相关论文: Analytical solution of generalized Burton--Cabrera…

Burton-Cabrera-Frank (BCF) theory has proven to be a versatile framework to relate surface morphology and dynamics during crystal growth to the underlying mechanisms of adatom diffusion and attachment at steps. For an important class of…

A method based on the kinetics of adatoms on a growing surface under epitaxial growth at low temperature in (1+1) dimensions is proposed to obtain a closed form of local growth equation. It can be generalized to any growth problem as long…

A discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating…

Spiral surface growth is well understood in the limit where the step motion is controlled by the local supersaturation of adatoms near the spiral ridge. In epitaxial thin-film growth, however, spirals can form in a step-flow regime where…

We have developed a continuum model that explains the complex surface shapes observed in epitaxial regrowth on micron scale gratings. This model describes the dependence of the surface morphology on film thickness and growth temperature in…

Surface growth, by association or dissociation of material on the boundaries of a body, is ubiquitous in both natural and engineering systems. It is the fundamental mechanism by which biological materials grow, starting from the level of a…

An extension of the Burton-Cabrera-Frank model [Phil. Trans. R. Soc. London, Ser. A 243, 299 (1951)] including diffusion along steps and entropic step-step interaction is introduced. This extended model is successfully applied to simulate…

We study the dynamics of a stepped crystal surface during evaporation, using the classical model of Burton, Cabrera and Frank, in which the dynamics of the surface is represented as a motion of parallel, monoatomic steps. The validity of…

A continuum model for growth of solids is developed, considering adatom deposition, surface diffusion, and configuration dependent incorporation rate. For amorphous solids it is related to surface energy densities. The high adatom density…

The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling…

We propose a one-dimensional model based on the Burton-Cabrera-Frank equations to describe the electromigration-induced step bunching instability on vicinal surfaces. The step drift resulting from atomic evaporation and/or deposition is…

We analyze the effect of nonlinear boundary conditions on an advection-diffusion equation on the half-line. Our model is inspired by models for crystal growth where diffusion models diffusive relaxation of a displacement field, advection is…

We present a fast Monte-Carlo algorithm for simulating epitaxial surface growth, based on the continuous-time Monte-Carlo algorithm of Bortz, Kalos and Lebowitz. When simulating realistic growth regimes, much computational time is consumed…

We present models of surfaces of crystals in an environment where molecular beam epitaxy (MBE) and related methods of crystal growth like atomic layer epitaxy (ALE) can be performed. Besides detailed models of reconstructed (001) surfaces…

In this thesis we present a kinetic Monte Carlo model for the description of epitaxial graphene growth. Experimental results suggest a growth mechanism by which clusters of 5 carbon atoms are an intermediate species necessary for nucleation…

The propagation of sidewall steps during the growth of nanowires is calculated in the frame of the Burton-Cabrera-Frank model. The stable shape of the nanowire comprises a cylinder section on top of a cone section: their characteristics are…

We study a continuum model for solid films that arises from the modeling of one-dimensional step flows on a vicinal surface in the attachment-detachment-limited regime. The resulting nonlinear partial differential equation, $u_t =…

A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by…

We study a recently proposed nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. (80), 4221 (1998)]. A careful…

We studied the step dynamics during sublimation and growth in the presence of electromigration force acting on the adatoms. In the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps we formulate a…