扩散吸附物附着驱动二维单畴生长的标度理论
Scaling theory for two-dimensional single domain growth driven by attachment of diffusing adsorbates
摘要：
外延生长方法是在衬底上制备大面积薄膜的关键技术，但由于控制生长过程的各种因素，生长条件的合理优化是相当困难的。数学模型是研究控制因素对磁畴生长影响的一种方法。本研究的动机是最近发现的域半径和时间的化学气相沉积石墨烯之间的比例关系。在数学上，我们需要解决Stefan问题;当边界移动时，其位置应该与获得扩散吸附物的空间分布所需的边界条件分开确定。我们推导出一个封闭的增长速率常数定义为域面积除以持续时间的方程。我们得到近似的解析表达式的增长率的增长速率常数表示为二维扩散常数和吸附剂的附着到固体域的速率常数的函数。在实验中，通过停止源气体流来减小面积。从理论上得到了面积减小率。所得理论结果为研究畴生长的控制因素提供了基础。
英文摘要：
Epitaxial growth methods are a key technology used in producing large-area thin films on substrates but as a result of various factors controlling growth processes the rational optimization of growth conditions is rather difficult. Mathematical modeling is one approach used in studying the effects of controlling factors on domain growth. The present study is motivated by a recently found scaling relation between the domain radius and time for chemical vapor deposition of graphene. Mathematically, we need to solve the Stefan problem; when the boundary moves, its position should be determined separately from the boundary conditions needed to obtain the spatial profile of diffusing adsorbates. We derive a closed equation for the growth rate constant defined as the domain area divided by the time duration. We obtain approximate analytical expressions for the growth rate; the growth rate constant is expressed as a function of the two-dimensional diffusion constant and the rate constant for the attachment of adsorbates to the solid domain. In experiments, the area is decreased by stopping the source gas flow. The rate of decrease of the area is obtained from theory. The theoretical results presented provide a foundation to study controlling factors for domain growth.
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