Hidden Markov Models for Endpoint Detection in Plasma Etch Processes

We investigate two statistical detection problems in plasma etch endpoint detection: change-point detection and pattern matching. Our approach is based on a segmental semi-Markov model framework. In the change-point detection problem, the change-point corresponds to state switching in the model. For pattern matching, the pattern is approximated as a sequence of linear segments that are modeled as segments (states) in the model. The segmental semi-Markov model is an extension of the standard hidden Markov model (HMM), from which learning and inference algorithms are presented to solve the problems of change-point detection and pattern matching in a Bayesian framework. Results on both simulated data and real data from semiconductor manufacturing illustrate the flexibility and accuracy of the proposed framework. 200 210 220 230 240 250 260 4500 5000 5500 6000 6500 7000 Time (s) In te ns ity (a .u .) Figure 1: An illustrative example of a change-point detection problem from plasma etching. Data are from a commercial LAM 9400 plasma etch machine.

[1]  Fredrik Gustafsson,et al.  Adaptive filtering and change detection , 2000 .

[2]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[3]  Richard F. Gunst,et al.  Applied Regression Analysis , 1999, Technometrics.

[4]  Hiroshi Imai,et al.  An optimal algorithm for approximating a piecewise linear function , 1986 .

[5]  Duane S. Boning,et al.  Low open-area endpoint detection using a PCA-based T/sup 2/ statistic and Q statistic on optical emission spectroscopy measurements , 2000 .

[6]  Costas J. Spanos,et al.  Modeling and filtering of optical emission spectroscopy. Data for plasma etching systems , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[7]  S. W. E. Earles,et al.  Optimal polygonal approximation of digitized curves , 1994 .

[8]  A. El-Shaarawi,et al.  Inference about the Point of Change in a Regression Model , 1981 .

[9]  Mari Ostendorf,et al.  From HMM's to segment models: a unified view of stochastic modeling for speech recognition , 1996, IEEE Trans. Speech Audio Process..

[10]  Donald J. Berndt,et al.  Using Dynamic Time Warping to Find Patterns in Time Series , 1994, KDD Workshop.

[11]  Duane S. Boning,et al.  Endpoint prediction for polysilicon plasma etch via optical emission interferometry , 1997 .

[12]  Chin-Hui Lee,et al.  Automatic recognition of keywords in unconstrained speech using hidden Markov models , 1990, IEEE Trans. Acoust. Speech Signal Process..

[13]  P. Lerman.  Fitting Segmented Regression Models by Grid Search , 1980 .

[14]  D. Hawkins.  POINT ESTIMATION OF THE PARAMETERS OF PIECEWISE REGRESSION MODELS. , 1976 .

[15]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[16]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[17]  Randy Moore,et al.  Application of neural networks to plasma etch end point detection , 1996 .

[18]  Padhraic Smyth,et al.  Deformable Markov model templates for time-series pattern matching , 2000, KDD '00.

[19]  Ronald L. Allen,et al.  Multiresolution pattern detector networks for controlling plasma etch reactors , 1995, Advanced Lithography.

[20]  T. Lai.  Sequential changepoint detection in quality control and dynamical systems , 1995 .

[21]  Michèle Basseville,et al.  Detection of abrupt changes: theory and application , 1993 .

[22]  D. Hinkley.  Inference in Two-Phase Regression , 1971 .