Extensive work on metal-catalyst-assisted vapor-liquid-solid (VLS) growth has been focused on nanometer-scale wires (nanowires) and there have been several studies modelling the effect of diameter, growth time, surface diffusion, etc. on these nanowires. In this context of nanowires, since the catalyst is so small, one could and researchers have ignored the effect of the requirement to supersaturate the catalyst. In this work, an analytical growth model is presented to explain the effect of supersaturation on the size of micrometer-scale catalysts and resulting films grown via the VLS mechanism by chemical vapor deposition by introducing the idea of “multi-scale” supersaturation (supersaturation as a function of catalyst size). The proposed model is derived from a materials balance relation which reduces to the nanowire equation (without the need for considering catalyst supersaturation) for sufficiently small radii. By including the supersaturation term, the model predicts the existence of the maximum size range of film at certain growth conditions which is not present in the pre-existing models. The model could also explain the “induction time” required for the catalyst to reach a supersaturation state to begin VLS growth. More importantly, it agrees with the available experimental data of VLS lateral heteroepitaxy of micrometer-scale Ge films on Si substrate which suggests that 0.0379 mol/cm3 of Ge atoms are required to supersaturate the Au catalyst at the growth conditions studied (375 °C). This new perspective on the multi-scale supersaturation effect unravels the role of the supersaturation term that had been hidden for more than half a century.

中文翻译：

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通过包含多尺度过饱和来协调纳米级和微米级 VLS 生长：应用于硅上横向 Ge 薄膜的生长模型


金属催化剂辅助气液固（VLS）生长的大量工作集中在纳米级线（纳米线）上，并且已经有几项研究模拟了直径、生长时间、表面扩散等对这些线的影响。纳米线。在纳米线的背景下，由于催化剂非常小，研究人员可以忽略催化剂过饱和要求的影响。在这项工作中，提出了一个分析生长模型，通过引入“多尺度”过饱和的概念（过饱和为催化剂尺寸的函数）。所提出的模型源自材料平衡关系，该关系在足够小的半径下简化为纳米线方程（无需考虑催化剂过饱和）。通过包含过饱和项，该模型预测了在某些生长条件下薄膜最大尺寸范围的存在，这在现有模型中是不存在的。该模型还可以解释催化剂达到过饱和状态以开始 VLS 生长所需的“诱导时间”。更重要的是，它与 Si 衬底上微米级 Ge 薄膜的 VLS 横向异质外延的可用实验数据一致，这表明在研究的生长条件（375 °C）下需要 0.0379 mol/cm3 的 Ge 原子才能使 Au 催化剂过饱和。这种关于多尺度过饱和效应的新视角揭示了隐藏了半个多世纪的过饱和项的作用。