基于混合梯度下降的高性能光刻机离轴照明衍射光学元件设计

A Mixed Gradient Algorithm for High Performance DOE Design in Off-Axis Lithography Illumination System

深紫外(DUV)光刻机照明系统普遍采用衍射光学元件(DOE)实现光瞳整形。根据光刻机的指标要求,衍射光学元件应具有高衍射效率和高均匀性的特点。传统的相位恢复算法如Gerchberg-Saxton(GS)及其改进算法,一般只能通过降低均匀性来提高衍射效率,无法得到最优的解。而全局优化算法如模拟退火法、遗传基因法等需要大量的计算时间,难以实现像素数目多的深紫外DOE的设计。为了克服上述困难,提出了一种基于GS的混合梯度下降算法,在迭代过程中对每次迭代的振幅进行加权反馈修正,在加快收敛速度的同时,减少误差,同时实现高效率和高信噪比。利用该算法对光刻需要的传统、四极照明光瞳、定制照明光瞳的DOE进行了设计,结果表明,实现传统和四极照明光瞳的16阶量化相位DOE的衍射效率均超过92%,而非均匀性分别为3.98%和2.3%。实现定制照明光瞳的DOE的衍射效率为91%,图形恢复误差为5.8%。该方法为获得高性能深紫外DOE提供一条可行的途径。

The diffractive optical element （DOE） is widely used to generate various illumination pupils in the deep ultraviolet （DUV） projection lithography system. According to the specifications of DUV lithography machines, the designed DOE should possess high diffraction efficiency and high uniformity. Traditional algorithms such as Gerchberg-Saxton （GS） algorithm （GSA） and modified GSA get high diffraction efficiency with low non-uniformity. Global searching methods such as gene algorithm and simulated annealing algorithm need huge computing effort to receive high diffraction efficiency and high uniformity. To address these issues, a mixed gradient algorithm based on GSA is proposed. It can accelerate the rate of convergence and improve the signal to noise ratio simultaneously, and the phase retrieval image is improved. The DOEs generating conventional, quadrupole and customized illumination modes are designed and analyzed based on the proposed method, then the phase is quantized with 16 levels. The diffraction efficiency will reach 92%, and the non-uniformities of the proposed algorithm can reach 3.98% and 2.3% for the conventional and quadrupole illumination modes, respectively. The received efficiency for customized DOE is 91%, and its pattern recoveryerror is 5.8%. It provides a practical method of DOE design in projection lithography system.