为实现掩模台水平向三自由度高精度的运动定位,掩模台测量系统需要建立准确的多自由度解耦测量模型。采用二维衍射平面光栅尺建立掩模台自由度位置测量系统,并主要分析平面光栅尺和读头产生的多个安装误差使测量掩模台位置存在偏差的原因。首先结合安装布局设计出三自由度位移模型,然后结合平面光栅尺和读头的安装误差,分析掩模台位置产生阿贝误差与余弦误差的原因,并设计补偿算法来减小掩模台位置误差,再通过MATLAB软件对模型进行仿真,发现耦合系数具有收敛性;最后提出一种误差校准方法,以双频激光干涉仪测量系统为基准,利用最小二乘法拟合平面光栅尺位置模型的自由度耦合系数。结果表明,该算法能有效地对掩模台的阿贝误差与余弦误差进行补偿,实现5 nm的测量系统不确定度。

To realize the horizontal positioning of a reticle stage with three degrees of freedom and high accuracy, it needs to establish an accurate multi-degree of freedom decoupling measurement model in the reticle-stage-measurement system. In this study, a two-dimensional diffraction planar grating is used to establish a reticle stage degree-of-freedom position measurement system, and the main reasons for the deviation in the position of the reticle stage are analyzed in terms of the multiple installation errors that are caused by the planar grating and read head. Firstly, the displacement model of the three degrees of freedom of the reticle stage is designed according to the installation layout; then, the installation errors of the planar grating and read head are combined to analyze the cause of the Abbe and cosine errors generated by the position of the reticle stage. A compensation algorithm is designed to reduce the position error of the reticle stage and then the model is simulated using MATLAB software, observing the convergence of coupling coefficient. Finally, a calibration error method is proposed. Using the dual-frequency laser interferometer measurement system as the benchmark and using the least squares method, the coupling coefficient of the degree of freedom of the planar grating position model is determined. Experimental results show that the proposed algorithm can effectively compensate the Abbe and cosine errors of the reticle stage; thus, the uncertainty in the measurement system reaches 5 nm.