Modeling Multilayer Pyramidal-Like Adsorbate Structures Growth During Deposition at Homoepitaxy

We perform a theoretical and numerical study of the process of epitaxial growth of pyramidal islands in adsorptive systems with interacting adsorbate within the framework of phase-field approach based on the Burton–Cabrera–Frank model. We discuss dynamics of the pattern formation and show that pyramidal-like adsorbate islands can be formed in the case of elevated values of the interaction energy of adatoms. By introducing fluctuations of the lateral lateral flux of adsorbate, we show that the multiplicative noise is able to change the type of surface structures and scaling properties of the growing surface. We generalize the phase-field model by taking into account the local change in the temperature of the growing surface caused by adsorption/desorption processes. We show that in such a system the local changes in the surface temperature can result in oscillatory dynamics of pattern formation. Analytic predictions were verified by numerical simulations. We discuss the statistical properties of the morphology of the growing surface during epitaxial growth. It will be shown that the number of pyramidal-like adsorbate structures decreases with time in a power-law form; the mean size of adsorbate islands grows in a power-law form over exposing time. We discus two different approaches to determine the distribution function of islands over sizes. It will be shown that these distributions are universal and invariant to a change in main system parameters.