Recursive Least Squares Estimation and Its Application to Shallow Trench Isolation

Jin WANG, S. Joe QIN*, Christopher A. BODE, Matthew A. PURDY

*Corresponding author for this work

Research output: Book Chapters | Papers in Conference ProceedingsConference paper (refereed)Referred Conference Paperpeer-review

1 Citation (Scopus)


In recent years, run-tc-run (R2R) control technology has received tremendous interest in semiconductor manufacturing. One class of widely used run-to-run controllers is based on the exponentially weighted moving average (EWMA) statistics to estimate process deviations. Using an EWMA filter to smooth the control action on a linear process has been shown to provide good results in a number of applications. However, for a process with severe drifts, the EWMA controller is insufficient even when large weights are used. This problem becomes more severe when there is measurement delay, which is almost inevitable in semiconductor industry. In order to control drifting processes, a predictor-corrector controller (PCC) and a double EWMA controller have been developed. Chen and Quo (2001) show that both PCC and double-EWMA controller are in effect Integral-double-Integral (I-II) controllers, which are able to control drifting processes. However, since offset is often within the noise of the process, the second integrator can actually cause jittering. Besides, tuning the second filter is not as intuitive as a single EWMA filter. In this work, we look at an alternative way-Recursive Least Squares (RLS), to estimate and control the drifting process. EWMA and double-EWMA are shown to be the least squares estimate for locally constant mean model and locally constant linear trend model. Then the recursive least squares with exponential factor is applied to shallow trench isolation etch process to predict the future etch rate. The etch process, which is a critical process in the flash memory manufacturing, is known to suffer from significant etch rate drift due to chamber seasoning. In order to handle the metrology delay, we propose a new time update scheme. RLS with the new time update method gives very good result. The estimate error variance is smaller than that from EWMA, and mean square error decrease more than 10% compared to that from EWMA. © (2003) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).
Original languageEnglish
Title of host publicationAdvanced Process Control and Automation, Proceedings Volume 5044
EditorsMatt HANKINSON, Christopher P. AUSSCHNITT
Number of pages12
ISBN (Print)0819448494
Publication statusPublished - 1 Jul 2003
Externally publishedYes
EventSPIE Conference: Advanced Process Control and Automation - Santa Clara, United States
Duration: 27 Feb 200328 Feb 2003


ConferenceSPIE Conference: Advanced Process Control and Automation
Country/TerritoryUnited States
CitySanta Clara


  • EWMA
  • Exponential forgetting
  • Recursive least squares
  • Run-to-run control
  • Shallow trench isolation


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