Abstract The equilibrations of initial surfaces bounded by envelope functions of the form h ( 0 ) - x α and consist of concentric circular monoatomic steps in two dimensions are studied in diffusion limited (DL) regime. Repulsive and attractive step interactions of the form w - 2 and w - 1 , respectively, where w is the step separation are considered. For certain parameter values of repulsive and attractive interactions an initial surface either equilibrates to a flat surface or step bunching occurs on the surface. The bunching - no bunching regions of initial surfaces in a parameter space are investigated and scaling characteristics of bunching/no bunching regions are obtained numerically. The bunching and no bunching regions scales as x 0 / x 0 ' γ N / N ' δ for a general surface where x 0 is the initial range of the surface and N is the initial number of steps on the surface. For all forms of initial surface ( α = 1 / 2 , 1 , 2 ), we find that γ : 1 / 2 and δ : 1 / 6 and these results for scaling can be generalized which takes into account both the size and the slope (and curvature) of the initial surface as provided in the text. Our findings can directly be tested experimentally.

中文翻译：

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半导体丘聚束区和非聚束区的标度特性

摘要 在扩散限制 (DL) 范围内研究了由 h ( 0 ) - x α 形式的包络函数界定并由二维同心圆单原子台阶组成的初始表面的平衡。分别考虑了 w - 2 和 w - 1 形式的排斥和吸引阶梯相互作用，其中 w 是阶梯分离。对于排斥和吸引力相互作用的某些参数值，初始表面要么平衡到平坦表面，要么在表面上发生阶梯聚束。研究了参数空间中初始表面的聚束-无聚束区域，并数值获得了聚束/无聚束区域的缩放特性。聚束区和无聚束区的比例为 x 0 / x 0 ' γ N / N ' δ 对于一般表面，其中 x 0 是表面的初始范围，N 是表面上的初始台阶数。对于所有形式的初始表面 ( α = 1 / 2 , 1 , 2 )，我们发现 γ : 1 / 2 和 δ : 1 / 6 并且这些缩放结果可以推广，同时考虑到尺寸和斜率（和曲率）的初始表面的文本中提供。我们的发现可以直接通过实验进行测试。