MIST

PUBLICATiONS

NIST SPECIAL PUBLICATION 260-1 21

U.S. DEPARTMENT OF COMMERCE/Technology Administration

National Institute of Standards and Technology

Standard Reference Materials:

Certification of a Standard Reference Material

for the Determination of Interstitial Oxygen

Concentration in Semiconductor Silicon

by Infrared Spectrophotometry

QC

100

.U57

NO. 260-1 21

199^j

Brian G. Rennex
Jhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . . . needed to improve product quality, to modernize

manufacturing processes, to ensure product reliability . . . and to facilitate rapid commercialization ... of

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'At Boulder, CO 80303. ^Some elements at Boulder, CO 80303.
NIST Special Publication 260-121

Standard Reference Materials:

Certification of a Standard Reference Material

for the Determination of Interstitial Oxygen

Concentration in Semiconductor Silicon

by Infrared Spectrophotometry

Brian G. Rennex

Semiconductor Electronics Division

Electronics and Electrical Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899-0001

U.S. DEPARTMENT OF COMMERCE, Ronald H. Brown, Secretary

TECHNOLOGY ADMINISTRATION, Mary L Good, Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, Arati Prabhakar, Director

Issued August 1994
National Institute of Standards and Technology Special Publication 260-121

Natl. Inst. Stand. Technol. Spec. Publ. 260-121, 81 pages (Aug. 1994)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1994

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

Standard Reference Materials (SRMs) as defined by the National Institute of

Standards and Technology (NIST) are well-characterized materials, produced in

quantity and certified for one or more physical or chemical properties. They are used to assure the accuracy and compatibility of measurements throughout the

Nation. SRMs are widely used as primary standards in many diverse fields in

science, industry, and technology, both within the United States and throughout

the world. They are also used extensively in the fields of environmental and

clinical analysis. In many applications, traceability of quality control and

measurement processes to the national measurement system is carried out through

the mechanism and use of SRMs. For many of the Nation's scientists and

technologists, it is therefore of more than passing interest to know the details

of the measurements made at NIST in arriving at the certified values of the SRMs

produced. The NIST Special Publication 260 Series is a series of papers reserved

for this purpose.

The 260 Series is dedicated to the dissemination of information on different

phases of the preparation, measurement, certification, and use of NIST SRMs. In

general, much more detail will be found in these papers than is generally

allowed, or desirable, in scientific journal articles. This enables the user to assess the validity and accuracy of the measurement processes employed, to judge

the statistical analysis, and to learn details of techniques and methods utilized

for work entailing greatest care and accuracy. These papers also should provide

sufficient additional information so SRMs can be utilized in new applications in

diverse fields not foreseen at the time the SRM was originally issued.

Inquiries concerning the technical content of this paper should be directed to

the author(s). Other questions concerned with the availability, delivery, price,

and so forth, will receive prompt attention from:

Standard Reference Materials Program

Bldg. 202, Rm. 204

National Institute of Standards and Technology

Gaithersburg, MD 20899

Telephone: (301) 975-6776

FAX: (301) 948-3730

Thomas E. Gills, Chief

Standard Reference Materials Program

iii
ACKNOWLEDGMENTS

The following contributions to this report are gratefully acknowledged: A. Baghdadi, R. I. Scace, and

E. J. Walters for their preparation of the report for the Grand Round Robin which laid the ground-work

for this report; A. Baghdadi for early contributions to the test methods for measurement of oxygen in silicon and for envisioning and beginning the current work; J. J. Filliben of the NIST Statistical Engineering Division for review of the statistical treatment of data; D. R. Ricks and J. M. Thomas of

the NIST Semiconductor Electronics Division for specimen preparation; the Materials Technology Group

of the Semiconductor Electronics Division for support of the SRM development; N. M. Trahey and

T. E. Gills of the NIST Office of Standards Reference Materials for funding support; J. P. Ehrstein for constant feedback and careful review of the various ideas of value to the study; and J. C. Geist for many

insightful remarks on experimental aspects of the project.

iv
OTHER NIST PUBLICATIONS IN THIS SERIES

Trahey, N.M., ed., NIST Standard Reference Materials

Catalog 1992-93, NIST Spec. Publ. 260 (February

1992). SN003-003-03 146-1*

Michaelis, R.E., and Wyman, L.L., Standard Reference

Materials: Preparation of White Cast Iron Spectrochemical Standards, NBS Misc. Publ. 260-1 (June

1964). COM74-11061**

Michaelis, R.E., Wyman, L.L., and Flitsch, R.,

Standard Reference Materials: Preparation of NBS

Copper-Base Spectrochemical Standards, NBS Misc.

Publ. 260-2 (October 1964). COM74-1 1063**

Michaelis, R.E., Yakowitz, H., and Moore, G.A.,

Standard Reference Materials: Metallographic Characterization of an NBS Spectrometric Low-Alloy

Steel Standard, NBS Misc. Publ. 260-3 (October

1964) . COM74-11060**

Hague, J.L., Mears, T.W., and Michaelis, R.E.,

Standard Reference Materials: Sources of

Information, Publ. 260-4 (February 1965). COM74-

11059**

Alvarez, R., and Flitsch, R., Standard Reference

Materials: Accuracy of Solution X-Ray Spectrometric

Analysis of Copper-Base Alloys, NBS Misc. Publ. 260-5 (February 1965). PB 168068**

Shultz, J.I., Standard Reference Materials: Methods for the Chemical Analysis of White Cast Iron Standards,

NBS Misc. Publ. 260-6 (July 1965). COM74-

11068**

Bell, R.K., Standard Reference Materials: Methods for the Chemical Analysis of NBS Copper-Base Spectrochemical Standards, NBS Misc. Publ. 260-7 (October

1965) . COM74-11067**

Richmond, M.S., Standard Reference Materials: Analysis

of Uranium Concentrates at the National Bureau of

Standards, NBS Misc. Publ. 260-8 (December 1965).

COM74-11066**

Anspach, S.C., Cavallo, L.M., Garfinkel, S.B., et al.. Standard Reference Materials: Half Lives of Materials Used in the Preparation of Standard Reference

Materials of Nineteen Radioactive Nuclides Issued by

the National Bureau of Standards, NBS Misc. Publ. 260-9 (November 1965). COM74-1 1065**

Yakowitz, H., Vieth, D.L., Heinrich, K.F.J. , et al., Standard Reference Materials: Homogeneity Characterization of NBS Spectrometric Standards II: Cartridge Brass and Low-Alloy Steel, NBS Misc.

Publ. 260-10 (December 1965). COM74-1 1064**

Napolitano, A., and Hawkins, E.G., Standard Reference

Materials: Viscosity of Standard Lead-Silica Glass,

NBS Misc. Publ. 260-1 1** (November 1966).

Yakowitz, H., Vieth, D.L., and Michaelis, R.E.,

Standard Reference Materials: Homogeneity Characterization of NBS Spectrometric Standards III: White

Cast Iron and Stainless Steel Powder Compact, NBS

Misc. Publ. 260-12 (September 1966).

Spijkerman, J.J., Snediker, D.K., Ruegg, F.C., et al., Standard Reference Materials: Mossbauer

Spectroscopy Standard for the Chemical Shift of Iron Compounds, NBS Misc. Publ. 260-13** (July 1967).

Menis, O., and Sterling, J.T., Standard Reference

Materials: Determination of Oxygen in Ferrous Materials (SRMs 1090, 1091, 1092), NBS Misc. Publ. 260-14** (September 1966).

Passaglia, E. and Shouse, P.J., Standard Reference

Materials: Recommended Method of Use of Standard

Ligh-Sensitive Paper for Calibrating Carbon Arcs Used in Testing Testiles for Colorfastness to Light,

NBS Spec. Publ. 260-15 (July 1967). Superseded by

SP 260-41.

Yakowitz, H., Michaelis, R.E., and Vieth, D.L.,

Standard Reference Materials: Homogeneity Characterization of NBS Spectrometric Standards IV: Preparation and Microprobe Characterization of W-20%

Mo Alloy Fabricated by Powder Metallurgical

Methods, NBS Spec. Publ. 260-16 (January 1969).

COM74-11062**

Catanzaro, E.J., Champion, C.E., Gamer, E.L., et al.. Standard Reference Materials: Boric Acid; Isotopic,

and Assay Standard Reference Materials, NBS Spec.

Publ. 260-17 (February 1970). PB 189457**

Geller, S.B., Mantek, P. A., and Cleveland, N.G.,

Calibration of NBS Secondary Standards Magnetic

Tape Computer Amplitude Reference Amplitude

Measurement "Process A", NBS Spec. Publ. 260-18

(November 1969). Superseded by SP 260-29.

Paule, R.C., and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements

on the Vapor Pressure of Gold (Certification of SRM

745). NBS Spec. Publ. 260-19 (January 1970).

PB 190071**

260-20: Unassigned

Paule, R.C., and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements

on the Vapor Pressures of Cadmium and Silver, NBS

Spec. Publ. 260-21 (January 1971). COM74-1 1359**

Yakowitz, H., Fiori, C.E., and Michaelis, R.E.,

Standard Reference Materials: Homogeneity Characterization of Fe-3 Si Alloy, NBS Spec. Publ. 260-22

(February 1971). COM74-1 1357**

V
Napolitano, A., and Hawkins, E.G., Standard Reference

Materials: Viscosity of a Standard Borosilicate Glass,

NBS Spec. Publ. 260-23 (December 1970).

COM71-00157**

Sappenfield, K.M., Marinenko, G., and Hague, J.L., Standard Reference Materials: Comparison of Redox

Standards, NBS Spec.. Publ. 260-24 (January 1972).

COM72-50058**

Hicho, G.E., Yakowitz, H., Rasberry, S.D., et al.. Standard Reference Materials: A Standard Reference

Material Containing Nominally Four Percent

Austenite, NBS Spec. Publ. 260-25 (February 1971).

COM74-11356**

Martin, J.F., Standard Reference Materials: NBS-U.S.

Steel Corp. Joint Program for Determining Oxygen

and Nitrogen in Steel, NBS Spec. Publ. 260-26

(February 1971). PB 81176620**

Gamer, E.L., Machlan, L.A., and Shields, W.R.,

Standard Reference Materials: Uranium Isotopic

Standard Reference Materials, NBS Spec. Publ. 260-27 (April 1971). COM74-1 1358**

Heinrich, K.F.J. , Myklebust, R.L., Rasberry, S.D., et

al., Standard Reference Materials: Preparation and

Evaluation of SRMs 481 and 482 Gold-Silver and

Gold-Copper Alloys for Microanalysis, NBS Spec.

Publ. 260-28 (August 1971). COM7I-50365**

Geller, S.B., Standard Reference Materials: Calibration

of NBS Secondary Standard Magnetic Tape (Computer Amplitude Reference) Using the Reference Tape

Amplitude Measurement "Process A-Model 2," NBS

Spec. Publ. 260-29 (June 1971). COM71-50282**

Supersedes Measurement System in SP 260-18.

Gorozhanina, R.S., Freedman, A.Y., and Shaievitch,

A.B., (translated by M.C. Selby), Standard

Reference Materials: Standard Samples Issued in the USSR (A Translation from the Russian), NBS Spec.

Publ. 260-30 (June 1971). COM71-50283**

Hust, J.G., and Sparks, L.L., Standard Reference

Materials: Thermal Conductivity of Electrolytic Iron SRM 734 from 4 to 300 K, NBS Spec. Publ. 260-31

(November 1971). COM71-50563**

Mavrodineanu, R., and Lazar, J.W., Standard Reference

Materials: Standard Quartz Cuvettes for High Accuracy Spectrophotometry, NBS Spec. Publ. 260-32

(December 1973). COM74-50018**

Wagner, H.L., Standard Reference Materials: Comparison of Original and Supplemental SRM 705, Narrow

Molecular Weight Distribution Polystyrene, NBS

Spec. Publ. 260-33 (May 1972). COM72-50526**

Sparks, L.L., and Hust, J.G., Standard Reference

Material: Thermoelectric Voltage of Silver-28 Atomic

Percent Gold Thermocouple Wire, SRM 733, Verses Common Thermocouple Materials (Between Liquid

Helium and Ice Fixed Points), NBS Spec. Publ. 260-

34 (April 1972). COM72-50371**

Sparks, L.L., and Hust, J.G., Standard Reference

Materials: Thermal Conductivity of Austenitic

Stainless Steel, SRM 735 from 5 to 280 K, NBS

Spec. Publ. 260-35 (April 1972). COM72-50368**

Cali, J. P., Mandel, J., Moore, L.J., et al.. Standard

Reference Materials: A Reference Method for the Determination of Calcium in Serum NBS SRM 915,

NBS Spec. Publ. 260-36 (May 1972).

COM72-50527**

Shultz, J.I., Bell, R.K., Rains, T.C., et al.. Standard

Reference Materials: Methods of Analysis of NBS

Clay Standards, NBS Spec. Publ. 260-37 (June

1972). COM72-50692**

Richard, J.C., and Hsia, J.J., Standard Reference

Materials: Preparation and Calibration of Standards

of Spectral Specular Reflectance, NBS Spec. Publ. 260-38 (May 1972). COM72-50528**

Clark, A.F., Denson, V.A., Hust, J.G., et al.. Standard

Reference Materials: The Eddy Current Decay

Method for Resistivity Characterization of

High-Purity Metals, NBS Spec. Publ. 260-39 (May

1972). COM72-50529**

McAdie, H.G., Gam, P.D., and Menis, O., Standard

Reference Materials: Selection of Differential Thermal Analysis Temperature Standards Through a Cooperative Study (SRMs 758, 759, 760), NBS Spec.

Publ. 260-40 (August 1972) COM72-50776**

Wood. L.A., and Shouse, P.J., Standard Reference

Materials: Use of Standard Light-Sensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for Colorfastness to Light, NBS Spec. Publ. 260-41

(August 1972). COM72-50775**

Wagner, H.L., and Verdier, P.H., eds.. Standard

Reference Materials: The Characterization of Linear

Polyethylene, SRM 1475, NBS Spec. Publ. 260-42

(September 1972). COM72-50944**

Yakowitz, H., Ruff, A.W., and Michaelis, R.E.,

Standard Reference Materials: Preparation and

Homogeneity Characterization of an Austenitic

Iron-Chromium-Nickel Alloy, NBS Spec. Publ. 260-43 (November 1972). COM73-50760**

Schooley, J.F., Soulen, R.J., Jr., and Evans, G.A., Jr., Standard Reference Materials: Preparation and Use of

Superconductive Fixed Point Devices, SRM 767,

NBS Spec. Publ. 260-44 (December 1972).

COM73-50037**

vi
Greifer, B., Maienthal, E.J., Rains, T.C., et al., Standard Reference Materials: Development of NBS

SRM 1579 Powdered Lead-Based Paint, NBS Spec.

Publ. 260-45 (March 1973). COM73-50226**

Hust, J.G., and Giarratano, P.J., Standard Reference

Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials: Austenitic

Stainless Steel, SRMs 735 and 798, from 4 to 1200

K, NBS Spec. Publ. 260-46 (March 1975).

COM75-10339**

Hust, J.G., Standard Reference Materials: Electrical Resistivity of Electrolytic Iron, SRM 797, and

Austenitic Stainless Steel, SRM 798, from 5 to 280

K, NBS Spec. Publ. 260-47 (February 1974).

