NAT L INST. OF STAND & TECH R.I.C.

A11103 b^3M5M

2

o

c NIST SPECIAL PUBLICATION 260-117

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

Standard Reference Materials:

Antireflecting-Chromium

Linewidth Standard, SRM 475,

for Calibration of Optical Microscope

Linewidth Measuring Systems

QC

100

.U57

260-117

1992

ol F. Vezzetti, Ruth N. Varner, and James E. Potzick
NATIONAL u, TE OF STANDARDS 4b

TECHNOLOGY

Research Information Center

Gaithersburg, MD 20899

DATE DUE

Demco, Inc. 36-233
NIST Special Publication 260-117

Standard Reference Materials:

Antireflecting-Chromium

Linewidth Standard, SRM 475,

for Calibration of Optical Microscope

Linewidth Measuring Systems

Carol F. Vezzetti

Ruth N. Varner

James E. Potzick

Precision Engineering Division

Manufacturing Engineering Laboratory

National Institute of Standards and Technology

Gaithersburg, MD 20899

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

TECHNOLOGY ADMINISTRATION, Robert M. White, Under Secretary for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY, John W. Lyons, Director

Issued January 1 992
National Institute of Standards and Technology Special Publication 260-117

Natl. Inst. Stand. Technol. Spec. Publ. 260-117, 49 pages (Jan. 1992)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1992

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

Standard Reference Materials (SRM's) as defined by the National Institute of

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

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

Nation. SRM's are widely used as primary standards in many diverse fields in

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

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

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

measurement processes to the national measurement system is carried out through

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

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

of the measurements made at NIST in arriving at the certified values of the SRM's

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

for this purpose.

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

phases of the preparation, measurement, certification, and use of NIST SRM's.

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

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

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

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

sufficient additional information so SRM's can be utilized in new applications

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

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

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

and so forth, will receive prompt attention from:

Standard Reference Materials Program

Bldg. 202, Rm. 204

National Institute of Standards and Technology

Gaithersburg, MD 20899

William P. Reed, Chief

Standard Reference Materials Program

iii
OTHER NIST PUBLICATIONS IN THIS SERIES

McKenzie, R. L., ed., NIST Standard Reference Materials Catalog 1990-91, NIST Spec. Publ. 260 (January

1990)

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

Materials: Preparation of White Cast Iron

Spectrochemical Standards, NBS Misc. Publ. 260-1

(June 1964). COM74-11061**

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

Reference Materials: Preparation of NBS CopperBase Spectrochemical Standards, NBS Misc. Publ. 260-2 (October 1964). COM74- 11063**

Michaelis, R. E., Yakowitz, H., and Moore, G. A., Stan- dard Reference Materials: Metallographic Characterization of an NBS Spectrometric Low-Alloy Steel Standard, NBS Misc. Publ. 260-3 (October 1964).

COM74- 11060**

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). PB 168068**

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

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

11068**

Bell, R. K., Standard Reference Materials: Methods for the Chemical Analysis of NBS Copper-Base

Spectrochemical Standards, NBS Misc. Publ. 260-7

(October 1965). COM74-11067**

Richmond, M. S., Standard Reference Materials:

Analysis of Uranium Concentrates at the National

Bureau of Standards, NBS Misc. Publ. 260-8

(December 1965). COM74-1 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). COM74-11065**

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). COM74-1 1064**

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

Materials: Viscosity of Standard Lead-Silica Glass,

NBS Misc. Publ. 260-11 (November 1966).

Yakowitz, H., Vieth, D. L., and Michaelis, R. E., Stan- dard Reference Materials: Homogeneity Characterization of NBS Spectrometric Standards III: White

Cast Iron and Stainless Steel Powder Compact, NBS

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

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).

Yakowitz, H., Michaelis, R. E., and Vieth, D. L., Stan- dard Reference Materials: Homogeneity Characterization of NBS Spectrometric Standards IV:

Preparation and Microprobe Characterization of W20% Mo Alloy Fabricated by Powder Metallurgical

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

COM74- 11062**

Paule, R. C, and Mandel, J., Standard Reference Materials: Analysis of Interlaboratory Measurements on

the Vapor Pressure of Gold (Certification of Standard

Reference Material 745). NBS Spec. Publ. 260-19

(January 1970). PB 190071**

Paule, R. C, and Mandel, J., Standard Reference Materials: Analysis of Interlaboratory Measurements on

the Vapor Pressures of Cadmium and Silver, NBS

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

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

Reference Materials: Homogeneity Characterization

of Fe-3 Si Alloy, NBS Spec. Publ. 260-22 (February

1971). COM74-1 1357**

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

Materials: Viscosity of a Standard Borosilicate Glass,

NBS Spec. Publ. 260-23 (December 1970). COM71-

00157**

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

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

COM72-50058**

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

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

Standard Reference Material Containing Nominally

Four Percent Austenite, NBS Spec. Publ. 260-25

(February 1971). COM74-11356**

iv
Martin, J. F., Standard Reference Materials: National

Bureau of Standards-US Steel Corporation Joint Pro- gram for Determining Oxygen and Nitrogen in Steel, NBS Spec. Publ. 260-26 (February 1971). PB

81176620**

Garner, E. L., Machlan, L. A., and Shields, W. R., Stan- dard Reference Materials: Uranium Isotopic Standard

Reference Materials, NBS Spec. Publ. 260-27 (April

1971). COM74-1 1358**

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

Michaelis, R. E., Standard Reference Materials:

Preparation and Evaluation of SRM's 481 and 482

Gold-Silver and Gold-Copper Alloys for

Microanalysis, NBS Spec. Publ. 260-28 (August

1971).COM71-50365**

Geller, S. B., Standard Reference Materials: Calibration of NBS Secondary Standard Magnetic Tape (Computer Amplitude Reference) Using the Reference

Tape Amplitude Measurement "Process A-Model

2," NBS Spec. Publ. 260-29 (June 1971). COM71-

50282**

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). COM7 1-50283**

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). COM74-50018**

Wagner, H. L., Standard Reference Materials: Comparison of Original and Supplemental SRM 705, Nar- row Molecular Weight Distribution Polystyrene, NBS

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

Sparks, L. L., and Hust, J. G., Standard Reference Materials: Thermal Conductivity of Austenitic Stainless

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

Cali, J. P., Mandel, J., Moore, L. J., 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**

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., Gam, 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**

Wagner, H. L., and Verdier, P. H., eds., Standard Refer- ence 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., Stan- dard 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 LeadBased Paint, SRM 1579, NBS Spec. Publ. 260-45

(March 1973). COM73-50226**

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

Materials: Thermal Conductivity and Electrical

Resistivity Standard Reference Materials: Austenitic

Stainless Steel, SRM's 735 and 798, from 4 to 1200

K, NBS Spec. Publ. 260^6 (March 1975). COM75-

10339**

Hust, J. G., Standard Reference Materials: Electrical Resistivity of Electrolytic Iron, SRM 797, and Austenitic Stainless Steel, SRM 798, from 5 to 280 K,

NBS Spec. Publ. 260-47 (February 1974). COM74-

50176**

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

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

SRM 934, NBS Spec. Publ. 260^18 (May 1974).

Superseded by NIST Spec. Publ. 260-1 13. Carpenter, B. S., and Reimer, G. M., Standard Reference

Materials: Calibrated Glass Standards for Fission

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

1974). COM74-5 1185**

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

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). COM75-10698**

Mavrodineanu, R., and Baldwin, J. R., Standard Refer- ence Materials: Glass Filters As a Standard Reference

Material for Spectrophotometry-Selection, Preparation, Certification, Use-SRM 930 NBS Spec. Publ. 260-51 (November 1975). COM75- 10339**

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

Materials: Thermal Conductivity and Electrical

Resistivity Standard Reference Materials 730 and

799, from 4 to 3000 K, NBS Spec. Publ. 260-52

(September 1975). COM75-1 1 193**

Durst, R. A., Standard Reference Materials: Standardization of pH Measurements, NBS Spec. Publ. 260-53 (February 1988, Revision of December 1975

version).

Burke, R. W., and Mavrodineanu, R., Standard Refer- ence Materials: Certification and Use of Acidic Potas- sium Dichromate Solutions as an Ultraviolet

Absorbance Standard, NBS Spec. Publ. 260-54

(August 1977). PB272168**

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

Douglas, T. B., Standard Reference Materials: Enthal- py and Heat Capacity; Molybdenum SRM 781, from

273 to 2800 K, NBS Spec. Publ. 260-55 (September

1977). PB272127**

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

Reference Materials: Standard Thermocouple Material, Pt-67: SRM 1967, NBS Spec. Publ. 260-56

(February 1978). PB277172**

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

Materials: Polyester Film for Oxygen Gas Transmission Measurements SRM 1470, NBS Spec. Publ. 260-

58 (June 1979). PB297098**

Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel, J., and Moody, J. R., Standard Reference Materials: A

Reference Method for the Determination of Sodium

in Serum, NBS Spec. Publ. 260-60 (August 1978).

PB286944**

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

Materials: The Characterization of Linear

Polyethylene (SRM 1482, 1483, 1484), NBS Spec.

Publ. 260-61 (December 1978). PB289899**

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

Materials: Temperature Reference Standard for Use

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

(April 1979). PB294245**

Velapoldi, R. A., Paule, R. C, Schaffer, R„ Mandel, J., Machlan, L. A., and Gramlich, J. W., Standard Refer- ence Materials: A Reference Method for the Deter- mination of Potassium in Serum, NBS Spec. Publ. 260-63 (May 1979). PB297207**

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). PB80-132046**

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). PB300461**

Venable, W. H., Jr., and Eckerle, K. L., Standard Refer- ence Materials: Didymium Glass Filters for

Calibrating the Wavelength Scale of Spectrophotometers-SRM 2009, 2010, 2013, and 2014, NBS Spec.

