Industrial Engineering and Management Systems

Korean Institute of Industrial Engineers (대한산업공학회)
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Recursive Least Squares Run-to-Run Control with Time-Varying Metrology Delays

  • Fan, Shu-Kai (Department of Industrial Engineering and Management, Yuan Ze University) ;
  • Chang, Yuan-Jung (Department of Industrial Engineering and Management, Yuan Ze University)
  • Received : 2010.03.10
  • Accepted : 2010.07.14
  • Published : 2010.09.01
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Abstract

This article investigates how to adaptively predict the time-varying metrology delay that could realistically occur in the semiconductor manufacturing practice. Metrology delays pose a great challenge for the existing run-to-run (R2R) controllers, driving the process output significantly away from target if not adequately predicted. First, the expected asymptotic double exponentially weighted moving average (DEWMA) control output, by using the EWMA and recursive least squares (RLS) prediction methods, is derived. It has been found that the relationships between the expected control output and target in both estimation methods are parallel, and six cases are addressed. Within the context of time-varying metrology delay, this paper presents a modified recursive least squares-linear trend (RLS-LT) controller, in combination with runs test. Simulated single input-single output (SISO) R2R processes subject to various time-varying metrology delay scenarios are used as a testbed to evaluate the proposed algorithms. The simulation results indicate that the modified RLS-LT controller can yield the process output more accurately on target with smaller mean squared error (MSE) than the original RLSLT controller that only deals with constant metrology delays.

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References

  1. Butler, S. W. and Stefani, J. A. (1994), Supervisory runto- run control of polysilicon gate etch using in situ ellipsometry, IEEE Transactions on Semiconductor Manufacturing, 7(2), 193-201. https://doi.org/10.1109/66.286855
  2. Carlson, A. and DiBiase, D. (2002), Effect of metrology time delay on overlay APC, Proceedings of SPIE, 4692, 1-16.
  3. Chamness, K., Cherry, G., Good, R., and Qin, S. (2001), A comparison of R2R control algorithms for the CMP with measurement delay, AEC/APC XIII Symposium, 1-4.
  4. Chen, A. and Guo, R. (2001), Age-based double EWMA controller and its application to CMP processes, IEEE Transactions on Semiconductor Manufacturing, 14(1), 11-19. https://doi.org/10.1109/66.909650
  5. Daniel, W. W. (1990), Applied Nonparametric Statistics, Boston.
  6. del Castillo, E. and Hurwitz, A. M. (1997), Run-to-run process control: Literature review and extensions, Journal of Quality Technology, 29(2), 184-196.
  7. del Castillo, E. and Yeh, J.-Y. (1998), An adaptive runto- run optimizing controller for linear and nonlinear semiconductor processes, IEEE Transactions on Semiconductor Manufacturing, 11(2), 285-295. https://doi.org/10.1109/66.670178
  8. del Castillo, E. (1999), Long run and transient analysis of a double EWMA feedback controller, IIE Transactions, 31(12), 1157-1169.
  9. del Castillo, E. (2001), Some properties of EWMA feedback quality adjustment schemes for drifting disturbances, Journal of Quality Technology, 33(2), 153-166.
  10. Fan, S.–K. S., Jiang B. C., Jen, C.–H., and Wang, C.–C. (2002), SISO run-to-run feedback controller using triple EWMA smoothing for semiconductor manufacturing processes, International Journal of Production Research, 40, 3093-3120. https://doi.org/10.1080/00207540210141652
  11. Good, R. P. and Qin, S. J. (2006), On the Stability of MIMO EWMA Run-to-Run Controllers with Metrology Delay, IEEE Transactions on Semiconductor Manufacturing, 19(1), 78-86. https://doi.org/10.1109/TSM.2005.863211
  12. Ingolfsson, A. and Sachs, E. (1993), Stability and sensitivity of an EWMA controller, Journal of Quality Technology, 25(4), 271-287.
  13. Lo, L.–C. (2007), Adaptive Adjustment Scheme of Time-Varying Metrology Delay using RLS-type Controllers, master thesis, Department of Industrial Engineering and Management, Yuan Ze University, Taoyuan County, Taiwan 320.
  14. Moyne, J., del Castillo, E., and Hurwitz. A. M. (2001), Run-to-Run Control in Semiconductor Manufacturing, Boca Raton, FL: CRC Press.
  15. Siegel, S. and Castellan, N. J. (1988), Nonparametric systems for the Behavioral, Sciences, McGRAWHILL.
  16. Wang, J., Qin, S. J., Bode, C. A., and Purdy, M. A. (2003), Recursive Least Squares Estimation and Its Application to Shallow Trench Isolation, Proceedings of SPIE-International Society for Optical Engineering, 5044, 109-120.
  17. Wang, J., He, Q. P., Qin, S. J., Bode, C. A., and Purdy, M. A. (2005), Recursive Least Squares Estimation for Run-to-Run Control with Metrology Delay and Its Application to STI Etch Process, IEEE Transactions on Semiconductor Manufacturing, 18(2), 309-318. https://doi.org/10.1109/TSM.2005.846819
  18. Wu, M. F., Lin, C. H., Wong, S. H., Jang, S. S., and Tseng, S. T. (2006), Performance Analysis of EWMA Controller Subject to Metrology Delay, AEC/APC Symposium Asia 2006, Taiwan.