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REFERENCE

NBS

PUBLICATIONS

NATL INST OF STANDARDS & TECH R.I.C.

A1 11 02623854

Jerke, John M/lnterlaboratory study on I QC100 .U57 NO. 400-74 1982 VI 9 C.I NBS-P

CO Q« NBS SPECIAL PUBLICATION 400-74

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

Semiconductor Measurement Technology:

Interlaboratory Study on

Linewidth Measurements for

Antireflective Chromium

Photomasks
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act ot Congress on March 3, I90I. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities^ — Radiation Research — Chemical Physics —

Analytical Chemistry — Materials Science

THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities;

provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering^ — Manufacturing

Engineering — Building Technology — Fire Research — Chemical Engineering^

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

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

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

Programming Science and Technology — Computer Systems Engineering.

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. 'Some divisions within the center are located at Boulder, CO 80303.
Semiconductor Measurement Technology:

Interlaboratory Study on Linewidth Measurements

for Antireflective Chromium Photomasks

John M. Jerke

M. Carroll Croarkin

Ruth N. Varner

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

Sponsored jointly by NBS and the:

Defense Advanced Research Projects Agency

1400 Wilson Blvd.

Arlington, VA 22209

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued Novennber 1982

^^^\-r OF

*2
Library of Congress Catalog Card Number: 82-600642

National Bureau of Standards Special Publication 400-74

Natl. Bur. Stand. (U.S.), Spec. Publ. 400-74, 191 pages (Nov. 1982)

CODEN: XNBSAV

u s. GOVERNMENT PRINTING OFFICE

WASHINGTON; 1982

For Sale by the Superintendent of Documents, U S Government Printing Office, Washington, D.C. 20402.

Price $7.00

(Add 25 percent for other than U.S. mailing.)
TABLE OF CONTENTS

Page

Preface vl

Abstract and Key Words 1

1 . Introduction ..... . 2

2. Description of Study 4

2.1 NBS Artifact 4

2.2 NBS Measurement System 5 2.3 Procedures 6

2.4 Participants' Measurement Systems 8

3. Statistical Analysis ' 9

3.1 Approach 10

3.2 Graphical Analysis 11 3.2.1 Individual Measurement Systems ... 11 3.2.2 Youden Plots 12

3.3 Detection of Outliers 13

3.3.1 Isolated Outliers 13

3.3.2 Entire Day's Measurements as Outliers 14

3.4 Calibration Curves 15

3.4.1 Line-Spacing Calibration 16

3.4.2 Linewidth Calibration 18

3.5 Assessment of Line-Spacing and Linewidth Calibrations .... 19

3.5.1 Measurement Systems Combined 19

3.5.2 Individual Measurement Systems 20

3.5.3 Measurement Process Standard Deviation 20

3.5.4 Uncertainty of Corrected Linewidth Values 20

3.6 Sources of Measurement Errors 21

3.6.1 Between-Day Differences in Calibration Curves .... 21 3.6.2 Linearity Assumption 23

3.6.3 Differences Between Operators 24

3.7 Effects of Using Adjusted NBS Values 25

4. Discussion 26

4.1 NBS Recommended Procedures 26

4.2 Linewidth Calibration Curves 27

4.3 Polarity Dependence of Linewidth Calibration 27

4.4 Measurement Process Standard Deviation 28

4.5 Linearity of Calibration Curve 29

5. Concluding Remarks 30

6. References 32

iii
Appendix A - Design of a Pattern on a Photomask-Like Physical Standard

for Evaluation and Calibration of Linewidth-Measuring

Systems (reprint) 89

Appendix B - NBS Linewidth and Line-Spacing Values for Artifacts .... 97

Appendix C - Recommended Procedures for Photomask Linewidth

Measurements (AR-Chromium) 98

Appendix D - Participants' Linewidth and Line-Spacing Measurements ... 137

Appendix E - Graphical Diagnosis of Interlaboratory Test Results

(reprint) 176

Appendix F - Calibration Curve from Method of Least Squares 181

Appendix G - Standard Deviation of the Residual 183

LIST OF FIGURES

1. Photograph of overall pattern on NBS antiref lective-chromium

artifact 35

2. Photograph of central area of NBS antiref lective-chromium

artifact 36

3. Photograph of basic measurement pattern on NBS antiref lectivechromium artifact , 37

4. Schematic of physical profile of opaque line on NBS antiref lectivechromium artifact 38

5. Examples of differences between participant's linewidth measurements and NBS linewidth values as a function of NBS values .... 39

6. Youden plots of differences between participant's raw linewidth

measurements on opaque lines (rows A and C) and NBS values .... 41

7. Youden plots of differences between participant's raw linewidth

measurements on clear lines (rows B and D) and NBS values 51

8. Youden plots of differences between participant's corrected

linewidth measurements on opaque and clear lines (rows C and D)

and NBS values 61

9. Daily changes in linear linewidth calibration curve for one operator 71

10. Dependence of systematic linewidth measurement errors on line

polarity 72

iv
11. Residiial linewidth measurement errors of video image-scanning

measurement system 73

LIST OF TABLES

1 . Uncertainty Assigned to NBS Linewidth Measurements for

Inter laboratory Study 74

2. Measurement Systems Used by Participants in Inter laboratory

Study 75

3. Codes for Identifying Participants' Measurement Systems in

Figures 6, 7, and 8 76

4. Least-Squares Estimates of Intercept a and Slope 3 for LineSpacing Calibration Curves and Student's t Statistics 77

5. Least-Squares Estimates of Intercept a and Slope 3 of Linewidth

Calibration Curves and Student's t Statistics for Opaque Lines

(Row A) and Clear Lines (Row B) 78

6. Frequency of Differences Between Participant's Linewidth

Measurements and NBS Values on Opaque Lines (Row C) 79

7. Frequency of Differences Between Participant's Linewidth

Measurements and NBS Values on Clear Lines (Row D) 81

8. Random Error Limits for Linewidth Measurements Corrected by

Linear Calibration Curve, Process Standard Deviations, and

Degrees of Freedom 83

9. F Statistics for Detecting Between-Day Differences in Linewidth

Calibration Curves, Degrees of Freedom, and Pooled Standard

Deviations from Linear Fit 84

10. Standard Deviations of Repetition, Process Standard Deviations,

Degrees of Freedom, and F Statistics for Testing Linearity of

Linewidth Calibration Model 86

11. Frequency of Differences Between Participant's Linewidth

Measurements and NBS Values for Two Operators on E^ich of Three

Measurement Systems 87

V
PREFACE

This National Bureau of Standards (NBS) study was initiated in the Optics and

Micrometrology Section, Mechanics Division, in cooperation with the Optical

Physics Division, as a part of the Semiconductor Technology Program based in

the Electronic Technology Division. Related work continues in the

Semiconductor Materials and Processes Division, one of the two Divisions

comprising the Semiconductor Technology Program at the present time. This

Program serves to focus NBS research on improved measurement technology for

the use of the semiconductor device community in specifying materials,

equipment, and devices in national and international commerce, and in

monitoring and controlling device fabrication and assembly. This research

leads to carefully evaluated, we11- documented test procedures and associated

technology which, when applied by the industry, are expected to contribute to

higher yields, lower cost, and higher reliability of semiconductor devices

and to provide a basis for controlled improvements in fabrication processes

and device performance. By providing a common basis for the purchase

specifications of Government agencies, improved measurement technology also

leads to greater economy in Government procurement. Financial support of the

Program has been provided by a variety of Federal agencies: The Defense

Advanced Research Projects Agency; The National Bureau of Standards; The

Division of Electric Energy Systems, Department of Energy; The Defense

Nuclear Agency; The C. S. Draper Laboratory; The Naval Air Systems Command;

The Air Force Wright Aeronautical Laboratories; The Army Electronics

Technology and Devices Laboratory; The Naval Weapons Support Center; The

Solar Energy Research Institute; The Naval Avionics Center; The Lewis

Research Center, National Aeronautics and Space Administration; The Office of

Naval Research; and The Naval Ocean Systems Center. The specific work

reported herein was supported jointly by DARPA and NBS.'*'

This study depended on the cooperation of ten companies which are part of the

U.S. microelectronics industry. These companies provided the personnel,

facilities, and time necessary to make the measurements according to NBS

procedures, return the data and artifacts to NBS, and respond to follow-up

inquiries from NBS during the data analysis. For these efforts, special

thanks are gratefully made to these ten companies and to the individual

operators who participated in the study.

Special acknowledgment is gratefully made to the following NBS staff: Arie

W. Hartman and Fred W. Rosberry^ for measuring linewidths and line spacings

on the ten artifacts used in this study; Dr. Dennis A. Swyt for analysis of

the NBS measurement data and for his contributions to the design of the

artifact used in this study; William R. Smallwood''" for remeasurements of

the artifacts following their return from industry; Dr. Diana Nyyssonen and

Dr. W. Murray Bullis^' for their helpful suggestions in the design of the

study and the analysis of the results; Dr. James J. Filliben for making

alterations and additions to the computer software used to plot the results;

and Dr. Clifford H. Spiegelman and Dr. Keith R. Eberhardt for their helpful

advice on the statistical analysis. Special acknowledgment is also made to

the NBS Office of Measurement Services which supported part of this study.

t Through ARPA Order 2397.

§ Retired.

% Present address: Fairchild R&D Laboratories, Palo Alto, CA.

vi
Disataimev

Certain commercially available materials or instruments are identified in

this publication for the purpose of providing a complete description of the

work performed. The experiments reported do not constitute an evaluation of

the performance characteristics of the products so identified. In no case does such identification imply recommendation or endorsement by the National

Bureau of Standards nor does it imply that the items identified are necessarily the best available for the purpose.

vii

Semieonduetov Measurement Teahnotogy

Interlabora tory Study on Linewidth Measurements

for Antiref lective Chromium Photomasks

John M. Jerke

Semiconductor Materials and Processes Division

Center for Electronics and Electrical Engineering

M. Carroll Croarkin and Ruth N. Varner

Statistical Engineering Division

Center for Applied Mathematics

National Bureau of Standards

Washington, DC 20234

Ahstvaet: Optical microscopes fitted with a micrometer attachment are commonly used to measure small linewidths and other

critical dimensions on Integra ted-circuit (IC) photomasks. In

the absence of calibrated linewidth standards, users have experienced systematic measurement errors much larger than required

manufacturing tolerances. As IC linewidths approach 1 tjn with a 10 percent tolerance, the need for calibration standards and

improved measurement procedures becomes even more important.

This report discusses the results of an interlabora tory study to

evaluate a National Bureau of Standards (NBS) prototype calibration standard for linewidth measurements on IC photomasks and

procedures for adjusting and calibrating optical-microscope systems in the 0.5- to 1 2- ;in measurement range. Using procedures

furnished by NBS, industrial participants measured line spacings

and linewidths on NBS antiref lective-chromium artifacts. A com- parison of NBS linewidth values with participants' measurements

showed that most differences were less than ±0.3 \m. A linewidth

calibration significantly reduced systematic errors for most

systems. Outliers in the data showed the need for measurementcontrol procedures. The standard deviation of the measurement

process was ±0.1 or larger for about half of the systems. For

some systems, there were significant day-to-day differences and

operator differences.

The study showed that the NBS artifact and recommended procedures

were adequate for calibrating an optical-microscope system which

was in a state of statistical control. This study led to the

issuance of NBS Standard Reference Material 474 (Optical Microscope Linewidth-Measurement Standard).

Key words: dimensional measurements; filar micrometer; imageshearing micrometer; integrated circuits; interlabora tory study;

Kohler illumination; line-spacing measurements; linewidth calibration; linewidth measurements; measurement uncertainty; micrometrology; optical microscope; photomask; semiconductor technology; statistical tests.

1
1 . INTRODUCTION

Optical imaging systems which use an optical microscope fitted with some type

of measurement attachment are commonly used for linewidth measurements in the

0.5- to 12-ym range on Integra ted-circuit (IC) photomasks. Differences as

large as 1 ym for linewidth measurements on the same photomask exist for

different types of optical imaging systems, different systems of the same

type, different operators on the same system, and measurements made by the same operator at different times of the day. Such differences are, for

example, much larger than the required tolerances of 10 percent or less on 1-

to 2-ym wide lines for Very Large Scale Integration (VLSI) geometries.

Although some of these differences can be attributed to manufacturing

tolerances or human errors, a much larger source of measurement differences

is the diversity of methods used by these systems for detecting line edges

and determining linewidth [ 1 ]

The term linewidth, as used in semiconductor technology, has traditionally

been defined in a variety of ways depending upon its specific application.

For example, the width of a line on a photomask used in photolithographic

projection printing is defined differently from the width of a photoresist

window used for etching a sublayer, or the width of a conducting line used

for electrical measurements of an IC device. In the present case, linewidth

is defined, at a given cross section of the line, as the distance between the

air/line-material boundaries at some specified height above the interface

between the patterned layer in which the line is formed and the underlying

layer. The physical basis for various applications or methods of measuring

linewidth may result in measurements being made at different heights above

the interface. For this reason, differences may be expected between

measurements made optically, electrically, or with a scanning electron

microscope. Only optical measurements are considered in this report.