Publ. 260-66 (October 1979). PB80- 104961**

Velapoldi, R. A., Paule, R. C, Schaffer, R., Mandel, J., Murphy, T. J., and Gramlich, J. W., Standard Refer- ence Materials: A Reference Method for the Deter- mination of Chloride in Serum, NBS Spec. Publ. 260-67 (November 1979). PB80-110117**

Mavrodineanu, R., and Baldwin, J. R., Standard Refer- ence Materials: Metal-On-Quartz Filters as a Standard

Reference Material for Spectrophotometry SRM

2031, NBS Spec. Publ. 260-68 (April 1980). PB80-

197486**

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). PB80-209117**

Marinenko, R. B„ Biancaniello, F., Boyer, P. A., Ruff, A. W., and DeRobertis, L., Standard Reference Materials: Preparation and Characterization of an Iron- Chromium-Nickel Alloy for Microanalysis, NBS

Spec. Publ. 260-70 (May 1981). PB84-165349**

Seward, R. W., and Mavrodineanu, R., Standard Refer- ence Materials: Summary of the Clinical Laboratory

Standards Issued by the National Bureau of Standards, NBS Spec. Publ. 260-71 (November 1981).

PB82-135161**

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

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

Mandel, J., Standard Reference Materials: SRM 900,

Antiepilepsy Drug Level Assay Standard, NBS Spec.

Publ. 260-72 (June 1981). PB81-220758

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

Materials: A Standard Reference Material Containing

Nominally Fifteen Percent Austenite (SRM 486),

NBS Spec. Publ. 260-73 (January 1982). PB82-

215559**

Marinenko, R. B., Standard Reference Materials:

Preparation and Characterization of K-4 1 1 and K-4 14 Mineral Glasses for Microanalysis: SRM 470, NBS

Spec. Publ. 260-74 (April 1982). PB82-221300**

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

Materials: Preparation and Calibration of First Surface Aluminum Mirror Specular Reflectance Stan- dards (SRM 2003a), NBS Spec. Publ. 260-75 (May

1982). PB82-221367**

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

Materials: A Standard Reference Material Containing

Nominally Five Percent Austenite (SRM 485a), NBS

Spec. Publ. 260-76 (August 1982). PB83-1 15568**

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). PB83-

117325**

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

Materials: Standard Reference Material Containing

Nominally Thirty Percent Austenite (SRM 487), NBS

Spec. Publ. 260-78 (September 1982). PB83-

115576**

Richmond, J. C, Hsia, J. J., Weidner, V. R., and Wilmering, D. B., Standard Reference Materials: Second

Surface Mirror Standards of Specular Spectral Reflec- tance (SRM's 2023, 2024, 2025), NBS Spec. Publ. 260-79 (October 1982). PB84-203447**

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) . PB84-216894**

Burke, R. W., and Mavrodineanu, R., Standard Refer- ence Materials: Accuracy in Analytical

Spectrophotometry, NBS Spec. Publ. 260-81 (April

1983). PB83-214536**

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). PB83-

220723**

Bowers, G. N., Jr., Alvarez, R., Cali, J. P., Eberhardt, K.

R., Reeder, D. J., Schaffer, R., and Uriano, G. A., Standard Reference Materials: The Measurement of

the Catalytic (Activity) Concentration of Seven En- zymes in NBS Human Serum SRM 909, NBS Spec.

Publ. 260-83 (June 1983). PB83-239509**

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). PB84-109552**

Swyt, D. A., Standard Reference Materials: A Look at Techniques for the Dimensional Calibration of Stan- dard Microscopic Particles, NBS Spec. Publ. 260-85

(September 1983). PB84-1 12648**

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). PB84-

143296**

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

1969: Rubidium Triple-Point - A Temperature Refer- ence Standard Near 39.30 °C, NBS Spec. Publ. 260-

87 (December 1983). PB84- 149996**

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 Environmental

Standard Reference Materials, NBS Spec. Publ. 260-

88 (March 1984). PB84-2 18338**

Hust, J. G., Standard Reference Materials: A FineGrained, Isotropic Graphite for Use as NBS Thermophysical Property RM's from 5 to 2500 K, NBS

Spec. Publ. 260-89 (September 1984). PB85-

112886**

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). PB85-1 15814**

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). PB85-

118594**

Carpenter, B. S., Standard Reference Materials:

Calibrated Glass Standards for Fission Track Use

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

Publ. 260-92 (September 1984). PB85-1 13025**

vis
Ehrstein, J.R., Standard Reference Materials: Preparation and Certification of Standard Reference Materials for Calibration of Spreading Resistance Probes,

NBS Spec. Publ. 260-93 (January 1985). PB85-

177921**

Gills, T. E., Koch, W. F., Stolz, J. W., Kelly, W. R., Paulsen, P. J., Colbert, J. C, Kirklin, D. R., Pei, P.T.S., Weeks, S., Lindstrom, R. M., Fleming, R. F., Greenberg, R. R., and Paule, R. C, Standard Reference

Materials: Methods and Procedures Used at the National Bureau of Standards to Certify Sulfur in Coal

SRM's for Sulfur Content, Calorific Value, Ash Content, NBS Spec. Publ. 260-94 (December 1984).

PB85- 165900**

Mulholland, G. W., Hartman, A. W., Hembree, G. G., Marx, E., and Lettieri, T. R., Standard Reference

Materials: Development of a 1 |im Diameter Particle Size Standard, SRM 1690, NBS Spec. Publ. 260-95

(May 1985). SN003-003-02665-4*

Carpenter, B. S., Gramlich, J. W., Greenberg, R. R., Machlan, L. A., DeBievre, P., Eschbach, H. L., Meyer, H., Van Audenhove, J., Connolly, V. E., Trahey, N. M., and Zook, A. C, Standard Reference

Materials: Uranium-235 Isotopic Abundance Stan- dard Reference Materials for Gamma Spectrometry

Measurements, NBS Spec. Publ. 260-96 (September

1986). PB87-108544**

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

Materials: Summary of the Coal, Ore, Mineral, Rock,

and Refactory Standards Issued by the National

Bureau of Standards, NBS Spec. Publ. 260-97 (September 1985). SN003-003-02688-3*

Hust, J. G, Standard Reference Materials: Glass Fiber- board SRM for Thermal Resistance, NBS Spec. Publ. 260-98 (August 1985). SN003-003-02674-3*

Callanan, J. E., Sullivan, S. A., and Vecchia, D. F., Standard Reference Materials: Feasibility Study for the Development of Standards Using Differential Scanning Calorimetry, NBS Spec. Publ. 260-99

(August 1985). SN003-003-02675-1*

Taylor, J. K., Standard Reference Materials: Handbook

for SRM Users, NBS Spec. Publ. 260-100 (September

1985). PB86-1 10897**

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

1970, Succinonitrile Triple-Point Standard: A

Temperature Reference Standard Near 58.08 °C, NBS

Spec. Publ. 260-101 (March 1986). SN003-003-

02722-7*

Weidner, V. R., Mavrodineanu, R., Mielenz, K. D., Velapoldi, R. A., Eckerle, K. L., and Adams, B., Standard Reference Materials: Holmium Oxide Solution Wavelength Standard from 240 to 640 nm - SRM

2034, NBS Spec. Publ. 260-102 (July 1986). PB86-

245727**

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

Fiberblanket SRM for Thermal Resistance, NBS

Spec. Publ. 260-103 (September 1985). SN003-003-

02687-5*

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

Materials: Summary of the Biological and Botanical

Standards Issued by the National Bureau of Stan- dards, NBS Spec. Publ. 260-104 (November 1985).

SN003-003-02704-9*

Mavrodineanu, R., and Rasberry, S. D., Standard Refer- ence Materials: Summary of the Environmental Research, Analysis, and Control Standards Issued by the National Bureau of Standards, NBS Spec. Publ. 260-

105 (March 1986). SN003-003-02725-1*

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

and Procedures Used at the National Bureau of Stan- dards to Prepare, Analyze, and Certify SRM 2694,

Simulated Rainwater, and Recommendations for Use,

NBS Spec. Publ. 260-106 (July 1986). PB86-

247483**

Hartman, A. W., and McKenzie, R. L., Standard Refer- ence Materials: SRM 1965, Microsphere Slide ( 10 |im

Polystyrene Spheres), NBS Spec. Publ. 260-107

(November 1988).

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

Materials: Summary of Gas Cylinder and Permeation

Tube Standard Reference Materials Issued by the National Bureau of Standards, NBS Spec. Publ. 260-

108 (May 1987).

Candela, G. A., Chandler-Horowitz, D., Novotny, D. B., Marchiando, J. F., and Belzer, B. J., Standard Refer- ence Materials: Preparation and Certification of an

Ellipsometrically Derived Thickness and Refractive

Index Standard of a Silicon Dioxide Film (SRM

2530), NIST Spec. Publ. 260-109 (October 1988).

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

Materials: PorUand Cement Chemical Composition

Standards (Blending, Packaging, and Testing), NBS

Spec. Publ. 260-1 10 (February 1988).

Gladney, E. S., O'Malley, B. T., Roelandts, L, and Gills, T. E., Standard Reference Materials: Compilation of

Elemental Concentration Data for NBS Clinical,

Biological, Geological, and Environmental Standard

Reference Materials, NBS Spec. Publ. 260-111

(November 1987).

viii
Marinenko, R. B., Blackburn, D. H., and Bodkin, J. B., Standard Reference Materials: Glasses for

Microanalysis: SRM's 1871-1875, NIST Spec. Publ. 260-112 (February 1990).

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

Materials: Description and Use of a Precision Thermometer for the Clinical Laboratory, SRM934, NIST

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

Vezzetti, C. F., Varner, R. N. and Potzick, J. E., Standard

Reference Materials: Bright-Chromium Linewidth

Standard, SRM476, for Calibration of Optical Microscope Linewidth Measuring Systems, NIST Spec.

Publ. 260-114 (January 1991).

Williamson, M. P., Willman, N. E., and Grubb, D. S., Standard Reference Materials: Calibration of NIST

Standard Reference Material 3201 for 0.5 Inch (12.65

mm) Serial Serpentine Magnetic Tape Cartridge,

NIST Spec. Publ. 260-115 (February 1991).

Mavrodineanu, R. , Burke, R. W., Baldwin, J. R., Smith,

M. V., and Messman, J. D., Standard Reference Materials: Glass Filters as a Standard Reference Material

for Spectrophotometry and Selection, Preparation,

Certification and use of SRM 930 and SRM 1930,

NIST Spec. Publ. 260-1 16 (in prep).

*Send order with remittance to Superintendent of

Documents, U.S. Government Printing Office,

Washington, DC 20102. Remittance from foreign

countries should include an additional one fourth of

the purchase price for postage.

