ABSTRACT
Irreversible one-dimensional (1D) epitaxial growth at small coverages via the recently suggested two-step growth protocol [Tokar and Dreyssé, Surf. Sci. 637-638, 116 (2015)] has been studied with the use of the kinetic Monte Carlo and the rate-equation techniques. It has been found that similar to the two-dimensional (2D) case the island capture zones could be accurately approximated with the Gamma probability distribution (GD). Coverage independence of the average island sizes grown at the first step that was also found in two dimensions was observed. In contrast to 2D case, the shape parameter of the GD was also found to be coverage-independent. Using these two constants as the input, an analytical approach that allowed for the description of the commonly studied statistical distributions to the accuracy of about 2% has been developed. Furthermore, it was established that the distributions of the island sizes and the interisland gaps grown via the two-step protocol were about 50% narrower than in the case of nucleation on random defects, which can be of practical importance. Equivalence between the GD shape of the island size distribution in the scaling regime and the linear dependence of the capture numbers on the island size in the rate-equation approach has been proved.
ABSTRACT
We introduce a simple model of strained epitaxy to study the growth of coherent several-monolayers-high nanoislands at low coverage. The size mismatch between the substrate (which is assumed to be rigid and passive) and the growing overlayer is modelled by the hard-sphere interaction between the adatoms. In the case of positive misfit the sphere diameter is larger than the substrate lattice parameter. Elastic interactions are described within the harmonic approximation to the substrate potential in the vicinity of the deposition sites. With additional attractive interaction between the nearest neighbour atoms the model exhibited the growth of miniature nanoislands of several morphologies with their kinetics similar to those found in real quantum dot (QD) systems. The 3D QDs exhibited narrow distributions of their heights, diameters and volumes in qualitative agreement with experimental observations.
ABSTRACT
If a stochastic system during some periods of its evolution can be divided into noninteracting parts, the kinetics of each part can be simulated independently. We show that this can be used in the development of efficient Monte Carlo algorithms. As an illustrative example, the simulation of irreversible growth of extended one-dimensional islands is considered. The approach allowed us to simulate the systems characterized by parameters superior to those used in previous simulations.
ABSTRACT
We consider a one-dimensional lattice gas model of strained epitaxy with the elastic strain accounted for through a finite number of cluster interactions comprising contiguous atomic chains. Interactions of this type arise in the models of strained epitaxy based on the Frenkel-Kontorova model. Furthermore, the deposited atoms interact with the substrate via an arbitrary periodic potential of period L. This model is solved exactly with the use of an appropriately adopted technique developed recently in the theory of protein folding. The advantage of the proposed approach over the standard transfer-matrix method is that it reduces the problem to finding the largest eigenvalue of a matrix of size L instead of 2(L-1), which is vital in the case of nanostructures where L may measure in hundreds of interatomic distances. Our major conclusion is that the substrate modulation always facilitates the size calibration of self-assembled nanoparticles in one- and two-dimensional systems.
ABSTRACT
Layer-resolved self-consistent electronic calculations of magnetic anisotropy energy (MAE) provide new insight to the off-plane magnetization observed in Pd capped Co films on Pd(111). We demonstrate that the transition from perpendicular to in-plane phases with increasing film thickness involves an intermediate spin-canted phase. The interfaces responsible for the stability of the off-plane easy axes are characterized microscopically. A local analysis of the MAEs reveals an unexpected internal magnetic structure of the Co-Pd interfaces in which the magnetic moments and spin-orbit interactions at the Pd atoms play a crucial role.
ABSTRACT
We consider a one-dimensional lattice gas model in which the atoms interact via an infinite number of cluster interactions within contiguous atomic chains plus the next-nearest-neighbor pairwise interaction. All interactions are of arbitrary strength. An analytical expression for the size distribution of atomic chain lengths is obtained in the framework of the canonical ensemble formalism. Application of the exact solution to the problems of self-assembly and self-organization is briefly discussed.
