Layout Decomposition Co-Optimization for Hybrid E-Beam and Multiple Patterning Lithography
Layout Decomposition Co-Optimization for Hybrid E-Beam and Multiple Patterning Lithography
复制标题
DOI：
10.1109/tcad.2015.2512903
复制
发表时间：
2016-09
影响因子：
2.9
通讯作者：
Yunfeng Yang;W. Luk;H. Zhou;Changhao Yan;Xuan Zeng;Dian Zhou
中科院分区：
文献类型：
--
作者：
Yunfeng Yang;W. Luk;H. Zhou;Changhao Yan;Xuan Zeng;Dian Zhou
随着特征尺寸的不断缩小和电路复杂性的迅速增加，一种更先进的混合光刻，它结合了多重图案化和电子束光刻（EBL），有望进一步提高图案分辨率。在本文中，我们制定的布局分解问题，这种混合光刻作为一个最小的顶点删除<inline-formula><tex-math notation="LaTeX">${K}$</tex-math></inline-formula>-分区问题，其中<inline-formula><tex-math notation="LaTeX">${K}$</tex-math></inline-formula>是在多重图案的掩模的数量。通过在冲突图构建阶段为每个缝合候选者在两个特征顶点之间添加虚拟顶点，统一考虑缝合最小化和EBL吞吐量。对于<inline-formula><tex-math notation="LaTeX">${K} {=} 2$</tex-math></inline-formula>，我们提出了一个原始-对偶（PD）方法来有效地解决潜在的最小奇循环覆盖问题。此外，链分解算法被用来删除所有的“非循环”的边缘。此外，我们调查两个版本的PD方法，一个平面化和一个没有。对于<inline-formula><tex-math notation="LaTeX">${K} {>} 2$</tex-math></inline-formula>，我们提出了一种随机初始化的局部搜索方法，迭代地应用PD求解器。实验结果表明，与两阶段的方法相比，我们提出的方法减少了EBL的使用65.5%，平均为基准的双重模式和38.7%的三重模式。
As the feature size keeps scaling down and the circuit complexity increases rapidly, a more advanced hybrid lithography, which combines multiple patterning and electron-beam lithography (EBL), is promising to further enhance the pattern resolution. In this paper, we formulate the layout decomposition problem for this hybrid lithography as a minimum vertex deletion <inline-formula> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula>-partition problem, where <inline-formula> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> is the number of masks in multiple patterning. Stitch minimization and EBL throughput are considered uniformly by adding a virtual vertex between two feature vertices for each stitch candidate during the conflict graph construction phase. For <inline-formula> <tex-math notation="LaTeX">${K} {=} 2$ </tex-math></inline-formula>, we propose a primal-dual (PD) method for solving the underlying minimum odd-cycle cover problem efficiently. In addition, a chain decomposition algorithm is employed for removing all “noncyclable” edges. Furthermore, we investigate two versions of the PD method, one with planarization and one without. For <inline-formula> <tex-math notation="LaTeX">${K} {>} 2$ </tex-math></inline-formula>, we propose a random-initialized local search method that iteratively applies the PD solver. Experimental results show that compared with a two-stage method, our proposed methods reduce the EBL usage by 65.5% with double patterning and 38.7% with triple patterning on average for the benchmarks.