**May be ordered from: National Technical Information Services (NTTS), Springfield, VA 22161.
Contents

1. Introduction 1

2. Physical Characteristics of SRM 475 1

3. Calibration of SRM 475 2

3.1 The Measurement System 2

3.2 SRM Calibration Procedure 3

3.3 Specimen and Measurement Axis Alignment 3

3.4 Feature Measurement Sequence 4

3.5 Edge Location Determination 5

3.6 Precision and Accuracy of the SRM Calibration 6

4. Using SRM 475 9

4.1 Special Precautions 9

4.2 Microscope Calibration Procedures 11

Acknowledgments 14

References 14

Table 16

Figures 17

Appendix: Process Control for SRM 475 Calibrations 26

A. Introduction 26

B. Initialization of Process Parameters 26

C. Procedures for Process Control 28

D. Updating Process Parameters 30

E. Uncertainty Statement for SRM 475 32

Acknowledgments 34

References 34

Tables 35

Figures 36

x
ANTIRBFLECTING-CHROMIUM LINEWIDTH STANDARD, SRM 475,

FOR CALIBRATION OF OPTICAL MICROSCOPE

LINEWIDTH MEASURING SYSTEMS

C. F. Vezzetti, R. N. Warner, and J. E. Potzick

National Institute of Standards and Technology

Gaithersburg, Maryland 20899

ABSTRACT

The precise and accurate measurement of feature dimensions on photomasks, such as those

used in the production of integrated circuits, becomes increasingly difficult as the dimensions

approach the wavelength of the light used to make the measurement. The undesirable effects

of optical diffraction obsure the location of the feature edges. Raggedness and non-vertical

walls along the edges add to the uncertainty of the measurement.

Standard Reference Material SRM 475 was developed for use in calibrating optical

microscopes for measuring linewidths in the range of 0.9 to 10.8 fcm on antireflectingchromium photomasks. The SRM, the measurement system, and the procedures used to calibrate the SRM are described. The algorithm for determining the line edge location uses a

threshold criterion derived from analysis of microscope image profiles. The profiles are predicted by computer modeling based on the theory of partial coherence. The performance

of the system is monitored by measuring line features on a control photomask before and

after calibrating each SRM.

Precautions concerning care and handling and instruction for the use of SRM 475 to calibrate

optical microscopes for photomask linewidth measurement are given.

KEY WORDS: accuracy; antireflecting-chromium; calibration; control charts; critical

dimensions; integrated circuits; linewidth measurement; optical microscope; photomask;

precision; semiconductor industry; standard reference material; statistical process control;

threshold; uncertainty.

xi

1. Introduction

The ability to measure and control critical dimensions during the production of integrated

circuits is essential to the semiconductor industry. Many measuring systems claiming high

precision are now commercially available for measuring some of these critical dimensions.

As part of a continuing effort to provide means for calibrating these systems, the National

Institute of Standards and Technology (NIST) has developed Optical Microscope Linewidth

Measurement Standard Reference Materials.

Standard Reference Material (SRM) 475 is designed for calibrating optical microscope

systems to measure linewidths on antireflecting-chromium photomasks. It was produced with

conventional technology by a commercial photomask manufacturing facility. In addition to isolated opaque and clear lines for linewidth calibration, this SRM contains line patterns for

checking length scale, adjusting video-type micrometers, and detecting mechanical or optical

nonlinearities. The design of the calibrated pattern is described in section 2. A photometric microscope with lenses selected for least aberration was modified at NIST for

calibrating the SRM line features with green light illumination of wavelength 0.53 /xm.

Except for the initial positioning, aligning, and focusing of the photomask, the entire

calibration process is automated. Linewidths are determined from the image profile (image

intensity versus position across a feature) based on a considerable amount of theoretical work

conducted to establish the location on the observed image profile that corresponds to the

physical edge of a feature. The quality of the feature edge geometry of a sample from each

production batch of SRM photomasks is examined with a scanning electron microscope

(SEM). The limit of accuracy of the calibration measurements given in the certificate data is based on this sampled edge geometry and the agreement between theoretically modeled and

experimentally generated image profiles. Section 3 contains brief descriptions of the NIST

linewidth calibration system and the automated calibration process as well as discussions of

the line edge location algorithm, precision, and accuracy.

Section 4 gives information and precautions on the care and use of this SRM to calibrate an

optical linewidth measuring system. Because of the variety of linewidth measurement

systems in use today, no attempt has been made to give specific instructions for each type of

microscope.

The process control procedures used in the calibration of this SRM are discussed in some

detail in the Appendix.

2. Physical Characteristics of SRM 475

SRM 475 is made from an antireflecting-chromium photoplate by conventional photolithographic techniques. The substrate is a quartz plate of a type commonly used for fabricating

integrated circuit photomasks, nominally 63.5 x 63.5 x 1.5 mm (2.5 x 2.5 x 0.060 in). The

nominal thickness of the chromium layer is 100 nm.

1
Figure 1 shows the overall pattern on the chromium-coated side of the standard. The cross- shaped relatively clear area contains a series of horizontal and vertical lines that are used to help locate the basic measurement pattern which is repeated at eight locations around the

center of the standard as shown in figure 2 (a magnified view of central area of fig. 1).

A pattern identification number (1 through 8) is located to the left of each basic pattern.

Only one of these eight patterns is certified by NIST; it is identified on the accompanying

certificate.

Figure 3 shows the details of the features in each of the eight identical patterns on the SRM.

Letters A, B, E, F, and G designate the row locations, and numbers 0 through 9 designate

column locations. Thus, each feature can be identified by its row and column coordinates;

for example, A-5 refers to the opaque line in row A and column 5. Row A consists of

opaque lines on a clear background, and row B consists of clear lines on an opaque

background. These opaque and clear lines are used for calibrating optical microscopes used

to measure linewidths of isolated lines of either or both polarities. Row E consists of

patterns with opaque line pairs (the two interior lines of shorter length) for calibrating the

length scale of optical microscopes by measuring the distance between line centers (pitch).

Row F consists of patterns with two adjacent lines and the intervening space (two interior

lines of longer length and the intervening space) with approximately equal line and space

widths. These patterns are used in setting the line-to-space ratio (contrast, threshold level, or

linearity) on video image-scanning instruments. The widths of the left interior line and

central space are certified. Row G consists of two patterns, with a series of 10

approximately equally spaced opaque lines in each pattern, to be used as a linear scale in

checking for errors in the linewidth measurement system (e.g., the magnification as a

function of position over the field of view). The center-to-center distances from the first line

to each of the other nine lines of these patterns are certified. All rows on this SRM contain

a broken horizontal fiducial line which is used to define the measurement position of each

pattern.

3. Calibration of SRM 475

3.1 The Measurement System

All measurements of the SRM feature dimensions were performed at NIST in a laboratory

with temperature controlled at 21 °C (± 2°) on the optical linewidth measurement system

diagrammed in figure 4 [1].

The carefully aligned optical transmission microscope is mounted on a vibration isolation

table. The photomask is placed on a scanning piezoelectric flexure-pivot stage with finely

controlled motion in the X (scanning) and Z (focus) directions; this stage is mounted on

another stage with coarse motion leadscrews in the X and Y directions to allow positioning of

the desired feature in the field of view.

The two outer lines of each pattern in rows E and F serve as "guard lines" during the

photolithographic etching process to equalize proximity effects along the line edges and are

not calibrated.

2
The photomask is illuminated from below with Kohler illumination (i.e., each point on the

lamp filament evenly illuminates the entire specimen) from an incandescent source filtered at 530 nm wavelength with a coherence parameter of 2/3 (.60 numerical aperture condenser

lens and .90 numerical aperture objective lens). A 20 x 400 jxm slit is fixed on axis in

the image plane in front of a photomultiplier tube. Image magnification at the slit is 157

times, giving an effective measurement area on the photomask of 0.127 x 2.55 fxm, which is centered top-to-bottom on the feature (at the fiducial line). The photomultiplier output is amplified and digitized by a 12-bit analog-to-digital converter (ADC). Stage motion in the

scanning direction is measured by a laser interferometer with resolution of 125 points per

micrometer. All these devices are connected via appropriate control hardware and IEEE-488

bus to a dedicated desktop digital computer.

3.2 SRM Calibration Procedure

An outline of the overall calibration procedure is charted in figure 5. Before each complete

SRM calibration, selected features on a control photomask are measured and compared with

control history to ensure that the system has not changed or drifted. These selected features

include spacing patterns E-4, E-5, and G-l which have been independently calibrated by the

Dimensional Metrology Group at NIST [2] to provide traceability to the standard meter.

Each feature on the SRM being calibrated is then measured in sequence and the sequence

repeated nine times. After each SRM calibration is completed, the control photomask is measured again.

All measurements, including the control measurements, are entered into the linewidth

database. After the calibration measurements are completed the database is searched to ensure that the control was measured before and after the calibration and that these two

control measurements were statistically invariate. The database entries for the calibration are combined and examined statistically: the standard deviation for each feature is calculated,

number of measurements checked, etc. Criteria must be met for each of these statistical

factors. If necessary, more measurements can be made and added to the database.

Once all the above conditions are met, the certificate is printed and the SRM linewidth

standard is released to the Standard Reference Materials Program Office for sale. All of the

calibration database files for this serial number are then stored on one flexible disk along

with summary data. The disk is kept for archival storage along with the printed calibration

results for each measurement, a printed summary of the statistical data, and dark-field

illumination micrographs of the calibrated pattern.

3.3 Specimen and Measurement Axis Alignment

The measurement axis is the axis of the interferometer laser beam (actually the geometric

center of the four beams used in this interferometer) and is defined as the X-axis. The

scanning axis is the axis of motion of the piezoelectric scanning stage, and the specimen axis

is a line on the surface of the photomask perpendicular to the length of the linewidth feature

being measured. Ideally these axes would coincide, but in practice it is not possible to locate

these axes with great precision.

3
In this application the perpendicular distance between parallel lines (the right edge and left edge of a feature) is measured. It is important to align the specimen axis with the

measurement axis, but slight misalignment of the scanning axis causes no error because only

the component of motion parallel to the measurement axis is measured and this is also the

component parallel to the specimen axis. In other words, a scanning axis misalignment will cause the width measurement to "slide" slightly along the length of the line, but it will

always be parallel to the line's width. Even so the scanning axis is aligned as carefully as

possible, first by aligning the leadscrew stage by moving it back and forth in the Y direction

and adjusting its rotation in the X-Y plane until the interferometer indicates no periodic

change in X, and then by geometrically aligning the piezoelectric stage by eye.

