Kardar--Parisi--Zhang Roughening Associated with Nucleation-Limited Steady Crystal Growth

The roughness of crystal surfaces and the shape of crystals play an important role in multiscale phenomena. For example, the roughness of a crystal surface affects the frictional and optical properties of the material such as ice or silica. For the roughness of a crystal surface, theoretical studies based on the symmetry principle predicted that the growing surfaces of crystal growth would be classified in the universal class of Kardar-Parisi-Zhang (KPZ) but experiments only rarely observe KPZ properties. To fill this gap, extensive numerical calculations of the crystal growth rates and the surface roughness (surface width) are performed for a lattice model with a size in the nanoscale range using the Monte Carlo method. The results indicate that a (001) surface is smooth within the single nucleation growth region. In contrast, the same surface is atomically smooth but thermodynamically rough in the poly-nucleation growth region in conjunction with a KPZ roughness exponent. Inclined surfaces are known to become Berezinskii--Kosterlitz--Thouless (BKT) rough surfaces both at and near equilibrium. The two types of steps associated with the (001) and (111) terraces were found to induce KPZ surface roughness, while the interplay between steps and multilayered islands promoted BKT roughness.