Tensor-based process control and monitoring for semiconductor
  manufacturing with unstable disturbances
Yanrong Li Juan Du Fugee Tsung Wei Jiang
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.