A111D3 D7TDbb

NIST

PUBLICATIONS

NATL INST OF STANDARDS & TfCH,,^.'.C.

A1 11 03079066

NIST SPECIAL PUBLICATION 400-82

U.S. DEPARTMENT OF COMMERCE/National Institute of Standards and Technology

Semiconductor Measurement Technolog

Database for and Statistical Analysi

of the Interlaboratoiy Determinatio

of the Conversion Coefficient for the Measuremer

of the Interstitial Oxygen Content of Silico

by Infrared Absorptio

A. Baghdadi, R. I. Scace, and E. J. Walters^ Editors
NATIONAL INSTITUTE OF STANDARDS &

TECHNOLOGY

Research Morraation Center _ Gaithersburft MD 20899

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3 Located at Boulder, CO, with some elements at Gaithersburg, MD.
Semiconductor Measurement Technology:

ClCloo

Database for and Statistical Analysis

of the Interlaboratory Detennination

of the Conversion Coefficient for the Measurement

of the Interstitial Oxygen Content of Silicon

by Infrared Absorption

Asian Baghdadi, Robert I. Scace, and E. Jane Walters, Editors

Semiconductor Electronics Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

July 1989

NOTE: As of 23 August 1988, the National Bureau of

Standards (NBS) became the National Institute of

Standards and Technology (NIST) when President

Reagan signed into law the Omnibus Trade and

Competitiveness Act.

f U.S. DEPARTMENT OF COMMERCE, Robert A. Mosbacher, Secretary

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Raymond G. Kammer, Acting Director
Library of Congress Catalog Card Number: 89-600739

National Institute of Standards and Technology Special Publication 400-82

Natl. Inst. Stand. Technol. Spec. Publ. 400-82, 179 pages (July 1989)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASfflNGTON: 1989

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402-9325
PREFACE

This report contains complete supporting information on a worldwide interlaboratory ex- periment to determine the conversion coefficient relating infrared (IR) measurements of

interstitial oxygen in silicon to absolute measurements (charged particle activation analysis, photon activation analysis, inert gas fusion analysis). The interstitial content of silicon

wafers destined for integrated circuit manufacture is tightly specified by process engineers

because precise knowledge of the oxygen content is required in order to design the fabrication process. Controlled precipitation of oxygen during processing creates gettering

centers within the bulk of the silicon, which serve to trap fast-diffusing impurities such as

iron, nickel, and cobalt. Infrared measurements, since they are nondestructive, quick, and

inexpensive, are routinely used to monitor the oxygen content of production wafers. However, the infrared measurements are relative measurements only. The infrared technique

must be calibrated by other methods which are capable of measuring the oxygen content

of silicon directly. These absolute measurements are destructive and expensive, so they

cannot be used to monitor production wafers, but are used in this study to calibrate the

infrared measurements.

A number of workers have reported values for this conversion coefficient in recent years;

most of them are in general agreement with one another but differ significantly from the

value required by ASTM and DIN standards. The present work, in which all of the recent

workers in the subject were participants, was done to establish this important relationship

as careftdly as possible. The result is being incorporated in revised ASTM standards. A

description of the experiment is being published*. It shotdd be read as a necessary adjunct

to this report, which does not repeat much of the published information. A preprint

appears as Appendix C.

This report contains many details of the work, including the complete set of data obtained

in the study (Appendices A and B), that could not be included in a journal article for

space reasons. The report makes this information available to any interested persons,

including the participants. It also makes the IR database accessible for the future, if it shotdd become possible to realize a substantial improvement in the accuracy and statistical

distribution of the absolute methods, which accounts for most of the uncertainty in the

conversion coefficient. The material specimens are being retained at the National Institute

• Baghdadi, A., BuUis, W. M., Croarkin, M. C, Li, Y., Scace, R. I., Series, R. W., Stallhofer,

P., and Watanabe, M., Interlaboratory Determination of the Calibration Factor for the

Measurement of the Interstitial Oxygen Content of Silicon by Infrared Absorption, /.

Electrochem. Soc. 136, 2015-2024 (July 1989).

iii
of Standards and Technology (formerly National Bureau of Standards) and could be used

for further study.

The experimental design is detailed in the Journal of the Electrochemical Society paper and

described briefly in section 1 of this report. It is a complex design, intended to allow a large

number of IR laboratories (18) to participate in parallel over a reasonably short period of

time. Eight sets of virtually identical specimens were cut from 20 specially grown silicon

ingots. Seven sets were circulated for IR measurements, each accompanied by a "zerooxygen" reference specimen and a sapphire plate used in an instrumental check. Charged

particle activation analysis measurements were made following the IR measurements on

some of these sets. The photon activation and inert gas fusion analyses were made on

larger pieces taken from a neighboring part of the ingots. Over 2500 IR measurements and

235 absolute measurements were reported and are included in this report.

The price of complexity in experimental design is difficulty in statistical analysis. M. C.

Croarkin, whose report is in section 4, participated in the design of the experiment and

was the principal statistical consultant. A second approach was contributed by J. Mandel,

author of section 5, who is well known for his work on methods for analyzing data from

interlaboratory experiments. The two analyses take quite different approaches, but yield

comparable (though slightly different) results. Croarkin's analysis focuses on the main

bodies of data, one from the IR work and the other from the absolute measurements,

to seek the conversion coefficient as the relating constant between them. Her work uses methods perhaps more familiar to most researchers. Mandel, on the other hand, looked

for relationships, laboratory by laboratory, to see whether or not one can find useful

information on within-laboratory and between-laboratory differences. We have chosen to

take as the result for publication the one from Croarkin, in part because the effects of

possible material inhomogeneities can be assessed more clearly from her approach. The

fact that the two approaches, using significantly different methods, yield similar results

lends considerable credence to both and to the work as a whole.

iv
Table of Contents

Page

1. Introduction 1

2. Infrared Absorption Test Method 8

3. Absolute Test Methods: Reports from the Laboratories 10

Centre de Recherches Nucleaires, Strasbourg, J. Stoquert 11

Iristitute for Nuclear Sciences, Rijksuniversiteit Gent, K. Strijckmans 15

Max-Planck-Institut fur Metallforschung, Dortmund, E. Grallath 16

Bundesanstali fur Materialprufung (BAM), Berlin, B. F, Schmitt 18

Institut fur Kernphysik, Johann Wolfgang Goethe Universitdt, Frankfurt, K. Bethge 19

AERE Harwell, Oxfordshire, J. Hislop and D. Wood 20

Institute of Physical and Chemical Research (RIKEN), Wako, Saitama,

T. Nozaki 21

Center for Chemical Characterization and Analysis, Texas A & M University,

College Station, E. Schweikert 23

4. Statistical Analysis Relating the Infrared Measurements to the Absolute

Measurements, M. C. Croarkin 24

5. Statistical Analysis of the Data, J. Mandel 77

6. Acknowledgments 112

Appendix A. Infrared Absorption Data 113

Appendix B. Absolute Analysis Data 133

Appendix C. Preprint: Interlaboratory Determination of the Calibration Factor

for the Measurement of Interstitial Oxygen Content of Silicon by Infrared

Absorption, J. Electrochem. Soc 139

V
List of Figures

Page

1-la. Schematic of lOO-mm-diameter silicon crystal showing four 2-mm-thick

slices for infrared absorption and CPAA measurements, a 10-mm-thick

slug for PAA and IGFA measurements, and the 100-mm-wide section

reserved for future work 4

1-lb. Diagram of 2-mm-thick slice, showing test squares 1 to 4, 25 mm on a side;

identification markings (04-02-Ox); and the location of the infrared

measurements (x) 5

4-la. For test set 1, differences of each laboratory's triplicate measurements

from the mean of IR laboratories vs. oxygen concentration showing

systematic errors among IR laboratories 28

4-lb. For test set 2, differences of each laboratory's triplicate measurements

from the mean of IR laboratories vs. oxygen concentration showing

systematic errors among IR laboratories 29

4-lc. For test set 3, differences of each laboratory's triplicate measurements

from the mean of IR laboratories vs. oxygen concentration showing

systematic errors among IR laboratories 30

4-ld. For test set 4, differences of each laboratory's triplicate measurements

from the mean of IR laboratories vs. oxygen concentration showing

systematic errors among IR laboratories 31

4-le. For test set 5, differences of each laboratory's triplicate measurements

from the mean of IR laboratories vs. oxygen concentration showing

systematic errors among IR laboratories 32

4-lf. For test set 6, differences of each laboratory's triplicate measurements

from the mean of IR laboratories vs. oxygen concentration showing

systematic errors among IR laboratories 33

4-lg. For test set 7, differences of each laboratory's triplicate measurements

from the mean of IR laboratories vs. oxygen concentration showing

systematic errors among IR laboratories .34

4-lh. For JEIDA set 1, differences of each laboratory's triplicate measurements

from the mean of IR laboratories vs. oxygen concentration showing

systematic errors among IR laboratories 35

vi
4-2. Total standard deviations in absorption units coded by test set vs. oxygen

concentration showing instrumental variability and dispersion among IR

laboratories as a function of oxygen concentration 38

4-3. Percentage differences from the average IR absorption coefficient for test sets

2, 3, 4, 5, and 6 vs. net absorption coefficient showing inhomogeneity among

specimens within an ingot 43

4-4a. For Lab 21, test set 2, IR absorption coefficients plotted vs. CPAA measurements

on the same test squares 45

4-4b. For Lab 22, test set 3, IR absorption coefficients plotted vs. CPAA measurements

on the same test squares 46

4-4c. For Lab 23, test set 4, IR absorption coefficients plotted vs. CPAA measurements

on the same test squares 47

4-4d. For Lab 26, test set 4, IR absorption coefficients plotted vs. CPAA measurements

on the same test squares 48

4-5a. IR absorption coefficients for each test square in test set 2, delineated and

ranked alphabetically by CPAA according to laboratory 21, the convention

being that the symbol A refers to the specimen with the lowest oxygen con- centration £md the symbol T, the specimen with the highest oxygen

concentration 49

4-5b. IR absorption coefficients for each test square in test set 4, delineated and

ranked alphabetically by CPAA according to laboratory 26, showing

consistency of CPAA values 53

4-6a. For Lab 21, test set 2, standardized residuals from linear fit to test set data

vs. predicted IR absorption coefficients 57

4-6b. For Lab 22, test set 3, standardized residuals from linear fit to test set data

vs. predicted IR absorption coefficients 58

4-6c. For Lab 23, test set 4, standardized residuals from linear fit to test set data

vs. predicted IR absorption coefficients 59

4-6d. For Lab 26, test set 4, standardized residuals from Hnear fit to test set data

vs. predicted IR absorption coefficients 60

4-6e. For Lab 25, test sets 2, 3, 4, 5, and 6, standardized residuals from linear fit to test set data vs. predicted IR absorption coefficients 61

4-6f. For Lab 24, test sets 2, 3, 4, 5, and 6, standardized residuals from linear fit to test set data vs. predicted IR absorption coefficients 62

vii
4-6g. For Lab 28, test sets 2, 3, 4, 5, and 6, standardized residuals from linear fit to test set data vs. predicted IR absorption coefficients 63

4- 7a. For Lab 21, standardized residuals from linear fit to JEIDA data plotted vs. predicted IR absorption coefficient 64

4- 7b. For Lab 22, standardized residuals from linear fit to JEIDA data plotted vs. predicted IR absorption coefficient 65

4-7c. For Lab 23, standardized residuals from linear fit to JEIDA data plotted vs. predicted IR absorption coefficient 66

4-7d. For Lab 27, standardized residuals from linear fit to JEIDA data plotted vs. predicted IR absorption coefficient 67

4- 8. Standardized residuals from linear fit to data from absolute laboratories 21,

23, 26, and 25 plotted against run numbers 71

5- la. For Lab 21, oxygen content vs. infrared absorption coefficient 92

5- lb. For Lab 21, standardized residual errors ("H-Values") for each specimen ... 93

5-2a. For Lab 22, oxygen content vs. infrared absorption coefficient 94

5-2b. For Lab 22, standardized residual errors ("H-Values") for each specimen ... 95

5-3a. For Lab 23, oxygen content vs. infrared absorption coefficient 96

5-3b. For Lab 23, standardized residual errors ("H-Values") for each specimen ... 97

5-4a. For Lab 24, oxygen content vs. infrared absorption coefficient 98

5-4b. For Lab 24, standardized residual errors ("H-Values") for each specimen ... 99

5-5a. For Lab 25, oxygen content vs. infrared absorption coefficient 100

5-5b. For Lab 25, standardized residual errors ("H-Values") for each specimen . , 101

5-6a. For Lab 26, oxygen content vs. infrared absorption coefficient 102

5-6b. For Lab 26, standardized residual errors ("H-Values") for each specimen . . 103

5- 7a. For Lab 28, oxygen content vs. infrared absorption coefficient 104

5-7b. For Lab 28, standardized residual errors ("H-Values") for each specimen . . 105

5 8. Standard deviation between replicates for laboratory 25 107

5-9. Standard deviation between replicates for laboratories 21, 23, and 26 ... 108

viii
List of Tables

Page

1-1. Experimental plan 2

4-1. Design for infrared measurements 26

4-2. Pooled standard deviations reflecting within-laboratory precision in absorption

units 37

4-3. Total standard deviations reflecting within-laboratory and betweenlaboratory variability 39

4-4. Average differences between test set 1 and test set 7 as measured by four

coordinating laboratories 41

4-5. Differences between test set 1 and another test set as observed by each

coordinating IR laboratory 42

4-6. Results of fitting IR dat £L £LS CL linear function of absolute data showing F

statistics for testing lack of fit 56

4-7. Restdts of fitting absolute data as a function of IR data showing estimates of

the intercept term A and slope C 69

4-8. Results of fitting absolute data from laboratories 21, 23, 25, and 26 as a linear

function of IR data on test sets 2, 3, 4, 5, and 6 showing estimates of the

intercept A and conversion coefficient C 72

4-9. Total standard deviations reflecting dispersion within and among IR

laboratories 73

4-10. Restdts of fitting IR data as a linear function of absolute data showing F

statistics for testing lack of fit 73

4-11. Residts of fitting absolute data as a linear function of IR data showing

estimates of the intercept A and slope C 74

4- 12. Differences between conversion coefficients computed from test sets data

and JEIDA data 74

5- la. Absolute Laboratory 21 vs. IR 78

5-2a. Absolute Laboratory 22 vs. IR 80

5-3a. Absolute Laboratory 23 vs. IR 82

5-4a. Absolute Laboratory 24 vs. IR 84

ix
5-5a. Absolute Laboratory 25 vs. IR 86

5-6a. Absolute Laboratory 26 vs. IR 88

5-7a. Absolute Laboratory 28 vs. IR 90

5-8. Results of the analyses Ill

X
1. INTRODUCTION

A. Baghdad! and R. L Scace

This Special Publication* contains the data collected for the worldwide, double-roundrobin determination of the conversion coefficient used to calculate the interstitial oxygen

content of silicon from infrared absorption measurements. It also contains detailed statistical analyses of those data. A paper describing the results of this study is being published by

the Journal of the Electrochemical Society.^ It should be considered the official result of the

study. The approach taken to determine the conversion coefficient was to conduct interlaboratory round robins for both the infrared measurements and the absolute measurements.

The infrared measurements were carried out at 18 laboratories in China, Europe, Japan,

and the United States (see table 1-1), using either dispersive infrared (DIR) or Fourier

transform infrared (FTIR) spectrometers. The absolute measurements were carried out at eight laboratories in Europe, Japan, and the United States, using either charged-particle

activation analysis (CPAA), photon activation analysis (PAA) or inert gas fusion analysis

(IGFA).

Table 1-1 outlines the experimental plan for this study. It can be used to follow any

test set throughout the study. For example, test set 2 was measured by IR at Toshiba,

Nippon Telegraph and Telephone, Komatsu, Hitachi, and then Toshiba again. After the

IR measurements, it was measured by CPAA.

The sample sets were produced specifically for this project by eight leading producers of

semiconductor silicon. The samples were cut from 20 different 100-mm-diameter silicon

crystals with room-temperature free-carrier concentrations of less than 2 X 10^^ cm~^. The

crystals were grown so that the IR absorption coefficient at 1107 cm"-' due to oxygen for

all the slices were distributed relatively uniformly from about 0.9 cm~^ to about 5 cm~^.

Each laboratory contributing specimens cut a 120-nmi-long section from each crystal. Two

2-mm-thick slices, a 10-mm-thick slug, and then two more 2-mm slices were cut from the

end of this section, as shown in figure 1-la. The 2-mm slices were polished on both sides.

The 10-mm-thick slug was reserved for PAA or IGFA measurements. Samples for the

destructive PAA and IGFA measurements were cut from the 10-mm slugs as they were

* Certsiin commercial equipment, instruments, or materials are identified in this paper in or- der to adequately specify the experimental procedure. Such identification does not imply

recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

^ Baghdadi, A., Bullis, W. M., Croarkin, M. C, Li, Y., Scace, R. I., Series, R. W., Stallhofer,

P., and Watanabe, M., Interlaboratory Determination of the Calibration Factor for the

Measurement of the Interstitial Oxygen Content of Silicon by Infrared Absorption.

1
Table 1-1. Experimental plan*

JEIDA SETS TEST SETS*

j-i J-Z J-o 1 L

oo

A e0 0 71 i US 1 \JS i <J3 1 Ua

IN 1 1 IN rJ3 IN 1 1 In r>3 IN £>a JvUM

nil lYUJIN nil MwIN 11 r A /-I WAV-'

i Ua CTT 1 <Ja CTT CPAA llf K

/TTJ A A CPAA ir K

NRS NRS 11 XJk/ CPAA RSR RSR TOS« CPAA RSR RSR

WAC WAC WAC

MUL NBS-* NBS"* MUL

CPAA GEC SIM SIM CPAA GEC SIM SIM

WAC« RSR DNS WAC RSR

CPAA TOS'' TEM NBS** DNS TEM NBS**

ZJU ENS' ZJU

sss SSS

SIM CPAA SIM

TOS** TOS'' NBS"* NBS** NBS-*

" 10-mm slugs cut from ingots were used for destructive PAA meeisurements in UK and Germany, as well as for IGFA in Germany

* Test set 8 was reserved for high-temperature anneal and remeasure for total oxygen

* Transit only, no measurements

Home location

* ENS measured only specimens from ingots 2101-05 to 2109-05

Participating laboratories (Regional coordinators in boldface followed by standards organization):

TOS Toshiba Ceramics, JEIDA

HIT Hitachi

KQM Komatsu Electronic Metals

NTT Nippon Telegraph and Telephone

NBS National Bureau of Standards (U.S.), ASTM

MON Monsanto

SIL Siltec Silicon

WAC Wacker Chemitronic, DIN

TFK Telefunken

RSR Royal Signals and Radar Establishment (U.K.)

DNS Dynamit Nobel Silicon

ENS Ecole Normale Superieure, Universite Paris VII, France

GEC Genered Electric Company, Ltd.

MUL MuUards, Ltd.

SIM Shanghai Institute of Metallurgy (Academia Sinica)

SSS Shanghai Second Smelting Plant

TEM Tianjin Electronic Materials Research Institute

ZJU Zhejiang University

2
I

needed. Two of the four 2-inin slices were used for the IR and CPAA measurements. The

remainder of each crystal was set aside for future or follow-up experiments.

The nominal oxygen concentration was measured by the silicon producers. They measured

the IR absorption at least three times at each of four positions on each slice 90 deg apart

located 18.5 ±1.0 mm from the center of the slice, with one measurement on each of the

four radii at 45 deg to the bisector of the primary flat. The oxygen concentration reported

weis the average of these measurements. The maocimum difference in the IR absorption

coefficient due to oxygen in slices cut from either side of the 10-mm slug was less than 0.06

cm~^. These measurements were used to qualify the test sets prior to the round robin.

Four squares, 25 ± 1 mm on a side, were cut from the center of each of 2 slices from

each of the 20 crystals, as shown in figure 1-lb. Each square was laser marked or scribed

in the corner nearest the center of the slice with a three-part code which identified the

preparing organization, the set number from that organization, and the square number.

There were eight squares, marked 1 through 8, prepared from each crystal. Thus there were

8 essentially equivalent test sets of 20 squares each specially prepared for this study. In

addition to these 8 sets of 20 squares, 3 sets of 7 samples each were suppHed by the Japan

Electronic Industry Development Association (JEIDA). The eight test sets prepared for

this study were designated Test Sets 1 through 8, and the JEIDA test sets were designated

JEIDA Sets 1 through 3. Test sets 2 through 6 also included an oxygen-free float-zoned

(FZ) reference square, and a sapphire filter to be used in an instrumental check.

The thicknesses of the test and reference squares were measured at the National Institute

of Standards and Technology (formerly National Bureau of Standards), Toshiba Ceramics,

Wacker Chemitronic, and the Shanghai Institute of Metallurgy. All replicate thickness

measurements agreed to within ±0.05%.

Section 2 of this publication describes the procedural instructions given to the infrared

laboratories. Since the methodology for each of the absolute measurements was developed

individually at each of the absolute laboratories, section 3 consists of separate reports from

each of the laboratories describing the techniques they used.

The statistical analysis used to obtain the conversion coefficient quoted in the paper submitted to the Journal of the Electrochemical Society was carried out by M. Carroll Croarkin

of the Statistical Engineering Division at the National Institute of Standards and Technology. This analysis is described in section 4. The general methodology used for this analysis

was to develop an empirical straight line fit relating the oxygen content as determined by

the absolute laboratories to the infrared absorption coefficient as determined by the IR

laboratories. The slope of the straight Hne is the conversion coefllcient. The analysis ac- counts for the fact that there is random error in both the absolute and IR measurements.

3
2 2 10 22 100 mm

for infrared measurement

Slug for PAA and IGFA

Reserved for future work

Figure 1-la. Schematic of lOO-mm-diameter silicon crystal showing four 2-inm-thick slices

for infrared absorption and CPAA measurements, a 10-mm-thick slug for PAA and IGFA

measurements, and the 100-mm-wide section reserved for future work.

4
Figure 1-lb. Diagram of 2-mni-tliick slice, showing test squares 1 to 4, 25 mm on a side;

identification markings (04-02-Ox); and the location of the infrared measurements (x). A

second similar slice contains test squares 5 to 8.

5
The data from the 18 IR laboratories were all consistent with each other, and therefore

data from all the IR laboratories were included in the final computation of the conversion

coefficient.

The data from the absolute laboratories were not as consistent. Significant "outliers" were identified and excluded. After their exclusion, the data from each of the absolute

laboratories were further analyzed to decide whether to include that laboratory's data in

the final computation. Since the IR data were consistent with each other, they were used

as the baseline for evaluating the results from the absolute laboratories. The absolute

results were tested by determining whether, when plotted against the IR data, they fit the

model of a straight line with a zero intercept. The data from five of the eight laboratories

fit this model. The data from three laboratories did not fit the model and were, therefore,

excluded in the final computation of the conversion coefficient. The conversion coefficient

was calculated by pooling absolute data on the test sets as a single data set and fitting a zero-intercept straight line to the average of the infrared data. Absolute data on the

JEIDA sets were used to corroborate the results.

An alternative analysis of the data was carried out by John Mandel of the National Measurement Laboratory of the National Institute of Standards and Technology. This analysis

is described in section 5. This analysis also concluded that the data from the same three

laboratories should be excluded. Mandel's analysis differed from Croarkin's analysis in

many respects. The most important difference was that, while Croarkin pooled all the

absolute data into a single data set, Mandel obtained a slope from each individual absolute laboratory by fitting its data to a straight line against the average of the IR data for

each ingot. Mandel assigned a weighting factor to the slope obtained from each of the

absolute laboratories, based upon the quality of fit for each laboratory's data, and used

that weighting factor in calculating the final value for the conversion coefficient.

Croarkin's analysis yielded a conversion coefficient of 6.28 ± 0.18 ppma/cm"^, and Mandel's analysis yielded a conversion coefficient of 6.03 ± 0.108 ppma/cm"'',* with limits to

random errors in both analyses estimated as twice the standard deviation of the estimated

conversion coefficient. Random errors are due to nonreproducibility among and between

the different laboratories. Systematic error, as estimated by Croarkin, is due to possible

inhomogeneity in the sample set. The fact that two fundamentally different analytical

approaches yield results in reasonable agreement with each other shows that the data are

"robust," i.e., data that are not sensitive to the particular analytical approach used in

evaluating it. The two analyses essentially differ on how the data from the different absolute laboratories, which used different methodologies, should be combined. Croarkin's

analysis placed all the individual data points on an equal footing. Mandel's analysis eval-

* Mandel's result here is quoted in ppma/cm~^ to allow a direct comparison with Croarkin.

His calculations in section 5 use /xg/g as the unit of concentration.

6
uated each of the absolute laboratories based upon the quality of the fit of its data to the

model, and then assigned weights to each of the laboratories accordingly in combining the

data. Mandel's analysis thus rests upon the assumption that all the errors in each absolute

laboratory would affect the quality of the fit to the model. That ignores the possibiUty of

systematic errors that are proportional to the oxygen content. Croarkin's analysis makes

no such explicit assumption. All three absolute analytical methods used in this study rely

upon several calibration steps. Any error in one of these steps would result in a systematic

error proportional to the oxygen content of the sample.

Appendices A emd B contain data obtained by the infrared laboratories and from the

absolute laboratories, respectively. Appendix C is a preprint of the results of this study,

to be published in the Journal of the Electrochemical Society.

7
2. INFRARED ABSORPTION TEST METHOD

Instructions to the Participating IR Laboratories

Make IR absorption measurements by the difference method using the oxygen-free FZ

reference supplied. Single- or double-beam techniques may be used with either FTIR

or dispersive IR spectrophotometers. In either case, report measurement conditions and

instrument used to your coordinating laboratory on the data cover sheet supplied.

Immediately prior to the initial measurement in any laboratory, etch the silicon test squares

(including the reference specimen) in HF to remove any surface oxide. Record spectra over

the wavenumber range from 450 to 1350 cm~^. Use the following test conditions:

Resolution: 4 cm"-' at 1107 cm"-'

Number of scans: Minimum of 64 (Note: For dispersive instruments which do not

have an averaging capability, use an equivalent scan speed.)

Measurement location: Center of square

Detector: Tri-Glycerine Sulfide (TGS), if available

Perform the following instrumental checks immediately prior to each set of measurements

using the measurement conditions outlined above (except where noted otherwise in 2 and

5):

1. Establish the 100% baseline. On double-beam instruments, record the transmittance spectrum with the sample and reference beams both empty. On single-beam

instruments, obtain the ratio of two spectra taken with the reference specimen in

the sample beam; after taking the first reference spectrum, wait for a time equivalent to that which will be required to collect the sample spectra in the measurement

sets before taking the second reference spectrum. Provide a hard copy of the 100%

line over a wavenumber range which includes 900 to 1300 cm~^; use an expanded

transmittance scale, a scale from 97 to 103% with an interval of at least 1%/inch

(0.5%/cm is preferred).

2. Establish the 0% line (dispersive instruments only). With the sample beam blocked,

record the instrument zero over the range 900 to 1300 cm""^. Provide a hard copy

of the 0% line over this wavenumber range on an expanded transmittance scale.

3. Determine whether stray light is present. Run an air- reference transmittance spectrum using the sapphire cut-off filter supplied. Provide a hard copy of the spectrum

8
over the range 900 to 1300 cm ^ on an expanded transmittance scale, with an

interval of at least 1%/inch (0.5%/cm is preferred).

4. Determine mid-scale linearity. Run an air-reference transmittance spectrum using

the reference specimen over the wavenumber range 450 to 4000 cm~^. Report

the transmittance at both 1107 and 4000 cm~^ and provide a hard copy of the

transmittance spectrum.

5. Establish the throughput characteristics (FTIR instruments only). Record a background spectrum with the sample beam empty over the wavelength range from 450

to 4000 cm"-' and provide a hard copy of this spectrum.

Measure the test samples at least three (3) times over a three- (3-) or more day period. Before measuring the samples, allow them to come to thermal equilibrium near the

spectrometer. Supply the infraxed spectra as ratioed transmittance spectra. For measure- ments on double-beam (dispersive) instruments, the oxygen-free reference should be in

the reference beam and the oxygen- containing sample should be in the sample beam. For

measurements on single-beam (FTIR) instruments, the transmittance spectrum should be

obtained from the ratio of the transformed emission spectrum of the oxygen-containing

sample to the transformed emission spectrum of the oxygen-free reference. Supply a hard

copy of each ratioed spectrum together with the results of the instrumental checks.

