Intrinsic Step Jamming in Nanometer-Scale KPZ-Like Rough Surfaces under Interface-Limited Crystal Growth and Retreat

We investigate intrinsic step jamming at the nanometer scale on Kardar–Parisi–Zhang (KPZ)-like, kinetically roughened two-dimensional (2D) crystal surfaces embedded in three-dimensional (3D) space using Monte Carlo simulations of a restricted solid-on-solid (RSOS) model. In this model, transport processes, such as surface and volume diffusion, elastic interactions, the Ehrlich–Schwoebel effect, and explicit step–step interactions, are excluded. Intrinsic step jamming emerges under nonequilibrium driving as a consequence of asymmetric atomic attachment and detachment at step edges under the RSOS nonpenetrability constraint and persists on nanometer-scale surfaces, with step congestion becoming pronounced at characteristic length scales of approximately 1.6 nm for (111) stepped surfaces in the present model. This inhomogeneity is directly reflected in the terrace width histogram and corresponds to transient nanoscale traffic-jamlike clusters rather than conventional step bunching. The behavior is analogous to jamming in the asymmetric simple exclusion process (ASEP) at the phenomenological level, including multilane variants. Intrinsic step jamming governs surface morphology, producing bell- or cup-shaped surface undulations associated with positive or negative skewness in the surface-height-difference distribution. Strategies to suppress intrinsic step jamming are also discussed.