A Hybrid Method for the Structural Evolution of Stepped Surfaces

The Burton-Cabrera-Frank (BCF) model describes the structural evolution of vicinal surfaces in terms of an incoming particle flux and concentration-dependent desorption and surface diffusion terms. A continuum formulation of the BCF scheme given by a phase-field implementation for the moving-boundary problem yields the long-term evolution of the step structure during a step-flow growth mode. Phenomena like step bunching or meandering are well covered by such an approach, but the nucleation of additional structures is not. A particle-based Ising-type approach with a Metropolis-Monte-Carlo kinetics provides such nucleation processes in a temperature-controlled manner and on a shorter time and length scale.

We have integrated both approaches in a hybrid algorithm, which describes adsorption, nucleation, and structure evolution processes at solid-liquid and solid-gas interfaces on both time and length scales. The short-term nucleation from individual adatoms or molecules is resolved by the Monte-Carlo generated dynamics of an anisotropic Ising model, whose interaction parameters stem from first-principles calculations. The long-term microstructure dynamics on the vicinal surface is calculated using the phase-field method. Several growth modes are distinguished by the present scheme: In addition to step-flow growth the nucleation processes on the terraces can lead to roughening or an epitaxial layer-by-layer growth controlled by temperature and by flux. This hybrid algorithm has been applied to the decoration of structured crystalline surfaces with optically active molecules and to the coverage of glass surfaces with inhibitor molecules, which suppress glass corrosion.