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

Abstract

We investigate an intrinsic step-jamming phenomenon at the nanometer scale on Kardar-Parisi-Zhang (KPZ)-like kinetically roughened crystal surfaces that arises during interface-limited steady crystal growth or retreat. Monte Carlo simulations using the Metropolis algorithm on a restricted solid-on-solid (RSOS) lattice model demonstrate that intrinsic step jamming persists on surfaces below 20 nm. In the present model, transport processes such as surface and volume diffusion are excluded, as are elastic interactions, step-step repulsion or attraction, and stoichiometric effects. We show that intrinsic step jamming arises from asymmetric fluctuations in atomic attachment and detachment driven by biased transition probabilities under the SOS restriction, leading to collective step congestion. Asymmetric fluctuations also determine whether adatom or hole clusters grow or recede. This mechanism bears close similarity to jamming phenomena in the asymmetric simple exclusion process (ASEP), including multi-lane variants. In contrast, symmetric thermal fluctuations generate adatom or hole clusters on terraces, thereby suppressing intrinsic step jamming. Possible routes to suppress intrinsic step jamming, including experimentally accessible strategies, are also discussed.