Misalignment of the specimen axis with the measurement axis will lead to a geometric error proportional to 1 - cos(misalignment angle). This alignment is checked by scanning and

measuring the X position of the center of the long vertical fiducial line at the right side of the

pattern (see fig. 3) near its top and bottom ends. The angle of rotation of the specimen can be calculated from the positions of these centers and the nominal distance between them.

After the specimen has been mounted and aligned by eye, the alignment is checked and

readjusted until the program indicates the specimen is properly aligned. The calibration

program will not commence taking data unless the misalignment angle is less than + 0.1°.

This allows a maximum cosine error of 1.5 ppm, or .06 nm on the longest feature on this

photomask. If the specimen is tilted (i.e., the specimen stage is rotated about the Y-axis),

the leading and trailing edges of the longer patterns will not both be in focus, and this

condition will be detected in the measurements.

A significant potential error source is the Abbe error caused by possible offset between the

measurement axis and the specimen axis in combination with angular motion of the scanning

stage. The Abbe offset in the linewidth measurement system is less than about 2 mm.

Comparison of pitch measurements made on this apparatus and on the NIST Line Scale

Interferometer (see sec. 3.6) allow compensation for errors of this type. Small random

rotations of the scanning stage contribute to the measured random uncertainty.

3.4 Feature Measurement Sequence

A flow chart of the main steps of the feature measurement sequence is given in figure 6. The feature to be measured is first centered in the field of view, then focused and scanned as

the optical profile position and intensity data are taken and stored as two one-dimensional

arrays. The data are then low-pass filtered to reduce extraneous noise and processed to find

the edge locations. Linewidth is then calculated.

Position and intensity data points are correlated by alternately triggering the interferometer

and the voltmeter to take one reading each in a software loop while the scanning stage is moving. There may be a few clock cycles delay between the two readings of a data pair, but

this delay is very small (corresponding to 2 nm/ms of delay) and is the same at leading and

trailing edges; thus, it cancels in the linewidth or pitch calculation.

4
Image profiles such as those in figure 7 are presented on the computer screen during data

acquisition and processing to allow monitoring system operation. After passing several data

quality checks, the results are entered into a database for the SRM being calibrated.

A more detailed description of the measurement sequence and system can be found in

reference [1].

3.5 Edge Location Determination

Analysis of optical microscope imaging gives the following equation for image intensity at the edge of a line [3]:

where Tcis the intensity of the light at the threshold point (edge) on the image profile (see

fig. 8); I

a

is the intensity of the light passing through the not-perfectly-opaque chromium

layer; Imis the intensity of the light passing through the clear areas (beyond the diffraction

peaks); and is the optical phase difference of the light transmitted through these two areas. Rt is a theoretically derived ratio, of approximately 0.25, which varies slightly depending on

the coherence factor, viewing slit width, focus, proximity of the next edge, and other

imaging conditions. For the conditions of measurement of this SRM in the NIST calibration

system, Rt varies from 0.25 to 0.28 (see last paragraph of this section).

Real microscope images often include some flare light (light scattered off the microscope

components illuminating the otherwise opaque features on the photomask from above or reaching the image plane by indirect paths). In nonlaser illumination systems, this light is temporally incoherent with respect to the light comprising the diffraction pattern (image

profile) and simply adds incoherently (intensity-wise) to each intensity of the image profile.

To a first approximation the intensity of the flare light is not a function of position across a

feature. Therefore, the effect of the flare light can be incorporated into eq (1) by simply

subtracting its value from each intensity component on the image profile:

where the prime designates an observed intensity (including the effects of diffraction,

transmission, and flare) and where If is the magnitude of the flare light component in the

image profile for each feature. Substituting into eq (1) gives:

t = Rt U - 9

+ " 9+ 2H~9 (h- 9

cos ^

+ 9

5
Both 4> and 1^ must be known to evaluate the threshold condition. 7^ is feature and

background dependent and must be determined for each feature. For this SRM, where the

antireflecting-chromium layer can be considered to be homogeneous, the transmittance (Tr)

and 0 can be taken as constants and Ia can be expressed as (Tr x 1^. Then, considering

that (lm

-

1

0) equals (im -/

0 )and substituting in eq (2), it can be shown that

//= vi-{Trxfj\l(l-Tr). (4)

The transmittance of the SRM was determined by using the linewidth measuring system to measure the intensity of light passing through the chromium near the center of the large

chromium-covered upper-left quadrant of the mask and found to be about 0.18% of the

incident intensity.

There is no known simple method for determining 4>. However, a recent study of image

profiles generated by a computer model [3], developed by D. Nyyssonen, of the NIST

microscope system indicates that linewidth uncertainty from not knowing this phase

difference is no greater than 15 nm if the threshold intensity used to determine the edge

location is that for the case where <f> equals tt/2. This uncertainty is included in the

systematic error budget. The model is based on the theory of partial coherence and allows

variation of image formation conditions such as: linewidth, wavelength of incident radiation,

transmittance and phase of the object and background illumination, and slit width. Profiles

generated by this model agree very closely with profiles generated from the measurement

data. Profiles were generated for lines and spaces 0.50 to 15 fxm wide where the

transmittance of the "opaque" areas is 0.2% and 4> ranges from 0 to it. The results of the

study also indicate that the relative threshold intensity varied from 25% to 28% of (lm

- I

Q) over the range of widths simulated, (fig. 9). Therefore, an algorithm for determining

linewidth was implemented that assumes a phase difference of x/2 and iteratively selects the

threshold intensity ratio from this model-generated data according to the linewidth of the

feature being measured.

3.6 Precision and Accuracy of the SRM Calibration

The SRM certificate reports the measured linewidths and pitches (spacings). The reported

values are the average of at least nine repeated measurements. The certified linewidths and

pitches have separate uncertainty values because of subtle differences in the way errors affect

the measurement of widths and pitches. The uncertainty statement given is based on two

contributing factors: precision and accuracy.

Process precision is defined as the variability observed in repeated measurements of a single

physical quantity under essentially the same conditions [4] and is intended to describe the

reproducibility of the measuring device, the optical microscope, as well as all of the

environmental conditions which may affect the measurement [5]. A numerical value for

process precision cannot be determined until the measuring system is operating in a state of

statistical control and the source of variability is shown to be random in nature and

stochastically stationary. When these criteria have been met the process standard deviation

6
quantifies this random error. The value for the process precision on the certificate of

calibration includes the variability of the control measurements and the variability of the nine

repeated SRM measurements. The details for computing this value are given in the

Appendix.

Accuracy is the closeness of agreement between an observed value and the true value [6].

Pitch measurements of several features in a control SRM have been independently calibrated

by the Dimensional Metrology Group on the NIST Line Scale Interferometer. Comparison

of these measurements with measurements of the same features made on the NIST optical

linewidth measurement system provides a scale correction factor to be applied to the SRM

calibration measurements. Typically, the scale correction factor is equal or nearly equal to 1.0, indicating there is no significant scale difference between the two measurement systems.

This comparison adds a small systematic uncertainty to all measurements (see appendix, sec. E).

The laser interferometer used to make these dimensional measurements is subject to a

sinusoidal nonlinearity along the beam path due to polarization mixing. This leads to a maximum periodic systematic error of —3.5 nm every one-quarter wavelength (0.16 ^m) for

the four beam differential interferometer used here [7]. Since repeat measurements of each

photomask feature are made at substantial time intervals, thermal drift in the apparatus

insures that these measurements are randomly distributed over this quarter-wavelength

period. Thus this error is random, with deviations from the mean wavelength equally likely

to be positive or negative, and is included in the calculation of process precision.

The index of refraction of air, and hence the interferometer wavelength, depends on its temperature, pressure, and composition (relative humidity, C02 , etc). In this measurement

system this can lead to error in two ways: the index error times the interferometer deadpath

changes the apparent position in the measurement of each edge, and the index error times the

measured length changes the length scale.

The deadpath here (the minimum distance between the fixed and moving mirrors) is about 1 cm. The measurement of linewidth or pitch, however, is a differential measurement in that

the difference of the positions of the leading and trailing edges is measured by measuring the

positions of both edges within a very short time (19 s for the longest pattern on this SRM);

the line's width is being measured, not its position. A deadpath error can occur then only if the index of refraction changes in this time interval. Since such changes (caused, for

instance, by convective turbulence) are equally likely to be positive as negative, this type of

error is random and is included in the measured precision. The maximum magnitude of this

deadpath error is 30 nm/°C/min, but since the temperature must decrease after it increases,

this error is random and not systematic.

If the temperature is constant but not at the nominal value (20 °C) there will be an index of

refraction error of approximately 1 ppm/°C. The worst case error for a 3 °C temperature

offset is then 0.11 nm. An atmospheric pressure deviation of 30 mm Hg from the nominal

760 mm Hg changes the index of refraction by 9 ppm, leading to a 0.34 nm error on the

longest feature. Deviation from nominal of the other factors listed above results in similar

but much smaller random errors.

7
In the field of optical submicrometer linewidth metrology, the ideal reference standard with

features which have vertical walls and smooth edges does not exist. Instead, real features

have erratically varying, nonvertical edge geometries and raggedness along their length [8]

(see fig. 10). The effective length of the viewing slit in the NIST instrument is 2.6 pm, and

the linewidth reported is the average over this length, positioned at the center of the line.

Therefore, both the nonvertical edge geometry and the raggedness along the length of the line are estimated as averages along the edge of the line. To quantify these systematic

uncertainties the feature edge geometry is examined with a scanning electron microscope. As

this examination precludes use of the photomask as an SRM, only one sample from each

photomask production batch is examined.

Typically, the SEM micrographs of the photomask features show that the raggedness along

the length of a line is less than 30 nm and has a spatial period of 100 nm or less. If the

user's measurements of this SRM are also averaged over a length comparable to that of the

NIST viewing slit, uncertainties due to edge raggedness become insignificant.

A determination of the uncertainty caused by the nonvertical edge geometry is accomplished

by estimating the difference between the edge location at the top surface and the

corresponding edge location at the substrate level, as illustrated in figure 11. Estimates are made at uniform intervals along a 1 section of the sample as imaged in an oblique view

SEM micrograph. The uncertainty is determined as the average of these estimated edge

location differences. For width measurements, edge location errors for the right and left edges tend to add; thus the linewidth uncertainty is twice the edge location uncertainty [9].

