We present numerical methods to enable accurate and robust level-set based simulation of anisotropic wet etching and non-planar epitaxy for semiconductor fabrication. These fabrication techniques are characterized by highly crystal orientation-dependent etch/growth rates, which lead to non-convex Hamiltonians in their description by the level-set equation. As a consequence, instable surface propagation may emerge, leading to unphysical results. We propose a calibration-free Stencil Lax-Friedrichs scheme and an advanced adaptive time-stepping approach, tailored to the level-set speed functions associated with anisotropic etching and epitaxy. The scheme calculates the numerical dissipation based on information about the local geometry and the nature of the etch rates/growth function, which enables an optimized trade-off between overly rounding of sharp geometric features and stable surface propagation. Furthermore, we introduce the deposition top layer method, which allows for robust handling of multiple material regions in non-planar epitaxy simulations. Both methods are demonstrated in a prototypical implementation, which is used to validate the capability and accuracy of our approaches. In particular, two-dimensional wet etching and three-dimensional epitaxy simulations are performed and characteristic geometry parameters are compared to the ideally expected values, showing robustness and high accuracy.

中文翻译：

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多材料湿蚀刻和非平面选择性外延的水平集方法

我们提出了数值方法，以实现半导体制造的各向异性湿法蚀刻和非平面外延的准确和稳健的基于水平集的模拟。这些制造技术的特点是高度依赖于晶体取向的蚀刻/生长速率，这导致在水平集方程的描述中出现非凸哈密顿量。因此，可能会出现不稳定的表面传播，导致非物理结果。我们提出了一种免校准的 Stencil Lax-Friedrichs 方案和一种先进的自适应时间步进方法，专为与各向异性蚀刻和外延相关的水平集速度函数量身定制。该方案根据有关局部几何形状和蚀刻速率/生长函数的性质的信息计算数值耗散，这可以在锐利几何特征的过度圆角和稳定的表面传播之间实现优化的权衡。此外，我们引入了沉积顶层方法，该方法允许在非平面外延模拟中对多个材料区域进行稳健处理。这两种方法都在原型实现中进行了演示，用于验证我们方法的能力和准确性。特别是，进行了二维湿法蚀刻和三维外延模拟，并将特征几何参数与理想的预期值进行了比较，显示出稳健性和高精度。这两种方法都在原型实现中进行了演示，用于验证我们方法的能力和准确性。特别是，进行了二维湿法蚀刻和三维外延模拟，并将特征几何参数与理想的预期值进行了比较，显示出稳健性和高精度。这两种方法都在原型实现中进行了演示，用于验证我们方法的能力和准确性。特别是，进行了二维湿法蚀刻和三维外延模拟，并将特征几何参数与理想的预期值进行了比较，显示出鲁棒性和高精度。