Forward all data to your coordinating laboratory, which will forward a complete set to

Asian Baghdadi at the National Bureau of Standards.

Supplementary Instructions for Toshiba Ceramics, NBS, and Wacker: Please measure or

verify the thickness of all test and reference squares sent to you and report the results of

the thickness measurements to Asian Baghdadi at NBS.

9
3. ABSOLUTE TEST METHODS: REPORTS FROM THE LABORATORIES

This section was compiled from reports submitted by each of the absolute laboratories

describing the procedures they used to measure the oxygen content of the test specimens.

The charged particle activation analysis method was used by five laboratories, the photon

activation analysis method was used by two laboratories, and one laboratory used inert

gas fusion analysis.

10
Centre de Recherches Nucleaires, Strasbourg

Report from Dr. J. Stoquert

A. METHOD

1. Irradiation:

The samples are irradiated by the ^He beam of the tandem Van de GraafF accelerator

of the Centre de Recherches Nucleaires. The beam passes through aluminum and silicon

absorbers before irradiating the samples. The oxygen is activated through the reaction:

After irradiation, the Si samples are etched to avoid errors due to surface contamination

and recoil implantation.

TypiceJ values of the experimental conditions are:

incident ^He"^"*" beam energy, before absorbers: 20 MeV.

beam current: 150 nA (20 nA for AI2O3 reference)

absorber thicknesses: Al: 50 /zm Si: 85 /xm

etched thickness: 15 fim

effective '^He energy Ej at the entrance of the sample, after etching, is 11.92 MeV.

The sample eind the two absorbers were fixed in a Faraday cup and the total charge

integrated for each run:

irradiation time 30 min (30 s for AI2O3 reference).

B. ACTIVITY MEASUREMENT

The f3'^ spectrometer consists of two Nal 7-ray detectors (2x2 inches) at 180 deg from each

other. They detect in coincidence the two 7-rays emitted at 180 deg during the positron

annihilation. A classical fast-slow double-coincidence circuitry screens out the background

7-rays. The fast coincidence windows are 15 ns; the slow coincidence window is centered on

the 511-keV peak. The backgroimd counting rate (without any source between detectors)

is 1.2 counts per minute.

The activity curve is registered on a multiscale analyzer (2 min/channel) which counts the

number of disintegrations as a function of time.

11
One activated isotope (example: O in AI2O3):

N = Noe-^*

where No counts/channel at the end of the irradiation.

A = 7^ where To.5 is the period, and No is determined by a least-squares fit of the

experimental data (A fixed).

C. POSSIBLE INTERFERENCES

Several isotopes are activated by the ^He beam by the reactions

"si(3He,p)30p /3 + ,2^min 30g.

and

^2C(^He,*He)"C "fi

The total count is given by:

N = Nie-^'* + iVje-^'* + JVae"^'* + N4 .

The experimental data are fitted by least squares to determine Ni, N2, N3 with

_ in2 ^_ . Ti = —— = 2.5 mm

Ai

T2 = — = 20 min

A2 ^ '^2 . T3 = —— = 110 rrnn

A3

N4 = 2.4 counts per channel .

12
For each irradiation, the quantity A is calculated:

A

Q (1 - e-^*«")(l - e-^*TM0 '

where Q is the charge, <,vr is the irradiation time (30 min for Si), and tcotmt is the counting

time per channel.

D. CONCENTRATION CALCULATION

The nimaber n of atoms/cm^ is given by

n =

pEi <r{E)

JEg S{E) dE

where Eg is the threshold energy; Ei is the incident energy; <t{E) is the reaction cross- es

dz section; emd S{E) = 4^ is the stopping power.*

E. ERRORS

a) Em:

Ishii et al. showed that errors = ±5% at Ei ~ 12 MeV do not introduce significant errors in F (see fig. 1 of their paper; F is the relative content of a given isotope). That

error is therefore neglected, and only errors due to the measurements of A and Ei are considered.

b) A and Eii

dn dA <T{Ei)S{Em)

n A Y.{Ei)S[Ei)

dA <T{Ei)

dEi

A ll{Ei) S{Em)dx ,

* For a detailed discussion of the average stopping power method, see Ishii et al.. The Average

Stopping Power Method for Accurate Charged Particle Activation Analysis, Nucl. Instr. Meih. 150, 213 (1978).

13
where dx is the error in absorber thickness and etched thickness measurement contributing

to an error of Ei (effective incident energy).

The random error in the measurement, estimated from these factors, is 4%, when the same

absorber is used for both the specimen and the reference measurements. A higher error,*

however, was estimated for the silicon reference sample, which had a very low oxygen

content.

c) Possibility of Systematic Errors:

Errors due to interfering reactions are minimized by the choice of an incident beam energy

Ei ^ 12 MeV. There is a low probability for significant interfering reactions at this energy.

The Al absorber is chosen so as to limit the recoil implant of other ions into the silicon.

Carbon deposition during irradiation is observed and evaluated by the To.5 = 20 min

component of the decay curve. Correlation with etching thickness and total irradiation

time is clearly seen, but no effect on the oxygen concentration is seen when the specimens

are correctly etched.

Two possible errors may be due to absorption. The ^He intensity diminution in Si and

Al absorbers is neglected. The 7-ray at 511-keV absorption in the samples is taken into

account using tables from J. H. Hubbell, Applied Radiation & Isotopes 33, 1269 (1982).

The stopping power calculation data are taken from ^He tables of J. F. Ziegler, Helium:

Stopping Power and Ranges in All Elemental Matter (Pergamon Press, New York, 1977).

The Bragg additivity rule was used for AI2O3.

The cross-section values for ^^0(^He,p)^®F were taken from Hahn and Ricci, Phys. Rev.

146, No. 3, 650 (1966), for energies below 10 MeV; and from Markovitz and Mahony,

Analytical Chemistry 34, No. 3, 32 (1982), for energies from 10 to 14 MeV.

* Regolini, Stoquert, et al. (ref. 15, Appendix C) estimate an error of ±20% in their measurement of low oxygen content silicon. [Note added by the editors.]

14
Institute for Nuclear Sciences, Rijksuniversiteit Gent

Report from Dr. K. Strijckmajis

METHOD

Charged particle activation analysis is applied using the ^^0(^He,p)^®F (Q > 0) reaction

(18F : to.5 = 109.8 min; ;5+-emitter).

SAMPLE AND STANDARDS

SiHcon samples were provided by P. Stallhofer, Wacker-Chemitronic. The surface of the

silicon samples was rough on receipt. Quartz was used as an oxygen standard.

EXPERIMENTAL

Samples and standard, placed behind a copper foil serving as beam intensity monitor

and an aluminium foil, were irradiated with 20 MeV ^He particles. After irradiation,

the samples were chemically etched in a mixture of concentrated HNO3/HF/CH3COOH

(68/9/23, v,v,v) to remove a 5.2 to 6.2 mg/cm^ surface layer. No interference from surface

oxygen occurs for a chemical etch exceeding 3 mg/cm"^ as experimentally determined.

Samples and standards were measured repeatedly with 7—7 coincidence set-up with two

Nal(Tl) detectors at 180 deg to obtain the decay curve. ANALYSIS

The decay curve was analyzed using the CLSQ program of Gumming.* The best fit for

the half-Hfe of ^^F yielded 110.4 ± 1.7 min (mean =b standard deviation for 17 decay curve

aneJyses of the Si samples), which agrees with the literature value of 109.8 min.

To correct for the different stopping power of standard versus sample, the numerical integration method^ was appHed, using the stopping power data of Ziegler^ and the excitation

function data of Vandecasteele et al.§.

The method is interfered with by F and Na to an extent of 5% for equal concentrations.

The analyzed mass is ^20 mg. One sample was analyzed for each irradiation campaign

and it yielded a standard deviation of 13%, which corresponds with the reproducibility

attainable with this method at this concentration level.

* J. Gumming in Applications of Computers to Nuclear and Radiochemistry, G. O'Kelley,

Ed., NAS-NS 3107 (1963).

^ G. Vandecasteele and K. Strijckmans, J. Radioanal. Chem. 57, 121 (1980).

^ J. F. Ziegler, Helium: Stopping Power and Ranges in All Elemental Matter (Pergamon

Press, New York, 1977).

§ G. Vandecasteele, F. Adams, and J. Hoste, Anal. Chim. Acta 71, 67 (1974).

15
Max-Planck-Institut fur Metallfonchung, Dortmund

Report from Dr. E. Grallath

SPECIMEN PREPARATION

The specimens were cleaned prior to analysis according to the procedure of the BCR: etch

1 to 1.5 m in a mixture of 3:5:3 v/v/v HF (40%) : HNO3 (d=1.4) : acetic acid (96%)

at room temperature; wash three times in water; wash three times in methanol; dry in a warm air stream. During etching and rinsing, an ultrasonic bath was used. The samples

were stored dustfree before analysis (maximum 2 h).

ANALYTICAL APPARATUS

Oxygen determination by the carrier-gas fusion extraction process was done with a LeyboldHeraeus NOA 2003 nitrogen-oxygen analyzer. Helium was the carrier gas. In contrast with

the usual apparatus of this type, the equipment is fitted with a more sensitive CO detector

(IR absorption, 5000 ppm BINOS). It also has the capability for heating the specimen in a graphite crucible under temperature program control. A Leco double crucible was used.

In this arrangement, the outer crucible is heated directly by the passage of electric current.

The inner crucible, which contains the specimen, is only indirectly heated; it thus has a more uniform temperature distribution.

ANALYTICAL PROCEDURE

About 1 g nickel is placed in the inner crucible and heated gas-free to about 2000 "C for

1.5 min. After the temperature is reduced to about 1500 °C (temperature program), the

prepared specimens (three to four pieces per analysis) are dropped into the nickel bath

through an airlock. At the same time, the temperature program starts a linear heating of

the crucible up to about 1800 °C within 10 s. The oxygen present in the specimen (and on

the surface) is set free as CO by melting of the specimen, is carried by the carrier gas to

the CO detector, and measured. A Spectra-Physics SP 4200 computing integrator at the

output of the detector is used for evaluating the signal. A new crucible is used for each

analysis.

CALIBRATION

Calibration of the equipment is done with a calibration gas. This is done by introducing,

with a built-in thermostated dosing apparatus, 536 /iL of a calibration gas mixture (29.86

±0.12 vol% CO, 20.23 ± 0.15 vol% N2, balance He; from Messer Griesheim) dynamically diluted 10:90 with He into the carrier gas stream of the apparatus. This calibration

procedure passes a dose of 9.8 /zg of oxygen as CO over the hot crucible.

16
CALCULATIONS

A blank value of 0.1-^g oxygen per cm^ of specimen surface is subtracted from the gross

measured value. This correction value was determined from 13 blank determinations with

specimens 3R, 133R, 137R, and 256R provided by the BCR as "zero material." Prom the

value for xj, of 0.35 //g O (s=0.15 fig O), and under the assumption that practically the

entire bleink value rises from the specimen surface, a residual surface oxygen content of 0.1

/zg/ cm^ follows. Prom the blank value scatter, the detection limit (3 s) of the procedure

is calculated to be 0.45 fig.

17
Bundesanstalt fur Materialprufung (BAM), Berlin

Report from Dr. B, F. Schmitt

METHOD

The method used was photon activation analysis of oxygen.

SPECIMENS

The specimens were rectangular parallelopipeds 5 by 5 by 8 mm'. The reference used was

BeO. The specimen mass was about 880 mg, and the reference specimen's mass was about

28 mg. The specimens and reference specimens were wrapped in Al foil.

ACTIVATION

The maximum electron energy was 30 MeV. The electron current was 100 fiA. The specimens were irradiated for 4 min, except for specimen 10/4, which was irradiated for 10 min.

The specimens were rotated during activation in the photon stream.

ETCHING

After irradiation, specimens were etched in concentrated HF-HNO3 for about 10 s. Etch

loss was about 30 to 50 mg.

HEAT EXTRACTION

Heat extraction was carried out in a graphite crucible at 2020 °C, with a helium carrier

gas stream at 0.2 liters per minute, and 1.3 g iron as the bath metal. The CO was oxidized

to CO2 by Schiitze reagent. The CO2 was absorbed by ascarite (sodium asbestos).

ANALYSIS

The -^^O concentration was determined from coincidence measurement of annihilation ra- diation of positron decay. Final results were determined by calculation programs DKLIE

and KNOFB.

18
Institut fur Kernphysik, Wolfgang Goethe Universitdt, Frankfurt

Report from Dr. K. Bethge

METHOD

The method used was charged particle activation analysis, based upon the reactions

and

i«0('He,n)i»Ne -^^^F —."O .

The irradiation energy was 10-MeV 'He''"*' particles. After irradiation, the surface was re- moved by etching of 16 /zm. Thereafter, the irradiating energy was 8.8 MeV. The difference

is due to the energy loss of the 'He''"'' in the surface region,

ETCHING

The specimens were etched after irradiation for 90 s in 30 mL of etching agent. The etch

used was HF:HN03 in a 1:5 ratio by volume. Approximately 16 fim. of silicon on the

surface was etched away.

MEASUREMENT

Two Nal detectors were arranged in opposition with a small gap between them, into which

the specimens were inserted. The detectors were used in coincidence. The background

counting rate was 0.05 counts per second, which was subtracted from the starting counting

rate. There is no known interfering half-life for oxygen in silicon (to. 5 =109.7 min). Carbon,

with a half-life of 20.3 min, can easily be distinguished. The estimated error for a single

measurement is approximately ±16%. The statistical error depends upon the counting

rate.

CALIBRATION

As standard, an Si02 target was used for measuring the excitation function of the nuclear

reaction.

CALCULATIONS

The oxygen concentrations were calculated using known cross sections <t(E) and known

ranges of 'He ions in silicon.

19
AERE Harwell, Oxfordshire

Report from Drs. J. Hislop and D. Wood

METHOD

The method used was photon activation analysis, based upon the reaction

as described previously in J. Hislop et al., J. Electrochem. Soc. 133, 189 (1986).

The potential interfering reactions are

and

2«Si(7,/)^^0.

Both these reactions are considered negligible under the irradiation conditions used.

The 7 rays are bremsstrahlung from 32-MeV electrons colliding with a 3-mm-thick tungsten

target. Integrated current is 6 to 7 ^A, as measured on the tungsten converter with sample

rotation during irradiation.

ETCHING

After irradiation, the specimens were etched twice using a mixture of HF/HNO3 /glacial

HAc. Approximately 2% by weight was removed from the surface.

SAMPLES

The samples were 6 mm by 6 mm by 2 mm of silicon.

CALIBRATION

Li2B4 07 pellets were used as the standards, without radiochemical separation.

MEASUREMENT

The oxygen was first separated from the silicon using inert gas fusion at 2000° C with a copper/graphite powder flux. C^^O was adsorbed on "Hopcalite." Recovery is estimated

to be greater than 95%, based upon analyses of Si02 layers of known thicknesses.

The concentration of ^^O was measured using ^'^ annihilation radiation in Nal coincidence

counters.

20
Institute of Physical and Chemical Research (RIKEN), Wako, Saitama

Report from Dr. T. Nozaki*

METHOD

The method used was charged particle activation analysis, based upon the reaction ^^O

(^e,p) ^*F. There are practically no interfering reactions for the semiconductor silicon

matrix in the procedure described below.

ACTIVATION

The samples were bombarded behind a 50-/zm-thick aluminum foil. The acceleration energy

of the 'He particles was 18 MeV, and the energy on the sample is estimated at 15 MeV.

The incident particle flux was 2 to 4 /zA and was kept as constant as possible in each

bombardment, which was continued for 10 or 20 min.

ETCHING

From the bombarded sample, a surface layer of 23 ± 1 ^va. in thickness was removed by

etching with HF-HNO3 (1 vol : 3 vol).

MEASUREMENT

The annihilation radiation was usually measured a Ge(Li) detector. A polyethylene plate

was inserted between the detector and the bombarded side of the sample plate in contact

with both, for the minimization of the bremsstrahlung due to '^Si formed from the matrix

sihcon. The measurement was initiated at about 1 h from the end of bombardment and

usually repeated four times with about 1-h intervals, with each measurement continuing

200 s or 4 min. The 7-ray spectrum was analyzed by a microcomputer for the removal of

the bremsstrahlung interference, and the result was often checked by manual analysis. For

the sample of the lowest oxygen content, the annihilation radiation was measured by two

BGO detectors operated in coincidence. This detection is of higher efficiency but is more

sensitive to minute geometrical variation than the Ge(Li) counting.

CALIBRATION AND CALCULATION

A silica plate covered with a 20-/im aluminum foil was bombarded with a lower flux for a shorter time (3- to 6-/iC fluence) for use as a standard. The aluminum foil is almost

equivalent in 'He energy loss to the sample surface removed by etching. Eight such sil-

* Present address: Kitasato University, Sagan^hara, Kanagawa 228, Japan

21
ica standard plates were bombarded in a 20-h cyclotron machine time to ascertain the

reproducibility.

The following relation was used for the calculation of oxygen content:

where [^®F Sat. Act.] is the saturation activity for l-/xA bombardment of the given

sample. The factor 0.4904 was obtained by graphical integration from the excitation

REPRODUCIBILITY

From 1982 to 1985, the oxygen content of a silicon plate of presumably uniform oxygen

content was determined repeatedly by the above procedure. The results were 9.86, 9.71,

10.05, 9.87, 10.20, 10.08, 10.13, and 10.28 /zg/g ([mean] = 10.04, <t = 0.18). In the present

work, each sample was analyzed at least twice. When the two results deviated more than

5% from each other, the analysis was repeated further.

[O Content of Si (wt fraction)] = 0.4904

[18F Sat. Act. in SiOa]

'

function of the •'*0('He,p) ^*F reaction* and the stopping powers of the two matrices.^

* T. Nozaki et al.. Int. J. Appl Radiat. Isotopes 25, 393 (1974).

^ J. F. Ziegler, Helium: Stopping Power and Ranges in All Elemental Matter (Pergamon

Press, New York, 1977).

22
Center for Chemical Characterization and Analysis, Texas A & M University

Report from Dr. E. Schweikert

METHOD

The method used was charged particle activation analysis, based upon the reactions

^«0(^He,p)^«F

and

^«0('He,n)^«Ne F .

There are two possible interfering reactions:

^^(^He,a)i«F and ^^iCEe^xY'F .

ETCHING

3 mg/cm^ were removed from the surface.

IRRADIATION

The maximum energy of the beam produced by the Cyclotron was 18 MeV. After passing

through an Al monitor foil and accounting for the 3 mg/cm"^ removed from the surface

after irradiation, the energy of the beam actually impinging upon the measured specimen

was 14.3 MeV.

CALIBRATION

Three Si samples with oxygen levels at 9.8, 6.7, and 14.3 ppm (weight), respectively, were

used for standards. These Si standards were determined by French colleagues using triton

activation [^^0{^ H,ny^ F].

Muscovite [KAl2Si3AlOio{OH)2] standards were also used, with agreement in the specific

axtivities from the muscovite as well as from the silicon standards.

MEASUREMENT

The comparator method described in Anal. Chem. 42, 1525 (1970) was also used.

23
4. STATISTICAL ANALYSIS RELATING THE INFRARED MEASUREMENTS

TO THE ABSOLUTE MEASUREMENTS

by

M. Carroll Croarkin

Statistical Engineering Division

4.1 PURPOSE OF THE ANALYSIS

The purpose of the analysis is to develop a conversion coefficient for relating infrared (IR)

measurement of the net absorption coefficient of oxygen in silicon wafers to the absolute

determination of oxygen concentration by charged particle activation analyses (CPAA),

photon activation analyses (PAA), and inert gas fusion analysis (IGFA). The data amassed

by the study came from eighteen IR laboratories, four CPAA laboratories, two PAA laboratories, and one IGFA laboratory.

4.2 ARTIFACTS FOR THE STUDY

Twenty silicon ingots with varying concentrations of oxygen were specifically prepared for

the study. A 10-mm slug was cut from each ingot and prepared for PAA and IGFA. Two

slices, intended for IR analysis and CPAA, were cut from segments adjacent to each slug

so as to minimize the effect of material inhomogeneities on the study. The slices were

then quartered with the specimens from the first slice designated as test specimens 1 to 4

and the specimens from the second slice designated as test specimens 5 to 8. Eight test

sets, each made up of 20 specimens (one specimen from each ingot), were then packaged

for circulation to the IR laboratories and CPAA laboratories. Test set 8 was reserved for

other evaluations.

Additional sets of test samples, supplied by JEIDA, were also circulated to the laboratories

participating in this study. However, the data obtained on the JEIDA samples were only

used to confirm the results obtained in this study. They were not used in the computation

of the conversion coefficient itself.

4.3 GENERAL METHODOLOGY

The general methodology is to develop an empirical calibration curve which relates absolute determinations to net IR absorption coefficients. If the empirical curve has a zero

intercept, then the slope of the empirical curve is the conversion coefficient from net absorption coefficient to oxygen concentration. In the analysis we account for the fact that

there are random errors in both the IR measurements and the measurements made by

absolute methods. Detailed consideration is given to several assumptions that are critical

to the validity of the results, including: 1) ingot homogeneity; 2) linearity of absolute

24
determinations relative to IR determinations; 3) zero intercept; and 4) agreement among

absolute methods.

4.4 ABSOLUTE MEASUREMENTS BY CPAA, PAA, AND IGFA

Charged particle activation analyses were performed on test sets 2, 3, and 4 after IR measurements on these test sets were completed. Results are reported in micrograms of oxygen

per gram (/ig/g) of silicon. One laboratory measured test set 2; between two and four independent measurements were reported for each specimen. One laboratory measured test

set 3; one measurement was reported for each specimen. Two laboratories measured test

set 4; the first laboratory made 3 independent measurements on each specimen, and the

second laboratory made a single measurement on 10 of the specimens in the test set and

2 measurements on 5 of the specimens.

Photon activation and inert gas fusion analyses on the slugs provided for that purpose

were reported by three laboratories.

Test sets measured by each absolute laboratory

Method Laboratory ID Test Set ID

CPAA 21 2

CPAA 22 3

CPAA 23 4

CPAA 26 4

PAA 25 10-mm slug

PAA 24 10-mm slug

IGFA 28 10-mm slug

4.5 POTENTIAL PROBLEMS

The interlaboratory study lacks closure because artifacts were generally measured by both

IR and CPAA only within a national region. Thus, there is closure within a region but

not from region to region. This inadequacy is immaterial if test specimens within an ingot

are equivalent with respect to oxygen concentration. This premise is examined in sections

4.9 and 4.12 of this report.

Consistency within individual IR laboratories must be demonstrated, meaning that each

IR laboratory must produce net absorption coefficients which are a linear function of

oxygen concentration. Consistency of measurements for absolute laboratories must also

be demonstrated in the sense that different absolute measurement methods must agree.

These issues are examined in sections 4.7, 4.12, and 4.14.

25
4.6 INFRARED MEASUREMENTS

Five IR laboratories, designated as coordinating laboratories within a country or region,

and 13 auxiliary IR laboratories participated in the study. Test sets 1 and 7 were circulated

among the coordinating laboratories. No other laboratories measured these test sets. Test

sets 2 through 6 were circulated according to the scheme shown in table 4-1. Circulation

for each of test sets 2 through 6 was generally restricted to a single country or region.

Participants in the study were asked to provide data from triplicate runs on each specimen

from the test set. Coordinating laboratories were asked to provide both "before" and

"after" triplicate measurements on the test set.

In order to assign equal weight to each IR laboratory, only data on test sets 2 through 6

are used for developing the calibration curves. Data on test sets 1 and 7 were used for

diagnostic purposes.

Table 4-1. Design for infrared measurements

Test Sets

1 2 3 4 5 6 7

Lab

1 X

2 X

3 X

4 X

5 X

6 X

8 X

9 X

10 X

11 X X X

12 X

13

15

X

X

XX

16 X XX

17 X X X

18 X

19 X X X

31 X

26
4.7 VALIDATION OF THE INFRARED DATABASE

In order to validate the extraction of transmission data from graphs to the database,

the range (difference between the largest and smallest of the triplicate net absorption

coefficients) was examined for each specimen and each laboratory. Coefficients with large

ranges were checked for mis-recordings. Approximately 30 mis-recordings were identified

in this majiner and corrected. Large ranges which could not be accounted for by the

transmission data were flagged as outliers. Measurements on 12 specimens were flagged in

this manner.

Consistency of infrared measurements within individual IR laboratories is illustrated in

figures 4-la through 4-lh where, for each specimen, differences for each laboratory from

the mean of edl laboratories are plotted versus oxygen concentration. The plots also il- lustrate that there are systematic differences among the IR laboratories and that these

differences axe a function of oxygen concentration. The plots also identify as outliers three

groups of triplicate measurements (see test set 4) which are not consonant with the other

measurements

.

4.8 PRECISION OF INFRARED MEASUREMENTS

Two levels of measurement precision are identified in this study. The first is related to

the ability of the IR laboratories to make repeated measurements in the short run and is quantified by a within (laboratory) standard deviation. The absorption coefficients for a

single test set are denoted by Xijk where Xijk denotes the fc*'* measurement for the j*^

laboratory on the i*'* specimen.

For the i*^ specimen and the j*^ laboratory, a within standard deviation from r measure- ments is defined as

with degrees of freedom Uij = (r — 1) and where

fc=i

A pooled within standard deviation is defined for the j*^ laboratory over the n specimens

by the general formula

27
E

CO — ^

CO o

LU E O u- Z LU

m O

DC

liJ ^

to

a:

O

CO

m

<

0.3

0.2-

0.1 -

0-

-0.1-

-0.2

Test Set 1 ^ Lab 17

(Z) Lab 13

A Lab 16

B Lab 11 C Lab 19

*

6

t

A

9 n

B

§

iB

*' IB

C

c

5 10 15

OXYGEN CONCENTRATION ([ig/g)

20

Figure 4-la. For test set 1, differences of each laboratory's triplicate measurements from

the mean of IR laboratories vs. oxygen concentration showing systematic errors among IR

laboratories.

28
E

CO

LLI O

O E

Z LL

LU LU

tr o

UJ O

LL X

Si

Q.

DC

O

CO

CD

<

0.3

0.2 -

0.1 -

0

-

-0.1 -

-0.2 -

-0.3

Test Set 2

* Lab 17

A Lab 6

B Labs

C Lab 12

It ^A.

f

B

B

*

C C

*

^ B

5 10 15

OXYGEN CONCENTRATION (|Lig/g)

20

Figure 4-lb. For test set 2, differences of each laboratory's triplicate measurements from

the mean of IR laboratories vs. oxygen concentration showing systematic errors among IR

laboratories.

29
E

CO

LU

[St

m o

t Q

o

CO

CO

<

0.4

0.3 -

0.2 -

0.1 -

0

-

-0.1

-0.2

-0.3

Test Set 3

* Lab 1

A Lab 9

B Lab 15

t

I

B

4 4aA^

A

A

A

A

A

A

A

§

* *

5 10 15

OXYGEN CONCENTRATION (|ig/g)

20

Figure 4-lc. For test set 3, differences of each laboratory's triplicate measurements from

the mean of IR laboratories vs. oxygen concentration showing systematic errors among IR

laboratories.

30
0.3

1 0.2 H

CO

^LiJ 0.1 i

COO

LU LL

OU.

Z LU

LU O

oco

crO

CO

CD

<

0

-

-0.1-

0.2 -

-0.3

Test Set 4

A Lab 18

B Lab 19

A

§

A

A

A

A

A

A

AAaA

B B_ B

B

5 10 15

OXYGEN CONCENTRATION (\ig/g)

20

Figure 4-ld. For test set 4, differences of each laboratory's triplicate measurements from

the meem of IR laboratories vs. oxygen concentration showing systematic errors among IR

laboratories.

31
E

3^

CO

UJ O

O E

Z Li. LU LU

DC O

lU o

O

ICL

DC

O

O)

CD

<

0.2

0.1

0.1 -

-0.2

Test Set 5

* Lab 4

O Lab 5

A Lab 10

B Lab 13

C Lab 31

a

i It'

I

! H!

8**

5 10 15

OXYGEN CONCENTRATION (ng/g)

20

Figure 4-le. For test set 5, differences of each laboratory's triplicate measurements from

the mean of IR laboratories vs. oxygen concentration showing systematic errors among IR

laboratories.

