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This work provides a ground for a quantitative interpretation of experiments on step bunching during sublimation of crystals with a pronounced Ehrlich-Schwoebel (ES) barrier in the regime of weak desorption. A strong step bunching…
We use kinetic Monte Carlo simulations to understand growth- and etching-induced step bunching of 6H-SiC{0001} vicinal surfaces oriented towards [1-100] and [11-20]. By taking account of the different rates of surface diffusion on three…
We devise a new 1D atomistic scale model of vicinal growth based on Cellular Automaton. In it the step motion is realized by executing the automaton rule prescribing how adatoms incorporate into the vicinal crystal. Time increases after…
Step meandering due to a deterministic morphological instability on vicinal surfaces during growth is studied. We investigate nonlinear dynamics of a step model with asymmetric step kinetics, terrace and line diffusion, by means of a…
We study a recently proposed nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. (80), 4221 (1998)]. A careful…
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…
We propose a one-dimensional model based on the Burton-Cabrera-Frank equations to describe the electromigration-induced step bunching instability on vicinal surfaces. The step drift resulting from atomic evaporation and/or deposition is…
We studied the step dynamics during sublimation and growth in the presence of electromigration force acting on the adatoms. In the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps we formulate a…
In order to study the unstable step motion on vicinal crystal surfaces we devise vicinal Cellular Automata. Each cell from the colony has value equal to its height in the vicinal, initially the steps are regularly distributed. Another array…
Turing instabilities for a two species reaction-diffusion systems is studied under anisotropic diffusion. More specifically, the diffusion constants which characterize the ability of the species to relocate in space are direction sensitive.…
We formulate a new (1+1)D step model of potentially unstable vicinal growth that we call "C+ - C-" model and study the step bunching process in it. The basic assumption is that the equilibrium adatom concentrations on both sides of the step…
We studied the step dynamics during crystal sublimation and growth in the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps. For this limit we formulate a model free of the quasi-static…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
Turing patterns emerge from a spatially uniform state following a linear instability driven by diffusion. Features of the eventual pattern (stabilized by non-linearities) are already present in the initial unstable modes. On a uniform flat…
We study the effect of crystal symmetry and step-edge diffusion on the surface current governing the evolution of a growing crystal surface. We find there are two possible contributions to anisotropic currents, which both lead to the…
The steps at the crystal surfaces could be transparent for the migrating adatoms. In the case of significant transparency the velocity of a given step in a given moment is affected by detachment of atoms from rather distant steps in rather…
Bunching and meandering instability of steps at the 4H-SiC(0001) surface is studied by the kinetic Monte Carlo simulation method. Change in the character of step instability is analyzed for different rates of particle jumps towards step. In…
We study the evolution of step bunches on vicinal surfaces using a thermodynamically consistent step-flow model that (i) circumvents the quasistatic approximation that prevails in the literature by accounting for the dynamics of adatom…
We study the step bunching kinetic instability in a growing crystal surface characterized by anisotropic diffusion. The instability is due to the interplay between the elastic interactions and the alternation of step parameters. This…
Step meandering instability in a Burton-Cabrera-Frank (BCF)-type model for the growth of an isolated, atomically high step on a crystal surface is analyzed. It is assumed that the growth is sustained by the molecular precursors deposition…