Abstract
As production requirements in semiconductor manufacturing continue to escalate, it is rarely possible to perform quality measurements on a product before subsequent process operations are performed. This delay between manufacturing and metrology coupled with inaccurate process models can lead to closed-loop instabilities. This paper investigates the effect of metrology delay on the closed-loop stability of a multiple input - multiple output exponentially weighted moving average run-to-run controller. The generalized Routh-Hurwitz stability criteria are used to derive the necessary and sufficient conditions for stability. A sufficient condition for stability is then derived for systems with any length of metrology delay. This condition states that if all of the eigenvalues of a model-mismatch matrix fall inside a circle with unit radius and centered at {1,0} on the complex plane, then the closed-loop system is stable.
| Original language | English |
|---|---|
| Pages (from-to) | 78-86 |
| Number of pages | 9 |
| Journal | IEEE Transactions on Semiconductor Manufacturing |
| Volume | 19 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Feb 2006 |
| Externally published | Yes |
Funding
Manuscript received December 2, 2003; revised November 21, 2005. The work of S. J. Qin was supported by the National Science Foundation of China through an Overseas Outstanding Young Investigator Award and by the National Science Foundation under CAREER Award CTS-9985074. The work of R. Good was supported by the APC Group, AMD’s Fab 30, Dresden, Germany.
Keywords
- Exponentially weighted moving average (EWMA)
- Measurement delay
- Run-to-run control
- Stability
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