32
0.2

E

C/)

Iy=o

a.DC

O

CO

m

<

0.1 -

0

-

-0.1 -

-0.2

Test Set 6

* Lab 16

A Lab1

B Lab 2

C Lab 3

B

B

A

5 10 15

OXYGEN CONCENTRATION (\ig/g)

20

Figure 4-lf. For test set 6, differences of each laboratory's triplicate measurements from

the mean of IR laboratories vs. oxygen concentration showing systematic errors among IR

laboratories.

33
E

CO

ICO o

Z LU

LIJO

mil

U- z

u-O

QiQo

CO

CO

<

0.3

0.2 -

0.1 -

0

-

-0.1 -

-0.2

Test Set 7

* Lab 17

O Lab 13

A Lab 16

B Lab 11 C Lab 19

i

I

A

A

c

5 10 15

OXYGEN CONCENTRATION (|ig/g)

20

Figure 4-lg. For test set 7, differences of each laboratory's triplicate measurements from

the mean of IR laboratories vs. oxygen concentration showing systematic errors among IR

laboratories.

34
0.3

E

CO

I0.2

0.1

0

1 LU

CO 7Z

LLi y

OLJ_

z

^

£8 -0.1

si^ H -0.2 H

o

CO

CD

<

A

A

JEIDA Set 1 * Lab 17

A Lab 6

B Lab 8

C Lab 12

I

I

5 10 15

OXYGEN CONCENTRATION (jig/g)

20

Figure 4-lh. For JEIDA set 1, differences of each laboratory's triplicate measurements from

the mean of IR laboratories vs. oxygen concentration showing systematic errors among IR

laboratories. Note that the y-axis scale has been changed, compared to the previous plots.

35
with degrees of freedom Vj = Vij + • • • + Vnj where the Sij represent the within standard

deviations for the n specimens and the Uij represent the corresponding degrees of freedom.

Pooled standard deviations for each laboratory are shown in table 4-2.

The second level of measurement precision is related to the ability of the IR laboratories

to agree among themselves in making measurements on the same artifacts. For the i*^

specimen from a single test set, a total standard deviation for the m laboratories which

measured the test set is estimated by

1/2

(4-3)

with degrees of freedom i/j = (m — 1 ) and where

1 m

36
Table 4-2. Pooled standard deviations reflecting within-laboratory

precision in absorption units

Lab No. Within Std Dev Degrees of Freedom

1 0.03265 52

2 0.02552 54

3 0.01313 12

4 0.01824 54

5 0.02736 26

6 0.02942 54

8 0.03642 54

9 0.02761 54

10 0.02352 54

11 0.02225 184

12 0.03144 52

13 0.01809 188

15 0.01552 54

16 0.01518 188

17 0.03446 176

18 0.02802 48

19 0.01293 184

31 0.01749 9

37
0.30

CO

> c

Q O

Q *= < O

Q c Z 2

< <o O

0.25 -

0.20

0.15 -

0.10 -

0.05 -

0

0

4

T

i|

11 14

9 T

5 10 15

OXYGEN CONCENTRATION (|Lig/g)

20

Figure 4-2. Total standard deviations in absorption units coded by test set vs. oxygen

concentration showing instrumental variability and dispersion among IR laboratories as a

function of oxygen concentration.

38
Table 4-3. Total standard deviations reflecting within-laboratory

and between-laboratory variability

Ingot No. Total Standard Deviation Degrees of Freedom

Absorption Units Percentage

(net absorption)

2101 0.0376 2.6 21

2102 0.0543 2.9 21

2103 0.0559 2.4 21

2104 0.0678 2.4 21

2105 0.0712 2.2 21

2106 0.0823 2.4 21

2107 0.0881 2.3 20

2108 0.1081 2.5 20

2109 0.1451 3.0 17

1101 0.0619 2.1 19

1102 0.0523 2.3 19

1201 0.0905 2.4 19

1202 0.0944 2.4 19

1203 0.0866 2.4 19

1204 0.0787 2.3 20

501 0.0858 2.4 20

401 0.0669 2.2 19

301 0.0760 2.4 20

201 0.0470 2.2 20

101 0.0255 3.1 20

39
Figure 4-2 is a plot of total standard deviations by test set plotted versus oxygen concentration showing the relationship to oxygen concentration. Table 4-3 lists total standard

deviations, pooled over the seven test sets from each ingot, in absorption units and as percentages of net absorption showing these standard deviations as a constant percentage

of measurement units.

4.9 HOMOGENEITY OF OXYGEN WITHIN AN INGOT

Test set 1 and test set 7 were measured by the coordinating laboratories. Thus, differences

in net absorption coefficients between two specimens from a single ingot, one assigned to

test set 1 and the other assigned to test set 7, give an estimate of ingot inhomogeneity

that is free of laboratory bias. The differences averaged over four of the coordinating

laboratories are shown in table 4-4 as a percentage of net absorption. The table shows

ingot inhomogeneities varying between 0.1% and 3.7%.

Ingot homogeneity for test sets 2, 3, 4, 5, and 6 is critical because these sets are used

to relate infrared absorption coefficients to total oxygen concentration. Each coordinating

laboratory provided IR measurements on one of these test sets in addition to measurements

on test sets 1 and 7. Refer to table 4-1 for the scheme of test sets as measured by each

laboratory.

Table 4-5 shows the differences between net absorption coefficients for test set 1 and another

test set measured by the same coordinating laboratory. Differences which are significant

at the 95% probability level are shown with a superscripted a. The t statistics [4-1] for

testing significance were constructed as

Differences in average absorption coefficients for two test sets

* ~ 7=7=—

' — n; • \^ ~ '^^)

^2/3 Within standard deviation for j*" laboratory

There are significant differences among specimens from the same ingot for about 20% of

the specimens. The differences are largest for ingot 2109 which has the highest oxygen

concentration. The table shows that laboratories with good precision can detect inhomogeneities within ingots. However, these differences may not be significant relative to the

precision of the absolute laboratories.

Percentage differences from the average IR absorption coefficient over test sets 2, 3, 4,

5, and 6 are shown in figure 4-3 where the numbers in the figure refer to test set. The

plot shows that the range of absorption coefficients for specimens from the same ingot is usually less than 5% except for the ingot with the largest oxygen content where the range

is about 7%. Whether or not differences of this magnitude will impact the study and the

estimation of a conversion coefficient is not clear at this point; this question is examined

in section 4.12.

40
Table 4-4. Average differences between test set 1 and test set 7

as measured by four" coordinating laboratories

Units in percentages of net absorption coefficients

Ingots % Diff Ingots % Diff

2101 0.7 1102 0.3

2102 1.9 1201 0.4

2103 1.8 1202 0.3

2104 3.7 1203 0.8

2105 0.5 1204 1.1

2106 0.2 101 0.3

2107 0.4 201 0.8

2108 0.0 301 1.4

2109 1.4 401 0.5

1101 0.3 501 0.1

"Laboratory 17 was excluded because of poor precision relative to the other coordinating

laboratories. See table 4-2.

41
Table 4-5. Differences between test set 1 and another test set as observed by each coordinating IR laboratory

Net Absorption Units

TT? T ah- 1 7 1

X X

1X Q«7 1xo? 1xofi Ingot 1—9 1 —

X —

1X —4

1—X s»

o 1 —X —

0 0^9 0 019 —0—U.UU*! 004 —0—U.UU0071 0U.UUii 009

91 09 0 0^9 0 094 0u.ux^ 01 9 0U.UrtO 04Q« 0u.ux^ 01 9

91 0 0Q9<* —0 004 —0—U.UUt7 OOQ 0 049<* 0 04^** U.UriO

91 04 0 0^1 0u.uuo OOfi 0U.UXU 01 0 U.Ul/O 0u.xuo 1 O^^** 91 0 O^^i —0 009 0U.UXt 01 4 0U.UUf 004 0U.UU^ 009

91 Ofi 0 044 —0—U.UU«7 OOQ 0u.uuu 000 0 0^9<* 0U.UXU 01 0

91 07 0 094 0U.UXU 01 0 0U.UUD OOR 0u.uux 001 0 099

91 OR 0 1 4Q* 0U.UU^ 009 —0—U.UU0071 0U.UXU 01 0 0u.uoo 0^R<»

91 OQ 0 01

U.UX X —0 1 41 <» —U.X'xX 0 1 ^0" u.xou —0 OSQ<* —0—U. 1XoZR9<* 1101 0 00^ —0 09Q 0 099<* 0U.UX>7 01 Q 0U.UUX 001

1 1 09 0 00^ —0U.UX1 01 4 _0U.UU0071 0U.UUO OOS 0U.UXU 01 0

1201 0.019 0.002 0.008 0.027 -0.013

1202 0.013 -0.039'* 0.010 0.018 -0.014

1203 0.063" -0.028 -0.022" 0.015 -0.014

1204 -0.024 0.003 0.000 0.032" -0.017

101 0.017 -0.015 -0.015 0.000 0.002

201 -0.002 -0.014 0.004 0.035" 0.013

301 o.oro** 0.023 -0.013 0.076" 0.024

401 0.039 -0.026 0.000 -0.004 -0.011

501 -0.022 -0.025 0.002 0.020 0.003

"Indicates a significant difference at the 95% probability level.

42
5

0 1 2 3 4 5

IR ABSORPTION COEFFICIENT

Figure 4-3. Percentage differences from the average IR absorption coefficient for test sets

2, 3, 4, 5, and 6 vs. net absorption coefficient showing inhomogeneity among specimens

within an ingot.

43
4.10 CHANGES IN OXYGEN CONCENTRATION WITHIN A SPECIMEN

Coordinating laboratories were required to make measurements on the test set that circulated within their respective countries or regions, both before and after circulation to the

auxiliary laboratories. The differences between the average absorption coefficients from

"before" and "after" measurements can be tested for significance. The statistic for testing

for a change in a single artifact as measured by the j*^ laboratory is constructed as

^ Differences in average "before" and "after" coefficients for one specimen

y2/3 Standard deviation for j*^ laboratory

Of the 80* specimens which saw both before and after measurements, seven show a significant change at the 95% probability level, hardly more than is expected to occur at

random. Thus, it is concluded that the artifacts were unchanged with respect to oxygen

concentration during the time that they circulated among the IR laboratories.

4.11 IDENTIFICATION OF OUTLIERS IN THE CPAA DATA

Outliers in the absolute data are identified by a procedure that compares the ranking of

oxygen concentration for the 20 ingots according to IR determinations with the ranking

according to the absolute determinations. The technique relies on the consistency among

infrared measurements and is most effective where the absolute data have high precision

and where oxygen concentrations are spread evenly across the regime. It is helpful for

identifying fairly laxge outliers, especially where there are obvious anomalies which are not

easily resolved.

Figures 4-4a to 4-4d are plots of the IR measurements by individual IR laboratories on

a single test set versus absolute measurements by a single CPAA laboratory on the same

test set. Thus, figure 4-4a shows a plot of IR measurements on test set 2, as measured by

the five coordinating laboratories, plotted versus the corresponding CPAA meastirements

by laboratory 21. A few of the data points appear to be misplaced relative to the others.

To clarify the situation, figure 4-5a shows IR measurements for each specimen in test

set 2 connected by lines. ^ The individual points represent measurements by individual

laboratories plotted against the linearity of the IR instrument in that laboratory. The plots

* Laboratory 17 reported "before" but not "after" measurements.

^ For convenience, this figure has been broken up into three parts, the first covering the

range 0 to 2.5 cm~^, the second covering the range 2.5 to 4 cm~^, and the third, the range

from 4 to 5 cm~^.

44
2 7 12 17

OXYGEN CONTENT (by CPAA, iig / g)

Figure 4-4a. For Lab 21, test set 2, IR absorption coefficients plotted vs. CPAA measure- ments on the same test squares.

45
2 7 12 17

OXYGEN CONTENT (by CPAA, |ig / g)

Figure 4-4b. For Lab 22, test set 3, IR absorption coefficients plotted vs. CPAA measure

ments on the same test squares.

46
Lab 23

2 7 12 17

OXYGEN CONTENT (by CPAA, |ig / g)

Figure 4-4c. For Lab 23, test set 4, IR absorption coefficients plotted vs. CPAA measure- ments on the sajne test squares.

47
5 -T

U ~] 1 !

' 1

1 2 7 12 17

OXYGEN CONTENT (by CPAA, lig / g)

Figure 4-4d. For Lab 26, test set 4, IR absorption coefficients plotted vs. CPAA measure

ments on the same test squares.

48
52 54 56 58 60

INSTRUMENT LINEARITY

62

Figure 4-5a (pages 49-51). IR absorption coefficients for each test square in test set 2,

delineated and ranked alphabetically by CPAA according to laboratory 21, the convention

being that the symbol A refers to the specimen with the lowest oxygen concentration and

the symbol T, the specimen with the highest oxygen concentration. Lines I and and J and

O and P, out of aJphabeticaJ order indicating an improper oxygen measurement by the

CPAA laboratory, are flagged as outUers.

49
52 54 56 58 60 62

INSTRUMENT LINEARITY

50
CO 5.00

UJ

O

INSTRUMENT LINEARITY

51
corresponding to the 20 specimens are ranked sequentially by CPAA oxygen concentration

according to laboratory 21, the convention being that the symbol A refers to the specimen

with lowest oxygen concentration, and the symbol T refers to the specimen with highest

oxygen concentration.

Because of the internal consistency of the IR laboratories in determining absorption coefficients, the rankings provide a mechanism for identifying outliers in the CPAA data. A line

that is out of sequential order with respect to the alphabet indicates an improper oxygen

measurement by the CPAA laboratory. Specimens ^120102 and #50102, identified in the

graph by lines P and O, appear to have been interchanged; both specimens are flagged

as outliers. The rankings for specimens ^1^210502 and ^^40102, identified by lines J and I, respectively, are likewise unsatisfactory; these two specimens are also flagged as outliers.

All outliers were omitted from further consideration.

In a similar analysis in figure 4-5b, absorption coefficients for test set 4 as seen by two IR

laboratories are ranked by CPAA oxygen concentrations according to laboratory 26. This

analysis indicates possible problems among the specimens identified by lines H, I, J, and

K; the problems are not resolvable and are not considered egregious enough to warrant the

data being fiagged as outlying.

4.12. DIAGNOSTIC TESTS FOR ABSOLUTE DETERMINATIONS

In this section, absolute laboratories are evaluated individually by regarding IR measure- ment as the dependent variable and absolute measurement as the independent variable

in a linear model. See figure 4-4 where IR measurements on a single test set are plotted

versus absolute measurements on the same test set. This approach is taken, even though

absolute measurements may be less precise than IR measurements, so that the aptness of

the linear model can be tested relative to the dispersion among IR laboratories.

The model

Xij, = a + l3Zi-\- Cij. i = l,...,n

,

. , (4-5)

with slope P and intercept a describes a linear relationship between the two types of

measurements where the quantity Zi represents the average absolute measurement on the

i*^ specimen; the term Xij, represents the IR measurement on the V'^ specimen by the

j*'' IR laboratory; and the ^j^. represent random error terms which are assumed to be

independent and come from a distribution with mean zero and standard deviation cr^. The

standard deviations <Ti represent the total standard deviations that describe the dispersion

among IR laboratories, and the index i indicates dependence on oxygen concentration.

52
CO 2.5

Iz

LiJ O

iT 2.0 -

LU

O

O

Q.

DC

O

CO

CO

<

LJJ <

LU

1.5 -

1.0 -

0.5

0

52 54 56 58 60

INSTRUMENT LINEARITY

62

Figure 4-5b. IR absorption coefficients for each test square in test set 4, delineated and

ranked alphabetically by CPAA according to laboratory 26, showing consistency of CPAA

values.

53
CO

Iz

UJ

g

u.

LU

O

z

S

H

Q.

CC

O

CO

CD

<

0

<

tr

>

<

4.0

3.5 -

3.0 -

2.5

52 54 56 58 60

INSTRUMENT LINEARITY

62

54
Results of a diagnostic test for the absolute measurements are shown in table 4-6. The F

statistics [4-3] in the table test the goodness of fit where large values of F indicate lack of

fit of the experimental data to the linear model.*

The F statistic compares the dispersion of IR data about the fitted line with the dispersion

among IR laboratories. If the comparison is unfavorable, a large F statistic results. Such

a finding can be caused by: i) an improper model; ii) an erroneous measurement by the

absolute laboratory; or iii) inhomogeneity within an ingot. Homogeneity is not an issue

for cases (1), (2), (3), and (4) where the CPAA measurements made at each coordinating

laboratory axe paired with the IR measurements made on the same specimens.

The F statistics for laboratories 21 and 26 on test sets 2 and 4, respectively, are satisfactory,

indicating that the results for these laboratories are consistent with a model that is linear

in the IR data. It is noted that four specimens, identified as outliers (see the section on

outHers for CPAA data) for laboratory 21, are excluded from the analysis. The F statistic

is not satisfactory for this laboratory if these specimens are included.

For these two laboratories, the cases are included where the IR measurements for all test

sets are regressed against the absolute measurements (cases (la) and (4a)). The lack of fit for these cases is indicative of inhomogeneity among test squares and should be compared

with the concordancy achieved for IR measurements made on the same specimens as the

absolute measurements.

The F statistic for laboratory 23 is marginal; the F statistic for laboratory 22 is unsatisfactory. Plots of studentized residuals^ from the least-squares analyses versus IR absorption

coefficients are shown in figure 4-6. Residual plots provide amphfication of the information contained in the F statistic and should be used in conjunction with the F statistic

in assessing goodness of fit. Ideally, the residuals should be distributed randomly about

zero with no obvious patterns or extreme values. Nonrandom patterns and clumping of

residuals are indicative of measurement anomalies.

* Because the precision of IR measurements is nonconstant across oxygen concentrations, a weighted least-squares fit [4-2] is appropriate for making this test. This procedure assigns

weights to the IR measurements which are inversely proportional to the square of the

standard deviations ai where estimates for cr^ are given by the total standard deviations

in table 4-3.

^ The residuals are standardized so that they are distributed approximately according to

Student's t distribution [4-4]; values should fall in the interval (-3, +3).

55
Table 4-6. Results of fitting IR data" as a linear function of absolute data

showing F statistics for testing lack of fit

Case At- 1 X Absolute Abs Abs IK Ur r

T 1 Lab Method lest bet lest set OI J^lt

C* ± X * X

* otatistK

(1) 21 /^D A A 2 2

'7 A 74 1.9

(la) 21 /-CD CFAAA A 2 2,3,4,5 & 6 293 15.9

(2) 22 /-CD A A oo

oO 16 "ICC o6 155.3

(3) 23 CrAA /~cr> A A 4 4 25 5.9

ZD i.D

(4a) 26 CPAA 4 2,3,4,5 &: 6 312 26.0^

(5) 25 PAA 10-mm slugs 2,3,4,5 &: 6 294 32.6'' (5a) 25 PAA 10-mm slugs 2,3,4,5 &; 6 257*= 12.8''

(6) 24 PAA 10-mm slugs 2,3,4,5 & 6 218 412.5''

(6a) 24 PAA 10-mm slugs 2,3,4,5 & 6 201** 285.9''

(7) 28 IGFA 10-mm slugs 2,3,4,5 &: 6 294 216.3''

(7a) 28 IGFA 10-mm slugs 2,3,4,5 &: 6 277*= 164.6''

"IR data with fewer than triplicate measurements excluded from the analysis.

''Indicates lack of fit at the 99% probabiUty level.

'^Ingots ^2105 and ^2102 excluded from the analysis.

''Ingot :^1102 excluded from the analysis.

56
3.75

<

2.25

0.75

CO

-J

<

9

CO

UJ

(£

O

tuN

g -0.75

<O

2.25

-3.75

1 Lab 21

_ Test Set 2 •

•

• # •• •

• •• • • • • •

• • • ••• • • • • • • •

• • • • —

• • •

• •

• • • • • •

1 8.2436E-01 2.7371 E+00 4.6498E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm"'')

Figure 4-6a. For Lab 21 (CPAA), test set 2, standardized residuals from linear fit to test

set data vs. predicted IR absorption coefficients.

57
CO

—I

<

9

LU

GC

O

LUN

O

<Q

z

<

I-

-3.75

8.6544E-01 2.6663E+00 4.4673E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm-"")

Figure 4-6b. For Lab 22 (CPAA), test set 3, standardized residuals from linear fit to test

set data vs. predicted IR absorption coefficients.

58
<

Q

CO

LU

CC

O

LUN

a

CC

<

Q

3.75

2.25

0.75

-0.75

<

*" -2 25

-3.75

Lab 23

Test Set 4

1

7.8895E-01 2.4111 E+00 4.0333E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm"'')

Figure 4-6c. For Lab 23 (CPAA), test set 4, standardized residuals from linear fit to test

set data vs. predicted IR absorption coefficients.

59
CO

<

9

CO

LU

cc

o

LUN

O

<

Q

Z

<

I3.75

2.25

0.75

-0.75

2.25

-3.75

1 Lab 26

1 est bet 4 •

• •

• • • •

•

• ••

• • • • •

• • • •

• •

•

1 7.761 9E-01 2.561 1 E+00 4.3460E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm-l)

Figure 4-6d. For Lab 26 (CPAA), test set 4, standardized residuals from linear fit to test

set data vs. predicted IR absorption coefficients.

60
<

9

CO

LU

cc

a

LU

Q

cc

<

<

Ico

3.75

2.25

0.75

-0.75 -

-2.25

Ingots

2105, 2102

•• ••

• ••

• ••

• •

Lab 25

Test Sets 2, 3, 4, 5, 6

-3.75

8.1710E-01 2.7672E+00 4.7174E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm-1)

Figure 4-6e. For Lab 25 (PAA), test sets 2, 3, 4, 5, and 6, standardized residuals from

linear fit to test set data vs. predicted IR absorption coefficients.

61
-J

<

9

LU

DC

O

LUN

O

GC

<

Q

<

3.75

2.25

0.75

-0.75

-2.25

-3.75

r

Lab 24

Test Sets 2, 3, 4, 5, 6

Ingot 1102

1

1.4554E+00 2.6571 E+00 3.8588E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm-"")

Figure 4-6f. For Lab 24 (PAA), test sets 2, 3, 4, 5, and 6, standardized residuals from

linear fit to test set data vs. predicted IR absorption coefficients.

62
CO

<

9

CO

LU

cc

Q

LU

Q

<Q

z

<

Ico

3.75

2.25

0.75

-0.75

2.25

Lab 28

Test Sets 2, 3, 4, 5, 6

Ingot 1102

-3.75

8.7361 E-01 2.8503E+00 4.8270E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm"'')

Figure 4-6g. For Lab 28 (IGFA), test sets 2, 3, 4, 5, and 6, standardized residuals from

linear fit to test set data vs. predicted IR absorption coefficients.

63
C/D

<

ID

9

CO

UJ

cc

Q

UJN

Q

<

Q

<

H

CO

3.75

2.25

0.75

-0.75'-

-2.25

-3.75

1 Lab 21

JEIDA Set

•

• •

• •

• •

• • •

• • • •

• • • • •

•

•

1

•

1 .5760E+00 2.661 7E+00 3.7474E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm-1)

Figure 4-7a. For Lab 21, standardized residuals from linear fit to JEIDA data plotted vs. predicted IR absorption coefficient.

64
CO

—I

<

ZDQ

CO

LU

CC

Q

LUN

O

<Q

<

3.75

2.25

0.75

-0.75

-2.25

-3.75

1 Lab 22

JEIDA Set

•

•

•

• •

•

•• • • •

•

1 9.8286E-01 1.9037E+00 2.8245E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm-l)

Figure 4- 7b. For Lab 22, standardized residuals from linear fit to JEIDA data plotted vs. predicted IR absorption coefficient.

65
CO

—I

<

9

CO

LU

tr

o

UJN

o

<

<

Ico

3.75

2.25 -

0.75

-0.75 -

b -2.25 -

-3.75

8.7404E-01 2.0631 E+00 3.2521 E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm-1)

Figure 4-7c. For Lab 23, standardized residuals from linear fit to JEIDA data plotted vs. predicted IR absorption coefficient.

66
3.75

2.25 -

0.75-

(

(

-0.75"-

-2.25 -

-3.75

9.1815E-01 2.3548E+00 3.791 4E+00

PREDICTED IR ABSORPTION COEFFICIENTS (cm-l)

Figure 4-7d. For Lab 27, standardized residuals from linear fit to JEIDA data plotted vs. predicted IR absorption coefficient.

CO

—I

<

9

CO

LU

cr

Q

LU

O

<Q

z

<

Ico

67
The residual plots for laboratories 21, 23, and 26 (figs. 4-6a, 4-6c, and 4-6d) are satisfactory.

The residual plot for laboratory 22 (fig. 4-6b) is unsatisfactory. It is characterized by such

clumping of residuals for each specimen that individual residuals are not always visible in

the plot. This behavior implies agreement among IR laboratories and erratic responses by

the absolute laboratory.

The F statistic for laboratory 25 is somewhat large, but the residual plot (fig. 4-6e) does

not indicate erratic or nonlinear behavior for the absolute method but rather anomalous

results for ingots #2102 and #2105. Recomputation omitting the data on these ingots

reduced the F statistic to the same order of magnitude as the F statistics for cases (la)

and (4a).

The F statistics for laboratory 24 (case 6) and laboratory 28 (case 7) indicate egregious

lack of fit. For laboratory 24, the residual plot (fig. 4-6f) shows an erratic pattern which is presumably caused either by the composition of the individual slugs from the ingots or by

measurement problems in the laboratory. For laboratory 28, the residual plot (fig. 4-6g)

indicates that the IR data are not a linear function of the absolute data over all concentrations. In fact, the plot indicates quadratic behavior, meaning that the IR measurements

cannot be related to absolute oxygen concentrations via a simple conversion coefficient.

In order to eliminate the possibility that a few slugs are affected by ingot inhomogeneity,

a recomputation was done for laboratories 24 and 28 omitting the data on ingot #1102

which appear to be anomalous. The recomputations reduced the F statistics, but not to

an acceptable level.

4.13 ESTIMATION OF A CONVERSION COEFFICIENT FOR EACH ABSOLUTE

LABORATORY

The linear statistical model of the last section does not account for the fact that both

the absolute measurements and the infrared measurements are subject to random error. Fuller [4-5] proposes the following model where both types of measurements are subject to

random error; namely,

Zi^ A + C{Xi + ii) + ei i = l, ...,n (4-6)

where Zi represents the average measurement by an absolute laboratory on the i^^ specimen; Cj represents an associated random error term; Xi represents the average IR value

over all laboratories measuring the i^^ specimen; and represents the associated random

error term. The terms Cj are assumed to be independent and come from a distribution with

standard deviation cr. All random error terms are assumed to be mutually independent.

Given the model defined in eq (4-6), Fuller has shown that the ordinary least-squares

estimate of the slope C is biased towards zero. The bias, in this case, is approximately —0.005/ig/g and is not significant for this study.

68
Therefore, we simplify the model by deleting the error terms so that

Zi = A^CXi^ti i = l,...,n. (4-7)

Furthermore, based on multiple measurements by some absolute laboratories, it is assumed

that the random error terms have standard deviations inversely proportional to oxygen

concentration. The data from the study were analyzed by a weighted least-square technique that allows for the dependence of precision on oxygen concentration and for multiple

measurements by absolute laboratories. Results are shown in table 4-7.

Where the intercept term A is effectively zero, the slope C can be used as a factor for

converting from IR absorption coefficient to total oxygen concentration. The t statistics in

table 4-7 indicate whether or not a laboratory is producing a calibration curve with zero

intercept.

Table 4-7: Results of fitting absolute data as a function of IR data

showing estimates of the intercept term A and slope C

Abs Abs IR Intercept i Slope Std Dev Residual DF

Case Lab Test Set Test Set A Statistics C of C Std Dev V

(1) 21 2 2 -0.037 -0.27 3.569 0.052 0.222 14

(la) 21 2 2,3,4,5,6 -0.022 -0.15 3.583 0.054 0.234 14

(2) 22 3 3 2.391 3.32** 2.243 0.253 0.779 17

(2a) 22 3 2,3,4,5,6 2.378 3.29" 2.277 0.258 0.787 17

(3) 23 4 4 -0.151 -0.23 3.584 0.231 0.641 12

(3a) 23 4 2,3,4,5,6 -0.161 -0.25 3.528 0.226 0.633 12

(4) 26 4 4 0.239 1.50 3.678 0.057 0.270 14

(4a) 26 4 2,3,4,5,6 0.370 1.86 3.552 0.071 0.341 15

(5) 25'' 10- mm slug 2,3,4,5,6 -0.009 -0.08 3.252 0.045 0.124 12

(6) 24"= 10- mm slug 2,3,4,5,6 -0.268 -0.26 3.040 0.354 0.697 9

(7) 28^= 10-mm slug 2,3,4,5,6 -1.302 -2.95" 3.505 0.169 0.472 13

"Indicates that the intercept is significantly different from zero at the 95% probability level.

