相关论文: Conserved Growth on Vicinal Surfaces

We introduce a new equation describing epitaxial growth processes. This equation is derived from a simple variational geometric principle and it has a straightforward interpretation in terms of continuum and microscopic physics. It is also…

The deposition dynamics of particles (or the growth of a rigid crystal) on a disordered substrate at a finite deposition rate is explored. We begin with an equation of motion which includes, in addition to the disorder, the periodic…

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…

We study unstable epitaxy on singular surfaces using continuum equations with a prescribed slope-dependent surface current. We derive scaling relations for the late stage of growth, where power law coarsening of the mound morphology is…

The conserved Sine-Gordon Equation with nonconserved shot noise is used to model homoepitaxial crystal growth. With increasing coverage the renormalized pinning potential changes from strong to weak. This is interpreted as a transition from…

We study the step bunching kinetic instability in a growing crystal surface characterized by anisotropic diffusion. The instability is due to the interplay between the elastic interactions and the alternation of step parameters. This…

We developed a consistent mathematical model for isotropic crystal growth on a substrate covered by the mask material with a periodic series of parallel long trenches where the substrate is exposed to the vapor phase. Surface diffusion and…

Flat surface phases are unstable during growth and known to become rough. This does not exclude the possibility that surface reconstruction order persists in rough growing surfaces, in analogy with so-called equilibrium reconstructed rough…

We study conserved models of crystal growth in one dimension [$\partial_t z(x,t) =-\partial_x j(x,t)$] which are linearly unstable and develop a mound structure whose typical size L increases in time ($L = t^n$). If the local slope ($m…

Below the roughening transition, crystal surfaces exhibit nanoscale line defects, steps, that move by exchanging atoms with their environment. In homoepitaxy, we analytically show how the motion of a step train in vacuum under strong…

We consider a simple model for the growth of isolated steps on a vicinal crystal surface. It incorporates diffusion and drift of adatoms on the terrace, and strong step and kink edge barriers. Using a combination of analytic methods and…

A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…

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…

As a departure from existing continuum approaches for describing the stability and evolution of surfaces of crystalline materials, this article provides a description of surface evolution based on the physics of the main feature imposed by…

Mathematical model that allows for direct tracking of the homoepitaxial crystal growth out of the window etched in the solid, pre-deposited layer on the substrate is described. The growth is governed by the normal (to the crystal-vapor…

A limited mobility nonequilibrium solid-on-solid dynamical model for kinetic surface growth is introduced as a simple description for the morphological evolution of a growing interface under random vapor deposition and surface diffusion…

We propose a variational framework for accretive surface growth driven by an optimality principle. Rather than prescribing a kinetic law, the configuration at each time step is obtained, within a time-discrete setting, as the solution of a…

As an introductory lecture to the workshop an overview is given over continuum models for homoepitaxial surface growth using partial differential equations (PDEs). Their {\em heuristic derivation} makes use of inherent symmetries in the…

We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models. We show…

A growth model which describes the deposition of particles (or the growth of a rigid crystal) on a disordered substrate is investigated. The dynamic renormalization group is applied to the stochastic growth equation using the Martin, Sigga,…