COM74-50176**

Mangum, B.W., and Wise, J. A., Standard Reference

Materials: Description and Use of Precision Thermometers for the Clinical Laboratory, SRM 933 and

SRM 934, NBS Spec. Publ. 260-48 (May 1974).

Superseded by NIST Spec. Publ. 260-i 13. COM74-

50533**

Carpenter, B.S., and Reimer, G.M., Standard Reference

Materials: Calibrated Glass Standards for Fission

Track Use, NBS Spec. Publ. 260-49 (November

1974). COM74-51185**

Hust, J.G., and Giarratano, P.J., Standard Reference

Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials: Electrolytic Iron, SRMs 734 and 797 from 4 to 1000 K,

NBS Spec. Publ. 260-50 (June 1975).

COM75-10698**

Mavrodineanu, R., and Baldwin, J.R., Standard

Reference Materials: Glass Filters As a SRM for Spectrophotometry-Selection, Preparation,

Certification, and Use-SRM 930 NBS Spec. Publ. 260-51 (November 1975). COM75-10339**

Hust, J.G., and Giarratano, P.J., Standard Reference

Materials: Thermal Conductivity and Electrical Resistivity SRMs 730 and 799, from 4 to 3000 K,

NBS Spec. Publ. 260-52 (September 1975).

COM75-11193**

Durst, R.A., Standard Reference Materials: Standardization of pH Measurements, NBS Spec. Publ. 260-

53 (December 1978). Superseded by SP 260-53 Rev. 1988 Edition. PB88217427**

Burke, R.W., and Mavrodineanu, R., Standard Reference

Materials: Certification and Use of Acidic Potassium

Dichromate Solutions as an Ultraviolet Absorbance

Standard, NBS Spec. Publ. 260-54 (August 1977).

PB272168**

Ditmars, D.A., Cezairliyan, A., Ishihara, S., et al., Standard Reference Materials: Enthalpy and Heat

Capacity; Molybdenum SRM 781, from 273 to 2800

K, NBS Spec. Publ. 260-55 (September 1977).

PB272127**

Powell, R.L., Sparks, L.L., and Hust, J.G., Standard

Reference Materials: Standard Thermocouple

Material, Pt-67: SRM 1967, NBS Spec. Publ. 260-56

(February 1978). PB277172**

Cali, J. P., and Plebanski, T., Standard Reference

Materials: Guide to United States Reference

Materials, NBS Spec. Publ. 260-57 (February 1978).

PB277173**

Barnes, J.D., and Martin, G.M., Standard Reference

Materials: Polyester Film for Oxygen Gas Transmission Measurements SRM 1470, NBS Spec. Publ. 260-58 (June 1979). PB297098**

Chang, T., and Kahn, A.H., Standard Reference

Materials: Electron Paramagnetic Resonance Intensity Standard: SRM 2601; Description and Use, NBS

Spec. Publ. 260-59 (August 1978). PB292097**

Velapoldi, R.A., Paule, R.C., Schaffer, R., et al., Standard Reference Materials: A Reference Method

for the Determination of Sodium in Serum, NBS

Spec. Publ. 260-60 (August 1978). PB286944**

Verdier, P.H., and Wagner, H.L., Standard Reference

Materials: The Characterization of Linear Polyethylene (SRMs 1482, 1483, 1484), NBS Spec. Publ. 260-61 (December 1978). PB289899**

Soulen, R.J., and Dove, R.B., Standard Reference

Materials: Temperature Reference Standard for Use

Below 0.5 K (SRM 768), NBS Spec. Publ. 260-62

(April 1979). PB294245**

Velapoldi, R.A., Paule, R.C., Schaffer, R., et al.. Standard Reference Materials: A Reference Method

for the Determination of Potassium in Serum, NBS

Spec. Publ. 260-63 (May 1979). PB297207**

Velapoldi, R.A., and Mielenz, K.D., Standard Reference

Materials: A Fluorescence SRM Quinine Sulfate Dihydrate (SRM 936), NBS Spec. Publ. 260-64

(January 1980). PB80 132046**

Marinenko, R.B., Heinrich, K.F.J., and Ruegg, F.C.,

Standard Reference Materials: Micro-Homogeneity

Studies of NBS SRM, NBS Research Materials, and

Other Related Samples, NBS Spec. Publ. 260-65

(September 1979). PB300461**

Venable, W.H., Jr., and Eckerle, K.L., Standard

Reference Materials: Didymium Glass Filters for Calibrating the Wavelength Scale of Spectrophotometers (SRMs 2009, 2010, 2013, 2014). NBS

Spec. Publ. 260-66 (October 1979). PB80104961**
Velapoldi, R.A., Paule, R.C., Schaffer, R., et al., Standard Reference Materials: A Reference Method

for the Determination of Chloride in Serum, NBS

Spec. Publ. 260-67 (November 1979). PB80110117**

Mavrodineanu, R., and Baldwin, J.R., Standard

Reference Materials: Metal-On-Quartz Filters as a SRM for Spectrophotometry SRM 2031, NBS Spec.

Publ. 260-68 (April 1980). PB80197486**

Velapoldi, R.A., Paule, R.C., Schaffer, R., et al.. Standard Reference Materials: A Reference Method

for the Determination of Lithium in Serum, NBS

Spec. Publ. 260-69 (July 1980). PB80209117**

Marinenko, R.B., Biancaniello, F., Boyer, P. A., et al., Standard Reference Materials: Preparation and Charactenzation of an Iron-Chromium-Nickel Alloy for Microanalysis: SRM 479a, NBS Spec. Publ. 260-70

(May 1981). SN003-003-02328-1*

Seward, R.W., and Mavrodineanu, R., Standard

Reference Materials: Summary of the Clinical Laboratory Standards Issued by the National Bureau

of Standards, NBS Spec. Publ. 260-71 (November

1981). PB82135161**

Reeder, D.J., Coxon, B., Enagonio, D., et al.. Standard

Reference Materials: SRM 900, Anti-epilepsy Drug

Level Assay Standard, NBS Spec. Publ. 260-72 (June

1981). PB81220758

Interrante, C.G., and Hicho, G.E., Standard Reference

Materials: A Standard Reference Material Containing

Nominally Fifteen Percent Austenite (SRM 486),

NBS Spec. Publ. 260-73 (January 1982).

PB82215559**

Marinenko, R.B., Standard Reference Materials: Pre- paration and Characterization of K-411 and K-412

Mineral Glasses for Microanalysis: SRM 470, NBS

Spec. Publ. 260-74 (April 1982). PB82221300**

Weidner, V.R., and Hsia, J.J., Standard Reference

Materials: Preparation and Calibration of First Surface Aluminum Mirror Specular Reflectance

Standards (SRM 2003a), NBS Spec. Publ. 260-75

(May 1982). PB82221367**

Hicho, G.E., and Eaton, E.E., Standard Reference

Materials: A Standard Reference Material Containing

Nominally Five Percent Austenite (SRM 485a), NBS

Spec. Publ. 260-76 (August 1982). PB83 115568**

Furukawa, G.T., Riddle, J.L., Bigge, W.G., et al.. Standard Reference Materials: Application of Some

Metal SRMs as Thermometric Fixed Points, NBS

Spec. Publ. 260-77 (August 1982). PB831 17325**

Hicho, G.E., and Eaton, E.E., Standard Reference

Materials: Standard Reference Material Containing

Nominally Thirty Percent Austenite (SRM 487), NBS

Spec. Publ. 260-78 (September 1982). PB83 1 15576**

Richmond, J.C., Hsia, J.J., Weidner, V.R., et al.. Standard Reference Materials: Second Surface Mirror

Standards of Specular Spectral Reflectance (SRMs

2023, 2024, 2025), NBS Spec. Publ. 260-79 (October

1982). PB84203447**

Schaffer, R., Mandel, J., Sun, T., et al., Standard

Reference Materials: Evaluation by an ID/MS

Method of the AACC Reference Method for Serum

Glucose, NBS Spec. Publ. 260-80 (October 1982).

PB84216894**

Burke, R.W., and Mavrodineanu, R., Standard Reference

Materials: Accuracy in Analytical Spectrophotometry, NBS Spec. Publ. 260-81 (April 1983).

PB83214536**

Weidner, V.R., Standard Reference Materials: WTiite

Opal Glass Diffuse Spectral Reflectance Standards for

the Visible Spectrum (SRMs 2015 and 2016), NBS

Spec. Publ. 260-82 (April 1983). PB83220723**

Bowers, G.N., Jr., Alvarez, R., Cali, J. P., et al.. Standard Reference Materials: The Measurement of

the Catalytic (Activity) Concentration of Seven

Enzymes in NBS Human Serum (SRM 909), NBS

Spec. Publ. 260-83 (June 1983). PB83239509**

Gills, T.E., Seward, R.W., Collins, R.J., et al., Standard Reference Materials: Sampling, Materials

Handling, Processing, and Packaging of NBS Sulfur

in Coal SRMs 2682, 2683, 2684, and 2685, NBS

Spec. Publ. 260-84 (August 1983). PB84109552**

Swyt, D.A., Standard Reference Materials: A Look at Techniques for the Dimensional Calibration of

Standard Microscopic Particles, NBS Spec. Publ. 260-85 (September 1983). PB841 12648**

Hicho, G.E., and Eaton, E.E., Standard Reference

Materials: A SRM Containing Two and One-Half

Percent Austenite, SRM 488, NBS Spec. Publ. 260-86 (December 1983). PB84143296**

Mangum, B.W., Standard Reference Materials: SRM

1969: Rubidium Triple-Point - A Temperature

Reference Standard Near 39.30° C, NBS Spec. Publ. 260-87 (December 1983). PB84149996**

Gladney, E.S., Bums, C.E., Perrin, D.R., et al., Standard Reference Materials: 1982 Compilation of

Elemental Concentration Data for NBS Biological,

Geological, and Environmental Standard Reference

Materials, NBS Spec. Publ. 260-88 (March 1984).

PB84218338**

Hust, J.G., Standard Reference Materials: A FineGrained, Isotropic Graphite for Use as NBS

Thermophysical Property RMs from 5 to 2500 K,

NBS Spec. Publ. 260-89 (September 1984).

PB85 112886**

vili
Hust, J.G., and Lankford, A.B., Standard Reference

Materials: Update of Thermal Conductivity and

Electrical Resistivity of Electrolytic Iron, Tungsten,

and Stainless Steel, NBS Spec. Publ. 260-90

(September 1984). PB85115814**

Goodrich, L.F., Vecchia, D.F., Pittman, E.S., et al.. Standard Reference Materials: Critical Current Measurements on an NbTi Superconducting Wire

SRM, NBS Spec. Publ. 260-91 (September 1984).

PB85 118594**

Carpenter, B.S., Standard Reference Materials: Calibrated Glass Standards for Fission Track Use

(Supplement to NBS Spec. Publ. 260-49), NBS Spec.

Publ. 260-92 (September 1984). PB85 113025**

Ehrstein, J.R., Standard Reference Materials: Preparation

and Certification of SRM for Calibration of

Spreading Resistance Probes, NBS Spec. Publ. 260-93 (January 1985). PB85 177921**

Gills, T.E., Koch, W.F., Stolz, J.W., et al.. Standard

Reference Materials: Methods and Procedures U.sed

at the National Bureau of Standards to Certify Sulfur

in Coal SRMs for Sulfur Content, Calorific Value,

Ash Content, NBS Spec. Publ. 260-94 (December

1984). PB85 165900**

Mulholland, G.W., Hartman, A.W., Hembree, G.G., et

al., Standard Reference Materials: Development of a 1mm Diameter Particle Size Standard, SRM 1690,

NBS Spec. Publ. 260-95 (May 1985). PB861 13693**

Carpenter, B.S., Gramlich, J.W., Greenberg, R.R., et

al.. Standard Reference Materials: Uranium-235

Isotopic Abundance Standard Reference Materials for Gamma Spectrometry Measurements, NBS Spec.

Publ. 260-96 (September 1986). PB87 108544**

Mavrodineanu, R., and Gills, T.E., Standard Reference

Materials: Summary of the Coal, Ore, Mineral,

Rock, and Refactory Standards Issued by the National Bureau of Standards, NBS Spec. Publ. 260-97

(September 1985). PB861 10830**

Hust, J.G., Standard Reference Materials: Glass

Fiberboard SRM for Thermal Resistance, NBS Spec.

Publ. 260-98 (August 1985). SN003-003-02674-3*

Callanan, J.E., Sullivan, S.A., and Vecchia, D.F.,

Standard Reference Materials: Feasibility Study for the Development of Standards Using Differential Scanning Calorimetry, NBS Spec. Publ. 260-99

(August 1985). PB86 106747**

Taylor, J.K., Trahey, N.M., ed.. Standard Reference

Materials: Handbook for SRM Users, NBS Spec. Publ. 260-100 (February 1993). PB93183796**

Mangum, B.W., Standard Reference Materials: SRM

1970, Succinonitrile Triple-Point Standard; A

Temperature Reference Standard Near 58.08° C,

NBS Spec. Publ. 260-101 (March 1986).

PB86197100**

Weidner, V.R., Mavrodineanu, R., Mielenz, K.D., et

al., Standard Reference Materials: Holmium Oxide

Solution Wavelength Standard from 240 to 640 nm - SRM 2034, NBS Spec. Publ. 260-102 (July 1986).

PB86245727**

Hust, J.G., Standard Reference Materials: Glass

Fiberblanket SRM for Thermal Resistance, NBS

Spec. Publ. 260-103 (September 1985).

PB86109949**

Mavrodineanu, R., and Alvarez, R., Standard Reference

Materials: Summary of the Biological and Botanical

Standards Issued by the National Bureau of

Standards, NBS Spec. Publ. 260-104 (November

1985). PB86155561**

Mavrodineanu, R., and Rasberry, S.D., Standard

Reference Materials: Surnmary of the Environmental

Research, Analysis, and Control Standards Issued by

the National Bureau of Standards, NBS Spec. Publ. 260-105 (March 1986). PB86204005**

Koch, W.F., ed., Standard Reference Materials: Methods

and Procedures Used at the National Bureau of

Standards to Prepare, Analyze, and Certify SRM

2694, Simulated Rainwater, and Recommendations

for Use, NBS Spec. Publ. 260-106 (July 1986).

PB86247483**

Hartman, A.W., and McKenzie, R.L., Standard

Reference Materials: SRM 1965, Microsphere Slide (10 /xm Polystyrene Spheres), NBS Spec. Publ. 260-107 (November 1988). PB89153704**

Mavrodineanu, R., and Gills, T.E., Standard Reference

Materials: Summary of Gas Cylinder and Permeation

Tube Standard Reference Materials Issued by the National Bureau of Standards, NBS Spec. Publ. 260-108 (May 1987). PB87209953**

Candela, G.A., Chandler-Horowitz, D., Novotny, D.B.,

et al.. Standard Reference Materials: Preparation and

Certification of an Ellipsometrically Derived

Thickness and Refractive Index Standard of a Silicon Dioxide Film (SRM 2530), NIST Spec. Publ. 260-109 (October 1988). PB89133573**

Kirby, R.K., and Kanare, H.M., Standard Reference

Materials: Portland Cement Chemical Composition

Standards (Blending, Packaging, and Testing), NBS

Spec. Publ. 260-110 (February 1988).

