Error modeling and analysis of dual-frequency laser interferometry in scanning beam interference lithography system
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摘要:
扫描干涉场曝光技术(SBIL)是制作单体大面积高精度光栅的有效途径，采用双频激光干涉仪反馈工作台位置进行干涉条纹的精确拼接，测量误差会不可避免的引入光栅刻线误差，降低光栅衍射波前质量。针对工作台位移测量误差，分析了激光干涉仪自身结构因素引起的本征误差，提出了复杂环境下激光干涉仪本征误差指标评价方法；建立了实际工况与经验公式相结合的死程误差和测量光程变化误差理论模型；通过构建平移和旋转算子，推导了工作台任意点旋转和平移之间的耦合关系，模拟了不同工作台姿态滚转角下的测量误差。进行了位移误差实验和光栅扫描曝光实验，实验结果表明，位移误差与理论计算结果一致，制作200 mm×200 mm光栅的衍射波前为0.278
λ @632.8 nm。本文的分析方法贯通了光栅衍射波前与测量误差的传递链路，为制作米级尺寸纳米精度全息光栅奠定了理论和实验基础。Abstract:Scanning interference field exposure (SBIL) is an effective way to fabricate monomeric large-area high-precision gratings. Using dual-frequency laser interferometer feedback table position to splicing interference fringes accurately, the measurement error will inevitably introduce grating engraving error and reduce the diffraction wavefront quality of grating. The intrinsic error caused by the structure of laser interferometer is analyzed, and the evaluation method of the intrinsic error index of laser interferometer in complex environment is proposed. The theoretical models of dead path error and measuring optical path variation error combined with actual working conditions and empirical formulas are established. By constructing translation and rotation operators, the coupling relationship between rotation and displacement of any point of the table is deduced, and the measurement errors under different table attitude roll angles are simulated. The displacement error experiment and grating scanning exposure experiment are carried out. The experimental results show that the displacement error is consistent with the theoretical calculation results. The diffraction wavefront of the 200 mm×200 mm grating is 0.278λ@632.8nm. The analytical method in this paper connects the transmission link between the grating diffraction wavefront and the measurement error, and lays a theoretical and experimental foundation for the fabrication of meter-size nano-precision holographic gratings.
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图 2 双频激光干涉测量系统原理图
Figure 2. Dual-frequency laser interferometry system schematic diagram
图 4 空气折射率随温度和压强变化曲线
Figure 4. Variation curve of air refractive index with temperature and pressure
图 5 滚转角对激光干涉仪测量精度的影响 (a) 理想情况下，x轴测量镜测量点Q；(b) 工作台在原点o处旋转α角；(c) 工作台在标记点Q旋转α角。
Figure 5. The impact of roll angle on the measurement accuracy of laser interferometers. (a) Measuring point Q when the workbench is not rotating. (b) Workbench rotates α at origin O. (c) Workbench rotates α around point Q.
图 7 不同旋转角下测量轴偏移量对测量误差
Figure 7. Measurement axis offset vs. measurement error at different rotation angles
图 15 激光干涉仪与光栅干涉仪稳定性对比
Figure 15. Stability comparison between laser interferometer and grating interferometer
图 16 光栅干涉仪与激光干涉仪差值频谱分析
Figure 16. Spectrum analysis of difference between grating interferometer and laser interferometer
表 1 空气折射率和环境影响系数
Table 1. Values of laboratory environmental parameters
参数 数值 标准空气折射率 1.000273 激光器真空波长/nm 632.991528 空气波长/nm 632.818663 温度敏感性/°C−1 −1.004×10−6 湿度敏感性/(%RH)−1 −6.401×10−9 压强敏感性/Pa−1 0.200×10−8 
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表 2 测量系统精度
Table 2. Measurement system error
误差项 误差值(nm) 激光器波长稳定性 8.00 电子学误差 0.15 光学非线性误差 4.40 光学温度漂移误差 0.08 测量镜面形误差 51.64 死程误差 79.73 光程变化误差 12.80 工作台姿态误差 18.00 RSS 97.95
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