SCALING APPROACH TO ANOMALOUS SURFACE ROUGHENING OF THE (d+1)-DIMENSIONAL MOLECULAR-BEAM EPITAXY GROWTH EQUATIONS

To determine anomalous dynamic scaling of continuum growth equations, López12 proposed an analytical approach, which is based on the scaling analysis introduced by Hentschel and Family.15 In this work, we generalize this scaling analysis to the (d+1)-dimensional molecular-beam epitaxy equations to determine their anomalous dynamic scaling. The growth equations studied here include the linear molecular-beam epitaxy (LMBE) and Lai–Das Sarma–Villain (LDV). We find that both the LMBE and LDV equations, when the substrate dimension d>2, correspond to a standard Family–Vicsek scaling, however, when d<2, exhibit anomalous dynamic roughening of the local fluctuations of the growth height. When the growth equations exhibit anomalous dynamic scaling, we obtain the local roughness exponents by using scaling relation α loc =α-zκ, which are consistent with the corresponding numerical results.