Emergence of regular meandered step structure in simulated growth of GaN(0001) surface

Step meandering during the growth of gallium nitride crystal is studied on using kinetic Monte Carlo method. Cause of instability is identified to be the particle advection caused by the step flow. Growth process is conducted in N-rich conditions and GaN(0001) surface kinetics is modeled by setting jump probabilities for Ga atoms adsorbed at the surface. We show that at low enough temperatures and relatively high external particle fluxes periodic regular pattern of meanders is created with its wavelength inversely proportional to the particle flux. An increase of the meander amplitude saturates after some period and further crystal grow is stationary, creating “finger-like” structure. For medium fluxes regular structure of meanders builds up for low or zero value of Schwoebel barrier. For higher fluxes wavelengths of meanders become shorter than the terrace width and they start to grow independently and finally transfer the surface to a rough structure. For very low fluxes or at relatively high temperatures steps move steadily remaining their initial shapes of straight, parallel lines.

► Growth process of GaN(0001) is studied by kinetic Monte Carlo method.
► Regular meander patterns emerge for low enough particle fluxes.
► Meander amplitude saturates leading to the step stationary motion.
► Particle exchange between terraces via step is crucial in this process.
► For high Shwoebel barrier or high particle fluxes rough surface builds up.