We investigate the influence of strain-sharing and finite-size effects on the morphological instability of hetero-epitaxial nanomembranes made of a thin film on a thin freestanding substrate. We show that long-range elastic interactions enforce a strong dependence of the surface dynamics on geometry. The instability time-scale τ is found to diverge as (e/H)^−α with α = 4 (respectively 8) in thin (resp. thick) membranes, where e (resp. H) is the substrate (resp. nanomembrane) thickness, revealing a huge inhibition of the dynamics as strain sharing decreases the level of strain on the surface. Conversely, τ vanishes as H² in thin nano-membranes, revealing a counter-intuitive strong acceleration of the instability in thin nanomembranes. Similarly, the instability length-scale displays a power-law dependence as (e/H)^−β, with β = α/4 in both the thin and thick membrane limits. These results pave the way not only for experimental investigation, but also, for the dynamical control of the inescapable morphological evolution in epitaxial systems.

中文翻译：

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当有限尺寸效应决定应变独立式纳米膜的生长动力学时

我们研究了应变共享和有限尺寸效应对薄独立基板上薄膜制成的异质外延纳米膜形态不稳定性的影响。我们表明，长程弹性相互作用强制表面动力学对几何形状的强烈依赖性。发现在薄（或厚）膜中，不稳定性时间尺度τ发散为 ( e / H ) ^{− α} ，其中α = 4（分别为 8），其中e（分别为H）为基质（分别为纳米膜）厚度，揭示了当应变共享降低了表面应变水平时对动力学的巨大抑制。相反，τ在薄纳米膜中以H ²形式消失，揭示了薄纳米膜中不稳定性的反直觉强烈加速。类似地，不稳定性长度尺度显示幂律依赖性为 ( e / H ) ^{− β}，其中在薄膜和厚膜极限下β = α /4。这些结果不仅为实验研究铺平了道路，而且也为外延系统中不可避免的形态演化的动态控制铺平了道路。