MONTE-CARLO SIMULATION AND DYNAMIC SCALING OF SURFACES IN MBE GROWTH

Film growth by molecular-beam epitaxy is modeled by a simple solid-on-solid model using Monte Carlo simulations. L X L substrates are used and both deposition and surface diffusion are allowed to occur simultaneously. Surface roughness is studied by measuring different surface characteristics: interface width, reflection high-energy electron-diffraction intensity, and kink density are calculated from configurations generated by simulation. We find a region of temperature and flux for which apparent layer-by-layer growth occurs. For long times, the interface width grows logarithmically with time, and its saturated value diverges logarithmically with substrate size. This unusual result suggests that within the context of this model all growing surfaces are asymptotically rough for infinite lateral extent. Because of the logarithmic behavior of the interface width, our model falls into the Edwards-Wilkinson universality class. The growth is intermediate between two-dimensional and three-dimensional nucleation and is experimentally observed in many epitaxial systems.