The linewidth uncertainty value given on the certificate data sheet for rows A, B, and F

includes the uncertainty resulting from the nonideal edge geometry estimated from the SEM

micrographs (typically around ±30 nm), +15 nm introduced by assuming a phase difference

of tt/2 radians (see sec. 3.4); and ±5 nm of less quantitatively defined systematic errors.

Because pitch measurements involve measuring the distance from one location (left edge,

right edge, or center) on one feature to the same location on another feature, edge detection

errors tend to cancel and are not included in the uncertainty reported for row E and row G

measurements.

The measurement precision is determined for each SRM photomask as described in the

Appendix and the pooled 95% confidence levels are reported for the width (rows A, B, and

F) and pitch (rows E and G) measurements on the certificate data sheet.

The uncertainty of the width and pitch values reported is a combination of the appropriate

systematic uncertainties and measurement precision. A summary of the error components is given in table 1.

8
The user is advised to examine the edge properties of the production photomasks to be

measured. If the quality of the edges of the features on the user's photomasks is significantly

inferior to that of this SRM, an additional level of uncertainty should be added to the

uncertainty of measurements made on the user's photomasks.

4. Using SRM 475

The following section provides information on the care and handling of the SRM photomask

and gives basic instructions and precautions on its use for calibrating optical microscope

systems for measuring linewidths of features on antireflecting photomasks or similar artifacts.

4. 1 Special Precautions

Contamination or damage can change the measured linewidths, invalidating the NIST

calibration. Particular care should be taken during use to avoid bringing the microscope

objective, or any other object, into contact with the top (chromium-coated) surface of the

SRM. It is recommended that users calibrate secondary standards of their own design and

use these in routine calibrations while keeping the NIST standard in safe storage. If this is done, the secondary standards should be checked periodically against the NIST standard.

Also, it may be advisable for the user to calibrate one or more of the uncalibrated patterns on the SRM for use in the event that the NIST calibrated pattern is destroyed.

Precautions should be taken to prevent the accumulation of airborne and other contaminants on the SRM. If cleaning becomes necessary, use only noncorrosive wetting solutions

(surfactants) at room temperature.

For cleaning we recommend the following procedure:

Soak the SRM for 15 minutes to several hours in a mild solution of commercial mask

cleaner and de-ionized water.

While the mask is still immersed, brush the coated side gently with a soft lens

brush - stroke parallel to the calibrated line length and in one direction.

Rinse the mask thoroughly with de-ionized water.

Blow away water droplets with a stream of clean, dry air or nitrogen at room

temperature.

If the contamination persists, apply a few drops of undiluted mask cleaner directly on the

SRM before repeating the above cleaning process.

Removing fingerprints or other greasy contamination may require rinsing the SRM with

alcohol or acetone and repeating the above cleaning process.

Inappropriate use of the NIST linewidth standards can result in inaccurate calibrations and

may invalidate traceability to NIST. The practices most apt to give inaccurate calibrations

when using the NIST linewidth standard include:

9
Using the linewidth standard to calibrate a measurement system that will then be used to measure linewidths on specimens with optical properties that differ significantly from

those of the standard (for example, features on silicon wafers). One important

requirement for accuracy is that the image profile (or diffraction pattern) of the edge

have the same shape for both the standard and the user's specimens. These image

profiles will not have the same shape if the optical properties of the standard and the

user's specimens differ.

When calibrating optical measuring systems that use transmitted light it is especially

important that the transmittance of the standard and the user's specimen match at the

measuring wavelength. The transmittance of SRM 475 is less than 0.2% at a wavelength of 0.53 /xm. Line edge location conditions for photomasks with

transmittance greater than about 0.5% may be significantly different from those of the

SRM.

When calibrating optical measuring systems that use reflected light, the standard and the

user's specimen should match even more closely. The more important properties to match are the complex reflection coefficient of the patterned metal layer and the

substrate, the thickness of the patterned layer, and the transmittance of the patterned

layer.

Using the linewidth standard to calibrate a scanning electron microscope. This SRM is designed specifically for use with optical microscopes and, as no criterion has been

established for edge location in an SEM image, this SRM cannot be used to calibrate an SEM for linewidth measurements. Its use in an SEM is further discouraged because the

profile of the feature could change as a result of coating the SRM with an evaporated

film to reduce electrical charging, of deposition of contamination during operation of the

SEM, and of detachment of the chromium during cleaning to remove evaporated films or contaminants. (The substrate of this SRM is quartz and, even when low-voltage SEM

techniques are used it is next to impossible to view the SRM features in the SEM

without first coating the sample).

Failing to correct for scattered (or flare) light. Although the chromium pattern on SRM

475 is not highly reflective, it includes isolated features surrounded by various large

clear areas and the image profiles may exhibit a moderate component of scattered light

which may vary from feature to feature and from the user's specimen. The intensity of

the scattered light should be subtracted from all measured intensity levels before

determining the edge location. This correction has been made in the calibration of SRM

475. If the user cannot make this correction, the reflectance and transmittance of the

standard used for calibration should match the reflectance and transmittance of the user's

specimen at the measuring wavelength. At the present time, NIST has a companion

bright-chromium linewidth standard (SRM 476) that has the same pattern as SRM 475.

We recommend that the user: (1) use the SRM that most closely matches the specimens

to be mesured and (2) make the scattered light correction outlined in step 7.

10
d. Using the NIST linewidth standards to generate a calibration curve that is then used for

features that are larger than the largest or smaller than the smallest feature on the

standard. The nominal linewidth range of SRM 475 is from 0.9 to 10.8 /xm and this

SRM will not adequately calibrate a microscope outside of this range. This is especially

true for extensions much below the nominal range where the calibration curve becomes

nonlinear. NIST is developing another antire fleeting-chromium linewidth standard,

SRM 473, that will extend the linewidth range down to 0.5 /*m and up to 30 fxm.

The user should be aware that all standards have a precision and accuracy of calibration

associated with them and, to this extent, are not perfect. The calibration of a microscope

using a standard has an imprecision associated with that calibration and also has an

imprecision associated with the subsequent use of that calibrated microscope to measure an unknown specimen. Therefore, the accuracy of the user's measurements cannot exceed the

accuracy of the standard. The uncertainty of the final measurement on the unknown

specimen is a combination of the accuracy of the standard used for calibration, the precision

of the calibration measurements using the standard, and the precision of the measurements of

the unknown specimen.

These and other topics are discussed more fully in the references [1, 14]. The need to use good measurement techniques to achieve the best results with these linewidth standards

cannot be overemphasized. The user who knows more about the potential problems is more

likely to make better use of the linewidth standard.

4.2 Microscope Calibration Procedures

The following procedure is recommended for using this SRM to calibrate optical microscope

systems for measuring linewidths on antireflecting photomasks. It is assumed the user is familiar with the operation of the microscope system being calibrated, and no attempt is made to give detailed instruction on the use of microscope systems; however, instructions on

setting up an optical microscope with Kohler illumination for dimensional measurements can be found in reference [10].

Procedures

1 . Set up the measurement system for

dimensional measurements using the

same procedures that will be used

for measuring photomasks.

2. Locate within the microscope field-ofview the specific pattern group on the

SRM that has been calibrated by NIST

Explanatory Notes

Follow manufacturers instructions or

consult reference [10] for recommended

procedures including adjustments for

Kohler illumination.

Each pattern group has a pattern number

located to the left of row E. The SRM

Certificate identifies the calibrated

pattern group (see fig. 2).

11
Procedures - continued

3. Check the resolving power of the

microscope objective by focusing on feature G-0. If the objective

cannot clearly resolve the 10 lines, use another objective.

4. Align the SRM so that lines are measured in a direction perpendicular

to their length.

5. Adjust the measurement system length

scale to give the same reading for the

spacing of the two inner lines of

feature E-5 (see fig. 3) as the NIST

value.

6. Check for mechanical nonlinearity and/ or optical distortion by measuring the

spacings of the 10 lines in feature

G-0 (or G-l) and comparing the results

with the NIST values.

For all further measurements, use only

the portion of the field of view

corresponding to the location where

the differences from NIST values are

relatively constant or that portion

of the video-display which exhibits

minimum distortion.

7. Adjust the line-to-space ratio by

measuring the calibrated line and

space of a feature in row F.

Subtract out the flare light (Q for

each measurement by shifting the

intensity zero level so that ig = 0

(see fig. 8).

Explanatory Notes - continued

The features within each pattern group

are located by reference to an alphanumeric grid with the letters A, B, E,

F, and G identifying the row and the

numbers 0 through 9 identifying

the column (see fig. 3).

The long vertical line, running

from row A to row G at the far

right (see fig. 3) may be used

as an alignment aid.

Do not use any other standards or procedures for this adjustment of

the length scale unless specifically instructed otherwise by the

manufacturer of the instrument.

To differentiate between optical

and mechanical errors, multiple

tests must be made. For example,

repeat the test with interchanged

optics while using the same screw

thread to determine if a given

error pattern is due to mechanical

errors rather than optical distortion. If the errors are small,

restricting the field of view may

eliminate the necessity of

identifying the error source.

The widths of the left inner (long)

line and the adjacent space between

the two inner lines are certified.

Determination of If for each feature

by using eq (4) (sec. 3.5) would be

time consuming and impractical for the

user; however, because the transmittance

of this SRM is less than 0.2%, /0 and If

are nearly identical and the user may

consider all measured /0 intensity to be

flare light.

12
Procedures - continued Explanatory Notes - continued

Adjust system contrast, brightness (on

video-type image-scanning micrometer

attachments) and/or threshold until

both (line and space) measured widths

agree as closely as possible with the

NIST values.

Determine the ratio 1^/1^ and use this ratio

to set the threshold level for each

subsequent measurement in this calibration

session.

Accurate linewidth measurements require a fixed relationship between a threshold

in the image intensity profile, which

corresponds to the physical line-edge

location, and the video output or other

signal from which the measurement is obtained.

NOTE: If any changes other than refocusing, repositioning and adjusting for flare are

inadvertently made during the following steps, discard the data and start again with

step 5.

Measure and record the widths of the

calibrated features in rows A and B.

Use the same focusing criteria

throughout.

