancy of neighbouring sites. To meet this need, a rigorous theoretical analysis of the distribution of adsorbates on surface sites has been developed, first for uncorrelated adsorption, and then for cases where the occupation of a site affects the probability of occupation of a neighbouring site. Statistical parameters can be measured from experimental images and related directly to the theoretical model, with allowance being made for defects and edge effects. By analysing scanning tunnelling microscope images in this way, it is found that trimethylgallium on GaAs(001)-(2 × 4) exhibits enhanced nearest neighbour occupation, whereas ethylene on Si(001)-(2 × 1) shows nearest neighbour repulsion.

A proposed structure of the nucleus for gas-source epitaxial growth of silicon

Abstract A novel structure has been observed by scanning tunneling microscopy (STM) on the Si(001) surface after exposure to disilane between 400 and 600 K. The feature is a bright square, with dark lines running across it forming a cross. The proposed structure, a ring of four silicon atoms bonded together and connected by one back-bond per atom to the underlying silicon dimers, has been modelled using tight-binding and density functional theory (DFT) calculations. This ring has been found to be energetically stable with respect to isolated ad-dimers. As it is the first feature to form from disilane fragments with increasing temperature, and its local bonding configuration is very similar to the rebonded B-type step edge which is known to be the favoured adsorption site for epitaxial growth, it may play a crucial role as the nucleus of the new epitaxial layer during gas-source growth of silicon.

Rotation of a silicon dimer over the trench between dimer rows on the Si(001) surface

The behaviour of ad-dimers on the Si(001) surface is of great importance during epitaxial growth. In particular, during gas source growth, dimers form over the trench between dimer rows in the non-epitaxial orientation and must rotate before being incorporated into an epitaxial island. A rotation mode for dimers in this position is described, which leads to an understanding of an important step in the growth process. The mode is modelled with ab initio methods, and a barrier is found entirely in line with available experimental observations.