PUBLICATIONS

NATL INST OF STAND & TECH

A 11 10 7 257747

*<"?EAU OV NBS SPECIAL PUBLICATION 260-93

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

Standard Reference Materials:

Preparation and Certification

of SRM's for Calibration

of Spreading Resistance Probes

QC100

U57

No. 269-93"

1985

c, 2
TM he National Bureau of Standards was established by an act of Congress on March 3, 1901. The §[ Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is performed by the National Measurement Laboratory, the National Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Center for Materials

Science.

The National Measurement Laboratory

Provides the national system of physical and chemical measurement;

coordinates the system with measurement systems of other nations and

furnishes essential services leading to accurate and uniform physical and

chemical measurement throughout the Nation's scientific community, in- dustry, and commerce; provides advisory and research services to other Government agencies; conducts physical and chemical research; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Basic Standards2 Radiation Research Chemical Physics

Analytical Chemistry

The National Engineering Laboratory

Provides technology and technical services to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement

capabilities; provides engineering measurement traceability services; develops

test methods and proposes engineering standards and code changes; develops and proposes new engineering practices; and develops and improves mechanisms to transfer results of its research to the ultimate user. The

Laboratory consists of the following centers:

Applied Mathematics

Electronics and Electrical Engineering2 Manufacturing Engineering

Building Technology

Fire Research Chemical Engineering2

The Institute for Computer Sciences and Technology

Conducts research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and economy in Government

operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing

the Federal Information Processing Standards Program, developing Federal ADP standards guidelines, and managing Federal participation in ADP

voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and provides the technical foundation for computer-related policies of the Federal Government. The Institute consists of the following centers:

Programming Science and

Technology Computer Systems

Engineering

The Center for Materials Science

Conducts research and provides measurements, data, standards, reference

materials, quantitative understanding and other technical information funda- mental to the processing, structure, properties and performance of materials; addresses the scientific basis for new advanced materials technologies; plans

research around cross-country scientific themes such as nondestructive

evaluation and phase diagram development; oversees Bureau-wide technical programs in nuclear reactor radiation research and nondestructive evaluation; and broadly disseminates generic technical information resulting from

its programs. The Center consists of the following Divisions:

Inorganic Materials Fracture and Deformation3 Polymers

Metallurgy Reactor Radiation

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address

Gaithersburg, MD 20899.

2 Some divisions within the center are located at Boulder, CO 80303. 'Located at Boulder, CO, with some elements at Gaithersburg, MD.
James R. Ehrstein

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Gaithersburg, MD 20899

NATIONAL BUREAU

OF STANDARDS

LIBRARY Standard Reference Materials:

Preparation and Certification

of SRM's for Calibration

of Spreading Resistance Probes

no. Xc&^Z

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director Issued January 1985
Library of Congress Catalog Card Number: 84-601158

National Bureau of Standards Special Publication 260-93

Natl. Bur. Stand. (U.S.), Spec. Publ. 260-93, 40 pages (Jan. 1985)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1985

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

Standard Reference Materials (SRM's) as defined by the National Bureau of Standards are "wel 1 -characteri zed materials, produced in quantity, that calibrate a measurement system to assure compatibility of measurement in the Nation." SRM's are widely used as primary standards in many diverse fields of science, industry, and technology,

both within the United States and throughout the world. For many of the Nation's scientists and technologists it

is of more than passing interest to know the measurements obtained and methods used by the analytical community

when analyzing SRM's. An NBS series of papers, of which this publication is a member, called the NBS Special Publication - 260 Series is reserved for this purpose. This 260 Series is dedicated to the dissemination of information on all phases of the preparation, measurement,

and certification of NBS- SRM's. In general, 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 the greatest care and accuracy. It is also hoped that these papers'will provide sufficient additional information not found on the certificate so that new applications in diverse fields not foreseen at the time the SRM was originally issued will be sought and found. Inquiries concerning the technical content of this paper should be directed to the author. Other questions concerned with the "avai 1 abil ity, delivery, price of specific SRM's should be addressed to: Office of Standard Reference Materials

National Bureau of Standards Gaithersburg, MD 20899

Stanley D. Rasberry, Chief

Office of Standard Reference Materials

i i i
OTHER NBS PUBLICATIONS IN THIS SERIES

Catalog of NBS Standard Reference Materials

(1984-85 edition), Catherine H. Hudson, ed., NBS

Spec. Publ. 260 (February 1984). Michaelis, R. E., and Wyman, L. L. Standard

Reference Materials: Preparation of White Cast

Iron Spectrochemical Standards. NBS Misc. Publ. 260-1 (June 1964). CO M74- 1 106 1 **

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 LowAlloy Steel Standard. NBS Misc. Publ. 260-3 (October 1964). COM74-1 1060** Hague, J. L. Mears, T. W., and Michaelis, R. E., Standard Reference Materials: Sources of

Information, NBS Misc. 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 (March 1965). PBI68068**

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). COM74-1 1066** Anspach, S. C, Cavallo, L. M. Garfinkel, S. B. Hutchinson, J. M. R., and Smith, C. N., 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). COM74-1I065**

Yakowitz, H., Vieth, D. L., Heinrich, K. F. J., and

Michaelis, R. E., Standard Reference Materials: Homogeneity Characterization of NBS Spectrometric Standards II: Cartridge Brass and LowAlloy Steel, NBS Misc. Publ. 260-10 (December

1965). COM74-11064**

Napolitano, A., and Hawkins, E. G., Standard Reference Materials: Viscosity of Standard

Lead-Silica Glass, NBS Misc. Publ. 260-11 (November 1966). NBS Misc. Publ 260-11** 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). NBS Misc. Publ. 260-12**

Spijkerman, J. L., Snediker, D. K., Ruegg, F. C,

and DeVoe, J. R., Standard Reference Materials: Mossbauer Spectroscopy Standard for the Chemical Shift of Iron Compounds, NBS Misc. Publ. 260-13 (July 1967). NBS Misc. Publ.

260-13**

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

Materials: Determination of Oxygen in Ferrous

Materials - SRM 1090, 1091, and 1092, NBS

Misc. Publ. 260-14 (September 1966). NBS Misc. Publ. 260-14**

Passaglia, E., and Shouse, P. J., Standard Refer- ence Materials: Recommended Method of Use

of Standard Light-Sensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for Colorfastness to Light, NBS Misc. Publ. 260-15 (June 1967). (Replaced by NBS Spec. Publ.

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). COM74-1 1062** Catanzaro, E. J., Champion, C. E., Garner, E. L., Marinenko, G., Sappenfield, K.. M., and Shields, W. R., Standard Reference Materials: Boric

Acid; Isotopic and Assay Standard Reference

Materials, NBS Spec. Publ. 260-17 (February

1970). Out of Print. Geller, S. B., Mantek, P.A., and Cleveland, N.

G., Standard Reference Materials: Calibration of NBS Secondary Standard Magnetic Tape (Computer Amplitude Reference) Using the Reference Tape Amplitude Measurement

"Process A," NBS Spec. Publ. 260-18 (November

1969). (See NBS Spec. Publ. 260-29.) Paule, R. C, and Mandel, J., Standard Reference

Materials: Analysis of Interlaboratory Measurements on the Vapor Pressure of Gold (Certifica- tion of Standard Reference Material 745). NBS

Spec. Publ. 260-19 (January 1970). PB190071**

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). COM74-11359**

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**

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., Marineko. G.. and Hague, J. L., Standard Reference Materials: Comparison

of Redox Standards, NBS Spec. Publ. 260-24 (January 1972). COM72-50058**

iv
Hicho, G. E., Yakowitz, H., Rasberry, S. D., and

Michaelis, R. E., Standard Reference Materials: A Standard Reference Material Containing

Nominally Four Percent Austenite, NBS Spec.

Publ. 260-25 (February 1971). COM74-1 1356** Martin, J. F., Standard Reference Materials:

National Bureau of Standards-US Steel Corporation Joint Program for Determining Oxygen and Nitrogen in Steel, NBS Spec. Publ. 260-26

(February 1971). 85 cents* PB 81176620

Garner, 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-

11358**

Heinrich, K. F. J., Myklebust, R. L., Rasberry, S. D., and Michaelis, R. E., Standard Reference Materials: Preparation and Evaluation of SRM's 481 and 482 Gold-Silver and GoldCopper Alloys for Microanalysis, NBS Spec.

Publ. 260-28 (August 1971). COM71-50365**

Geller, S. B., Standard Reference Materials: Cali- bration 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

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). COM7 1-50563** Mavrodineanu, R., and Lazar, J. W., Standard

Reference Materials: Standard Quartz Cuvettes,

for High Accuracy Spectrophotometry, NBS

Spec. Publ. 260-32 (December 1973). 55 cents* SN003-003-01213-1 Wagner, H. L., Standard Reference Materials: Comparison of Original and Supplemental SRM 705, Narrow Molecular Weight Distri- bution Polystyrene, NBS Spec. Publ. 260-33 (May 1972). COM72-50526**

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

Materials: Thermoelectric Voltage, NBS Spec.

Publ. 260-34, (April 1972). COM72-5037 1 ** Sparks, L. L., and Hust, J. G., Standard Refer- ence Materials: Thermal Conductivity of

Austenitic Stainless Steel, SRM 735 from 5 to 280 K, NBS Spec. Publ. 260-35 (April 1972.) 35 cents* COM72-50368**

Cali, J. P., Mandel, J., Moore, L. J., and Young, D.

S., Standard Reference Materials: A Referee 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, and Menis,

O., Standard Reference Materials: Methods of Analysis of NBS Clay Standards, NBS Spec.