Do not refocus between setting on the

left and right edges of the same line.

Make all measurements in the same

direction of travel.

Subtract out the flare light as in

step 7.

9. Measure and record the line spacings

(pitch) of NIST calibrated line pairs

in row E.

For optical systems with Kohler

illumination, a fine bright band

(or other diffraction effects) may

appear along the edge of the

line image at best focus.

Some mechanical systems exhibit

backlash when their direction of

travel is changed.

A flare-light correction should be

made when measuring linewidths on all photomasks (not only this standard).

10. Derive the calibration curves as described in reference [11].

These calibration curves apply only

to this system/operator combination.

The system is now ready for measurement of other antireflecting-chromium photomasks or

artifacts with similar optical properties to SRM 475 (low reflectance and very low

transmittance) using the same threshold value and flare-light correction procedure. If the

13
user attempts to measure artifacts with chromium layers having transmission much greater

than 0.2%, it may be necessary to measure the phase angle, <j>, and use eq (3) to determine a

different edge location threshold. These procedures are beyond the scope of this report.

Repeat the complete calibration procedure on a routine periodic basis and whenever a

substantial change is made in the measurement system. The time between periodic

calibrations may have to be determined empirically.

ACKNOWLEDGMENTS

Parts of this document (especially the procedures in sec. 4) are based on the earlier SRM 474

and SRM 475 Handbook prepared by Diana Nyyssonen and John Jerke.

The photomicrographs used to examine the edge geometry were provided by the Scanning

Electron Microscope Section (Sam Jones, William Keery, and Michael Postek) of the

Microelectronics Dimensional Metrology Group.

Many thanks to Robert Larrabee for his guidance and advice and to Beverly Wright for

typing the numerous revisions of this document.

REFERENCES

[1] Potzick, J., "Automated Calibration of Optical Photomask Linewidth Standards at the

National Institute of Standards and Technology," SPIE Vol. 1087, Integrated Circuit

Metrology, Inspection, and Process Control, San Jose, CA, February 1989.

[2] Beers, J., "Length Scale Measurement Procedures at the National Bureau of

Standards", Natl. Bur. Stand. (U.S), NBSIR 87-3625, 1987.

[3] Nyyssonen, D., "Linewidth Measurement with an Optical Microscope: The Effect of

Operating Conditions on the Image Profile," Applied Optics Vol. 16, August 1977,

pp. 2223-2230.

[4] Ku, H.H., "Statistical Concepts in Metrology - With a Postscript on Statistical

Graphics," Natl. Bur. Stand. (U.S.) Spec. Publ. 747, August 1988, pp. 12.

[5] Croarkin, C, "Measurement Assurance Programs Part II: Development and

Implementation," Natl. Bur. Stand. (U.S.) Spec. Publ. 676-11, 1985, pp. 23.

[6] 1986 Annual Book of ASTM Standards, "Statistical Terminology for Statistical

Methods," Designation E 456-83a, American Society for Testing and Materials, 1916

Race Street, Philadelphia, PA 19103.

14
[7] "High Performance Motion Control for Precision Equipment," Hewlett Packard,

1990, p. 34.

[8] Nyyssonen, D. and Larrabee, R.D., "Sub micrometer Linewidth Metrology in the

Optical Microscope," J. Res. Natl. Bur. Stand. (U.S.), May-June 1987, pp. 189-190.

[9] Potzick, J., "Practical Photomask Linewidth Measurements," SPIE Vol. 1261-13,

Integrated Circuit Metrology, Inspection, and Process Control, San Jose, CA, 1990.

[10] Annual Book of ASTM Standards, Part 43, "Standard Practice for Preparing an Optical

Microscope for Dimensional Measurements," Designation F 728-81, American Society

for Testing and Materials, 1916 Race Street, Philadelphia, PA 19103.

[11] Croarkin, C. and Varner, R.N., "Measurement Assurance for Dimensional

Measurements on Integrated Circuit Photomasks," Natl. Bur. Stand. (U.S) Tech. Note

1164, August 1982.

[12] Bullis, W.M. and Nyyssonen, D., "Optical Linewidth Measurements on Photomasks

and Wafers," Chapter 7 in VLSI Electronics: Microstructure Science, Semiconductor

Microlithography, Vol. 3, N.G. Einspurch, Editor, pp. 119-126 (Academic Press, New

York, NY, 1982).

[13] Nyyssonen, D., "Linewidth Calibration for Bright-Chromium Photomask," NBSIR 86-

3357, Natl. Bur. Stand. (U.S.), May 1986.

[14] Jerke, J.M., Croarkin, M.C., and Varner, R.N., "Interlaboratory Study on Linewidth

Measurement for Antireflective Chromium Photomasks," Natl. Bur. Stand. (U.S.)

Spec. Pub. 400-74, 1982.

15
Table 1. A listing of error sources and their contributions to overall measurement

uncertainty. Errors are determined in a worst-case sense; scale factor uncertainties (in ppm)

are multiplied by the largest dimension measured, giving scale errors of 0.03 nm (systematic)

and 0.14 nm (random) for the largest linewidth (10.8 /xm) and 0.11 nm (systematic) and 0.48

nm (random) for the largest pitch (36 itm). Net random error is derived from the

measurements.

SUMMARY OF ERROR COMPONENTS

Systematic Linewidth Pitch

Laser wavelength accuracy 0.1 ppm 0.1 ppm A ST Axis alignment 3.0 ppm 3.0 STppmr Abbe error

1 0.0 ppm 0.0 ppm

Substrate thermal expansion 1 0.0 ppm 0.0 ppm

Refractive index of air 0.0 ppm 0.0 ppm rr Chrome edge geometry 50 nm2 0.0 nm

Chrome transmission magnitude & phase 15 nm2 0.0 nm

Comparison to Standard Meter 2.0 nm 3.0 nm

Other errors 3 nm 0.0 nm

TYPICAL SYSTEMATIC UNCERTAINTY 70 nm2 TOTAL 3.1 nm TOTAL

Random

Substrate thermal expansion 1.2 ppm 1.2 ppm

Refractive index of air 12 ppm 12 ppm

Deadpath refractive index 6.0 nm 6.0 nm

Polarization mixing 3.5 nm 3.5 nm

Vibration and noise unknown unknown

TYPICAL RANDOM UNCERTAINTY3 17 nm TOTAL 15 nm TOTAL

(from measurements)

^hese scale factor errors are removed by comparing the linewidth calibration system

with the NIST Linescale Interferometer, which measures pitch only, giving traceability

to the standard meter (see sec. 3.3, p. 4). 2Typical: depends on photomask batch.

One standard deviation for a single measurement. Long-term [6 months, frequent

mounting and dismounting] and short-term standard deviations do not differ

significantly.

16
Figure 1. A view of the overall pattern on SRM 475. The basic measurement pattern is repeated eight times about the center. The horizontal and vertical lines help locate the

patterns.

II H

Figure 2. A view of the center of the SRM. The pattern number given with the serial

number on the calibration sheet identifies which pattern has been measured by NIST.

Pattern identification numbers can be seen to the left of each basic measurement pattern.

17
B

D 1 a 3 H 56109

I I I -H I I I I I

B I 1

D 1 a 3 H 55155

H"H"HH»I-H-e-|ii|-H-H"H"ID

F-|

1

G —II —111 G

Figure 3. A view of one basic measurement pattern on the SRM. The individual lines and

line patterns are located by reference to an alphanumeric grid with the letters identifying the

row and the numbers identifying the columns. The long vertical line on the right is used to align the pattern on the measurement system. The broken horizontal lines mark the central

calibrated area of the features.

Calibration values are given for: widths of opaque lines in row A and clear lines in row B;

center-to-center spacing of the two inner (short) lines of each line pattern in row E; widths of

the left inner (long) line and the space to its right of each line pattern in row F; and center- to-center spacings of lines relative to the first line on the left of each line pattern in row G.

18
Figure 4. Schematic of the NIST automated optical linewidth calibration system. The

photomask is placed on the scanning piezoelectric stage and is illuminated from below with

partially coherent light from a filtered incandescent source. The measuring slit remains fixed

while the image of the feature being measured is scanned past the slit by moving the

photomask. The motion is measured with a laser interferometer and the image intensity at the slit is monitored with a photomultiplier. The digitized and amplified output of the

photomultiplier and the interferometer output are connected via the IEEE-488 bus to the

computer.

19
Find & Correct Problem

Summarize Data

Store Data

Print Certificate

( Stop )

Figure 5. Flow chart outline of the overall calibration procedure for the calibration of SRM

photomasks with the NIST optical linewidth measurement system. First, measurements are made on a control photomask and tested statistically to determine if the system is operating

properly. Then, the SRM photomask is calibrated and the system operation is checked again

by measuring the control photomask. If all tests indicate the system is within statistical

control, a calibration certificate can be printed for the SRM photomask.

20
Mount Mask

Enter I.D. Set Measurement Series j Set Number of Series

Find 1st Feature in Series

Center and Focus

Feature

Collect & Filter Measurement Data (X&P)

Calculate Width

or Pitch Perform Tests

Find Next

Feature

No

Last Series?

Yes

Print Error Message

Figure 6. Flow chart of the main steps of the measurement sequence performed by the NIST

optical linewidth measurement system. Each feature on the SRM photomask is centered in

the microscope field of view, focused, and measured in sequence. The sequence is repeated

until each feature has been measured nine times. The optical profile position (X) and

intensity (P) are measured and the data are stored as two one-dimensional arrays.

21
A. Profile typical of

an opaque line in row

A. The vertical

fiducial s mark the

positions of the line

edges.

B. Profile typical of

a clear line (space) in

row B. The vertical

fiducials mark the

positions of the space

edges.

C. Profile typical of

a line pair in row E.

The vertical fiducials

mark the positions of

the line centers. The

profile includes the

two outer guard lines as well as the

line-spacing pair.

240 245 25 0

Figure 7. Samples of optical profiles (measured light intensity versus position) displayed on the computer screen during the calibration process. The vertical axes are relative light

intensity and the horizontal axes are position in /xm. The horizontal lines are fiducials

marking the relative intensity levels of the clear and coated areas and the threshold.

