Model-based multiple patterning layout decomposition

Daifeng Guo, Haitong Tian, Yuelin Du, Martin D. F. Wong
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引用次数: 2

Abstract

As one of the most promising next generation lithography technologies, multiple patterning lithography (MPL) plays an important role in the attempts to keep in pace with 10 nm technology node and beyond. With feature size keeps shrinking, it has become impossible to print dense layouts within one single exposure. As a result, MPL such as double patterning lithography (DPL) and triple patterning lithography (TPL) has been widely adopted. There is a large volume of literature on DPL/TPL layout decomposition, and the current approach is to formulate the problem as a classical graph-coloring problem: Layout features (polygons) are represented by vertices in a graph G and there is an edge between two vertices if and only if the distance between the two corresponding features are less than a minimum distance threshold value dmin. The problem is to color the vertices of G using k colors (k = 2 for DPL, k = 3 for TPL) such that no two vertices connected by an edge are given the same color. This is a rule-based approach, which impose a geometric distance as a minimum constraint to simply decompose polygons within the distance into different masks. It is not desired in practice because this criteria cannot completely capture the behavior of the optics. For example, it lacks of sufficient information such as the optical source characteristics and the effects between the polygons outside the minimum distance. To remedy the deficiency, a model-based layout decomposition approach to make the decomposition criteria base on simulation results was first introduced at SPIE 2013.1 However, the algorithm1 is based on simplified assumption on the optical simulation model and therefore its usage on real layouts is limited. Recently AMSL2 also proposed a model-based approach to layout decomposition by iteratively simulating the layout, which requires excessive computational resource and may lead to sub-optimal solutions. The approach2 also potentially generates too many stiches. In this paper, we propose a model-based MPL layout decomposition method using a pre-simulated library of frequent layout patterns. Instead of using the graph G in the standard graph-coloring formulation, we build an expanded graph H where each vertex represents a group of adjacent features together with a coloring solution. By utilizing the library and running sophisticated graph algorithms on H, our approach can obtain optimal decomposition results efficiently. Our model-based solution can achieve a practical mask design which significantly improves the lithography quality on the wafer compared to the rule based decomposition.
基于模型的多模式布局分解
作为最有前途的下一代光刻技术之一,多模光刻技术(MPL)在与10nm及以上技术节点同步的过程中发挥着重要作用。随着特征尺寸的不断缩小,在一次曝光中打印密集的布局已经变得不可能。因此,双模光刻(DPL)和三模光刻(TPL)等MPL技术得到了广泛的应用。关于DPL/TPL布局分解有大量的文献,目前的方法是将该问题表述为一个经典的图着色问题:布局特征(多边形)由图G中的顶点表示,当且仅当两个对应特征之间的距离小于最小距离阈值dmin时,两个顶点之间存在一条边。问题是使用k种颜色为G的顶点上色(DPL为k = 2, TPL为k = 3),这样由一条边连接的两个顶点就不会被赋予相同的颜色。这是一种基于规则的方法,它将几何距离作为最小约束,简单地将距离内的多边形分解为不同的蒙版。这是不希望在实践中,因为这个标准不能完全捕捉光学的行为。例如,它缺乏足够的信息,如光源特性和最小距离外多边形之间的影响。为了弥补这一不足,SPIE 2013.1首次提出了一种基于模型的布局分解方法,根据仿真结果制定分解标准。然而,该算法1是基于光学仿真模型的简化假设,因此在实际布局中的应用受到限制。最近AMSL2还提出了一种基于模型的布局分解方法,该方法通过迭代模拟布局,需要大量的计算资源,并且可能导致次优解。这种方法也可能产生太多缝线。本文提出了一种基于模型的MPL布局分解方法,该方法使用预先模拟的频繁布局模式库。我们没有在标准图着色公式中使用图G,而是构建了一个扩展图H,其中每个顶点代表一组相邻的特征以及着色解决方案。通过利用库并在H上运行复杂的图算法,我们的方法可以有效地获得最优的分解结果。与基于规则的分解相比,我们基于模型的解决方案可以实现实用的掩模设计,大大提高了晶圆片上的光刻质量。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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