Filip Krzyżewski

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 metal organic vapor phase epitaxy or hydride vapor phase epitaxy 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 in 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. Furt...

Coexistence of bunching and meandering instability in simulated growth of 4H-SiC(0001) surface

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 the experiment effective value of jump rates can be controlled by impurities or other growth conditions. An anisotropy of jump barriers at the step influences the character of surface structure formed in the process of crystal growth. Depending on the growth parameters different surface patterns are found. We show phase diagrams of surface patterns as a function of temperature and crystal growth rate for two different choices of step kinetics anisotropy. Jump rates which effectively model high inverse Schwoebel barrier (ISB) at steps lead either to regular, four-multistep or bunched structure. For weak anisotropy at higher temperatures or for lower crystal growth rates meanders and mounds are formed, but on coming towards lower temperatures and higher rates, we observe...

Step bunching process induced by the flow of steps at the sublimated crystal surface

Stepped GaN(0001) surface is studied by the kinetic Monte Carlo method and compared with the model based on Burton-Cabrera-Frank equations. Successive stages of surface pattern evolution during high temperature sublimation process are discussed. At low sublimation rates, clear, well defined step bunches form. The process happens in the absence or for very low Schwoebel barriers. Bunches of several steps are well separated, move slowly and stay straight. Character of the process changes for more rapid sublimation process where double step formations become dominant and together with meanders and local bunches assemble into the less ordered surface pattern. Solution of the analytic equations written for one dimensional system confirms that step bunching is induced by the particle advection caused by step movement. Relative particle flow towards moving steps becomes important when due to the low Schwoebel barrier both sides of the step are symmetric. Simulations show that in the opposite limit of very high S...

Coupling of orthogonal diffusion modes in two-dimensional nonhomogeneous systems

Collective diffusion coefficient in a two-dimensional lattice gas on a nonhomogeneous substrate is investigated using variational approach. In our model particles reside and jump randomly between adsorption sites modeled as potential wells with different depths. Site blocking is the only allowed particle-particle interaction mechanism. It is shown that the value of the diffusion coefficient in one lattice direction depends nontrivially on the rate and the character of the particle jumps in other directions. The collective diffusion coefficient increases, eventually approaching values predicted within the mean-field approximation when the jump rate increases in the direction perpendicular to that in which the diffusion coefficient is measured. Analytical predictions of our model are supported by the Monte Carlo simulation performed for selected systems.

Unstable vicinal crystal growth from cellular automata

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 keeps the adatoms, initially distributed randomly over the surface. The growth rule defines that each adatom at right nearest neighbor position to a (multi-) step attaches to it. The update of whole colony is performed at once and then time increases. This execution of the growth rule is followed by compensation of the consumed particles and by diffusional update(s) of the adatom population. Two principal sources of instability are employed – biased diffusion and infinite inverse Ehrlich-Schwoebel barrier (iiSE). Since these factors are not opposed by step-step repulsion the formation of multi-steps is observed but in general the step bunches preserve a finite width. We monitor the developing surface patterns and quantify the observations by scaling laws with focus on ...

Segregation in a noninteracting binary mixture.

Process of stripe formation is analyzed numerically in a binary mixture. The system consists of particles of two sizes, without any direct mutual interactions. Overlapping of large particles, surrounded by a dense system of small particles, induces indirect entropy driven interactions between large particles. Under an influence of an external driving force the system orders and stripes are formed. Mean width of stripes grows logarithmically with time, in contrast to a typical power law temporal increase observed for driven interacting lattice gas systems. We describe the mechanism responsible for this behavior and attribute the logarithmic growth to a random walk of large particles in a random potential created by the site blocking due to the small ones.