Thermal roughening of an SOS-model with elastic interaction

We analyze the effects of a long-ranged step-step interaction on thermal roughening within the framework of a solid-on-solid model of a crystal surface by means of Monte Carlo simulation. A repulsive step-step interaction is modeled by elastic dipoles located on sites adjacent to the steps. In order to reduce the computational effort involved in calculating interaction energy based on long-ranged potentials, we employ a multi-grid scheme. As a result of the long-range character of the step interaction, the roughening temperature increases drastically compared to a system with short-range cutoff as a consequence of anti-correlations between surface defects

Strukturbildung an Kristalloberflächen unter elastischer Wechselwirkung

Due to a mismatch between the adsorbate and the substrate the components of heteroepitaxial structures often are elastically strained. In homoepitaxy elastic interactions arise from inhomogeneities of the local electronic bonds near steps and adatoms. On flat substrates or adsorbate layers the elastic strain produces long-range interactions between steps, islands and single adatoms. Incorporating heteroepitaxial and homoepitaxial interactions into a particle based model the effects of long-range elastic interactions on two-dimensional surfaces are studied employing Monte-Carlo methods. The simulations are made possible by a new type of multi-grid scheme, which reduces the order of the computational costs. Shortrange interactions are taken into account exactly. Long-range interactions are resolved only on a course-grained level but in a way that the correct asymptotics is reproduced. In the limit of submonolayer epitaxy the elastic r$^{−3}$ interaction between adatoms delays the process of island nucleation. In the low coverage limit a new scaling law is found, which reduces the behavior of the system to universal functions. On crystal surfaces elastic effects generate a repulsive r$^{−2}$ interaction between steps. Depending on the ratio of step interaction strength and local step energy the roughening temperature of the surface can increase by more than a factor of three in comparison to a purely local model