In an effort to provide the microelectronics industry with calibration

standards and procedures for determining and reducing systematic linewidthmeasurement errors, the National Bureau of Standards (NBS) undertook an effort in late 1974 to develop a linewidth standard and procedures for using

this standard with different types of measurement systems [2]. A pilot

inter laboratory study involving NBS and three companies was conducted in mid1977 to determine the suitability of a chromium-on-glass artifact as a linewidth standard, to evaluate NBS recommended measurement procedures as a protocol for making linewidth measurements, and to elicit comments from the

participants for possible improvements in the standard and procedures [3].

This study showed linewidth-measurement differences as large as 0.5 ym on a nominally 3-ym-wide line among companies, among divisions of the same company, and among groups of the same division of the same company. The

results of this relatively modest pilot study were subsequently used as a basis for redesigning the artifact [4] and revising the measurement

procedures.

A full-scale inter laboratory study involving NBS and ten companies was conducted in 1978-79 to evaluate the revised linewidth-measurement procedures

and to determine the suitability of the redesigned antiref lecti ve chromiumon-glass artifact as an NBS linewidth standard. In addition, this

inter laboratory study was designed to enable organizations using optical2
linewidth measurement systems to determine their relative measurement capability and the degree of improvement they can expect from the use of a calibrated linewidth standard and accompanying measurement procedures.

This report presents the results of the full-scale interlaboratory study.

Section 2 of the report provides a description of the NBS artifact, the

specified measurement procedures, and the measurement systems used by the

participants in the study. Section 3 is a statistical analysis of the data

provided by the participants and includes consideration of outliers, derivation of the calibration curves, and a discussion of the sources of measurement errors. Section 4 uses the results of the statistical analysis in section 3 to address several questions about the artifact, the measurement procedures, and the measurement systems used by the participants, including the

effects of applying a linewidth calibration curve to reduce systematic errors, the dependence of systematic errors on the line polarity (clear or opaque), and the effect of the measurement process standard deviation on the

linewidth calibration curve. Section 5 summarizes the important results of

this study.

The appendices include both data and reference material required for a more

complete understanding of this study and the resulting conclusions. Appendix

A is a reprint of an article describing the basis for the design of the artifact used in this study. Appendix B gives the NBS measurements for all of

the artifacts. Appendix C is the set of instructions sent to each participant, and Appendix D gives the raw data received from each. Appendix E is a reprint describing the method of Youden plots used in the analysis of the

data. Appendices F and G give the mathematical derivation of the calibration

curves and standard deviation of the residuals, respectively.

3
2. DESCRIPTION OF STUDY

Each of the ten participating companies received from NBS one antiref lective

(AR) chromium artifact''", procedures for adjusting the measurement systems

and making measurements, a Wratten 60 (green) filter^, and data sheets. In

contrast with the earlier blind pilot study in which industrial participants

adjusted their measurement systems by their own techniques and standards,

participants in the full-scale study were asked to follow only those

procedures recommended by NBS and to use only the NBS-furnished line-spacing

values and line-to-space ratio for adjusting their measurement systems.

The industrial participants in the interlaboratory study included

manufacturers of photomasks, ICs, and linewidth-measurement equipment. In some companies, more than one division or group participated in the study.

In these cases, each division or group received a separate set of

instructions and data sheets, but measured the same artifact.

Each participating group used one or more linewidth-measurement systems

representative of those commonly used for critical dimensional measurements

in the IC industry.

The present study was restricted to measurements in bright-field transmitted

light. It is preferred that linewidth measurements on photomasks be made in

transmitted light. In reflected light, the line-image quality is degraded

because of the strong wavelength dependence of the relative phase and

contrast at the line edges and the poor (compared to transmitted-light

measurements) signal-to-noise ratio for most specimens [5]. To reduce the

image blurring due to this wavelength dependence would require the use of a filter with a much narrower spectral bandwidth than that of the Wratten 60

filter used in this study.

2.1 NBS Artifact

The nine artifacts used in the study were made from AR-chromium photoplates

by conventional photolithographic techniques. The substrate was soda-lime

glass nominally 6.35 by 6.35 by 0.15 cm (2.5 by 2.5 by 0.060 in,). The

nominal thickness of the two-part AR-chromium layer was 120 nm.

Figure 1 shows the overall pattern of the artifact. The cross-shaped clear

area contains a series of horizontal and vertical lines which are used to

help locate the basic measurement pattern. The basic pattern is repeated at

eight locations around the center of the artifact as shown in figure 1, Figure 2 is a magnified view of the central area of the artifact. Each basic

pattern is located near the end of a horizontal or vertical line or both. An

underlined number (1 through 8) is located next to each basic pattern. These

numbers were used to identify which one of the eight basic patterns was to be

measured in the study.

Figure 3 shows the basic measurement pattern on the artifact. Letters A

through F designate the row location, and numbers 0 through 9 designate the

t Two of the ten companies used the same artifact at different times.

§ See disclaimer, p. vii.

4
column location for each line, line pair, or other pattern element; for ex- ample, A-6 refers to the opaque line in row A and column 6. Rows A and C

contain opaque lines on a clear background, and rows B and D contain clear

lines on an opaque background. These opaque and clear lines are used for

calibrating the optical microscope to measure linewidths of both polarities

(opaque and clear). In each of these rows there are ten lines with nominal

widths from 0.5 to 12 \m randomly distributed in the row. Row E consists of

opaque line pairs (two interior lines of equal length) for calibrating the

optical microscope to measure line spacing or pitch. The nominal line

spacings of these line pairs are from 2 to 1 1 wi randomly distributed in the

row. Row F consists of adjacent lines and spaces (two interior lines of

equal length and intervening space) of approximately equal widths for setting

the line-to-space ratio on video image-scanning micrometer attachments. The

rationale for the design of this artifact is discussed in Appendix A [6]

2.2 NBS Measurement System

The artifacts were originally measured at NBS on a scanning opticalmicroscope system that was designed at NBS and is considerably different from

any measurement system used by participants in this interlaboratory study.

This NBS system is described in reference 4.

Two trained NBS operators measured a total of ten artifacts. After shipment

from NBS, one artifact developed persistent contamination and was not used in

this study. Four measurements were made of each linewidth in rows A, B, C,

and D and of each line spacing in row E. The mean values of the four

measurements for each of these patterns on the nine artifacts used in the

study are given in Appendix B. The widths of an opaque line and the adjacent

clear space in pattern F-5 were also measured. This line-to-space ratio for

F-5 and the line-spacing value for pattern E-5 were furnished to the

participants for adjusting their measurement systems. (See sec. 2.3.)

After the artifacts were measured on the NBS scanning optical-microscope

system and shipped to the participants, another NBS scanning opticalmicroscope system with several improvements became operational. An

intercomparison between the improved system and the system originally used to measure the artifacts showed that the latter system exhibited significant

flare or scattered light. Furthermore, other developments showed the need to

include a correction for the optical-phase difference at the line edge in the

coherent edge-detection algorithm used for linewidth measurements on ARchromium photomasks [7] . Therefore, remeasurements of the artifacts were made with the improved system following the study. A comparison of the

remeasurements with the original measurements showed that the flare present

in the system used to make the original measurements and the exclusion of the

correction for optical-phase difference in the original measurements

introduced a larger systematic error in the original NBS linewidth values

than was first estimated. (See sec. 3.7.)

The uncertainties assigned to the original NBS linewidth measurements on the

artifacts are given in table 1 . The systematic component due to line-edge

detection is an approximation of the systematic error in relating the exact

position along the edge profile of the material line to the transmittance

5
threshold at which the scanning optical-microscope system detects the line

edge. The value of ±0.05 \sn for this systematic error is a conservative

estimate based on a line profile with a 70 deg line-edge slope and a 1 20 nm thickness as shown in figure 4. The other systematic component in table 1 includes systematic errors due to flare and the absence of a correction for

optical-phase difference in the original linewidth measurements. Because

flare is greater for an opaque line on a clear background than the reverse,

this systematic component is slightly larger for rows A and C. The overall

linewidth-measurement uncertainty can be estimated by adding in quadrature

all of the systematic uncertainty components and the random error component.

Using this approach and the error components given in table 1, the overall

uncertainty for the NBS linewidth value is given by

/(0.05 ym)2+ (0.05 ym) ^ + (0.10 pm) ^ =: ±0.12 ym.'''

2.3 Procedures

The recommended linewidth-measurement procedures furnished to each participant are reproduced in Appendix C. The procedures include specimen handling,

equipment selection, microscope setup, method of measurement and data taking,

and instructions for returning the data and artifact to NBS. The procedures

also provide explanatory notes and background information on some of the

procedural steps. The participants were invited to write any comments on these procedures directly in the procedures booklet and return it to NBS.

In selecting measurement equipment for the study, participants were asked to

choose a microscope objective with a numerical aperture of 0.65 or larger and

a condenser with a numerical aperture two-thirds that of the objective. The

relatively high numerical aperture objective is necessary to resolve

micrometer and submicrometer-wide lines on the artifact. The two-thirds

ratio of condenser to objective numerical aperture provides an image with

steep edge gradients while maintaining image brightness [8]. As a result,

the repeatability of edge settings used in measurement eyepieces and

photometric line profiles is improved.

Participants were asked to adjust the microscope for Kohler illumination

which provides uniform illumination of the specimen, reduces stray light, and

results in bright images with good contrast. After adjusting for Kohler

illumination, the participants were asked to check the resolving power of the

objective by observing a pair of nominally 1-ym-wide lines on the artifact

(pattern E-2). (See fig. 3.) Instructions were also provided for obtaining

best focus by visual focusing either through the microscope or on the face of

the cathode ray tube in video systems.

t By comparison, the overall uncertainty currently assigned to NBS Standard

Reference Materials 474 and 475 (Optical Microscope Linewidth Measurement

Standards), which are measured on an improved version of the scanning

optical-microscope system, is only ±0.05 ym. The dominant contribution to

this uncertainty is the estimated maximum systematic error resulting from

the finite material edge slope. The estimated random error component is

less than ±0,02 ym (three sigma ) . Corrections are now made for both flare

and optical-phase difference at the line edge,

6
Participants were asked to place the broadband Wratten 60 green filter

supplied by NBS between the light source and condenser. The use of such a spectral filter is intended to improve image quality. Optical microscopes

are generally designed for optimum performance at or near a wavelength of 530

nm. Therefore, with white-light illvtmination, the imaging optics will

typically exhibit chromatic aberrations. Studies have shown significant

differences between optical line-edge profiles for white light and filtered

green light [9]

.

Participants were asked either to adjust their instruments to read directly

the value of an NBS-furnished length scale on the artifact (pattern E-5 ) or

to determine a length-scale calibration factor based on the NBS value and

correct their linewidth measurements by this factor. Those participants who

used a video image- scanning system were also asked to adjust the system until

the ratio of the width of a designated opaque line to the width of the

adjacent clear line on the artifact (pattern F-5) was equal to the NBSfurnished ratio. This adjustment corrects for linewidth errors due to an incorrect electronic edge-detection threshold introduced by the video

processing.

Additional detailed instructions were provided to the participants for making

measurements with some types of micrometer attachments. For example,

participants using an image-shearing measurement system were asked to make

linewidth measurements in a double-shear mode and line-spacing measurements

in a modified single-shear mode. For other types of measurement systems,

such as those with video and optical image-scanning micrometer attachments,

the instructions were general and intended only as guidelines. Such

measurement systems are usually either custom designed or the operator

controls vary considerably between types and models; therefore, it is

difficult to provide specific instructions for each of these systems.

A sample of the information and data sheets given to the participants is

shown in Appendix C, Attachment F. Participants were asked to fill out pertinent information about their companies and their measurement equipment.

This information was later used by NBS to determine if the participant's

equipment had met the specifications required for the study. Participants

were also asked to enter the date and time at the beginning and end of each

set of measurements.

Participants were asked to assign to the study two trained operators who made

linewidth measurements as part of their routine inspection of photomasks or

as part of the manufacture and inspection of measurement systems or dimensional standards. Each of the two operators was asked to make four

independent sets of measurements on each measurement system to give a total

of eight sets of measurements for each system. Operators were asked to start

from the beginning of the recommended procedures for each set of measurements

and to arrange their schedule so that each operator made only one set of

measurements each day. (See Appendix C, Attachment G for the suggested

schedule.) For each set of measurements, the operator was asked to measure

all ten linewidths in each of the rows A, B, C, and D and all ten line

spacings in row E. (See fig. 3.)

7
The recommended procedures stressed the importance of making one set of

measurements at one setting and making no changes to the measurement system,

except focusing and moving the artifact, between the first and last

measurement. If any other changes were made, the operator was asked to start

over from the beginning of the recommended procedures.

2.4 Participants' Measurement Systems

The measurement systems used by the participants in the study were basically

an optical microscope to which any one of a variety of micrometer attachments

was added [10]. The five types of micrometer attachments used in the study

were: (1) optical filar, (2) video filar, (3) image shearing with optical

display, (4) optical image scanning, and (5) video image scanning. Table 2 lists the measurement systems used by the participants. Data from some measurement systems were not analyzed by NBS because either the participant

did not furnish all the requested data or did not follow directions. An

alphanumeric code shown in table 2 is used to identify those systems for

which data analyses are presented.

