arXiv subjects

Magdalena A. Załuska-Kotur

Publications and source records attributed to Magdalena A. Załuska-Kotur.

15 recordsLinked to original sources

arXiv2026

Complex surface patterning in homo- and heteroepitaxial contexts: (simultaneous) step bunching and step meandering

We confront a meso-scale continuum model, archetypical for the heteroepitaxial context, with an atomistic Vicinal Cellular Automaton (VicCA), built as a homoepitaxial counterpart, to show that in (2+1)D complex surface instabilities are fundamental growth phenomena rather than context-specific artifacts. Our approach is to first construct a Ginzburg-Landau-type model, designed to extend the previously (1+1)D Tersoff-type models to (2+1)D. We complement the continuum approach with a discrete one - the VicCA, in which we use a novel version of the potential landscape for the diffusing particles - a double-well potential located at each step edge. Importantly, this framework also captures both step bunching and step meandering. While these behaviors are rarely treated together in earlier approaches, they naturally coexist in real materials. Thus we establish a cross-context correspondence at the level of obtained morphologies and morphology diagrams and, additionally, a multiscale perspective on the governing parameters, bridging the gap between the mesoscale and atomistic modeling.

cond-mat.mtrl-sci↗

arXiv2026

Morphological Transition: From Meanders to Mound Structures

Mound formation on flat and miscut crystal surfaces exhibits distinct growth behaviors. While mound structures are the predominant feature on flat surfaces, miscut surfaces display a smooth transition from meandered patterns to three-dimensional mounds, depending on both internal and external conditions. We investigate this morphological evolution-from meander-like surface patterns to faceted pyramidal structures-using a Vicinal Cellular Automaton modeling framework. The transition is shown to be governed by the competition between the Ehrlich-Schwoebel barrier and adatom mobility on terraces. Under moderate barrier strengths and sufficiently high terrace diffusivity, the system demonstrates a reversible transition from mounded configurations to regular step meandered patterns. This reveals a complex interplay between kinetic barriers and mass transport. Our simulations cover a wide range of growth conditions, including variations in deposition flux, surface diffusion rates, temperature, and miscut angle. By applying the height-height correlation function, we calculate the correlation lengths along and across the steps and analyze their scaling behavior. These results offer insight into the continuum pathways that connect distinct classes of surface structures and provide a unified framework for describing pattern evolution across different crystal growth regimes.

cond-mat.mtrl-sci↗

arXiv2026

Shape Selection in Nanopillar Formation

Crystal growth processes produce a diverse array of surface formations, primarily distinguished by their geometric shapes. While some structures strictly adhere to the underlying crystal symmetry, others exhibit universal circular or oval geometries. Utilizing Vicinal Cellular Automata (VicCA) modeling, we demonstrate that these morphological differences depend on the spatial distribution of the growth potential. Specifically, local potential variations concentrated around surface steps drive the formation of the lattice symmetry - following structures, whereas global potentials - often originating from defects-generate universal spherical or oval shapes. Furthermore, we illustrate how these morphologies are influenced by the growth parameters such as sticking coefficient or diffusion coefficient. Although the positioning of surface defects is difficult to control, we show that temperature and external particle flux can be effectively used to steer and manipulate surface pattern formation.

cond-mat.mtrl-sci↗

arXiv2025

Engineering 2D Surface Patterns with the VicCa Model

We employed the VicCA model to investigate the influence of step-edge potential on nucleation and pattern formation, aiming to gain deeper insights into island formation and growth. Our study explores fractal structures governed by general cellular automaton (CA) rules, as well as compact structures shaped by density-dependent attachment mechanisms. We demonstrate that modifications to the CA framework have a significant impact on surface patterning, emphasizing the critical role of adatom attachment rules and the substantial effect of potential well depth on the resulting surface morphology.

cond-mat.mtrl-sci↗

arXiv2025

Step meandering: The balance between the potential well and the Ehrlich-Schwoebel barrier

This study presents a comprehensive and innovative exploration of how the surface potential energy landscape influences meander formation. Using the Vicinal Cellular Automaton model, which distinguishes surface diffusion from adatom incorporation into the crystal, the research delves into various factors affecting surface pattern dynamics. By isolating the diffusion process within a defined energy potential, the study provides a detailed analysis of how changes in the potential energy well and the barrier at the top of the step contribute to meander formation. Remarkably, the results reveal that the mere presence of a potential well at the step's bottom is sufficient to induce meandering. The role of the Ehrlich-Schwoebel barrier on formed meanders is further investigated, and a mechanism for meander formation is proposed to clarify this process. The derived relation successfully reflects the wavelength of the meandered patterns observed in the simulations, emphasizing its reliability. Overall, the results illustrate the crucial influence of the surface energy potential's shape in driving surface pattern formation.

