同质外延生长中台阶流局部几何规律的出现
Emergence of local geometric laws of step flow in homoepitaxial growth
摘要：
在粗糙化过渡层之下，晶体表面呈现出纳米级的线缺陷，即台阶，它们通过与环境交换原子而移动。在同质外延，我们分析表明如何在真空中的一步训练的运动在强解吸下可以近似描述的非线性法律，依赖于当地的几何特征，如每个步骤的曲率，以及适当定义的有效梯田宽度。我们假设，每一个步骤的边缘，一个自由的边界，可以表示为一个光滑的曲线在一个固定的参考平面足够长的时间。除了表面扩散和蒸发，正在考虑的过程包括在缓慢变化的几何形状，材料沉积在表面上，附着和分离的原子在步骤，步骤边缘扩散，和步骤渗透性的动力学步骤的相互作用。我们的方法依赖于边界积分方程的adatom通量负责步骤流。通过应用渐近，有效地治疗的扩散项的自由边界问题作为一个奇异摄动，我们描述了一个密切的联系，普遍字符之间的步骤动力学和局部几何。
英文摘要：
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 desorption can be approximately described by nonlinear laws that depend on local geometric features such as the curvature of each step, as well as suitably defined effective terrace widths. We assume that each step edge, a free boundary, can be represented by a smooth curve in a fixed reference plane for sufficiently long times. Besides surface diffusion and evaporation, the processes under consideration include kinetic step-step interactions in slowly varying geometries, material deposition on the surface from above, attachment and detachment of atoms at steps, step edge diffusion, and step permeability. Our methodology relies on boundary integral equations for the adatom fluxes responsible for step flow. By applying asymptotics, which effectively treat the diffusive term of the free boundary problem as a singular perturbation, we describe an intimate connection of universal character between step kinetics and local geometry.
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