8
3. STATISTICAL ANALYSIS

In the earlier pilot study involving NBS and three companies, the differences

between NBS linewidth values and linewidth measurements made by industry

using commercially available optical-microscope systems were largely

systematic [11]. In-house NBS studies also showed the presence of systematic

differences between NBS values and linewidth measurements made on several

types of measurement systems widely used in the IC industry [12], Analysis

of optical imaging in a microscope has shown that these systematic errors in

linewidth measurements are due, in large part, to using either an improper

measuring scale or an optical threshold that does not correspond to the true

line-edge location or both [13,14]. An additional systematic error may arise

as the linewidth approaches the optical resolution of the system and the line

image takes on the characteristics of the impulse response of the imaging

system [15].

In the absence of a linewidth standard, users of linewidth-measurement

systems have commonly taken the approach of using a line-spacing standard to

calibrate their systems for linewidth measurements [16]. An in-house NBS

study suggested that all of the systematic linewidth errors could not be

eliminated by using this line-spacing calibration [17]. The in-house study

did show, however, that systematic errors could be virtually eliminated by

the use of a standard with both calibrated line spacings and linewidths.

The earlier pilot study involved measurements at only three points over the 1 to 1 0 ym range and indicated that for some systems the observed linewidths

were not a linear function of NBS values at linewidths approaching 1 \sr [18].

This nonlinear behavior may have been due to the limited optical resolution

of these measurement systems. Other common causes of nonlinear behavior are

worn screw threads in the micrometer attachment, optical distortion in the

imaging optics, and distortion in the cathode ray tube of video systems. A

linewidth calibration curve based on a few linewidths would not be sufficient

for measurement systems that show a nonlinear relationship between the

observed linewidths and the NBS values.

The revised artifact [19] used in the present interlaboratory study was designed to overcome some of the limitations encountered in these earlier

studies. The revised artifact contained a variety of linewidths sufficient

for determining whether or not the observed linewidth values were a linear

function of NBS values over the 0.5 to 1 2 ym range. The artifact also

contained a variety of line spacings for determining the measuring-scale

errors separately from other types of systematic errors. The artifact was also designed to determine the extent to which systematic linewidth errors could be eliminated by using a linewidth calibration. For this purpose, the

artifact had two sets of both clear and opaque lines. One set (rows A and B) was used to establish the calibration curves for each type of line. The

other set (rows C and D) was used as the "unknown" lines to be measured and

subsequently corrected by the linewidth calibration. (See fig. 3.)

Results from earlier studies also showed that systematic linewidth errors may

be masked by a large scatter in the data due to differences in focus

settings, poor image quality, and inability to repeat edge settings [20].

Therefore, the procedures used in the present interlaboratory study were

9
designed to help control the linewidth-measurement process so that, to the

greatest extent possible, a repeatable relation existed between the line-edge

location and the edge-detection threshold.

The analysis of the data from the present interlaboratory study was designed

to determine for each measurement system the magnitude of the random and

systematic linewidth-measurement errors, the feasibility of a linear

linewidth calibration curve, and the effectiveness of the NBS artifact and

recommended procedures for eliminating measurement errors.

3.1 Approach

The basic approach used in the statistical analysis of the data from the

interlaboratory study was first to use the differences between the

participant's measurements and the NBS values on rows A (opaque lines), B

(clear lines), and E (line spacings) for deriving linear linewidth

calibration curves, and second to determine to what extent the application of

these calibration curves eliminated any systematic errors in linewidth

measurements made by the participants on rows C (opaque lines) and D (clear

lines). (See fig. 3.) Many of the statistical concepts and procedures used

in this analysis are discussed in reference 21.

The following questions were addressed in the statistical analysis:

1 . Are the participants in agreement with each other and with NBS

in measuring linewidths on the artifacts or are there systematic

differences among the participants and between NBS and each

participant? (See sec. 3.2.)

2. How often are data outliers occurring that are large enough to

perturb the results? (See sec. 3.3.)

3. If systematic linewidth errors exist, can a correction based solely

on a linear line-spacing calibration eliminate these errors?

(See sec. 3.4.1.)

4. If a line-spacing calibration is not sufficient for eliminating

all systematic errors, can a correction based on a linear linewidth

calibration that uses ten linewidths on the artifact eliminate

these systematic errors? (See sec. 3.4.2.)

5. What are the measurement process precision (random error) and the

measurement uncertainty of linewidths that are corrected based on

the derived linewidth calibration curve? (See sec. 3.5.3.)

6. Are the measurement systems sufficiently stable so that the same linewidth calibration curve can be used on a day-to-day basis? (See

sec. 3.6.1.)

7. Are the participant's linewidth measurements a linear function of

NBS values? (See sec. 3.6.2.)

8. Are there operator differences within each company? (See sec. 3.6.3.

10
3.2 Graphical Analysis

3.2.1 Individual Measurement Systems

As a first step in analyzing the data from the interlaboratory study, the

differences between the participant's measurements^ and NBS values

(participant's measurement minus NBS value) for each measurement system were plotted against the NBS values for rows A, B, C, D, and E. Examples of these

difference plots are shown in figure 5. The numbers on the plots indicate

different days on which the artifact was measured, and each day's

measurements are connected by solid lines. If all eight measurement

repetitions were completed, there are eight curves for each measurement

system. However, the numbers on the curves do not necessarily represent the

order in which the measurements were taken. The ordering is arranged so that

curves 1 through 4 are for the data from the first operator in chronological

order, and curves 5 through 8 are the data from the second operator in

chronological order. The same pattern is followed for fewer than eight

repetitions, e.g., in the case of six repetitions, curves 1 through 3 are the

data from the first operator and curves 4 through 6 are the data from the

second operator.

Ideally all the data points in a difference plot of the type shown in figure

5 should be scattered randomly along the y = 0 line (differences from NBS are plotted on the y-axis), thereby indicating negligible systematic error. Obviously the maximum spread among the data points must also be sufficiently

small for the intended purpose of the system.

In the nonideal situation, there may be systematic errors which are constant

over the entire dimensional range of linewidths; in this case, a straight

line fitted to the linewidth differences would have a slope of zero. There

may be systematic errors which are not constant, but can be eliminated by a correction based on a calibration curve. The minimal requirements for

successfully calibrating a measurement system are the following: (1) the

data be in a state of statistical control [22], (2) the data points be

scattered in such a way that there are no discernible patterns indicating

operator differences or large day-to-day differences in the system, and (3)

the data points fall roughly along a smooth curve such as a straight line.

Examples of typical measurement problems encountered in the study are illustrated in figure 5. In figure 5(a) an entire day's measurements are out of

control. (See sec. 3.3.2.) In figure 5(b) isolated outliers in the data are

so pronounced that the system cannot be successfully calibrated using the

linewidth artifact until these outliers are eliminated. (See sec, 3,3,1,)

In figure 5(c) there are significant differences between the two operators,

and it may be necessary to establish a separate calibration curve for each

operator. (See sec. 3,6,3.) In figure 5(d) the system is obviously

nonlinear; that is, the differences from NBS values do not vary linearly with

linewidth, and a calibration curve based on a linear fit may not be adequate

to calibrate the system. (See sec. 3.6.2.)

t The raw data from the participants are given in Appendix D, table D-1

,

11
3.2.2 Youden Plots

The individual plots for each measurement system, such as those shown in

figure 5, are sufficient to determine measurement differences from NBS, but

these plots do not show the relationship of one participant to the other

participants. For this reason, plots depicting the linewidth differences

from NBS values at each nominal linewidth and each polarity (opaque and

clear) for all the measurement systems are given in figures 6 and 7. For

these plots, each measurement system is identified by a single letter code,

(See table 3. ) In cases where more than one difference value is plotted at

the same point, a number indicates the total number of coincident values.

Plots of this type are called Youden plots after W, J. Youden who pioneered

this method of graphical analysis in the inter laboratory evaluation of test

methods. A general discussion of the Youden methodology is given in Appendix

E [23], Basically, two similar objects are measured by each participant, and

the measurement of one object is plotted agaiast the measurement of the other

object. In the present case, the objects are linewidths of the same polarity

and nominal linewidth. For example, the measurements on the nominally 2- ymwide opaque line in row A are plotted against the measurements on the nominally 2-ym-wide opaque line in row C. However, each company measured a different artifact; therefore, in order to compare all the measurement systems

on one Youden plot, the points plotted are the measurement differences from

NBS. The origin (0,0) indicates no difference from NBS values. In this type

of plot, it is easy to spot the measurement systems that are far removed from

the others and also to identify the systems with differences greater than any

given amount.

Most of the linewidth differences plotted in figures 6 and 7 are clustered

about a 45-deg line passing through the origin, thereby indicating a combination of systematic and random errors. If only systematic differences

existed among the systems, all the points would fall on this line; that is, a measurement system that consistently produces results that are high

relative to NBS values on both rows A and C by the same amount has only

systematic differences. Small departures from the 45-deg line are attributed

to random error. Systems which give points distinctly removed from this line are not producing consistent results. Furthermore, when all of the points

for the eight repetitions are sufficiently close together and close to the

45-deg line, but removed from the origin, the system is showing consistent

systematic error and a small random error. In this case, it should be

possible to eliminate the systematic error by a proper calibration

procedure.

The Youden plots shown in figures 6 and 7 answer the following question:

Are the participants in agreement with each other and with NBS in measuring

linewidths on the artifact? The answer to both parts is largely no. In

general, there are systematic differences among the participants and between

each participant and NBS. This is consistently true for both polarities

(opaque and clear) and for all linewidths from 0.5 through 12 ym with the

differences being somewhat larger for the larger linewidths. Only six

measurement systems showed differences from NBS greater than 0.5 ym.

12
3.3 Detection of Outliers

Before proceeding with the analysis, all data on rows A, B, and E were edited

for outliers. An outlier is an observation that appears to deviate markedly

from other members of the sample in which it appears [24]. It is necessary

to eliminate such discordant values from the calibration data because even a single outlier can seriously perturb the calibration curve. Two types of

outliers are identified in the data as given in Appendix D, table D-1

.

Isolated outliers are flagged by a zero (0), and an entire day's measurements

that are out of statistical control and considered outliers are flagged by

two's (2).

3.3.1 Isolated Outliers

The choice of an appropriate test for eliminating outliers is complicated by

the variety of data involved. The test that was used is recommended as a good general approach even though the probability levels cannot be computed

exactly [25]. This test works well for the inter laboratory data in that it

basically rejects only those points which appear to be out of statistical

control on the difference plots for each measurement system.

The rejection criterion for individual points is based on the assumption that

the measurements yj^.: can be described by the following model:

y. . = Y + a. + 3. + e. . ID 1 D ID

1 — 1f...fk

j = 1,...,m

where k is the number of repetitions, m is the number of patterns per

row''', e^j are random errors, and the (k+m+l ) parameters y, a^, and

3j are unknowns to be estimated.

For each measurement y^^ j , a residual is computed as follows;

6. . = y. . - ( Y + ot. + 3.

)

ID ID 'id

where the caret (a) signifies the least-squares estimate of the parameter.

The measurement is rejected if t^^ > 3.5 or if t^j < -3.5§ where

*

t. . =

ID

ID

6. . ID and s definition of

is the standard deviation of the residual. See Appendix G for a

t Since there are ten lines in each row, m = 10 in most cases. In those cases where data are missing, m < 10.

§ The distribution of the t* statistic is not known, and therefore an

exact probability level cannot be computed for this test. However, the

critical value of 3.5 corresponds to the 0.999 probability level for

Student's t-test with 60 degrees of freedom.

13
This rejection criterion was applied to all the data (rows A, B, C, D, and E)

three times iteratively to guarantee that extreme outliers could not mask the

effect of other outliers; that is, after an outlier was identified and

removed, the test was repeated. Twenty isolated outliers were identified by

this test for a total of eight measurement systems. Three of the isolated

outliers are shown in figure 5(b). (Two other data points were considered to

be transcription errors and are also flagged with a zero in Appendix D, table

table D-1 . )

3.3.2 Entire Day's Measurements as Outliers

The identification of an entire day's measurements as outliers is based on

the assumption that each day's measurements can be described by a linear

function of the NBS linewidth values. (See sec. 3,4.) Trie intent is to test

whether or not the data for one day have a different intercept and slope than

the data for the other days combined.

First, for all measurements y^^ j , the least squares estimates of the

coefficients are obtained for a straight line of the form

. = + 3q X i=1 , . . . , k ( 1 ) j=1 , . . . , m

where Xj are the NBS linewidth values, oq is the intercept, and 3q is

the s lope

Secondly, to test the measurements for day p, ypj (j = 1,...,m), the

following indicator function x is defined as follows:

* ^ / 1 if i = p

^i

I

0 if i ^ p

This function allows for an incremental change in the slope or intercept

for day p by fitting all the measurements to an equation of the form

* o * i = l,..,,k

y . . = a + a X. + 3 x . +3 x.x. / (2)

ID 1 2 1 13 2 3 1 3 = 1,...,m

where ct^^, a^* 3j^/ and are coefficients to be estimated.

The sum of squares for error for eq (1) has n-2 degrees of freedom and is

given by km

A 2 SSE(I) = Yl E ^^ij - ^ - ^0

i=l j=1

where the caret (a) signifies a least-squares estimate of the coefficient,

and n is the total number of measurements.