cond-mat.mes-hall↗

arXiv2023

Diffusion-Dependent Pattern Formation on Crystal Surfaces

The growth of a crystal is usually determined by its surface. Many factors influence the growth dynamics. Energy barriers associated with the presence of steps most often decide about the emerging pattern. The height and type of Ehrlich-Schwoebel step barriers lead to the growth of nanocolumns, nanowires, pyramids, and bunches or meanders in the same system. Surface diffusion is another factor that determines the nature of growth. We used the (2+1)D cellular automaton model to investigate the additional effect of diffusion along with step barriers. We show that when we only change the diffusion rate, the length of the meanders or the height of the bunches increase, while the cracked structure of the nanopillars changes into very long, tall nanowires. We show that the length of the step-step correlation is a good characterization of the resulting patterns.

cond-mat.mtrl-sci↗

arXiv2019

Scaling-up Simulations of Diffusion in Microporous Materials

We introduce and demonstrate the coarse-graining of static and dynamical properties of host-guest systems constituted by methane in two different microporous materials. The reference systems are mapped to occupancy-based pore-scale lattice models. Each coarse-grained model is equipped with an appropriate coarse-grained potential and a local dynamical operator, which represents the probability of inter-pore molecular jumps between different cages. Both the coarse-grained thermodynamics and dynamics are defined based on small-scale atomistic simulations of the reference systems. We considered two host materials: the widely-studied ITQ-29 zeolite and the LTA-zeolite-templated carbon, which was recently theorized. Our method allows representing with satisfactory accuracy and a considerably reduced computational effort the reference systems while providing new interesting physical insights in terms of static and diffusive properties.

physics.comp-ph↗

arXiv2018

Unstable dynamics of model vicinal crystal surfaces: Initial and intermediate stages

We approach the old-standing problem of vicinal crystal surfaces destabilized by step-down and step step-up currents from a unified modelling viewpoint with focus on both the initial and the intermediate stages of the instability. We develop further our atomistic scale model of vicinal crystal growth (Gr) destabilized by SD drift of the adatoms in order to account for also the vicinal crystal sublimation (Sbl) and the SU drift of the adatoms as an alternative mode of destabilization. In order to study the emergence of the instability we use the number of steps in the bunch (bunch size) N as a measure and probe with small-size systems the models stability against step bunching (SB) on a dense grid of points in the parameter space formed by the diffusion rate/step transparency, surface miscut and drift direction, for each of the four possible cases - Gr+SD, Gr+SU, Sbl+SD, Sbl+SU. The obtained stability diagrams show where the system is initially most unstable and provide a ground to study there the intermediate stages of the developed instability quantifying the surface self-similarity by the time-scaling of N. For each of the four enumerated cases we show that it reaches the universal curve N=2sqrt(T/3), where T is the time, properly rescaled with the model parameters. We confirm the value of the numerical pre-factor with results from a parallel study of models based on systems of ordinary differential equations (ODE) for the step velocity.

cond-mat.mtrl-sci↗

arXiv2017

Step bunching with both directions of the current: Vicinal W(110) surfaces versus atomistic scale model

We report for the first time the observation of bunching of monoatomic steps on vicinal W(110) surfaces induced by step up or step down currents across the steps. Measurements reveal that the size scaling exponent γ, connecting the maximal slope of a bunch with its height, differs depending on the current direction. We provide a numerical perspective by using an atomistic scale model with a conserved surface flux to mimic experimental conditions, and also for the first time show that there is an interval of parameters in which the vicinal surface is unstable against step bunching for both directions of the adatom drift.

cond-mat.mtrl-sci↗

arXiv2016

Self-organizing structures in immiscible crystals

Spinodal decomposition process in the system of immiscible PbTe/CdTe compounds is analyzed as an example of a self-organizing structure. The immiscibility of the constituents leads to the observed morphological transformations like anisotropy driven formation of quantum dots and nanowires, and to the phase separation at the highest temperatures. Proposed model accomplishes bulk and surface diffusion together with the anisotropic mobility of material components. We analyze its properties by kinetic Monte Carlo simulations and show that it is able to reproduce all of the structures observed experimentally in the process of PbTe/CdTe growth. We show that studied mechanisms of dynamic processes play different role in the creation of zero--, one--, two-- and finally three-dimensional structures. The shape of grown structures is different for relatively thick multilayers when bulk diffusion cooperates with the anisotropic mobility, in annealed structure when isotropic bulk diffusion only decides about the process and finally for thin multilayers when surface diffusion is the most decisive factor. We compare our results with experimentally grown systems and show that proposed model explains the diversity of observed structures.