Publ. 260-37 (June 1972). COM72-50692**

Richmond, J. C, and Hsia, J. J., Standard Refer- ence 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., and

Powell, R. L., 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., Garn, P.D., and Menis, O., Standard Reference Materials: Selection of Thermal

Analysis Temperature Standards Through a Cooperative Study (SRM 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 LightSensitive Paper for Calibrating Carbon Arcs Used in Testing Textiles for Colorfastness to Light, NBS Spec. Publ. 260^1 '(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**

Greifer, B., Maienthal, E. J., Rains, T. C, and

Rasberry, S. D., Standard Reference Materials: Powdered Lead-Based Paint, SRM 1579, NBS

Spec. Publ. 260-45 (March 1973). COM73-

50226**

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and

Electrical Resistivity Standard Reference Materials: Austenitic Stainless Steel, SRM's 735 and

798, from 4 to 1200 K, NBS Spec. Publ. 260-46 (March 1975). SN003-O03-0 1278-5*

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 Refer- ence Materials: Description and Use of Precision Thermometers for the Clinical Laboratory, SRM 933 and SRM 934, NBS Spec. Publ. 260-48 (May 1974). 60 cents* SN003-003-0 1278-5 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

v
Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials:

Electrolytic Iron, SRM's 734 and 797 from 4 to 1000 K, NBS Spec. Publ. 260-50 (June 1975). $1.00* SN003-003-0 1425-7 Mavrodineanu, R., and Baldwin, J. R., Standard

Reference Materials: Glass Filters As a Standard Reference Material for Spectrophotometry;

Selection; Preparation; Certification; Use-SRM

930, NBS Spec. Publ. 260-51 (November 1975). $1.90* SN003-003-01481-8

Hust, J. G., and Giarratano, P. J., Standard Refer- ence Materials: Thermal Conductivity and Electrical Resistivity Standard Reference Materials 730 and 799, from 4 to 3000 K, NBS Spec. Publ. 260-52 (September 1975). $1.05* SN003-003-

01464-8 Durst, R. A., Standard Reference Materials: Standardization of pH Measurements, NBS

Spec. Publ. 260-53 (December 1975, Revised). $1.05 SN003-003-01551-2

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). $3.00* SN003-003-

01828-7

Ditmars, D. A., Cezairliyan, A., Ishihara, S., and

Douglas, T. B., Standard Reference Materials: Enthalpy and Heat Capacity; Molybdenum SRM 781, from 273 to 2800 K, NBS Spec. Publ. 260-55 (September 1977). $2.20* SN003-003-

01836-8

Powell, R. L., Sparks, L. L., and Hust, J. G., Standard Reference Materials: Standard

Thermocouple Materials, Pt.67: SRM 1967, NBS

Spec. Publ. 260-56 (February 1978). $2.20* SN003-003-0 18864

Cali, J. P. and Plebanski, T., Guide to United

States Reference Materials, NBS Spec. Publ. 260-57 (February 1978). $2.20* PB 277173

Barnes, J. D., and Martin, G. M., Standard Refer- ence Materials: Polyester Film for Oxygen Gas

Transmission Measurements SRM 1470, NBS

Spec. Publ. 260-58 (June 1979) $2.00* SN003-

003-02077 Chang, T., and Kahn, A. H. Standard Reference

Materials: Electron Paramagnetic Resonance

Intensity Standard; SRM 2601, NBS Spec.

Publ. 260-59 (August 1978) $2.30* SN003-

003-01975-5 Velapoldi, R. A.. Paule, R. C, Schaffer, R., Mandel, J., and Moody, J. R., Standard Refer- ence Materials: A Reference Method for the Determination of Sodium in Serum, NBS Spec.

Publ. 260-60 (August 1978). $3.00* SN003-003

01978-0

Verdier, P. H., and Wagner. H. L., Standard Refer- ence Materials: The Characterization of Linear Polyethylene (SRM 1482, 1483, 1484), NBS

Spec. Publ. 260-61 (December 1978). $1.70* SN0O3-OO3-O20O6-1

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). $2.30* SN003-003-

02047-8 Velapoldi, R. A., Paule, R. C, Schaffer, R. Mandel, J., Machlan, L. A., and Gramlich, J. W., Standard Reference Materials: A Reference Method for the Determination of Potassium in Serum. NBS Spec. Publ. 260-63 (May 1979). $3.75* SN003-003-02068

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

Reference Materials: A Fluorescence Standard

Reference Material Quinine Sulfate Dihydrate (SRM 936), NBS Spec. Publ. 260-64 (January

1980). $4.25* SN003-003-02 148-2 Marinenko, R. B., Heinrich, K. F. J., and Ruegg,

F. C, Standard Reference Materials: Micro- Homogeneity Studies of NBS Standard Reference

Materials, NBS Research Materials, and Other Related Samples. NBS Spec. Publ. 260-65

(September 1979). $3.50* SNOO3-O03-O21 14-1 Venable, W. H., Jr., and Eckerle, K. L., Standard

Reference Materials: Didymium Glass Filters for Calibrating the Wavelength Scale of Spectro- photometers (SRM 2009, 2010, 2013). NBS Spec.

Publ. 260-66 (October 1979). $3.50* SN0O3-OO3-

02127-0

Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel,

J., Murphy, T. J., and Gramlich, J. W., Standard

Reference Materials: A Reference Method for the Determination of Chloride in Serum, NBS Spec.

Publ. 260-67 (November 1979). $3.75* SN003-

003-02136-9 Mavrodineanu, R. and Baldwin, J. R., Standard

Reference Materials: Metal-On-Quartz Filters as a Standard Reference Material for Spectrophoto- metry-SRM 2031, NBS Spec. Publ. 260-68

(April 1980). $4.25* SNOO3-O03-O2 167-9 Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel, J., Machlan, L. A., Garner, E. L., and

Rains, T. C, Standard Reference Materials: A

Reference Method for the Determination of Lithium in Serum, NBS Spec. Publ. 260-69 (July)

1980). $4.25* SN003-003-02214-4 Marinenko, R. B., Biancaniello, F., Boyer, P. A., Ruff, A. W., DeRobertis, L., Standard Reference

Materials: Preparation and Characterization of an Iron-Chromium-Nickel Alloy for Microanalysis, NBS Spec. Publ. 260-70 (May 1981). $2.50* SN0O3-O03-O2328-I 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). $6.50* SN003-003-02381-7

Reeder, D.J., Coxon, B., Enagonio, D., Christensen,

R. G., Schaffer, R., Howell, B. F., Paule, R. C,

Mandel, J., Standard Reference Materials: SRM

900, Antiepilepsy Drug Level Assay Standard, NBS Spec. Publ. 260-72 (June 1981). $4.25* SN003-003-02329-9

vi
Interrante, C. G., and Hicho, G. E., Standard Refer- ence Materials: A Standard Reference Material Containing Nominally Fifteen Percent Austenite (SRM 486), NBS Spec. Publ. 260-73 (January

1982). $2.75* SN0O3-OO3-O2386-8 Marinenko, R. B., Standard Reference Materials: Preparation and Characterization of K-411 and

K-414 Mineral Glasses for Microanalysis: SRM

470. NBS Spec. Publ. 260-74 (April 1982). $3.50 SN003-003-023-95-7

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). $3.75 SN003-O03-023-99-O

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). $3.50 SN003-003-024-33-3 Furukawa, G. T., Riddle, J. L., Bigge, W. G., and

Pfieffer, E. R., Standard Reference Materials: Application of Some Metal SRM's as Thermometric Fixed Points, NBS Spec. Publ. 260-77 (August 1982). $6.00 SN003-003-024-34-1

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). $3.75* SN003-003-024-35-0 Richmond. J. C. Hsia, J. J. Weidner. V. R., and

Wilmering. D. B., Standard Reference Materials: Second Surface Mirror Standards of Specular

Spectral Reflectance (SRM's 2023. 2024, 2025). NBS Spec. Publ. 260-79 (October 1982). $4.50* SN003-003-024-47-3

Schaffer, R.. Mandel, J.. Sun. T., Cohen. A., and

Hertz, H. S., Standard Reference Materials: Evaluation by an ID/ MS Method of the AACC

Reference Method for Serum Glucose, NBS

Spec. Publ. 260-80 (October 1982). $4.75* SN003-

003-024-43-1 Burke, R. W., and Mavrodineanu. R. (NBS retired). Standard Reference Materials: Accuracy in Analytical Spectrophotometry. NBS Spec. Publ. 260-81 (April 1983). $6.00* SN003-003-024-8

Weidner, V. R., Standard Reference Materials: White Opal Glass Diffuse Spectral Reflectance Standards for the Visible Spectrum (SRM's 2015 and 2016). NBS Spec. Publ. 260-82 (April 1983). $3.75* SN003-003-024-89-9**

Bowers, G. N., Jr., Alvarez. R.. Cali. J. P. (NBS

retired), Eberhardt, K. R., Reeder. D. J.. Schaffer, R., Uriano, G. A., 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). $4.50* SN003-003-024-

99-6

Gills, T. E., Seward, R. W., Collins, R. J., and

Webster, W. C, Standard Reference Materials: Sampling, Materials Handling, Processing, and Packaging of NBS Sulfur in Coal Standard

Reference Materials, 2682, 2683, 2684, and 2685, NBS Spec. Publ. 260-84 (August 1983). $4.50* SN003-003-025-20-8

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). $5.50* SN003-003-

025-21-6 Hicho. G. E. and Eaton. E. E., Standard Reference Materials: A Standard Reference Material

Containing Two and One-Half Percent Austenite. SRM 488, NBS Spec. Publ. 260-86 (December

1983) . $1.75* SN003-003-025-41-1 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). $2.25* SN003-003-025-44-5 Gladney. E. S., Burns. C. E., Perrin. D. R , Roelandts. I., and Gills, T. E., Standard Reference Materials: 1982 Compilation of Elemental

Concentration Data for NBS Biological, Geological, and Evironmental Standard Reference

Materials. Spec. Publ. 260-88 (March 1984). SN003-003-02565-8

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

Thermophysical Property RM's from 5 to 2500 K. NBS Spec. Publ. 260-89 (September 1984). 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) Goodrich. L. F.. Vecchia. D. F., Pittman. E. S., Ekin, J. W.. and Clark, A. F., Standard Reference

Materials: Critical Current Measurements on an NbTi Superconducting Wire Standard Reference

Material, NBS Spec. Publ. 260-91 (September

1984) . 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). Ehrstein. J., Preparation and Certification of Standard Reference Materials for Calibration of Spreading Resistance Probes, NBS Spec. Publ. 260-93 (In Press).

