Piecewise nonlinear regression: a statistical look at lamp performance

Galen D. Halverson; M. Guyene Hamilton

doi:10.1117/12.250902

13 September 1996 Piecewise nonlinear regression: a statistical look at lamp performance

Galen D. Halverson, M. Guyene Hamilton

Proceedings Volume 2876, Process, Equipment, and Materials Control in Integrated Circuit Manufacturing II; (1996) https://doi.org/10.1117/12.250902
Event: Microelectronic Manufacturing 1996, 1996, Austin, TX, United States

Abstract

Ultraviolet (UV) thickness measurement equipment has little room for variation when determining ultra thin films which are 70 angstroms or less. High lamp performance is critical for measurement validity. A quality conscious semiconductor must have data to verify a vendor claim of 'The lamp performance will perform with no degradation for up to (xxx) hours of normal operation.' In this article we review a real case where data was collected and examined to answer important questions about lamp performance in UV measurement equipment. How long could a lamp be used before performance degraded enough to necessitate a lamp replacement? This article will illustrate how we used standards and actual measurements to collect data for this study. Plots are included showing actual collected data followed by a discussion of alternative methods for statistical examination of the data. This discussion will include an illustration of an original and useful statistical approach for determining the point in time when degradation is noticeable. The method for examining data begins with a well known but not too frequency used concept known as piecewise linear regression with a fixed point of join. Then we enhance the method by turning the join point into a variable that is 'floated' using an iterative non-linear regression approach.

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Galen D. Halverson and M. Guyene Hamilton "Piecewise nonlinear regression: a statistical look at lamp performance", Proc. SPIE 2876, Process, Equipment, and Materials Control in Integrated Circuit Manufacturing II, (13 September 1996); https://doi.org/10.1117/12.250902

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KEYWORDS

Lamps

Data modeling

Performance modeling

Ultraviolet radiation

Semiconductors

Statistical analysis

Thin films

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