含随机测量时延的EWMA批间控制器设计
Design of run to run controller with stochastic metrology delay

批间控制(RtR)是半导体晶圆生产过程控制的有效算法. 然而, 受测量手段与测量成本的限制, 难以实时检 测晶圆的品质数据, 即: 存在一定的测量时延, 通常该测量时延是随机, 时变的, 且直接影响批间控制器的性能. 为 此, 本文基于指数加权移动平均(EWMA)算法, 提出一种含随机测量时延的扰动估计方法. 在分析测量概率的基础 上, 建立包含测量时延概率的扰动估计表达式; 并采用期望最大化(EM)算法估计该测量时延的概率; 然后分析系统 可能存在的静差项, 给出相应的补偿算法; 最后讨论系统的稳定性. 仿真实例验证所提算法的有效性.
Run to run control (RtR) is an effective algorithm for semiconductor manufacturing process. Due to the limitation of measurement methods and cost, it is difficult to measure wafer quality in time (i.e., metrology delay) during the manufacturing process. In general, metrology delay is random and time-varying, which directly deteriorate the performance of RtR controller. To overcome this issue, a novel disturbance estimation integrated into exponentially weighted moving average (EWMA) algorithm is presented in this paper. Firstly, taking the probability of measurement into consideration, the formulation of disturbance estimation with the probability of metrology delay is established. Then, the probability of metrology delay is estimated by expectation maximization (EM) algorithm. Thirdly, the stability is analyzed and the static offset existing in the system is compensated. As a result, an EWMA algorithm resolving the stochastic metrology delay is formed. Finally, the simulation cases demonstrate the effectiveness of the proposed algorithm.