PB88193347**

Gladney, E.S., O'Malley, B.T., Roelandts, 1., et al.. Standard Reference Materials: Compilation of

Elemental Concentration Data for NBS Clinical,

Biological, Geological, and Environmental Standard

Reference Materials, NBS Spec. Publ. 260-111

(November 1987). PB88156708**

ix
Marinenko, R.B., Blackburn, D.H., and Bodkin, J.B., Standard Reference Materials: Glasses for Microanalysis: SRMs 1871-1875, NIST Spec. Publ. 260-112 (February 1990). PB90215807**

Mangum, B.W., and Wise, J. A., Standard Reference

Materials: Description and Use of a Precision

Thermometer for the Clinical Laboratory, SRM 934,

NIST Spec. Publ. 260-113 (June 1990).

PB90257643**

Vezzetti, C.F., Vamer, R.N., and Potzick, J.E., Standard Reference Materials: Bright-Chromium

Linewidth Standard, SRM 476, for Calibration of

Optical Microscope Linewidth Measuring Systems,

NIST Spec. Publ. 260-114 (January 1991).

PB91 167163**

Williamson, M.P., Willman, N.E., and Grubb, D.S.,

Standard Reference Materials: Calibration of NIST

SRM 3201 for 0.5 in. (12.65 mm) Serial Serpentine

Magnetic Tape Cartridge, NIST Spec. Publ. 260-1 15 (February 1991). PB91 187542**

Mavrodineanu, R., Burke, R.W., Baldwin, J.R., et al.. Standard Reference Materials: Glass Filters as a Standard Reference Material for Spectrophotometry - Selection, Preparation, Certification and Use of SRM

930 and SRM 1930, NIST Spec. Publ. 260-116

(March 1994). SN003-00303256-5*

Vezzetti, C.F., Vamer, R.N., and Potzick, J.E., Standard Reference Materials: Antiretlecting-Chromium Linewidth Standard, SRM 475,

for Calibration of Optical Microscope Linewidth

Measuring Systems, NIST Spec. Publ. 260-117

(January 1992). PB92-149798**

Williamson, M.P., Standard Reference Materials: Calibration of NIST Standard Reference Material

3202 for 18-Track, Parallel, and 36-Track, Parallel Serpentine, 12.65 mm (0.5 in), 1491 cpmm (37871

cpi), Magnetic Tape Cartridge, NIST Spec. Publ. 260-118 (July 1992). PB92-226281**

Vezzetti, C.F., Vamer, R.N., and Potzick, Standard

Reference Materials: Antireflecting-Chromium

Linewidth Standard, SRM 473, for Calibration of

Optical Microscope Linewidth Measuring System,

NIST Spec. Publ. 260-119 (September 1992).

Caskey, G.W., Philips, S.D., Borchardt., et al.. Standard Reference Materials: A Users' Guide to NIST SRM 2084: CMM Probe Performance

Standard, NIST Spec. Publ. 260-120 (1994).

Rennex, B.C., Standard Reference Materials:

Certification of a Standard Reference Material for the Determination of Interstitial Oxygen Concentration in Semiconductor Silicon by Infrared

Spectrophotometry, NIST Spec. Publ. 260-121

(1994).

*Send order with remittance to: Superintendent of

Documents, U.S. Government Printing Office,

Washington, DC 20102. Remittance from foreign

countries should include an additional one fourth of

the purchase price for postage.

**May be ordered from: National Technical Information

Services (NTIS), Springfield, VA 22161.

For information phone (703-487-4650)

To Place an Order with PB# phone (800-553-6847)

X
TABLE OF CONTENTS

Page

Preface iii

Acknowledgments . . ; iv

Abstract 1

I. Introduction 2

A. SRM Objective 2

B. Background 2

C. SRM Description 3

D. Overview 3

n. Apparatus 4

in. Absolute Oxygen Measurements 6

IV. Determination of SRM Conversion Coefficient 6

V. Drift Compensation •

. . . 7

VI. Performance Evaluation Runs 8

VII. Uncertainty Estimates 10

VIII. Results and Conclusions 13

References 15

APPENDIX A. Certificate A-1

APPENDIX B. Calculation of Absorption Coefficient Peak Height B-1

APPENDIX C. Issues Related to the Conversion Coefficient C-1

APPENDIX D. Production Run Protocol D-1

APPENDIX E. Unit Conversions E-1

xi
LIST OF FIGURES'

Page

1. NIST FTIR configuration 16

2. Transmittance spectra for oxygen and float-zone specimens 17

3. Absorption coefficient spectra for both oxygen and float-zone specimens and the

difference spectrum between them 18

4. Absorption coefficient versus absolute oxygen concentration with the conversion

coeftlcient (6.205 ppma*cm) equal to the inverse of the slope (0.1612/ppma'cm)

for the case where the regression line is constrained to pass through the origin 19

5. Absorption coefficient versus absolute oxygen concentration with a slope of

0. 1646/ppma • cm and an intercept of -0.074 cm"' for the case where the regression

line is not constrained to pass through the origin 20

6. Time plots of normalized absorption coefficient peak heights for the eight-specimen

calibration set (cm ' vs chronological test points occurring roughly once every three

hours) 21

7. Time plots of absorption coefficient peak heights for specimen 1 of the eightspecimen calibration set 22

8. Time plots of absorption coefficient peak heights (cm"') for specimen 2 of the eightspecimen calibration set 23

9. Time plots of absorption coefficient peak heights (cm"') for specimen 3 of the eightspecimen calibration set 24

10. Time plots of absorption coefficient peak heights (cm"') for specimen 4 of the eightspecimen calibration set 25

11. Time plots of absorption coefficient peak heights (cm ') for specimen 5 of the eightspecimen calibration set 26

12. Time plots of absorption coefficient peak heights (cm"') for specimen 7 of the eightspecimen calibration set 27

13. Time plots of absorption coeftlcient peak heights (cm"') for specimen 8 of the eightspecimen calibration set 28

14. Time plots of normalized absorption coefficient peak heights for the performance

evaluation set 29

'Throughout the figure and table captions it should be understood that the term oxygen concentration

refers to oxygen number fraction. When multiplied by 10^, it is referred to as ppma by convention.

xii
LIST OF FIGURES (continued)

Page

15. Time plots of absorption coefficient peak heights for the low-oxygen specimen of the

performance evaluation set 30

16. Time plots of absorption coefficient peak heights for the medium-oxygen specimen of the

performance evaluation set 31

17. Time plots of absorption coefficient peak heights for the high-oxygen specimen of the

performance evaluation set 32

18. Histogram for time plots of absorption coefficient peak heights for the low-oxygen

specimen of the performance evaluation set 33

19. Histogram for time plots of absorption coefficient peak heights for the medium-oxygen

specimen of the performance evaluation set 34

20. Histogram for time plots of absorption coefficient peak heights for the high-oxygen

specimen of the performance evaluation set 35

21. Time plots of mean values over a daily run of oxygen concentration for the low-oxygen

specimen of the performance evaluation set 36

22. Time plots of mean values over a daily run of oxygen concentration for the mediumoxygen specimen of the performance evaluation set 37

23. Time plots of mean values over a daily run of oxygen concentration for the high-oxygen

specimen of the performance evaluation set 38

24. Histogram comparing measured oxygen concentrations among all SRM float-zone

specimens 39

25. Histogram for repeated measurements of oxygen concentrations on a single float-zone

specimen 40

26. Histogram for a material uniformity study of percent difference values in measured oxygen

concentration for positional offsets of 2 mm 41

xiii
LIST OF TABLES

L Conversion coefficient data using absolute oxygen concentration data from the GRR

and absorption coefficient data from the SRM 2551 certification 42

2. Percent difference in absorption coefficient peak height due to positional shifts of

2 mm from center position 43

3. Summary of uncertainty estimates 45

4. Percent difference in absorption coefficient peak height after later repeats 46

5. Percent difference in absorption coefficient peak height for three remeasurements with

different locations of the specimens in their holder , 47

6. Certified interstitial oxygen values for the 100 SRM sets (ppma) 48

7. Center thickness values for the 100 SRM sets 52

xlv
Standard Reference Materials:

CERTIFICATION OF A STANDARD REFERENCE MATERIAL FOR THE

DETERMINATION OF INTERSTITIAL OXYGEN CONCENTRATION IN

SEMICONDUCTOR SILICON BY INFRARED SPECTROPHOTOMETRY

Brian G. Rennex

Semiconductor Electronics Division

National Institute of Standards and Technology

Gaithersburg, MD 20899, USA

ABSTRACT

A Standard Reference Material, SRM-2551, has been prepared, measured, and certified for the

determination of interstitial oxygen number fraction (commonly referred to as the oxygen concentration)

in semiconductor silicon. This SRM is intended for calibration of infrared spectrophotometers used to measure the 1107 cm"' interstitial oxygen peak in silicon. Its purpose is to enable its users to improve

their measurement agreement. The expanded SRM uncertainty is 0.17% for the low-oxygen specimens,

0.13% for the medium-oxygen specimens, and 0.12% for the high-oxygen specimens. The certifying

instrument was a Fourier-transform infrared spectrophotometer which measured the oxygen peak height.

Specimens from an earlier international Grand Round Robin (GRR) were used to convert these infrared

values to oxygen number fraction (concentration) values. A major source of uncertainty had been

measurement drift; this was largely compensated using a control specimen. The remaining sources of

uncertainty were instrument reproducibility, nonuniformity in oxygen concentration and thickness over

the specimen area, and variation in residual oxygen in the SRM float-zone specimens, each of which

float-zone specimens served as the zero-oxygen reference for a measurement. These sources were combined in quadrature to arrive at the above-quoted 2a estimate of expanded SRM uncertainty. This

SRM uncertainty applies to a "derived" oxygen number fraction which is first measured by an infrared

technique and which is then converted to an oxygen number fraction. The oxygen number fraction

previously measured in the GRR has a much larger uncertainty than the expanded SRM uncertainty.

Key words: oxygen; silicon; FTIR; Standard Reference Materials.

1
I. INTRODUCTION

A. SRM OBJECTIVE

This report documents the development of Standard Reference Material (SRM) 2551 for the measurement

of interstitial oxygen number fraction (commonly referred to as oxygen concentration) in silicon. This

SRM was produced at the National Institute of Standards and Technology (NIST). The purpose of SRM

2551 is to provide a basis for measurement consistency throughout the semiconductor industry. That is, this standard is intended to enable a group of its users to have agreement among their measurements.

The expanded SRM uncertainty ranges from 0. 12% to 0. 17% for three oxygen levels. These values are much lower than the uncertainty for absolute oxygen measurements in which case the interlaboratory

variability can be as large as 10 to 30% [1-5]. Improvement in measurement consistency is more useful

to users for quality control or comparison than is reliance on the uncertainty of absolute oxygen

determination. This report shows that the measurement consistency achievable with SRM 2551 is based

primarily on the reproducibility of the certifying infrared instrument. Therefore, the emphasis of this work was to document thoroughly the NIST instrument reproducibility. It is important to note that even though the certified parameter and its expanded uncertainty are given in units of oxygen number fraction

(concentration), the certified parameter is a "derived" oxygen number fraction first measured by a relative

infrared technique and then converted to an oxygen number fraction. The directly measured oxygen

number fraction cannot be determined by this infrared technique, nor can it be measured with the quoted

expanded SRM uncertainty.

B. BACKGROUND

The measurement of the interstitial oxygen number fraction of semiconductor silicon has long been of

scientific interest, and it is important for manufacturers of silicon and of semiconductor devices. The

concentration of oxygen in silicon affects the formation of Si-0 precipitates which serve as gettering sites for unwanted fast-diffusing impurities. It also affects, by a precipitation-hardening mechanism, distortions

of silicon wafers during the thermal treatments they experience during integrated circuit manufacture.

Both of these practical considerations require highly reproducible measurements for control of oxygen

levels by both suppliers and users of silicon wafers.

Customary semiconductor industry practice expresses "oxygen concentration" in several kinds of units. The unit "ppma" expresses it as a number fraction of interstitial oxygen atoms with respect to the total number of atoms in a volume of silicon bulk material, the unit "mg/kg" or ppm (wt) expresses it as a mass fraction, and the unit "10^^ atoms/cm^" expresses it as a concentration of interstitial oxygen atoms

in a cubic centimeter of silicon. The preferred quantity in this report is the number fraction. Strictly

speaking, this quantity is just a number, but the commonly used unit (ppma) will be shown in parentheses

to avoid confusion with ppm (wt). In this report, when the term oxygen or oxygen value is used for brevity, it refers to interstitial oxygen number fraction. Conversions among these units are given in the

SRM certificate in appendix A, and an explanation of the conversions among these units is given in appendix E.

Measurement of the oxygen number fraction is commonly made by infrared spectrophotometry in which

the height of the strongest spectral oxygen peak, at 1107 cm"^ is determined. The database and test method for this infrared measurement are well established [1-7]. It is a relative technique that relies on

Beer's Law which states that interstitial oxygen number fraction is proportional to the infrared oxygen

absorption coefficient peak height. Industry uses the infrared technique for measurement of this oxygen

2
peak height because it is quick, precise, nondestructive, and inexpensive, while the direct measurement

of oxygen number fraction is destructive, difficult, expensive, and imprecise.

Absolute (direct) oxygen measurements must be performed to determine the conversion coefficient

between infrared measurements and absolute oxygen measurements. These include charged-particle

activation analysis using cyclotron-accelerated alpha particles, high-energy photon activation using ~ 30

MeV electrons to create xrays, and gas fusion techniques. Over the years, several different conversion

coefficients have been adopted by various standards-writing organizations, depending on the state of the

measurement art at the time. There were significant discrepancies among the early values, but more

recent work has produced conversion coefficients in much better agreement with the current

internationally accepted value. That number is the result of the Grand Round Robin (GRR), a major

worldwide experiment completed in 1988 [1,2]; it has been adopted by all of the major standards-writing

organizations active in the semiconductor field. ^ More recently, a European (BCR) reference material

for oxygen in silicon was completed in 1991 [3-5].

The GRR report is a sister document to this report. The GRR produced interlaboratory data for both

infrared peak height and absolute oxygen measurements. The certification procedure for SRM 2551

utilized a subset of GRR specimens for which a determination of absolute oxygen concentration had been

made.

C. SRM DESCRIPTION

Appendix A is a sample SRM 2551 Certificate which contains the following: an SRM Set description,

a summary of the test method for the infrared measurement and the optical peak height calculation, a summary of uncertainties, recommendations for calibration of a user instrument with an SRM set, and

instructions for handling SRM specimens. Note that the term total SRM precision in the certificate corresponds to the term expanded SRM uncertainty in this report. Briefly, an SRM set consists of a float- zone specimen with a nominal zero oxygen concentration and three Czochralski silicon specimens with

oxygen number fractions (concentrations) at nominal values of 17 x 10"^, 23 x 10'^, and 26 x 10"^ (17, 23,

and 26 ppma). These specimens have nominal thicknesses of 2 mm; they are squares with nominal side

values of 25 mmx25 mm.

D. OVERVIEW

A brief overview of the report is given here as a road map for readers as they proceed through the more

detailed discussion to follow.

1) The primary SRM goal is to provide a basis for consistent measurement of oxygen in silicon for the semiconductor industry. This goal can be best accomplished with a reproducible infrared

instrument for development of the SRM and with reproducible infrared instruments calibrated

with the SRM [appendix A].

2) The infrared measurement is of a spectral oxygen absorption coefficient peak height [sec. II and

appendix B].

^American Society for Testing and Materials, Deutsches Institut fur Normung, Guo Biao (State

Standards of China), and Japan Electronic Industry Development Association.

