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.
KEYWORDS: Process control, Feedback control, Filtering (signal processing), Systems modeling, Device simulation, Control systems, Data processing, Performance modeling, Process modeling, Dynamical systems
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
random noise.
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.
A new design method for non-time based tracking controller is presented. The key to the non-time based control method is the introduction of a suitable action or motion reference variable other than time, which is directly related to the desired and measurable system output.It enables the construction of control system with integrated planning capability, in which planning becomes real-time closed-loop process. The new design method converts a controller designed by traditional time-based approach to a non-time based controller using action reference. It significantly simplifies the design procedure. The design method is exemplified by a unmanned vehicle tracking control problem. The design procedure and simulation results demonstrate the advantages of proposed method.
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