* Send order with remittance to Superintendent

of Documents. US Government Printing Office Washington. DC 20402. 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

Virginia 22161.

vii
Table of Contents

Page

Abstract and Key Words 1

1. Introduction 2

2. Material Preparation, Preliminary Characterization, and Ingot Selection 2

3. Certification Measurements 3 3.1 Slice Thickness Measurements 3 3.2 The Resistivity Measurement Test Station 3 3.3 Sampling Plan for Resistivity Measurements 3

4. Analysis of Resistivity Radial Profile Data to Generate Certified Resistivity and Range Values . 6 4.1 General Considerations 6 4.2 Calculating the Certified Resistivity Value 6 4.3 Use of the Range of Measured Values to Relate Slice Resistivity to Individual Chips .... 10 4.4 Auxiliary Procedure to Improve Quality of Certification 11 4.5 Examples of Certificate Data Tables Showing Certified and Noncertified Information .... 18

5. Relation Between Values Measured on a Starting Slice and Values for Individual Specimen Chips: Calculation of Certification Uncertainty 18 5.1 Overview 18 5.2 Uncertainty of Resistivity Values Due to Measurement Errors 18 5.3 Uncertainty of Resistivity Values Due to Silicon Slice Nonuni formity 19 5.4 Certification Uncertainty for Individual Calibration Chips in Each Set 19

b. Care and Use of Spreading Resistance SRM Sets 19

7. Acknowledgments 20

8. References 21 Appendix A - Comparison of Results from Three-, Four-, and Six-Diameter Sampling Plans 22 Appendix B - Procedures Used to Monitor and Evaluate the Long-Term Stability of the Four-Probe Test Station 26 Appendix C - Probability that the Error Bounds Based on the Certification Uncertainty Value Includes

the "True" Resistivity Values of All Chips from the Certified Region of a Slice .... 29

List of Figures

Page

1. Schematic diagram of thickness measurement locations: 1) three diameters which were scanned

for thickness uniformity using a contactless thickness gauge; large circles at the end of

each diameter represent the sensing area of the contactless gauge, scaled to a 3-in. diameter

slice; 2) five small circles at slice center and four half-radius points show the location of electronic-micrometer (certified) measurements 5

2. Schematic diagram of a 3-in. diameter slice showing: 1) three measurement diameters used for certification; 2) location of 29 measurement positions on each diameter, shown by short dashes

except for outermost positions which show the location of the probe points for the 1.59-mm probe;

and 3) all possible final chips of size 0.22 by 0.44 in. (shown in upper right quadrant) .... 5 3a. Examples of nonsymmetric resistivity profiles obtained during the certification procedure ... 7 3b. Examples of nearly symmetric, but off-center, profiles obtained during the certification pro- cedure 8

3c. Examples of symmetric profiles obtained during the certification procedure 9

vi i i
Page

4. Schematic diagram showing the chip-numbering sequence for a 3-in. diameter slice 10

5. Schematic diagram for 2-in. and 3-in. diameter slices: 1) possible inner starting points for data analysis, 2) possible outer stopping points for data analysis, and 3) layout of chips with

respect to these limits; to be usable, no part of a chip may extend more than 0.010 in. beyond

the analysis limits chosen 11

6a. Resistivity profile and data reduction for a symmetric profile with relatively small range value:

3-in. diameter, (100) p-type slice 12

bb. Resistivity profile and data reduction for a symmetric profile with relatively large range value:

3-in. diameter, (100) p-type slice 13

7a. Individual chip resistivity estimates for the symmetric profile shown in figure 6a, and six analyses of slice data using inner and outer radial limits as represented in figure 5 14

7b. Individual chip resistivity estimates for the symmetric profile shown in figure 6b, and six analyses of slice data using inner and outer radial limits as represented in figure. 5 15 Al. Example of three-, four-, and six-diameter profiles for a (111) n-type slice, approximately

0.002 a* cm 23

A2. Example of three-, four-, and six-diameter profiles for a (100) n-type slice, approximately

0.007 Q.cm 24

A3. Example of three-, four-, and six-diameter profiles for a (100) n-type slice, approximately

0.002 n.cm 25

bl. Resistivity measurements taken approximately biweekly on a prototype of SRM 1520, using a single four-probe 27

b2. Resistivity measurements as in Figure Bl except for resistivity level 27

B3. Resistivity measurements taken at irregular intervals over approximately four years on a low-resistivity slice from SRM 1520 28

b4. Resistivity measurements as in Figure B3 except at the higher resistivity level from SRM 1520 . 28

List of Tables

Page

1. Estimates of fine-scale resistivity striations for the ingots currently being used for the spreading resistance calibration SRMs 4 2a. Data table from the certificate of a set of SRM 2526 for (111) p-type silicon 16

2b. Oata table from the certificate of a set of SRM 2527 for (111) n-type silicon 17

Bl. Oata from a two-operator/two-instrument test performed at the inception of calibration of spreading resistance SRMs 26

ix

PREPARATION AND CERTIFICATION OF SPIVS FOR CALIBRATION OF SPREADING RESISTANCE PRORFS

James R. Ehrstein Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards Gaithersburg, MD 20899

This Special Publication describes the material selection, characterization, data analysis, and mea- surement process control procedures for four types of Standard Reference Materials (SRMs), available from

the National Bureau of Standards, for calibration of spreading resistance measurements on semiconductor

silicon. Each of the four comprises a single combination of silicon conductivity-type and crystal 1 ographic orientation and contains 16 rectangular silicon chips which are certified for resistivity value based on four-probe resistivity measurements on the slices from which they were cut. The resistivity values of the chips in each set range from about 0.001 ft. cm to about 100 ft. cm. The uncertainty of the certified resis- tivity, as it applies to any individual chip, depends both on the uniformity of the starting slice and on the inherent measurement process uncertainty. The procedure for determining this uncertainty, which is specifically evaluated and tabulated on the certificate for each SRM set, is described.

Key words: resistivity; silicon; spreading resistance measurements; standard reference materials.

1
1. INTRODUCTION

This Special Publication describes the material selection, characterization, data analysis, and mea- surement process control procedures for four Standard Reference Materials (SRMs) for spreading resistance measurements on semiconductor silicon. The four Standard Reference Materials are SRM 2526 for (111) p-type silicon, SRM 2527 for (111) n-type silicon, SRM 2528 for (100) p-type silicon, and SRM 2529 for (100) n-type silicon. These SRMs are sets of single crystal silicon specimens. Each set contains specimens with resistivity values (approximately three

per decade) from about 0.001 n-cm, to about 100 ft. cm, with which to generate a spreading resistance-to- resistivity calibration for a spreading resistance probe. The intended application for the calibrations obtained with these SRMs is depth profiling of most common silicon i ntegrated-c i rcu i t and discrete-device

structures using ASTM Method F 672 [1].* Because the electrical response of a spreading resistance probe

is a function of both the conductivity-type and the crystal 1 ographic orientation of the silicon being measured, the calibration set (or sets) must be chosen by the user to match the test specimens being pro- filed or otherwise measured. The silicon specimens in each of these SRM sets are provided in the form of rectangular chips for convenience of use. They are to be polished, lapped, or otherwise prepared in a manner, and with a frequency, established by the user prior to use for calibrating a spreading resistance

probe.

The certificate provided with each set gives three certified values for each specimen chip in that

set: Resi sti vity , Range (of measured values), and Uncertainty (of certified resistivity value). The defi- nition of these terms is given in section 4.5 of this report. The values reported for each specimen chip were measured on the slice from which that chip was cut. The certificate also gives additional, non-certified information for each chip: dopant, crystal growth process, an estimate of spatial fine-scale resis- tivity variation, and, where calculable, an estimate of the macroscopic resistivity variation for the

chip.

2. MATERIAL PREPARATION, PRELIMINARY CHARACTER I ZATI ON , AND INGOT SELECTION Sections of single-crystal silicon ingots 2 to 3 in. in diameter were purchased for these SRMs from a number of commercial silicon suppliers. Below resistivities of about 20 Q.cm, the crystals were almost exclusively Czochralski (Cz) grown. Above this value, float-zone grown (FZ) p-type crystals and neutron transmutation doped (NTD) n-type crystals were used. The p-type crystals were exclusively boron-doped. Although some arsenic- and antimony-doped ingots were evaluated, all n-type ingots finally selected were phosphorus-doped because of their superior uniformity of resistivity. (Phosphorus-doped crystals will be used exclusively for future n-type sets unless present material supply at a given resistivity is exhausted

and replacement crystals are only available with arsenic or antimony doping.)

All ingot sections were verified for crystal 1 ographic orientation using either x-ray Laue diffraction

or preferential cry sta 1 1 ographi c etch tests. The conductivity type of each was verified using the hot- probe procedure of ASTM Method F 42 [2]. All ingots were tested for center-point resistivity at both ends

by the four-probe technique using ASTM Method F 43 [3]. This procedure was used to allow a tentative se- lection of those ingots, and the preferred end of each of those ingots, which would give the desired dis- tribution of resistivity values in each of the four SRMs. Each ingot was then screened for resistivity

uniformity by measuring the radial resistivity variation on the selected end of the ingot using four-probe measurements and the basic procedures of ASTM Method F 81 [4]. A number of ingots were dropped from con- sideration at this stage due to excessive radial variation of resistivity.''" Those ingots accepted for use were sliced and the slices lapped on both sides to meet the surface preparation procedure of ASTM Method F 84 [6] and to optimize the thickness uniformity of the slices. Nominal slice thickness after lapping was 625 M m.

* Individual copies of all ASTM Methods cited in this report are available for a nominal fee from American Society for Testing and Materials, 1916 Race St., Philadelphia, PA 19103. They are available collec- tively in section 10.05 of the Annual Book of ASTM Standards, available from the sane source.

t Macroscopic radial variation of resistivity, as well as fine-scale variation (striations) , is a conse- quence of fluctuations in dopant incorporation during crystal growth. The magnitude and spatial pattern

of these fluctuations depend on the segregation coefficient of the dopant as well as thermal variations

at the growth interface of the evolving crystal. While it may be possible to minimize these dopant fluctuations (resistivity variations) by optimal control of crystal growth conditions, they cannot be eliminated [5].

2
Screening for spatial fine-scale resistivity variations was then performed. One slice from each ingot was polished with 0.5-pm grit diamond compound and spreading resistance measurements were made along one diameter to evaluate the fine-scale variations of resistivity (resistivity striations) [7]. A step incre- ment of 100 nm was used for the measurements. Occasionally, auxiliary scans were made at step increments

as small as 10 M m, or were made on another diameter. The outermost 2 mm at each end of the diameter were excluded from the scans. It was not known initially what level of fine-scale resistivity uniformity would

be obtainable from commercial silicon crystals. Target values for maximum allowable fine-scale resistivity

variation were set at 10% for the p-type material and 20% for the n-type material. When measurements

exceeded these target values, replacement ingots were sought. In cases where two or more ingots were available with similar resistivity values, the fine-scale resistivity variation was used in conjunction

with the coarse-scale resistivity variation, as measured by four probe, to select the best ingot at that resistivity level. Ingots were selected which were comfortably below the target striation values for all but a few resis- tivity levels, for which the target was just met, and the highest resistivity level in the (100) p-type

SKM, for which the fine-scale variation was found to be about 14%. A replacement ingot for this level was not obtainable.

