Source mask and polarization optimization (SMPO) is a promising extension of the widely used resolution enhancement technology, source mask optimization (SMO), to further enhance chip manufacturability beyond 28-nm node. Our work is aimed to develop an efficient gradient-based SMPO method by employing the hybrid Hopkins–Abbe imaging model to fulfill the goal. In addition to source and mask variables, the model is adapted to also include polarization variables to realize the optimization. Compact formulas for forward and backward model application are derived. The computation benefits from precomputed transmission cross coefficients and features high efficiency. Validity of the method is confirmed by case studies. For dense array pattern case, the optimal source and polarization can be found analytically. SMPO optimized results match well with the theoretical expectations. In addition, process window, mask error enhancement factor, and normalized image log-slope for the studied cases all get improved over the counterpart SMO results, which employ commonly used polarization. Runtime analysis shows the method is computationally efficient. Our work provides a valid way to optimize polarization together with source and mask.

中文翻译：

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基于混合Hopkins–Abbe模型的基于梯度的源掩模和偏振优化

源掩模和极化优化（SMPO）是对广泛使用的分辨率增强技术源掩模优化（SMO）的有前途的扩展，以进一步增强28 nm节点以外的芯片可制造性。我们的工作旨在通过使用霍普金斯-阿贝混合成像模型来实现目标，从而开发出一种有效的基于梯度的SMPO方法。除了源和掩模变量之外，该模型还适用于包括极化变量以实现优化。推导了用于正向和反向模型应用的紧凑公式。该计算得益于预先计算的传输交叉系数，并且具有高效率。案例研究证实了该方法的有效性。对于密集阵列图案的情况，可以通过分析找到最佳光源和极化。SMPO优化结果与理论预期非常吻合。此外，研究案例的处理窗口，掩模误差增强因子和归一化图像对数斜率都比使用常用极化方法的对应SMO结果有所改善。运行时分析表明该方法在计算上是有效的。我们的工作为优化偏振以及光源和掩模提供了一种有效的方法。