^Ingots :^2102 and 7^2105 excluded from this analysis.

•^Ingot ^1102 excluded from these analyses.

69
4.14 ESTIMATION OF A FINAL CONVERSION COEFFICIENT

There are two issues which must be resolved before a final conversion coefficient can be

estimated from this study. First of all, there is a question as to whether a better estimate

for the conversion coefficient is attained by averaging the IR data over test sets 2, 3, 4, 5,

and 6, or by considering only IR data from the same test set as the absolute data. Table

4-7 lists results for both alternatives for the CPAA laboratories.

Where homogeneity is in question, we prefer measurements on the same physical artifacts.

This course of action is not wholly satisfying for this study because we do not have absolute

measurements on test set 5 and test set 6. Thus, the IR measurements on test sets 5 and

6 can only be tied to oxygen concentrations via the measurements on the 10-mm slugs.

For this reason, IR measurements are averaged over all test sets, and the resulting bias is taken as a component of uncertainty in the final conversion coefficient.

The second fundamental question of how data from the absolute laboratories are combined

to construct a final conversion coefficient is resolved by fitting all data from equivalent

laboratories to the linear model (4-7) and taking the resulting slope as the best unbiased

estimate of the conversion coefficient. This approach assumes that measurements by all laboratories are consistent and without bias, meaning that a zero intercept and a single

slope characterize the relationship between IR measurements and absolute measurements.

Data from laboratories 22 and 28 are excluded because of nonzero intercepts (table 4-7)

and lack of fit (table 4-6). Data from laboratory 24 are excluded because of lack of fit (table 4-6).

We check the assumption of a zero intercept by a weighted fit to model (4-7) for data from

laboratories 21, 23, 25, and 26. The t statistic for A in table 4-8 shows that the intercept

term is not significantly different from zero. Therefore, a conversion coefficient is used to

relate IR measurement to oxygen concentration. The conversion coefficient C is estimated

from the model restricted to have zero intercept. Results are shown in table 4-8.

The plot of standardized residuals in figure 4-8 shows a slight offset for laboratory 25 and

excellent agreement for the other three laboratories. The small value of the F statistic for

testing the goodness of fit indicates that the restricted linear model is appropriate relative

to the dispersion among absolute measurements by the four absolute laboratories.

70
CO

-J

<

9

CO

LU

cr

Q

LU

Q

DC

<Q

z

<

co

3.75

2.25

0.75

-0.75

-2.25

-3.75

1 1

1

1 T

-

• •

—

••

•

- • • • • • • • •• ••• • •

• • • — • •

• • • •• » • • •

• » • ••••

• • •

• •

• ••

Lab 21 Lab 23 Lab 26 Lab 25

1 1 1 1 1.0 31.0

RUN NUMBERS

61.0

Figure 4-8. Standardized residuals from linear fits to data from absolute laboratories 21,

23, 26, and 25 plotted against run numbers.

71
A final conversion coefficient based on data from these four laboratories is 3.575 parts per

million (weight) (ppmw) per cm"-'. The uncertainty associated with this value is discussed

in the last section.

Table 4-8. Restdts of fitting absolute data from laboratories 21, 23, 25, and 26

as a linear function of IR data** on test sets 2, 3, 4, 5, and 6 showing estimates

of the intercept A and conversion coefficient C

Intercept Std Dev t Statistic

A of A for A

0.070 0.079 0.88

Slope'' Std Dev F Statistic

C of C for Lack of Fit

3.575 0.023 0.67

"IR data with fewer than triplicate measurements excluded from the analysis.

''Model reduced to have zero intercept.

4.15 JEIDA SPECIMENS

In addition to the test squares that were specifically prepared for this study, 21 specimens,

grouped into three test sets which had been used in an earlier Japanese study [4-6] were made available for the current international study. The analysis is restricted to data on

JEIDA set 1 which was measured by four absolute laboratories. A limitation on this

portion of the data base is that the IR measurements on the JEIDA specimens were made

by four laboratories within a single national region. Therefore, the JEIDA data are used

to corroborate the results from the test sets.

Total standard deviations across IR laboratories as defined by eq (4-3) are shown in table

4-9 for each specimen.

72
Table 4-9. Total standard deviations reflecting dispersion within and among IR laboratories

Specimen ID Total standard deviation Degrees of freedom

Absorption units Percent

J - 2 0.0402 4 4

J - 6 0.0870 4 4

J - 8 0.1680 4 4

J - 16 0.0809 3 4

J - 17 0.1376 4 4

J - 23 0.0712 4 4

J - 25 0.0910 5 4

We apply the same diagnostic techniques to the measurements by the four CPAA laboratories on the JEIDA samples as were applied to the measurements on the test sets. Restdts

for model (4-5) are shown in table 4-10.

Homogeneity is not an issue in this analysis because all absolute laboratories measured the

same specimens. Studentized residuals from the fits are plotted versus predicted oxygen

concentration in figure 4-7.

Table 4-10. Results of fitting IR data as a linear function of absolute data

showing F statistics for testing lack of fit

Case Absolute Abs IR DF F

Lab Test Set Test Set of Fit Statistic

(1) 21 JEIDA JEIDA 33 5.6'*

(2) 22 JEIDA JEIDA 28 173.5"

(3) 23 JEIDA JEIDA 33 53.6'*

(4) 27 JEIDA JEIDA 33 3.9

" Indicates lack of fit at the 99% probability level.

Estimates of the conversion coefficient C, according to the model in eq (4-7), are shown

in table 4-11 for the JEIDA specimens. Weighted least-squares analyses account for independent measurements of oxygen concentration by some absolute laboratories and for

precision of absolute measurements as a function of oxygen concentration. Because the

total standard deviations in table 4-9 are based on very few degrees of freedom, standard

deviations for equivalent specimens from table 4-3 are used in the calculations.

73
Table 4-11. Resiilts of fitting absolute data as a linear function of IR data

showing estimates of the intercept A and slope C

Abs Abs IR Intercept Slope Std Dev Residual DI

Case Lab Test Set Test Set A C of C Std Dev

(1) 21 JEIDA JEIDA -0.372 3.696 0.147 0.489 5

(2) 22 JEIDA JEIDA -0.622 4.251 1.219 1.727 4

(3) 23 JEIDA JEIDA -0.244 3.358 0.428 0.734 5

(4) 27 JEIDA JEIDA -0.037 3.553 0.094 0.269 5

4.16 COMPARISON BETWEEN RESULTS FOR TEST SETS AND JEIDA

SPECIMENS

Absolute laboratories 21, 22, and 23 measured both the JEIDA specimens and a test set. The differences between conversion coefficients calculated from the data on the test sets and

those calculated from the data on the JEIDA specimens are shown in table 4-12. Differences

in slopes for the two sets of artifacts are not significant relative to laboratory precision. This

is true even for laboratory 22 which shows such divergent results. Laboratory 27, which

measured only the JEIDA specimens, is compared with laboratory 26, which measured

only test set 4.

Table 4-12: Differences between conversion coefficients computed from test sets data

and JEIDA data

Absolute Diff in Slopes Std Dev ^-Statistic

Lab Test Set - JEIDA Diff t

21 -0.127 0.081 0.8

22 -2.008 1.245 1.6

23 0.226 0.486 0.5

26 - 27 0.125 0.110 1.1

74
4.17 CONVERSION COEFFICIENT AND ASSOCIATED UNCERTAINTY

The conversion coefficient C for converting from IR measurement to total oxygen concentration is 3.575 ppmw per cm~^ with a total uncertainty of ±0.10 ppmw per cm~^ (This

translates to 6.28 parts per million (atomic) (ppma) per cm~-^ with a total uncertainty of

±0.18 ppma/cm-^)

The random component of the uncertainty is taken to be two times the standard deviation associated with the estimate of C or 0.046 /ig/g. The systematic component of the

uncertainty is estimated to be 0.057 //g/g. The total uncertainty is the linear sum of the

random and systematic components.

The systematic component accounts for any error in the conversion coefficient that we

may have incurred by averaging the IR data over all test sets. This component accounts

for the effect of inhomogeneities which occur at random within an ingot as well as any

offset for a regional group of IR laboratories relative to the other IR laboratories. A bound

for this error is difficult to calculate from the data of this experiment. We can, however,

estimate the average effect from the data of laboratories 21, 23, and 26 (table 4-7). For

each laboratory, we calculate the difference between a conversion coefficient based on IR

and absolute measurements on the same specimens and a conversion coefficient based on IR

measurements averaged over all test sets. The average difference over the three laboratories

of 0.057 /ig/g is our best estimate of systematic error.

4.18 CONCLUSION

Data from each absolute laboratory have been examined in detail to determine if the laboratory is producing measurements consistent with IR measurements. Absolute measurements

shovJd be a linear function of IR measurements for the range of oxygen concentrations in

the study (0 to 10 /ig/g). Diagnostic tests for zero intercept (table 4-7) and goodness of

fit to the Unear model (table 4-6) confirm that measurement problems or inhomogeneities

invahdate the results for three absolute laboratories (22, 24, 28). The final conversion coefficient is based on data from four absolute laboratories that measured the specimens that were fabricated especially for this study (21, 23, 25, 26). Data from absolute laboratories

that measured only the JEIDA specimens are in agreement with the final result.

The study has shown that IR laboratories are internally consistent in measuring interstitial

oxygen and that systematic differences among laboratories can be as large as 0.6 absorption

units at the highest oxygen concentrations. Because the final conversion coefficient is based

on an average of IR laboratories, an IR laboratory that is systematically biased from the

average by ±0.3 absorption units could have a bias as large as ±2 /xg/g (or ±3 ppma) in

its determination of oxygen concentration using the recommended conversion coefficient.

75
REFERENCES

[4-1] Hogg, R. v., and Craig, A. T., Introduction to Mathematical Statistics (The Macmillan

Co., New York, 1965).

[4-2] Draper, N. R., and Smith, H., Applied Regression Analysis, Second Edition (John

Wiley k Sons, Inc., New York, 1981), p. 111.

[4-3] Ibid., p. 33.

[4-4] Ibid., p. 144.

[4-5] Ftdler, W. A., Measurement Error Models (John Wiley & Sons, Inc., New York, 1987),

p. 13.

[4-6] lizuka, T., Takasu, S., Tajima, M., Arai, T., Nozaki, T., Inoue, N., and Watanabe,

M., /. Electrochem. Soc. 132, 1707 (1985).

\ 76
5. STATISTICAL ANALYSIS OF THE DATA

by

John Mandel

National Measurement Laboratory

5.1 SCOPE

The analysis described in this report deals with the comparisons of the resvilts obtained

by "absolute" methods of measurement, i.e., by laboratories 21, 22, 23, and 26 for CPAA,

24 and 25 for PAA, eind 28 for IGFA, with those obtained by the infrared (IR) method.

For the latter, only sets 2 to 6 were included.

5.2 DATA

The full data for the infreired laboratories are listed in Appendix A, and for the absolute

laboratories in Appendix B of this Special Publication. Tables 5-1 through 5-7 contain the

data used for this analysis as the results &om the absolute laboratories listed against the

average IR absorption coefficient for each ingot. Figures 5-la through 5-7a are plots of

the oxygen content as determined by each of the absolute laboratories versus the infrared

absorption coefficient. Figures 5-lb through 5-7b are bar plots showing the standardized

residual errors ("H-Values") for each specimen.

5.3 METHODS OF ANALYSIS AND RESULTS

Each of the absolute laboratories for which replicate measurements of the absolute method

exist was einalyzed by the same statistical technique. This was a straight-line fit in which

allowance was made for two sources of variability: replication error and additional lackof-fit. The straight line is assumed to go through the origin. The mathematical model

is

Vij = + 6i-\- Sij ,

where:

Xi = IR measurement for ingot i.

yij = absolute measurement for ingot i, replicate j.

Si = "lack-of-flt" error for point i, this point consisting of the abscissa Xi and an

ordinate y^, equal to the average of the replicates for ingot i.

77
Table 5-la. Absolute Laboratory 21 vs. IR (average of sets 2 to 6)

IR (cm ^) Oxygen Content (/ig/g)

0.806 2.83 2.85

1.429 4.62 5.35 5.01

1.882 6.89 6.66

2.140 7.56 7.67

2.256 7.94 7.90

2.279 8.42 8.12

2.814 10.04 9.70 10.17

2.957 10.34 10.05

2.961 11.09 11.07

3.108 11.63 11.69

3.124 10.87 11.01

3.403 12.40 12.22

3.466 11.94 12.17 12.92

3.530 12.63 12.41

3.543 12.98 13.27

3.724 12.95 12.56

3.836 13.07 13.69 13.56

3.902 14.54 14.19

4.280 15.59 16.24

4.770 16.62 16.59

Fitted equation is: Y = 3.575881 *X.

Standard error of B = 0.0220.

Within standard deviation = 0.0793322 *X(I).

Between standard deviation = 8.216614E-02 *X(I).

78
Table 5- lb

X Y Y Resid. Weight

0.8060 2.8400 2.8822 -0.0422 1.56E+02

1.4290 4.9933 5.1099 -0.1166 5.53E+01

1.8820 6.7750 6.7298 0.0452 2.85E+01

2.1400 7.6150 7.6524 -0.0374 2.21E+01

2.2560 7.9200 8.0672 -0.1472 1.99E+01

2.2790 8.2700 8.1494 0.1206 1.95E+01

2.8140 9.9700 10.0625 -0.0925 1.43E+01

2.9570 10.1950 10.5739 -0.3789 1.16E+01

2.9610 11.0800 10.5882 0.4918 1.15E+01

3.1080 11.6600 11.1138 0.5462 1.05E+01

3.1240 10.9400 11.1711 -0.2311 1.04E+01

3.4030 12.3100 12.1687 -0.1413 8.72E+00

3.4660 12.3433 12.3940 -0.0507 9 41E+00

—n 1 n9Q 8 11 Fi-uon

3.5430 13.1250 12.6693 0.4557 8.05E+00

3.7240 12.7550 13.3166 -0.5616 7.29E+00

3.8360 13.4400 13.7171 -0.2771 7.68E+00

3.9020 14.3650 13.9531 0.4119 6.64E+00

4.2800 15.9150 15.3048 0.6102 5.52E+00

4.7700 16.6050 17.0570 -0.4520 4.44E+00

79
Table 5-2a. Absolute Laboratory 22 vs. IR (average of sets 2

IR (cm~^) Oxygen Content (fJig/g)

0.8060 3.60

1.4290 5.70

1.8820 8.90

2.2560 7.30

2.2790 7.70

2.8140 9.20

2.9570 10.30

2.9610 8.80

3.1080 11.00

3.1240 6.50

3.4030 9.60

3.4660 8.60

3.5300 10.20

3.5430 9.60

3.7240 13.50

3.8360 11.10

3.9020 11.30

4.2800 11.40

4.7700 13.20

Fitted equation is: Y = 3.20475 *X.

Standard error of B = 0.1568.

Standard deviation of fit = 0.6834658 *X(I).

80
Table 5-2b

X Y Y Resid. Weight

0.8060 3.6000 2.5830 1.0170 3.30E+00

1.4290 5.7000 4.5796 1.1204 1.05E+00

1.8820 8.9000 6.0313 2.8687 6.04E-01

2.2560 7.3000 7.2299 0.0701 4.21E-01

2.2790 7.7000 7.3036 0.3964 4.12E-01

2.8140 9.2000 9.0182 0.1818 2.70E-01

2.9570 10.3000 9.4764 0.8236 2.45E-01

2.9610 8.8000 9.4893 -0.6893 2.44E-01

3.1080 11.0000 9.9604 1.0396 2.22E-01

3.1240 6.5000 10.0116 -3.5116 2.19E-01

3.4020 9.6000 10.9058 -1.3058 1.85E-01

3.4660 8.6000 11.1077 -2.5077 1.78E-01

3.5300 10.2000 11.3128 -1.1128 1.72E-01

3.5430 9.6000 11.3544 -1.7544 1.71E-01

3.7240 13.5000 11.9345 1.5655 1.54E-01

3.8360 11.1000 12.2934 -1.1934 1.45E-01

3.9020 11.3000 12.5049 -1.2049 1.41E-01

4.2800 11.4000 13.7163 -2.3163 1.17E-01

4.7700 13.2000 15.2867 -2.0867 9.41E-02

81
Table 5-3a. Absolute Laboratory 23 vs. IR (average of sets 2 to

IR (cm-i) Oxygen Content (/zg/g)

0.8060 2.60

1.8820 7.20

2.1400 7.60

2.2790 7.70

2.9570 11.70

2.9610 10.00

3.1080 10.80

3.1240 11.50 11.20

3.4030 11.70 11.30

3.5300 13.30 11.90

3.5430 12.90

3.7240 12.60

3.8360 14.00

3.9020 15.00 14.70

Fitted equation is: Y = 3.562814 *X.

Standard error of B = 0.0548.

Within standard deviation = 0.1214559 *X(I).

Between standard deviation = 0.1721403 *X(I).

82
Table 5-3b

X Y Y Resid. Weight

0.8060 2.6000 2.8716 -0.2716 3.47E+01

1.8820 7.2000 6.7052 0.4948 6.36E+00

2.1400 7.6000 7.6244 -0.0244 4.92E+00

2.2790 7.7000 8.1197 -0.4197 4.34E+00

2.9570 11.7000 10.5352 1.1648 2.58E+00

2.9610 10.0000 10.5495 -0.5495 2.57E+00

3.1080 10.8000 11.0732 -0.2732 2.33E+00

3.1240 11.3500 11.1302 0.2198 2.77E+00

3.4030 11.5000 12.1243 -0.6243 2.33E+00

3.5300 12.6000 12.5767 0.0233 2.17E+00

3.5430 12.9000 12.6231 0.2769 1.79E+00

3.7240 12.6000 13.2679 -0.6679 1.62E+00

3.8360 14.0000 13.6670 0.3330 1.53E+00

3.9020 14.8500 13.9021 0.9479 1.77E+00

83
Table 5-4a. Absolute Laboratory 24 vs. IR (average of sets 2

T"r> / — 1\ IR (cm ) Oxygen Content (/ig/gj

1.4290 O Tn 3.70

1.8820 4.60

2.1400 6.10

2.2560 8.50

2.8140 8.40

2.9570 9.50

2.9610 10.30

3.4660 9.70

3.5430 12.60

3.8360 11.50

4.2800 11.70

4.7700 12.00

Fitted equation is: Y = 2.994181 *X.

Standard error of B = 0.1297.

Standard deviation of fit = 0.4493328 *X(I).

84
Table 5-4b

X Y Y Resid. Weight

1.4290 3.7000 4.2787 -0.5787 2.43E+00

1.8820 4.6000 5.6351 -1.0350 1.40E+00

2.1400 6.1000 6.4075 -0.3075 1.08E+00

2.2560 8.5000 6.7549 1.7451 9.73E-01

2.8140 8.4000 8.4256 -0.0256 6.25E-01

2.9570 9.5000 8.8538 0.6462 5.66E-01

2.9610 10.3000 8.8658 1.4342 5.65E-01

3.4660 9.7000 10.3778 -0.6778 4.12E-01

3.5430 12.6000 10.6084 1.9916 3.95E-01

3.8360 11.5000 11.4857 0.0143 3.37E-01

4.2800 11.7000 12.8151 -1.1151 2.70E-01

4.7700 12.0000 14.2822 -2.2822 2.18E-01

85
Table 5-5a. Absolute Laboratory 25 vs. IR (average of sets 2 to 6)

IR (cm ^) Oxygen Content (/ig/g)

0.8060 2.2000 2.5900 2.8100 2.6000 2.6500 2.2000 2.7200 2.7200

1.4290 3.7800 4.7500 5.0800 4.8800 4.8500 4.7000 4.2800 4.7800

1.8820 5.7600 5.7200 5.1600 5.5300 4.9100 5.9500 5.7000 5.8600

2.1400 6.7000 6.8000 6.9500 7.6200 7.0400 6.7100 6.7300 7.9400

2.2560 7.6600 7.2800 7.7800 7.3400 7.0800 7.3500 7.1700

2.2790 7.1500 6.6500 7.1600 6.7800 7.5000 7.0500 7.5600 7.1500

2.8140 8.8400 9.4900 9.3900 8.5300 9.3600 9.0200 9.8900 9.6600

2.9570 9.6200 9.4000 10.3600 10.5000 10.1000 9.7800

2.9610 8.9700 9.7600 9.8000 10.1000 9.9400 9.8000 9.8500 10.3700

3.1080 9.0400 9.2900 10.7500 10.1700 9.7800 9.8000 10.9100 10.1900

3.1240 9.6300 10.3200 10.4500 9.3300 8.0900 8.1900 10.3900 9.5200

3.4660 11.2000 10.8200 10.6600 11.4100 11.3900 11.2700 10.9800 12.0600

3.5430 12.4700 12.6200 12.0800 11.2300 10.9400 11.6900 12.4200 11.7700

3.8360 12.4000 13.2200 12.3600 11.0800 10.9700 12.6400 12.8000 12.6600

4.2800 14.5000 14.3000 13.0000 13.6300 13.4100 13.1300 13.4800 13.7300

4.7700 14.9000 15.7600 13.8900 14.9800 16.4500 14.8000 16.5700 15.1400

Fitted equation is: Y = 3.218106 *X.

Standard error of B = 0.0272.

Within standard deviation = 0.1894086 *X(I).

Between standard deviation = 8.515099E-02 *X(I).

86
Table 5-5b

X Y Y Resid. Weight

0.8060 2.5613 2.5938 -0.0325 1.31E+02

1.4290 4.6375 4.5987 0.0388 4.17E+01

1.8820 5.5738 6.0565 -0.4827 2.41E+01

2.1400 7.0612 6.8867 0.1745 1.86E-I-01

2.2560 7.3800 7.2600 0,1200 1.59E-I-01

2.2790 7.1250 7.3341 -0.2091 1.64E+01

2.8140 9.2725 9.0558 0.2167 1.08E+01

2.9570 9.9600 9.5159 0.4441 8.64E+00

2.9610 9.8237 9.5288 0.2949 9.72E+00

3.1080 9.9913 10.0019 -0.0106 8.82E+00

3.1240 9.4900 10.0534 -0.5634 8.73E+00

3.4660 11.2237 11.1540 0.0698 7.09E+00

3.5430 11.9025 11.4018 0.5007 6.79E+00

3.8360 12.2663 12.3447 -0.0784 5.79E+00

4.2800 13.6475 13.7735 -0.1260 4.65E+00

4.7700 15.3113 15.3504 -0.0391 3.75E+00

87
Table 5-6a. Absolute Laboratory 26 vs. IR (average of sets 2 to 6)

IR (cm ^) Oxygen Content (/ig/g)

0.8060 3.2200 2.9200

1.8820 6.6500 7.1700 7.2600

2.1400 8.4800 8.1200

2.2560 8.7700 8.3100 8.3900

2.2790 8.7900 8.7300 8.8500

2.9570 11.2800 10.9000 11.2400

2.9610 10.7500 9.6400 10.4900

O.IUOU 1 1 47nn 1XU.O n R7nn 1 \J\J 3.1240 11.5200 11.2200 12.0900

3.4030 13.2800 12.7700 11.5100

3.4660 13.6700 12.9500 12.9100

3.5300 12.9900 12.3800 13.3000

3.5430 13.4800 12.9500 13.0700

3.7240 13.8500 13.1600 13.3900

3.8360 14.4300 13.6300 14.2200

3.9020 14.5700 13.9200 14.2900

4.7700 16.2100 16.3800

Fitted equation is: Y = 3.701534 *X.

Standard error of B = 0.0282.

Within standard deviation = 0.1316959 *X(I).

Between standard deviation = 8.562864E-02 *X(I).

88
Table 5-6b

\r1

XTY Kesid. Tir_; _'Li. Weight

U.oUdU o.UiUU 0.0866 9.D2il(+01

1 sfion l.oOZU 1 .UZD

1

n nanA U.UDU4

0 1 Ann o.ouuu 7 QOI q n 9707 i.oorj-\-\ji

Q AQnn O.OuU 1 n 1 QQ*} l.oUil(-|-Ui

o. < yuu Q /I tKQ n tKAO 1.41 Hi+Ui

111 Ann n 1 QA et

1 n OQ^Q iu.youz —U.DDDy o. ivrj-\-\J\J

O.lUoU 1 1 tifi/i/i 7 QQP_Lnn

ii.DiUU ll.OOOO n nAdA 7 Q1 1? j^nn 1 .olHi+UU

iz.oyoo —U.U 1 Do D.oyxii-|-uu

3.4660 13.1767 12.8295 0.3471 6.35E+00

3.5300 12.8900 13.0664 -0.1764 6.12E+00

3.5430 13.1667 13.1145 0.0521 6.07E+00

3.7240 13.4667 13.7845 -0.3178 5.50E+00

3.8360 14.0933 14.1991 -0.1058 5.18E+00

3.9020 14.2600 14.4434 -0.1834 5.01E-f00

4.7700 16.2950 17.6563 -1.3613 2.75E+00

89
Table 5-7a. Absolute Laboratory 28 vs. IR (average of sets 2 to 6)

IR (cm-i) Oxygen Content (fig/g)

0.8060 1.8000

1.4290 3.8000

1.8820 4.8000

2.1400 5.8000

2.2560 8.1000

2.2790 6.5000

2.8140 8.6000

2.9570 9.8000

2.9610 8.9000

3.1080 8.2000

3.1240 10.8000

3.4660 10.6000

3.5430 10.2000

3.8360 11.6000

4.2800 15.9000

4.7700 15.4000

Fitted equation is: Y = 2.998246 *X.

Standard error of B = 0.1032.

Standard deviation of fit = 0.412666 *X(I).

90
Table 5- 7b

X Y Y Resid. Weight

0.8060 1.8000 2.4166 -0.6166 9.04E+00

1.4290 3.8000 4.2845 -0.4845 2.88E+00

1.8820 4.8000 5.6427 -0.8427 1.66E+00

2.1400 5.8000 6.4162 -0.6162 1.28E+00

2.2560 8.1000 6.7640 1.3360 1.15E+00

2.2790 6.5000 6.8330 -0.3330 1.13E+00

2.8140 8.6000 8.4371 0.1629 7.42E-01

2.9570 9.8000 8.8658 0.9342 6.72E-01

2.9610 8.9000 8.8778 0.0222 6.70E-01

3.1080 8.2000 9.3185 -1.1185 6.08E-01

3.1240 10.8000 9.3665 1.4335 6.02E-01

3.4660 10.6000 10.3919 0.2081 4.89E-01

3.5430 10.2000 10.6228 -0.4228 4.68E-01

3.8360 11.6000 11.5013 0.0987 3.99E-01

4.2800 15.9000 12.8325 3.0675 3.21E-01

4.7700 15.4000 14.3016 1.0984 2.58E-01

91
92
3

2

-

1 -

0

-1 -

2 - 3 -

H-Values - Lab 21

I. .1

Figure 5-lb. For Lab 21, standardized residual errors ("H-Values") for each specimen.

93
ABSORPTION COEFFICIENT (cm-^)

Figure 5- 2a. For Lab 22, oxygen content vs. infrared absorption coefficient.

94
H-Values - Lab 22

3

2

-

1 -

0

-1

2

3

I I

Figure 5-2b. For Lab 22, standardized residual errors ("H-Values") for each specimen.

95

H-Values - Lab 23

3

"

2

-

1 -

0

-

-1 -

-2 - -3 -

Figure 5-3b. For Lab 23, standardized residual errors ("H-Values") for each specimen.

97
98
H-Values - Lab 24

3

2 h

1

0

-1

2

3

Figure 5-4b. For Lab 24, stajidardized residual errors ("H-Values") for each specimen.

99
12 3 4

ABSORPTION COEFFICIENT (cm-i

Figure 5-5a. For Lab 25, oxygen content vs. infrared absorption coefficient.

100
3

2

1

0

1

2

3 L

H-Values - Lab 25

j.'.ii I III.! I.I.

Figure 5-5b. For Lab 25, standardized residual errors ("H-Values") for each specimen.

101
102
3

2

1 h

0

1

2

3

H-Values - Lab 26

II

Figure 5-6b. For Lab 26, standardized residual errors ("H-Values") for each specimen.