For all ingots used in these SRMs, the estimate of maximum fine-scale resistivity variation obtained

from the spreadi ng-resi stance measurements is reported on each SRM certificate. For the test slices from some ingots, resistivity variations of the reported magnitude occurred at only a few isolated places along

the diameter tested; for other test slices, such resistivity variations were pervasive along the diameter. Because fine-scale resistivity variations generally change from slice to slice for a given ingot, the values reported on the certificate, measured on a single slice from each ingot, must be considered as representative only; they are not certified. A summary of these fine-scale resistivity estimates for the ingots used for the four spreading resistance SRMs as they are currently being issued is given in table 1. All slices intended for use were qualified for uniformity of thickness by scanning along three diam- eters using a contactless thickness gauge. One of the diameters scanned was oriented parallel to the slice-orientation flat and the other two were oriented at ±60 deg with respect to the first diameter. The

scan along each diameter included all points except the outermost 6 mm; see figure 1. For slice acceptance, the measured thickness was required to be constant to 1%, or better; typically, the values for a yiven slice were constant to better than 0.4%.

3. CERTIFICATION MEASUREMENTS

3.1 Slice Thickness Measurements

The thickness value actually used to compute slice resistivity values from the electrical measurements

was the average of five thickness values measured with an electronic contacting micrometer. These five values were taken at the slice center and at four points located at half-radii along each of two perpendicular diameters. The accuracy of these individual measurements, traceable to precision gauge blocks, was better than ±1 u m. Figure 1 shows a schematic diagram of the thickness measurement locations used for the preliminary uniformity qualification and those used for calculation of the resistivity values.

3.2 The Resistivity Measurement Test Station

The resistivity measurement station employed for certification of all slices used for these SRMs consisted of 1) a precision six-decade dc constant-current supply with regulated current capability from

10"8 to 10' 1 A; 2) a 6-1/2 digit DVM with resolution to 0.1 pV; 3) a series of standard resistors, with values from 0.01 to 10,000 ft, each known to better than 10 parts per million, for monitoring the dc current

value; 4) a manual stage capable of radial and azimuthal (r,e) motion sufficient to measure all points on any diameter of a slice up to 4-in. diameter; 5) a copper-block heat sink with an imbedded thermistor calibrated to 0.01°C against an NBS-traceabl e glass-bulb thermometer and with a centering fixture capable

of centeriny circular slices (up to 3-in. diameter) on the stage to within 0.0015 in.; and 6) a four-point

probe with a spacing of 1.59 mm (0.0625 in.) as required by ASTM F 81 [4]. Since the measurement procedure

relies on the ratio of voltage measurements (between the silicon slice and the standard resistors), measurement accuracy depends primarily on DVM linearity rather than on DVM accuracy. Tests of this linearity, made by comparing different pairs of standard resistors, show it to run from about 0.0012% when

all voltages are 10 mV or above to about 0.1% when the voltages can only be measured to about 3-1/2 digits,

as is the case for slices below about 0.001 ft. cm. 3.3 Sampling Plan for Resistivity Measurements

It was expected from the nature of silicon crystal growth, and supported by previous experience, that the resistivity variation for most of the slices would be primarily radially dependent with a high degree

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Figure 1. Schematic diagram of thickness measurement locations: 1) three diameters which were scanned for thickness uniformity using a contactless thickness gauge; large circles at the end of each diameter represent the sensing area of the contactless gauge, scaled to a 3-in. diameter slice; 2) five small circles at slice center and four half-radius points show the location of electronic-micrometer (certified) measurements.

Figure 2. schematic diagram of a 3-in. diameter slice showing: 1) three measurement diameters used for certification; 2) location of 29 measurement positions on each diameter, shown by short dashes except for outermost positions which show the location of the probe points for the 1.59-mm probe; and 3) all possible

final chips of size 0.22 by 0.44 in. (shown in upper right quadrant).

5
of aziinuthal (rotational) symmetry. Based on this expectation, a resistivity measurement sampling plan was designed which emphasized the determination of the radial resistivity variation for each slice. This sam- pling plan required resistivity measurements at the slice center and at intervals of 0.1 in. along each of the three diameters, 60 deg apart, that were used in the thickness uniformity scan with the contactless thickness gauge.* The measurement procedure of ASTM Method F 81 [4] was used at each location; this required that the probe array be oriented perpendicular to the measurement diameter. For each slice, dc current values were set to obtain a probe voltage of 10 to 12 mV, except for the very lowest resistivity

specimens for which it was not possible to supply enough current to obtain 10 mV. For these specimens the probe voltage was that obtainable with a measurement current of 100 mA.

In this manner, a total of b7 measurements (19 along each diameter) was obtained on each 2-in. diam- eter slice and a total of 81 measurements (29 per diameter) on each 3-in. diameter slice. Three of these, one from each diameter, were located at the slice center. Figure 2 shows the schematic location for these resistivity measurements on a 3-in. diameter slice, together with the arrangement of SRM chips which could

be cut from one quadrant of such a slice. The three-diameter profiles obtained on virtually all (111) slices showed a high degree of azimuthal (rotational) symmetry; this azimuthal symmetry was found much less often for the (100) slices. A number of examples of the resistivity data obtained using this procedure are shown in figures 3a, b, and c with the vertical axis scales shown as percent difference from the average resistivity value at the slice center. Separate tests were run to gauge the effectiveness of the three-diameter plan for evaluating the range

of resistivity variation on specimens which had shown a variety of patterns of resistivity variations. These tests used two other sampling plans, each acquiring approximately the same number of total measurements per slice as were taken with the three-diameter plan, but with more emphasis placed on measuring

azimuthal variation of resistivity and less on measuring radial variation. Results of this comparison of sampling plans are illustrated in Appendix A. The superior effectiveness of the three-diameter plan in evaluating the range of resistivity variation over a full slice, without extraneous effects due to slice flats, is shown. After characterization with the three diameter samp ling plan, each of the slices was cut into a number

of rectangular chips and the chips distributed among a number of sets of the appropriate SRM, according to conductivity type and crystal orientation. Each SRM set in turn contains one chip at each available resis- tivity level. Figure 4 shows the schematic arrangement of all chips which might potentially be used from

a 3-in. diameter slice, together with the chip identification code which is used for record keeping and which appears on the contents list of all spreading resistance SRM sets.

4. ANALYSIS OF RESISTIVITY RADIAL PROFILE DATA TO GENERATE CERTIFIED RESISTIVITY AND RANGE VALUES

4. 1 General Considerations

Although the three-diameter sampling plan was found to be effective for characterizing the resistivity variation on each slice as a whole, measurements were not obtained at the location of all chips which could

be cut from within the sampled region of that slice. As a result, individual resistivity values for each

of the chips were not obtainable with the three-diameter plan. A procedure was designed for calculating a single representative resistivity value for each slice from the array of resistivity values measured; this representative value is the certified Res i sti vity for the slice as a whole and for all the chips cut from the slice. A "measure of the goodness" with which this single representative resistivity applies to the individual chips from the slice was also derived. This "measure of goodness," called the Uncertainty , is formally defined in section 5.4: "Certification Uncertainty for Individual Calibration Chips in Each Set." The value of the Uncertainty will be related to the resistivity variation ( Range of values) measured on each slice and to the underlying random and systematic errors in the measurement process.

4.2 Calculating the Certified Resistivity Value Three general methods for calculating the certified Resistivity value were considered. In the order

of the amount of available data base from each slice, they were: 1) calculation of the average of all mea- sured values, 2) calculation of the mean resistivity at each radial position followed by calculation of the average of the lowest and highest of those mean values, and 3) calculation of the average of the maximum

and minimum single individual values measured on the slice. Two requirements were established to evaluate these three methods: 1) the method used had to be compatible with minimizing the worst-case difference

between the derived slice Resistivity value and the value likely to be appropriate for any individual chip used from that slice, and 2) the method had to be compatible with a wide variety of profile shapes, magni-

* A four-point probe measures a local average resistivity over a center-weighted area related to the probe spacing. For a probe with the spacing used for these resistivity measurements, little additional infor- mation on resistivity variation would be provided by a sampling plan with spatial intervals between mea- surement locations smaller than 0.1 in.

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Figure 4. Schematic diagram showing the chip-numbering sequence for a 3-in. diameter slice. (Chips actually used for SRM sets depend on the region selected following analysis of profile data from each slice.)

tudes, and degrees of symmetry. The first requirement suggested some form of mid-range value would be appropriate for minimizing the worst-case difference; the second requirement suggested that any procedure

based on averages be carefully examined for applicability to slices with nonsymmetric profiles. Since use of the average of all measured values would weight the calculated resistivity to the most common values measured on a slice, and therefore increase the error for chips used from other portions of the slice, the averaging of all measured values was discarded as being nonacceptabl e. The method based on maximum average and minimum average values was also discarded, since, as can be seen in figure 3, for slices with nonsymmetric profiles, such local averages are not meaningful representations of the data. The third method considered, using the average of maximum and minimum individual measured values, satisfied both evaluation requirements. Since this method gives a resistivity value which is a midpoint of the range

of all measured values without respect to where those values were measured, it does not bias the result toward the low or high side of the measurement range or to any specific portion of the slice. Consequently, it minimizes the worst-case differences between the "representative" value which would be certified for the entire slice and the "true," but unknown, value for chips taken from the vicinity of either the lowest

or hiyhest values measured on the slice. Further, since it avoids use of averages as a function of posi- tion, it is applicable both to symmetric and nonsymmetric profiles. As noted, this procedure does not weight the final result to the most common measured value. In this sense the final Re si st i vi ty may not be the "most correct" representation of the slice as a whole; nevertheless, it is the "fairest" representation

since it balances the error among individual chips, and consequently, it balances the risk of error borne

by individual set users. 4.3 Use of the Range of Measured Values to Relate Slice Resistivity to Individual Chips

In conjunction with use of this average of individual measurement extrema as the certified slice

Resi sti vi ty , the difference, or Range , between these maximum and minimum values was chosen as the basis for calculating the "goodness" with which the certified Resistivity represented the resistivity of the individual chips cut from the slice. Such a procedure does have two identifiable drawbacks, however. The first, applicable to slices with symmetric profiles, is that it may be overly conservative.* The second draw- back primarily applies to slices with noticeably nonsymmetric profiles. For such slices, with symmetry absent, it is not possible to correlate data obtained along different diameters and to estimate the extent

* When evaluating measurement error or uncertainty, using a "conservative" value means using a value which

is somewhat inflated, i.e., on the high side of the likely values.

10
to which the maximum and minimum observed values represent real resistivity extrema rather than measurement

errors. Consequently, for nonsymmetric profiles, the Range of observed values may understate the true resistivity variation. However, guard factors (as explained in section 5.4 on certification Uncertainty ) are used to protect against such underestimation, and where the original maximum or minimum appeared sig- nificantly inconsistent with the shape of the profile, complete remeasurement of slices was employed to protect against significant overestimation.

