Polarization Aberration Compensation Method for Lithographic Projection Lens Based on a Linear Model

提出一种基于线性模型的光刻投影物镜偏振像差补偿方法。根据Hopkins矢量部分相干成像理论,推导了投影物镜含有偏振像差时交替型相移掩模(Alt-PSM)光栅图形的空间像光强分布以及偏振像差引起的光栅图形成像位置偏移(IPE)与最佳焦面偏移(BFS)的解析表达式。利用该解析表达式建立了偏振像差与光栅图形成像质量(IPE、BFS)的线性模型。通过该线性模型能快速计算偏振像差线性灵敏度,调整控制相应的标量像差补偿量,从而减小偏振像差对光栅图形成像质量的不利影响,实现偏振像差补偿。该方法的补偿效果主要与标量像差调整精度以及光栅图形对标量像差的灵敏度有关。仿真结果表明,该补偿方法能有效地减小偏振像差引起的IPE以及不同栅距的光栅图形的BFS差值,从而提高光栅图形成像质量。Based on a linear model, a novel method to compensate the polarization aberration of lithographic projection lens is proposed. By using the Hopkins vector theory of partially coherent imaging, the analytical expressions of the aerial image, as well as the image placement error (IPE) and the best focus shift (BFS) induced by the polarization aberrations are derived for the alternating phase-shift mask (Alt-PSM) grating pattern. Based on these analytical expressions, a linear relation model is established between the polarization aberration and the image quality (IPE, BFS). By calculating the polarization aberration linear sensitivities and adjusting the scalar aberrations based on the linear model, the adverse influences of the polarization aberrations on image guality can be minimized, i.e., realizing polarization aberration compensation. The compensation accuracies are dependent on the scalar aberration adjustment accuracy of the projection lens and the sensitivity of the grating pattern to the scalar aberration. The simulation results show that the IPE and the BFS difference of the gratings with different pitches can be effectively reduced, and the image quality can be improved by the polarization aberration compensation method