Surface patterns due to step flow anisotropy formed in crystal growth process

The growth of gallium nitride on a GaN(0001) surface was conducted in an N-rich state for both metal organic vapor phase epitaxy (MOVPE) and hydride vapor phase epitaxy (HVPE) methods and therefore it was controlled by surface diffusion of Ga adatoms. At these conditions two consecutive atomic steps on the GaN(0001) surface had one or two broken bonds. Consequently, their kinetic properties were different. According to the wurtzite symmetry, the step had a trigonal symmetry preserving the number of broken bonds for rotation by 2π/3 and exchanging the step type for rotation by π/3. The simplest model was introduced which allowed the growth of a GaN crystal to be simulated at this surface, preserving the lattice symmetry, and taking into account the presence of one or two broken bonds for the consecutive step order and orientation. The Monte Carlo simulations of the model showed that, depending on the terrace width, the steps either tended to group in a double step structure, or, for wider terraces, formed wave-like structures (step meandering). The results of the Monte Carlo simulations exactly recovered the structures that were observed in the Atomic Force Microscopy images of a GaN surface grown by MOVPE.