| Popis: |
In this thesis, we develop a number of theoretical approaches that can be used to investigate the nucleation and growth of islands in submonolayer deposition. In particular, we consider initially a rate-equation approach in which we propose a system of differential equations as a mean-field model of the submonolayer deposition of monomers onto a surface. A key feature of these equations is that they depend explicitly on a parameter known as the critical island size. We use rigorous and novel mathematical techniques to obtain results on the asymptotic behaviour of the point island size distribution. A fragmentation theory approach is also used in a one-dimensional model to obtain information on the asymptotic behaviour of the distribution of gaps between islands, the latter being represented by points on a line. This then leads to corresponding results for the capture zone distribution (CZD) associated with the islands. The CZD asymptotic forms that we obtain will be seen to differ from those of the Generalised Wigner Surmise (GWS) which has recently been proposed for island nucleation and growth models. The results predicted by our fragmentation approach and by the GWS are compared to kinetic Monte Carlo simulation data, and although this highlights both strengths and deficiencies in each approach, it also provides evidence that the fragmentation approach is more satisfactory than the GWS. ii We conclude by presenting a model for the nucleation of point islands in one dimension that leads to distributional fixed point equations. This approach develops a new retrospective view of how the inter-island gaps and capture zones have developed from the fragmentation of larger entities. Solutions of these equations are compared to the simulation data, and to theoretical models based on more traditional fragmentation theory approaches. These comparisons confirm the competitive performance of the distributional fixed point equations. |