cond-mat.mtrl-sci↗

arXiv2014

Diffusion of Ga adatoms at the surface of GaAs(001) c(4x4) $α$ and $β$ reconstructions

Diffusion of Ga adatom at the As rich, low temperature c(4$\times$4) reconstructions of GaAs(001) surface is analyzed. We use known energy landscape for the motion of Ga adatom at two different $α$ and $β$ surface phases to calculate diffusion tensor by means of the variational approach. Diffusion coefficient describes the character of low density adatom system motion at the surface. The resulting expressions allow to identify main paths of an adatom diffusion and to calculate an activation energy of this process. It is shown that diffusion at the $α$ surface is slower and more anisotropic than this for the $β$ surface.

cond-mat.stat-mech↗

arXiv2011

Long time evolution of meandered steps during the crystal growth processes

Step meandering during growth of gallium nitride (0001) surface is studied using kinetic Monte Carlo method. Simulated growth process, conducted in N-rich conditions are therefore controlled by Ga atoms surface diffusion. The model employs dominating four-body interactions of Ga atoms that cause step flow anisotropy during growth. Overall kinetics and shape selection features of step meandering are analyzed assuming their dependence on the external particle flux and on the temperature. It appears that at relatively high temperatures and low fluxes steps move regularly preserving their initial shapes of straight, parallel lines. For higher fluxes and at wide range of temperatures step meandering happens. It is shown that, depending on the initial surface parameters, two different scenarios of step meandering are realized. In both these regimes meandering has different character as a function of time. For relatively high fluxes meanders have wavelengths shorter than the terrace width and they grow independently. Eventually surface ends up as a rough structure. When flux is lower regular pattern of meanders emerges. Step meander even if Schwoebel barrier is absent. Too high barrier destroys step stability. The amplitude of wavelike step meanders increases in time up to a saturation value. The mechanism of such meander development is elucidated.

cond-mat.stat-mech↗

arXiv2011

Structures built by steps of evaporated crystal surface Monte Carlo simulations and experimental data for GaN epi layers

We present Monte Carlo simulation data obtained for the annealed surface GaN(0001) and compare them with the experimental data. High temperature particle evaporation is a part of substrate preparation processes before epitaxy. The ideal surface ordering expected after such heating is a pattern of parallel, equally distanced steps. It appears however, that different types of step structures emerge at high temperatures. We show how the creation of characteristic patterns depends on the temperature and the annealing time. The first pattern is created for a very short evaporation time and consists of rough steps. The second pattern built by curly steps is characteristic for longer evaporation times and lower temperatures. The third pattern, in which steps merge together creating bunches of steps happens for the long enough time. At higher temperatures, bunches of steps bend into the wavy-like structures.

cond-mat.stat-mech↗

arXiv2010

Double step structure and meandering due to the many body interaction at GaN(0001) surface in N-rich conditions

Growth of gallium nitride on GaN(0001) surface is modeled by Monte Carlo method. Simulated growth is conducted in N-rich conditions, hence it is controlled by Ga atoms surface diffusion. It is shown that dominating four-body interactions of Ga atoms can cause step flow anisotropy. Kinetic Monte Carlo simulations show that parallel steps with periodic boundary conditions form double terrace structures, whereas initially V -shaped parallel step train initially bends and then every second step moves forward, building regular, stationary ordering as observed during MOVPE or HVPE growth of GaN layers. These two phenomena recover surface meandered pair step pattern observed, since 1953, on many semiconductor surfaces, such as SiC, Si or GaN. Change of terrace width or step orientation particle diffusion jump barriers leads either to step meandering or surface roughening. Additionally it is shown that step behavior changes with the Schwoebel barrier height. Furthermore, simulations under conditions corresponding to very high external particle flux result in triangular islands grown at the terraces. All structures, emerging in the simulations, have their corresponding cases in the experimental results.

cond-mat.mtrl-sci↗

arXiv2009

Diffusion of atoms interacting by long-range and oscillating forces

Collective diffusion coefficient in a one dimensional lattice gas adsorbate is calculated using variational approach. Particles interact via either a long-range, or a long range electron-gas-mediated (for a metallic substrate), or a Lennard-Jones interaction. Diffusion coefficient as a function of the adsorbate density strongly depends on the relationship between the substrate lattice constant and the characteristic length of the inter--particle interaction potential (which determines positions of the potential energy minima). The diffusion coefficient at fixed density as a function of the interaction characteristic length has an oscillating character due to the interplay between the inter--particle distances allowed by the substrate lattice structure and the average inter--particle distances which minimize the total interaction energy.

cond-mat.mtrl-sci↗