3
3) An SRM conversion coefficient for the NIST spectrometer was determined using a procedure to convert infrared values used for certification to an oxygen scale based on the GRR [sec. Ill and

IV and appendix C].

4) A control specimen was used to monitor drift during all measurements. Data for this control

specimen were then used to compensate for drift. This compensation improved instrument

reproducibility by about a factor of 3 [sec. V].

5) Performance evaluation runs were made after each group of four SRM sets had been measured.

These runs provided data for an estimate of instrument reproducibility both before and after drift compensation [sec. VI].

6) Production runs were made on the SRM sets; each set comprised three oxygen specimens (each

at a different oxygen level) and a nominally zero-oxygen specimen [appendix D].

7) The main sources of uncertainty were determined and combined in quadrature to estimate the

expanded SRM uncertainty. The four significant sources of uncertainty in the infrared

measurement are drift, which is largely compensated; instrument repeatability along with random

effects due to specimen changing, which lead to any random variation that remains after drift compensation; nonuniformity in the oxygen concentration and the specimen thickness over the area of specimen subtended by the FTIR beam; and variation in the small amount of residual

oxygen in the SRM float-zone specimens, each of which serves as the zero reference for the

determination of a, for a particular SRM set [sec. VII].

8) The result is a 2a estimate of expanded SRM uncertainty which varies from 0. 17% for the lowoxygen specimens to 0. 12% for high-oxygen specimens. This value meets projected IC industry

requirements into the next century [sec. VIII].

II. APPARATUS

A Fourier Transform Infrared spectrophotometer (FTIR) was used to measure infrared transmittance

through silicon specimens; Figure 1 shows schematically the optical configuration of the NIST FTIR.

This instrument operated at the 4 cm'^ resolution required by the ASTM test method for determination

of oxygen in silicon, and its small size and rigid construction contribute to good quantitative repeatability

[6].

Appendix B explains the derivation of the spectral absorption coefficient peak height, a, from the

transmittance peak height. This o; is independent of specimen thickness since it is the quotient of the

absorbance and the specimen thickness. Figures 2 and 3 show typical spectra in the region of the 1107

cm'^ oxygen peak.

It was discovered that the measured a was extremely sensitive to the angular orientation of the silicon

wafer in the FTIR, possibly due to the high index of refraction of silicon. Changes in orientation due

to specimen removal and reloading caused sufficient specimen rotation to, in turn, cause large and abrupt

offsets in a (of about 0.5%). A possible explanation for this error would be that both the infrared beam

and the infrared detector are nonuniform, and a tiny shift of the beam with respect to the detector results

4
in a significant shift in the measured intensity. Also, the just-mentioned abrupt shifts in a were not eliminated by the drift compensation to be discussed in section V.

This error was eliminated by use of a light cone which made the focused beam position on the detector

less sensitive to the orientation of the specimen. Losses within the light cone resulted in a loss of about

half the signal intensity, but the error in reproducibility was completely eliminated. This was proven in section VI (as is shown in tigs. 14 to 17), where it can be seen that any shifts in a, which occurred when

the performance evaluation specimens were replaced, occurred in all specimens and, hence, could be drift compensated. That is, the shifts in a occurred in a proportionate manner for all specimens; this behavior

is referred to in this report as "tracking" of the time plots among the measured specimens. Before the

light cone was employed, the shifts for different specimens did not track, indicating that the cause of the

shifts was somehow dependent on what had happened to an individual specimen.

The light cone used at the detector was a gold-plated, f/4 light cone with the following dimensions: length = 6 mm; entry diameter = 2 mm; and exit diameter = 1 mm. The multiple reflections in the light cone

scrambled the beam in the sense that a particular original direction of a beam ray would not determine

its final position on the detector in a manner corresponding to simple geometrical optics.

The NIST FTIR is housed in a room which was temperature-controlled to 21 + 0.5 °C. Temperature

control was important because temperature fluctuations appeared to be the primary cause of measurement

drift. The temperature at the sample holder was 27.8 ± 0.5 °C. Temperature stability within the sample

chamber was ensured by waiting an hour following sample loading, before measurement began.

To automatically measure many specimens, a sample holder was used. Up to nine specimens were loaded

in this 3x3 (position) sample holder, which could be repositioned to within better than a micrometer by

an automatic x-y positioner. The alignment procedure was first to align the center of the sample holder

with the infrared beam, using an IR sensitive film. Then an iris, located 50 mm before the sample

chamber focal point, was centered, via a manual x-y positioner, onto the center of the sample holder; the

iris was adjusted so that the beam diameter at the specimen was 5 mm. The specimen was located 50

mm behind the sample chamber focal point. The infrared beam was normal to the specimen surface.

The NIST FTIR instrument allows normal incidence because light reflected from the detector or the

specimen back into the interferometer cannot result in a spurious contribution to the modulated signal.

This is because the corner-cube size is 2.5 times the beam size, and the beam illuminates only one side

of the corner cube. The result is that the beam is translated laterally in such a way that it cannot return

to the detector. A 2-mm-diameter deuterated-triglycine-sulfate (DTGS) detector was used at the same

temperature as that of the sample chamber temperature. This minimized any spurious effects due to background blackbody radiation. To confirm that there was no error due to blackbody radiation from

components in the optical path, the IR source was turned off, at which time there was no measurable

interferogram or spectrum whatsoever.

A manual x-y positioner was used to locate the light cone optimally over the detector, and a manual x-y-z positioner was used to optimize the signal by moving the detector in all three directions while monitoring

the detector signal. This alignment was done whenever the open-beam signal decreased below a certain

threshold, which was roughly 96% of the maximum signal. This monitoring was done throughout the

period of SRM tests.

5
III. ABSOLUTE OXYGEN MEASUREMENTS

Calibration of the NIST FTIR instrument was based on infrared measurements of a set of eight specimens

for which a determination of absolute oxygen concentration had previously been made in the Grand

Round Robin (GRR) [1,2]. This eight-specimen set is a subset of 20 specimens (from 20 ingots at 20

distinct levels of oxygen) used in the GRR, and it is referred to here as the eight-specimen calibration

set. Eight specimens were used since only eight specimens (plus a float-zone specimen) could be

accommodated on the instrument sample holder at one time. The GRR determination of absolute oxygen was based on data from charged particle activation analysis. These oxygen measurements were made on

specimens that had originally been adjacent to the wafers reserved for optical measurements. There were two such wafers from each of 20 ingots (at 20 oxygen levels), and each wafer provided four specimens

for the optical measurements by GRR participants.

The uncertainties for these absolute techniques are not well characterized, but their uncertainty is much

larger than the expanded SRM uncertainty, which is less than 0.2%. The spread of data among the

different laboratories which made the absolute oxygen measurements was 10 to 30% [1,2J. In a subsequent BCR study, the intra-laboratory reproducibility of absolute measurements was +4%, and a propagation of errors estimate of absolute uncertainty was ±6% [3-5]. Since these absolute oxygen

uncertainties, which are the best currently possible due to the limitations of the existing measurement

techniques, are large, one must use these data (averaged over a number of specimens and laboratories)

simply to arrive at a scaling factor for the measured optical parameter. This scaling is achieved with the

conversion coefficient to be discussed in the next section.

Using only GRR data, a comparison was made between the GRR conversion coefficient based on

specimens at all 20 GRR oxygen levels, as well as the conversion coefficient based on the eight-specimen

subset used as the NIST calibration set. The GRR conversion coefficient for the 20-specimen regression

is 3.575 mg/(kg'cm) [6.275 ppma/cm] versus 3.549 mg/(kg'cm) [6.230 ppma/cm] for the eightspecimen subset. The respective standard deviations of these coefficients are 0.6% and 1.2%. The eightspecimen set yields a conversion coefficient that is 0.72% less than that from the full 20-specimen GRR

set. The T-factor for comparison of these two slopes or conversion coefficients is 0.52, indicating that they are not statistically different. Nevertheless, to ensure that the certified oxygen values are as representative as possible of all the GRR data for absolute oxygen, the original oxygen values of the eight

specimens have been scaled up by 0.72%. These adjusted oxygen values appear in table 1.

IV. DETERMINATION OF SRM CONVERSION COEFFICIENT

As stated in the introduction, the basic strategy of this SRM certification is to take advantage of a precise

infrared measurement technique to provide an SRM with high internal consistency. This is accomplished

by the determination of an SRM conversion coefficient for the NIST FTIR to convert precisely measured

values of a to certified values in oxygen units. This was done using mean absolute oxygen values from

the GRR work. Then, even though the absolute uncertainty of any particular oxygen value is large, the

measurement consistency or reproducibility of the certified values within the SRM is good.

There were two requirements for determination of the SRM conversion coefficient. First, in the previous

section, there was an explanation of the provisions taken to make the absolute oxygen values of the eightspecimen set representative of the GRR. Second, the conversion coefficient must be specific to the NIST

FTIR.

6
The conversion coefficient specific to the NIST FTIR was used for this SRM certification to eliminate

any bias between the NIST FTIR and the mean response of all infrared instruments used to determine the

GRR conversion coefficient. That is, the internationally recognized conversion coefficient determined

in the GRR is an average based on measurements by many infrared laboratories, each of which had a bias

with respect to the group average. The set of laboratory bias values can be quantified by a standard

deviation, namely the interlaboratory variability. The la interlaboratory variability for the GRR was

2.7%. Although the current NIST FTIR was not used in the GRR, it would also be expected to have a laboratory bias.

If the GRR conversion coefficient were used for the SRM certification, the calculated oxygen values

would be biased from the results of the GRR by the amount of the NIST FTIR laboratory bias. For

clarity, this point is explained in mathematical terms in appendix C. The conclusion is that the

conversion coefficient measured with the NIST FTIR should be used as the SRM conversion coefficient

in this work, and this, in turn, will enable the SRM users to also achieve measured oxygen values

consistent with the GRR.

The absorption coefficient values (shown in table 1 and figs. 4 and 5) for the conversion coefficient

determination were taken by the NIST FTIR in a 6-day test run for the eight-specimen calibration set mentioned in the previous section (III). Absorption coefficient oxygen peak heights were measured 55

times, with each data point being the average of 300 scans. These eight specimens covered a range of

nominal oxygen number fraction values between 9x10'^ and 29x10"^ (9 ppma and 29 ppma); these

specimens and a GRR float-zone (zero oxygen) specimen were mounted simultaneously in the specimen

holder. The sequence of measurements for each repeat was open beam, float-zone, and then each of the

eight specimens. Acquisition of these 55 sets of data points resulted in a total test time of 6 days, which

can be seen by inspection of figures 6 to 13 to be sufficient to achieve good statistics and to achieve a good evaluation of the drift compensation, to be explained below.

A conversion coefficient is determined by a linear regression fit to data for absolute oxygen concentration versus a. The absolute oxygen values representative of the Grand Round Robin study described in section III are shown in table 1 , which also has the mean a values from the test run on the eight-specimen

calibration set. The resuUing plot is fitted with a straight line which passes through the origin as shown

in figure 4. The slope of this line is M^j^^ = 0. 1612 x 10^ cm"^ [0. 1612 (ppma -cm)"'] which corresponds

to an SRM conversion coefficient of 6.205 x 10'^ cm (ppma -cm). In figure 5, if the straight line is not constrained to pass through the origin, the oxygen intercept value is -0.074 cm'^ and the slope is 0. 1670 X 10^ cm"^ [(ppma-cm)"^]. Because of the large scatter of absolute oxygen number fraction values

about the fitted line, the assumption of the line passing through the origin is not unreasonable. Also, this assumption was used in the determination of the GRR conversion coefficient.

V. DRIFT COMPENSATION

The above-mentioned time plots on the eight-specimen calibration set can also be used to evaluate drift compensation. Figure 6 shows these time plots as percent changes (from the mean) of a for all eight

specimens; that is, the values plotted are divided by the average over the entire run, and this quotient is then multiplied by 100. These curves are offset by 0.4% with increasing oxygen value, for clarity of

viewing. They track one to another, which means that any drift causes the same approximate percent

changes for each curve. The specimen (third from the top in fig. 6) closest to the center of the SRM

7
oxygen range [at 24 x 10"^ (24 ppma)] was used here as a control specimen for drift compensation. This same specimen was used as the control specimen for the production runs and for the performance

evaluation runs discussed later.

The formula for drift compensation is the following.

ry. ,' = ry. (rv / d )

'J *-*i,jV*-^cmean' ^c.j/

Here, "i" refers to a test specimen, and "c" refers to the control specimen. The equation applies to a set of single data points "j" taken in concurrent test runs. Here, a-^-/ is the compensated a, otij is the

uncompensated a, both for the test specimen; a^-.j is the uncompensated a for the control specimen, and

a^^^ is the mean of all the a values for the control specimen. If the drift compensation worked exactly,

the set of j values of a,/ would have a constant value. In fact, this set has a distribution characterized

by a mean and a standard deviation, and the latter gives the drift-compensated reproducibility. Other data

plots related to drift compensation are shown in section VI on performance evaluation runs and in section VII on uncertainty estimates.

Figures 7 to 13 show, for each of the seven other calibration specimens, time plots of the measured a

and of the drift-compensated a. The "x" indicates a measured point, and the "c" indicates a compensated

point. Figures 7 and 8, for the lowest oxygen levels, show that drift compensation is not complete

because the corrected curve is not flat. Even so, there is substantial compensation, and the percent

standard deviation of the corrected points of the curve about its mean is reduced by a factor of two over

that of the uncorrected points. As the oxygen level increases to the range of the SRM [17x10^^ to 26x10"^ (17 ppma to 26 ppma)], the corrected curve is very flat and the percent standard deviation

values, i.e., the instrument repeatability values, are improved by a factor of 3 to 4 over those of the time

plots of uncompensated data. The empirical conclusion is that drift in a is substantially reduced in the

oxygen range covered by the oxygen SRM.

VI. PERFORMANCE EVALUATION RUNS

Performance evaluation runs were taken concurrently (i.e., overnight) with the SRM production runs to monitor the instrument and to acquire the data needed to estimate the instrument reproducibility over the

entire period of these production runs. Performance evaluation runs were taken every day after two

production runs had been taken (during that same 24-h period). The approximate timing was two

consecutive 8-h production runs, followed by a 7-h performance evaluation run, with about an hour for specimen changing. Even though the performance evaluation runs were concurrent and alternating with

the production runs, they are discussed before the production runs. This is because the performance

evaluation provides an estimate of instrument reproducibility which is needed for the discussion of the

uncertainty associated with production runs, which is given in the next section.

The performance evaluation set was taken from specimens used in the Grand Round Robin study. [1,2]

This set was similar to those of the SRM production runs because it used the same control specimen, and

it had a float-zone specimen and specimens at three comparable levels of oxygen. Its protocol was also

the same as that for the production runs except that it was measured twice as frequently. The production

run protocol is given in appendix D.

8
The purpose of performance evaluation runs was twofold. First, they verified that the measured peak

heights of all specimens tracked. The term "tracking" means that temporal percent changes in all measured oxygen or a values were roughly the same. Second, the performance evaluation runs produced

a large database for determination of instrument reproducibility, and this database covered the entire

period of time over which the productions runs were made. Here, reproducibility is distinguished from

repeatability, which refers to repeated measurements when the specimen holder has been moved, but

when the specimens have not been removed from the specimen holder. Reproducibility refers to the case when specimens have been unloaded from and reloaded into the specimen holder, and it provides

information regarding the equivalence of the measurement for all SRM sets measured over the course of

the certification. As is seen in section VII on uncertainties, the NIST FTIR reproducibility is the largest

contributor to the expanded SRM uncertainty.