4.4 Auxiliary Procedure to Improve Quality of Certification

The use of the individual maximum and minimum measured values to calculate certified values for each slice left one degree of freedom to improve the quality of certification (i.e., reduce the Uncertainty ) for each slice and for the chips used from that slice. This was the choice of the area of the slice from which

the final chips would be taken (and consequently the portion of the profile data which was used to extract

the certified values). Before a procedure to select the slice area could be formulated (as described below), it was necessary

to determine the size of the chips which would be cut from the slices. Choice of chip size was a com- promise between making the chips large enough so that they would last for a reasonable amount of time in use and making them small enough both to obtain a reasonable chip yield from each slice and to assure that the variations in resistivity which occurred on any one chip would be acceptably small. After numerous computational tests on data from a variety of profile types, a chip size of 0.22 in. by 0.44 in. (approx.

b.6 by 11.2 mm) was found to be a reasonable compromise.

The selection of the size and location of the slice area to be used for SRM chips was done in con- junction with target values for the certification Uncertainty and with the development and application of

an auxiliary analysis procedure. Target values for maximum Uncertainty were set at 5% for p-type specimens

and at 1L)% for n-type specimens. The auxiliary analysis procedure entailed estimation of the lowest and highest resistivity values likely to be encountered on any chip cut from each starting slice. This chip estimation procedure, which was applied to all slices for which the range of values was judged adequately

Figure 5. Schematic diagram for 2-in. and 3-in. diameter slices: 1) possible inner starting points for data analysis (solid line arcs), 2) possible outer stopping points for data analysis (dasned line arcs),

and 3) layout of chips with respect to these limits; to be usable, no part of a chip may extend more than

U.01U in. beyond the analysis limits chosen.
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value: 3-in. diameter, (100) p-type slice.

Kadi a 1 Distance Average & Standard Extremum Values

From Center Deviation (by position) (by position)

(cm.) (inch) Ave. of all (ls%) Min. val. Max. val u.uuu (0.00J 0.013653 0.11 0.01364 0.01367

0.254 (0.10) 0.013617 0.27 0.01355 0.01365

0.508 (0.20) 0.013557 0.34 0.01350 0.01363

0.762 (0.30) 0.013567 0.48 0.01348 0.01364

1.016 (0.40) 0.013620 0.32 0.01355 0.01367

1.270 (0.50) 0.013650 0.25 0.01361 0.01369

1.624 (0.60) 0.013693 0.29 0.01363 0.01375

1.778 (0.70) 0.013727 0.22 0.01369 0.01377

Z.O'dZ (0.80) 0.013733 0.33 0.01366 0.01378

2.28b 0.90) 0.013733 0.31 0.01369 0.01381

2.540 (1.00) 0.013750 0.27 0.01369 0.01380

2.794 (1.10) 0.013832 0.20 0.01379 0.01387

3.048 (1.20) 0.013878 0.21 0.01385 0.01392

3.302 (1.30) 0.013932 0.24 0.01389 0.01398

3.bbb (1.40) 0.014047 0.43 0.01396 0.01412

large compared to the scatter in the data, and for which the resistivity profile symmetry was judged high, was implemented in the following manner. The resistivity values from each of the three diameters (each of six radii) were averaged as a function of distance from the slice eepter. The radial distances from the slice to the nearest and farthest points of each chip were used as a "window" on the average radial profile

to calculate the lowest and hiyhest expected resistivity values for that chip. Where calculated, the estimates of lowest and highest expected resistivity for each chip are reported on the SRM certificates. These estimates are not certified, however, both because portions of the slice from which some chips were

cut were not intersected by any measurement diameter and because the assumption of radial symmetry of resistivity, even when apparent in the available data, may not strictly be true. Tnese estimates of the highest and lowest expected resistivity for each chip, together with the calcu- lated values of Resi sti vity and Range which resulted from analyzing each of several possible circular or annular regions of each slice, were used to make final decisions on how much of a given slice to use for bRM chips. Figure 5 shows a number of possible inner and outer radial limits for defining the region

12
2

o

d:

LU O

o <

LU LU

OC > LU <

Lttr

LUO

2.0

I V 1.62 -2.29 -0.76 (cm) 0.76 1.50 -0.90 -O.iO (in) 0 . io - DISTANCE FROM CENTER

2.29 i.82 0.9 0 1.50

Fiyure bb. Resistivity profile and data reduction for a symmetric profile with relatively large range

value: 3-in. diameter, (100) p-type slice.

Kadial Distance Average & Standard Extremum Values From Center Deviation (by position) (by position)

I cm.

)

(inch) Ave. of all (ls%) Min. val. Max. val o.oou (0.00) 80.3450 0.68 79.803 80.895

0.254 (0.10) 80.4110 0.67 79.873 81.045

0.508 (0.20) 7y.3333 1.25 77.708 80.361

0.7b2 (0.30) 76.9457 1.00 76.115 78.063

1.01b (0.40) 75.1402 0.62 74.446 75.681 1.27U (0.50) 74.2007 0.63 73.413 74.748

1.524 (O.bO) 74.4767 0.38 74.120 74.804

1.778 10.70) 75.4172 0.48 74.918 75.922

2.032 (0.80) 76.2908 0.48 75.856 76.705 2.28b o.yo 77.0875 0.84 76.411 78.265

2.540 (i.oo) 77.4457 0.61 76.663 77.946

Z. 794 (1.10) 77.5387 0.99 76.479 78.713

3.048 {1.20) 77.8560 0.37 77.597 78.339

3.302 77.6107 0.59 76.940 78.211

3.bbb \VM 77.8692 0.58 77.319 78.692

analyzed on 2-in. and 3-in. slices and the relation of those limits to the chips which would be cut from one quadrant of those slices. Examples of application of these analysis procedures to slice profiles are shown in the next two figures. Fiyure b shows the resistivity profiles for two 3-in. slices having profiles sufficiently symmetric

to estimate resistivity values for individual chips. Figure 7 shows the analysis sheets for these two slices, yiviny resistivity estimates for individual chips at the top of the sheets followed by the values

of resistivity and range that were calculated using the data from various regions of each slice (as shown schematically in fiy. 5). For the slice whose profile is shown in fig. 6A (analyses shown in fig. 7A), all chips have an estimated uniformity of 2.2%, or better, and are considered acceptable for use. Since the range values calculated for any of the six slice regions chosen for analysis are considered reasonable,

analysis jtb which includes the entire slice is chosen as the appropriate compromise between chip quality, certified Range value, and yield. In contrast with this is the slice whose profile is shown in fig. 6B (analyses shown in fig. 7B). For this slice, the first two chips listed (taken from the center region of

13
CHIP ANALYSIS

CHIP CODE ESTIMATED MIN/MAX %DIFF

CHIP 11 U. 013557 0.013653 0.71 CHIP 21 0.013559 0.013701 1.05 CHIP 31 0.013632 0.013733 0.74

CHIP 41 0.013713 0.013747 0.25 CHIP 51 0.013733 0.013871 1.00 CHIP 61 0.013832 0.014036 1.48 CHIP 12 0.013632 0.013735 0.75

CHIP 22 0.013648 0.013747 0.73 CHIP 32 0.013701 0.013832 0.96

CHIP 42 0.013733 0.013902 1.23 CHIP b2 0.013747 0.014047 2.18

CHIP 13 0.013733 0.013975 1.76 CHIP 23 0.013735 0.014036 2.20

SLICE ANALYSES

1; OOTEK RAD. THIS ANAL. 1 INCLODES .22x.44 in. CHIP #'s MINIMUM MAXIMUM

MEAN = RANGE (X) =

.2, INNER RADIUS 0.0 in.

: 11 21 31 41 51 12 22 32 EXTREMA 0.013480

0.013920 0.013700

3.21

2) OUTER RAD. THIS ANAL. INCLUDES .22x.44 in. CHIP # MINIMUM

MAXIMUM

MEAN = RANGE (%) =

1.3, INNER RADIUS 0.0 in.

s: 11 21 31 41 51 12 22 32 42 EXTREMA 0.013480

0.013980 0.013730

3.64

3) OUTER RAD. THIS ANAL. INCLUDES .22x.44 in. CHIP # MINIMUM

MAXIMUM

MEAN = RANGE (%) =

1.3, INNER RADIUS 0.2 in.

s: 21 31 41 51 12 22 32 42 EXTREMA

0.013480

0.013980 0.013730

3.64 OUTER RAD. THIS ANAL. 1.3, INNER RADIUS 0.4 in. INCLUDES .22x.44 in. CHIP #'s: MINIMUM

MAXIMUM

MEAN = RANGE (%)

31 41 51 EXTREMA

0.013550 0.013980

0.013765

3.12

12 22 32 42

5) UUTER RAD. THIS ANAL. INCLUDES ,22x.44 in. CHIP #' MINIMUM MAXIMUM

MEAN = RANGE (%) =

1.4, INNER RADIUS 0.5 in.

s: 41 51 61 22 32 42 52 13 23 EXTREMA 0.013610

0.014120

0.013865

3.68 OUTER RAD. THIS ANAL. 1.4, INNER RADIUS 0.0 in. INCLUDES .22x.44 in. CHIP #'s:

MINIMUM

MAXIMUM

MEAN = RANGE (X)

11 21 31 41 51 61 12 22 32 42 52

13 21 EXTREMA 0.013480

0.014120 0.013800

4.64 STRIATION MAGNITUDE (%) 6.

Fiyure 7a. Individual chip resistivity estimates for the symmetric profile shown in figure 6a, and six analyses of slice data using inner and outer radial limits as represented in figure 5. Since all chips are estimated to be acceptably uniform and since all slice analyses have acceptable range values, analysis #6

is chosen as the best compromise between yield, chip quality and certified range value.

14
CHIP ANALYSIS

CHIP CODE ESTIMATED MIN/MAX %D I F F CHIP 1

74. 276 80.411 8. 26 CHIP 21 74.2U1 78.856 6.27 CHIP 31 74.201 76.231 2. 74 CHIP 41 75.041 77.388 3.13 CHIP 51 76.928 77 . 808 1.14

Cn 1 r 6

77 . 539 77.855 0 41 CHIP 12 74^201 77"! 113 3^2

CHIP 22 74.201 77.388 4.30 CHIP 32 74.686 77.539 3.82

CHIP 42 76.231 77.855 2.13 CHIP 52 77.388 77.869 0.62

CHIP 13 76.928 77.855 1.20 CHIP 23 77.113 77.855 0.96

SLICE ANALYSES

1) OUTER RAD. THIS ANAL. 1.2. INCLUDES .22x.44 in. CHIP #'s: MINIMUM MAXIMUM

MEAN = RANGE (%)

INNER RADIUS 0.0 in.

11 21 31 41 51 12 22 32 EXTREMA

73.4130 81.0450

77.2290

9.88

2) OUTER RAD. THIS ANAL. 1.3. INCLUDES ,22x.44 in, CHIP #'s: MINIMUM

MAXIMUM

MEAN = RANGE (%) =

INNER RADIUS 0.0 in.

