Kardar–Parisi–Zhang roughening associated with nucleation-limited steady crystal growth

The roughness of crystal surfaces and the shape of crystals play important roles in multiscale phenomena. For example, the roughness of the crystal surface affects the frictional and optical properties of materials such as ice or silica. Theoretical studies on crystal surfaces based on the symmetry principle proposed that the growing surfaces of crystal growth could be classified in the universal class of Kardar–Parisi–Zhang (KPZ), but experiments rarely observe KPZ properties. To fill this the gap, extensive numerical calculations of the crystal growth rates and the surface roughness (surface width) have been performed for a nanoscale lattice model 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.