The performance evaluation data plots described next are time plots of a, the parameter determined in test runs by the NIST FTIR. Figure 14 shows normalized (percent of average value) plots of o; for the

performance evaluation specimens. The symbols L, M, H, and C refer to the low, medium, high, and

control specimens, respectively, and each curve is offset by 0.5%. Specimen C was used as the control

specimen for both performance evaluation and production runs because it is centrally located in terms of

oxygen level. The term normalized means that each curve represents percent changes from its own mean

value over time. Note that the number of points in each run may vary. A symbol "0" below the curve

indicates the first of several single points (4 to 20) in a run. As was stated earlier, there was actually a time gap (typically of about 17 h or more for the two production runs) immediately before each "0"

point. The data points in figure 14 were not compensated for drift. It is evident that the curves track

according to the drift, and this corroborates the use of a control specimen for drift compensation.

Drift compensated curves for the three oxygen specimens are shown in figures 15 to 17, and their

distributions are shown in figures 18 to 20. These distributions are reasonably gaussian. Values

averaged over the three specimens are used to estimate standard deviation values from the three

compensated and the three uncompensated curves, and these average percent values are adjusted to correspond to the average value of oxygen number fraction [21.2x10"^ (21.2 ppma)] for these three

specimens. The average standard deviation for the uncompensated curves in figures 15 to 17 is 0.147%

or 0.499 cm"'. The average standard deviation (referred to as o,^^ where "rep" refers to reproducibility)

for the compensated curves in figures 18 to 20 is 0.185 cm' or 0.055%. This is an improvement by a

factor of 2.7 over the standard deviation values for the uncompensated data.

As can be seen from table 6 (discussed later), the three nominal oxygen levels are 17 x 10 ^ 23 x 10"^ and

26x10-' (17, 23, and 26 ppma). The percent value of o,,^ of 0.055% (0.0115x10"' [0.0115 ppma)]

corresponded to an average oxygen value of 21.2 x 10"' (21.2 pprna). Using this value to estimate a^ep for the three SRM levels results in values of o,,^ equal to 0.068% for 17x la' (17 ppma), 0.050% for

23 X 10"' (23 ppma), and 0.044% for 26 x la' (26 ppma). These values are components of the SRM

uncertainty discussed in section VII.

Comparison of the set of figures 15 to 17 with the set of figures 10 to 13 reveals another important result,

namely, that the repeatability and the reproducibility for drift-compensated points are virtually the same.

This means that reloading specimens does not result in significant additional errors in the FTIR

measurement. This was not the case until the light-cone detector assembly discussed in section II was

used.

9
VII. UNCERTAINTY ESTIMATES

In this section, the various sources of uncertainty are discussed in detail. These values are then combined

in quadrature and multiplied by two to arrive at the estimate of expanded SRM uncertainty to be reported

with the certified SRM values. The four significant sources of uncertainty in the infrared measurement

are drift, which is largely compensated; instrument reproducibility, which is the random variation that remains after drift compensation; the variation in the small amount of residual oxygen in the SRM float- zone specimens, each of which serves as the zero reference for the determination of a, for a particular

SRM set; and nonuniformity in the oxygen concentration and the specimen thickness over the area of

specimen subtended by the FTIR beam.

The measurement consistency achievable with SRM 2551 is based primarily on the reproducibility of the

certifying infrared instrument. The stated uncertainty is an expanded (2cr) uncertainty with which the

oxygen scale obtained from the eight-specimen calibration set is reproduced in each of the SRM sets. Therefore, the emphasis of this work was to document thoroughly the NIST instrument reproducibility

which is determined with a type A evaluation in ISO terminology [8]. It is irnportant to note that even

though the certified parameter and its uncertainty are given in units of oxygen number fraction

(concentration), the certified parameter is a value first measured by an infrared technique and then

converted to oxygen number fraction units. Absolute oxygen number fraction cannot be directly

measured by this infrared technique nor can it be measured with the quoted expanded SRM uncertainty.

The first significant uncertainty is the reproducibility of the optical measurement of the absorption

coefficient. The measurement protocol for production runs is described in appendix D. It explains that

all specimens in two SRM sets and a control specimen were measured consecutively and repeatedly and

that an a. value for each specimen is the average of four (single) test points taken over a period of 8

hours. Also, a check was made that the transmittance at 2000 cm"^ was within 2% of the expected value

of 54% [6,7]. :

Drift compensation was used for all production runs because they took place over many weeks, and there was drift over this period of time that was several times larger than any random variation. With

reference to the expression for drift compensation in section V, the adjustment of each a point for each

specimen of each SRM set was accomplished as follows. Mean a values for a particular production run, based on four or more points or repeats, were calculated for each of the three SRM set specimens, a^,

and for the control specimen, a^. Compensated mean SRM values oc^' were then calculated using a grand

mean value, a^^^ggp, for the control specimen based on data taken over the entire period of SRM

measurement, along with the mean values a^ and a^.

For each SRM specimen, four repeats were made to ensure that the instrument was in steady state and

that there was no chance of using a single outlier value for the SRM. It would have been desirable to take statistical advantage of the fact that there were four test points. If these points had been

uncorrected, the estimate of uncertainty in the mean oc would have equaled the standard deviation divided

by the square root of the four points taken for each run.

The requirement of no correlation is equivalent to the requirement that all drift has been compensated.

To test for correlation of mean values of compensated a from each performance evaluation run for three

levels of oxygen, figures 21 to 23 show that drift has been reduced from that seen in figures 15 to 17 for

the compensated a values. Note that the figures 15 to 17 differ from the other figures in that they show

every point in a run rather than just the mean values (of all the points in each run). Even though the drift

10
has been reduced, it is clearly still present in the plot of mean values shown in figure 21 for low oxygen,

it is less evident in figure 22 for medium oxygen, and it is virtually gone in figure 23 for high oxygen.

That is, in figure 21, the same drift pattern as that seen in figure 15 is reduced but still apparent. Note

that the standard deviations in figures 15 to 17 are based on a population of individual test points, not on a population of already averaged values of test points. Thus, if drift had been successfully

compensated (i.e., if the resulting distribution were random), the standard deviation values (of the means)

of figures 15 to 17 would have been reduced over those in figures 21 to 23 [by l/(n^^), where n was

about 6]. The reduction in a-values is insignificant for the low oxygen specimens, somewhat significant

for the medium oxygen specimens, and significant for the high oxygen specimens. That is, the actual

values decrease from 0.059% to 0.055% for low oxygen, from 0.059% to 0.047% for medium oxygen,

and from 0.046% to 0.028% for high oxygen. This indicates that drift is slightly reduced for low

oxygen, somewhat improved for medium oxygen, and significantly improved for high oxygen.

Even so, a conservative approach was taken — not to divide by 2, but rather to use the above-quoted

values of standard deviation of the population, a^^p, to estimate the standard deviation of the means. That

is, the standard deviation is used for the standard deviation of the mean; its values are 0.068% for

17x10"^ (17 ppma), 0.050% for 23x10"^ (23 ppma), and 0.044% for 26x10"^ (26 ppma).

The second significant source of uncertainty is the variation of oxygen among the SRM 2551 float-zone

specimens. The float-zone specimen in each SRM set is used to subtract the phonon or silicon structure from the measured absorption coefficient spectrum to arrive at the pure oxygen peak. These float-zone

specimens used in the SRM sets are assumed to have zero oxygen. In fact, they have a small and

variable amount of residual oxygen. This variation would cause a first SRM user (with a first float-zone

specimen) to differ in a measured unknown oxygen value from a second SRM user (with a second float- zone specimen) who had measured the same unknown specimen. This systematic difference in the

measured oxygen values would be equal to the difference between the two float-zone oxygen values.

To estimate this component of uncertainty, a series of test runs were made in which each SRM float-zone

specimen was measured with reference to the GRR float-zone specimen. The distribution of the

difference between the SRM float-zones and the GRR float-zone is shown in figure 24. The mean value was 0.0112x10"^ (0.0112 ppma). That is, the GRR float-zone specimen was 0.0112x10"^ (0.0112

ppma) less than the mean of the SRM float-zone specimens. The standard deviation was 0.007x10"^

(0.007 ppma), which includes the actual variation in float-zone oxygen levels, as well as the instrument

reproducibility for this measurement.

This instrument reproducibility was determined by measuring the same specimen throughout the course of all float-zone tests. The histogram for this measurement is shown in figure 25, and it has a standard

deviation of 0.006 xlO"^ (0.006 ppma). If this reproducibility had been significantly smaller than the

above-mentioned standard deviation of 0.007 x 10"^ (0.007 ppma), it would have been possible to adjust

each SRM float-zone oxygen number fraction (concentration) to a common value. However, the two

values (0.006 and 0.007) were comparable, and no adjustments for individual specimens were made.

Instead, the overall standard deviation value of 0.007x10'^ (0.007 ppma) is used to estimate the

uncertainty due to float-zone variation.

Also, since the GRR float-zone oxygen number fraction (concentration) was 0.01 12 x 10"^ (0.01 12 ppma)

lower than the mean value for all SRM float-zone values, each reported oxygen value in table 6 has been

increased by 0.01 12 x 10'^ (0.0112 ppma) over the value arrived at by multiplying the SRM conversion

coefficient by the measured oxygen absorption coefficient peak height. Thus, even though it is not

11
possible to measure the actual oxygen content of a single float-zone specimen with the infrared technique,

the lowest value available, namely that of the GRR tloat-zone specimen, was used as the best

approximation of the zero oxygen level.

Other SRM uncertainties are due to (1) the thickness measurement and (2) variation of oxygen

concentration and thickness over the illuminated area of the specimen. The combination is the total material nonuniformity uncertainty.

Thickness appears in the expression for absorption coefficient; its uncertainty has two aspects. First, the

uncertainty of a single thickness measurement is 0.2 ixm, or 0.01 % of the 2-mm thickness for the SRM

specimens. Second, a single point was used to estimate the average thickness over the 6-mm circle

sampled by the infrared beam, and this single value is not perfectly representative of the average value

because the specimen is not perfectly flat. This discrepancy is called the thickness representativeness

uncertainty, and it was estimated as follows. Comparisons were made on several specimens between a center point and an average of five points, one at the center and the other four near the four corners of

a 5 x5 mm square. These comparisons gave a value of 0.015% as the average absolute difference and

0.03% as an upper limit (2a value) for these difference values. Thus, the thickness representativeness

standard deviation equals 0.015%.

Another error arises from differences in the positioning of an SRM specimen with respect to the FTIR

beam, in conjunction with any nonuniformity of oxygen concentration and thickness across a specimen.

That is, this measurement had uncertainty contributions from both thickness and oxygen nonuniformity.

To estimate this combined uncertainty, repeated points were taken at different positions of the FTIR beam

on a specimen.

It was estimated that 1 mm would be an upper limit on the uncertainty in positioning of the FTIR beam

at the center of the specimen. The beam was moved twice this distance, or 2 mm, to get better statistics by working with a larger discrepancy. Ten repeated measurements were made with the specimen in the

original position and then in a position 2 mm away. The conservative assumption was made that errors due to half the offset, namely 1 mm, would be half of those for the 2-mm offset. This is conservative

because this error depends on the lack of overlap between two beam positions, and this lack of overlap

does not depend linearly on the beam displacement due to the circular beam geometry. Beam-offset

measurements were made on four specimens taken from each of the three levels of oxygen, or on a total of 12 specimens.

Table 2 and figure 26 show data for the positioning uncertainty study. The o; data is presented in sets of three for each specimen, one at an original position and two at positions 2 mm away from the original

position. The second column gives the percent difference in a between the original position and the two

offset positions. The third column gives the standard deviation in a for each of the ten repeats at a particular position. The average of all standard deviation values for these repeats was 0.031%, and the

range of standard deviation values is also shown in table 2.

To decide if the differences due to repositioning are caused by material nonuniformity or instrument

repeatability, note that the uncertainty in the mean value at each position is estimated as 0.031% divided

by the square root of 10, or roughly 0.01%. The upper limit on the percent differences (column 2 of

table 2) due to repositioning was 0.10%. This value is significantly larger than the just-described

12
uncertainty of the mean of 0.01 % at a particular position, and therefore there is good confidence that any

measured difference larger than 0.01 % is due to a difference in oxygen concentration and/or thickness

at the two positions.

The upper limit estimate of the material nonuniformity uncertainty (a 2a value due to a 1-mm offset), as distinguished from the 2-mm offset used in the test, was one-half this value, or 0.05%. The standard

deviation for the material nonuniformity (aj^J is 0.025%. This 0.025% figure is added in quadrature

to the single-point thickness uncertainty of 0.01% and the thickness representativeness uncertainty of

0.015%, to arrive at 0.031 % for the total material nonuniformity uncertainty which is rounded to 0.03%.

The combined SRM uncertainty for the FTIR measurement was calculated by combining in quadrature

(1) the reproducibility standard deviation, (2) the float-zone standard deviation, and (3) the total material

nonuniformity standard deviation. The expanded SRM uncertainty was calculated as twice the combined

SRM uncertainty. This gives the following values for expanded SRM uncertainty for the low, medium,

and high levels of oxygen: 0.17% for 17x 10"^ (17 ppma), 0.13% for 23x 10"^ (23 ppma), and 0.12%

for 26 X 10"^ (26 ppma). The corresponding values in oxygen number fraction (ppma) are: 0.029 x 10"^ (0.029 ppma) for 17x 10'^ (17 ppma), 0.030 x 10"^ (0.030 ppma) for 23 x 10"^ (23 ppma), and 0.031 x 10"

^ (0.031 ppma) for 26x10'^ (26 ppma). Table 3 gives a summary of how the various individual

uncertainties contribute to the expanded SRM uncertainty. The terms combined and expanded uncertainty

are consistent with the new ISO terminology, and all of the component uncertainties were arrived at with

a type A evaluation, meaning that repeated values were taken to establish a statistical basis for the various

estimates [8]. A total of seven SRM sample sets (21 specimens) were remeasured to check this expanded SRM

uncertainty estimate, and all remeasured values lay within the tolerance interval defined by this estimate.

These data are shown in table 4. The standard deviation of these percent differences is 0.044% which

is comparable to the FTIR reproducibility (0.044% to 0.068%), and the mean offset was 0.05% which

indicated that a small amount of drift had occurred over the period of 3 months between the original

measurements and the later repeat measurements.

In a second check, three remeasurements were made for a pair of SRM sample sets in which the

specimens were put into several different locations in the specimen holder. This was to check for any

anomalous effects due to either specimen position or order of specimen measurement within the holder.

Again, all remeasured values lay within the tolerance equal to the expanded SRM uncertainty. Table 5

shows these data, and the standard deviation of these percent differences was 0.049%.

VIII. RESULTS AND CONCLUSIONS

The certified derived oxygen number fraction values, as scaled to the GRR, for each SRM 2551 set are given in table 6. The estimate of expanded SRM uncertainty is summarized in table 3, thickness values

are given in table 7, and appendix A consists of a sample SRM 2551 Certificate Report. Appendix E

derives the conversions among the various units of oxygen number fraction (concentration).

13
Key features of the SRM measurements were the following:

1) The FTIR instrument reproducibility of 0.05% was an improvement over typical previous values

which ranged from about one-half to several percent. The 2a values of expanded SRM

uncertainty for the low, medium, and high oxygen levels were 0.17%, 0.13%, and 0.12%.