103
104
3

2

1

0

1

2

3 L

H-Values - Lab 28

Figure 5- 7b. For Lab 28, standardized residual errors ("H-Values") for each specimen.

105
eij = replication error.

It is assumed that both Si and e,j are proportional to a;,-. The hypothesis that the standard

deviation of the replication error is proportional to X (the IR value) can be experimentally

checked. In figure 5-8, the standard deviations calculated at each Xj are plotted against

Xi, for the data from laboratory 25, and a straight line going through the origin has been

fitted to these data, because the intercept is not statistically significant. The slope of the

straight line is signific9,ntly different from zero. The data for the other laboratories are not as conclusive as for laboratory 25, but they do not contradict the assumption that the

standard deviation of replication is proportional to Xi. This is shown in figure 5-9 where,

again, a line going through the origin has been fitted to the combined data for all three

laboratories.

Assuming that both 6i and Cij are proportional to Zj, we can estimate the factors of

proportionality from the analysis. The procedure is based on the following considerations.

Let yi represent the average of all replicates yij at the point i. Then

(1) the variance of yi is equal to

Var{yi) = <Ti+(Tl/ni , (5-1)

where rij is the number of replicates yij at the point i.

(2) By assumption, we have

<r| = clxi (5 — 2a)

<tI = c\xi . (5 - 26)

An estimate for C2 is readily obtained by regressing a\ (which can be observed at each Xi

for which there are at least two measurements) on Zj. Thus the problem is to estimate c\.

Var{yi) = x]

Ui

(5-3)

where has been determined.

The weight of yi is equal to

Wi = (5-4)

106
107
1.6 2.4 3.2

IR VALUE

Figure 5-9. Standard deviation between replicates for laboratories 21, 23, and 26.

108
Since Wi is the exact weight,

N -2

or

Y^Wi{yi-yiy-{N -2) = 0, (5-5)

t

where y,- is the estimated value of y,-.

The object is to solve eq (5-5) for ci, with the value for Wi substituted from eq (5-4). This

is done by an iterative process.*

The analysis resulted in the following:

(a) an estimate ^ for the slope (3 and

(b) a "weight" based, for each point, on the appropriate combination of the errors of 6

and e.

In addition, estimates were obtained for the standard error of ^.

Tables 5-2, 5-4, and 5-7 contained only single measurements by the absolute methods. For

these tables, the standard deviation of replication could not be estimated.

To detect, and safeguard against, questionable measurements, two graphical procedures were used:

(1) a graph of the individual e^j estimates in a standardized scale,

(2) a graph of the fitted straight line, together with the plotted points (xi,yi).

The graphs of the first type revealed two questionable values, one for lab 23, and one for

lab 26.

The graphs of the second type revealed large differences in lack-of-fit between different

labs, but in no case was there any evidence of nonlinearity (curvature), thus justifying the

* Paule, R. C, and Mandel, J., Consensus Values and Weighting Factors, J. Res. Natl. Bur.

Stand. 87, 377 (1982).

109
linear fitting procedures.

For labs 23 and 26, the fit was repeated after replacing, in both cases, the questionable

value by the average of the remaining replicates. The figures corresponding to these labs

are, however, based on the original data.

5.4 RESULTS OF THE ANALYSIS

Table 5-8 lists the results of the analyses.

The slopes vary appreciably between labs, but the two most discrepant values (for labs 22

and 24) are based on data showing considerable scatter (see figs. 5-2a and 5-4a).

Laboratories 22 and 28 can be eliminated, since a separate analysis shows that there is evidence of nonzero intercept for both. Laboratory 24 had no replicate determinations.

In addition, the fit for this laboratory is appreciably worse than for laboratories 21, 23,

25, and 26, as seen from the standard deviations listed. Laboratories 25 and 26 are not

consistent with laboratories 21 and 23, nor are they consistent with each other: their slopes

are definitely different. If, nevertheless, laboratories 21, 23, 25, and 26 are combined in a

single set, the results are as follows (a single regression):

slope = 3.435 /tig/g cm~^

standard error of slope = 0.031

ci = 0.188 C2 = 0.168

In conclusion, if laboratories 22, 24, and 28 are eliminated, the remaining four laboratories

are still somewhat incompatible. Combining them, nevertheless, yields the above result.

Converted to ppma/cm~^, the conversion coefficient is 6.030, with an error, based upon

two standard deviations, of 0.108.

110
Table 5-8. Results of the analyses

Slope Multiplier for Standard Deviation"

Laboratory Value Standard Error Fit Replication

21 3.5759 0.0220 0.082 0.079

22 3.2048 0.1568 0.683 NR*"

23 3.5628 0.0548 0.172 0.121

24 2.9942 0.1297 0.449 NR

25 3.2181 0.0272 0.085 0.189

26 3.7015 0.0282 0.086 0.132

28 2.9982 0.1032 0.413 NR

" Values of Cj for C2 , respectively.

No replicates were made.

Ill
6. ACKNOWLEDGMENTS

The editors wish to express their appreciation for the successful completion of this project

to a great number of organizations and individuals. The silicon crystals used for this

study were generously supplied by Japan Silicon, Komatsu Electronic Materials, Monsanto

Electronic Materials, Osaka Titanium Corporation, Shin-Etsu Handotai, Siltec Silicon,

Toshiba Ceramics, and Wacker Chemitronic. Union Carbide provided the sapphire squares

used in the instrumental verification procedure.

We would like to thank the individual researchers at the IR laboratories: Dr. D. Andrews

(General Electric Co., Ltd.), Mr. P. Ashby (Mullards, Ltd.), Dr. M. Domenici (Dynamit Nobel SiUcon), Dr. K. Graff (Telefunken), Dr. N. Inoue (Nippon Telegraph &: Telephone), Li Guang Ping (Tianjin Electronic Materials Research Institute), Lin Yu Ping

(Zhejiang University), E. Ohashi (Komatsu Electronic Materials), Dr. B. Pajot (Ecole

Normale Superieure), Dr. L. Shive (Monsanto Electronic Materials), H. Suzuki (Hitachi),

and Ye Yu Zong (Shanghai Second Smelting Plant).

We would also like to thank those responsible for making the very difHctilt absolute measurements of the oxygen content of the silicon specimens: Dr. K. Bethge (Institut fiir Kernphysik, Johann Wolfgang Goethe Universitat, Frankfurt), Dr. E. Grallath (MaxPlanck-Institut fiir Metallforschung, Dortmund), Dr. T. Nozaki (Institute of Physical and

Chemical Research (RIKEN), Wako, Saitama), Dr. B. Schmitt (Bundesanstalt fiir Materialpriifung, Berlin), Dr. E. Schweikert (Center for Chemical Characterization and Analysis,

Texas A &c M. University), Dr. J. Stoquert (Centre de Recherches Nucleaires, Strasbourg),

Dr. K. Strijckmans (Institute for Nuclear Sciences, Rijksuniversiteit Gent), and Drs. D.

Wood and J. Hislop (AERE Harwell, Oxfordshire).

The cooperation of Dr. H. Marchandise and the Community Bureau of Reference (BCR)

was very important, as it enabled us to include results obtained at four additional highly

skilled laboratories on this project.

112
APPENDIX A. INFRARED ABSORPTION DATA

^C IIXCXX XJCiU i'W C0 Xjillcaxl Ijr Absorption Coefficient (cm ^)

TDxxJ i^c vex X cLX cLlXiC lex 1 2Ami 3

1 m m 1

1

X X 0u .ou 10 *^4 1 0 79426 0 78753 0 77693

10101 13 0 10 .^1 8 0 79884 0 79668 0 80341

1 01 01 1 fi 0u. 10xu 0 0 81489 0.81794 0 82054

1 01 01 1X 71 0 70 uO.U ^R fi 0 80165 0 87771 0 84324

1 01 01 1X Qi7 0u.xu10 t^1 ^ 0 76870 0 76422 0 77142

1 01 09 fi 1 00 ^0 0 0\J * 75161 1 W X V X 0 77353 0 72648

1 01 09 fio 0u.xu10 ou^fi .u0 0 811 82 0 81765 0 82679

1 01 09 1XZ9 nu.xu1 n fin DU.Un 0 85147 0 86596 0 86478

1 01 09 1X 71 0u.zu9n tifi 9 0 81186 0 89501 0 81 1 18

1 01 09 1X 7I 0U. 701 u fi 0 79145 0 8251

7

0 84786

1 01 01 Q 0u.ou10 Q^71 .U0 0 85020 0 86185 0V/ • 86626 w vy V-l ^

1 01 01 X X 0u.ou10 uo.o ^1 8 0 82065 0 80801 0\J ^KJ81021 X\J ^ X

1 01 01 1

1

1

X

0u.ou10 *^4 1 0 81039 0 79203 0V/ • 80184 vj Vy X

1X 01U X 01uo XQ 0u .^u 90 ^9 0 83091 0 83095 0V/ • 82877 v^ 1

1X 01U X 04fx 1xoR 0u.xu10 OOfil . Q«7 0 81291 0 81291 0 72803

1X 01U X 04Ul 1X Q>7 0u.xu10 f^l 0 78160 0 78687 0 78160

1X 01U X 0^U«J 4 0u.xu10 fil ux .*±4 0 78798 0.79350 0.79033

10105 KJ 0 20 57 0 0 78640 0.78871 *

1X 01U X 0^uo 1X 0u 0u.xu10 .54 0 0.79817 0vy • 80165 \j vy ^ vy \^ 0.79925

1X 01U X 0^ 1

1

xo 0 90 54 7 0 80731 0.79144 0.80165

1 01 0"^ 1

1

xo 0u.^u90 54 0 0.79411 0vy • 80976 \j vy %y vy 0.79843

1X 01U X Ofi uu 1X 0u.xu10 52 8 0 80967 0vy • 79055 f V vy i-y 0.78429

1xuxuo 01 Ofi o 0u.xu10 54 7 0.79244 0vy • 78083 1 w Vy V-/ 1-* 0vy • 80758 v-* V/ I v^

1XUXUD m nfi oo nu.xu1 n uO.U 51 n 0.77877 * *

1XUXUD m nfi 1XDfi 0u.xu10 55 n 0 81518 0 82648 0vy • 81963 ^ V vy »^

1XUXUD 01 Ofi 1XOfi 0u.xu10 o«j 55 .u0 0 81726 0vy 82086 V-/ &j vy vy \^ 0.81060

XUXU 1 1

1

X 1 0u.ou10 54 1 0.79911 0Vy 80783 V-/ vy 1 %J 0.79671

1iUiU ni n7J 1

1

lo nu.xu1 n 54 4 0.78757 0 81258 0.77876

iUiU / 1 fi ID nu.xuin 55 0 0U.OUUt7^ 80fiQ9 U .O X X X

O

0 89091

1 m f\'7 1U1U7 1 / n '7{\ U. < U Oo.D 0.79758 0.81714 0.86572

10107 19 0.10 53.5 0.76016 0.75224 0.74876

20101 11 0.30 54.3 2.13201 2.12148 2.11088

20101 13 0.10 53.8 2.15474 2.14686 2.13951

20101 16 0.10 55.0 2.17514 2.17254 2.16592

20101 17 0.70 58.6 2.13015 2.15738 2.23449

20101 19 0.10 53.5 2.08669 2.06833 2.08981

113
20102 6 1.00 52.0 2.05042 2.02528 2.00244

20102 8 0.10 56.0 2.13852 2.20527 2.15269

20102 12 0.10 60.0 2.22755 2.25392 2.25735

20102 17 0.20 56.2 2.17904 2.16400 2.18645

20102 17 0.70 58.6 2.16066 2.18645 2.16391

20103 9 0.30 57.0 2.16263 2.23655 2.26892

20103 11 0.30 53.8 2.13711 2.17568 2.14170

20103 11 0.30 54.3 2.13575 2.14742 2.12416

20103 15 0.20 52.5 2.15924 2.16724 2.15348

20104 18 0.10 53.9 2.16342 2.17307 2.15741

20104 19 0.10 53.5 2.07411 2.07411 2.08479

20105 4 0.10 61.4 2.11033 2.07692 2.12611

20105 5 0.20 57.0 2.12300 2.12343 * 20105 10 0.10 54.0 2.10919 2.11840 2.10919

20105 13 0.20 54.7 2.08079 2.11840 2.13728

20105 13 0.20 54.0 2.11156 2.12757 2.11379

20106 1 0.10 52.8 2.10845 2.12847 2.12982

20106 2 0.10 54.7 2.14212 2.12759 2.15617

20106 3 0.10 53.0 2.07019 * * 20106 16 0.10 55.0 2.16285 2.15822 2.15359

20106 16 0.10 55.0 2.14052 2.15031 2.14758

20107 11 0.30 54.3 2.08993 2.15004 2.11242

20107 13 0.10 54.4 2.11562 2.13084 2.12947

20107 16 0.10 55.0 2.16223 2.14433 2.15169

20107 17 0.70 58.6 2.10041 2.17801 2.14988

20107 19 0.10 53.5 2.06563 2.06104 2.05184

30101 11 0.30 54.3 3.07490 3.10083 3.06504

30101 13 0.10 53.8 3.16260 3.10583 3.12973

30101 16 0.10 55.0 3.13851 3.15289 3.13920

30101 17 0.70 58.6 3.12571 3.28810 3.24562

30101 19 0.10 53.5 3.01453 2.96598 3.00756

30102 6 1.00 52.0 2.99891 2.97951 2.97855

30102 8 0.10 56.0 3.10318 3.15683 3.16441

30102 12 0.10 60.0 3.24207 3.30780 3.30755

30102 17 0.20 56.2 3.14228 3.14437 3.16268

30102 17 0.70 58.6 3.22369 3.17221 3.20718

30103 9 0.30 57.0 3 30981 3 29790 3 24562

30103 11 0.30 53.8 3.09087 3.09087 3.09321

30103 11 0.30 54.3 3.08707 3.08879 2.99630

30103 15 0.20 52.5 3.12092 3.12906 3.13004

30104 18 0.10 53.9 3.08044 3.15604 3.15302

114
30104 19 0.10 53.5 3.00253 3.01175 3.01175

30105 4 0.10 61.4 3.03711 3.05662 3.05765

30105 5 0.20 57.0 3.08722 3.00129 * 30105 10 0.10 54.0 3.14616 3.07031 3.08020

30105 13 0.20 54.0 3.06266 3.08236 3.05497

30105 13 0.20 54.7 3.07469 3.03807 3.05662

30106 1 0.10 52.8 3.05070 3.11954 3.07745

30106 2 0.10 54.7 3.13176 3.08722 3.12734

30106 3 0.10 53.0 3.00119 * * 30106 16 0.10 55.0 3.10959 3.11841 3.11905

30106 16 0.10 55.0 3.12722 3.12217 3.10959

30107 11 0.30 54.3 3.02370 3.02852 3.04010

30107 13 0.10 54.4 3.07738 3.07683 3.03962

30107 16 0.10 55.0 3.11370 3.10412 3.11497

30107 17 0.70 58.6 3.09194 3.17195 3.14268

30107 19 0.10 53.5 2.96174 2.97086 2.96613

40101 11 0.30 54.3 2.92016 2.91498 2.91541

40101 13 0.10 53.8 2.93342 2.91971 2.97136

40101 16 0.10 55.0 3.00099 2.97212 2.98538

40101 17 0.70 58.6 3.01729 3.03904 2.99258

40101 19 0.10 53.5 2.85945 2.84124 2.85960

40102 6 1.00 52.0 2.81613 2.84898 2.83511

40102 8 0.10 56.0 2.94690 2.96887 2.99001

40102 12 0.10 60.0 3.07337 3.09874 3.09767

40102 17 0.20 56.2 2.95500 2.98453 2.99341

40102 17 0.70 58.6 3.01059 3.02115 3.00544

40103 9 0.30 57.0 3.09157 3.13096 3.11259

40103 11 0.30 53.8 2.94943 2.93945 2.90716

40103 11 0.30 54.3 2.94963 2.92133 2.95678

40103 15 0.20 52.5 2.96413 2.98201 2.98084

40104 18 0.10 53.9 2.94267 2.92786 2.99374

40104 19 0.10 53.5 2.84586 2.84586 2.86893

40105 4 0.10 61.4 2.93046 2.93959 2.92683

40105 5 0.20 57.0 2.97873 2.97632 * 40105 10 0.10 54.0 2.95643 2.94661 2.94703

40105 13 0.20 54.7 2.96053 2.93252 2.94204

40105 13 0.20 54.0 2.93124 2.95968 2.95994

40106 1 0.10 52.8 2.91881 3.00962 3.00005

40106 2 0.10 54.7 2.99650 2.98651 3.01389

40106 3 0.10 53.0 2.93358 2.93306 * 40106 16 0.10 55.0 2.99482 2.99512 3.00005

115
40106 16 0.10 55.0 2.98558 2.98042 2.99359

40107 11 0.30 54.3 2.88204 2.93731

A /\AAKK 2.93255

40107 13 0.10 54.4 2.96129 2.96081 2.95144

40107 16 0.10 55.0 3.01891 3.00966

A

A ^ A

A 3.02424

40107 1 '7 17

A ^A

0.70 58.6

OOO 1 1 o 2.88113O 1 ^ OA ^ 3.16897

OA P >4OO 3.05433

40107 1 A19

A 1 A 0.10 53.5OO ^7*7AA 2.87704OO /?OOA 2.86330 2.86791

50101 11

A OA 0.30 54.3 3.52696 3.48858O ylO 1 AA 3.48190

50101 lo 0.10 53.8 3.52092 3.50716

A P >| P 1 O 3.54518

50101 16

A 1 A 0.10 CPA 55.0O Ef'TAAA 3.57909 3.61445O P O /* To 3.58678

50101 1 T17

A TA 0.70 58.6 3.46553O P O 1 OA 3.58180O P AOO "1 3.59381

50101 1 A19

A 1 A 0.10 P O P 53.5O y4OA^A 3.42064O >4A >l P O 3.40452 3.40690

50102 6 1 A

A 1.00 P OA

52.0 3.36723 3.32441 3.36761

50102 8 A 1 A 0.10 56.0 3.53380 3.61436

O P ^7

A -1 3.56721 P Al AO 50102 1 O12 A 1 A 0.10 ^ A A

60.0

O ^ 1 AlO 3.61913O ^1 ^AA 3,71709 3.72704

A "1 AO 50102 17A OA 0.20 56.2O ET P OAO 3.55293O P O P o^ 3.58527

A P A

OO 3.56983

50102 17 0.70 58.6 3.59260 3.68472 3.61646

50103 9 0.30 57.0 3.73610 3.76438

AA 3.72162

50103 11 0.30 53.8 3.53462 3.53314 3.51657

50103 11 0.30 54.3 3.54058 3.51634 3.51426

50103 15 0.20 52.5 o p^

A p^ c% 3.54058O P^A 3.54980A

n

AAA 3.53922

50104 18 0.10 53.9 3.56113 3.56841

O P AO T/* 3.59876

50104 19 0.10 53.5 3.40879 rt

A t\0 ^

3.40879

A

A t\000 3.40888

50105 4 0.10 61.4 3.48457

O i4 P P A^ 3.45597O >lT P ^ A 3.47569

50105 5 0.20 57.0 3.51422 3.49955

50105 10 0.10 54.0 3.52162 3.51101 3.51701

50105 13 0.20 54.7 3.53830 3.47342 3.50043

50105 13 0.20 54.0 3.47903 3.50694 3.50554

50106 1 0.10 52.8 3.58426 3.54583 3.56103

50106 2 0.10 54.7 3.56824 t\

VMAAA

3.57338

A ^ ^f7 liA 3.57742

50106 3 0.10 53.0

g\AA y> ^ A 3.44662

50106 16 0.10 55.0 3.57947 3.60201 3.57930

50106 16 0.10 55.0 3.60071 3.59166

A P TAA >l 3.57804

50107 11 0.30 54.3 3.48208

A ^ ^ n ^ A 3.46863 3.49799

50107 13 0.10 54.4 3.51737 3.51596 3.52056

50107 16 0.10 55.0 3.60211 3.59534

AKA THA 3.58710

50107 17 0.70 58.6 3.54056

A p^n ^ ^ 3.53601 3.65768

50107 19 0.10 53.5 3.41442 3.42488 3.42024

110101 11 0.30 54.3 2.91676 2.92601 2.91676

110101 13 0.10 53.8 2.95736 2.95736 2.97117

110101 16 0.10 55.0 3.00568 3.01866 2.99052

110101 17 0.70 58.6 3.00972 3.01866 2.98687

116
110101 19 0.10 53.5 2.87180 2.87619 2.88495

110102 6 1.00 52.0 2.88070 2.84423 2.80848

110102 8 0.10 56.0 2.97269 3.00237 3.00483

110102 12 0.10 60.0 3.09488 3.12439 3.08219

110102 17 0.20 56.2 2.97751 3.01642 3.00639

110102 17 0.70 58.6 2.94112 3.07944 3.01782

110103 9 0.30 57.0 3.13847 3.13142 3.13341

110103 11 0.30 54.3 2.93507 2.96206 2.94937

110103 11 0.30 53.8 2.96708 2.94415 2.95823

110103 15 0.20 52.5 3.00341 2.99348 2.98649

110104 18 0.10 53.9 2.53476 2.52559 * 110104 19 0.10 53.5 2.85855 2.85424 2.85439

110105 4 0.10 61.4 2.95144 2.93883 2.95529

110105 5 0.20 57.0 2.95846 2.99109 * 110105 10 0.10 54.0 2.94153 2.93688 2.94153

110105 13 0.20 54.7 2.95032 2.93198 2.94593

110105 13 0.20 54.0 2.95267 2.96269 2.94485

110106 1 0.10 52.8 2.94620 2.99585 2.93836

110106 2 0.10 54.7 2.99071 2.98139 2.98469

110106 3 0.10 53.0 2.91099 2.92367 * 110106 16 0.10 55.0 3.01060 2.99771 3.00252

110106 16 0.10 55.0 3.00658 3.00252 2.97319

110107 11 0.30 54.3 2.94859 2.93081 2.94916

110107 13 0.10 54.4 2.89603 2.94010 2.94449

110107 16 0.10 55.0 3.00143 2.99551 2.99624

110107 17 0.70 58.6 2.91719 2.98452 3.02449

110107 19 0.10 53.5 2.88997 2.84598 2.85054

110201 11 0.30 54.3 2.22233 2.22453 2.23115

110201 13 0.10 53.8 2.23780 2.24221 2.26007

110201 16 0.10 55.0 2.28496 2.28393 2.25564

110201 17 0.70 58.6 2.23001 2.27097 2.28852

110201 19 0.10 53.5 2.16537 2.15580 2.17179

110202 6 1.00 52.0 2.13873 2.10716 2.11919

110202 8 0.10 56.0 2.22529 2.26530 2.27331

110202 12 0.10 60.0 2.33451 2.38495 2.35748

110202 17 0.70 58.6 2.26093 2.25319 2.29296

110202 17 0.20 56.2 2.25319 2.25126 2.27476

110203 9 0.30 57.0 2.37283 2.36042 2.36311

110203 11 0.30 53.8 2.24775 2.23004 2.25864

110203 11 0.30 54.3 2.23559 2.22674 2.25888

110203 15 0.20 52.5 2.27138 2.26329 2.25584

117
110204 18 0.10 53.9 2.68774 2.71329 2 69247

110204 19 0.10 53.5 2.16982 2 16221 2.18151

110205 4 0.10 61.4 2.23037 2.23598 2 22493

110205 5 0.20 57.0 2.22473 2.27314 * 110205 10 0.10 54.0 2.23265 2.21172 2.24813

110205 13 0.20 54.0 2.24885 2.26910 2.26471

110205 13 0.20 54.7 2.26028 2.24038 2.26366

110206 1 0.10 52.8 2.24245 2.28005 2 25613

110206 2 0.10 54.7 2 32172 2 26128 2Arf a 30721 VVy 1 Arf X 110206 3 0.10 53.0 2 21061 * * 110206 16 0.10 55.0 2.28955 2 28416 2^ • 28170 ^V—' X 1 vy 110206 16 0.10 55.0 2.28170 2.26946 2.27630

110207 11 0.30 54.3 2.22788 2.25682 2.24265

110207 13 0.10 54.4 2.20287 2.25480 2 25919

110207 16 0.10 55.0 2.28306 2.27663 2.26837

110207 17 0.70 58.6 2.29474 2.32702 2 26077

110207 19 0.10 53.5 2 16613 2 19328 2M a 18031 X \J Vy V X 120101 11 0.30 54.3 3 70632 3 70632 3Va 70557 1 WW

120101 13 0.10 53.8 3.70745 3V a 69198 W 4/ X V\J 3 74238

120101 16 0.10 55.0 3 76453 3.74654 3V a 78019 1 Wvy X ty 120101 17 0.70 58,6 3 80071 3 76549 3.78547

120101 19 0.10 53.5 3.61115 3 58825 3V • 60995 \J vy *y v w 120102 ^ ^\J -L. \J 6 1.00 52.0 3 52076 3.49841 3V a 49243 X ty ^ A V

120102 ^ \J A. \J 8 0.10 56.0 3 72129 3 73905 3.71813

120102 12X A 0vy • 10X v/ 60 0 3 89357 3V a 90517 4/ \y ly X 1 3 92305

120102 17 0 70 58 6 3 75529 3 86402 3W a 78175 1 U X 1 V

120102 17 0.20 56.2 3 75229 3.76740 3.77443

120103 X ^V X V/ V g 0 30 57 0 3 92000 3 93871 3 89287

120103 X ^W X V/ V* 11X X 0.30 53.8 3 70557 3 < 72169 1 ^ X Vy V 3 72232

120103 X ^vy X vV 11X X 0.30 54.3 3 72169 3 69021 3W a 70105 Vy X Vy Vy 120103 15X tJ 0 20 52.5 3 73588 3 75399 3 73960

120104 18X w 0.10 53.9 3Va 78255 1 3V • 68190 \y V X ly vy 3.74142

120104 X ^w X \J i 19X ty 0 10 53.5 3 58746 3W a 60110 V/ V/ X XV/ 3V a 59685 VV Vy V>/ Vy 120105 X X V1^ 4 0.10 61.4 3.67451 3V a 66912 W1/ X ^ 3\J a 66823 Vy Vy Vy ^v 120105 5 0 20 57 0 3tiF • 71144 1 X X X X 3.71467