11 21 31 41 51 12 22 32 42 EXTREMA

73.4130 81.0450

77.2290

9.88

3) OUTER RAD. INCLUDES .22x.44 THIS ANAL. 1.3, in. CHIP #'s: MINIMUM

MAXIMUM

MEAN = RANGE {%) =

INNER RADIUS 0.2 in. 21 31 41 51 12 22 32 42 EXTREMA

73.4130 80.3610

76.8870

9.04

4) OUTER RAD. THIS ANAL. 1.3 INCLUDES .22x.44 in. CHIP #'s: MINIMUM MAXIMUM

MEAN = RANGE (%) =

INNER RADIUS 0.4 in. 31 41 51 12 22 32 42 EXTREMA

73.4130

78.7130 76.0630

6.97

5) OUTER RAD. THIS ANAL. INCLUDES .22x.44 in. CHIP # MINIMUM MAXIMUM

MEAN = RANGE (%) =

1.4, INNER RADIUS 0.5 in.

s: 41 51 61 22 32 42 52 13 23 EXTREMA

73.4130

78.7130 76.0630

6.97

6) OUTER RAD. THIS ANAL. 1.4, INCLUDES .22x.44 in. CHIP #'s: MINIMUM

MAXIMUM

MEAN = RANGE (%) =

INNER RADIUS 0.4 in. 31 41 51 61 12 22 32 42 52 13 23 EXTREMA

73.4130

78.7130 76.0630

6.97 STRIATION MAGNITUDE (%) 14.

Fiyure 7b. Individual chip resistivity estimates for the symmetric profile shown in figure 6b, and six analyses of slice data using inner and outer radial limits as represented in figure 5. Estimates for chips

11 and 21 show unacceptable nonuniformity; analysis #6 which ignores the core of the slice out to a radius

of 0.4 in. is chosen as the best compromise.

15
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iri o r- OOOOOOtflOeCOCM

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16
Fine

Scale

Resistivity

Variation

Estimates

of

Chip

Minimum

and

Maximum

Values**

0.000764-0.000786 0.00250-0.00257 0.00492-0.00511 0.00857-0.00876 0.0268-0.0275 0.0551-0.0562 0.153-0.158 0.290-0.301 0.529-0.541 N.A. 2.77-2.89 6.43-6.52 11.5-11.9 N.A. N.A. N.A.

Growth*

Process

I 1111111111111111

Uncertainty.

IP

ji

000778 00249 00510 00862 0271 0549 152 301 535 35 87 62 2 7 8 ooooooooo.-i<N<£>.-iii)'tfin

1N01 1N02 1N03 1N04 1N05 1N06 1N07 1N08 1N09 1N10 1N11 1N12 1N13 1N14 1N15 1N16

17
the slice) are estimated to be unacceptably nonuniform. Consequently, this region of the slice is excluded

from use, and the first three slice analyses are rejected. The last three modes of slice analysis (all of which omit the center region of the slice but differ in the area ana number of chips included) have the same calculated Range value. Of these, analysis #6 which includes the annular area between radial values

of 0.4 and 1.4 in. is chosen as tne best compromise since it offers the widest choice of chips without inflation of the Range value.

4. b Examples of Certificate Data Tables Showing Certified and Noncertified Information Tables 2a and b show certificates for two actual SRM sets, one p-type and one n-type, illustrating the certified and noncertified information specifically evaluated for the components of each SRM set. The certified Re si sti vi ty is the average of the minimum and maximum individual measured resistivity values in the region of the slice chosen for use. The certified Range is the difference between tnese minimum and maximum values expressed as a percent of the certified Resi sti vity . Tne exact meaning of the certified Uncertainty will be explained in the following section. Note however, that except for the eighth level of the p-type set (specimen code 1P08) , it was always possible to stay within the target values for Uncertai nty , 5% for p-type slices and 10% for n-type slices.

5. RELATION BETWEEN VALUES MEASURED ON A STARTING SLICE AND VALUES FOR INDIVIDUAL SPECIMEN CHIPS: CALCULATION OF CERTIFICATION UNCERTAINTY

b. 1 Overview

As already described, as a natural consequence of silicon crystal growth, none of tne starting silicon slices from which the cmps in these SRM sets were cut had uniform resistivity. However, for each slice, the amount of nonum formi ty was estimated from an array of resistivity measurements using tne three-diam- eter sampling plan. A single resistivity value, the average or tne highest and lowest values measured within the selected region, was then calculated and certified to represent the slice (and all chips from the selected region). That one certified Resi sti vity value then appears on the certificate for each SRM set which contains a chip from that slice. The most important question to anyone using such cnips to establish a resistivity to spreading resis- tance calibration is: "How well does each certified Resi sti vity value on my certificate represent the resistivity value of the corresponding chip in my set?" To put the question another way: "What error in resistivity scale am I likely to experience curing spreading resistance calibration when I use the value on the certificate?" In the next three sections, an expression for this "error" in resistivity values will be developed. It will be shown to be composed of two types of measurement system error, or uncertainty, which essentially have a fixed value regardless of resistivity level (sec. 5.2), and an error, or uncertainty, based on the nonuni formi ty of each slice, the value of which therefore changes from slice to slice (sec. 5.3). Finally, the manner for combining these two contributions will be given and a Douna on the combined

"error" will be derived to form a parameter termed the certification Uncertainty (sec. 5.4).

b.2 Uncertainty of Resistivity Values Due to Measurement Errors

The short-term ranaom error, or measurement scatter, associated witn trie four-prooe resistivity mea- surements can be estimated from the standard deviation of a number of measurements taken with different prooe orientations at the center of a slice in the manner described in ASTM Method F 84 [6]. Such esti- mates of tne precision have been found in this laboratory to vary from about 0.1% to aoout 0.4%, depending

on specimen resistivity and surface preparation. The value of 0.4% is used as a conservative estimate of the short-term random error (one standard deviation) for the certification of these spreaaing resistance

SRMs.

An estimate of the snort-term systematic error between the resistivity scale in effect at the time of any of the certification measurements and the long-term average response of the NBS resistivity measurement facility is obtained from several long-term measurement reproducibility studies at NBS. These studies, primarily based on specimens at approximately 0.1 and 10 ft. cm, including slices from SRM 1521, indicate that a value of 0.33% is a conservative estimate of the long-term random error, one standard deviation, of the NBS resistivity measurement process due to unknown sources (see Appenaix B for examples of these data). This value is supported by less extensive studies of slices from SRM 1522 and SRM 1523 which have resis- tivity values from 0.01 to 180 ft. cm. For measurements on any one slice (taken at any given time), or for any one chip in a user's SRM set, this error acts as a short-term systematic error or bias (with a maximum absolute value (3a) of 1%) compared to the long-term NBS baseline. However, for tne full array of chips in

a typical SRM set (which come from slices measured over a period of several months), this long-term error

is unlikely to act as a systematic bias with constant value. Therefore, insofar as it affects the relation between the Resi sti vity values (on the certificate) for a complete set of SRM chips and the long-term NBS baseline, this error is best modeled as an additional component of random error.

18
This long-term random error is taken to be independent of the short-term random error. Because they

are considered independent, they can be combined in root-mean-square fashion to give a combined random error of U.52% (one standard deviation). This total random error, which relates a single measured value

such as an observed minimum or maximum resistivity to the NBS baseline, can be stated at the 99% confidence

level (three standard deviations) as 1.56%. In other words, there is a 99% confidence that the resistivity

value measured at a single location on a slice is within 1.56% of the resistivity scale established by the long-term NBS baseline.*

This is a conservative statement for the error of a single feature from a nonsymmetric profile. It is even more conservative for a maximum or minimum taken from a symmetric profile.

b. 3 Uncertainty of Resistivity Values Due to Silicon Slice Nonuni f ormi ty Because the four-probe averages over an area, the effect of thickness nonuni formity on these measurements is expected to be no worse than ±0.2% [8], The allowances built into the "guard factor" (next section) as well as the conservative estimates of the measurement process error are considered sufficient

to implicitly allow for such errors due to thickness fluctuations. Therefore, no explicit term for thickness fluctuations is used. For a typical chip in an SRM set, the primary source of error between the "true," but unknown, resistivity value of the chip and the value given on the certificate is due to the

radial nonuni formity of resistivity of the starting slice. As a result of this nonuni formity , only a few chips from each slice have resistivity values which actually fall at the Resistivity' certified for that

slice. However, the use of maximum and minimum individual measurement values from each slice to calculate

the Range values and the use of an additional allowance for unmeasured portions of the slice via the "guard factor" are considered a conservative allowance for all resistivity variations on the region of the slice which was used.

b.4 Certification Uncertainty for Individual Calibration Chips in Each Set

A parameter, called the Uncertainty , \, can be expressed based on the combined effects of measurement

error and the observed silicon slice nonuni formi ty. This expression, which is evaluated separately for each chip in any of these SRM sets, is given as a percent of the certified Resistivity by:

I = [K ( Range /2) + 1.56], % . The guard factor, K, which is assigned the value 1.1 for slices with symmetric profile data and the value

1.2 for slices with nonsymmetric profile data, allows for possible additional resistivity excursions on unmeasured diameters as well as for errors caused by thickness variations. The Range value appropriate to each chip in a set is given in table 1 of the certificate for that set. The term 1.56% includes, at the

yy% confidence level, the effects of both short-term and long-term random errors, previously discussed.

Values of the Uncertainty , are also given in table 1 of each certificate for each of the chips in that

set. The Uncertainty , £

, can be used to calculate bounds on the resistivity values of any slice which

should include the true" values of all chips cut from the certified region of that slice relative. These

resistivity bounds are given by: Resistivity (1 ± £/100) . A derivation is given in Appendix C for the confidence level of the resistivity bounds. Except where

the stated Range value is small, the dominant term in the calculated Uncertainty and the resulting resistivity bounds are due to the resistivity nonuniformity of the starting slice. Because resistivity values

are determined by the crystal growth process, the nonuniformity is not random. Therefore, the stated Range

values cannot be used to estimate any other statistical parameter, such as a 90% confidence level, for the uncertainty of individual chip resistivity values.

6. CARE AND USE OF SPREADING RESISTANCE SRM SETS Each silicon chip in these Spreading Resistance SRM sets is waxed to one facet of a dual-angle beveling block. The nominal angles on each block are 0.5 deg and 3 deg. The angles were chosen to be compatible with many common spreading resistance applications. The blocks themselves can be directly

mounted on most spreading resistance instruments. The underside of each block is inscribed with a four- character code. The first character is "1" for (111) orientation or "0" for (100) orientation. The second

character is "N" or "P" for the conductivity type. The third and fourth characters are a two-digit code

for the resistivity level of the particular chip mounted on that block. The resistivity level code for all

* The value printed on the certificate, 1.57%, is slightly different from the value given here which is based on a more refined error model.