2) Ample statistics show that the expanded SRM uncertainty applied over the entire period of SRM

measurements and over all SRM sets.

3) Improved accuracy resulted from four factors: a small, rigid instrument was used; an x-y

positioner was used to obtained automatic repeats over long periods of time; a control specimen was used to compensate for drift; and a light-cone with an x-y-z positioning capability was used

to avoid errors due to specimen positioning.

4) A test method and computer program with some new features was used to calculate the absorption

coefficient peak height [appendix 2].

5) The measured absorption coefficient peak height varies with temperature in this range with a coefficient of 0.0016 K ' |7,91, while the actual oxygen number fraction (concentration) remains

constant. This means that the certified estimate of oxygen number fraction (concentration) can be used without adjustment even if a user's measurement temperature is different from the value

used in the SRM 2551 work. However, the user must expect his own oxygen conversion

coefficient (explained in sec. IV and appendix 3) to vary with temperature according to the above

temperature coefficient.

6) Finally, the purpose of this SRM is to provide a standard which enables, in principle, a group

of SRM users to have agreement within twice the expanded SRM uncertainty. The quoted

expanded SRM uncertainty was achieved by a strategy to utilize an FTIR instrument to measure

highly precise and relatively consistent values of an optical parameter proportional to oxygen

number fraction (concentration). Our belief is that the measurement consistency so achieved is more relevant to user needs for quality control and interlaboratory comparison than any statement

referring only to the uncertainty of a direct or absolute determination of oxygen number fraction

(concentration).

ADDENDUM - The following additional information is given here in view of a recent publication [11]. All SRM 2551 specimens are n-type. This means that there there is no measurable error due to free- carrier absorption in the vicinity of the 1 107 cm ' oxygen peak [12].

14
A. Baghdadi, R.I. Scace, and E.J. Walters, Semiconductor Measurement Technology: Database

for and Statistical Analysis of the Interlaboratory Determination of the Conversion Coefficient

for the Measurement of the Interstitial Oxygen Content of Silicon by Infrared Absorption, NIST

Special Publication 400-82 (1989).

A. Baghdadi, W.M. Bullis, M.C. Croarkin, L. Yue-Zhen, R.I. Scace, R.W. Series, P. Stallhofer, and M. Watanabe, Interlaboratory Determination of Calibration Factor for the Measurement of the Interstitial Oxygen Content of Silicon by Infrared Absorption, J. Electrochem. Soc. 136 (7), 2015-2024 (July 1989).

S. Vandendriessche, B. Griepink, H. Marchandise, and K. Strijckmans, The Certification of Low

Oxygen Content in Semiconductor Silicon (CRM 368), BCR Information Report EUR 12927 EN

(1990). Published by the Commission of European Communities, Directorate-General,

Telecommunications, Information Industries and Innovation, L-29l0 Luxembourg, Catalogue

number: CD-NA-12927-EN-C.

S. Vandendriessche, B. Griepink, H. Marchandise, B. Pajot, R. Murray, K. Graff, and K.

Strijckmans, The Certification of a Reference Material for the Determination of Oxygen in Semiconductor Silicon by Infra-Red Spectrometry (CRM 369), BCR Information Report EUR

12928 EN (1991). Published by the Commission of European Communities, Directorate-General,

Telecommunications, Information Industries and Innovation, L-2920 Luxembourg, Catalogue

number: CD-NA-12928-EN-C.

R. Murray, K. Graff, B. Pajot, K. Strijckmans, S. Vandendriessche, B. Griepink, and H.

Marchandise, Interlaboratory Determination of Oxygen in Silicon for Certified Reference

Materials, /. Electrochem. Soc. 139 (12), 3582 (1992).

ASTM Standard F 1 188, Standard Test Method for Interstitial Atomic Oxygen Content of Silicon

by Infrared Absorption, ASTM, Philadelphia, PA (1990).

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. [In German. An English translation is published in the Annual Book of ASTM

Standards, Vol. 10.05, ASTM, Philadelphia, PA (1993).]

Guide to the Expression of Uncertainty in Measurement, ISO, Geneva Switzerland, 1993.

Available from Bureau International des Poids et Mesures, Pavilon de Breteuil, F-92312 Sevres

Cedex, France.

F. Schomann and K. Graff, Correction Factors for the Determination of Oxygen in Silicon by

IR-Spectrometry, J. Electrochem. Soc. 136, 2025 (1989).

R.D. Deslattes, Annual Review of Physical Chemistry 31, 435 (1980).

Kitagawara, Y., Tamatsuka, M., Takenaka, T., "Accurate Evaluation of Interstitial Oxygen

Concentrations in Medium-Resistivity Si Crystals" J. Electrochem. Soc. 141 (5), 1362-1364 (May

1994).

Gladden, W.K., Baghdadi, A., "Free Carrier Absorption and Interstitial Oxygen Measurements,"

Emerging Semiconductor Technology, ASTM STP 960, D.C. Gupta and P.H. Langer, Eds.,

American Society for Testing and Materials (1986).

15
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41
TABLE 1 . SRM 255 1 conversion coefficient data using absolute oxygen

concentration data from the GRR and absorption coefficient data

from the NIST FTIR

specimen code

irom L»KK [ij

oxygen concentration

(ppma)*

absorption coefficient

(cm )

210101 8.678 1.4431

210201 12.334 1.8983

ZIUjUI Z.ZJOU

210401 17.325 2.8752

210501 20.356 3.1340

210701 23.524 3.8646

210801 26.821 4.3172

210901 28.721 4.7014

* After adjustment of 0.072% to agree with the full GRR specimen set [sec. III].

42
TABLE 2. Percent difference in absorption coefficient peak iieight due to positional shifts of 2 mm

from center position

oi (cm'^) % change of a % standard deviation beam position

2.6842 reference value 0.051 center wWA A L WA

2.6841 0.004 0.034 2-mm t-^ A A AA A A shift ljAAAXL

2.6832 0.040 0.033 2-mm shift

2.6996 reference value 0.027

2.7015 -0.070 0.037 2-mm ^ 111111 Olllll shift

2.6970 0.100 0.035 2-mm AAA-AAA OAAAAL shift

3.6293 reference value 0.019 center WWA AIWA

3.6266 0.070 0.024 2-mm Ami A A AX A A shift L7AAAAI.

3.6325 -0.090 0.040 2-mm shift

3.5109 reference value 0.023 center

3.5126 -0.050 0.035 2-mm shift

3 5119 -0.030 0.021 2-mm i-J A A AX A A shift kjAAXAi.

4.1906 reference value 0.029 center

4 1890 0.040 0.037 2-mm ^ A A AJ A A shift LjAAAAk

4 1909 -0.007 0.017 2-mm ^ 111X11 shift LjlllXl

4 1683 rpfprence value 0.042 center wwl It wl

4.1703 -0.050 0.018 2-mm shift

4.1676 0.020 0.033 2-mm shift

2.7022 reference value 0.031 center

2.7034 0.044 0.036 2-mm shift

2.7029 0.026 0.027 2-mm shift

43
TABLE 2. (continued)

a (cm'^) % change of a % standard deviation beam position

3.6346 rpference value 0.039 renter

3.6326 -0.055 0.029 9-mm Qhift

3 6363 0.047 0.039 2-mm ^hift

4.1971 reference value 0.025 renter

4.1963 -0.019 0.031 2-mm ^ lillll dllllL 'jhift

4.1979 0.019 0.032 9-mm ^ lillll olllll Qhift

2 6818 rpference value 0.041 renter L'^llL^l

2.6828 0.038 0.033 2-mm shift

2.6824 0.023 0.030 2-mm shift

3.4924 reference value 0.018 center

3.4941 0.049 0.032 2-mm shift

3.4920 -0.011 0.029 2-mm shift

4.1659 reference value 0.017 center

4.1682 0.056 0.026 2-mm shift

4.1678 0.046 0.023 2-mm shift

44
TABLE 3. Summary of uncertainty estimates

source of uncertainty oxygen la (%) 2o (%)

