In this thesis, we look into the problem of finding an analytical model for the submonolayer nucleation processes on a substrate. More specically, we explore the Distributional Fixed Point Equation (DFPE) approach of modelling the size distribution of the gaps between nucleated islands (GSD) on a one dimensional substrate, and the size distribution of capture zones (CZD) around the islands (areas where a free monomer is more likely to be absorbed into the relevant island than to escape to the next one).The DFPEs incorporate information about the critical island size, the nucleation mechanism (via diffusing monomers or through deposition) and the probability P(a) of a new island nucleation occurring at a position a inside a gap. The corresponding distribution Pz for the capture zones is derived from the fragmentation probability P for the gaps, so it cannot be directly observed.We develop a strategy to solve the inverse problem of calculating the distribution P and Pz from the Integral Equation form of the DFPE, for a known GSD and CZD, in which we build P and Pz as a finite Fourier series. Additionally, we solve the inverse problem in another way: by using the Tikhonov regularisation method, and compare these results against each other and with the theoretical predictions. For the case of the gaps, we can directly measure P during the kinetic Monte Carlo simulations. We compare the results to the previously calculated P and find good consistency.For the capture zones, we define an alternative distribution, one that can be measured: the probability of fragmenting a zone at a position a, Q(a). We then create an DFPE for this distribution Q, and we also use it to directly sample CZD. Since both approaches give promising results, we conclude our work by testing them on a two dimensional substrate, where we find that only the latter approach gives good results.
|Date of Award||1 Oct 2017|
- University Of Strathclyde
|Sponsors||University of Strathclyde|
|Supervisor||Paul Mulheran (Supervisor) & Michael Grinfeld (Supervisor)|