Browse Prior Art Database

Cubic Spline Fit for Calibration of Thin Film Measurement Tools

IP.com Disclosure Number: IPCOM000086249D
Original Publication Date: 1976-Aug-01
Included in the Prior Art Database: 2005-Mar-03
Document File: 6 page(s) / 174K

Publishing Venue

IBM

Related People

Ananthakrishnan, RB: AUTHOR

Abstract

Semiconductor manufacturing has a need to monitor and control very thin transparent film coatings on substrates. Several of the nondestructive film thickness measuring tools depend on the application of incident light of known wavelength and on changing this wavelength in a controlled way.

This text was extracted from a PDF file.
At least one non-text object (such as an image or picture) has been suppressed.
This is the abbreviated version, containing approximately 57% of the total text.

Page 1 of 6

Cubic Spline Fit for Calibration of Thin Film Measurement Tools

Semiconductor manufacturing has a need to monitor and control very thin transparent film coatings on substrates. Several of the nondestructive film thickness measuring tools depend on the application of incident light of known wavelength and on changing this wavelength in a controlled way.

One method of accomplishing this is to use a circular filter whose transmission wavelength is a function of its angular position. The technique described here outlines a method of determining this functional relationship more accurately than before. The prior techniques consisted of finding a best fit cubic, in the least square sense, through several measured data points in the plot of transmission wavelength versus angular position.

The present technique consists of fitting cubic splines through these measured data points. Cubic splines are several individual cubics computed in such a way that they pass through all the measured data points exactly, and have been blended or smoothed out at these connecting points.

Say the x and y coordinates of the Cartesian system are functions of the parameter u:

(Image Omitted)

891 and 892.

The curve joining each successive pair of points is a cubic spline with 0 < or = u < or = 1. Consider the catenation of cubics p(1)p(2) and p(2) p(3). The attenuated curve is forced to have up to second-order continuing at the point p(2). Of course, at all other points, the curve, a regular p...