Zhou Peng, Wise Steven, Li Xiangrong, Lowengrub John
Department of Astronautical Science and Mechanics, Harbin Institute of Technology, Harbin 150001, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 1):061605. doi: 10.1103/PhysRevE.85.061605. Epub 2012 Jun 28.
A diffuse interface model is developed to investigate the growth and coarsening in driven thin films under the influence of strong surface energy anisotropy, misfit strain, mass deposition, and diffusion. Two high-order regularizations are used to remove the ill-posedness introduced by the strong anisotropy: a Willmore (or bending energy) regularization and a simplified linear regularization. For similar effective growth rates and regularization strengths, the two regularizations undergo similar dynamics and coarsening, as peaks (antikinks) and valleys (kinks) of the corrugated surface are removed as the film grows. Competition among the influence of elastic strains, surface energy anisotropy and the rate of deposition lead to a change in the coarsening events compared to that observed in unstressed thin films. As the rate of deposition is increased, the primary coarsening events change from a combination of both antikink-ternary and binary events at low deposition rates, to binary events at moderate rates, and finally to kink-ternary events at high rates. The kink-ternary events are the only coarsening events observed in growing unstressed films at all deposition rates. Accordingly, the coarsening dynamics of two-dimensional (2D) stressed films is much faster than for unstressed films at low deposition rates. In addition, deep grooves may form in the film due to the Asaro-Tiller-Grinfeld instability and may lead to the breakup of the film into islands. At higher deposition rates, the evolution of stressed films is found to become limited by the surface energy anisotropy and the regularizations, which inhibits groove formation. The corresponding coarsening events and rates then tend toward those observed in unstressed films. Preliminary results of 3D thin films indicate that coarsening processes in elastically stressed films are also much faster than their unstressed counterparts at low deposition rates. In three dimensions, however, the coarsening events are also found to involve saddles.
开发了一种扩散界面模型，以研究在强表面能各向异性、错配应变、质量沉积和扩散影响下驱动薄膜中的生长和粗化过程。使用两种高阶正则化方法来消除由强各向异性引入的不适定性：一种是威尔莫尔（或弯曲能）正则化，另一种是简化的线性正则化。对于相似的有效生长速率和正则化强度，两种正则化经历相似的动力学和粗化过程，随着薄膜生长，波纹表面的峰（反扭结）和谷（扭结）会被消除。与无应力薄膜中观察到的情况相比，弹性应变、表面能各向异性和沉积速率的影响之间的竞争导致粗化事件发生变化。随着沉积速率的增加，主要粗化事件从低沉积速率下反扭结 - 三元和二元事件的组合，变为中等速率下的二元事件，最终变为高速率下的扭结 - 三元事件。扭结 - 三元事件是在所有沉积速率下生长的无应力薄膜中观察到的唯一粗化事件。因此，在低沉积速率下，二维（2D）应力薄膜的粗化动力学比无应力薄膜快得多。此外，由于阿萨罗 - 蒂勒 - 格林菲尔德不稳定性，薄膜中可能会形成深槽，并可能导致薄膜破裂成岛状。在较高沉积速率下，发现应力薄膜的演化受到表面能各向异性和正则化的限制，这抑制了沟槽的形成。相应的粗化事件和速率随后趋向于在无应力薄膜中观察到的情况。三维薄膜的初步结果表明，在低沉积速率下，弹性应力薄膜中的粗化过程也比无应力薄膜快得多。然而，在三维中，粗化事件还涉及鞍点。
