Nano-Sized Pyramidal Pattern Formation During Epitaxial Growth in the Framework of Phase Field Modeling

We study processes of pyramidal pattern formation at epitaxial growth in the framework of phase-field theory by taking into account interactions of adsorbate, local variations of adsorbate temperature and fluctuations of diffusion flux. It is found that pattern formation processes and pattern morphology can be controlled by fluctuations of the total diffusion flux fluctuations. In the framework of generalized phase-field model by taking into account local change in the surface temperature at adsorption/desertion processes it is shown that at early stages of the system evolution the oscillatory regime of pattern formation is realized. It is shown that the frequency of temperature oscillations increases with the deposition rate growth. It was shown that fluctuations of the diffusion flux can crucially change dynamics of islands growth and govern morphology of the surface pattern. It is found that in the generalized model pyramidal structures are characterized by large differences in heights between two neighbor terraces and can be formed at low of interaction strength of adatoms. Growth and roughness exponents are obtained. Island size dynamics manifesting a self-similar behavior and universality of the probability density over the island size are analyzed.