19
four sets currently runs from "01" to "16". This four-digit chip-identifying code is also given in the first column of the certificate and on the SRM set contents list packed with each set. When establishing a spreading resistance calibration relation, the spreading resistance values obtained on each calibration specimen will have a precision determined by the surface preparation used, by the stability of the probes being used, and by the underlying resistivity striation structure of the specimen. Prior to the first use of these SRM specimens, it is recommended that each chip be polished, preferably with fine grain diamond, 0.5-gm grain size, or less, across the entire surface area and then checked for striation structure with a spreading resistance probe. The user should then evaluate the need for a sampling plan to minimize possible uncertainty in future spreading resistance calibrations caused by any striations observed. This procedure is particularly recommended for calibration chips which will be used to calibrate measurements on epitaxial structures. Good spreading resistance practice dictates that the specimen to be tested and the calibration speci- mens be prepared as similarly as possible. This includes use of the same surface preparation procedure and subsequent thermal or chemical treatment, and in the case of bevel sectioning, trying to keep the beveled area of test and calibration samples of similar size. Where the application of these calibration sets is primarily to depth profiling of beveled specimens, it may be advisable to cut each of the calibration chips

in the SRM sets into several smaller chips of the size normally used for the depth-profile test specimens. Any such cutting of the calibration chips should be done with a diamond saw and should not be attempted with a scribe and break technique. This should be done only after the chip has been initially characterized for uniformity, as in the preceding paragraph.

No recommendation is made here regarding the polishing procedure to be used for preparing the calibra- tion chips and test specimens in actual use, since the choice of procedure must often be dictated by the nature of the test specimen [9,10]. No recommendation is made regarding the acceptability of the common expedient of mounting all calibration specimens on a single fixture for simultaneous preparation. All such options regarding the nature of surface preparation of the calibration specimens as well as the required frequency of repreparati on should be established by the user. A statistical summary of intralaboratory short-term repeatability and long-term reproducibility of spreading resistance measurements, derived from a multi-laboratory experiment, for three common surface preparations is contained in ASTM Method F 525-83, Measuring Resistivity of Silicon Wafers Using a Spreading Resistance Probe [11]. ACKNOWLEDGMENTS

The able assistance of L. A. Robinson and J. M. Thomas in slice fabrication and crystal 1 ographic ori- entation verification and of D. R. Reese in the resistivity characterization of the starting crystals and slices is gratefully acknowledged. Special appreciation is expressed to D. R. Ricks for extensive and dedicated effort in the certification measurements, detailed record keeping, and packaging of these SRMs. Sincere appreciation is also expressed to Dr. J. Lechner of the NBS Statistical Engineering Division for consultation in designing the data analysis procedure. Finally, to N. Belecki, B. Bell, and G. Carver as members of the CALCOM review panel, appreciation is expressed for extended discussions of the certification

and documentation procedures.

20
REFERENCES

1. Standard Method for Measuring Resistivity Perpendicular to the Surface of a Silicon Wafer Using a Spreading Resistance Probe, Designation F 672-80, 1983 Annual Book of ASTM Standards, Vol. 10.05, ASTM, Philadelphia, PA 19103.

2. Standard Test Methods for Conductivity Type of Extrinsic Semiconducting Materials, Designation F 42-

77, ibid.

3. Standard Test Methods for Resistivity of Semiconductor Materials, Designation F 43-78, ibid.

4. Standard Method for Measuring Radial Resistivity Variation on Silicon Slices, Designation F 81-77,

ibid.

b. Zulehner W. , and Huber, D. , Czochral ski -Grown Silicon in Crystals, Growth, Properties, and Applications, vol. 8, J. Grabmaier, Ed., Spri nger-Verl ag , Berlin (1982).

fa. Standard Method for Measuring Resistivity of Silicon Slices with a Collinear Four-Probe l\rray, Designation F 84-73, op. cit.

7. Ehrstein, J. R., Ricks, D. R., and Robinson, L. A., Spreading Resistance Measurements, Measurement

Techniques for High Power Semiconductor Materials and Devices: Annual Report, Oct. 1, 1977 to Sept.

30, 1978, NBSIR 79-1756, F. F. Oettinger, Ed. (1979).

8. Bullis, W. M. , Standard Measurements of the Resistivity of Silicon by the Four-Probe Method, NBSIR 74- 496, pp. 30-31, 1974.

9. Gruber, G. A., Profiling Ion-Implanted Layers With the Spreading Resistance Probe, Proc. of the Microelectronics Measurement Tech. Seminar, San Jose, March 1981, pp. IV-41, IV-58, Benwill Publishing

Co. , Boston, MA 02215.

10. Ehrstein, J. R. , Effect of Specimen Preparation on the Calibration and Interpretation of Spreading Resistance Measurements, Semiconductor Silicon 1977, H. R. Huff and E. Sirtl, Eds., pp. 377-386, The Electrochemical Society, Princeton, NJ 08540.

11. Standard Method for Measuring Resistivity of Silicon Wafers Using a Spreading Resistance Probe, Designation F 525-83, 1983 Annual Book of ASTM Standards, op. cit.

21
APPENDIX A COMPARISON OF RESULTS FROM THREE-, FOUR-, AND SIX-DIAMETER SAMPLING PLANS Figures A-l through A-3 compare the amount of detail obtained with the three-diameter measurement plan and with two alternate sampling plans. All three sampling plans acquire approximately the same amount of

total data on each slice. These alternate plans utilized 1) measurements at intervals of 0.15 in. along

four diameters, 45 deg apart, and 2) measurements at intervals of 0.2 in. along six diameters, 30 deg apart. However, as can generally be seen, the four-diameter and six-diameter sampling plans, while adding

more information about azimuthal resistivity variation, generally fail to provide as much information about

the range of resistivity variation of a slice as the three-diameter sampling plan. Further, significant measurement error was often encountered at the end of one diameter with both the four-diameter and six- diameter sampling plans due to proximity to the slice-orientation flat. Therefore, the three-diameter

sampliny plan is seen to be superior to the others for extracting the resistivity structure of a slice while avoidiny spurious effects at the slice flat.

22
-2.79

-1. lu

-1 . bd •0.66 0.5b (cm) 0.56

•0.22 (in) U.22 2.79

1.10

-2.7b -1.09

-0.3b (cm) 0.56 -0.22 (in) 0.22

1.67 0.66

SLICE FLAT-

-2.7b -1.67 -0.56 (cm) 0.56 1.67 2.78 -1.09 -0.6b -0.22 (in) 0.22 0.66 DISTANCE FROM CENTER -

Figure Al. Example of three-, four-, and six-diameter profiles for a (111) n-type slice, approximately

0.UU2 n.cm.

23
-2.54 -1.00 1.52 -0.51 (cm) 0.51

•0.60 -0.20 (in) 0.20 1.52 2.54 0.60 1.0 0

SLICE FLATA

^^^^^^^^

•2.54 1.00-0.51 (cm) 0.51

-0.20 (in) 0.20

1.52 2.54 0.60 1.00

SLICE FLAT-

•2.54 -1.52

•1.00 -0.60

-0.51 (cm) 0.51 -0.20 (in) 0.20 DISTANCE FROM CENTER1.52 2.54

0.60 1.00

Figure A2. Example of three-, four-, and six-diameter profiles for a (100) n-type slice, approximately

U.U07 s2«cm.

24
2.54

•1.00

•2.54

•1. 0 0

-1.52 -0.51 (cm) 0.51 0.60 -0.20 (in) 0.20

1. 52 0.60

SLICE FLAT—

2.54 1.00

9 ^ -A / .

-0.51 (cm) -0.20 (in) 0.51 0.201.52

0.60

-2.54 -1.52 -1.00 -0.6U-0.51 (cm) 0.51

-0.20 (in) 0.2u

1.52 2.54 0.60 1.0 0 DISTANCE FROM CENTER

Figure A3. Example of three-, and four-, and six-diameter profiles for a (100) n-type slice approximately

U.002 a- cm.

25
APPENDIX B PROCEDURES USED TO MONITOR AND EVALUATE THE LONG-TERM STABILITY

OF THE FOUR-PROBE TEST STATION

Two basic types of procedures have been used both to monitor and maintain the long-term stability of the four-probe test station and to estimate measurement uncertainty due to long-term random scatter in system performance. The first is the use of control charts to track the stability of the total measurement system: current supply, DVM, standard resistor bank, and four-probe. The second is the performance of periodic two-operator/two-instrument experiments.

Control chart data were taken rather intensively for a few slices over a period of about two years in conjunction with the issuance of the first silicon resistivity SRMs in 1974. They have also been taken much less intensively, but with a continually evolving collection of slices (now totaling 60) from every crystal ever used to produce SRMs 1521, 1522, and 1523. Four examples of control chart data are shown in figures B-l through B-4. The first two show data taken approximately biweekly over slightly more than two years on two slices that were prototypes of SRM 1520. The second two figures show data taken much less frequently, but with four different four-probes, over four years' duration, for two actual slices from SRM

1520. These four figures substantiate the statement in section 5.2 that long-term stability of the measurement is within 1%. Two-operator, two-instrurnent tests are periodically employed because of a potential ambiguity in interpreting the control charts reported here. Control charts monitor the stability of the entire measurement process, not only of the equipment used but also of the specimen itself. Hence the data are sensitive

not only to probe wear and to drifts in the current supply, standard resistor, and DVM but also to the effects of cumulative probe damage on the silicon slices or to changes in the near-surface conduction

process due to relapping or cleaning of a slice.

The two-operator, two-instrument procedure makes no assumptions regarding the long-term stability of a specimen. Rather, by use of two separate measurement systems, each meeting the requirements (in this case)

of ASTM F 84, and two different operators to take data on a variety of test specimens, it is possible to evaluate measurement control at any given time, with negligible uncertainty caused by chanqes in the specimens. Table B-l shows data from the two-operator/two-instrument experiment which was done just prior to beginning the certification of spreading resistance SRMs in 1982. Data such as these can be used to esti- mate systematic biases due to equipment or to operator procedure over a wide range of resistivity values, instrument system 1, the more automated of the two in table B-l, was the one used for certification of the spreading resistance SRM slices.

