With the development and popularity of sensors installed in manufacturing
systems, complex data are collected during manufacturing processes, which
brings challenges for traditional process control methods. This paper proposes
a novel process control and monitoring method for the complex structure of
high-dimensional image-based overlay errors (modeled in tensor form), which are
collected in semiconductor manufacturing processes. The proposed method aims to
reduce overlay errors using limited control recipes. We first build a
high-dimensional process model and propose different tensor-on-vector
regression algorithms to estimate parameters in the model to alleviate the
curse of dimensionality. Then, based on the estimate of tensor parameters, the
exponentially weighted moving average (EWMA) controller for tensor data is
designed whose stability is theoretically guaranteed. Considering the fact that
low-dimensional control recipes cannot compensate for all high-dimensional
disturbances on the image, control residuals are monitored to prevent
significant drifts of uncontrollable high-dimensional disturbances. Through
extensive simulations and real case studies, the performances of parameter
estimation algorithms and the EWMA controller in tensor space are evaluated.
Compared with existing image-based feedback controllers, the superiority of our
method is verified especially when disturbances are not stable.

该论文提出了一种新颖的高维基于图像的覆盖误差处理控制与监测方法，利用有限的控制配方来减少覆盖误差。通过构建高维过程模型并提出不同的张量与向量回归算法来估计模型中的参数，减轻维度诅咒。基于张量参数的估计，设计了指数加权移动平均（EWMA）张量数据控制器，其稳定性经过理论保证。为了防止无法控制的高维扰动的显著漂移，检测控制残差。通过大量的仿真和真实案例研究，评估了参数估计算法和张量空间中 EWMA 控制器的性能。与现有的基于图像的反馈控制器相比，我们的方法在扰动不稳定时表现出明显的优势。