极紫外波段平面变栅距全息光栅的优化设计

Design of a Varied-Line-Space Plane Grating in EUV Spectrum

为制作应用于极紫外波段（50～150nm）的变栅距全息光栅，提出了一种新的应用于球面波曝光系统的优化算法，即改进的局部优化算法。根据仪器使用要求构建了期望刻线密度函数，并以此建立优化目标函数，其特点是使四个目标函数转化为多变量、带约束的一个目标函数，变为非线性优化问题。使用改进的局部算法时，由于对目标函数进行了加权，赋予了初值多样性，限定了记录参数取值，给出了刻线密度系数的约束条件，从而改变了各项系数对目标函数值的贡献，有效地降低了刻线密度函数系数的误差，提高了刻线函数符合程度及光栅分辨率。与常规局部优化算法相比较，使用改进的局部优化算法可使刻线密度函数与期望刻线密度函数绝对误差在0-0．02line／nm范围内，提高一个数量级，分辨能力可由4000提高至17000以上。结果表明，只要优化方法选择得当，使用简单的球面波曝光系统可以制作高分辨率的变栅距全息光栅。

To make varied-line-space holographic grating which in applied in the extreme ultraviolet band （50- 150 nm）, a new optimization algorithm applied to spherical wavefront system is proposed, named the improved local optimization algorithm. According to the request of instruments, expected varied-line-space holographic grating density function is built. Based on this density function, the merit function is given, of which characteristic is transforming four merit functions to one merit function which has multivariate and nonlinear constrains. Using the improved local algorithm, the error of groove density coefficient is reduced and the resolution of gratings is improved due to the weighted, the diversity of the initial value, the limitation of the recording parameters values range and the constraint of groove density coefficients. Compared with the conventional local optimization algorithm, using the improved local optimization algorithm makes absolute error between design and expected groove density in 0-0.02 line/mm range. And the order of magnitude is improved and the resolution increases from 4000 to above 17000. Results show that by adopting the suited optimization algorithm, varied-line-space plane grating with a high resolution can be made in the spherical wavefront system.