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.

翻译：摘要：随着制造系统中传感器安装的发展与普及，制造过程中采集到的复杂数据给传统过程控制方法带来了挑战。针对半导体制造过程中采集的高维图像基叠加误差（以张量形式建模）的复杂结构，本文提出了一种新的过程控制与监测方法。该方法旨在利用有限的控制配方减少叠加误差。我们首先建立高维过程模型，并提出不同的张量对向量回归算法来估计模型参数，以缓解维数灾难。随后，基于张量参数估计值，设计了针对张量数据的指数加权移动平均（EWMA）控制器，其稳定性在理论上得到保证。考虑到低维控制配方无法补偿图像上所有高维扰动，对控制残差进行监测以预防不可控高维扰动的显著漂移。通过大量仿真和实际案例研究，评估了参数估计算法和张量空间中EWMA控制器的性能。与现有基于图像的反馈控制器相比，我们的方法尤其在扰动不稳定时展现出优势。