Modeling the vertical growth of van der Waals stacked 2D materials using the diffuse domain method
Modeling the vertical growth of van der Waals stacked 2D materials using the diffuse domain method
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DOI：
10.1088/1361-651x/ab5e9a
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发表时间：
2019-11
影响因子：
1.8
通讯作者：
Zhenlin Guo;Christopher C. Price;V. Shenoy;J. Lowengrub
中科院分区：
文献类型：
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作者：
Zhenlin Guo;Christopher C. Price;V. Shenoy;J. Lowengrub
垂直堆叠单层石墨烯和其他原子薄二维材料由于其在制造具有特定设计性能的材料方面的潜力而引起了相当大的研究兴趣。化学气相沉积已被证明是一种高效和可扩展的制造方法。然而，缺乏对机械的理解阻碍了控制制造过程的努力，超出了经验的试错方法。在本文中，我们建立了二维材料垂直生长的一般多尺度Burton-Cabrera-Frank型模型，以预测任意形状层垂直与平面内（单层）生长的必要生长条件。这扩展了之前的工作，我们开发了这样一个模型，假设层是全面的（Ye等人2017年ACS Nano 11 12780-8）。为了对模型进行数值求解，我们使用相场/漫射域方法对系统进行了重新表述，使方程能够在固定的规则域中求解。我们使用二阶精确的自适应有限差分/非线性多重网格算法对离散系统进行离散和求解。我们研究了层间范德华相互作用能、动力学附着率、边缘能和沉积通量等参数对层生长和形貌的影响。虽然有利于垂直生长的条件通常遵循我们为圆形层导出的解析热力学标准，但在生长过程中，层边界可能会发展出显著的曲率，这与实验观察结果一致。我们的方法为控制和优化多层二维材料的生长提供了一个机制框架。
Vertically-stacked monolayers of graphene and other atomically-thin 2D materials have attracted considerable research interest because of their potential in fabricating materials with specifically-designed properties. Chemical vapor deposition has proved to be an efficient and scalable fabrication method. However, a lack of mechanistic understanding has hampered efforts to control the fabrication process beyond empirical trial-and-error approaches. In this paper, we develop a general multiscale Burton–Cabrera–Frank type model of the vertical growth of 2D materials to predict the necessary growth conditions for vertical versus in-plane (monolayer) growth of arbitrarily-shaped layers. This extends previous work where we developed such a model assuming the layers were fully-faceted (Ye et al 2017 ACS Nano 11 12780–8). To solve the model numerically, we reformulate the system using the phase-field/diffuse domain method that enables the equations to be solved in a fixed regular domain. We use a second-order accurate, adaptive finite-difference/nonlinear multigrid algorithm to discretize and solve the discrete system. We investigate the effect of parameters, including the van der Waals interaction energies between the layers, the kinetic attachment rates, the edge-energies and the deposition flux, on layer growth and morphologies. While the conditions that favor vertical growth generally follow an analytic thermodynamic criterion we derived for circular layers, the layer boundaries may develop significant curvature during growth, consistent with experimental observations. Our approach provides a mechanistic framework for controlling and optimizing the growth multilayered 2D materials.