The sum of squares for error for eq (2) has n-4 degrees of freedom and is

given by km

A A 2

SSE(2) = Z (^ij - «1 - Vi - ^l^j - ^2^j^i^ • i=1 j=l

14
An F-test is used to decide if the fit from eq (2) effects a significant

reduction in the sum of squares for error. All the measurements for day p are rejected if

F =

- ^) SSE(I) - SSE(2) , . t

2 SSE(2) .01 i' r

where is the degrees of freedom in the numerator of F, and is the

degrees of freedom in the denominator of F.

This F-test was applied to the data from rows A, B, and E for all measurement

systems. In all cases for which an out of control condition was identified

for either row A (opaque lines) or row B (clear lines) or both, the

corresponding measurements in rows C (opaque lines) or row D (clear lines) or both could readily be identified as also out of control by inspecting the

difference plots of the type shown in figure 5.

Nine days of measurements from a total of five measurement systems were

rejected by this test. This means that one-fourth of the measurement systems

experienced problems severe enough to invalidate an entire day's

measurements. Thus, problems of this type should not be regarded as rare events, but are to be expected in day-to-day operations.

3.4 Calibration Curves

The derivation and application of calibration curves in this study involves

the following steps for each measurement system: (1) a linear line-spacing

calibration curve is derived from measurements on row E; (2) a statistical

test is used to determine the significance of the slope and intercept of the

line-spacing calibration curve, and if either the intercept or slope, or

both, are found to be statistically significant, the line-spacing calibration

is used to correct linewidth measurements from rows A, B, C, and D; (3) a linear linewidth calibration curve is derived from measurements of opaque

lines on row A where these linewidth values may have been corrected for line

spacing in step 2; (4) a statistical test, similar to that in step 2, is used

to determine the significance of the slope and intercept of the linewidth

calibration curve, and if either the intercept or slope, or both, are found

to be statistically significant, the linewidth calibration is used to correct

linewidth measurements from row C; and (5) steps 3 and 4 are repeated for

clear lines on rows B and D, respectively.

The linear calibration curves are derived from a least-squares technique [26]

that treats the participant's repeated measurements of each pattern as the

unknown variable and the corresponding NBS value as the known variable.

§

t The critical value F ( \)y v ) is obtained from a table of the F

distribution for a probability level of 0.99 with v = 2 and = (n - 4)

§ In an unpublished work, Bruce Hoadley, Statistical Engineering Division,

NBS, shows that the linear fit is not significantly affected by both

variables being in error if the standard deviation of the known variable is

a sufficiently small fraction of the intervals between the known values.

In this case, the standard deviation in the NBS linewidth values could be

as large as 0.35 ym without affecting the results.

15
This technique guarantees that the standard deviations of the linear fits are proper estimates of the measurement process standard deviation. The general

form of this calibration curve is discussed in Appendix F.

The assumption has been made that a linear calibration curve is adequate to

describe the relationship between the participant's measurements and the NBS

values. An examination of the plots of differences between the participant's

measurements and NBS values suggests that this assumption is satisfactory for

most measurement systems. (For example, see figs. 10 and 11.) The linearity

assumption is discussed further in section 3.6.2.

3.4.1 Line-Spacing Calibration

We now address the following question: Is a correction based solely on a line-spacing calibration (row E) sufficient to bring the participants into

agreement among themselves and with NBS? The line-spacing calibration curve

is described by the following model:

yj^j = a + 3 Xj i=1,...,Wj (3)

j =1 , . . . ,

where y^j is the line-spacing measurement, Xj is the NBS line-spacing

value, i denotes the ith repetition on the same pattern, j denotes the jth

pattern in the row,"'' v/j is the number of repetitions of the jth

pattern, § a is ti^e intercept, and 3 is the slope. The least-squares

estimates a and 3 are defined in Appendix F by eqs (F-5) and (F-6),

respectively.

Line-spacing calibration curves of the form given by eq (3) were derived for

each system from the participant's measurements of the ten patterns in row E. The least-squares estimates of the intercept and slope of these calibration

curves are given in table 4. If a = 0.0 and 3 = 1.0, then no line-spacing

correction is needed. Table 4 shows, however, that for all systems the

estimated intercepts and slopes are at least slightly different from zero and

one, respectively. In order to determine whether or not these differences

are statistically significant, and thus whether or not a line-spacing

correction should be applied, the following statistics [27] are used in

separate tests:

ti = a/s^

and ^ (4)

t2 = (1-3)/s3

A A

where s^ and s^ are the standard deviations of a and 3/ respectively.

These standard deviations are given by eqs (F-7) and (F-8) in Appendix F.

t j = 1 corresponds to the first, or leftmost, pattern in the row; for

example, line A-0 in row A. (See fig. 3.)

§ Since the data were edited for outliers, w. < k for some measurement

systems.

16
The intercept is judged significantly different from zero if

and the slope is judged significantly different from one if

where v is the degrees of freedom and t 025^ """^ ^® critical value

of Student's t distribution with v degrees of freedom that is exceeded with

2.5 percent probability.

As shown in eq (4), the magnitude of the intercept and slope are considered

relative to the measurement system precision. Therefore, a value of a far

from zero or a value of 3 far from one may not be significant according to

the t statistic if the precision is poor (i.e., a large imprecision). In

this case, the intercept or slope are not known well enough to provide a reliable calibration curve. On the other hand, a value of a close to zero or

a value of 3 close to one may be significant if the precision is good (i.e.,

a small imprecision). In this case, the calibration curve would be useful

for correcting measurements,

A significant finding for the slope implies that the errors vary with the

line-spacing dimension, whereas a significant finding only for the intercept

implies that there is a constant offset independent of spacing.

The test statistics ti and t2 are shown in table 4 for all twenty

measurement systems. This table shows that either the intercept or the

slope, or both, are significant at the 95 percent probability level for seven measurement systems. Only one of these systems exhibits a relatively

constant offset (system 1 4C ) . Therefore, a line-spacing correction was applied to the linewidth data on rows A, B, C, and D for each of these seven

systems as follows:

A

* 11 1 = 1 , . . . ,w. y = — . j

ID ^ D = 1 , . . . ,m

p where yf.; is the linewidth measurement corrected for line-spacing

calibration, y^j is the uncorrected linewidth measurement, and a and 3 are the least-squares estimates of the intercept and slope of the linear

line-spacing calibration curve. For the thirteen measurement systems which

do not require line-spacing correction, y*j = Yij*

To assess the effects of the line-spacing correction, the differences between

the participant's linewidth measurements corrected for line-spacing and NBS

linewidth values were plotted for rows A and B for each of the seven measurement systems identified in table 4 as needing line-spacing correction. Analysis of these difference plots show that the effect of this correction differs widely among the seven systems. For systems 5V and 15B, which show the

largest line-spacing differences from NBS values on row E, linewidth

differences are reduced significantly by the line-spacing correction. For the

17
other five systems, there is either a slight reduction or slight increase in

the linewidth differences. In no cases are the systematic linewidth

differences between the participant's measurements and NBS values eliminated

by applying a line-spacing correction.

3.4.2 Linewidth Calibration

The next consideration is the following question: If a line-spacing calibration is not sufficient for eliminating all systematic errors, can a linewidth

calibration that uses ten lines on the artifact substantially reduce these

systematic errors? The linewidth calibration curve for row A or B is

described by the following model:

* y..=a+bx. i=1,...,w.

^ j = 1,...,m3

where y^j is the linewidth measurement corrected for line-spacing

calibration, Xj is the NBS linewidth value, a- is the intercept, b is the

slope, and the subscripts are the same as those defined for eq (3). The

least-squares estimates of a and b are given by eqs (F-5) and (F-6) in

Appendix F where a replaces a, b replaces 3/ and y replaces y.

Student's t-tests for the linewidth calibration curves similar to the tests

for the line-spacing calibration curves in section 3.4.1 were made. The

resulting t statistics and the least-squares estimates of the intercepts and

slopes of the calibration curves for both opaque and clear lines are shown in

table 5. As indicated in this table, either the intercept of the linewidth

calibration curve is significantly different from zero or the slope is

significantly different from one, or both, for most of the twenty measurement

systems

For the measurement systems with a linewidth calibration curve that has a slope significantly different from one, the user will benefit from applying

this calibration curve to linewidth measurements. For the other measurement

systems, the systematic differences from NBS values do not vary significantly

over the dimensional range of linewidths, and a correction for a constant

offset is probably sufficient.

Since thirty-four out of the forty calibration curves show a statistically

significant departure from the ideal intercept (a=0.0) or slope (b=1.0) or both, corrections based on the linewidth calibration curves were applied to

the data for all twenty systems in order to simplify the computations.

Specifically, a linewidth correction based on row A (opaque lines) was applied to the linewidth data on row C (opaque lines), and a linewidth

correction based on row B (clear lines) was applied to the linewidth data on row D (clear lines) as follows:

* A

V - a ** 11 1 = 1 , . . . ,w. y . . = — . T "^iD ^ D = 1,...,m-^

where y-i -; is the linewidth measurement corrected for both line-spacing

and linewidth calibrations, y^ • is the linewidth measurement corrected

18
for line-spacing calibration, and a and b are the least-squares estimates of

the intercept and slope of the linear linewidth calibration curve. (For

systems not requiring a line-spacing correction, y^^j =

^i j • ^ corrected

linewidths y^^j for rows C and D are given in Appendix D table D-2.

3.5 Assessment of Line-Spacing and Linewidth Calibrations

As discussed in section 3.4.2, the linewidth calibration curves for opaque

and clear lines are based on measurements of lines in rows A and B,

respectively, and measurements of lines in rows C and D are, in turn,

corrected by the appropriate calibration curve. For some systems, the

linewidth measurements are also corrected for a line-spacing calibration.

The following thesis is proposed: if these calibration curves are capable of

eliminating systematic errors between the user's system and the NBS system,

the corrected linewidth measurements for either opaque or clear lines will

have zero offset from the NBS system except for random error.

3.5.1 Measurement Systems Combined

In order to assess the effects of both line-spacing and linewidth calibrations on the measurement systems, Youden plots similar to those discussed

in section 3.2.2 are given in figure 8.

Recall that the points on a Youden plot correspond to measurements on two

similar objects plotted against each other and that the pattern created by

the accumulated points over all repetitions indicates the nature of the errors affecting the measurement systems. In the case of uncorrected

linewidth measurement differences from NBS as shown in the Youden plots of

figures 6 and 7, the errors are a combination of systematic and random errors

as indicated by the points clustering about a 45-deg line.

It seems reasonable to use the corrected measurements on the C and D rows as

the two similar objects in a Youden plot in which the corrected linewidth

measurement differences from NBS are plotted against each other for lines of

the same nominal size. The proposed thesis is demonstrated if the resulting

points form a circle about the origin (0,0), thereby indicating only random

errors. If the center of the circle is substantially offset from the origin

or if the points cluster along a line, the calibration curves are not

adequately correcting for one or both line polarities.

Figure 8 shows the Youden plots of the differences between the corrected

linewidth measurements and NBS values for opaque lines (row C) and clear

lines (row D).''' a comparison of figure 8 with figures 6 and 7 shows that

the points for the corrected measurements are distributed relatively evenly

among the four quadrants of a circle centered at or near the origin.

Therefore, most of the systematic linewidth error has been removed for the

measurement systems by using linewidth calibration curves.

t When an entire day's measurements have been identified as outliers for rows A or B, the corresponding day's measurements for rows C or D have been

deleted from figure 8 because the calibration curve is not capable of

rectifying out-of-control conditions. (See sec. 3.3.2 and Appendix D.

)

19
3.5.2 Individual Measurement Systems

For each measurement system, a comparison of the raw data on rows C and D is

made with the same data corrected for both line-spacing (if required) and

linewidth calibrations. Frequency tables of differences from NBS values for

both the raw data (R) and the corrected data (C) are given in table 6 for row

C and in table 7 for row D, The frequencies for the raw and corrected data are given in the left and right columns, respectively, for each measurement

system. These frequency tables show the changes in the distribution of

linewidth-measurement differences from NBS brought about by the line-spacing

and linewidth calibrations.

The linewidth calibration should produce a symmetric distribution of corrected linewidth values that are centered about a zero difference and approximate

a normal distribution. For a few systems, the raw data already shows such a symmetric distribution. For almost all the other systems, however, there is a definite improvement with the linewidth calibration. In the few cases where the improvement is not sufficient, the between-day or between-opera tor

measurement differences may be too large or a linear calibration curve may be

inadequate. (See sec. 3.6.)

3.5.3 Measurement Process Standard Deviation

For this study, estimates of the process standard deviation for linewidth

measurements corrected for line spacing were made for each measurement

system. This standard deviation is given byw

m : -11/2

j=i i=i

(n-2)

where

and

y^

= a + bx.

= E w

Values of s^^ are shown in table 8 for both opaque

and clear lines for all twenty measurement systems.

3.5.4 Uncertainty of Corrected Linewidth Values

A crucial factor in assessing the possible benefits derived from calibrating

an optical linewidth-measurement system by using an NBS calibrated linewidth

artifact is the resulting measurement uncertainty. This uncertainty includes

the limits to random error for the measurement system and any systematic

errors affecting the measurement process. The uncertainty associated with

the NBS values assigned to the artifact is a systematic error in the

participant's measurement process.

