Implementation of crystal structure into the das sarma-tamborenea and wolf-villain molecular beam epitaxy growth models

Abstract

The energetically driven Ehrlich–Schwoebel (ES) barrier had been generally accepted as the primary cause of the growth instability in the form of quasi-regular mound-like structures observed on the surface of thin film grown via molecular beam epitaxy (MBE) technique. Recently the second mechanism of mound formation was proposed in terms of a topologically induced flux of particles originating from the line tension of the step edges which form the contour lines around a mound. Through large-scale simulations of MBE growth on a variety of crystalline lattice planes using limited mobility, solid-on-solid models introduced by Wolf–Villain and Das Sarma–Tamborenea in 2+1 dimensions, we propose yet another type of topological uphill particle current which is unique to some lattice, and has hitherto been overlooked in the literature. Without ES barrier, our simulations produce spectacular mounds very similar, in some cases, to what have been observed in many recent MBE experiments. On a lattice where these currents cease to exist, the surface appears to be scale-invariant, statistically rough as predicted by the conventional continuum growth equation. We notice unstable mound-like morphologies for the structures with the roughness exponent greater than 0.67. The correlation functions are also studied to confirm the existence of mounds on the film surfaces. We find oscillations of the correlation function which correspond to the presence of mounds on the film surfaces.