SIMULATION STUDIES OF LEAD AND SILICON SURFACES

Abstract

Since its inception, the field of surface science has undergone such rapid expansion that dozens of scientific journals nowadays have either devoted entire sections or are specifically tailored for the dissemination of new results from its numerous respected practitioners. This expansion has been driven by the combination of the ready availability of ultrahigh vacuum environments, the development of techniques for the preparation of macroscopic single crystal surfaces, and the application of an increasingly complex array of surface analytical techniques, which have made possible characterizations of the structures and reactivity of a wide range of surfaces. On the theoretical side, progress has been made in the improvement of current simulation methods such as Monte Carlo and Molecular Dynamics, couple with the constructions of novel interatomic potentials for the study of complex surface structures ranging from compound semiconductors to high Tc superconductors and fullerenes. In tire past, simple two-body potentials have been used for the study of condensed matter due to computational efficiency. However, it was soon found that only a limited class of materials could be reasonably modelled with such potentials, namely rare gas solids and some simple metals. Applications to other materials such as semi-conductors and transition metals have resulted in poor agreement with experimental observation since the very important many-body effects in these materials are not accounted for. In the present work, we employ two very different potentials, one belonging to the class of cluster potentials for the study of Si atoms on Si surfaces while the other, belonging to the class of pair functionals is used to study phase transitions on Pb surfaces. This thesis is organized as follows. In chapter 1, we give an introduction to the glue Hamiltonian and explain the fitting process used to obtain a reasonable potential for fcc lead. A brief description of the molecular dynamics methods is also presented. This is followed by a study of surface disordering and premelting on Pb(110) surface in Chapter 2. Several computer codes were developed to calculate quantities of interest in atom scattering experiments, in particular the dynamic structure factor which can provide insights into the diffusional properties of atoms in a thin molten layer. Chapter 3 illustrates further the usefulness of the glue potential in a seminal investigation of incomplete melting on Pb(100). The stability of this surface up to Tm corresponds well with recent experimental results. In Chapter 4, we present an improved version of the Stillinger-Weber potential for the study of silicon surfaces. Included in the discussion is a short exposition of the Metropolis algorithm used in the context of canonical Monte Carlo simulation. Following this is an investigation of the migration of single Si adatoms and ad-dimers on Si(001) in Chapter 5. Here, we showed that the path of easy diffusion is parallel to the substrate dimer rows, in accordance with STM observations. We then end this thesis with a detailed study of adatom-step interaction in Chapter 6, followed by some suggestions of further work in Chapter 7.