SLICE Op. 1 / Inst. 1 Op. 1 / Inst. 2 Op. 2 / Inst. 1 Op. 2 / Inst. 2 U.01-6

0.01-36 0.01285 (0.19%) 0.U130U (0.17%) 0.01286 (0.13%) 0.01303 (0.09%) 0.01283 (0.11%) 0.01303 (0.10%) 0.01289 (0.11%) 0.01304 (0.15%) 0.1-29 0.1-57 0.09384 (0.18%) 0.09346 (0.12%) 0.09399 (0.23%) 0.09357 (0.19%) 0.09398 (0.12%) 0.09345 (0.17%) 0.09388 (0.08%) 0.09338 (0.23%) 1-38

1-64 0.8837 (0.11%) 0.8124 (0.16%) 0.8870 (0.28%) 0.8095 (0.04%) 0.8857 (0.36%) 0.8119 (0.37%) 0.8847 (0.20%) 0.8133 (0.16%) 10-35 1U-52 8.918 (0.08%) 8.637 (0.23%) 8.931 (0.14%) 8.662 (0.17%) 8.919 (0.19%) 8.618 (0.21%) 8.912 (0.30%) 8.644 (0.09%) 25-10

25-20

24.75 (0.13%) 24.75 (0.26%) 24.75 (0.05%) 24.77 (0.05%) 24.71 (0.07%) 24.74 (0.12%) 24.72 (0.11%) 24.72 (0.06%) 75-1U

75-20

79.42 (0.19%) 79.77 (0.17%) 79.54 (0.10%) 79.79 (0.12%) 79.40 (0.14%) 79.67 (0.17%) 79.42 (0.09%) 79.67 (0.10%) 180-10

180-20

188.9 (0.11%) 190.1 (0.23%) 189.3 (0.11%) 190.2 (0.07%) 188.8 (0.14%) 189.9 (0.23%)

189.1 (0.10%

190.0 (0.13%)

Table Bl Data from a two-operator/two-i nstrument test performed at the inception of cali- bration of spreading resistance SRMs. Each box shows the average of six readings and the percent standard deviation of those readings.

26
0.080

0.079

g 0.078 > AVG

F 0.077

CO

LU

tr 0.076

0.075

• • • •

Slice Relapped

•

w

• •

J L J L J L Jan. 1972

Feb. 1973

July

1974

Figure Bl. Resistivity measurements taken approximately biweekly on a prototype of SRM 1520, using a single four-probe. Each entry shows the average of six readings taken in the manner of ASTM F 84.

21.40

21.20

a 21.00

£ AVG

p 20.80

CO

ES -1%-h

20.60

20.40

••••• • • ••

Slice Relapped

J L

• • • • •

J I Jan. 1972

Feb. 1973

July

1974

Figure B2. Resistivity measurements as in Figure Bl except for resistivity level

27
0.1225

0.1215 ~ 1%—

oG 0.1205

H AVG

p 0.1195

CO

CO 0.1185

0.1175

% M

ABC AB AB ABC ABC ABC ABC ABC ACD ACD ACD BCD CD CD CD CD CD CD CD C March

1974

March

1975

Sept.

1978

Figure B3. Resistivity measurements taken at irregular intervals over approximately four years on a low- resistivity slice from SRM 1520. Four different four-probes: A, B, C, D were used. Probes A, B, and C met the requirements of ASTM F 84; probe D used intentionally worn pins. Each entry shows the average of six readings taken in the manner of ASTM F 84.

1 1.55r11.45 - I

1%-

S 11-35 t AVG >

11.25

COm

or. 11.15

• • • • • —

^ Qg |ABC AB AB ABC ABC ABC ABC ABC ACD ACD ACD BCD CD CD CD CD CD CD CD CD CD March March Sept.

1974 1975 1978

Fiyure B4. Resistivity measurements as in Figure B3 except at the higher resistivity level from SRM 1520.

28
APPENDIX C PROBABILITY THAT THE RESISTIVITY BOUNDS BASED ON THE CERTIFICATION UNCERTAINTY VALUE INCLUDE THE "TRUE" RESISTIVITY VALUES OF ALL CHIPS FROM THE CERTIFIED REGION OF A SLICE

It was shown in section 5.2, based on consideration of random errors in the measurement process, that

there is a 99% probability that any single measured value is within 1.56% of its "true" value. That is, it is within 1.56% of the value that would be obtained if measurements were made repeatedly at the same lccation over an extended period of time with the NBS resistivity measurement system. The question to be an- swered is how well two such measured values, one a minimum observed value, the other a maximum observed

value, taken from the same set of measurements are likely to describe the full range of "true" resistivity

values of the slice on which they were obtained. Considering only the points actually measured on any slice, we can define Rm -j n as the "true," but unknown, minimum resistivity and Ym i n as the measured value corresponding to Rmin . Corresponding definitions are taken for Rmax and Ymax . We will ignore the guard factor, K, at this point; this is equivalent

to assuming that measurements have been taken at the locations of actual minimum and maximum resistivity and

that the only difference between measured and "true" values are due to measurement process errors. We will take T to be a "margin of error" and ask the general question, "When we quote Ymax and Ym -j n as defining

the observed range, what is the probability that the range given by Ymax + T and Ym -j n - T covers the range

of true values?"

This probability can be symbolically written as the simultaneous probability

P

( Y max

+ T

>

R maxand Y min " T

< R min)

and Y . - R . mi n mm

At the time we measure the value Y max , it differs from Rmax because of two types of errors: a shortterm random measurement error, e^ and a short-term systematic error, g, with a fixed value for any one slice which comes from the distribution of long-term random measurement errors. Similarly, Ym -j n and R m -j n differ by the combination of 3 and e . Therefore, in the previous probability statement, we can substitute

for Ymax

- Rmax and Y min - Rmin to write:

P (e + e

i > - T and g + e£

< T) .

The problem is to evaluate the simultaneous probability that for some margin of error, T, yet unspecified, the allowance made for errors of types g and e is sufficient to cover the value chosen for T. As explained in section 5.2, g and e are assumed to come from random distributions with standard deviations of 0.33% and 0.4%, respectively. Because g occurs in both terms with a common value which comes from the long-term random-error distribution, we must evaluate a convolution of probabilities, for all possible

values of 0

E b P(e = b) . P(g + e

2

< T and g + e

]

_ > - T"| = b) ,

where b is any of the allowed values of 6. Using the assumed Gaussian distributions for the errors, r and

e, and a value for T of 1.56%, this probability can be readily evaluated by numerical integration. The result of integrating over all allowed values for 6 is a probability of 0.997. Therefore, having allowed for the effects of random error to be up to 1.56% (three standard deviations) of the measured value, there is a probability of 0.997 that the observed maximum and minimum resis- tivities will cover the "true" maximum and minimum resistivities, for the set of locations measured. This

is an idealized model: it does not account for the effects of thickness fluctuations or of additional excursions of resistivity on nonmeasured diameters. In an effort to account for these possibilities, a guard factor, K, with a value of 1.1 or 1.2 is also used. The probability statement can then be rewritten

as:

p f Y = + * Range + T > R' and Y . - ( K :^ * Range - T < R '

. 1

, n max 2

a max mm 23 min' '

29
where K' (nax and R' m -j n do not necessarily occur at the locations of Ymax and Ym -j n

. This probability cannot

be directly evaluated since it depends not only on the measurement errors but also on the distribution of "true" values on the slice; this distribution is unknown. Plausibility arguments can be made, however, reyarding the applicability of the ideal case probability to three classes of profiles:

1) For slices that are truly rotational ly symmetric, no additional resistivity excursions exist on nonmeasured diameters, and the guard factor of 1.1 times the measured range is more than adequate to account

for the effects of thickness fluctuations [8]. Moreover, since there are three measurements (at the center) or six measurements (at any other location) made of the minimum or maximum value, evaluating

the contribution of the short-term error as 0.4% is to noticeably overstate its effect for such profiles. As a result, the appropriate probability for this case should be at least 0.997, as calculated

based on a random error contribution of 0.4%.

2) For slices that are nearly symmetric, the contribution of the short-term error is still generally overstated, although there may be somewhat less than six chances at each off-center radial position for determining the maximum or minimum value. This overstatement of the short-term error should be suffi- cient to compensate for unrecognized errors due to thickness fluctuations. Evidence from tests run with three-, four-, and six-diameter profiles on slices with a variety of profile range values, both symmetric and nonsymmetric in shape, indicate that a guard factor of 1.1 is more than adequate to account for additional resistivity excursions. Again, the appropriate probability for these slices

should be close to the 0.997 value.

3) For slices that are not symmetric, the maximum or minimum value generally occurs at only one measurement point. Hence, there is no safety margin in the short-term error related to having more than one available measurement; there is, however, some safety margin arising from assigning a worst-case value

of U.40% as the short-term standard deviation of the measurement process. In addition, the guard

factor is set at 1.2 times the range for increased safety. Finally, the four- and six-diameter measurements, even on nonsymmetric slices, showed no meaningful increase in calculated range above the value determined from the three-diameter measurements. It is therefore expected that the probability

of covering the range of true values on a nonsymmetric slice using 1) the observed maximum and minimum

values, 2) a guard factor of 1.2, and 3) 1.56% to allow for random errors is near the calculated

0.997.

30
BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

' REPORT NO. NBS/SP-260/93

2. Performing Organ. Report No. 3. Publication Date January 1985

4. title and subtitle Standard Reference Materials:

Preparation and Certification of SRM's for Calibration of Spreading Resistance Probes

5. AUTHOR(S) James R. Ehrstein

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) NATIONAL BUREAU OF STANDARDS DEPARTMENT OF COMMERCE GAITHERSBURG , MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

Same as in item 6 above.

10. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 84-601158

FJ7J Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here) This Special Publication describes the material selection, characterization, data

analysis, and measurement process control procedures for four types of Standard Reference Materials (SRMs), available from the National Bureau of Standards, for calibration of spreading resistance measurements on semiconductor silicon. Each of

the four comprises a single combination of silicon conductivity-type and crystallographic orientation and contains 16 rectangular silicon chips which are certified for resistivity value based on four-probe resistivity measurements on the slices from which they were cut. The resistivity values of the chips in each set range from about 0.001 ft. cm to about 100 ft. cm. The uncertainty of the certified

resistivity, as it applies to any individual chip, depends both on the uniformity of the starting slice and on the inherent measurement process uncertainty. The procedure for determining this uncertainty, which is specifically evaluated and tabulated on the certificate for each SRM set, is described.

12. KEY WORDS (Six to twefve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons) resistivity; silicon; spreading resistance measurements; standard reference materials

13. AVAILABILITY

[X] Unlimited

FJ7J For Official Distribution. Do Not Release to NTIS

[X~l Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402. Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

40

•Ct U.S. GOVERNMENT PRINTING OFFICE: 1985-461-105/10188 SCOMM-DC 6043-P80

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