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.

Figures (6)

• Figure 1: Representative kinetic roughening behaviors under interface-limited steady crystal growth and retreat. (a) Kinetic roughening diagram for the (001) surface as a function of temperature and driving force, showing smooth, Berezinskii-Kosterlitz-Thouless (BKT) rough, and Kardar-Parisi-Zhang (KPZ)-like kinetically rough regimes. (b) Kinetic roughening diagram for inclined surfaces, illustrating the dependence of kinetic roughening behavior on surface slope. (c)-(f) Logarithmic plots of surface height difference distributions for selected conditions. (g),(h) Scaled surface widths as functions of system size used to classify kinetic roughening regimes. These panels provide background context for the present study and define the kinetic roughening landscape in which the microscopic behavior of surface steps is investigated. Panels (a) to (h) are reproduced or adapted from Refs. akutsu23akutsu24-2akutsu25-2 under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
• Figure 2: Terrace width $\ell$ and step height $n$ with the (001) terrace. Upper panel: an overhead view of a surface. Broken lines show the lattice structure. Thick, light-blue lines show surface steps. Lower panel: a side view of the surface along the dotted line in the upper panel.
• Figure 3: Terrace width histograms (TWHs). $\hbox{$k_{\rm B}T$}/\epsilon = 0.4$. $L=320 \sqrt{2}$. (a) Logarithmic histogram of the (111) terrace width. The mean terrace width $\ell_0^{(111)} = 2.02 a$. Light green circles: $p=1.061$. (b) Logarithmic histogram of the (001) terrace width. The mean terrace width $\ell_0 = a/p = 14.14 a$.
• Figure 4: Example of surface undulations. (a) $\hbox{$k_{\rm B}T$}/\epsilon = 0.4$, $L=80 \sqrt{2}$. $N_{\rm step} = 88$. $\Delta \mu/\epsilon = 1.4$. In the white ellipses, typical surface undulations are visible. (b) $\hbox{$k_{\rm B}T$}/\epsilon = 0.63$, $L=320 \sqrt{2}$. $\Delta \mu/\epsilon = 0.8$. (c) An example of a wide (001) terrace. (d), (e) Attachment and Detachment of an atom at a configuration at a half-crystal site, respectively. (f), (g) An example of a side view of the KPZ-like2 rough surface when it grows/recedes. (h), (i) An example of a perspective view of the KPZ-like1 rough surface when it grows/recedes. Detailed explanations are given in Sec. "'Intrinsic Step-Jam'.
• Figure 5: Illustration of the poly-nuclear growth process on the (001) surface. (a) A perspective view. (b) An overhead view.