Dixit Gopal Krishna, Ranganathan Madhav
Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208016, India.
Nanotechnology. 2018 Sep 7;29(36):365305. doi: 10.1088/1361-6528/aacc5b. Epub 2018 Jun 13.
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.
在连续介质模型的框架内，评估了弹性各向异性对预图案化衬底上量子点形成和演化的作用。我们首先扩展了表面演化的公式，以考虑弹性各向异性。使用小斜率近似，我们推导了演化方程，并展示了如何使用精确且高效的程序，针对条纹和蛋盒图案化衬底，将其数值实现到线性和二阶。利用衬底的半无限性质，在自由表面和薄膜 - 衬底界面的其他边界条件下求解弹性问题。量子点相对于图案的峰谷的定位，由图案的长度尺度与阿萨罗 - 蒂勒 - 格林菲尔德不稳定性的波长之间的竞争来解释，而这种竞争也受弹性各向异性的影响。点的排列受薄膜的弹性各向异性与图案取向之间竞争的影响。确定了图案反转的区域，其中量子点仅在图案的谷中形成，它是平均薄膜厚度和弹性各向异性的函数，并分析了这种反转随高度变化的时间尺度。
