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首页> 外文期刊>Journal of Computational Physics >A Level Set Approach to a Unified Model for Etching, Deposition, and Lithography Ⅱ: Three-Dimensional Simulations
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A Level Set Approach to a Unified Model for Etching, Deposition, and Lithography Ⅱ: Three-Dimensional Simulations

机译：用于蚀刻，沉积和光刻的统一模型的水平集方法Ⅱ：三维模拟

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摘要

We apply a level set formulation to the problem of surface advancement in three-dimensional topography simulation of deposition, etching, and lithography processes in integrated circuit fabrication. The level set formulation is based on solving a Hamilton-Jacobi-type equation for a propagating level set function, using techniques borrowed from hyperbolic conservation laws. Topologi-cal changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. The equations of motion of a unified model, including the effects of isotropic and unidirectional deposition and etching, visibility, surface diffusion, reflection, and material dependent etch/deposition rates are presented and adapted to a level set formulation. In Part Ⅰ of this paper, the basic equations and algorithms for two-dimensional simulations were developed. In this paper, the extension to three dimensions is presented. We show a large collection of simulations, including three-dimensional etching and deposition into cavities under the effects of visibility, directional and source flux functions, evolution of lithographic profiles, discontinuous etch rates through multiple materials, and non-convex sputter yield flux functions. In Part Ⅲ of this paper, effects of reflection and re-emission and surface diffusion will be presented.
机译：我们对集成电路制造中的沉积，蚀刻和光刻工艺的三维拓扑模拟中的表面推进问题应用了水平集公式。水平集公式是基于使用双曲守恒定律借用的技术求解传播的水平集函数的Hamilton-Jacobi型方程。在这种设置下自然可以得到地形变化，拐角和尖角发展以及几何特性（例如曲率和法线方向）的准确确定。提出了统一模型的运动方程，包括各向同性和单向沉积和蚀刻，可见性，表面扩散，反射以及与材料有关的蚀刻/沉积速率的影响，并适用于水平设定公式。在本文的第一部分中，开发了二维模拟的基本方程和算法。在本文中，提出了对三个维度的扩展。我们展示了大量模拟，包括在可见性，方向和源通量函数，光刻轮廓的演变，通过多种材料的不连续蚀刻速率以及非凸溅射成品率通量函数的影响下进行的三维蚀刻和在空腔中的沉积。在本文的第三部分中，将介绍反射和再发射以及表面扩散的影响。

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