  The crossover from a Berezinskii--Kosterlitz--Thouless (BKT) rough surface to
a Kardar--Parisi--Zhang (KPZ) rough surface on a vicinal surface is studied
using the Monte Carlo method in the non-equilibrium steady state in order to
address discrepancies between theoretical results and experiments. The model
used is a restricted solid-on-solid (RSOS) model with a discrete Hamiltonian
without surface or volume diffusion (interface limited growth/recession). The
temperature, driving force for growth, system size, and surface slope
dependences of the surface width are calculated for vicinal surfaces tilted
between the (001) and (111) surfaces. The surface velocity, kinetic coefficient
of the surface, and mean height of the locally merged steps are also
calculated. In contrast to the accepted theory for (2+1) surfaces, we found
that the crossover point from a BKT (logarithmic) rough surface to a KPZ
(algebraic) rough surface is different from the kinetic roughening point for
the (001) surface. The driving force for crystal growth was found to be a
relevant parameter for determining whether the system is in the BKT class or
the KPZ class. It was also determined that ad-atoms, ad-holes, islands, and
negative-islands block surface fluctuations, which contributes to making a
BKT-rough surface.