120105 10 0.10 54.0 3 68175 3%J a 69902 *y V vy Arf 3 69448

iZUiUO 1 Q n on tJl.U O.D / 0»1 9 71 1 /I A

120105 13 0.20 54.7 3.69264 3.68445 3.68357

120106 1 0.10 52.8 3.69914 3.78070 3.79844

120106 2 0.10 54.7 3.74748 3.75676 3.72532

120106 3 0.10 53.0 3.62697 3.67170 *

118
120106 16 0.10 55.0 3.76454 3.79210 3.77413

120106 16 0.10 55.0 3.77617 3.75598 3.73514

120107 11 0.30 54.3 3.65490 3.69271 3.69001

120107 13 0.10 54.4 3.68547 3.69908 3.70360

120107 16 0.10 55.0 3.75196 3.73920 3.76447

120107 17 0.70 58.6 3.69353 3.85205 3.68090

120107 19 0.10 53.5 3.58078 3.59150 3.60387

120201 11 0.30 54.3 3.89005 3.84058 3.84507

120201 13 0.10 53.8 3.87200 3.87200 3.92408

120201 16 0.10 55.0 3.96732 3.94821 3.87512

120201 17 0.70 58.6 3.97062 3.99288 3.92062

120201 19 0.10 53.5 3.76536 3.76781 3.76088

120202 6 1.00 52.0 3.70593 3.64849 3.71133

120202 8 0.10 56.0 3.86081 3.91334 3.95991

120202 12 0.10 60.0 4.06767 4.10416 4.12080

120202 17 0.20 56.2 3.94013 3.94547 3.95894

120202 17 0.70 58.6 3.96287 3.96287 3.81282

120203 9 0.30 57.0 4.11354 4.09109 4.12507

120203 11 0.30 54.3 3.89457 3.86722 3.93223

120203 11 0.30 53.8 3.89884 3.90568 3.86948

120203 15 0.20 52.5 3.93538 3.93708 3.93623

120204 18 0.10 53.9 3.91786 3.88061 3.89108

120204 19 0.10 53.5 3.74105 3.76756 3.75403

120205 4 0.10 61.4 3.84610 3.85052 3.85277

120205 5 0.20 57.0 3.88861 3.95347 * 120205 10 0.10 54.0 3.89108 3.84829 3.90692

120205 13 0.20 54.0 3.87691 3.92910 3.88827

120205 13 0.20 54.7 3.87748 3.85500 3.88197

120206 1 0.10 52.8 3.91483 3.95407 3.94069

120206 2 0.10 54.7 3.95749 3.91893 3.93374

120206 3 0.10 53.0 3.82559 3.83685 * 120206 16 0.10 55.0 3.92758 3.93865 3.96541

120206 16 0.10 55.0 3.94244 3.91855 3.92726

120207 11 0.30 54.3 3.83716 3.83716 3.85055

120207 13 0.10 54.4 3.86854 3.88201 3.84833

120207 16 0.10 55.0 3.93214 3.89879 3.95055

120207 17 0.70 58.6 3.98582 4.01843 3.95213

120207 19 0.10 53.5 3.75215 3.75215 3.76573

120301 11 0.30 54.3 3.42589 3.49319 3.49905

120301 13 0.10 53.8 3.49597 3.49597 3.51676

120301 16 0.10 55.0 3.55401 3.55384 3.57519

119
120301 17 0.70 58.6 3.60433 3.60369 3.61876

120301 19 0.10 53.5 3.39674 3.38548 3.39343

120302 6 1.00 52.0 3.35881 3.28295 3.29295

120302 8 0.10 56.0 3.44139 3.58280 3.52000

120302 12 0.10 60.0 3.65772 3.69183 3.69330

120302 17 0.70 58.6 3.60115 3.68702 3.50149

120302 17 0.20 56.2 3.54720 3.54884 3.54284

120303 9 0.30 57.0 3.66841 3.67831 3.68096

120303 11 0.30 54.3 3.49106 3.48347 3.52811

120303 11 0.30 53.8 3.51779 3.49717 3.49132

120303 15 0.20 52.5 3.52950 3.53705 3.51783

120304 18 0,10 53.9 3.53401 3.52795 3.55571

120304 19 0.10 53.5 3.40257 3.43588 3.40257

120305 4 0.10 61.4 3.48527 3.49977 3.45186

120305 5 0.20 57.0 3.52821 3.54416 * 120305 10 0.10 54.0 3.50286 3.50735 3.50876

120305 13 0.20 54.0 3.54288 3.52353 3.51905

120305 13 0.20 54.7 3.53262 3.50146 3.51917

120306 1 0.10 52.8 3.55358 3.61789 3.52961

120306 2 0.10 54.7 3.59749 3.59962 3.60003

120306 3 0.10 53.0 3.47266 3.48442 * 120306 16 0.10 55.0 3.57627 3.59882 3.58470

120306 16 0.10 55.0 3.53678 3.58470 3.60452

120307 11 0.30 54.3 3.50673 3.50514 3.51693

120307 13 0.10 54.4 3.50941 3.53328 3.52733

120307 16 0.10 55.0 3.59538 3.56157 3.59792

120307 17 0.70 58.6 3.59864 3.60522 3.71599

120307 19 0.10 53.5 3.42364 3.42939 3.43390

120401 11 0.30 54.3 3.37070 3.40015 3.39118

120401 13 0.10 53.8 3.40253 3.39684 3.39802

120401 16 0.10 55.0 3.45059 3.43457 3.46678

120401 17 0.70 58.6 3.42050 3.39449 3.44543

120401 19 0.10 53.5 3.29620 3.27991 3.29620

120402 6 1.00 52.0 3.22888 3.25933 3.23032

120402 8 0.10 56.0 3.37555 3.43791 3.41280

120402 12 0.10 60.0 3.50511 3.58684 3.58203

120402 17 0.20 56.2 3.42907 3.43409 3.46964

120402 17 0.70 58.6 3.40869 3.45982 3.45982

120403 9 0.30 57.0 3.56980 3.60483 3.56843

120403 11 0.30 53.8 3.38267 3.40860 3.36586

120403 11 0.30 54.3 3.39844 3.39421 3.36006

120
1 on

A c\f> 12U403 15 0.20 52.5 3.41465 3.42899 3.42648

12U404 18

AA 0.10 53.9 3.45059 3.48590 3.40650 1 OH/l r\A 1 A19 A 1 A 0.10 53.5 3.29055 3.28151 3.30052

120405 4 0.10 61.4 3.33329 3.32642

AAA 3.33773

120405 5 A OA 0.20 57.0 3.36320 3.37029

120405 •1

A10A 1 A 0.10 54.0 3.36985 3.34405

nA

AA 3.36533

120405 13

A OA 0.20 54.0 3.37522 3.37305

AAA ^\A 3.36293

120405 13

A OA 0.20 54.7 3.37436 3.35306

nA

n

JA y% 3.37436 1 OA /I Atf 120406 1 A 1 A

0.10 f o o 52.8 3.36862 3.44971

AA ^ fx

A ^7 3.41297

120406 o2 A ^ /\ 0.10 54.7 3.42629

nn ^^^^^^ 3.39707 3.45257 1 OA AC\G 120406 3 A 1 A

0.10 Cf

OA

53.0 3.34162 3.34266 1 OA >l A^ 120406 16 A 1 A

0.10 55.0

OA *\AAQ 3.42448

OAA O/* f 3.44265 3.53485 1 OA AC\£i 120406 16 A 1 A 0.10 ET C A 55.0 O jl AO y1 O 3.40843 O j4 A ^O /4 3.40724 A A O 3.38786 1 OA >l A*? 120407 11 A OA 0.30 54.3 o o o o ^O 3.33373 3.33686 A A ^ f O K 3.34585 1 OA>1 AT 120407 13 A 1 A 0.10 54.4 O O C C ^ 3.34556 O O ^ yl A j4 3.37494 A A A -4 ^7 A 3.38170 1 OA /I AT 120407 16 A 1 A 0.10 CCA 55.0 O y4 1 O ^ A 3.41369 O O O AO O 3.38023 A A *y A 3.42487 1 OA /I AT 120407 1 T17 A TA 0.70 58.6 O A AAO C 3.49035 O y1 O 1 A yl 3.42194 A A O'y ff Q 3.48758 1 OA /I AT 120407 1 A19 A 1 A 0.10 53.5 O O^ 1 C >4 3.26154 O O C ^ 1 o 3.25613 O O^^AA 3.26609

O-f A1 Al 210101 11

n on O.oO 54. o 1 /• 01 TC 1.42175 "1

A OTO /I 1,42784 1 A'\ A'7A 1.41474

0"1 A"1 A"1 210101 13

A 1 A 0.10 53.8 1 ylOAAO 1.42903 t A OOOO 1.42388 1 /4 y1OC >1 1.44354

Ai 210101 16A 1 A

0.10

CCA 55.0 1.46775 1 y|C 1 1 C 1.45115 1 y| TOOT 1.47287

#\im Ai 210101 1 T17A '7A 0.70 CO o 58.6 1.46069 1 AA fy/i ^ 1.44767 1 y4AC 1 O 1.49512

210101 "1

A19A 1 A

0.10 CO c 53.5 1 A ^ OA^ 1.41206 1 O ^ >l

OA 1.36489 1 OT y< >1O 1.37443

210102 6 1 A

A 1.00 COA

52.0 1 O AO ^O 1.39378 •4 o O

AA^ 1.33996 1 O 1 ACO 1.31953

210102 8 0.10 56.0 1.40771 1 O

O ^ CA 1.38750 1 >4O /ICA 1.43450

210102 ^ o12 0.10 60.0 1 /< ^ o c o 1.46852 1 C "1

CC 1 1.51551 1 CAA >)O 1.50043

210102 17

A '7A 0.70 COa 58.6 1.38991 1.4d44o 1.446 / 5

210102 17

A OA 0.20 56.2 1 yi >4 A'TO 1.44973 "1 /IOCCA 1.43550 1 ylOOAO 1.42298

210103 9 A OA 0.30 c A

57.0 "1

CO A1 ^ 1.53016 f CAAA>I 1.50004 1 >i OOC "1 1.48251

210103 11 0.30

C y4O 54.3 1.41713 -I o 'TA'IA 1.37010 1 y< y1 AOA 1.44020

210103 11 0.30 CO o 53.8 1 A

C O^ 1.40536 1.40146 "1 >1 1 oc^ 1.41256

210103 15 0.20 52.5 1.41452 "1 v1 1 OOA 1.41320 1 O

AC C\f\ 1.39509

210104 18 0.10 53.9 1 >4

OO ^ A 1.42360 1.44836 1 >1 /? c o c 1.46585

210104 19 0.10 53.5 1.39350 1 O

TA 1 O 1.37918 1 OAATA 1.39079

210105 4 0.10 61.4 1 y| '1 O/* 1 1.41261 1 yl "1 ^ C

O 1.41652 "1 y1A >4OC 1.40485

210105 5 0.20 57.0 1 y4 O^

CA 1.42759 1 OAI AO 1.39108

210105 10 0.10 54.0 1.42380 1.41532 1 yi 1 e oo 1.41532

210105 13 0.20 54.0 1.42581 1.42605 1.43827

210105 13 0.20 54.7 1.42976 1.41532 1.47176

210105 31 0.10 * 1.45634 1.46702 * 210106 1 0.10 52.8 1.44842 1.44639 1.45710

121
210106 2 0.10 54.7 1.37464 1.41905 1.45274

210106 3 0.10 53.0 1.40359 1.41532

210106 16 0.10 55.0 1.46041 1.46329 1.45297

210106 16 0.10 55.0 1.44861 1.47257 1.46572

210107 11 0.30 54.3 1.37790 1.40799 1.41446

210107 13 0.10 54.4 1.41643 1.42996 1.41250

210107 16 0.10 55.0 1.46012 1.45851 1.45610

210107 17 0.70 58.6 1.43396 1.51592 1.46499

210107 19 0.10 53.5 1.38784 1.39048 1.36753

210201 11 0.30 54.3 1.84547 1.89910 1.88909

210201 13 0.10 53.8 1.87819 1.87904 1.92292

210201 16 0.10 55.0 1.90709 1.92304 1.92511

210201 17 0.70 58.6 1.91439 1.92570 1.94349

210201 19 0.10 53.5 1.83983 1.83577 1.85381

210202 6 1.00 52.0 1.75401 1.77198 1.78237

210202 8 0.10 56.0 1.88974 1.92809 1.88960

210202 12 0.10 60.0 1.94141 2.05423 1.98780

210202 17 0.70 58.6 1.93261 1.90537 1.90701

210202 17 0.20 56.2 1.91171 1.88150 1.89441

210203 9 0.30 57.0 1.96122 1.99166 1.97382

210203 11 0.30 53.8 1.85804 1.87356 1.85142

210203 11 0.30 54.3 1.84432 1.83901 1.87882

210203 15 0.20 52.5 1.90266 1.90258 1.90342

210204 18 0.10 53.9 1.90702 1.91740 1.89602

210204 19 0.10 53.5 1.83727 1.83727 1.81864

210205 4 0.10 61.4 1.83850 1.83850 1.87878

210205 5 0.20 57.0 1.83702 1.85456 * 210205 10 0.10 54.0 1.87335 1.87784 1.86885

210205 13 0.20 54.0 1.82883 1.83752 1.83036

210205 13 0.20 54.7 1.85079 1.84012 1.84253

210205 31 0.10 * 1.84429 1.83436 * 210206 1 0.10 52.8 1.86794 1.94269 1.93081

210206 2 0.10 54.7 1.89345 1.93421 1.88239

210206 3 0.10 53.0 1.81246 1.83032 * 210206 16 0.10 55.0 1.91529 1.86790 1.83586

210206 16 0.10 55.0 1.90810 1.90470 1.90504

210207 11 0.30 54.3 1.80767 1.82844 1.79991

210207 13 0.10 54.4 1.84089 1.86148 1.84354

210207 16 0.10 55.0 1.90060 1.89881 1.91417

210207 17 0.70 58.6 1.91662 1.98055 2.00715

210207 19 0.10 53.5 1.80896 1.83324 1.82865

122
210301 11 0.30 54.3 2.23219 2.28338 2.28876

210301 13 0.10 53.8 2.26761 2.28447 2.29812

210301 16 0.10 55.0 2.32546 2.33349 2.33384

210301 17 0.70 58.6 2.37569 2.40517 2.41856

210301 19 0.10 53.5 2.19034 2.20512 2.21494

210302 6 1.00 52.0 2.17246 2.18292 2.15580

210302 8 0.10 56.0 2.29032 2.32515 2.31334

210302 12 0.10 60.0 2.40187 2.42621 2.42621

210302 17 0.70 58.6 2.29729 2.37503 2.33988

210302 17 0.20 56.2 2.28638 2.31233 2.32413

210303 9 0.30 57.0 2.39961 2.42861 2.39166

210303 11 0.30 53.8 2.28778 2.26974 2.26954

210303 11 0.30 54.3 2.28545 2.25966 2.27201

210303 15 0.20 52.5 2.30061 2.30465 2.30360

210304 18 0.10 53.9 2.29844 2.33715 2.26306

210304 19 0.10 53.5 2.21385 2.19703 2.22583

210305 4 0.10 61.4 2.22616 2.23906 2.21150

210305 5 0.20 57.0 2.30372 2.28080 * 210305 10 0.10 54.0 2.24713 2.22375 2.22375

210305 13 0.20 54.0 2.25395 2.26279 2.24387

210305 13 0.20 54.7 2.24596 2.23932 2.23814

210305 31 0.10 * 2.30125 2.28391 * 210306 1 0.10 52.8 2.34682 2.26474 2.24725

210306 2 0.10 54.7 2.26474 2.27167 2.28336

210306 3 0.10 53.0 2.19153 2.19925 * 210306 16 0.10 55.0 2.27017 2.26601 2.28027

210306 16 0.10 55.0 2.30269 2.29697 2.26395

210307 11 0.30 54.3 2.21663 2.23953 2.24378

210307 13 0.10 54.4 2.23715 2.24947 2.23835

210307 16 0.10 55.0 2.26613 2.27285 2.27070

210307 17 0.70 58.6 2.32211 2.24204 2.29201

210307 19 0.10 53.5 2.17460 2.18522 2.15601

210401 11 0.30 54.3 2.81188 2.84265 2.82931

210401 13 0.10 53.8 2.82488 2.81603 2.86502

210401 16 0.10 55.0 2.89052 2.87782 2.89605

210401 17 0.70 58.6 2.85143 2.91858 2.96385

210401 19 0.10 53.5 2.78051 2.74112 2.74519

210402 6 1.00 52.0 2.74818 2.69994 2.71440

210402 8 0.10 56.0 2.81798 2.92716 2.89315

210402 12 0.10 60.0 2.97848 2.99688 3.01570

210402 17 0.70 58.6 2.89588 2.91945 2.89614

123
210402 17 0.20 56.2 2.87847 2.87884 2.88325

210403 9 0.30 57.0 2.99551 3.06222 2.96527

210403 11 0.30 53.8 2.81586 2.81586 2.82944

210403 11 0.30 54.3 2.84276 2.80231 2.82042

210403 15 0.20 52.5 2.85175 2.86970 2.85611

210404 18 0.10 53.9 2.87092 2.83086 2.85519

210404 19 0.10 53.5 2.75241 2.73171 2.75181

210405 4 0.10 61.4 2.73035 2.76982 2.74694

210405 5 0.20 57.0 2.80967 2.82706

210405 10 0.10 54.0 2.74775 2.73480 2.72613

210405 13 0.20 54.0 2.74132 2.76251 2.75822

210405 13 0.20 54.7 2.74755 2.72167 2.74775

210405 31 0.10 * 2.80586 2.80659 * 210406 1 0.10 52.8 2.79273 2.80489 2.72143

210406 2 0.10 54.7 2.76204 2.75102 2.75166

210406 3 0.10 53.0 2.70381 2.68268 * 210406 16 0.10 55.0 2.77943 2.77023 2.77535

210406 16 0.10 55.0 2.79627 2.79234 2.76155

210407 11 0.30 54.3 2.71359 2.75913 2.71975

210407 13 0.10 54.4 2.72001 2.73338 2.71581

210407 16 0.10 55.0 2.79085 2.77333 2.76894

210407 17 0.70 58.6 2.82544 2.83874 2.77345

210407 19 0.10 53.5 2.63554 2.64418 2.65736

210501 11 0.30 54.3 3.07580 3.07454 3.07944

210501 13 0.10 53.8 3.08478 3.10412 3.11409

210501 16 0.10 55.0 3.15028 3.15267 3.17098

210501 17 0.70 58.6 3.17027 3.21016 3.22962

210501 19 0.10 53.5 2.98932 2.98413 3.02197

210502 6 1.00 52.0 3.02338 3.01386 3.00850

210502 8 0.10 56.0 3.12723 3.16793 3.20601

210502 12 0.10 60.0 3.25326 3.29428 3.30240

210502 17 0.70 58.6 3.14970 3.18663 3.15415

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210503 9 0.30 57.0 3.28088 3.30322 3.28260

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210504 18 0.10 53.9 3.12394 3.11783 3.11698

210504 19 0.10 53.5 2.97788 2.99658 2.97879

210505 4 0.10 61.4 3.09074 3.08485 3.05682

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210505 10 0.10 54.0 3.09968 3.09918 3.09918

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210505 31 0.10 3.19800 3.19319 * 210506 1 0.10 52.8 3.19634 3.13700 3.13534

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210507 13 0.10 54.4 3.10917 3.10470 3.08536

210507 16 0.10 55.0 3.15861 3.16173 3.15670

210507 17 0.70 58.6 3.12971 3.19293 3.26825

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210601 13 0.10 53.8 3.44241 3.46429 3.47460

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210601 17 0.70 58.6 3.57812 3.51758 3.56051

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210602 6 1.00 52.0 3.30489 3.28629 3.34954

210602 8 0.10 56.0 3.48968 3.53911 3.51831

210602 12 0.10 60.0 3.62407 3.65626 3.55176

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210605 4 0.10 61.4 3.44103 3.40474 3.40563

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741709 8 0.10 56.0 3.21498 3.24188 3.23969

741709 12 0.10 60.0 3.41149 3.44401 3.41841

741709 17 0.20 56.2 3.27251 3.26194 3.24627

741709 17 0.70 58.6 3.33383 3.36701 3.27439

742011 1 0.10 52.8 2.56544 2.56373 2.57491

742011 2 0.10 54.7 2.59011 2.60319 2.60319

742011 3 0.10 53.0 2.48751 * 742011 16 0.10 55.0 2.60751 2.59795 2.60337

742011 16 0.10 55.0 2.59157 2.59469 2.61474

742011 18 0.10 53.9 2.59129 2.54604 2.59043

742011 19 0.10 53.5 2.46169 2.47805 2.48810

742210 4 0.10 61.4 3.62858 3.65339 3.67106

742210 5 0.20 57.0 3.70178 3.61501 * 742210 9 0.30 57.0 3.91487 3.91906 3.97995

742210 10 0.10 54.0 3.79436 3.72077 3.71004

742210 11 0.30 53.8 3.70178 3.72555 3.70467

742210 11 0.30 54.3 3.65999 3.71093 3.71147

742210 13 0.20 54.0 3.69842 3.71136 3.69494

742210 13 0.20 54.7 3.70856 3.71922 3.69303

742210 15 0.20 52.5 3.71982 3.73994 3.73484

742309 6 1.00 52.0 1.54635 1.53984 1.47828

742309 8 0.10 56.0 1.51578 1.55405 1.61825

742309 12 0.10 60.0 1.69996 1.72381 1.69888

742309 17 0.20 56.2 1.59306 1.58448 1.59103

742309 17 0.70 58.6 1.53886 1.56249 1.57141

742410 4 0.10 61.4 1.76132 1.76325 1.73748

742410 5 0.20 57.0 1.70306 1.77403 * 742410 9 0.30 57.0 1.82054 1.69872 1.69315

130
742410 10 0.10 54.0 1.80447 1.70913 1.74139

742410 11 0.30 53.8 1.73926 1.73595 1.71746

742410 11 0.30 54.3 1.69239 1.72371 1.61952

742410 13 0.20 54.0 1.64528 1.73979 1.69993

742410 13 0.20 54.7 1.73156 1.67928 1.69277

742410 15 0.20 52.5 1.65268 1.75532 1.62091

742509 6 1.00 52.0 1.79537 1.80115 1.86470

742509 8 0.10 56.0 1.95490 1.93225 1.93784

742509 12 0.10 60.0 2.07382 2.08109 2.06755

742509 17 0.70 58.6 1.96250 2.00401 1.97249

742509 17 0.20 56.2 1.96404 1.95941 1.92429

742611 1 0.10 52.8 1.87374 1.77894 1.88887

742611 2 0.10 54.7 1.86258 1.88907 1.93342

742611 3 0.10 53.0 1.86784 * * 742611 16 0.10 55.0 1.93628 1.93415 1.94035

742611 16 0.10 55.0 1.92119 1.93299 1.92490

742611 18 0.10 53.9 1.91515 1.90313 1.90245

742611 19 0.10 53.5 1.83491 1.81546 1.89195

747211 1 0.10 52.8 3.27458 3.20855 3.22037

747211 2 0.10 54.7 3.23709 3.26281 3.21424

747211 3 0.10 53.0 3.15541 * * 747211 16 0.10 55.0 3.24670 3.23678 3.25754

747211 16 0.10 55.0 3.22639 3.25299 3.26936

747211 18 0.10 53.9 3.23667 3.24744 3.27406

747211 19 0.10 53.5 3.09441 3.10343 3.11024

747610 4 0.10 61.4 1.77654 1.75004 1.80048

747610 5 0.20 57.0 1.76828 1.78436

747610 9 0.30 57.0 1.90586 1.91975 1.91084

747610 10 0.10 54.0 1.84874 1.79095 1.78911

747610 11 0.30 53.8 1.78768 1.78443 1.79312

747610 11 0.30 54.3 1.76892 1.78610 1.79311

747610 13 0.20 54.0 1.77961 1.78768 1.77334

747610 13 0.20 54.7 1.78656 1.77961 1.78401

747610 15 0.20 52.5 1.79569 1.80718 1.77140

747710 4 0.10 61.4 2.43467 2.41336 2.41410

747710 5 0.20 57.0 2.49194 2.44588

747710 9 0.30 57.0 2.60962 2.60436 2.59454

747710 10 0.10 54.0 2.50172 2.45474 2.45404

747710 11 0.30 53.8 2.45030 2.41764 2.41764

747710 11 0.30 54.3 2.41001 2.43610 2.46409

747710 13 0.20 54.0 2.45100 2.43911 2.45780

131
747710 13 0.20 54.7 2.43839 2.43911 2.45850

747710 15 0.20 52.5 2.46913 2.47561 2.45443

* Missing data

132
APPENDIX B. ABSOLUTE ANALYSIS DATA

^GOT LAB OXYGEN

1 I/O" /c 1 0101 21 9 83

0101 21^ X 2 85

0101 22 3 6

0101 23 2 6

0101 25 9 56

0101 26 3 99

0101 26 2 92

0101 28 1X 8

0201 21^ X 7 56

0201 21£d X 7 67

0201 23 7 6

0201 24 6V • 1X 0201 2'> 7 06

0201 26 8 48

0201 26 10 65

0201 26 a 12

0901 5 8

0101 91^ X 1X 1X .uo 61

0*101 \J%J\J X 21 11X X • 69

0101 22 11X X •vl0

0301 23 10 8

0301 \J%J\J X 25 9 99

0301 26 12.30

0301 \J\I\J X 26 11.47

0301 26 10.87

0301 \J%I\J X 28 8.2

0401 21^ X 11X X •yj09%^ 0401 21^ X 11X X « 07v/ 1 0401 VTtU X 22 8 8

0401 UtU X 23 10 0

u4Ul zo 7 n 0401 24 10.3

0401 25 9.82

0401 26 10.75

0401 26 9.64

0401 26 10.49

0401 28 8.9

133
UoUl 01Zl 1 o oo 12. n cm UoUl 0121 1 O 0*7 UoUl 22 ft A

y.D

UoUl Zo 1 O ft 12.9

UoUl 24 1 O

A

12.

UoUl OK25 1 1 ftft 11. yu

UoUi lo.4o

UoUi 2d 1 O

QK 12. yo

UOUI 2D 1 Q ft7 lO.U ( UoUi Ofi 20 1 ft O IU.2 1 1 ni 0121 1 ft tA

llUl 0121 1 ft ftK lU.Uo 1 1 m oo22 1 ft Q lU.O 1 1 fti llUl OQ2o 117 11.1 1llUl 1 m O/t 24 Q K y.o 1 1 fti llUl OK20 ft OA y.yo 1 1 fti ilUl OA2d 1 1 oo 11. 2o

llUl OA26 1 (\ nft lu.yo 1 1 fti llUl 26 1 1 O/l 11.24 1 1 fti llUl oo2o ft o y.o 1 1 ftO llvZ 0121 T CXA 1 .y4 1 1 ftO llUz 0121 •7 Oft / .yu 1 1 ftO oo22 / .O 1 1 ftO 0/1 24 Q K O.O 1 1 ftO OK2o 7 QQ 1 .OO 1 1 ftO OA2d Q 77 O.I I 1 1 ftO OA2d Q 11 o.ol 1 1 ftO IIUZ OA26 Q OO o.oy 1 1 ftO llUz oo2o Q 1 O.l 1 Ofti 12U1 oi21 1 O OK 12. yo

12U1 0121 1 O KA 12.56 1 Oft1 12U1 oo22 1 •> K lo.5

12U1 oo23 1 O

A 12.6

1201 26 13.85

1201 26 13.16

1201 26 13.39

1202 21 14.54

1202 21 14.19

1202 22 11.3

1202 23 15.0

1202 23 14.7

134
1202 26 14.57

1202 26 13.92

1202 26 14.29

1203 21 12.63

1203 21 12.41

1203 22 10.2

1203 23 13.3

1203 23 11.9

1203 26 12.99

1203 26 12.38

1203 26 13.30

1204 21 12.40

1204 21 12.22

1204 22 9.6

1204 23 11.7

1204 23 11.3

1204 26 13.28

1204 26 12.77

1204 26 11.51

2101 21 4.62

2101 21 5.35

2101 21 5.01

2101 22 5.7

2101 24 3.7

2101 25 4.64

2101 28 3.8

2102 21 6.89

2102 21 6.66

2102 22 8.9

2102 23 7.2

2102 24 4.6

2102 25 5.57

2102 26 6.65

2102 26 7.17

2102 26 7.26

2102 28 4.8

2103 21 8.42

2103 21 8.12

2103 22 7.7

2103 23 7.7

2103 25 7.13

135
ZIUO ZD 0. / y

ZlUo 2o

Q "70 0. / 0

01 ni Oft ZO

QQK 0.00

ZlUo ZO ft

K 0.0

01 H/l ZiU'l 01Zl 10.04

01Zi 0 ftO y.oy

01 n/1 01Zi 1 n 1 10.1 / 01 nyi zz 0 0 y.2

01 n/1 Z4QA 0.4

01 nA 2on 0*7 y.27

Zo

Q ft 0.0

ZiUO 01Zi 1 n Q*? iU.o 

ZiUO 01Zi ii.Ui

01 nti ziuo zz ft

K 0.0

ZiUD Zo 11

K 11.0

ZiUO Zo 110 ii.Z

ZlUo OKZO

n An y.4y

01nK ZlUo Oft 2o 1 1 CO 11.52

01 nK Ziuo Oft 2o 1 1 00 11.22

ZiUo Oft 20 1 0 no 12. uy

ZiUo OQ 1 n

Q lU.o

01 nc ZiUo 0121 1 1 r\A 11. y4

ziUb 0121 1 0 1 "7 12.1 ( ZiUo 0121 1 0 00 12. y2

01 f\ei ziUo 0022 0 ft O.D

01 no zlUo 0 A 24n

9.7

01 nc ZlUo 0 K 25 1 1 00 11.22

zlUo Oft 2o 1o.d7

01 nc ZlUo Oft 2o 1 0 nc 12. y5

2106 26 12.91

2106 28 10.6

2107 21 13.07

2107 21 13.69

2107 21 13.56

2107 22 11 1 11.1

210 / 002o 1 /I

n 14. 

