KEYWORDS: Feedback control, Process control, Control systems, Device simulation, Filtering (signal processing), Manufacturing, Data modeling, Process modeling, Semiconductor manufacturing, Systems modeling
We present a systematic robustness analysis for several feedback controllers used in photolithographic critical dimension (CD) control in semiconductor manufacturing. Our study includes several controllers based on either the exponentially weighted moving average (EWMA) estimation or Kalman filters. The robustness is characterized by two features, namely the controller's stability margin in the presence of model mismatch and the controller's sensitivity to unknown noise. Simulations on the closed-loop control system are shown for the performance comparison. Both the analysis and the simulations prove that the multiple-dimensional feedback controller developed in this paper using the average of previous inputs and outputs outperforms the other controllers in the group.
Proc. SPIE. 6152, Metrology, Inspection, and Process Control for Microlithography XX
KEYWORDS: Control systems, Data processing, Process control, Dynamical systems, Feedback control, Performance modeling, Systems modeling, Filtering (signal processing), Process modeling, Device simulation
In this paper, we present a study on the robustness comparison of several process feedbacks controllers. The
feedbacks include those based on either EWMA or Kalman Filter estimation. In addition, a new multiple
dimension feedback controller is introduced, which has a significantly improved robust stability and reduced
sensitivity to unknown noise. In the robustness study, we assume model mismatch and unknown disturbances.
Two issues of robustness are addressed in this paper, namely the region of model mismatch in which a process
feedback is stable; and the H-infinity gain of the controlled process from unknown noise to the system performance.
Simulations are shown to compare the performance of the feedbacks under model mismatch, system drifting, and
In this paper, a stability analysis is conducted for several feedback controllers of photolithography processes. We emphasize the stability of process controllers in the presence of model mismatch, and other uncertainties such as system drift and unknown noise. Real data of critical dimension (CD) in shallow trench isolation area from an Intel manufacturing fab is used for model analysis. The feedbacks studied in this paper include a controller based on an adaptive model, and several controllers based on existing estimation methods such as EWMA, extended EWMA, and d-EWMA. Both theoretical analysis and computer simulations are presented to show the stability of the controlled process under these feedbacks.
After we implemented the run-to-run feedback control system for lithographic stepper registration, we found that the metrology error introduced wrong control signals which drove the process away from normal operation. This paper presents methods of model-based fault detection and metrology error rejection. We use the fault detection method to monitor the health of run-to-run system and apply the error rejection method to proactively correct control signal to ensure the desired targets. Comparing to the old run-to-run system used in litho process that only provides warning limits and hard limits with fixed thresholds on individual physical variables, the proposed fault detection method is more sensitive to detect drift, shift and out-of-control points. It could have detected a real problem much quicker if this method was used. The error rejection method is very powerful to handle metrology errors as well as shift and drift by using the estimated output instead of the measured output. The experiments on the real data and simulation data validate the usefulness of the method.