The limits to random error for the measurement system must take into account

not only the variability in measuring the individual linewidths, but also the

20
error in deriving the linewidth calibration curve which is used to correct

the linewidth measurements. The calibration curve has an inherent uncer- tainty because if it were to be rederived at another time it may not duplicate the initial calibration curve. Therefore, the data for deriving the

calibration curve are a determining factor in the measurement process uncertainty. The problem of combining these errors is difficult [28] and is

addressed in reference 29, the results of which have been applied to this

analysis.

Table 8 gives limits to the random error E for a single measurement of either

an opaque or clear line. The interpretation of E is that the probability is

± E cover the NBS

(See sec. 3.4.2.) The total uncertainty for the measurement process is

greater than 0.99 that 95 percent of the intervals y**

* * linewidth value where y is the corrected linewidth value.

V = ± < E + BS

where Ajq3s is the uncertainty for the NBS linewidth values,

measurement uncertainties are listed in table 1. The NBS

Table 8 shows that about half of the measurement systems in this study have

random error limits (E) that are greater than 0,25 vim. Thus, the uncertainty

intervals for the corrected linewidth values are at least 0.5 \m. Adding the

NBS measurement uncertainties further increases these intervals. (See sec. 2.2.) These uncertainty intervals should not, however, be considered

representative of current measurement processes with these systems since the

measurement data were edited for outliers before deriving the calibration

curves. Instead, these uncertainties represent possibly the best values that

a user could achieve with an effective measurement control program.

3.6 Sources of Measurement Errors

It is difficult to pinpoint the cause of the relatively large measurement

uncertainties associated with most of the measurement systems. (See table

8. ) The magnitude of the process standard deviation s^ shown in table 8 is

obviously important. Other possible sources of error are: (1) inability to

repeat the calibration curve from day to day, (2) inadequacy of the linearity

assumption for the calibration curve, and (3) large differences among

different operators. Thie interlabora tory study was designed to reveal the

presence of these types of errors which are addressed in the following

discussion.

3.5.1 Between-Day Differences in Calibration Curves

In order to use a calibration curve based on several days' measurements, the same operator should be able to repeat the calibration curve with the same measurement system; i.e., the system must be in a state of statistical

control. In the present case, the slope and intercept of the linewidth

calibration curve must remain constant throughout all sets of measurements

made by the same operator.

Figure 9 shows two examples of linewidth calibration curves that change daily

for one operator on a given measurement system. (The data in figure 9(a) are

21
for a different operator and measurement system than the data in figure

9(b).) The linewidth measurement differences for one day are connected by

solid lines, and the corresponding linewidth calibration curve is represented

by a dashed line. In figure 9(a) the slope of the calibration curve is

changing from day to day while the intercept is relatively fixed. In figure

9(b) both the intercept and the slope are changing from day to day.

Obviously, the calibration curve for both of these examples does not repeat

satisfactorily from day to day, and the operator or measurement system or both are out of statistical control.

A test statistic has been devised to determine if the slope and intercept of

the linewidth calibration curve remain the same for each day's measurements.

For measurements y^^j on a given day, this test statistic is based on the

following linear model:

a. +

1

3. (x. - X ) 1 D

i — 1,...,lc

j = 1,...,m

where

m

X =2zl_

m

Xj is the NBS linewidth value, i denotes the day or ith repetition, j

denotes the jth line in the row, and and 3^ are the intercept and

slope, respectively, for each repetition. The least-squares estimates oi^ and ^or the ith repetition are given by eqs (F-5) and (F-6) in Appendix

F where x • - x replaces x .

J • J The test statistic is given by

F = 2(k-1)

i=l

i=1

i=1

1 2

^

i=1

where

A

a

i=1

A

a.1

and 3 =

i=1

'^1

If F > F Q^[2(k - 1), k(m - 2)], the calibration curve is not satisfactorily

repeated from day to day.

The F statistics and the pooled standard deviations Sp resulting from

fitting a separate calibration curve to each day's linewidth measurements are

22
listed in table 9^. There is a separate analysis for each operator on rows

A, B, C, and D. All the data were used, including values previously

identified as outliers. Even when the standard deviations shown in table 9 are consistent, the slope or intercept of the calibration curve or both can change significantly.

The test statistic is fairly conservative; that is, it flags only large

day-to-day changes in the calibration curve. A system that has several

asterisks in table 9 has a serious day-to-day control problem.

There is also ample evidence from this analysis that the two operators

should, for the most part, be treated separately. As indicated in table 9,

there are control problems with one or both operators for all measurement

systems except system 3V and 11F. For several of the systems, such as II and

5U, there are also control problems associated with only one line polarity

(clear or opaque). From this analysis users can hopefully recognize day-today variations in their measurement systems and possibly identify the sources

of this variability.

3.6.2 Linearity Assumption

A test based on the measurement repetitions was used to decide if a linear

fit is appropriate for a particular calibration curve [30], In this test,

the computed values at each linewidth as given by

y . = a + b X

.

3 3 are compared to the average of the repetitions at each linewidth, namely

w

.

* i = l y . = 3 = w

3 where Wj is the number of repetitions on the jth line.

Close agreement between the hypothesized curve and these averages is evidence

that the hypothesis is correct. The test is based on an F statistic, and the

assumption of linearity is rejected if

(n-2)s2 - {n-m)s2

^ = 1^ ' 1 ' ^Ol^"" - 2, n - m)

where n is the total number of measurements, m is the number of measurements

per row, sl measurement process standard deviation as given in sec. 3.5.3, and Sj^ is the standard deviation of the repetitions given by

t To compute these pooled standard deviations, the separate standard

deviations for each repetition were combined for each operator.

23
m

-1 1/2

. (y. - y . )2

3 3 '3

s.R n-m

This analysis has been applied to the linewidth data on rows A and B

corrected for line-spacing calibration. The resulting standard deviations of

the repetitions s-^, process standard deviations s-|^, degrees of freedom

V, and F statistics are given in table 10. As shown in this table, only

seven of the forty calibration curves have F values that are significant. A

significant F value implies that the system response is non-linear. Poor

system precision may mask non-linear behavior for some systems, and a significant F value for a system with very good precision, for example system

3V, would not necessarily mean that the calibration technique is

inappropriate but only that it may be improved upon. Considering the level

of system precision shown in table 8, non-linearity of the linewidth

calibration curve is not a significant source -of measurement error for the

majority of systems used in this study. In general, an interpretation of the

failure of the linear calibration model is best made by examining the

difference plots, such as those shown in figure 5, to determine whether a higher-order calibration curve is indicated or whether only certain regions

of the curve are non-linear.

As discussed in section 3.6.1, two operators on the same measurement system

often show significant measurement differences. Some of the difference plots

for the individual measurement systems also show these operator differences.

[For example, see fig, 5(c),] These operator differences were verified by an analysis of variance [31], Such operator differences raise the question of

whether or not it would be beneficial to have each operator maintain his or her own calibration curve.

To help answer this question, the two opera tor /system combinations for each

of three measurement systems (II, 81, and 8P) that showed the largest

differences between operators were analyzed as separate measurement systems.

Linewidth calibration curves based on measurements from rows A and B were derived for each of these six opera tor/system combinations, and the linewidth

measurements in rows C and D were corrected based on the appropriate

calibration curve. The results are shown in table 11.

Table 11(a) shows the frequencies of differences from NBS for the raw and

corrected linewidth values on row C for the six opera tor /system combinations.

Table 11(b) shows similar data for row D. In order to assess the results of

using separate calibration curves for each operator as compared with using a combined calibration curve for both operators, compare the corrected frequencies in table 11(a) with table 6 and the corrected frequencies in table 11(b)

with table 7. The interval from -0.05 up to 0.05 \m is of particular interest. Systems 81 and 8P show considerable improvement for the clear lines,

and system II shows considerable improvement for the opaque lines. For the

other combinations of system and polarity, the improvement is only slight

thereby indicating that we may not have accounted for all the sources of

3.5.3 Differences Between Operators

24
error by using separate calibration curves. The overall conclusion is that

separate calibration curves for each operator may result in significant

differences between corrected linewidth measurements made on the same

system.

3.7 Effects of Using Adjusted NBS Linewidth Values

As shown in table 1, there are systematic differences of about 0.1 pm between

the original linewidth measurements on the artifacts and their measurements

on an improved version of the NBS scanning optical microscope system. For

this reason, an effort was irade to determine the effects on the data analysis

of using NBS linewidth values that were adjusted to account for these

systematic differences.

For the video image-scanning measurement systems, participants used the

original NBS-furnished line-to-space ratio (pattern F-5) to set the

electronic edge-detection threshold; thus, it was not possible to determine

the effects of using adjusted NBS values. For the other measurement systems,

however, it was found that these effects were small. For example, the

magnitude of the linewidth differences between the participant's measurements

and NBS values changed slightly for some systems resulting in a slightly

different calibration curve. However, such minor changes do not

significantly affect the data analysis presented in the preceding sections

nor do they change the basic discussion and conclusions presented in the

following sections.

25
4. DISCUSSION

The interlaboratory study and the statistical analysis of the resulting data were designed to answer several questions about the artifact and measurement

procedures developed by NBS, as well as questions about the measurement systems used by the participants. The previous section on statistical analysis

addresses some of these questions. The present section elaborates on these

and related questions, provides guidelines to the participants for interpreting their results, and discusses the implications of these results for

the development of the NBS linewidth standard. Standard Reference Material

(SRM) 474.

4.1 NBS Recommended Procedures

The recommended procedures followed by the participants in the study were significantly different from most of the procedures used in the IC industry

for linewidth measurements on AR-chromium photomasks. The' procedures used i

industry typically differ between companies, between divisions within a company, and sometimes even between operators within the same group in a company. For example, the illumination systems in optical-microscope

measurement systems are usually not adjusted according to one accepted

method, such as Kohler illumination, and no effort is made to control the

degree of coherence in the illumination system. As a result, there arise a large number of different optical line-image profiles on which linewidth

measurements are made [32].

In the present study, the recommended procedures were designed (1) to eliminate measurement errors which may have been introduced if the participants

had adjusted their measurement systems in accordance with their own procedures and standards; (2) to reduce certain known sources of errors, such as chromatic aberrations in the optics and mechanical backlash in micrometer

attachments; and (3) to provide an optical line image with steep edge gradients, thereby reducing the effects of image-contrast variation among differ

ent measurement systems and improving the repeatability of edge settings.

The basic intent of these procedures was to provide a similar optical line

image with steep edge gradients in all measurement systems used in the study

so that any linewidth measurement differences among these systems would be

dependent primarily on the different edge-detection criteria and differences

in repeatability.

The differences between the procedures used in this study and the many techniques used in industry for linewidth measurements must be considered in

making comparisons of the participant's measurements with NBS values as well

as in determining the degree of improvement in linewidth measurements that

each participant can expect from using an NBS linewidth standard and

recommended measurement procedures. Therefore, the present discussion

applies primarily to this interlaboratory study and the eventual use of the

NBS linewidth standard (SRM 474) and measurement procedures which are based

on those used in the study.

For the most part, the participants reported little difficulty in following

the recommended measurement procedures. In a few cases, the participants

26
suggested changes and, whenever possible, these changes and other changes

based on recent NBS work have been made to the procedures.

4.2 Linewidth Calibration Curves

The Youden plots given in figures 6 and 7 clearly show the presence of

systematic errors in the participants' raw linewidth measurements. Although

the differences from NBS values are, in a few cases, as large as 1 ym, more

than 80 percent of the raw data exhibit systematic errors equal to or less

than ±0.3 \ia for both opaque and clear lines. Other studies, in which

linewidth measurements were made under conditions more closely representing

those found in industry, show significantly larger measurement differences

from NBS [18, 33]. Thus, it appears that even before a linewidth calibration

is applied to the data, the procedures and artifacts used in the present

study reduce measurement differences among different systems.

Only seven of the twenty measurement systems show significant differences

between line-spacing measurements and NBS values. Thus, the single linespacing value furnished by NBS to the participants was, in most cases,

sufficient for generating the proper length scale over the 0,5- to 12-ym

range. However, the line-spacing correction which was applied to the seven

systems showing significant line-spacing differences from NBS does not

eliminate all the systematic errors in the linewidth measurements. It is not

surprising that a proper line-scale adjustment to the measurement system or a line-spacing correction to the data does not eliminate all the systematic

error in a linewidth measurement. As discussed in reference 16, a linewidth

measurement, in contrast to a line-spacing measurement, involves systematic

errors of opposite signs in locating each edge of the line, and these errors

do not cancel as do the systematic errors of equal sign and magnitude in a line-spacing measurement.

The application of a linewidth calibration curve largely reduces the

systematic errors remaining in the participant's data after correction for

line-spacing differences from NBS. In a few cases, the linewidth calibration

curve is not very effective because the raw data show systematic and random

errors due to operator differences, day-to-day differences, or the inadequacy

of a linear calibration curve. For a few systems, the linewidth calibration

curve is largely unnecessary because the system was initially adjusted to

make it agree with both the NBS-f urnished line-spacing value and the line-tospace ratio. For these measurement systems, however, the derived linewidth

calibration curves still show a significant slope; thus, a single NBSfurnished line-to-space value is not entirely adequate for adjusting these

systems to measure linewidths over the entire 0.5- to 12- vim range.

4.3 Polarity Dependence of Linewidth Calibration

For most of the measurement systems, the systematic errors for measurements

of opaque lines in rows A and C are opposite in sign to the systematic errors

for measurements of clear lines in rows B and D. An example of this linepolarity dependence is shown in figure 10. The polarity dependence varies

with the type of measurement system and, in some cases, with the operator.

