DYNAMICS OF THE CURVATURE-ENERGY-DRIVEN SURFACES

Abstract

The dynamics of the curvature-energy-driven surfaces such as the dynamics of the orientational roughening (OR) transition and the dynamics of the molecular beam epitaxial (MBE) growth with the lattice pinning force are studied. For the dynamics of the OR transition, we first derive the lattice pinning force of the sine-Gordon model, which is in a peculiar form of [Formula: see text] where {êk} (k =1, 2, 3) are the basis vectors of the triangular lattice. The lattice pinning force is renormalized and contributes to the coarse-grained curvature force under the dynamic renormalization group transformation introduced by Nozières and Gallet [J. Phys. (Paris) 48, 353 (1987)]. The dynamic exponent is obtained as z =4 − ∊ with ∊ =2 − d and the mobility is scaled as r−2.51 ∊ in general dimension d ≤ 2. The tilt-tilt correlation function behaves logarithmically with spatial and temporal changes of scales in two dimensions. Next, we study the dynamic equation of the OR transition with the addition of the growth-induced nonlinear term proportional to ∇2 (∇ϕ)2. It is obtained that the OR transition occurs even in the presence of the growth-induced nonlinear term, but the nature of the phase transition changes by the nonlinear term. We compare our analysis with the recent study of the growth-induced roughening transition by Hwa, Kardar and Paczuski [Phys. Rev. Lett.66, 441 (1991)]. It is also found that the lattice pinning force is irrelevant to the MBE growth.