Competition between Kardar-Parisi-Zhang and Berezinskii-Kosterlitz-Thouless kinetic roughening on (001) singular surface: nucleation-limited steady crystal growth

Kinetic roughening of the (001) singular surface for nucleation-limited steady crystal growth is studied on the basis of a lattice model using the Monte Carlo method. At a sufficiently low temperature, there are two kinetic roughening points as the driving force for crystal growth Δμ increases. At a low driving force ΔμKPZ(001), there is the Karder-Parisi-Zhang (KPZ) roughening transition point. On the KPZ rough surface, elementary steps around islands are well defined though the surface is thermodynamically rough, with a roughness exponent α of 0.3869. At a relatively large driving force, the Berezinskii-Kosteritz-Thouless (BKT)-type kinetically rough region was found for ΔμBKT(001) < Δμ. Around the middle driving force between the two kinetic roughening points, the crossover area that starts from the driving force ΔμKtoT(001) was found. For ΔμKtoT(001) < Δμ, the surface grows linearly as the driving force increases (adhesive growth). The points ΔμKPZ(001), ΔμKtoT(001), and ΔμBKT(001) decrease with increasing temperature because the step free energy decreases.