27
In all cases, the polarity dependence arises from using an incorrect optical

threshold to locate the edge [34]. In the ideal case of identical, but

inverted, line-image profiles for opaque and clear lines, the systematic

errors resulting from using an incorrect optical threshold would be opposite

in sign and equal in magnitude. Although some of the measurement systems

show systematic errors for rows A and C that are approximately equal to those

for rows B and D but of opposite sign, many of the systems also show

systematic errors that are different in both magnitude and sign. (See fig.

10.) One reason for this behavior may be the effects of flare or scattered

light in the measurement system. Opaque lines on a clear background (row A)

may introduce more flare, which alters the line-image profile, than clear

lines on an opaque background (row B), As a result, the line-image profiles

for opaque and clear lines would no longer be identical (except for

inversion). Thus, using an incorrect optical threshold on these profiles

would give different systematic errors for linewidth measurements of opaque

and clear lines.

The two systems for which a linewidth calibration curve is largely

unnecessary still show some polarity dependence for the relatively small

residual differences from NBS. These systems were initially adjusted by the

participants so that the line-to-space ratio in pattern F-5 equaled the NBS

value. (See sec. 2.3.) This adjustment eliminated most of the systematic

error for row A at a linewidth of 5 ym which was the nominal width of both

the opaque and clear lines in pattern F-5. As shown in figure 11(a) for one

of these two systems, the average difference at 5 yi" ^or the five data sets

on row A is close to zero. However, figure 11(b) shows the average

difference at 5 on row B for this system to be close to 0.05 \sa. Again,

the effects of flare light may be responsible for this behavior. Pattern F-5

resembles the opaque lines on a clear background in row A more closely than

it resembles the clear lines on an opaque background in row B. Therefore,

adjusting the system to pattern F-5 would largely take into account the flare

present in the image profile for an opaque line in row A, but would not

correct the system for the different amount of flare present with a clear

line in row B.

4.4 Measurement Process Standard Deviation

The estimates of the standard deviation of the measurement process, as given

in table 8, are close to or greater than ±0.1 ym for about half of the

measurement systems. These relatively large values indicate that although

operators measured an artifact with lines that have steep material-edge

profiles and used procedures to provide an optical line image with steep edge

gradients, there is still difficulty with some systems in repeating line-edge

settings. Because the standard deviations in table 8 are based on measurement data that exclude outliers (see sec. 3.3), these standard deviations, in

spite of their large values, are not necessarily representative of the

participant's measurement process but are representative of a measurement

process that is in some degree of statistical control.

The F statistics in table 9 show that some systems have considerable difficulty maintaining a calibration curve with constant intercept and slope. In

order to utilize effectively a calibration technique, the operator must be

able to repeat the calibration curve for any measurf^-nent sequence; in this

28
case, the resulting standard deviation would be an estimate of the

measurement process precision. Where the calibration curve cannot be

successfully repeated from day to day, the measurement process is usually

said to have a between-day component of variance. In this situation, it is

not possible to reduce substantially the size of the uncertainty of a reported linewidth value by taking several measurements of the linewidth over

a short period and using the average value. The measurements would have to

be spread out over the same base period used for deriving the calibration

curves.

In cases where there are significant differences between operators, calibration curves based on only one operator are not applicable for correcting measurements made by the other operator. Calibration curves based on pooling

the data for both operators in this case would give a relatively large standard deviation and uncertainty associated with correcting a linewidth

measurement.

4.5 Linearity of Calibration Curve

Table 10 shows that linear calibration curves are adequate for most of the

measurement systems. For these systems, the artifact has a sufficient number

of linewidths over the 0.5- to 1 2- ijm range to derive a linear fit. The

systems requiring a nonlinear calibration curve show nonlinear behavior

over the lower or upper end of the dimensional range. [For example, see fig.

5(b).] Nonlinear behavior at the lower end of the dimensional range where

the linewidth is approaching the limiting resolution of the microscope optics

is expected [35]. Most of the optical systems used in the present study did

resolve the smaller lines. The nonlinear behavior at the upper end of the

dimensional range may be due to optical distortion in the outer part of the

field of view of the optical microscope. The edges of the larger lines are

located in the outer part of the field of view when they are centered for a measurement, and if distortion is present, these edges would appear curved.

29
5. CONCLUDING REMARKS

The present inter laboratory study has provided considerable information on

the usefulness of the NBS linewidth-measurement artifact and the associated

procedures for measuring linewidths on photomasks in transmitted light. In

addition, the study has shown the effects of using this artifact and procedures to calibrate a number of different types of measurement systems commonly used by the IC industry to measure linewidths on photomasks. These re- sults are discussed in detail in previous sections of this report and are summarized below.

5.1 The participants exhibit systematic differences among themselves

and from NBS on linewidth measurements of clear and opaque lines. These differences are, in a few cases, as large as 1 ym, but more than 80 percent of

the raw data shows differences less than ±0.3 ym. Although a line-spacing

calibration improves some of the largest systematic errors, this type of calibration is not sufficient to bring the participants into agreement with

NBS.

5.2 A linear form of the linewidth calibration curve is sufficient for

most of the measurement systems used in the study. In some cases, a constant

offset may be sufficient over the dimensional range of 0,5 to 12 ijm. For some systems, the initial adjustment of the system in accordance with an NBSfurnished line-to-space ratio and a line-spacing value may be sufficient for

ca libra tion,

5.3 A separate calibration curve or constant offset is required for

measuring lines of different polarity (opaque and clear). Many of the mea- surement systems appear to have flare, or scattered light, which affects the

magnitude of the systematic error for opaque lines as compared with the

systematic errors for clear lines.

5.4 The data from this study clarify the need for measurement-control

procedures in many of the measurement systems. Single outliers in the data are frequent. For several systems, an entire set of measurements (taken

during a single day by a single operator) is out of statistical control.

5.5 The standard deviation of the measurement process is close to or greater than ±0.1 ym for about half of the measurement systems. For some systems, there are also significant day-to-day differences and operator

differences. In these cases, the calibration curve may not be applicable to

measurements made on any given day, and calibration curves based on one operator may be restricted to measurements by the same operator.

5.6 The linewidth-measurement data from the opera tor /measurement systems used in the study fall into one of the three following categories: (1)

data with repeatability errors so large that a correction for systematic

errors is not meaningful for a single linewidth measurement; (2) data with

repeatability errors sufficiently small that corrections for systematic

errors can be made using a calibration curve for the measurement system based

on a reasonably small number of repeated measurements; and (3) data with insignificant repeatability errors such that small systematic errors can be

corrected by instrument adjustment, a calibration curve, or a constant offset

30
from NBS values over the entire dimensional range. Repeatability refers to

the variability between replicate measurements made on different days with

one operator/measurement system combination.

5.7 The NBS artifact and the recommended procedures are basically

adequate for calibrating an optical-microscope linewidth measurement system

in the 0.5- to 12-ijna region provided that the system is in a state of

statistical control. Based on the results of this study, the pattern on the

artifact was changed slightly and the procedures were rewritten to improve

their usefulness. The improved version of the artifact is being made

available as SRM 474 (Optical Microscope Linewidth Measurement Standard).

The new measurement procedures are being written as standard practices and

test methods in cooperation with the American Society for Testing and

Materials (ASTM) . In addition, the statistical procedures used in this study

for deriving and applying a calibration curve to reduce systematic

measurement errors, as well as statistical procedures for determining if the

measurement system is in a state of statistical control, are presented in NBS

Technical Note 1164 [36].

31
6. REFERENCES

1. Nyyssonen, D., and Jerke, J. M., Optical Linewidth Measurement - A Basic

Understanding, Proc . Microelectronics Measurement Technology Seminar,

San Jose, California, February 6-7, 1979, pp. 251-266.

2. Jerke, J. M., ed. , Semiconductor Measurement Technology : Accurate

Linewidth Measurements on Integra ted-Circuit Photomasks, NBS Spec,

Publ. 400-43, pp. 78-94 (February 1980).

3. Swyt, D. A., Rosberry, F. W., and Nyyssonen, D., Calibration of Optical

Microscopes for Photomask Linewidth Measurements, Proc. Microelectronics

Seminar INTERFACE '77 , Monterey, California, October 5-7, 1977,

Publication No. G-48, pp. 131-144 (Eastman Kodak Co., Rochester, New

York, 1978).

4. Swyt, D. A., An NBS Physical Standard for the Calibration of Photomask

Linewidth Measuring Systems, Effective Utilization of Optics in Quality

Assurance 129 , pp. 98-105 (Society of Photo-Optical Instrumentation

Engineers, Bellingham, Washington, 1978).

5. Nyyssonen, D,, Optical Linewidth Measurements on Wafers, Developments in

Semiconductor Microlithography III 135 , pp. 115-119 (Society of PhotoOptical Instrumentation Engineers, Bellingham, Washington, 1978).

6. Swyt, D. A., Design of a Pattern on a Photomask-Like Physical Standard

for Evaluation and Calibration of Linewidth -Measuring Systems, Solid

State Tech . 21 , 35-42 (Janiiary 1978).

7. Nyyssonen, D., Spatial Coherence: The Key to Accurate Optical

Micrometrology , Proc. Soc. Photo-Optical Ins trumenta tion Engineers 194 , Applications of Optical Coherence , 34-44 (1979).

8. Reference [2], pp. 16-35.

9. Nyyssonen, D., Linewidth Measurement with an Optical Microscope: The

Effect of Operating Conditions on the Image Profile, Appl. Optics 16 , No. 8, 2223-2230 (August 1977).

10. Nyyssonen, D., Linewidth Measurement Spotlight, Semiconductor

International 3, No. 3, 39-56 (March 1980).

11. Reference [3], pp. 136-138.

12. Swyt, D. A., and Rosberry, F. W. , A Comparison of Some Optical

Microscope Measurements of Photomask Linewidths, Solid State Tech. 20 , 70-75 (August 1977).

13. Einspruch, N. G. , ed., VLSI Electronics - Micros tructure Science , Vol.

3, Ch. 7 (Academic Press, Inc., New York, 1982).

14. Reference [4], pp. 102-104.

32
15. Reference [3], pp. 135-136.

16. Reference

17. Reference

18. Reference

19. Reference

20. Reference

[2], pp. 7-15.

[3], pp. 142-144.

[3], pp. 136-139.

[4], pp. 99-101.

[12], pp. 74-75.

21 . Ku, H. H. , ed. , Precision Measurement and Calibration - Statistical

Concepts and Procedures, NBS Spec. Publ. 300, Vol. 1 (February 1969).

22. Eisenhart, C. , Realistic Evaluation of the Precision and Accuracy of

Instrument Calibration Systems, NBS J. Res. 67C , No. 2, 161-187 (AprilJune 1963).

23. Youden, W. J., Graphical Diagnosis of Inter laboratory Test Results,

Industrial Quality Control 15 , 1-5 (May 1959).

24. Standard Recommended Practice for Dealing with Outlying Observations,

ASTM Designation E178, Annual Book of ASTM Standards , Part 41 (November

1981). (Available as a separate reprint from American Society for

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

25. Harnett, V., and Lewis, T. , Outliers in Statistical Data (John Wiley and

Sons, Inc., New York, 1978).

26. Neter, J., and Wasserman, W. , Applied Linear Statistical Models , pp.

21-48 (Richard D. Irwin, Inc., Homewood, Illinois, 1974).

27. Reference [26], pp. 113-121.

28. Lieberman, G. J., Miller, R. G., and Hamilton, M. A., Unlimited

Simultaneous Discrimination Intervals in Regression, Biometrika 54 , 133-

145 (1967).

29. Scheff^, H. , Rosenblatt, J., and Spiegelman, C, A Statistical Theory of

Calibration (to be published).

30, Reference [26], pp. 53-60.

31. Graybill, F. A., An Introduction to Linear Statistical Models , Vol. 1,

pp. 106-148 (McGraw Hill Book Company, Inc., New York, 1961).

32. Reference [10], pp. 39-40.

33. Reference [1], p. 256.

33
34. Reference [10], p. 47.

35. Reference [6], p. 38,

36. Croarkin, M. C, and Varner, R. N. , Measurement Assurance for

Dimensional Measurements on Integra ted-Circuit Photomasks, NBS Tech.

Note 1164 (August 1982).

34
Figure 1 . Photograph of overall pattern on NBS antiref lective-chromium artifact at

magnification of about 3.4X. (The horizontal and vertical lines help to locate the

eight basic measurement patterns in the center,

)

35
• 1 1 •

Figure 2. Photograph of central area of NBS antiref lective-chromium artifact at a magnification of about 16X. (The basic measurement pattern is repeated eight times

about the center, and each basic pattern is numbered. A number of the smallest lines

and spaces in each pattern do not appear in this photograph.

36
0 12 3 4

CT^i~i O

fl

£

E

F

I

C -I-I-I-I-I--I

D

Figure 3. Photograph of basic measurement pattern on NBS antiref lective-chromiam artifact

at a magnification of about 200X. (The individual lines and patterns are located by

reference to an alphanumeric grid with the letters A through F identifying the row and

the numbers 0 through 9 identifying the column.

)

37
150 nm

Figure 4. Schematic of physical profile of opaque line on NBS antiref lectivechromium artifact.