22
CO

z

LU

IOPTICAL MICROSCOPE

IMAGE PROFILE

it

T

"J]

Physical Line

Width

Figure 8. Schematic of the cross section of a vertical

-edged chromium line and

the corresponding optical

profile of its microscope

image. Im

is the intensity

of the light passing through

the clear area; IQ

is the

intensity of the light passing

through the chromium; Tc

is the intensity at the physical

edge (threshold); 7^ is the

intensity of the flare light.

The prime designates an observed intensity. The

vertical axis is optical

intensity and the horizontal

axis is distance.

Transparent Substrate

WIDTH (um)

Figure 9. Optical intensity [% of {lm

-I0

)] at edge location versus linewidth, from a computer

model of the NIST calibration system. Transmittance equals 0.2% and <j> equals x/2 radians.

23
Micrograph A Micrograph B

Figure 10. SEM micrographs showing the nonideal nature of line edges on an

antireflecting-chromium photomask. The scale is indicated by the row of eleven dots in the

lower right of each micrograph. The dots are 28 nm apart in micrograph A, and 30 nm

apart in B. Beam energy was 25 keV. The specimen in A is coated with gold; the specimen

in B is coated with carbon.

24
Figure 1 1 . Schematic representation (not to scale) of a line edge as seen in an oblique view

SEM micrograph. The uncertainty of linewidth measurements includes the uncertainty of the

edge location resulting from non-vertical physical edge profiles. Determination of this

uncertainty is accomplished by estimating the difference between the edge location at the top

surface (A) and at the substrate level (B). Estimates are made at uniform intervals along a

section of a specimen image in an SEM micrograph. The edge uncertainty reported is the

average of such estimates made by several individuals using several different micrographs.

25
Appendix

Process Control for SRM 475 Calibrations

A. Introduction

The procedures used to assure statistical control of the linewidth SRM measurement system

are defined. A control photomask with the same characteristics as the SRM photomask is used for measurement process control. Six of the features on the control photomask are measured each time an SRM photomask is calibrated. The six features are: the nominal 2.7

and 9.5 /xm lines from row A; the nominal 9.5 and 2.7 /xm lines from row B; and the

nominal 4.0 and 10.8 /xm pitch patterns from row E. These correspond to features A-0,

A-l, B-8, B-9, E-4, and E-5 as shown on the diagram of a pattern in figure 12.

The purpose of the control photomask measurements is to provide a database that can be

used to determine whether or not the measurement system is in a state of statistical control.

There are several factors which may cause the optical measurement system to be

out-of-control. There may be a change in the measurement system or a change in

environmental conditions. This document describes the initialization of the database of

control measurements, use of the database to determine if the measurement system is in

control, and the maintenance of the database over a long period of time.

B. Initialization of Process Parameters

When the measurement system is determined to be ready for performing SRM calibrations, a

database is initialized. This database consists of at least 15 sets of repeated measurements of

the six selected features on the control photomask taken over a period of several weeks [15].

This period is representative of the normal operating mode of the optical measurement

system. The six features measured are identified as A-0, A-l, B-8, B-9, E-4, and E-5.

These features cover the extremes of the feature sizes and the range of the feature locations on the photomask. The database includes not only the measured width or space but also

other pertinent information such as the date and time of the measurement and feature

identification and any other potentially useful information (temperature, scan rate, etc.).

A plot, measured width or pitch versus time, of the repeated measurements for each feature

is made to detect any possible anomalies in the measurement system and to verify that the

system produces stable measurements whose variability is random in nature. The control

database is accepted as being representative of the normal operating environment of the

measurement system if no more than 5 % of the measurements are suspected outliers

(unexplained anomalies). If this is not the case, an effort is made to determine the cause and

pertinent adjustments are made to the measurement system. The control database is then

reinitialized.

26
The initial control database is used to estimate the mean vector (accepted mean values for

each control feature) and the matrix of covariances between them. These are required

elements for the multivariate Hotelling's T

2

test statistic [16]. The details for computing the

estimate of the mean vector and the matrix of covariances are given below. The use of this

test statistic and updating procedure for this statistic are given in following sections of this

document.

From the database of control measurements for features A-0, A-l, B-8, B-9, E-4, and E-5, a

matrix [X] is constructed, as shown below, of the N initial repeated measurements on the

control photomask. Each of the features has the same number of repeated measurements,

XAQ,\ XA0,2 XA0,N

XAl,l XAl,2 XAl,N

^B8,l XB%,2 XBi,N

XB9,l XB9,2 XB9,N

XE4,l XE4,2 XE4,N

XE5,l XE5,2 XE5,N

where i = 1,2, ....6 and j = 1,2, iV

(B.l)

The average is computed for each of the features based on the A7 repeated measurements,

L A0

L B8

L E4

E

7=1

N

E

N

E

7 = 1

XA0- N

N

= I

7=1

XBS- N

N

XB9 = E

7=1

XE4- N

N

XE5 = E

7=1

^B9j

aT

N

(B.2)

These values are the elements of the vector of means as denoted below:

L A0

L A1

M =

L B8

L B9

E4

(B.3)

L E5

27
A matrix is computed of the differences of the measured values minus the mean values,

V u 1 and j = 1,2,. ...N,

and the variance-covariance matrix, S, of size 6x6, of the control database is computed with

elements:

N

? -

1 V (7 \ (7 \ where 1 = 1 > 2 >---- 6

S (B.5)

U

~ £ ( ( jk) and; = 1,2,....6 . 1

' PJ

The inverse of the variance-covariance matrix is computed and is used in conjunction with

future control measurements to determine if the measurement system remains in a state of

statistical control.

C. Procedures for Process Control

At the beginning of an SRM measurement session the features A-0, A-l, B-8, B-9, E-4 and

E-5 on the control mask are measured and the multivariate Hotelling's test statistic T

2

is computed as follows:

r

2 = N

AM

[Y - M\' S~ l [Y - M] (C.l)

where Y is a vector of newly determined widths and pitches for the above mentioned

features.

The system is in control at a 95% confidence level if

{N~

6)

T

2 < F 05 (6,N-6), (C2)

(AM)6 - 05

where the F 05 (6,N-6) values are found in table 2. The value (N-6) corresponds to v in

table 2.

At the end of the SRM measurement session, the control is remeasured and the test is repeated. If the system is still in control the SRM data are summarized and a certificate of

calibration produced. The value of ((N-6)/6(N-l))T2

is saved in the control database and the

system is ready for the next SRM measurements.

28
If the test indicates the system is not in control, the data are tagged when they are saved in

the control database. The system is then checked to determine the cause of the test failure.

A control chart may be used to determine which feature is causing the problem or to see

trends in the control data. A control chart for each feature is constructed from the control

database as follows:

The mean, X, and the standard deviation, a , for each feature are computed using the N

repeated measurements from the control database:

X =

N

E Xi

i=l

N

and a =

N

E (xf - X): i=l

(N-l)

(C.3)

Control limits are computed by using the following equations:

and

X ± a t 915(N-l) for the 2a limit

X ± a t 995(N-l) for the 3a limit.

(C.4)

The values for / are found in table 3. The value (N - 1) denotes degrees of freedom, df, in

table 3.

Figure 13 is an example of a control chart of the initial 81 measurements of feature A-0.

Future measurements are added to the chart. The control limits remain the same until the

process parameters are updated.

If it is determined that the cause of the failure did not affect the SRM measurements (for

example, the control photomask was misaligned), the appropriate adjustments are made and

the control photomask is remeasured. If the test then shows the process is in control, the

SRM data are summarized, a certificate of calibration produced, and the system is ready for

the next SRM measurements.

If it is determined that the cause of the failure may also have affected the SRM

measurements (for example, the air-conditioning unit malfunctioned during calibration), the

SRM must be re-measured after the problem has been corrected and the test indicates the

system is once again in control. Major changes to the measurement system dictate

reinitialization of the database.

29
D. Updating Process Parameters

If the measurement system remains unchanged, after collecting a minimum of 30 new (good)

sets of control photomask measurements, the process parameters, M, S, and a are updated.

Equation (B.3) is used to compute M2

, a vector of estimated means for the recently collected

control measurements; eqs (B.4) and (B.5) are used to compute S2

, the corresponding

variance-covariance matrix; and eq (C.3) is used to compute a2

, a vector of standard

deviations for the repeated measurements for each feature. In the updating process, values

that have been flagged as out of control are omitted.

Before updating the control database, a comparison is made between the two databases, the

old versus the new, to determine whether or not there is a significant difference in terms of

the mean vectors and the variance-covariance matrices. The equivalency of variancecovariance matrices is tested as follows:

let t = Nx + N2 , (DA)

where Nl = number of repeated observations in the control database

and N2 = number of repeated observations in the new set of control

observations.

The new control database will contain both new and old measurements.

Let

_ (iVA) + (N2S2) (D 2)

e

where S{ is the variance-covariance matrix of the current control database

and S2is the variance-covariance matrix of additional new control measurements.

Compute the statistic [17]:

D = 0.5/Vj trace [(5r5)5

_1

] 2 + 0.5/V

2 trace [(S2 -S)S~ x f\ ( D- 3 )

and test whether:

D < Xrf/0.05).

D is distributed as a chi-square random variable with df (degrees of freedom) = 0.5p(p+l)

where p = 6, the number of features measured. The value of X21 (0 05) is 32.67. If D <

32.67, then the differences between the old and new covariance matrices can be attributed to measurement error at the 95% confidence level. However, if the test fails, (D > 32.67),

30
this suggests that the process has changed in some manner and the cause needs to be

identified and evaluated. If the change is significant, appropriate action must be taken and

the control process re-initialized.

If the covariance matrices are statistically the same, the means are compared. To do this,

first a pooled covariance matrix is computed:

_ [(N.-DS, + (N2 -l)S2] (D 4)

p e-2

where S{ and S2 are defined in (D.2).

Then the statistic is computed:

I

2

= L_L (M, - Af,)' 5n (Mi - M7 )

(D- 5) (! -2)p (!)

1 2 p 1 2

and tested whether:

I

2 < F 05(p,e-p-l)

where Nlt N2 and £ are defined in (D.l),

A/j is the mean vector for the current database,

M2is the mean vector for the newly collected control data,

and p = 6, the number of measured features.