level

lU W yj .yjyjo yj. I ju

standard deviation due to FTIR reproducibility medium 0.050 0.100

high 0.044 0.088

low 0 041 0 082

standard deviation due to SRM

float-zone oxygen variability medium 0.030 0.060

high 0.027 0.054

low 0.030 0.060

standard deviation estimate

related to material uniformity medium 0.030 0.060

high 0.030 0.060

low 0.086 0.17

total SRM uncertainty

medium 0.067 0.13

high 0.060 0.12

45
TABLE 4. Percent difference in absorption coefficient peak height after later repeats

SRM set # oxygen level % difference difference in ppma

1 low -0.017 -0.0029

1 medium 0.035 0.0080

1 high 0.003 0.0008

15 low 0.042 0.0071

15 medium 0.062 0.0143

15 high 0.002 0.0005

17 low 0.050 0.0085

17 medium 0.082 0.0189

17 high 0.038 0.0100

18 low 0.097 0.0165

18 medium -0.007 -0.0016

18 high 0.017 0.0044

53 low 0.131 0.0223

53 medium 0.117 0.0257

53 high 0.017 0.0044

77 low 0.092 0.0156

77 medium 0.129 0.0271

77 high 0.065 0.0169

100 low 0.070 0.0110

100 medium 0.044 0.0092

100 high 0.070 0.0182

46
TABLE 5. Percent difference in absorption coefficient peak height for three remeasurements with

different locations of the specimens in their holder

SRM set # oxygen level % difference difference in ppma

15 low 0.060 0.0102

15 medium 0.035 0 0080

15 hieh iiigii 0.026 0 0068

15 low 0.034 0 0058

15 medium 0.006 0.0014

15 hiffh 0.019 0.0049

15 low 0.042 0.0071

15 medium 0.062 0.0143

15 hiph iiigii 0.002 0 0005

77 low -0.051 -0.0087

77 medium 0.004 0.0009

77 hiph -0.094 -0.0207

77 low 0.016 0.0027

77 medium 0.034 0.0102

77 high -0.058 -0.0151

77 low -0.024 -0.0041

77 medium 0.080 0.0176

77 high 0.098 0.0255

47
TABLE 6. Certified interstitial oxygen values for the 100 SRM sets (ppma)

set # low oxygen medium oxygen high oxygen

1 16.837 22.781 26.250

2 16.752 22.778 26.267

3 16.809 22.833 26.303

4 16.758 22.771 26.316

5 16.878 22.702 26.334

6 16.853 22.711 26.327

7 16.868 22.784 26.368

8 16.869 22.762 26.312

9 16.727 22.648 26.323

10 16.744 22.621 26.262

11 16.727 22.684 26.267

12 16.732 22.637 26.233

13 16.933 22.576 26.050

14 16.943 22.650 26.033

15 16.910 22.583 26.128

16 16.946 22.595 26.108

17 16.777 22.539 26.058

18 16.757 22.578 26.012

19 16.773 22.605 26.062

20 16.785 22.596 26.071

21 16.826 22.824 26.052

22 16.824 22.819 26.028

23 16.809 22.822 26.058

24 16.865 22.830 26.062

25 16.667 22.526 26.001

48
TABLE 6. (continued)

set low oxygen medium oxygen high oxygen

26 16.654 22.557 25.983

27 16.646 22.581 26.041

28 16.646 22.539 26.056

29 16.851 22.437 25.892

30 16.829 22.411 25.890

31 16.848 22.473 25.920

32 16.854 22.445 25.915

33 16.843 22.319 26.169

34 16.888 22.261 26.174

35 16.849 22.346 26.160

36 16.894 22.372 26.159

37 16.823 22.119 26.109

38 16.832 22.101 26.083

39 16.831 22.109 26.096

40 16.817 22.084 26.083

41 17.005 22.157 25.948

42 17.032 22.158 25.937

43 16.998 22.165 26.032

44 17.017 22.151 26.045

45 16.852 22.136 25.945

46 16.887 22.103 25.946

47 16.925 22.133 25.955

48 16.937 22.129 25.938

49 16.938 22.116 25.883

50 16.941 22.114 25.866

49
TABLE 6. (continued)

set # low oxygen medium oxygen high oxygen

51 16.990 22.083 25.897

52 16.984 22.107 25.894

53 16.957 22.125 25.608

54 16.865 21.956 25.946

55 16.866 22.021 25.903

56 16.846 22.004 25.926

57 16.814 21.998 25.922

58 16.904 22.013 25.908

59 16.831 22.017 25.898

60 16.873 22.008 25.894

61 16.823 21.924 25.950

62 16.789 21.885 25.986

63 16.841 21.895 26.033

64 16.827 21.917 26.018

65 16.736 21.802 26.060

66 16.755 21.804 26.007

67 16.752 21.856 26.003

68 16.764 21.851 26.021

69 16.620 21.790 25.896

70 16.607 21.882 25.868

71 16.625 21.830 25.890

72 16.647 21.811 25.876

73 16.746 21.738 25.752

74 16.716 21.776 25.797

75 16.768 21.803 25.879

50
TABLE 6. (continued)

set # low oxygen medium oxygen high oxygen

76 16.764 21.766 25.888

11 16.632 21.713 25.879

78 16.673 21.724 25.840

79 16.670 21.721 25.849

80 16.664 21.699 25.858

81 16.915 21.500 25.822

82 16.900 21.485 25.839

83 16.948 21.532 25.852

84 16.970 21.539 25.891

85 16.844 21.303 25.803

86 16.786 21.292 25.891

87 16.810 21.395 25.873

88 16.818 21.300 25.810

89 16.822 21.199 25.820

90 16.780 21.246 25.765

91 16.823 21.275 25.853

92 16.841 21.284 25.860

93 16.814 20.964 25.867

94 16.794 20.991 25.876

95 16.803 20.929 25.814

96 16.824 20.891 25.765

97 16.912 20.999 25.875

98 16.881 21.042 25.843

99 16.935 21.053 25.923

100 16.903 21.117 25.945

51
TABLE 7. Center thickness values for the 100 SRM sets (mm)

set # low oxygen medium oxygen high oxygen float-zone

1 2.0726 2.0347 2.0775 2.1207

2 2.0716 2.0331 2.0824 2.1213

3 2.0714 2.0323 2.0802 2.1244

4 2.0743 2.0296 2.0857 2.1233

5 2.0553 2.0824 2.0718 2.1150

6 2.0558 2.0829 2.0699 2.1207

7 2.0583 2.0834 2.0778 2.1132

8 2.0599 2.0830 2.0749 2.1206

9 2.0722 2.0687 2.1021 2.1203

10 2.0719 2.0684 2.1026 2.1192

11 2.0720 2.0711 2.0945 2.1180

12 2.0713 2.0732 2.0963 2.1160

13 2.0589 2.0638 2.0568 2.1140

14 2.0589 2.0669 2.0550 2.1153

15 2.0599 2.0656 2.0525 2.1131

16 2.0566 2.0666 2.0521 2.1172

17 2.0728 2.0726 2.0701 2.1174

18 2.0718 2.0720 2.0728 2.1206

19 2.0760 2.0737 2.0670 2.1165

20 2.0753 2.0750 2.0677 2.1184

21 2.0841 2.0901 2.0573 2.1279

22 2.0830 2.0897 2.0673 2.1243

23 2.0724 2.0879 2.0517 2.1297

24 2.0720 2.0888 2.0596 2.1249

25 2.0633 2.0814 2.0404 2.1205

52
TABLE 7. (continued)

set # low oxygen medium oxygen high oxygen float-zone

26 2.0631 2.0851 2.0419 2.1248

27 2.0693 2.0765 2.0372 2.1188

28 2.0674 2.0791 2.0395 2.1232

29 2.0759 2.0895 2.0697 2.1284

30 2.0776 2.0819 2.0711 2.1310

31 2.0779 2.0910 2.0604 2.1314

32 2.0783 2.0852 2.0611 2.1325

33 2.0760 2.0779 2.1013 2.1161

34 2.0739 2.0814 2.1037 2.1167

35 2.0770 2.0815 2.0956 2.1155

36 2.0755 2.0843 2.0970 2.1150

37 2.0570 2.0724 2.0455 2.1195

38 2.0602 2.0752 2.0426 2.1233

39 2.0564 2.0765 2.0452 2.1158

40 2.0572 2.0798 2.0432 2.1204

41 2.0515 2.0795 2.0703 2.1306

42 2.0503 2.0767 2.0709 2.1376

43 2.0498 2.0764 2.0764 2.1331

44 2.0480 2.0746 2.0750 2.1401

45 2.0412 2.0708 2.0609 2.1186

46 2.0406 2.0670 2.0628 2.1226

47 2.0417 2.0683 2.0660 2.1176

48 2.0430 2.0621 2.0688 2.1225

49 2.0461 2.1008 2.0739 2.1106

50 2.0436 2.0885 2.0721 2.1144

53
TABLE 7. (continued)

set # low oxygen medium oxygen high oxygen float-zone

51 2.0437 2.1017 2.0760 2.1078

52 2.0415 2.0904 2.0732 2.1114

53 2.0515 2.1012 2.0519 2.1350

54 2.0512 2.0956 2.0511 2.1347

55 2.0434 2.0972 2.0526 2.1399

56 2.0441 2.0912 2.0526 2.1391

57 2.0484 2.0721 2.0621 2.1296

58 2.0459 2.0773 2.0619 2.1248

59 2.0435 2.0773 2.0603 2.1294

60 2.0431 2.0796 2.0604 2.1211

61 2.0440 2.0561 2.0771 2.1184

62 2.0444 2.0661 2.0747 2.1211

63 2.0369 2.0620 2.0796 2.1237

64 2.0394 2.0685 2.0800 2.1272

65 2.0495 2.0817 2.0855 2.1252

66 2.0504 2.0820 2.0862 2.1283

67 2.0400 2.0799 2.0856 2.1242

68 2.0410 2.0796 2.0845 2.1243

69 2.0173 2.0910 2.0962 2.1269

70 2.0164 2.0955 2.0984 2.1265

71 2.0157 2.0892 2.0868 2.1274

72 2.0159 2.0918 2.0887 2.1258

73 2.0448 2.0863 2.0860 2.1333

74 2.0466 2.0839 2.0829 2.1351

75 2.0409 2.0921 2.0849 2.1330

54
TABLE 7. (continued)

set # low oxygen medium oxygen high oxygen float-zone

76 2.0410 2.0894 2.0839 2.1336

11 2.0413 2.0818 2.0845 2.1202

78 2.0419 2.0793 2.0836 2.1194

79 2.0363 2.0840 2.0832 2.1143

80 2.0376 2.0791 2.0839 2.1134

81 2.0122 2.0770 2.0838 2.0504

82 2.0153 2.0736 2.0817 2.0547

83 2.0105 2.0757 2.0856 2.0545

84 2.0132 2.0715 2.0823 2.0569

85 2.0161 2.0661 2.0884 2.0535

86 2.0176 2.0688 2.0910 2.0546

87 2.0165 2.0695 2.0883 2.0485

88 2.0173 2.0716 2.0899 2.0496

89 2.0157 2.0829 2.0874 2.0461

90 2.0164 2.0786 2.0926 2.0488

91 2.0168 2.0775 2.0875 2.0471

92 2.0168 2.0758 2.0899 2.0510

93 2.0200 2.0684 2.1344 2.0462

94 2.0228 2.0675 2.1361 2.0535

95 2.0173 2.0663 2.1335 2.0420

96 2.0200 2.0679 2.1348 2.0482

97 2.0113 2.0794 2.1372 2.0554

98 2.0123 2.0767 2.1389 2.0587

99 2.0062 2.0791 2.1349 2.0721

100 2.0061 2.0788 2.1359 2.0730

55

APPENDIX A. SAMPLE CERTIFICATE

Nntional Knslttutf of §?tanbar5s 3c ffirrhnnlngy

CGFrttftratF nf Analysts

Standard Reference Material 2551

Oxygen Concentration in Silicon Standard

SRMSetNo.: i

This Standard Reference Material (SRM) is intended for calibration of infrared spectrophotometers used to measure

the 1 107 cm"^ interstitial oxygen peak in silicon. Certified oxygen concentrations are given for low, medium, and

high oxygen level Czochralski specimens. Each SRM unit is a set of four specimens comprising a float-zone specimen [with minimal oxygen concentration less than 0.1 pans per million atomic (ppma)], and the three Czochralski specimens which cover a range of roughly 8.5-17 mg/kg (15-30 ppma - (IOC-88)). [1-3] Each

specimen has been individually measured and bears an SRM set number and a letter identification for each oxygen

level (L, M, or H). Each specimen is nominally 25-mm square and 2-mm thick and has been polished on both

sides. The specimen materials, which were obtained from Wacker Siltronic, Portland, OR, have resistivities greater than 3 ohm»cm.

CERTIFIED VALUES OF OXYGEN CONCENTRATION

Units Low Level ( L ) Medium Level ( M ) High Level ( H )

ppma 16.837 22.781 26.y50

mg/kg 9.591 12.S78 14.954

10'^ atoms/cm^ 8.408 11.377 13.109

UNCERTAINTY OF CERTIFICATION (ppma)*

0.029 (0.17 %) 0.030 (0.13 %) 0.031 (0.12 %)

NON-CERTIFIED THICKNESS VALUES (mm)

Float-Zone Low Level Medium Level High Level

2.1207 2.0726 2.0347 2.0775

" The stated uncertainty is the 2a precision with which the oxygen scale obtained from the eight-specimen cahbration set is reproduced in each

of the SRM sets. This does not include the uncertainty of the absolute values of oxygen for the calibration specimens. The certified portion of the SRM specimen is the central 6-mm diameter circle. Thickness values are not certified and are given as useful information only. To

convert from ppma to mg/kg, multiply by 0.56967; to convert from ppma to atoms/cm^ multiply by 0.49939 x lO'^.

Certification measurements were made by B.G. Rennex and sample preparation was done by J.M. Thomas, both of the NIST Semiconductor Electronics Division. The work was supported by the Materials Technology Group of

this Division. Review of the statistical analyses was performed by J.J. Fillibenof the NIST Statistical Engineering

Division.

The preparation, cenification, and issuance of this SRM were coordinated through the Standard Reference Materials Program by N.M. Trahey.

Gaithersburg, MD 20899

March 1, 1994

(over)

Thomas E. Gills, Acting Chief

Standard Reference Materials Program
Certification Apparatus: Power spectra were measured in the wavenumber vicinity of 1 107 cm ', the location of

the room temperature peak for interstitial oxygen, by a Fourier Transform Infrared (FTIR) spectrophotometer. The

detector system comprised a gold-plated light-cone and a 2 mm-diameter, room temperature deuterated-triglycinesulfate (DTGS) detector. The beam diameter at the specimen was 5 mm, and it was located at the specimen center

to within ± 1 mm. The wavenumber resolution was 4 cm"' . During the measurement, the sample chamber of the FTIR instrument was maintamed at a temperature of 27.8 ± 0.5 °C. No detectable spurious blackbody radiation was found. [4]

Certification Measurement Protocol: In general, a cenification measurement determination consisted of the following steps:

la. Two SRM sets of four specimens each were mounted on a sample holder, along with a control specimen of

known, medium oxygen concentration. After specimen loading, it was necessary to wait about an hour for transient thermal effects to reach steady state. Then, power spectra were measured in a test run in the following sequence: open beam; control specimen; first set (float-zone, low oxygen, medium oxygen, and

high oxygen); open beam; control specimen; and second set (float-zone, low oxygen, medium oxygen, and

high oxygen). ^

lb. Each power spectrum in the above test sequence was based on 90 scans, which took about five minutes, and

at least four repeats of this sequence were made for each run. Thus, a cenified oxygen value is computed

using the average of four 5-min measurements spaced over a period of roughly 8 h.

2. The transmission spectrum for each specimen was calculated as the ratio of the specimen power spectrum

over the open-beam power spectrum.

3. Absorption (coefficient) spectra were calculated for each test specimen and for each float-zone specimen. [1] The float-zone spectrum was then subtracted from the test specimen spectrum to arrive at the spectrum due

to oxygen only.

4. The oxygen peak height was obtained as follows. A Gaussian curve fit to the absorption spectrum was made

to determine the peak height and wavelength. A baseline was constructed, and the baseline value at the peak

wavelength was subtracted from the peak height to calculate the net oxygen peak height.

5. Data on the control specimen were used to make a linear compensation for instrument drift over time; this improved instrument reproducibility by about a factor of three. Measurements were made on a separate four- specimen set (comprising a float-zone specimen and specimens at three oxygen levels) between each SRM

run. These runs were made using the same procedure, including the use of a control specimen, as for the SRM runs, and they provided an estimate of the random uncertainty, or reproducibility, of the instrument over the entire period of SRM measurements.

Calibration of the NIST FTIR instrument was based on measurements of a subset of eight reference specimens from

a larger set of specimens previously used in an international study called the Grand Round Robin (GRR). [2,3] The

bias of the eight-specimen subset with respect to the complete GRR specimen set is -0.72%, as established by the GRR data. The measurements made to certify the SRM have been adjusted to eliminate this bias. These calibration measurements allowed a determination of an SRM conversion coefficient (from a to oxygen concentration) specific

to the NIST FTIR instrument. The certified SRM oxygen concentration values are based on this SRM conversion

coefficient, not on the GRR conversion coefficient. [4,5]

2
Also, a study was made to ascertain that no additional error was observed when repeated points were taken after a specimen had been removed from and replaced back into the sample holder. Initially, a significant offset occurred

due to removal and replacement of a specimen, perhaps because of non-uniformities in the beam and detector at this level of precision. This error was eliminated when a light-cone was used in the detector assembly. [4]

Uncertainties: The SRM uncertainty is based on the precision of the NIST FTIR spectrophotometer and on

uncertainties due to non-uniformity of thickness and oxygen concentration over the central 6-mm area of the SRM

specimen sampled by the FTIR beam. Standard deviations were estimated for the various contributing factors (all of which are ISO Type A) and added in quadrature. [6] This sum was multiplied by a factor of two to get a 2a

value for the expanded uncertainty. The first contributing factor is instrument reproducibility, as estimated by the standard deviation for data taken on the NIST FTIR for the four-specimen set. The standard deviation of the reproducibility, as determined in a series of measurements independent of and concurrent with the certification measurements, is 0.0115 ppma for all three oxygen levels. The second contributing factor is variability of both

thickness and oxygen concentration from one area to another over the specimen surface. The standard deviation

for this factor is 0.0051 ppma for low oxygen, 0.0069 ppma for medium oxygen, and 0.0078 ppma for high oxygen

specimens. The third contributing factor is variability of oxygen among the float-zone, or "zero-oxygen," SRM

specimens. The standard deviation for this variation is 0.007 ppma, for all three oxygen levels.

Adding these three values of standard deviation in quadrature, and multiplying by two, gives the following 2a

estimates of total SRM precision: 0.029 ppma (0.17%) for low oxygen specimens, 0.030 ppma (0.13%) for medium oxygen specimens, and 0.031 ppma (0.12%) for the high oxygen specimens. These values of total SRM

precision are intended to be of practical use for current IC industrial requirements. They are much smaller than

the uncertainty values of an absolute measurement of oxygen concentration. They are also much smaller than the interlaboratory variability of 2.7% (la) from the GRR report, and this interlaboratory variability is an indication of the interlaboratory agreement expected without an SRM. [2,3]

The certified oxygen concentration values are independent of temperature and are internally consistent from any one SRM specimen or set to any other, to within the above-stated total SRM precision. And, if two distinct instruments

calibrated by two different SRM sets were to have the same precision as the certifying spectrometer, the agreement

between their values for identical specimens would be described by a precision equal to roughly twice the total SRM

precision. That is, four separate a values - one for each SRM and one for each instrument - would be added in quadrature to estimate the total comparison standard deviation.

3
RECOMME>a)ED CALIBRATION AND HANDLING INSTRUCTIONS FOR SRM 2551

Calibration Procedure: The detailed procedure for calibration of a user instrument will depend on the particular

application. For guidance, a user should refer to standard test methods for measurement of oxygen in silicon. [ 1 ,7] More information is contained in the SRM certification repon and in documents which explain the SRM experiment

and the statistical methodology in greater detail. [4,5,8]

It is recommended that both the open beam and tloat-zone specimen be measured every time a calibration is made,

unless a user can demonstrate that this is unnecessary. Such a demonstration would involve a statistical comparison

of results with the open beam and float-zone spectra measured every time against results where this is not the case.

To obtain the best agreement with the cenified SRM values, a user must use a 5-mm beam and must locate this beam at the center of the SRM specimen, to within 1 mm. Also, the user should make sure that the temperatures

of the specimens to be measured are as close as possible to the temperatures of the SRM specimens. This is because

the user calibration factor is temperature dependent even though the certified oxygen value is not. [7] That is, the measured absorption coefficient peak height varies with temperature in this range with a coefficient of 0.0016 K"^

while the actual oxygen concentration remains constant. This means that the certified estimate of oxygen

concentration can be used without adjustment even if a user's measurement temperature is different from the value used in the SRM 2551. However, the user must expect his own oxygen conversion coefficient to vary with

temperature according to the just-quoted temperature coefficient.

The certified quantity is the interstitial oxygen concentration, OX^^^, for the low, medium, and high oxygen

specimens. This oxygen concentration is proportional to the height of the 1107 cm"' peak of the absorption

coefficient spectrum, with the constant of proportionality being the conversion coefficient. Without an SRM. a user

calculates an oxygen value, OX^, as a product of a measured absorption coefficient peak height and the internationally accepted conversion coefficient, C. [2,3] With the SRM, the instrument conversion coefficient must

be adjusted by a calibration factor determined from the calibration. This calibration factor is equal to the ratio, of (OX^n^/OXy), where OX^mi is the certified oxygen value for an SRM specimen, and OX^, is the measured oxygen

value for that same SRM specimen using the international value of C.

The subscript j = 1, m, or h. identifies each of the three SRM specimens. R^^ refers to the three calibration factor values obtained by the user, u, with the three SRM specimens. For the three SRM specimens, the ratios,

Ryj = (0X5rnij/0X^j) are the calibration factors for the user instrument, and the products, R^j x C, are the conversion

coefficients for the user instrument. These three conversion coefficients may now be used to calculate oxygen

values for unknown specimens.

In general, a user should evaluate the three calibration factors for the low, medium, and high level oxygen SRM

specimens, but then must choose which value to use in a particular measurement. If the three values are close (e.g.

within the reproducibility of the user instrument), the average of all three values should be used. If there are larger

differences in the three calibration factors, R^j, the user may use the calibration factor of the SRM specimen with

the closest value to that of the unknown specimen. Alternatively, a user can use an interpolation, an example of

which is given below. This example is for an unknown specimen with an oxygen value between those of the low

and medium level SRM specimens.