38
-0.75 L J I

0.0 2.0 4.0 6.0 8.0

NBS VALUES {/dm]

10.0 12.0

(a) One day's measurements (data set 5) out of statistical control.

0.75

NBS VALUES (/um]

(b) Significant isolated outliers. (Outliers are circled.)

Figure 5. Examples of differences between participant's linewidth measurements and NBS linewidth

values as a function of NBS values. (Each number represents one set of measurements.)

39
E

00

NBS VALUES [jum]

(c) Significant differences between two operators. (Data sets 1, 2, and 3 are

for the first operator, and data sets 4, 5, and 6 are for the second operator.)

0.0 2.0 4.0 6.0 8.0 NBS VALUES [fim]

(d) Nonlinear relationship.

Figure 5. Concluded.

40
E

CO

LUO

0.8

0.6

0.4

0.2

0

-0.2

0.4

0.6

-0.8

71

/

FF ^ F P TF 2F

212

GG 144^ 22

G 0^3 2 V2 P GN2N343C C

d 403N323 E KS229'—SH

HK 4HM 2 H OS I G H6 S K /

2 C D 0/

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW A |^tm)

0.6 0.8

a. Lines A-2 with mean NBS value of 0.71 \m and

lines C-3 with mean NBS value of 0.73 vim.

Figure 5. Youden plots of differences between participants' raw

linewidth measurements on opaque lines (rows A and C) and NBS values.

(Letters A through T represent different measurement systems as identified in table 3.

41
1 71

/

/

/ H

/

2 J/

0 32 3 , H 02/

OKD ' D ^

DD

I Q)y 0

I / 0

' / I

I TI AT 3/f'A

RV C3I

4F3F

I 2R232/C3F

S 2 0 0G3C P

E 4. 3/G

243G2

22229 3 C 3M23| H 2 C

/

/

/

/

V.

0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

DIFFERENCES, ROW A (^m)

b. Lines A-8 with mean NBS value of 1.27 ym and

lines C-6 with mean NBS value of 1.22 \m.

Figure 6 Continued.

42
LUO

0.8

0.6 -

0.4 -

E

o 0.2

0

S -0.2

Li- UO

-0.4

-0.6

-0.8

71

N N NN

N

NN

/

/

/ H

I C 22 1.

, PFI/A

C 222PP A

' FF 2 3/RI T

I G GCGFPJP

I G G3RTT

F 2A230

3 /'20 C

. _ 25422JE S 20S430 C

3 K. SHi S 2 / H I S

H

0 H K/ 0

0 0 4/2 0

^ D

0

K

1

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROWA(/xm|

0.6

c. Lines A-1 with mean NBS value of 1.91 jjm and

lines C-1 with mean NBS value of 1.70 tjm.

Figure 6 Continued.

43
02

D

D

I /

/

"71

/

/

/

E H

H 2

E KS 6592

H S| K S

/ 0 2H

3 1/ P

T IF T2

C T2 42

2 R2 R 2 F232PRR2 2 QS3 32G J 2H3 P J 223N_0

2J

C

0

/ 0

0 0

L.

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, R0WA()um)

0.6 0.8

d. Lines A-0 with mean NBS value of 2.47 ym and

lines C-8 with mean NBS value of 2.05 ym.

Figure 6 Continued.

44
o

CO

LUO

0.8

0.6

0.4

0.2

0

-0.2

0.4

-0.6

-0.8

71

/

/

FE29/I S SH

H2,M2S S 0 /H S HH

0 I /K H I

I P P /

I CT A 2T

I I3IP2

F[ G 2 244

I 23A3R0 F CC

SGF35220 C

J| GN4G 2

DO 0

/ 30

D 0 / 0

2 0 / D y D /

/

/

/

1^ \ \ 1

0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6

DIFFERENCES, ROWA(^tm)

e. Lines A-6 with mean NBS value of 3.66 lom and

lines C-7 with mean NBS value of 3.27 ym.

Figure 6 Continued.

45
E

CO

LUo

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

71

P C3 2/

T22 CC

F 2IR2 2 P P

I 2 SR/22 P

F SFF2R0H 2 T SHS244 3

G2AF4Q3 Q C

SHBa4JA2J S K 22E| F 0 KH K H3 E / OSH

0 / H

0 2

D /

— 2

DO

1 1 1 1

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW A (^m)

0.6 0.8

f. Lines A-3 with mean NBS value of 4.25 ]m and

lines C-0 with mean NBS value of 4.70 ]m.

Figure 6 Continued.

46
p CP 2

I / P

I I C C A 323TC

I 0 I422PI T

I 2222^ 2 S EF2Q2/50AT

J3 3N2 2S C

F2L56L-3

2233 A 22 /M 2 GS

S 2 El H E

D D /

/°

2 D /

D

0/yK 0

/ I / I / I

0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

DIFFERENCES, ROW A (^m)

g. Lines A-5 with mean NBS value of 5.27 vim and

lines C-5 with mean NBS value of 5.22 ym

(1 point fell outside of plotting range).

Figure 6 Continued.

47
o

0.8

0.6 -

0.4 - E

o 0.2

0

S -0.2

Ud

-0.4

0.6

-0.8

n 71

/

/

/ H

I /

R A2

142/2 A OP 12

I C 2C22

H3G0AN23

dF22G 3T 2 2 — E — 2K L62 NNN —

K K 02L432S C

d 32 HS

HFF 0

H / I K 0 I /" K 0 I 0

PP

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW A |/im)

0.6 0.8

h. Lines A-9 with mean NBS value of 6.13 ym and

lines C-9 with mean NBS value of 6.72 ym

(6 points fell outside of plotting range).

Figure 6 Continued,

48
E

O

LU

0.8

0.6

0.4

0.2

0

-0.2

0.4

0.6

0.8

"71

N32C2

I T2 N3d22

I 2 0/ TC

S22H23R

E J7S320 J 32222H F LE HS

K 2H32F2H SG

OF

1

P ?/

R2/ P 22 P 233P A /

/

/

0 F 2 / CO

) 0

OK

/

/

/

/

/

/

/

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW A (^tmj

0.6 0.8

Lines A-7 with mean NBS value of 7.42 ym and

lines C-2 with mean NBS value of 8.23 ym

(8 points fell outside of plotting range).

Figure 5 Continued.

49
I P P CP

N 12 ?

I 33 ,R2 C

I 2F2P 3/ R

S N JT 2 C 2 0 HT Nl 4 0/4 0 C H JG3 /2

53JA E C

F_4243 T_S . KFKL 23 C E KHKm/ I SG

S F 2H Is

—I

^ 71

/

/

/

/

/

/

/

3 / E K K F

I 2 H I

F /

/

/

/

/

/

L L0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

DIFFERENCES, ROW A (^tm)

j. Lines A-4 with mean NBS value of 10.54 urn and

lines C-4 with mean NBS value of 8.85 ym

(9 points fell outside of plotting range).

Figure 6 Concluded.

50
E

OS

LUO

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW B |/im|

0.6 0.8

a. Lines B-7 with mean NBS value of 0.72 \m and

lines D-6 with mean NBS value of 0.97 ym.

Figure 7. Youden plots of differences between participants' raw

linewidth measurements on clear lines (rows B and D) and NBS values.

(Letters A through T represent different measurement systems as identified in table 3.)

51
0.8

0.6

0.4

0.2

0

0.2

0.4

0.6

0.8

0

s s 0 FO

25

s s /

0 KTT

SK OSW T GTG 0 T |AE2LME

2 I332Q G D

H4A2 2

I I H74 |A

C P322PH 2

P 2C23 N P 'G d2 R4IR P

I C0^3R I I UJ 3 2 C

0 JJ

s OF

—71

/ -I

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW B (^tm)

0.6 0.8

b. Lines B-1 with mean NBS value of 1.55 \m and

lines D-3 with mean NBS value of 1.53 vim.

Figure 7 Continued.

52
0.8

0.6

0.4 h

^

0.2

o

LUo

0

S -0.2

LU

U.

U_

o

-0.4

-0.6

-0.8

/

L L

T 71

/

/

/

/

/

P P A46^| L CP 2C2 2 633CD22 21 H62332 P I QJ yN C /C C I C .

0

F FF 2SK0 S/

0 G 00

O/OTS

I OG T 2T S

I G SE

A2G02L2

AT4 2 S G

F S ?/

00

1

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW B (^m)

1

0.6 0.8

Lines B-8 with mean NBS value of 2.30 \m and

lines D-8 with mean NBS value of 2.10 ym.

Figure 7 Continued.

53
0.8

0.6

0.4

^

0.2

0

-0.2

-0.4

OS/

S OE/

I F 2/ 0

0 TK / S

1 T 2G SO

I ac^T S K2423G 2 0 _ ii£_L3]Z_ E

I 23 2 , E P2 30AN2I3

2 3R 33CH I 2N2/32 C

0/

0 FS/

/SF 0

F

F

D 3 R2

D 2 PC

0 0/

0.6

-0.8 1 1 1 1

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW B [^m]

0.6 0.8

d. Lines B-9 with mean NBS value of 2.81 yra and

lines D-1 with mean NBS value of 2.40 pm.

Figure 7 Continued.

54
E

oi

LUo

0.8

0.6

0.4

0.2

0

-0.2

-0.4

0.6

-0.8

ooq/

2 S3 /

K .2 F F

, OG/ S S

GE| 22T 2 S

C 2T 0

2 E22HG2 E T-L42-0 0_E

H N9BA

C PI II32A2|

P A342 G I D 3 R/ 22

J R3'32

D R2 P D / P D

D 2 D

C

I

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW B (^tm|

1

71

1

0.6 0.8

e. Lines B-3 with mean NBS value of 4.00 \im and

lines D-2 with mean NBS value of 3.60 \m.

Figure 7 Continued.

55
0.8

0.6

0.4

0.2 h

0

-0.2

-0.4

-0.6

-0.8

H

j S / 0

C /

, S 0 / F s

I K FO

E 2 00 / FS S

I 2 2 /S

1 M2E F

2 LE 7 0 P 432HG

4^ GTG —

PI 3 GN26B 2

13 ^2 G

PC2520

R23333C

P R ,AA

JO R N

2 / P D 0 0

D

D /2

/ D

1 1

"71

0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

DIFFERENCES, ROW B l^m)

f. Lines B-6 with mean NBS value of 4.62 yiti and

lines D-9 with mean NBS value of 5.03 \m.

Figure 7 Continued.

56
E

o

ui

LUO

z

0.8

0.6

0.4

0.2

0

-0.2

0.4

•0.6

-0.8

F 0 0

0 0 S 0

SS

E G22/S E

I E22M

C 3 2/2

I 2L0 0

G 35/222 _

N 2 3H 2 E CI4 2 10

5 N2/A G

C P 33A 31

I R R3/N PH I 0 d J 2 H CP

PJ

0

3^2

-D

1

71

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW B (^m)

0.6 0.8

g. Lines B-4 with mean NBS value of 5.64 ym and

lines D-4 with mean NBS value of 5.67 ym.

Figiare 7 Continued.

57
0.8

0.6

0.4

^

0.2

0

0.2

0.4

0.6

0.8

^ 71

s /

S S 2 EO S/S 0

0 OSO

/E F 0

TG KTO F

T G/

I L30 FE

I 34 H 0 B G4LH E F - HR2 A8BK G

P N IGA/2KNT S 2322RT3 I 2 3A n|

2J JJ3N3P

C JN C I P y C

JP

D ^ D

-0

1 1

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW B (^m)

0.6 0.8

h. Lines B-0 with mean NBS value of 6.53 ym and

lines D-0 with mean NBS value of 7.12 yni

(2 points fell outside of plotting range).

Figure 7 Continued.

58
0.8

0.6 I0.4

^

0.2 h

00

O

-0.2

-0.4

-0.6

-0.8

SK2

20

E al 43' 2 N_H703

2 22NN24G

H 214222 I PHAA 3233 0 | PC20 /R PC

0 2 C F 2J

G/M3

/

3TE

F S

' /S

0 F E2 S 0

2 0

0 2 /

2

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW B (^m)

/

0.6 0.8

i. Lines B-2 with mean NBS value of 7.94 \m and

lines D-7 with mean NBS value of 8.67 ym

(6 points fell outside of plotting range).

Figure 7 Continued.

59
0.8

0.6

0.4

0.2 h

0

-0.2

-0.4

-0.6

-0.8 V. L

^ 71

/ J

SF

0 S F/

F F SO / 0

0 S 0 0

0 SK /o

G Q KO

FE

H

I 2T3

G 3LLS2H

A3 GP229LH_ H.

; 2J40 3^1 C 2 N32RN

T 2 33^ R

I P P2/j H y I P

S E

C /?

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW B [fjim]

0.6 0.8

j. Lines B-5 with mean NBS value of 10.97 ym and

lines D-5 with mean NBS value of 9.41 pm

(8 points fell outside of plotting range).

Figure 7 Concluded.

