Kinetic-roughening diagrams between Kardar–Parisi–Zhang–like and Berezinskii–Kosterlitz–Thouless rough surfaces for steady crystal growth

Surface roughness at the nanometer scale influences various phenomena such as the morphology of crystallites at the micrometer scale, the structure factor in X-ray scattering, and backscattering in lidar used for passive remote sensing of ice clouds. In this study, the surface roughness and its roughness exponent are calculated for nano-scale two-dimensional surfaces in three dimensions during the steady growth of crystals using the Monte Carlo method on a lattice model. By monitoring the roughness exponent, slope-dependent kinetic roughening diagrams are constructed for universality classes. The diagrams provide insight into the intricate relationship between the roughness exponent and surface slope, as well as the driving force for crystal growth. The resulting diagrams reveal that at low temperatures, two Kardar-Parisi-Zhang (KPZ)-like kinetic roughening regions, KPZ-like1 and KPZ-like2, are separated by a region of Berezinskii-Kosterlitz-Thouless (BKT) roughening. At high temperatures close to but below the thermal roughening transition temperature of the (001) surface, another KPZ-like region, KPZ-like3, emerges for large driving forces for crystal growth. The terrace width histogram and surface height difference distribution function were also calculated using the Monte Carlo method and provide insight into how the surface crosses over to other classes or subclasses.