Morphological equilibration of a corrugated crystalline surface.
Morphological equilibration of a corrugated crystalline surface.
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DOI：
10.1103/physrevb.42.5013
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发表时间：
1990-09
期刊：
影响因子：
--
通讯作者：
Ozdemir;Zangwill
中科院分区：
文献类型：
--
作者：
Ozdemir;Zangwill
我们研究了波纹晶体表面平坦化的情况，当质量传输是由表面扩散驱动的，并且温度远低于平衡面的粗化温度。对于所考虑的几何体，问题是一维的，表面形态由由直的、平行的台阶分隔的梯田的集合组成。在这种情况下，动力学仅由一步一步的相互作用驱动。我们得到了表面轮廓z(x，t)的运动微分方程和梯田宽度为${\mathit{L}}_{\mathit{n}}$(T)的离散运动方程的分离变量(保形)解。这些方程的数值解表明，解析解很好地描述了后一种情况下的动力学。随着形态平衡的进行，我们发现z(x，T)\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}1}$和${\mathit{l}}_{\mathit{n}}$(t)\ensuremath{\sim}${\mathit{t}}^{1/5}$或${\mathit{l}}_{\mathit{n}}$(t)\ensuremath{\sim}${\mathit{t}}^{1/4}$，用于扩散受限或阶跃附着受限阶跃传播情况，分别进行了分析。这些预测适用于直接的实验测试。
We study the flattening of a corrugated crystal surface for the case when mass transport is driven by surface diffusion and the temperature is well below the roughening temperature of the equilibrium facet. For the considered geometry, the problem is one dimensional and the surface morphology consists of a collection of terraces separated by straight, parallel steps. In this situation, the kinetics is driven by step-step interactions alone. We obtain separated variable (shape-preserving) solutions to both the differential equation of motion for the surface profile z(x,t) and the discrete equations of motion for individual terraces' widths ${\mathit{l}}_{\mathit{n}}$(t). Numerical solutions of these equations demonstrate that the analytic solution well describes the kinetics in the latter case. As morphological equilibration proceeds, we find that z(x,t)\ensuremath{\sim}${\mathit{t}}^{\mathrm{\ensuremath{-}}1}$ and that ${\mathit{l}}_{\mathit{n}}$(t)\ensuremath{\sim}${\mathit{t}}^{1/5}$ or ${\mathit{l}}_{\mathit{n}}$(t)\ensuremath{\sim}${\mathit{t}}^{1/4}$ for the cases of diffusion-limited or step-attachment-limited step propagation, respectively. These predictions are amenable to direct experimental tests.