T

2

is a random variable with an F-distribution with p degrees of freedom in the numerator

and with t-p-l degrees of freedom in the denominator. The F 05 (pJ-p-l) value is given in

table I. If T

2 >F 05 (pJ-p-l), this suggests that there has been a change in the measurement

process. The change needs to be identified and appropriate action needs to be taken to reestablish the measurement system and begin the process control anew. However, if T

2 <F 05(p, t-p-l) then the differences between the old and new mean vectors can be

attributed to measurement error at the 95% confidence level. Since the test for equality of

means was only performed if the hypothesis of equal covariance matrices was not rejected, it can be said that there has been no statistically discernable change in the measurement process

at the 90% confidence level and the control may be updated to include the new

measurements. The covariance matrix is updated as shown in eq (D.4) and the current

covariance matrix is:

31
(D.6)

The mean vector is updated as shown below:

M = Nl Ml + N2M2 (D.7)

The standard deviation for each feature is updated as follows:

(Nl -l)o

2

l Nl + {N2 -\)o\n2 (D.8) a = Nl + N2 ~ 2

E. Uncertainty Statement for SRM 475

The uncertainties for the certified linewidth and pitch values given in the certificate include

small contributions from the measurement precision (random error) and a contribution from

the systematic error. The systematic error for both pitch and linewidth values includes a

length dependent contribution introduced by correcting the measurements to agree with the

NIST Line Scale Interferometer measurements (see sec. 3.5). The systematic error for the

linewidth values has a significant contribution (on the order of ± 0.05 /im) resulting from

the edge geometry of the features (see sec. 3.5). See table 1 for a detailed summary of error components.

Before determining the total uncertainty for the reported certificate values, it is assumed that

all the measurements on the SRM and in the control database have been corrected to compensate for the difference of measurements between the NIST Line Scale Interferometer

System and the optical linewidth measurement system. The correction factor is derived by

using the model given below and ordinary least squares to estimate a and its variance:

where X represents a measurement from the linewidth measurement system,

Y represents a measurement from the line scale measurement system,

and e is the random error of measurement.

Then the uncertainties, UL

and Up

, for linewidth and pitch measurements are determined by

the equations below:

X = a Y + e (E.l)

32
J2, The variance of each SRM measurement, s- , is ^^^

£ *

- '/

(E- 2)

a

n 1 1=1

where jr. is the average of the jth feature,

var(<i) is the estimated error of the slope,

a is the least squares determination of the slope,

and n is the number of repeated measurements.

2

The variance of the control measurements, bk , is

„2 -2 var(a) „T/ ,_ °* = c

k —V + ^

(E.3)

where c^is the average of the kth control feature

and CV^. is the Mi diagonal element of the variance-covariance matrix for the

control data.

Then the pooled variance from the N repeated measurements in the control database and the n repeated measurements of the SRM, s , is

P 2 Q 2 (AM) E ok + (n-1) E ^ (E 4)

/\2 — 1 / -

1

*

= (AM)/? + (#1-1)0

The uncertainty for pitch measurements is

U

p

= ±(1.96 sp

l\fn + systematic pitch uncertainty) /xm (E-5)

and the uncertainty for linewidth measurements is

UL

= ±(1.96 sp

l\fn + systematic linewidth uncertainty) fxm, (E.6)

where sp

is determined by using eqs (E.2), (E.3), and (E.4) for pitch and linewidth

measurements on the SRM and in the control database. Typically s = .015 fim and n = 9

repeat measurements. The factor 1.96 converts the uncertainty to the 95% confidence level.

33
ACKNOWLEDGMENTS

The authors thank Susannah Schiller for suggesting the statistical tools to assure process

control of the linewidth SRM measurement system and for her review of this documentation.

REFERENCES

[15] Croarkin, C. , Measurement Assurance Programs Part II: Development and

Implementation, Natl. Bur. Stand. (U.S.) Spec. Publ. 676-11, 1985, pp. 35.

[16] Anderson, T.W., "An Introduction to Multivariate Statistical Analysis," Second ed.

John Wiley and Sons, 1984. Chapter 5, pp. 156-190.

[17] ibid., p. 423.

34
Table 2. Critical Values of F.osCM) of the FDistribution

Table 3. Critical Values of t.m(df) and 1.995 (df)

of the Student's t Distribution

V F.05(6,v)

10 3.217

12 2.996

14 2.848

16 2.741 18 2.661 20 2.599 22 2.549 24 2.508 26 2.474 28 2.445 30 2.421 32 2.399 34 2.380 36 2.364 38 2.349 40 2.336 42 2.324 44 2.313 46 2.304 48 2.295 50 2.286 52 2.279 54 2.272 56 2.266 58 2.260 60 2.254 62 2.249 64 2.244 66 2.239 68 2.235 70 2.231 72 2.227 74 2.224 76 2.220 78 2.217 80 2.214 82 2.211 84 2.209 86 2.206 88 2.203 90 2.201 92 2.199 94 2.197 96 2.195 98 2.193 100 2.191 102 2.189 104 2.187 106 2.185 108 2.184 110 2.182 112 2.181 114 2.179 116 2.178 118 2.176 120 2.175

00 2.099

dt t.975 t.995

10 2.228 3.169 12 2.179 3.055 14 2.145 2.977 16 2.120 2.921 18 2.101 2.878 20 2.086 2.845 22 2.074 2.819 24 2.064 2.797 26 2.056 2.779 28 2.048 2.763 30 2.042 2.750 32 2.037 2.738 34 2.032 2.728 36 2.028 2.719 38 2.024 2.712 40 2.021 2.704 42 2.018 2.698 44 2.015 2.692 46 2.013 2.687 48 2.011 2.682 50 2.009 2.678 52 2.007 2.674 54 2.005 2.670 56 2.003 2.667 58 2.002 2.663 60 2.000 2.660 62 1.999 2.657 64 1.998 2.655 66 1.997 2.652 68 1.995 2.650 70 1.994 2.648 72 1.993 2.646 74 1.993 2.644 76 1.992 2.642 78 1.991 2.640 80 1.990 2.639 82 1.989 2.637 84 1.989 2.636 86 1.988 2.634 88 1.987 2.633 90 1.987 2.632 92 1.986 2.630 94 1.986 2.629 96 1.985 2.628 98 1.984 2.627 100 1.984 2.626 102 1.983 2.625 104 1.983 2.624

108 1.982 2.622 110 1.982 2.621 112 1.981 2.620 114 1.981 2.620 116 1.981 2.619 118 1.980 2.618 120 1.980 2.617

00 1.960 2.576

35
H

B

D133H 5E1B9

l-l-l-ll-H-l-l-l-l-l

B I

D 1 a 3 H 5 6 1 b g

E H"H1

1

hi

H

1

1

HI~e- 1

1

1 H'HH"H 1

1

\—

F

G ~1

Figure 12. A view of the basic pattern on the SRM 475 control photomask. Features 0 and

1 in row A, 8 and 9 in row B, and 4 and 5 in row E are measured before and after each

SRM is calibrated. Features 4 and 5 in row E and feature 1 in row G have been

independently calibrated on the NIST Linescale Interferometer by the NIST Dimensional

Metrology Group.

36
+0.04

E

it

LJJ O

z

LJJ DC

yj

LL

LL

o o

0

o

O ©

-• • • •••• • V

• •

•

-0.04

SUCCESSIVE MEASUREMENTS

Figure 13. Control chart of feature A-0. Line M is the mean; and lines L mark 95%

confidence level. The chart includes the first 81 measurements of the feature. Future

measurements are added to the chart.

37

4. TITLE AND SUBTITLE Antiref lect ing-Chromi urn Linewidth Standard, SRM

Microscope Linewidth Measuring Systems

475, for Calibration of Optical

5. AUTHOR(S)

Carol F. Vezzetti, Ruth N. Varner, and James E . Potzick

NIST-114A

(REV. 3-89) U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

BIBLIOGRAPHIC DATA SHEET

1. PUBLICATION OR REPORT NUMBER

NIST/SP-260/117

2. PERFORMING ORGANIZATION REPORT NUMBER

3. PUBUCATION DATE January 1992

6. PERFORMING ORGANIZATION (IF JOINT OR OTHER THAN NIST, SEE INSTRUCTIONS)

U.S. DEPARTMENT OF COMMERCE

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

GAITHERSBURG, MD 20899

7. CONTRACT/GRANT NUMBER

8. TYPE OF REPORT AND PERIOD COVERED

Final

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (STREET, CITY, STATE, ZIP)

Same as item #6,

10. SUPPLEMENTARY NOTES

DOCUMENT DESCRIBES A COMPUTER PROGRAM; SF-18S, FIPS 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.) The precise and accurate measurement of feature dimensions on photomasks, such as those

used in the production of integrated circuits, becomes increasingly difficult as the dimensions

approach the wavelength of the light used to make the measurement. The undesirable effects

of optical diffraction obsure the location of the feature edges. Raggedness and non-vertical

walls along the edges add to the uncertainty of the measurement.

Standard Reference Material SRM 475 was developed for use in calibrating optical

microscopes for measuring linewidths in the range of 0.9 to 10.8 Ltm on antireflectingchromium photomasks. The SRM, the measurement system, and the procedures used to calibrate the SRM are described. The algorithm fcr determining the line edge location uses a threshold criterion derived from analysis of microscope image profiles. The profiles are predicted by computer modeling based on the theory of partial coherence. The performance

of the system is monitored by measuring line features on a control photomask before and

after calibrating each SRM.

Precautions concerning care and handling and instruction for the use of SRM 475 to calibrate

optical microscopes for photomask linewidth measurement are given.

12. KEY WORDS (6 TO 12 ENTRIES; ALPHABETICAL ORDER; CAPITALIZE ONLY PROPER NAMES; AND SEPARATE KEY WORDS BY SEMICOLONS)

accuracy; antiref lecting-chromium; calibration; control charts; critical dimensions;

integrated circuits; linewidth measurement ; optical microscope; photomask; precision;

semiconductor industry; standard reference material; statistical process control;

threshold; uncertainty

13. AVAILABILITY UNLIMITED FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE TO NATIONAL TECHNICAL INFORMATION SERVICE (NTIS). X

X ORDER FROM SUPERINTENDENT OF DOCUMENTS, U.S. GOVERNMENT PRINTING OFFICE, WASHINGTON, DC 20402. ORDER FROM NATIONAL TECHNICAL INFORMATION SERVICE (NTIS), SPRINGFIELD, VA 22161.

14. NUMBER OF PRINTED PAGES

49

15. PRICE

ELECTRONIC FORM * U.S. G. P. 0.1991-311-891/40066

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0) TO E co