用连续介质模型研究同质外延晶面动力学的不对称性
Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model
摘要：
在没有外部材料沉积的情况下，晶体表面通常通过降低其自由能而松弛以变得平坦。我们研究了一个不对称的宏观高原，小平面，通过连续模型的周期性表面的松弛粗糙化转变温度以下的1+1维。该模型调用一个高度退化的抛物型偏微分方程（PDE）的表面扩散，这是有关的加权- $H^{-1}$（非线性）梯度流的凸，奇异的表面自由能同质外延。PDE的动机是由一个原子的断键模型和一个介观尺度模型的步骤。通过构建一个明确的解决方案的偏微分方程，我们证明了缺乏对称性的周期性表面轮廓的顶部和底部刻面的演变。我们明确的，分析的解决方案相比，通过正规化的表面自由能的PDE的数值模拟。
英文摘要：
In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface corrugation in 1+1 dimensions via a continuum model below the roughening transition temperature. The model invokes a highly degenerate parabolic partial differential equation (PDE) for surface diffusion, which is related to the weighted-$H^{-1}$ (nonlinear) gradient flow of a convex, singular surface free energy in homoepitaxy. The PDE is motivated both by an atomistic broken-bond model and a mesoscale model for steps. By constructing an explicit solution to the PDE, we demonstrate the lack of symmetry in the evolution of top and bottom facets in periodic surface profiles. Our explicit, analytical solution is compared to numerical simulations of the PDE via a regularized surface free energy.
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