2107 23 10.8

2107 24 11.5

2107 25 12.27

2107 26 14.43

2107 26 13.63

136
2107 26 14.22

01 nT 2107 0 0 28 11.6

2108 21 15.59

2108 21 16.24 0 "1 A 0 2108 22 11.4

2108 24 11.7

01 AO 2108 0 ff 25 13.65

r\ -| rvo 2108 28 15.9

01AA 2109 OH21 16.62 0 1 AA 2109 0121 16.59

01 AA 2109 0022 13.2 01 AA 2109 0 A 24 12.0

2109 0 P 25 15.31

01 AA 2109 0/! 26

H ^ OH 16.21

2109 26

H ^ 00 16.38

01 AA 2109 0028 15.4

2110 21 0.0454

2110 21 0.0462

2110 0023

A AO 0.02

2110 0 0 23

A AO 0.03

2110 0 P 25 0.06 n A AO 7402 21 0 P 0 2.53

^7 >1 AO 7402 21 0 A

A 2.99

T >( AO 7402 OH21 3.16

^7 y| AO 7402 OH21 0 TO 2.73

7402 0022 0 /? 2.6

7402 0023 0 00 2.22

7402 OT27 0 00 3.23

7402 OT27 0 OP 3.25

^7 <4 AO 7402 27 0 A

C 2.95

y4 AO 7402 27 2.87

7402 27 0 AA 3.90

7406 OH21 0 0 >l 8.24

7406 OH21 7.94

7406 0022 5.7

7406 0023

A ilH 9.41

7406 OT27 0 TH 8.71

7406 27 7.95

7408 21 13.39

7408 21 14.02

7408 21 13.40

137
7408 21 12.58

7408 23 11.41

7408 27 13.89

7408 27 13.09

7416 21 10.42

7416 21 10.53

7416 22 12.0

7416 23 8.67

7416 27 9.85

7416 27 9.86 • 7417 21 11.41

7417 21 11.18

7417 21 11.97

7417 21 11.19

7417 22 13.2

7417 23 10.10

7417 27 11.40

7417 27 11.19

7423 21 5.90

7423 21 5.07

7423 21 5.66

7423 21 5.94

7423 22 10.5

7423 23 5.53

7423 27 6.19

7423 27 5.24

7425 21 7.29

7425 21 7.19

7425 21 6.87

7425 21 7.65

7425 22 7.4

7425 23 7.19

7425 27 7.89

7425 27 6.88

138
APPENDIX C.

Interlaboratory Determination of the Calibration Factor for the Measurement

of the Interstitial Oxygen Content of Silicon by Infrared Absorption-t

A. Baghdadi,* W. M. Bullis,t M. C. Croarkin,§ Yue-zhen Li,^

R. 1. Scace,^ R. W. Series,^' P. Stallhofer,^ and M. Watanabe^

Abstract

We report an international interlaboratory dual experiment to determine the calibration

factor used to calculate the interstitial oxygen content of silicon from room-temperature

(300 K) infrared (IR) absorption measurements. We conducted round robins for both the

infrared and the absolute measurements on the same or equivalent specimens. The calibration factor for computing the oxygen content of silicon in parts per million atomic (ppma)

from a room-temperature measurement of the absorption coefficient at 1107 cm"-' was

determined to be 6.28 ± 0.18 ppma/cm~^. The IR round robin showed a reproducibility

on the order of 3%.

1. Introduction

This paper is a report of a world-wide interlaboratory experiment to determine the calibration factor used to calculate the interstitial oxygen content of silicon from roomtemperature infrared (IR) absorption measurements. The basic approach taken for this

experiment was to conduct both the infrared measurements and the absolute oxygen con- centration measurements at many different laboratories on the same or similar specimens.

The infrared measurements were carried out at 18 laboratories in China, Europe, Japan,

and the United States (see Table I), using either dispersive infrared (DIR) or Fourier transform infrared (FTIR) spectrometers. The absolute measurements were carried out at eight

laboratories in Europe, Japan, and the United States (see Table II), using charged-particle

^ Contribution of the National Institute of Standards and Technology (formerly National

Bureau of Standards). Not subject to copyright.

* Semiconductor Electronics Division, National Institute of Standards and Technology, Gaithersburg, MD

^ Siltec Silicon, Menlo Park, California

§ Statistical Engineering Division, National Institute of Standards and Technology

^ Shanghai Institute of Metallurgy, Shanghai, People's RepubUc of China ^ Center for Electronics and Electrical Engineering, National Institute of Standards and

Technology

* Royal Signals and Radar Establishment, Great Malvern, United Kingdom

" Wacker Chemitronic, Burghausen, West Germany

^ Toshiba Research and Development, Tokyo, Japan

139
activation analysis (CPAA), photon activation analysis (PAA), or inert gas fusion analysis

(IGFA).

Since Kaiser and Keck^ first showed a linear relationship between the oxygen content of

semiconductor silicon and IR absorption at 9.1 (1107 cm~^), there have been numerous

experiments which have attempted to establish a definitive value for the calibration factor.

The results of these experiments are summarized in Table III. The values proposed for the

calibration factor range from 4.9 ± 0.3 to 12.0 ± 1.4 ppma/cm"-' ^'^-^^ j^jote that even

the most recent determinations disagree by about 20%. At present, there are at least four

values in commercial use: the "old ASTM" value of 9.63,^^ the "DIN" and "new ASTM"

value of 4.9,1^'^® the "JEIDA" value of 6.06,^2 ^nd the Guo Biaot-designated value of 6.2."

The present study differs from all the previous work in that both the IR and the absolute

determinations were obtained from a substantial number of interlaboratory measurements.

Thus we could estimate the reproducibility of both types of measurements on a statistical

basis rather than rely on estimates of measurement errors provided by individual laboratories.

This work had three goals. The first was to provide an accurate and well-established

value for the calibration factor, using equivalent samples and up-to-date radio-analytical

methods. The second was to provide a basis for calculating the uncertainty in the value of

the calibration factor and to explain the sources of error for that uncertainty. The third,

and arguably the most important, goal was to provide a universally acceptable value for the

calibration factor. The present study includes participation by groups from the American

Society for Testing and Materials (ASTM), Deutsches Institut fiir Normung (DIN), the

Japan Electronic Industry Development Association (JEIDA), and the Academia Sinica, as well as contributions from all of the laboratories which have published recent measurements

of the calibration factor.

Two other multilaboratory experiments and their relationship to this work should be mentioned. The JEIDA work,^^ which was conducted from 1979 to 1982, was intended to

accomplish the same goals as the present experiment. Unexpected difficulties were en- countered in part from axial variations in the oxygen content of the parent crystals, which

caused the IR absorption data on neighboring slices to vary in a way which was difficult to

account for properly in the analysis. The original data were made available by JEIDA to

NBS for statistical examination. This analysis completely supported the JEIDA decisions

on exclusion of aberrant data but also revealed a hitherto unsuspected bimodal distribution

of the data. This distribution appears to have resulted from variations in the procedures

used by the infrared laboratories.^^

JEIDA generously made available 18 of the specimens from their experiment plus three

others from a standard reference set calibrated from that experiment. Data on these

specimens can be used to tie the present work back to the JEIDA experiment and thus to

^ Guo Biao designates the State Standards of China.

140
improve the basis for calibration of the JEIDA reference specimens. However, the JEIDA

specimens were not used in the calculation of the calibration factor: only the data obtained

on the specimens prepared especially for this study were used to compute the calibration

factor.

The second multilaboratory experiment, by the European Community Bureau of Reference

(BCR), is underway to provide calibrated reference specimens. The BCR kindly arranged

for absolute analyses of subsets of material from the present experiment by two laboratories

participating in their work. In addition, several of the IR laboratories in this experiment

are also involved in the BCR effort.

In this paper, we describe the silicon samples and the test matrix, the statistical analyses of

the data, and the determination of the conversion coefficient. The analyses and discussions

of the data presented here are necessarily brief: we present only a synopsis of the statistical

methods and the resulting conclusions. A more extensive description of the statistical

analyses, together with the complete data base and a more detailed description of the

experimented procedures used by the absolute laboratories, is being published concurrently

as a National Institute of Standards and Technology Special Publication. "^^

2. Experimental Plan

2.1 Test Samples

The silicon samples were produced specially for this project by eight leading producers of

semiconductor silicon. The samples were cut from 20 different 100-mm diameter silicon

crystals with room-temperature free carrier concentrations less than 2 x 10^^ cm~^. The

determination of the oxygen content of silicon crystals is not significantly affected by the

presence of free carriers at these concentrations.-^^ The crystals were grown so that the

IR absorption coefficient at 9.1 /xm due to oxygen for all the slices ranged from about 0.9

cm~^ to about 5 cm~^, with a relatively uniform distribution of values throughout the

entire range.

Each laboratory contributing specimens cut a 120-mm long section from each crystal. Two

2-mm thick slices polished on both sides, a 10-mm thick slug, and then two more 2-mm

slices were cut from the end of this section, as shown in Figure la. The 10-mm thick slug

was reserved for PAA or IGFA measurements. Samples for the destructive PAA and IGFA

measurements were cut from the 10-mm slugs as they were needed. Two of the four 2-mm

sHces were used for the IR and CPAA measurements. The remainder of each crystal was

set aside for future or follow-up experiments.

The nominal oxygen concentration was measured, by the silicon producers, as the average

of at least three separate IR measurements, at each of four positions on each slice, 90

degrees apart located 18.5 ±1.0 mm from the center of the slice, with one measurement

on each of the four radii at 45 degrees to the bisector of the primary flat. The maximum

141
spread in the IR absorption coefficient due to oxygen in slices cut from either side of the

10-mm slug was less than 0.06 cm~^.

Four squares, 25 ± 1 mm on a side, were cut from the center of each of two slices from

each crystal, as shown in Figure lb. Each square was laser marked or scribed in the

corner nearest the center of the slice with a three-part code which identified the preparing

organization, the set number from that organization, and the square number. There were

8 squares, marked 1 through 8, prepared from each crystal, yielding 8 equivalent test sets of 20 squares each. In addition to these 8 sets of 20 squares, 3 sets of 7 samples each were

supplied by JEIDA. Each of these samples had either been used in the JEIDA round robin

experiment^"^ or was part of JEIDA reference set 44.'^'^ The eight test sets prepared for this

study were designated Test Sets 1 through 8, and the JEIDA test sets were designated

JEIDA Sets 1 through 3. Test sets 2 through 6 also included an oxygen-free float-zoned

reference square and a sapphire filter to be used in an instrumental check.

The thicknesses of the test and reference squares were measured at the National Institute

of Standards and Technology (formerly National Bureau of Standards), Toshiba Ceramics,

Wacker, and the Shanghai Institute of Metallurgy. All replicate thickness measurements

agreed to within ±0.05%.

2.2 Test Matrix

Measurements were carried out in five separate geographic regions: The People's Republic

of China; Germany; Japan; United Kingdom, France and Italy; and the United States.

Table I lists the IR laboratories that participated in this study; a coordinating laboratory

for each region is listed in boldface. The coordinating laboratories in Germany, Japan,

and the United States represented DIN, JEIDA, and ASTM, respectively, as noted in

parentheses in Table I. The coordinating laboratory in China represented the Academia

Sinica. The coordinating laboratories played a central role in the experimental plan. One

of the test sets was assigned to each region. The coordinating laboratories made the first IR

measurements on that test set, passed them on for measurement by the other laboratories

in the region, and then made a second set of measurements after the other laboratories in

their region completed their IR measurements. Test set 2 was assigned to Japan, test set 3

to the United States, test set 4 to Germany, test set 5 to the United Kingdom, Prance and

Italy, and test set 6 to China. Test sets 1 and 7 were circulated among the coordinating

laboratories and were measured by IR at the same time as the initial measurements on the

set assigned to that region. Test set 8 was reserved to check whether the silicon crystals

contained significant amounts of precipitated oxygen. Since samples subjected to CPAA

are no longer suitable for IR analysis, each CPAA measurement was scheduled following

the IR analyses for that set of samples. Test sets 2 and 3 were measured by CPAA at

laboratories 21 and 22, respectively. Test set 4 was measured by CPAA at laboratories

23 and 26. Samples cut from the 10-mm slugs were subjected to PAA in the U.K. and in

Germany, and to IGFA in Germany.

JEIDA set J-1 was measured at all the Japanese IR laboratories, and then circulated for

142
CPAA measurements in Japan, the United States, Germany, and Belgium at the same time

as the assigned test sets were measured. JEIDA set J-2 was circulated for IR measurements

in the United States and the U.K., and JEIDA set J-3 was circulated for IR measurements

in Germany and China.

2.3 Sources of Error

The sources of error that were examined in this study are due to material inhomogeneity

ajid to laboratory performance. The dependence of the oxygen absorbance band on the

specimen temperature is not a significant source of error, as discussed in section 4.1. Material stability and freedom from precipitated oxygen are not significant; these points are

verified in section 4.2. The factors of laboratory performance which are discussed in sec- tions 4.1 and 4.2 include within-laboratory repeatability, between-laboratory reproducibility, and nonlinear behavior of the absolute laboratories relative to the IR laboratories.

The within-laboratory repeatability for individual IR laboratories was estimated from three

repetitions over a three-day period. The spread of the relative biases among IR laboratories, which was minimized by specifying the IR measurement procedure, was estimated

from differences among the 18 IR laboratories.

The experimental plan for absolute measurements did not specify repetitions on individual

specimens. Laboratory repeatability was estimated by the residual standard deviation of

the fit of absolute measurements to a linear function of the IR measurements."^^ Bias among

laboratories was a dominant source of error because of the lack of a specified operating

procedure. Failure of the measurements to conform to the linear model proved to be

another source of error for some absolute laboratories.

The error due to material inhomogeneity could only be partially quantified because of time

constraints on the experimental plan. Oxygen concentrations could be directly compared

only for test sets 1 and 7 because these were the only test sets measured by the same IR

laboratories. The possible effect of material inhomogeneity on the conversion factor was

included as a contribution to its uncertainty.

3. Measurement Procedures

A standard measurement procedure was specified for the IR measurements. This procedure is described in the following sub-section. However, we did not specify a standard

procedure for the absolute measurements. Each absolute laboratory followed its own interneJly developed procedures. This approach was necessary because there is no single

generally accepted procedure for the absolute measurements.

3.1 Infrared Measurements

The participating laboratories obtained the infrared spectra of the test squares according to

the specified procedure. Roughly two-thirds of the participating IR laboratories used FTIR

spectrophotometers. The remaining laboratories used DIR spectrophotometers, some of

143
which were computerized. Each laboratory conducted a series of instrumental checks in

addition to obtaining the spectra on the test squares:

1. The 100% base line was obtained to measure the "noise" level. On double beam

instruments, the transmittance spectrum was recorded with both the sample and

reference beams empty. On single-beam instruments, the transmittance spectrum

was obtained as the ratio of two spectra taken with the reference specimen in the

sample beam. The 100% base line was plotted over a wavenumber range covering

900 to 1300 cm-^

2. A 0% line was established, for DIR instruments only, by blocking the sample beam,

and recording the instrument zero over the range from 900 to 1300 cm~^.

3. The presence of stray light was detected by obtaining an air-reference transmittance

spectrum of the sapphire square provided with the test sets. The resulting spectrum

was plotted over the range from 900 cm~^ to 1300 cm~^. Sapphire is a cut-off filter

below 1180 cm~^, so that any signal detected in the region of the oxygen peak would

be due to light which did not pass through the sample.

4. The mid-scale linearity of each spectrophotometer was determined by obtaining an

air-reference spectrum of the silicon reference square over the wavenumber range

from 450 to 4000 cm~^. Since the transmittance of a silicon specimen which is polished on both sides can be calculated from the reflectivity of silicon,^ the observed

transmittance in regions of the spectrum where silicon is transparent can be used

to evaluate the linearity of the instrument at mid-scale.

5. The throughput characteristics of each FTIR spectrophotometer were reported by

plotting a single-beam spectrum, obtained with the sample beam empty, over the

wavenumber range from 450 to 4000 cm"-'.

6. The temperature in the laboratory and the temperature in the spectrophotometer

chamber were recorded with an accuracy of ±0.5°C.

A test method for determining the interstitial oxygen content of silicon wafers similar to

this method has been recommended to the ASTM for adoption.

Immediately prior to the initial measurement in any laboratory, all specimens, including the

reference specimen, were etched in hydrofluoric acid to remove any surface oxide. Infrared

transmittance spectra were obtained with a resolution, at 1107 cm~^, of 4 cm~^ for the

FTIR instruments and 5 cm~^ or better for the DIR instruments over (at least) the range

from 900 to 1300 cm~^. The squares were positioned so that the IR beam was centered

on the test squares. The test squares were measured three separate times over a three-

(or more) day period. On some double-beam DIR instruments, the transmittance spectra were obtained with the oxygen-free reference square in the reference beam, and the test square in the sample beam. On single-beam instruments, and on some computerized DIR

^ The transmittance of a silicon specimen polished on both sides should be 53.8%.

144
instruments, the transmittance spectra were computed as the ratio of the spectrum of the

test square to the spectrum of the reference square.

The data reported by each IR laboratory on the performance of its spectrophotometer

will be included in the National Institute of Standards and Technology Special Publication

mentioned above.

The original data, in the form of transmittance spectra, were sent to the National Bureau of

Standards for evaluation and data reduction. The base line transmittance at approximately

1107 cm~^ was obtained by drawing a straight line from 900 cm"-' to 1300 cm"-', and

the peak and base line transmittances were recorded. All of the spectra were read by

the same person. The absorption coefficient was calculated from the base line and peak

transmittances. The transmittance spectra obtained according to the procedure described

above can be derived as the ratio of two equations, one for the transmittance of each

specimen:^^

^

(l-iZfe-"«''(l-i?^e-^'---0

(l-i2)2e-«'=''(l-i22e-2«.=>=t)'

where T./^ is the ratio of the spectrum of the IR source with the sample in the IR beam

to the spectrum of the IR source with the reference specimen in the IR beam, at is the

absorption coefficient of the test crystal, is the absorption coefficient of the reference

crystal, xt is the thickness of the test crystal, is the thickness of the reference crystal,

and R is the reflectivity of the semiconductor. In the wavenumber region of interest, R —

0.30 for silicon. Note that T and a are functions of wavenumber.

Assuming that the absorption in the test crystal is due only to the host lattice, ax,, to

interstitial oxygen, a-nd to unknown instrumental effects, (Xua-,

The term a^, arises because actual instruments differ from the ideal instrument in several

significant respects. For example, the detector system may not be absolutely linear. Also,

in many instruments, the insertion of the sample into the sample beam results in a series

of extraneous reflections between the sample surfaces and the spectrometer components.

In double-beam instruments, it is very difficult to completely balance the two beams of the

spectrometer throughout the spectrum. The effect of these instrumental problems is to

shift the base line of the instrument. This will result in a change in the apparent absorption

spectrum.

Since the reference crystal does not contain a measurable concentration of oxygen, the

absorption in the reference crystal is due only to the host lattice and to the unknown

instrumental effects, so that

145
Note that ctur? although small, may be different from a^s- oll = 0-85 cm~-^ was used

as the value of the lattice absorption coefficient at 1107 cm~^. This value was measured

directly at the National Bureau of Standards from the spectrum of a 4.7-mm thick polished

float-zoned silicon crystal. However, the calculation of the absorption coefficient due to

oxygen is very insensitive to this value. For example, a change of 10% in this parameter

would result in a change of 0.25% in the calculated value of the absorption coefficient.

For convenience, we can define

e

and

— g-[(ax,+au,)j!,]

Then eq. (1) can be rewritten as

Solving for X

-f(1 - ' A^) + y^fJ-[l-i22^2]2 + 4.^2.52.2^2^^

If Xr ^ Xt, if a^r « otL, and assuming that a„r and a^, are small and varying slowly

with wavenumber, the net absorption coefficient due to interstitial oxygen can be calculated

from the peak and base line values of X by

InXp — InXh

oto = ,

where Xp and Xi, refer to X calculated using the peak and base line values of the transmittance at 1107 cm~-^, respectively.

146
3.2 Absolute Measurements

As noted above, each laboratory measuring the oxygen content of the silicon samples by an

absolute method used its own internally developed procedures. This was necessary because

there is no a priori basis for asserting that any particular procedure is fundamentally

superior to any other procedure for this particular impurity (oxygen) in this particular

matrix (silicon) at this particular concentration level (« 5 to 30 ppma). Moreover, by

using this approach, the expertise which had been developed at each of the laboratories

could be brought to bear on this project.

Table II lists five laboratories that used CPAA, two laboratories that used PAA, and one

laboratory which used IGFA. The latter two techniques require separation of the impurity

from the silicon matrix prior to the final measurement. All five CPAA laboratories used

the same nuclear reaction ( 0[^He,p) —^^^ -F), removed roughly the same amount of

surface material by etching, and used roughly the same nominal energy for the ^He ions.

However, the calibration technique varied among the laboratories, as did the number of

samples measured, and the number of times each sample was measured. The two PAA

laboratories also diflPered mainly in the calibration technique, in the number of samples

measured and in the number of repeated measurements.

4. Statistical Analysis

The calibration factor reported in section 5 was computed from the data base of IR and

absolute measurements which satisfy certain statistical criteria as outlined in this section. Isolated aberrant measurements and complete results from certain laboratories were

excluded. Estimates of precision were generated for both the IR and the absolute measurements. Also considered was whether the assumptions about the uniformity and quality of

the sample sets are supported by the experimental results.

Two performance criteria for the absolute laboratories were tested: conformance to a linear

model with a zero intercept, and goodness of fit to the linear model. These conditions ensure that a proportionality constant describes the relationship between IR absorbance

and oxygen concentration. Laboratories which failed either condition were excluded in the

computation of the conversion factor.

4.1 Infrared Data

To validate the data base that was used to compute the net absorption coefficients from

the spectral plots, the range or difference between the largest and the smallest of each

of the triplicate absorption coefficients was examined for each specimen, and for each

laboratory. Coefficients with ranges greater than 0.1 cm"-' were checked for mis-recordings,

and the data were accordingly corrected or verified as being correct. Coefficients that still showed a range greater than 0.1 cm~^ after verification" were flagged as "outHers". Twelve

measurements out of 1450 were flagged in this manner. A check on the consistency of IR

measurements from different laboratories on the same specimens identified three additional

147
measurements as outliers. All the outliers in the IR measurements were excluded from

further analyses. This data exclusion is consistent with the practices for dealing with

outliers described in ASTM E 691, Standard Practice for Conducting an Interlaboratory

Test Program to Determine the Precision of Test Methods.

The IR data base was restricted to the data obtained for test sets 2, 3, 4, 5, and 6, in order

to avoid biasing the results towards the coordinating laboratories (which also measured

test sets 1 and 7).

We can test whether the sample sets were substantially identical for the purposes of the

experiment. Based upon the measurements on test sets 1 and 7, which were measured by all the coordinating laboratories, the typical variation between test sets could be determined

for each oxygen concentration. Note that test sets 1 and 7 are geometrically the farthest

apart of any two test sets (see Figure lb). Since these test sets were measured by the

same laboratories, on the same days, the difference between the oxygen content measured

on these test sets is a measure of the homogeneity of the crystals' oxygen content. The

results, averaged over the five IR laboratories which measured both test sets, are shown in

column 3 of Table IV. Figure 2 shows the percentage difference between test set 7 and test

set 1, as measured by the IR absorption averaged over all five coordinating laboratories.

We cannot directly test how close the oxygen concentrations of the 10-mm thick slugs were

to the oxygen concentrations of the test wafers. Most of the test wafers were taken from

either side of the 10-mm slug. Thus the variation between test sets 1, 2, 3, and 4 (which were taken from one side of the slug), and test sets 5, 6, and 7 (which were generally taken

from the other side), is an indication of the maximum likely difference in oxygen content

between the wafers and the 10-mm slugs.

We show that the test sets did not change as they were circulated among the different IR

laboratories. The coordinating laboratories measured each test set circulated in their re- gion both before and after all the other laboratories in the region made their measurements.

Thus the differences in the "before" and "after" measurements can be tested for signifi- cance. Only seven of the eighty specimens given both "before" and "after" measurements

showed a significant apparent change in their oxygen concentration at the 95% probability

level. This is hardly more than would be expected to occur at random. Thus, we conclude

that the specimens were unchanged with respect to their oxygen concentrations during the

time they circulated among the IR laboratories.

The intensity of the oxygen band maximum absorbance is dependent upon the temperature of the specimen. The temperature dependence at about room temperature can be

estimated from the data presented in Figure la of Hrostowski and Kaiser's classic paper

on the infrared absorption of oxygen in silicon.^® The temperature dependence is roughly

linear near 300 K, with a slope of -0.09%/degree. Both the mean and the median temperatures in the spectrophotometer chambers in this round robin were 300 K. The range of

temperatures was from 293 to 309 K. Therefore, the warmest laboratory would be in error, due to the temperature difference, by 0.8%, and the coldest by -0.6%. However, since the

148
temperature dependence is linear, the errors introduced by laboratories above the mean

temperature, 300 K, are canceled by the errors introduced by laboratories below the mean

temperature. The temperature differences may contribute to the dispersion among the IR

laboratories, but will not introduce a bias in the value of the calibration factor.

Finally, we conclude that the test sets did not contain a significant concentration of precipitated oxygen. Test set 8 was used to test this assumption. The absorption coefficients of

all the specimens in this test set were measured at the National Bureau of Standards. The

test set was then annealed at 1300°C in nitrogen for one hour and then rapidly quenched

to room temperature. The absorption coefficients were then measured again on the same

spectrometer at NBS. The results of the before-anneal and after-anneal measurements of

the oxygen concentration are shown in Table V. These results show that the concentration

of noninterstitial oxygen in the specimens was not detectable by this test.

The precision of the infrared measurements was defined at two levels in this study. The

first is the ability of a given IR laboratory to make repeatable measurements in the short run (over three days, for most of the data obtained for this study). Table VI shows the

standard deviations reflecting the within-laboratory repeatability for each laboratory. The

second column shows the results in units of absorption coefficients (cm~^). The absorption

coefficients for the 20 crystals range from 0.8 to 4.7, and the average absorption coefficient

for the 20 crystals is roughly 3.01. A measure of the within-laboratory precision expressed

as the ratio of the standard deviation for each laboratory to the average IR absorption

coefficient is listed as a percentage in the third column of Table VI. The within-laboratory

precision ranges from 0.4% to 1.2% for all 18 IR laboratories.

The second level of precision is the ability of IR laboratories to agree with one another

when making measurements on the same set of samples, as measured by an interlaboratory standard deviation. For each oxygen concentration, these standard deviations were

pooled over the seven test sets. Table VII shows the standard deviations reflecting the

interlaboratory reproducibility. The third column of this table shows the interlaboratory

reproducibility in percentage terms over all the crystals. Systematic differences among

IR laboratories exist at the 2% to 3% level, but by using a large number of IR laboratories for this study, a representative result has been obtained. Note that the crystals with

the greatest nonuniformity did not show poorer interlaboratory reproducibility for the IR

measurements.

As a parenthetical note, we would like to observe that these results, obtained by comparing

the best efforts of many infrared laboratories around the world, have clear implications

vis-a-vis oxygen measurements at the supplier/user interface. Even under the best of

circumstances, a lack of reproducibiHty on the order of 3% may occur between two different

IR laboratories.

4.2 Absolute Data

To validate the absolute data base, two questions must be answered: which individual

data points must be excluded as outliers, and how should the overall results from each of

149
the individual absolute laboratories be evaluated? Large outliers in the absolute analysis

data can be identified by ranking the specimens in the order of their infrared absorption

coefficients, and then comparing that ranking to the order in which the specimens are ranked by each individual absolute laboratory. This procedure was used to exclude four

data points as outliers.

To evaluate the overall results of individual absolute laboratories is more difficult. The

measurement of oxygen concentration by an individual absolute laboratory should be re- lated to IR measurement by a linear function with zero intercept. Given that the conditions

of linearity and zero intercept hold, the slope of this line defines the calibration factor es- timated from the data for this particular laboratory.

Table VIII lists the results of a least squares fit to the absolute data as a function of the

IR data, averaged over all IR laboratories. The t statistics"^ in the table are used to judge

whether or not a given absolute laboratory has a nonzero intercept. A large value for

the t statistic is indicative of a nonzero intercept. Laboratories 22 and 28 show nonzero

intercepts which are significant at the 95% probability level. The intercept terms for all other laboratories are not statistically significant. Thus data from laboratories 22 and 28

are excluded from this study based upon their failure to agree with the model requirement

for a zero intercept.

The linearity of the data from each absolute laboratory was then tested. Regression analysis was carried out for each absolute laboratory with the IR measurement regarded as the

dependent variable and the absolute measurement regarded as the independent variable.

