弯曲衬底上应变异质外延薄膜形态失稳的相场模拟

PHASE FIELD MODELING OF MORPHOLOGICAL INSTABILITY OF STRAINED HETEROEPITAXIAL FILMS ON WAVY SUBSTRATES

论文旨在研究弯曲衬底上应变异质外延薄膜的表面非线性演化行为,研究采用了基于Eshelby等效方法的相场微弹性模型来模拟二维应变Si1-x Gex/Si薄膜/衬底系统的形态失稳.建立了关于等效特征应变和长程序参量的自由能泛函,数值求解了时间相关的Ginzburg-Landau动力学方程.系统自由能包括化学能,弹性应变能以及薄膜、衬底与真空相两两之界面能.跟踪了全时的形态演化过程,给出了指定时刻的量子点形态轮廓图.结果表明,量子点倾向于沉积在弯曲衬底的波谷处,波谷处是能量有利位置,量子点在此处比在波峰处更加稳定.论文所做的相场模拟可以用来预测量子点形成的轮廓、尺寸和位置,可以为控制和生成周期性自组装表面纳米结构提供理论指导.

This paper aims at investigating the surface nonlinear evolution behavior of strained hetero- epitaxial films on wavy substrates. In this work, the phase field microelasticity model is used, which is based on the Eshelby＇s equivalency approach,to simulate the morphological instability of the two-dimen- sional strained Sil-x Gex/Si film/substrate system. The free energy functional with respect to the equivalent eigenstrain and the long-range order parameter is established and the two time-dependent Ginzburg-Landau kinetic equations are solved simultaneously. The system free energy comprises chemical energy, elastic strain energy and interracial energy between film, substrate and vacuum phase. The morphological evolution process is tracked and the profile of the quantum dots is given at some specific time. The results indicate that the quantum clots are inclined to form at the trough of the wavy substrate which is an energy prefera- ble site and thus a more stable site than the crest. The profile,size and site of the quantum dots can be pre- dicted by the phase field modeling in this paper,which can provide a guideline for controlling and producing periodic self-assembly surface nanostructures.