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Consequences of elastic anisotropy in patterned substrate heteroepitaxy

机译：弹性各向异性在图案化底物杂膜中的后果

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摘要

The role of elastic anisotropy on quantum dot formation and evolution on a pre-patterned substrate is evaluated within the framework of a continuum model. We first extend the formulation for surface evolution to take elastic anisotropy into account. Using a small slope approximation, we derive the evolution equation and show how it can be numerically implemented up to linear and second order for stripe and egg-carton patterned substrates using an accurate and efficient procedure. The semi-infinite nature of the substrate is used to solve the elasticity problem subject to other boundary conditions at the free surface and at the film-substrate interface. The positioning of the quantum dots with respect to the peaks and valleys of the pattern is explained by a competition between the length scale of the pattern and the wavelength of the Asaro-Tiller-Grinfeld instability, which is also affected by the elastic anisotropy. The alignment of dots is affected by a competition between the elastic anisotropy of the film and the pattern orientation. A domain of pattern inversion, wherein the quantum dots form exclusively in the valleys of the patterns is identified as a function of the average film thickness and the elastic anisotropy, and the time-scale for this inversion as function of height is analyzed.
机译：在连续模型的框架内评估弹性各向异性对预定衬底的量子点形成和进化的作用。我们首先延长了表面演化的配方，以考虑弹性各向异性。使用小斜率近似，我们推出了进化方程，并展示了如何使用准确高效的过程来用线性和蛋纸图案基板的线性和秒顺序进行数字实现。基板的半无限性用于解决自由表面和薄膜基板界面处的其他边界条件的弹性问题。量子点相对于图案的峰和谷的定位是通过竞争的图案的长度和叶片 - 耕作 - Grinfeld不稳定性的波长之间的竞争来解释，这也受弹性各向异性的影响。点的对准受薄膜弹性各向异性与图案取向之间的竞争的影响。图案反演的域，其中仅在图案的谷的谷物中的量子点形式被识别为平均膜厚度和弹性各向异性的函数，并且分析了这种反转的时间尺度作为高度的函数。

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