Let OX^j|, OXyj^, and OX^ be the user-measured, peak-height values for the low and medium SRM specimens, and

for the unknown specimen, respectively. And, let R^j and R^^, be the previously determined calibration factors for the same SRM specimens. The interpolated value of the calibration factor, R^, is then:

R, = R„ + (OX, - 0X„) (R,^ - R„) / (0X„^ - 0X„,)

4
An interpolation in the range between the mid-oxygen specimen and the high-oxygen specimen can be made in an

equivalent manner.

Handling Procedures: The SRM specimens are mounted on aluminum templates. Do not touch the polished surfaces of the SRM specimens with the fingers or with any hard or abrasive material. Handle the specimens by holding the aluminum templates. If it should be necessary to remove specimens from these templates, please follow the instructions below:

1. Gradually warm the template to approximately 70 °C or vmtil the mounting wax begins to flow. Carefully remove

the specimen with non-metallic tweezers or with a vacuum wand, taking care not to scratch the specimen surface.

2. While the specimen is still warm, flush it with tepid methyl alcohol, or an alternative solvent, until all wax is removed. Clean cotton may be used with the alcohol.

3. After all traces of wax have been removed with the alcohol, wash with a warm solution of liquid detergent and deionized water to ensure that all wax residue has been removed. Then, rinse with de-ionized water to remove all traces of detergent.

4. Make a final rinse with methyl alcohol and blow dry with nitrogen to avoid spotting.

5. To replace a specimen into the alimiinimi templates, put four dabs of mounting wax on the four inside comers of

the template. Slowly heat the template imtil the wax begins to flow. Place the specimen (at room temperature)

squarely into the recesses of the template and continue to press it against the template with a cotton swab until the wax begins to flow again. Finally, allow the template to cool. ADDENDUM

The following additional information is given here in view of a recent publication [8]: All SRM 2551 specimens are ntype. This means that there is no measurable error due to free-carrier absorption in the vicinity of the 1 107 cm ' oxygen

peak [9].

5
REFERENCES

[1] ASTM Standard F1188, Standard Test Method for Interstitial Atomic Oxygen Content of Silicon by Infrared Absorption." Annual Book of ASTM Standards, Vol. 10.05. ASTM. Philadelphia. PA, 1991.

[2] Baghdadi. A.. Bullis, W.M., Croarkin. M.C., Li. Yue-zhen. Scace. R.I.. Series, R.W.. Stallhofer P., and

Watanabe, M., "Interlaboratory Determination of the Calibration Factor for the Measurement of Interstitial Oxygen Content of Silicon by Infrared Absorption," J. Electrochem. Soc. 136, 2015-2024, 1989.

[3] Baghdadi, A., Scace, R.I., and Walters, E.J., Semiconductor Measurement Techology: "Database for and

Statistical Analysis of the Interlaboratory Determination of the Conversion Coefficient for the Measurement of

the Interstitial Oxygen Content of Sihcon by Infrared Absorption," NIST Special Publication 400-82 . 1989.

[4] Rennex. B.J.. NIST Special PubUcation 260-121. Standard Reference Materials: "The certification of a Standard

Reference Material for the Determination of Interstitial Oxygen Concentration in Semiconductor Silicon by Infra- Red Spectrophotometer." (in prep).

[5] Rennex. B.J. and Ehrstein, J.R., "Methodology for the Utilization of High-Precision/Reduced-Absolute-Accuracy

Measurements in Standard Reference Materials." (to be pubhshed in the NIST J.' of Res., 1994).

[6] "Guide to the Expression of Uncertainty in Measuremeru," ISO. Geneva, Switzerland, 1993. Available from

Bureau International des Poids et Mesures, Pavilon de Breteuil, F-92312 Sevres Cedex, France.

[7] DIN Standard 50 438/1, "Determination of Impurity Content in Semiconductors by Infrared Absorption; Oxygen

in Silicon," Beuth Verlag, Berlin (1993) [in German. An Enghsh translation is published in the Annual Book of

ASTM Standards, Vol. 10.05, ASTM. Philadelphia. PA (1993).]

[8] Kitagawara. Y., Tamatsuka, M., Takenaka, T., "Accurate Evaluation of Interstitial Oxygen Concentrations in Medium-Resistivity Si Crystals," J. Electrochem. Soc. 141 (5), 1362-1364, May 1994.

[9] Gladden, W.K., Baghdadi. A.. "Free Carrier Absorption and Interstitial Oxygen Measurements. "Emerging

Semiconductor Technology, ASTM STP 960, D.C. Gupta and P.H. Langer, Eds., American Society for Testing

and Materials, 1986.
APPENDIX B. CALCULATION OF ABSORPTION COEFFICIENT PEAK HEIGHT

The following derivation expresses the absorption coefficient, ot, in terms of the measured transmittance,

T, through a double-side-polished wafer. These are spectral quantities which have peaks due to impurities. The goal is to calculate an oxygen peak height. Equation (1) expresses T in terms of a and

X, the wafer thickness. T is actually a ratio of a test specimen power spectrum over an open-beam power

spectrum. Figure 2 shows transmittance for the oxygen specimen and a float-zone specimen (nominally

with zero oxygen content) at the oxygen peak. Figure 3 shows absorption coefficient spectra for the

same, as well as their difference, which is the peak due to oxygen only.

The numerator incorporates the fact that there is a reflection at both surfaces and there is absorption

across the thickness of the wafer. The denominator results from multiple reflections within the specimen.

(1 - Rf e1 -

(1)

let z e

define C

2R^

define

(1 - Rf

Solving the quadratic equation in z gives

(2)

(3)

B-1
Note that T refers to a ratio of power spectra with and without a specimen in the spectrophotometer

beam; that is, T describes the loss due only to the specimen.

For the "oxygen in silicon" measurement, a is the sum of the following two terms: a^^ is the absorption

coefficient due to interstitial oxygen and a^^ is the absorption coefficient due to silicon. That is, the

measured for a silicon specimen with oxygen enables one to calculate via eq (3), and = a^^ +

ttjj. What is really needed is a^^, and this requires an independent measurement of a^j, which is measured on a float-zone, or zero-oxygen specimen. Then, = the measured value of minus the

measured value of a^^.

The peak height of a^^ is calculated by subtracting the value at the peak wave number of a baseline,

which is a straight line between the curve values on either side of the 1107 cm'^ oxygen peak. Ideally,

the baseline should be a constant zero; in practice it is not. A certain robustness is inherent to the method

since errors due to optics are cancelled to some extent by two features of the calculation. First, the float- zone spectrum is subtracted from the unknown oxygen specimen; next, the baseline level of oxygen is subtracted from the peak level. To the extent that errors in the measured T values are multiplicative, they

cancel. If these errors are additive, they cancel only partially, because of the nonlinearity of the

expression for o: in terms of T.

The following is a step-by-step explanation of the computer algorithm for calculation of oxygen

concentration in silicon.

1. Measure a power spectrum, P, for the following cases:

^open " reference (open beam)

Pf2 - silicon reference (floatzone, zero oxygen, or silicon background)

Pj - oxygen specimen (silicon plus oxygen structure)

2. Calculate transmission spectra for the silicon reference and oxygen specimens.

T — p /P * r ^ fz"- open T* = P /P s ^ s' ^ open

3. Calculate the absorption coefficient spectra, a^. and using eq (3) in this appendix.

4. Calculate the absorption coefficient due to interstitial oxygen.

«ox = «s - «r

5. Perform the curve fitting on the 1107 cm"^ oxygen peak as follows.

The baseline value is the average of two average values ~ of points between 1030 and 1050 cm'^ on one

side and between 1160 and 1180 cm"^ on the other side. The peak value is the result of a gaussian fit to points between 1096 and 1119 cm'^ The difference of these values is the absorption coefficient peak

height. Multiplication of this peak height by the conversion coefficient gives the oxygen concentration.

This method follows that of ASTM Method F1188 [6] except that the curve fitting is done on a^^ rather

than on T^ and the range of values for baseline averaging is slightly different.

B-2
APPENDIX C. ISSUES RELATED TO THE CONVERSION COEFFICIENT

One goal of the SRM was to arrive at oxygen values which are consistent with the earlier GRR work

[1,2]. The discussion below shows in mathematical terms that the use of the SRM conversion coefficient,

Cj, determined with the NIST FTIR for SRM 2551, avoids any bias between the values of the SRM 2551

specimens and the values of the GRR specimens. On the other hand, if another conversion coefficient,

e.g., the GRR value, were used, such a bias would occur.

The GRR study determined the GRR conversion coefficient, C, which was based on averages over many

specimens and many laboratories and which was based on both spectrometer and absolute measurements.

The combined results showed an interlab variability, which means that each instrument had a bias with

respect to the average for all instruments.

Let Ci be a set of N conversion coefficients for N instruments (laboratories) in a study in which absolute

measurements, Aj^, have been made on a set of specimens, "s," along with relative instrument

measurements, Rj^. Cj is the average of Rjs/Ajj for a particular instrument, "i." In the case of the

oxygen SRM, Aj^ is a value of oxygen concentration, and Rj^ is a peak height for the optically determined

absorption coefficient. A^ is the average value for all instruments for specimen "s" (i.e., C = XI C^/N).

Each Cj has a difference from C, Dj = Cj - C. Assume that sufficient measurement points have been

taken to ensure that the average of the Dj points is primarily due to the "i" instrument. This average

value, Dj, represents a systematic instrument bias which must be duly considered and used to achieve the correct absolute value as estimated by the GRR study.

If a specimen is measured by instrument "i," and if C (the GRR average value) is used to calculate each

Ajg, the value of Aj^ will be wrong by an amount equal to -Dj. That is, if only one instrument were used

to estimate each Aj^, and if it used C instead of Cj, the value would be wrong by -Dj. This situation

applies only when an instrument uses specimens for which each Aj^ (absolute oxygen value) was measured

in the GRR.

If an instrument does not have access to the specimens used for absolute determinations, then C (i.e., the

GRR mean value) conversion coefficient should be used, and the relevant precision for that measurement

is the interlab precision in the GRR study. For the GRR study, the interlab precision, as estimated by

1-sigma, was 2.7%; the comparable value for the NIST precision was approximately 0.05%. Thus, the

achievable internal consistency among high precision users of the NIST SRM can be about 50 times better

than the internal consistency without an SRM (when a user must use the GRR coefficient). Also, if independent SRM studies were to be made by two different standards laboratories, the difference between

their conversion coefficients would be the sum of any systematic difference in the absolute measurements

and the bias between the two optical instruments.

A related issue is how to handle differences between different standards which depend on an absolute

measurement with large uncertainties. The systematic difference in the absolute measurements would

result in a systematic difference between the two standard reference materials. Such a difference could

cause confusion among the various users of one or both of these standards. A practical solution which

may be considered for future cases where more than one standard is developed, would be to thoroughly

characterize the total systematic difference between two different standards and to report it to SRM users.

C-1

APPENDIX D. PRODUCTION RUN PROTOCOL

The measurement protocol was the following. Two sets of four wafers were placed in a 3 x 3 position

specimen holder. Although there was originally room for only nine specimens, it was necessary to measure ten positions in all - eight specimens for the two production sets and a control specimen and a location for an open beam. For this reason, the center position of the specimen holder contained a control specimen with one quadrant of its area removed. When this empty quadrant was in the beam,

an open beam spectrum was measured. When the opposite quadrant was in the beam, the control

specimen spectrum was measured. Before the quadrant was removed, a comparison was made between

the measured peak height at the center of the control specimen and at the quadrant to be used for the

oxygen measurement. The reason was that the optical measurements in the GRR had been made on the center of this specimen. The comparison between these two peak height values was within 0.01 % . For

this reason, the fact that the center is not used does not result in a significant error in the slope

determination discussed in section IV.

The measurement sequence was the following:

FIRST SET

1 . open beam

2. control specimen

3. float-zone specimen

4. "level 1" specimen

5. "level 2" specimen

6. "level 3" specimen

SECOND SET

7. open beam

8. control specimen

9. float-zone specimen

10. "level 1" specimen

11. "level 2" specimen

12. "level 3" specimen

This sequence was repeated four times, without reloading, to give four oxygen values with respect to the

float-zone specimen, for each of the three levels of oxygen peak height, for two complete specimen sets. Thus, each reported value of oxygen peak height is an average of four repeated measurements or points.

Having an average reduces the chance of outliers. Also, the use of time plots over 8 h for each

production run made it possible to verily that the curves for the various specimens were tracking in terms

of any drift that may have been present. This was a necessary requirement to ensure that spurious

transient effects were not present which might have affected the drift compensation.

Each spectrum was the result of 90 scans which took 4.5 min each. Spectra were checked for each run

to ensure that the transmission at 2000 cm"^ was within +2% of 53.8%, the expected value in nonabsorbing regions of the spectrum. The numbers of scans and repetitions were chosen as a compromise between achieving good averages for each point versus detailed information regarding drift.

D-1
The entire protocol required 8 h, and this resulted in measurement of two SRM sets. A wait period of an hour was required after loading of specimens, due to thermal transients caused by opening the

instrument cover. The spectrometer was housed in a room with a temperature control good to +0.5°C.

Two of these protocols were performed in a day; thus, four SRM sets were measured per day. The

remaining portion of the 24-h period was used to measure repeats of a set of performance evaluation

specimens. The protocol for these tests was similar to that for the production run sets except that only one set (of three oxygen specimens plus a float-zone specimen) was measured in sequence instead of two

sets. Control specimen measured values were used for drift compensation of the measured values for the

three specimens in each SRM set, and each report value was the average of four measured values.

D-2
APPENDIX E. UNIT CONVERSIONS

There are three units of oxygen number fraction (concentration) commonly used: parts per

milHon by weight (a mass fraction), ppm (wt) or mg/kg; parts per milhon atomic (a number

fraction) or (ppma); and number per cm^ times 10^^ (a concentration within bulk silicon). The

conversions between these are the following. Since ppm by itself is ambiguous, the (a) or (wt) are included.

0(10^' cm-') = (dsi*NVAo) * (ppm (wt)/10')

= 0.876633 * ppm (wt)

0(ppm (wt)) = (A0/A3.) * O ppm (a)

= 0.569668 * O ppm (a)

0(10^' cm-') = 0.876633 * 0.569668 * O ppm (a)

= 0.499389 * O ppm (a)

where

Ao

= density of silicon = 2.328995 g/cm' [10] = Avogadro's Number = 6.022169 * 10^' atoms/mol = atomic weight of oxygen = 15.9994 g/mol = atomic weight of silicon = 28.0855 g/mol

E-1

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materials, components, systems, and whole structures. The series presents research results, test methods, and performance criteria related to the structural and environmental functions and the

durability and safety characteristics of building elements and systems.

Technical Notes — Studies or reports which are complete in themselves but restrictive in their treatment of a subject. Analogous to monographs but not so comprehensive in scope or definitive

in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NIST under the sponsorship of other government agencies.

Voluntary Product Standards — Developed under procedures published by the Department of

Commerce in Part 10, Title 15, of the Code of Federal Regulations. The standards establish

nationally recognized requirements for products, and provide all concerned interests with a basis

for common understanding of the characteristics of the products. NIST administers this program

in support of the efforts of private-sector standardizing organizations.

Consumer Information Series — Practical information, based on NIST research and experience,

covering areas of interest to the consumer. Easily understandable language and illustrations provide useful background knowledge for shopping in today's technological marketplace.

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Federal Information Processing Standards Publications (FIPS PUB) — Publications in this series

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initial distribution is handled by the sponsor; public distribution is by the National Technical

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