This approach takes advantage of the repetitions across IR laboratories on each specimen

and evaluates the aptness of the linear model for each absolute laboratory.

If the linear model correctly describes the data, the total mean-squared error will be

attributable to replication error, i.e. the replication across IR laboratories as pooled over

all specimens. The other possible source of error is the "lack-of-fit" error, i.e., the failure

of the average IR values per specimen to fall close to the fitted line. The statistical device

for assessing the contribution from lack of fit is an F-test.^® A large F-statistic indicates a large component for lack of fit, indicating that the linear model does not adequately

describe the relationship between IR and absolute measurements.

For the first four entries of Table VIII, only IR data on the test set measured by a given

CPAA laboratory were used in the F-test so as not to contaminate the result by inhomogeneities or differences among test sets. For the PAA and IGFA laboratories which

measured the 10-mm slugs, the combined IR data from test sets 2, 3, 4, 5, and 6 were used

in the analysis.

The F-statistics are listed in Table VIII. The F-statistic for laboratory 25 was computed

by excluding anomalous results for two specimens (taken from crystals 2102 and 2105).

Exclusion of the data from these two crystals reduced the F-statistic to 12.8. To decide

whether this value is reasonable, we compare it with the F-statistic for laboratories 21, 23,

150
and 26 using the same IR data set that we used for laboratory 25. These F-statistics are shown as the last three entries in Table VIII, and are of comparable size. For laboratories

24 and 28, the exclusion of possibly anomalous data for a few crystals failed to reduce the

F-statistic to a satisfactory level. Figure 3 is the data from laboratory 28, plotted against

the absorption coefficient averaged over all IR laboratories.

The F-statistics, which are listed in Table VIII, are extremely large for laboratories 22,

24, and 28 indicating an egregious lack of fit. Thus, for the purpose of computing the

final calibration factor, the absolute data base is restricted to measurements by CPAA

laboratories 21, 23, and 26 and PAA laboratory 25. Absolute measurements by CPAA

laboratory 22, PAA laboratory 24, and IGFA laboratory 28 are excluded because they

failed either the test for linearity or the test for zero intercept or both tests.

The data for laboratory 27 also fit the zero-intercept linear model, as shown by the t- statistic and F-statistic for that laboratory in Table VIII. The data from laboratory 27,

which measured only the JEIDA specimens, is in excellent agreement with the data on the

same specimens from laboratories 21, 23, and 26. Thus, laboratory 27 provided important

confirmation of the results of other CPAA laboratories.

5. Calctdation of the Calibration Factor

There are two issues which must be resolved before a calibration factor can be calculated

from the data in this study. The first issue is whether the calibration factor should be

calctdated by averaging the IR data over test sets 2, 3, 4, 5, and 6, or by restricting

the IR data to the same test sets as the absolute data. If the crystals are sufficiently

homogeneous, the first approach is preferable because it includes a wider variety of IR

spectrophotometers. This approach was used and includes in the uncertainty of the final

calibration factor an allowance for systematic error due to the possible lack of absolute

homogeneity in the crystals.

The second issue is how to calculate the final calibration factor. We combined the data

from the equivalent absolute laboratories (i.e., laboratories 21, 23, 25, and 26) by fitting

the data to the linear model, weighted to account for the dependence of precision on oxygen

content, and take the resulting slope as the best estimate of the conversion factor. t This

approach assumes that the measurements by all laboratories are consistent and without

bias, i.e., a zero intercept and a single slope characterize the relationship between the IR

measurements and the absolute measurements.

The least-squares fit confirms that the intercept term is nonsignificant (0.12 ppma with a standard deviation of 0.14 ppma). CPAA laboratories 21 and 23 were the only laboratories

^ In fact, because the absolute measurements and the IR measurements are subject to ran- dom error, the least-squares estimate of the slope is biased towards zero^^. However, for

this data set, the estimate of the slope is only biased by -0.005 ppma/cm~^ which is not

significant for this study.

151
which reported detectable concentrations of oxygen in the "oxygen-free" reference specimens. The average of the oxygen concentrations they reported was 0.06 ppma. This value

is very small. For example, it is almost an order of magnitude smaller than the absolute

uncertainty in the CPAA measurements reported by laboratory 26, or calculated from the

repeated measurements for laboratory 21. Thus it is consistent with the zero intercept

model. Moreover, such a small oxygen concentration in the reference specimen would only

shift the straight line parallel to itself. It would have no effect on the slope, i.e. no effect

on the calibration factor itself.

The final calibration factor is calculated from the linear model restricted to have a zero

intercept, using data from all the IR laboratories and data from the absolute laboratories

21, 23, 25, and 26, excluding data taken on the JEIDA test sets. The F statistic for this fit is 0.67, indicating the appropriateness of the restricted linear model. Figure 4 is a plot of

the absolute data points used for the determination of the final calibration factor, plotted

against the average of the IR laboratory results. The straight line in this figure shows the

fit of the data to the restricted linear model.

6. The Calibration Factor

The calibration factor for computing the interstitial oxygen content in parts per million

atomic (ppma) from a measurement of the absorption coefficient at about 1107 cm"-', calculated from the data base which includes all 18 participating IR laboratories and the four

absolute laboratories whose data fit the restricted linear model, is 6.28 ±0.18 ppma/cm~*.

Absolute laboratories with large biases or nonlinear behavior were excluded. Differences

among the remaining laboratories are reflected in the standard deviation of the slope from

the fit. The random component of the uncertainty in the conversion factor is taken to be

twice the standard deviation of the estimate in the calibration factor, or 0.08 ppma/cm"-*.

A systematic component to the overall uncertainty is due to the lack of absolute homogeneity in the silicon crystals. This factor is estimated to be 0.10 ppma/cm~^, as explained

in the next paragraph. The overall uncertainty is the sum of the random and systematic

uncertainties.

The systematic uncertainty was assessed to account for the effect of possible crystal inhomogeneity. This was a potentially important effect, even though all the laboratories

measured samples obtained from the same set of 20 crystals. The data from laboratories

21, 23, and 26 provide a means of assessing the contribution to uncertainty from inhomogeneity. For each laboratory, the conversion factor as calculated from the total IR data

base was compared to the conversion factor calculated from the IR data base restricted

to the same test set subjected to CPAA measurement. On the average, this restriction

increased the calibration factor by 0.10 ppma. This increase is due to the inhomogeneity

in the ingot, as well as to differences due to the much smaller set of IR laboratories which

were included in the restricted data set. The increase can be used as an estimate of the

effect of inhomogeneity that contributes a systematic uncertainty of ± 0.10 ppma/cm"'' to

the uncertainty in the determination. Note that this estimate is consistent with the finding

152
of differences in the oxygen content between test set 1 and test set 7 of 1% to 2% for the

majority of crystals.

It is recommended that when an oxygen content determination is based upon the use of

the caHbration factor obtained in this work, 6.28 ± 0.18 ppma/cm~^, its use be denoted by

the acronym IOC-88 (International Oxygen Coefficient 1988). The use of this calibration

factor should be limited to the range of oxygen concentrations investigated in this paper, 0

to 30 ppma. Oxide precipitation may affect the validity of the calibration factor at higher

concentrations

.

7. Acknowledgments

The authors of this work wish to express their appreciation for the successful completion of

this project to a great number of organizations and individuals. The silicon crystals used

for this study were generously supplied by Japan Silicon, Komatsu Electronic Materials,

Monsanto Electronic Materials, Osaka Titanium Corporation, Shin-Etsu Handotai, Siltec

Silicon, Toshiba Ceramics, and Wacker Chemitronic. Union Carbide supplied the sapphire

squares used in the instrumental verification procedure. The authors would like to thank

the individual researchers at the IR laboratories: Dr. D. Andrews (General Electric Co.,

Ltd.), P. Ashby (Mullards, Ltd.), Dr. M. Domenici (Dynamit Nobel Silicon), Dr. K. Graff

(Telefunken), Dr. N. Inoue (Nippon Telegraph & Telephone), Li Guang Ping (Tianjin

Electronic Materials Research Institute), Lin Yu Ping (Zhejiang University), E. Ohashi

(Komatsu Electronic Materials), Dr. B. Pajot (Ecole Normale Superieure), Dr. L. Shive

(Monsanto Electronic Materials), H. Suzuki (Hitachi), and Ye Yu Zong (Shanghai Second

Smelting Plant). We would also like to thank those responsible for making the very diffi- ctdt absolute measurements of the oxygen content of the silicon specimens: Dr. K. Bethge

(Institut fiir Kernphysik, Wolfgang Goethe Universitat, Frankfurt), Dr. E. Grallath (MaxPlanck-Institut fiir Metallforschung, Dortmund), Dr. T. Nozaki (Institute of Physical and

Chemical Research (RIKEN), Wako, Saitama), Dr. B. Schmitt (Bundesanstalt fiir Materialpriifung, Berlin), Dr. E. Schweikert (Center for Chemical Characterization and Analysis,

Texas A & M University), Dr. J. Stoquert (Centre de Recherches Nucleaires, Strasbourg),

Dr. K. Strijckmans (Institute for Nuclear Sciences, Rijksuniversiteit Gent), and Drs. D.

Wood and J. Hislop (AERE Harwell, Oxfordshire).

The cooperation of Dr. H. Marchandise and the Community Bureau of Reference (BCR)

was very important, as it enabled us to include results obtained at four additional highly

skilled laboratories on this project. We would like to give special thanks to Dr. John

Mandel, statistician for the National Measurement Laboratory of the National Institute of

Standards and Technology, for his contributions to the analysis of the data base.

153
References

1. W. Kaiser and P.H. Keck, J. Appl. Phys. 28, 882 (1957).

2. W. M. Bullis, M. Watanabe, A. Baghdadi, Li Yue-zhen, R.I. Scace, R.W. Series, and

P. Stallhofer, in Semiconductor Silicon 1986, H.R. HufF, T. Abe, and B. Kolbesen,

editors, The Electrochemical Society (Pennington, New Jersey, 1986), p. 166.

3. M.L Iglitsin, G.P. Kekelidze, and G.V. Lazareva, Soviet Physics-Solid State 6, 2508

(1965).

4. G.I Alexandrova, A.M. Demidov, G.A. Kotel'nikov, G.P. Pleshakova, G.V. Suhov,

D.Y. Choporov, and G.I. Shmanenkova, Atomnaya Energiya 23, 106 (1967).

5. H.L. Rook and E.A. Schweikert, Anal Chem. 41, 958 (1969).

6. C.K. Kim, Radiochem. Radioanal. Lett. 2, 53 (1969).

7. J.A. Baker, Solid State Electronics 13, 1431 (1970).

8. C. Gross, G. Gaetano, T.N. Tucker, and J.A. Baker, This Journal 119, 7 (1972).

9. Y. Yatsurugi, N. Akiyama, Y. Endo, and T. Nozaki, This Journal 120, 975 (1973).

10. K. Graff, E. Grallath, S. Ades, G. Goldbach, and T. Tolg, Solid State Electronics

16, 887 (1973).

11. H. He, Y. Li, G. Xhao, R. Yan, Q. Lu, and M. Qi, Talanta 30, 761 (1983); Li Yuezhen and Wang Qimin, Review of Progress in Quantitative Nondestructive Evaluation, Vol. 5, 957 (1986).

12. T. lizuka, S. Takasu, M. Tajima, T. Arai, T. Nozaki, N. Inoue, and M. Watanabe,

Defects in Silicon, ECS Proceedings Vol. 83-9, p. 265 (1983); , This Journal

132, 1707 (1985).

13. H.J. Rath, P. Stallhofer, D. Huber, and B.F. Schmitt, J. Electrochem. Soc. 131,

1920 (1984).

14. K.G. Barraclough, R. W. Series, J.S. Hislop, and D.A. Wood, This Journal 133,

187 (1986).

15. J.L. Regolini, J. P. Stoquert, C. Ganter, and P. Siffert, This Journal 133, no. 10,

2165 (1986).

16. ASTM Standard Test Method F 121-79 for Interstitial Atomic Oxygen Content of

Silicon hy Infrared Absorption, 1979 Annual Book of ASTM Standards, Part 43.

17. DIN Standard 50 438/1, Determination of Impurity Content in Silicon by Infrared

Absorption: Oxygen, Beuth Verlag GmbH, Burggrafenstrasse 4-10, D-1000 Berlin

30, Federal Republic of Germany.

18. ASTM Method F 121-83, Standard Test Method for Interstitial Atomic Oxygen

Content of Silicon by Infrared Absorption, 1987 Annual Book of ASTM Standards,

154
Vol. 10.05.

19. T. lizuka, private communication.

20. National Institute of Standards and Technology Special Publication 400-82 (July

1989), Semiconductor Measurement Technology: Data, Procedures, and Statistical

Analyses of the Interlaboratory Determination of the Calibration Factor for the

Measurement of the Interstitial Oxygen Content of Silicon by Infrared Absorption,

edited by A. Baghdadi, R.I. Scace, and E.J. Walters.

21. W.K. Gladden and A. Baghdadi, in Emerging Semiconductor Technology, D.C.

Gupta and P.H. Langer, editors (American Society for Testing and Materials, Philadelphia, Pennsylvania, 1987), p. 353.

22. N. Inoue, T. Arai, T. Nozaki, K. Endo, and K. Mizuma, ibid, p. 365.

23. N.R. Draper and H. Smith, Applied Regression Analysis, Second Edition (John

Wiley & Sons, New York, N.Y., 1981), pp. 1-69.

24. ASTM Standard Practices F 120, Infrared Absorption Analysis of Impurities in

Single Crystal Semiconductor Materials, 1987 Annual ASTM Book of Standards,

Vol. 10.05.

25. ASTM Standard Practice E 691, Conducting an Interlaboratory Test Program to Determine the Precision of Test Methods, 1987 Annual ASTM Book of Standards,

Vol. 14.02.

26. H.J. Hrostowski and R.H. Kaiser, Phys. Rev. 107, 966-972 (1957).

27. N.R. Draper and H. Smith, Applied Regression Analysis, Second Edition (John

Wiley & Sons, New York, N.Y., 1981), p. 28.

28. Rid, p. 33-40.

29. See W.A. Fvdler, Measurement Error Models (John Wiley & Sons, New York, N.Y.,

1987), p. 13-27.

155
2 2 10 2 2 100 mm

Slices for infrared measurement

Slug for PAA and IGFA

Reserved for future work

Figure la: Schematic of 100-mm diameter silicon crystal showing four 2-mm thick slices

for infrared absorption and CPAA measurements, a 10-mm thick slug for PAA and IGFA

measurements, and the 100-mm wide section reserved for future work.

156
Figure lb: Diagram of 2-mm thick slice, showing test squares 1 to 4, 25 mm on a side;

identification markings (04-02-Ox); and the location of the infrared measurements (x). A

second similajr slice contedns tests squares 5 to 8.

157
3 6 9 12 15 18 21

INGOT (ARBITRARY NUMBER SEQUENCE)

Figure 2: Percentage difference in absorption coefficient between test set 7 and test set 1.

158
30

_

O

O

O>-X

o

25

20

15 -

10 -

5 -

O"

.0

O

yd

0

o

O /'

o"

o

o

/"o

0

0

1 ' \

' \ 12 ' r

5 4

ABSORPTION COEFFICIENT (CM-1)

Figure 3: Oxygen content determined by laboratory 28 plotted against the the average of

the infrared absorption coefficient for test sets 2, 3, 4, 5, and 6. The dashed line in the

figure is a least-squares fit of a second-order polynomial to the data, showing that the data

have a nonzero intercept and are not quite linear.

159
0 1 2 3 4 5

m ABSORPTION COEFFICIENT (cm~^)

(Average of test sets 2,3,4,5,6)

Figure 4: Oxygen content determined by laboratories 21, 23, 25, and 26 plotted against

the average of the infrared absorption coefficient for test sets 2, 3, 4, 5, and 6.

160
TABLE I: EXPERIMENTAL PLAN^

JEIDA SETS TEST SETSt

J-l J-2 J-3 1 2 3 4 5 6 7 TOS TOS TOS TOS

NTT NBS NBS NTT NBS NBS

KOM KOM

HIT MON WAC WAC HIT MON WAC WAC

TOS SIL TOS SIL

CPAA TFK CPAA TFK

NBS# NBS NBS

CPAA RSR RSR TOS# CPAA RSR RSR

WAC# WAC WAC

Vf TTT jVIU Li IN l3S<8l VTTTT CPAA GEC SIM SIM CPAA GEC SIM SIM

WAC# RSR DNS WAC# RSR

CPAA TOSO TEM NBSQ CPAA DNS TEM NBSQ

ZJU ENSti ZJU

SSS SSS

SIM CPAA SIM

TOSO TOS(tt NBSQ NBSQ NBSQ

X 10-mm slugs cut ftom ingots were used for destructive PAA measurements in UK and Germany, as well as for IGFA in Germany

t Test set 8 was reserved for high-temperature anneal and remeasure for total oxygen

# Transit only, no measurements

Q Home location

t] ENS measured only specimens from ingots 2101-05 to 2109-05

Participating laboratories (Regionzd coordinators in boldface followed by standards organization):

HIT Hitachi

KOM Komatsu Electronic Metals

NTT Nippon Telegraph and Telephone

TOS Toshiba Ceramics, JEIDA

NBS National Bureau of Standards (U.S.), ASTM

MON Monsanto

SIL Siltec Silicon

TFK Telefunken

WAC Wacker Chemitronic, DIN

DNS Dynamit Nobel Silicon

ENS Ecole Normale Superieure, Universite Paris VII, France

GEC General Electric Company, Ltd.

RSR Royal Signals and Rade^ Establishment (U.K.)

MUL MuUards, Ltd.

SIM Shanghai Institute of Metallurgy (Academia Sinica)

SSS Shanghai Second Smelting Plant

TEM Tianjin Electronic Materials Research Institute

ZJU Zhejiang University

161
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fel I*i 00* oj" oo"

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162
H

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<;a!

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CD<

Calibration Factor

(ppmacm) (c)

5.5

(e)

12.0±1.4 (f) 5.8±0.5 7.6±1.5 9.63±2.29 7.7±0.4 6.0

(i)

4.9±0.3 6.2±0.1 6.2±0.4 6.06±0.05 6.0±0.4 5.2±0.6 6.0±0.4

Range

of

Absorp

Coef

(cm"')

or

Oxygen

Cone

(ppma)

(c)

0.2-6.4 0.5-12.4 5-

10

4.8-9.4 6-

22

0.3-3.5 0.6-200.1-1.5 2-4 0.3-2.8 0.1-3.3 0.8-3.5 2-4.6 0.8-3.8 2-4

Sensitivity Limit (Chem, ppma)

, ., , <— . , CS—i ^ " ^ ta . . —^ O--' OO a ^

Stated

Error

(Chemical) (b) 6? ^ 6? T,. +12- g -H VI " -1 3 -H ^ V V -H V

Stated

Error

(Infrared)

No.

of

Data

Pts

Chem.

Analysis Method (a) VFA LD CPAA CPAA CPAA IGA CPAA CPAA VFA IGA CPAA CPAA PAA PAA CPAA

Year l/5<0<D<0«Ot^t— t^h-OOaOOOQOOOQO

Author

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&

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Baker Gross

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Barraclough

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Regolini

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163
TABLE IV: PERCENTAGE DIFFERENCE IN THE IR ABSORPTION COEFFICIENT

BETWEEN TEST SET 7 AND TEST SET 1,

AS MEASURED BY THE COORDINATING LABORATORIES

Oxygen Ingot Average 11 13 16 17 19

Content

(ppma)

4.99 101 0.618 -1.905 A A n 0.835 0.614 1.671 1.874

8.76 2101 0.527 1.500 0.874 0.388 -0.2.59

A ^ AA 0.133

11.88 2102 1.113 3.508 2.363 0.724 -2.088 1.059

13.36 201 0.910 0.188 4 A<4 n 1.012 A A A 0.850 1.437 1.062

13.90 1102 -0.507 -0.739 0.345 -0.052 -1.370 -0.720

14.52 2103 2.436 1.534 1.828 2.619 4.768 1.431

17.50 2104 3.719 3.434 3.959 3.823 3.392 3.989

17.90 1101 0.433 -0.788 1.185 0.240 0.988 0.538

19.20 2105 -0.348 -0.880 0.040 -0.033 0.199 -1.067

19.45 401 -0.560 -0.015 -0.556 -1.053 -0.614 -0.560

20.47 301 1.686 1.606 2.174 1.037 2.618 0.994

21.61 1204 0.638 1.433 0.933 1.286 -1.359 0.897

21.66 2106 0.093 -0.272 0.564 0.613 -0.339 -0.099

21.98 1203 -0.854 -1.062 -0.584 -0.672 -0.860 -1.094

22.40 1201 0.587 0.725 0.482 0.316 1.103 0.307

23.05 501 -0.107 0.464 0.183 -0.039 -0.875 -0.269

23.59 2107 0.598 1.103 0.768 0.130 1.238 -0.251

25.23 1202 0.143 0.439 0.593 0.078 -0.608 0.213

27.95 2108 0.304 -0.531 0.479 0.492 1.760 -0.678

28.28 2109 -1.161 -0.267 -1.327 -2.809 -0.264 -1.138

164
TABLE V: THE EFFECT OF HIGH-TEMPERATURE ANNEALING ON THE

MEASURED INFRARED ABSORPTION COEFFICIENT

(at 1107 cm-^)

ID Postl Post2 Posts Prel Pre2 Pre3 Post/

d Pre

210108 1.4288 1.3735 1.3800 1.3618 1.4041 1.3854 1.0075

210208 1.8270 1.9310 1.8641 1.8239 1.8743 1.9124 1.0021

210308 2.2072 2.2459 2.3120 2.2040 2.2117 2.2786 1.0106

210408 2.7782 2.7650 2.6718 2.7048 2.7249 2.7210 1.0079

210508 3.1787 3.1737 3.2144 3.1011 3.1281 3.1465 1.0204

210608 3.3974 3.4150 3.4091 3.4086 3.4485 3.4691 0.9899

210708 3.8922 3.9206 3.9050 3.8508 3.8043 3.8430 1.0191

210808 4.2430 4.2942 4.2632 4.2793 4.2680 4.3030 0.9961

210908 4.7098 4.7381 4.6664 4.7109 4.8121 4.8043 0.9851

110108 2.9882 2.9927 2.8955 2.9433 2.9576 2.9395 1.0041

110208 2.2115 2.2595 2.2017 2.2631 2.2568 2.2612 0.9840

7064 ^ 7568 3 6809 3 6982 3 7235 1 0106

120208 3.9940 3.9807 4.0064 3.9156 3.9411 3.8977 1.0193

120308 3.4531 3.5191 3.5380 3.5020 3.5213 3.5392 0.9950

120408 3.3934 3.3932 3.3706 3.3172 3.3727 3.4142 1.0053

10108 0.7940 0.7705 0.7683 0.7884 0.7911 0.8026 0.9793

20108 2.0787 2.0645 2.1321 2.1144 2.1180 2.1198 0.9879

30108 3.0921 3.0956 3.1082 3.0391 3.0527 3.0751 1.0141

40108 2.9476 2.9455 2.9308 2.9089 2.9656 2.9514 0.9998

50108 3.5803 3.5680 3.6012 3.4802 3.5131 3.5449 1.0200

(The disagreement between the post- and pre-anneal absorption coefficients ranges from

-2% to +2%, with an overall average of 0.3%).

165
TABLE VI: POOLED STANDARD DEVIATIONS REFLECTING THE WITHIN-LABORATORY

REPEATABILITY OF THE MEASUREMENT OF THE IR ABSORPTION COEFFICIENT

Laboratory Standard Deviation Ratio of S.D. Degrees of

to Average

(%)

1 0.03265 1.1 52

2 0.02552 0.8 54

3 0.01313 0.4 12

4 0.01824 0.6 54

5 0.02736 0.9 26

6 0.02942 1.0 54

8 0.03642 1.2 54

9 0.02761 0.9 54

10 0.02352 0.8 54

11 0.02225 0.7 184

12 0.03144 1.0 52

13 0.01809 0.6 188

15 0.01552 0.5 54

16 0.01518 0.5 188

17 0.03446 1.1 176

18 0.02802 0.9 48

19 0.01293 0.4 184

31 0.01749 0.6 9

166
TABLE VII: TOTAL STANDARD DEVIATIONS REFLECTING DISPERSION AMONG

THE IR LABORATORIES

Crystal TotjJ Standard Deviation Degrees

of Freedom*

X Cx CCXLbclgC V

dll^1 CJX V

\^cjn )

0 0^76 2 6 21

2102 0 0543 2 9 21

2103 ^ X V/0 0559 2 4 21M X 2104 0 0fi78 2 4 21

21 O^i 0VJ.W0711 x^2 2 2 21

2106\J\J 0 0823 2 4 21«X

2107 0 0881 2 3 20

21 08 0u*x1081 vox 2 5 20

21^X OQV«7 0 1451 3 0 17X i liUi U.UDiy O 1 1 Q

1102 0.0523 2.3 19

1201 0.0905 2.4 19

1202 0.0944 2.4 19

1203 0.0866 2.4 19

1204 0.0787 2.3 20

0101 0.0255 3.1 20

0201 0.0470 2.2 20

0301 0.0760 2.4 20

0401 0.0669 2.2 19

0501 0.0858 2.4 20

Note that formulas have been adjusted for missing data and/or outliers.

167
TABLE VIII. RESULTS OF FIT OF IR DATA AS A LINEAR FUNCTION

OF THE ABSOLUTE DATA FOR EACH ABSOLUTE LABORATORY

Absolute Absolute IR Intercept t Statistic F Statistic

Laboratory Test Set Test Set

21 2 2 -0.037 -0.27 1.9

22 3 3 2.391 3.32« 155.3

23 4 4 -0.151 -0.23 5.9

26 4 4 0.239 1.50 1.6

2r 10-mm slug 2,3,4,5,6 -0.268 -0.26 285.9

25* 10-mm slug 2,3,4,5,6 -0.009 -0.08 12.8

2r lO-mm slug 2,3,4,5,6 -1.302 -2.95" 164.6

27 J-1 J-1 -0.037 -0.21 3.9

21 ' --^^^ 2 2,3,4,5,6 -0.022 -0.15 15.9

- ^23. ^ 4 2,3,4,5,6 -0.161 -0.25 70.6

2r 4 2,3,4,5,6 0.370 1.86 26.0

Values of the t statistic which show a significant nonzero intercept at the 95% proba

bility level.

Crystals 2102 and 2105 were excluded from this analysis.

Crystal 1102 was excluded from this analysis.

168
NBS-n4A iREv. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions]

1. PUBLICATION OR

REPORT NO.

NIST/SP-400/82

2. Performing Organ. Report NoJ 3. Publication Date July 1989

4. TITLE AND SUBTITLE

Semiconductor Measurement Technology: Database for and Statistical Analysis of the

Interl aboratory Determination of the Conversion Coefficient for the Measurement of

the Interstitial Oxygen Content of Silicon by Infrared Absorption

5. AUTHOR(S)

A. Baghdad! , R. I. Scace, and E. J. Walters, editors

6. PERFORMING ORGANIZATION (If joint or other than NBS. see in struct/on s] NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

(lormerty NATIONAL BUREAU OF STANDARDS)

U.S. DEPARTMENT OF COMMERCE

GATTHERSBURG, MD 20899

7. Contract/Grant No,

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Same as Item #6

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 89-600739

I

[ Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significar^t informatior\. If document includes a si gnificant

bi bliography or literature survey, mention it here) This Special Publication contains the data collected for the worldwide, double--

round-robin determination of the conversion coefficient used to calculate the

interstitial oxygen content of silicon from infrared absorption measurements. It

also contains detailed statistical analyses of those data. A paper describing the

results of this study has been accepted for publication by the Journal of the

Electrochemical Society . It should be considered the official result of the study.

The approach taken to determine the conversion coefficient was to conduct interlaboratory round robins for both the infrared measurements and the absolute measurements. The infrared measurements were carried out at 18 laboratories in China,

Europe, Japan, and the United States, using either dispersive infrared (DIR) or Fourier transform infrared (FTIR) spectrometers. The absolute measurements were carried out at eight laboratories in Europe, Japan, and the United States, using

either charged-particle activation analysis, photon activation analysis, or inert

gas fusion analysis.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

charged-particle activation analysis; conversion coefficient; IR database; inert gas

fusion analysis; infrared spectroscopy; oxygen in silicon; photon activation analysis;

statistical analysis

13. AVAILABILITY

gXj Unlimited

I I For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

f^J^ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

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15. Price

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