晶圆校准器误差补偿与拟合算法的研究  

Research on Error Compensation and Fitting Algorithms of Wafer Alignment Calibrator

作　　者：刘暾东 陈锃琰 王若宇 唐之晨 郑鹏 LIU Tundong;CHEN Zengyan;WANG Ruoyu;TANG Zhichen;ZHENG Peng(Pen-Tung Sah Institute of Micro-Nano Science and Technology,Xiamen University,Xiamen,Fujian 361102,China;Xiamen Institute of Measurement and Testing,Xiamen,Fujian 361004,China)

机构地区：[1]厦门大学萨本栋微米纳米科学技术研究院,福建厦门361102 [2]厦门市计量检定测试院,福建厦门361004

出　　处：《计量学报》2024年第8期1115-1124,共10页Acta Metrologica Sinica

基　　金：国家市场监管总局科技计划(2022MK138)。

摘　　要：晶圆校准器作为半导体生产、检测中的重要设备,其圆心定位的精度容易受检测误差的影响,因此针对误差的补偿算法是提高晶圆校准精度的关键技术。针对检测误差中晶圆承载面倾斜影响采样精度问题,建立了晶圆倾斜后在水平面椭圆投影的物理模型,推导椭圆与晶圆圆心的解析关系,并采用相应的椭圆方程进行拟合。为了进一步提高补偿及拟合精度,提出了一种引入遗忘因子的扩展卡尔曼滤波的椭圆拟合算法,该算法采用密度聚类法及改进样本点分布的渐进一致采样进行数据预处理,并利用迭代重加权最小二乘法进行椭圆拟合,最终实现圆心的精确拟合。实验证明,在使用提出的方法进行误差补偿后,拟合精度达到99.95%,验证了其有效性。Wafer alignment calibrator plays a crucial role in semiconductor manufacturing and inspection processes.However,the accuracy of wafer center positioning can be affected by measurement errors.Consequently,the development of error compensation algorithms is paramount to refining the accuracy of wafer alignment calibrator.To address the impact of wafer carrier surface tilt on sampling accuracy,a physical model of a tilted wafer and its elliptical projection on the horizontal plane is established.An analytical relationship between the ellipse and the wafer center is derived from this model.Subsequently,an elliptical equation is employed for fitting purposes.To further enhance compensation and fitting accuracy,an extended Kalman filter-based ellipse fitting algorithm with a forgetting factor is proposed.This algorithm employs density-based spatial clustering of applications with noise for data preprocessing,coupled with improved progressive consistent sampling to improve the distribution of sample points.Additionally,an iterative reweighted least squares method is applied for ellipse fitting,resulting in high-precision estimation of the wafer center.Experimental results demonstrate that the proposed method achieves a fitting accuracy of 99.95%after error compensation,thus validating its effectiveness.

关 键 词：几何量计量 晶圆校准器 误差补偿 椭圆拟合 顺序抽样一致性 

分 类 号：TB92[一般工业技术—计量学]