论文标题
同性恋生长中阶段流的局部几何定律的出现
Emergence of local geometric laws of step flow in homoepitaxial growth
论文作者
论文摘要
在粗糙的过渡下，晶体表面表现出纳米级线缺陷，步骤，通过与环境交换原子。在同性恋中，我们通过分析显示在强解吸下真空训练的运动如何由依赖局部几何特征（例如每个步骤的曲率）以及适当定义有效的露台宽度的非线性定律近似描述。我们假设每个步骤边缘，一个自由边界，可以通过固定参考平面的平滑曲线表示足够长的时间。除表面扩散和蒸发外，所考虑的过程还包括缓慢变化的几何形状中的动力学步骤相互作用，从上方的表面上的材料沉积，原子在台阶上的附着和脱离，阶梯边缘扩散和步骤通透性。我们的方法依赖于负责阶跃流量的ADATOM通量的边界积分方程。通过应用渐近学，从而有效地将自由边界问题的扩散项视为奇异扰动，我们描述了步骤动力学与局部几何形状之间通用特征的紧密联系。
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.