60
a

o

oi

LU

C_3

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

—

1 1 1 1 1 1

—

— c

s

—

F K d — C KO —

0

S 2P

E2P2204I23 F C dJ5543222 0

C 3C32534D3 K - — — —— — —

A 40T6 02

222N 32P T G

PN| 3 2 K 6 2 H F — S S 0 —

0

I

1 1 1 1

1

1

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW C [fxm]

0.6 0.8

a. Lines C-3 with mean NBS value of 0.73 lam and

lines D-6 with mean NBS value of 0.97 \m

Figure 8. Youden plots of differences between participants' corrected

linewidth measurements on opaque and clear lines (rows C and D) and NBS

values. (Letters A through T represent different measurement systems

as identified in table 3.)

61
0.8

0.6

0.4

0.2

0

-0.2

-0.4

0.6

-0.8 1

E SEGF

0 I 0

0 SF43C20

0 P 2221 12 H 3 046PQ2

C 2J2H7954G3

AA052223

SH C4

C C 2J

H

2G2 as

1

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW C (^m)

0.6 0.8

b. Lines C-6 with mean NBS value of 1.22 ym and

lines D-3 with mean NBS value of 1.53 ym.

Figure 8 Continued.

62
0.8

0.6

0.4

^

0.2

</3 O

0

-0.2

-0.4

-0.6

-0.8

1

—

1 1 1 1 1

—

0

QK

c 0 D 22 F 0 R 1 F2 H

P 04FAG

S3 2223E3 C F —— — H552269432IP

2S2T 3302 2

- —

2 AG 0 K KH

C C SS 2 C Q T c — E SC

J

—

1 1

1

1

1

1

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW C [^um)

0.6 0.8

c. Lines C-1 with mean NBS value of 1.70 ym and

lines D-8 with mean NBS value of 2.10 ym.

Figure 8 Continued.

63
E

oenCO

0.8

0.6

0.4

0.2

0

-0.2

OFS

2 2 C

K E I HO

OOH 2 IHA

D 53265R32 0

2-PS34-3I-I- H

P 2524522D3

P 2P 3322JE2

2 2C F 2 S J E S

0

-0.4

0.6

-0.8

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW C l^tm)

0.6 0.8

d. Lines C-8 with mean NBS value of 2.05 )jm and

lines D-1 with mean NBS value of 2.40 ym.

Figure 8 Continued.

64
E

oenCO

LUo

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

1 I "

1 1

1

1

1 I 1

— 1 c 1 —

1 c — c 1 s —

S2 EJ

K H G J D

P 254|33IN 0

E R022563 IP 32 2K 2

F 22TF2 P 2DJ| 3 H G

c 1

1 0 —

1 c

I

,

—

1 1

1

1

1 1 1 1 1

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW C |^m)

0.6 0.8

e. Lines C-7 with mean NBS value of 3.27 ym and

lines D-2 with mean NBS value of 3.60 ym.

Figure 8 Continued,

65
0.8

0.6

0.4

0.2

0

-0.2

-0.4

0.6

-0.8 1

00"

0 0 I K ' C D2 I 2

3 PS022

NG3224 H D H453T 31 0— CA-24685— NS- SDP E283C KS

A E022E22 KH

F 2T

PD| F S 0

HA

I

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW C |^tm)

0.6 0.8

f. Lines C-0 with mean NBS value of 4.70 ym and

lines D-9 with mean NBS value of 5.03 lam.

Figure 8 Continued.

66
0.8

0.6

0.4

^

0.2

to

o

0

-0.2

-0.4

-0.6

-0.8

1 1 1 1 1 1

—

—

E —

HQ2 2 T D

2 343 OF P H 3S42 2 P —

A 2JRG262I4 K 2R 04K P SD d2 2 S CS P 2

F H 0

S HQ 0

1 1 1

1

1 1

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW C (^trn)

0.6 0.8

Lines C-5 with mean NBS value of 5.22 ym and

lines D-4 with mean NBS value of 5.67 ym.

Figure 8 Continued.

67
0.8

0.6

0.4 - ^

0.2

CO

LUO

0

-0.2

0.4

0.6

-0.8

0 2

T IT 2 K 2 E22 C PS H I 222

CPS2 5NF33A2

0_3_232E632 J_

C R0A44474 2 KG

GD6N322

NPq 2 HT N I d 2

P

F

F

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW C (^m)

1

0.6 0.8

h. Lines C-9 with mean NBS value of 6.72 ym and

lines D-0 with mean NBS value of 7.12 ym.

Figure 8 Continued.

68
0.8

0.6

0.4

0.2

o

oi

LUO

0

-0.2

-0.4

-0.6

-0.8

K I 0

0

E D F 0 J

2 COP AF

2 0 D0| 2 SAP

2 522TGN

D 23( 6 4N I — T24L368GTT

CS R G IV133I5 2P NN

E 3 »J| 23 2 D 5 2 2 E

1

0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW C (^m)

0.6 0.8

Lines C-2 with mean NBS value of 8.23 liiii and

lines D-7 with mean NBS value of 8.67 ym.

Figure 8 Continued.

69
0.8

0.6

0.4

^

0.2

o

CO

LUO

0

-0.2

-0.4

-0.6

-0.8

1 1 1 1 1 1

1

1

1

1

1

1

1 ^

0 F S F KP20J2 2 0

f PH 3 I 2D

H G T G 422 PI G 2 0364 NTF I — 22 At:E43R42 2S

S 313252 20 NG

C 2N2 P 0

OC 1 J CH

SFP 0 H

S JO

—

1

°

1 —

1

1 1

1

1

1 1 1

1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4

DIFFERENCES, ROW C (/xm)

0.6 0.8

Lines C-4 with mean NBS value of 8.85 \im and

lines D-5 with mean NBS value of 9.41 ]m.

Figure 8 Concluded.

70
Figure 9. Daily changes in linear linewidth calibration curve for one operator. (Linewidth measurement differences for one day are connected by solid lines, and the corresponding linewidth

calibration curve is represented by a dashed line.

)
0.4

NBS VALUES [fim]

(a) Opaque lines (row A).

NBS VALUES (Mm)

(b) Clear lines (row B).

Figure 10. Dependence of systematic linewidth measurement errors on line polarity.

72
0.4

0.2

E

UJI

0.0

0.2

-a4 J . L J i ao 2.0 4.0 6.0 8.0 NBS VALUES (mITi)

10.0 12.0

E

UJu

4.0 6.0 8.0 NBS VALUES [fxm]

(b) Clear lines (row B).

Figure 11. Residual linewidth measurement errors of video image-scanning measurement system.

73
Table 1 - Uncertainty Assigned to NBS Linewidth Measurements for

Inter labora tory Study

Estimated Systematic Components, jjm

Artifact

Number

Estimated Random

Component

( three sigma )

ym

Line-Edge

Detection

Flare and Optica 1-

Phase Correction

Rows

A and C

Rows

B and D

52, 54 - 60

53

±0. 03

±0.05

±0.05

±0.05

+0. 10

+0.10

-0.08

-0.08

^ These random components are also the uncertainty associated with the

line-spacing measurements on row E.

74
•feble 2 - Measurement Systems Used by Participants in Inter laboratory Study

Code Measurement System

11 Image shearing wit±i optical display ... . * Video image scanning

3V Video image scanning

41 Image shearing with video display

5U Optical filar

5Z Optical filar

Image shearing with optical display*

6A Video filar

7A Video filar

7C Video filar

71 Image shearing with optical display

81 Image shearing with optical display

8P Optical image scanning

9V Video image scanning

9W Video image scanning

1 01 Image shearing with optical display

1 IF Optical filar

111 Image shearing with optical display

* Optical image scanning

1 3C Video filar

131 Image shearing with optical display

14C Video filar

15B Video filar

Video image scanning*

* Data were not analyzed by NBS.

75
I^ble 3 - Codes for Identifying Participants' Measurement Systems in

Figures 6, 7, and 8

Code Code Measurement System

(See figs. 6, 7, and 8.) (See table 2.)

A II

B 3V

C 41

D 5U

E 5Z

F 6A

G 7A

H 7C

I 71

J 81

K 8P

L 9V

M 9W

N 101

0 IIP

P 111

Q 13C

R 131

S 1 4C

T 15B

Image shearing with optical

display

Video image scanning

Image shearing with video

display

Optical filar

Optical filar

Video filar

Video filar

Video filar

Image shearing with optical

display

Image shearing with optical

display

Optical image scanning

Video image scanning

Video image scanning

Image shearing with optical

display

Optical filar

Image shearing with optical

display

Video filar

Image shearing with optical

display

Video filar

Video filar

76
l^ble 4 - Least-Squares Estimates of Intercept a and Slope 3 for LineSpacing Calibration Curves and Student's t Statistics

Measurement a t

System

11 -0.034 -1.5 0.995 1.7

3V -0.009 -1.3 1 .001 -1.0

41 0.007 1.8 0.999 0.2

5U+ 0.035 1.4 0.882 29.5*

5Z+ 0.061 5.1* 0.994 3.0*

0.030 6.0* 0.996 4.0*

7A 0.017 2.1 0.998 2.0

7C"'' -0.094 -5.9* 1 .01

-5.5*

71 0.030 2.1 1'. 004 -2.0

81 0.025 0.6 0.996 0.7

8P -0.007 -0.5 1 .001 -0.5

9V -0.008 -1.3 1 .001 -1.0

9W -0. 008 -1.6 1 .002 -2.0

101 -0.019 -1.5 1 .003 -1,5

1 IF 0.021 0.9 1 .003 -1 ,0

111 0.024 1.0 1.004 -1.3

1 3C''" -0.1 33 -8.9* 1.014 -7.0*

131 0.013 0.8 0.997 1.5

^4C^ -0.053 -3.8* 1 .004 -2.0

15B+ 0.243 12.8* 0.986 4.7*

* Exceeds critical value for a two-sided test at the 0.95 probability level.

^ Needs line-spacing correction to linewidth data.

77
Table 5 - Least-Square Estimates of Intercept a and Slope b of Linewidth

Calibration Curves and Student's t Statistics for Opaque Lines

(Row A) and Clear Lines (Row B)

Measurement „ a ^ « ^

o ^ Row a ti 3 t2 System ^ t.

11 A 0.207 10.3* 0.993 1.7 B -0. 01

-0.5 0. 984 5.3*

3V A 0.000 0.0 0.999 1 .0 B -0.054 -7.7* 1 . 006 -6. 0*

41 A 0.175 6.2* 1 .002 -0.4

B -0. 1 28 -4.6* 0. 992 1 .

5U A -0.129 -5.6* 1 .001 -0.2

B 0. 1 68 5. 1 * 0. 994 1 .

5Z A -0.081 -2.5* 1 .009 -1 .5 B 0.016 0.9 1 . 008 -2. 7*

6A A 0.182 5.5* 0.974 4.3*

B 0. 3 30 17.4* 0. 996 1 3

7A A 0.108 9.0* 0.990 5.0*

B 0. 090 1 2. 9* 0. 992 8. 0*

7C A 0.092 5.7* 0.987 4.3*

Qa n n 1

1 9 1

71 A 0.224 16.0* 1 .001 -0.3

no -0. 1 59 -1 1 4* 1 . 004 -1

81 A 0.055 2.2 0.999 0.2

Q -0. 209 -7 7* 0,998

8P A -0.125 -1 3.9* 0.999 0.5

Q 0. 067 11,2* 0. 999 1 n

9V A -0.008 -0.6 0.999 0.5

B 0. 025 2 5* 1 . 003 -1 s

9W A -0.023 -1.9 0.998 1.0

aR IS 1 * V . -7 JO 1 n

101 A 0.079 4.2* 1 .000 0.0

oD — fi 1 fin - 1 7 H* —4 n*

11F A -0.172 -4.9* 1 .000 0.0

B 0.215 1.1* 1.012 -2.4*

111 A 0.245 18.8* 0.999 0.5 B -0.1 35 -7.9* 0.995 1.7

13C A 0.193 19.3* 0.995 2.5*

B 0.009 0.5 1 .000 0.0

131 A 0.157 13.1* 1 .010 -5.0*

B -0.209 -10.0* 1 .010 -2.5*

140 A 0.073 4.3* 0.995 1.7

B 0.307 15.3* 0.996 1.0

15B A 0.037 2.2 0.992 2.7*

B -0.001 -0.1 0.981 6.3*

* Exceeds critical value for two-sided test at the 0.95 probability level.

78
O^ble 6 — Frequency of Differences Between I^rticipant's Linewidth Measurements and NBS Values on Opaque Lines (Row C)'''

Number of Differences

System: II 3V 41 5U 5Z 6A 7A 7C 71 81 Difference

Intervals, ym R C R C R C R C R C R C R C R C R C R C

-1 . 00 to -0.95 **   **  ** ** 2   1 **  ** * **   **  ** -** ~** -0.95 to -0.90 ** * ** .** ** * **   **  **   **  **   **  **

-0.90 to -0. 85   **  ** ** 6   **  ** ** * **   **  ** * -0.85 to -0.80 **   **  * ** 1 ** 1 1   **  **   **  ** ** **

-0.80 to -0. 75 * ** * ** ** ** 1 * **   **  «* **   **  ** **

-0.75 to -0.70   **  **   5 **  **   **  **   **  **   ** 

-0.70 to -0.65 * ** ** «* ** ** 3   **  **   **  ** «* **   ** 

-0.65 to -0.60 **   **  ** 4   **  * **   **  ** * ** **

-0.60 to -0.55   **  **   3 **  **   **  **   **  **   ** 

-0.55 to -0.50 **   **  ** 1   **  **   **  ** ** * **  

-0. 50 to -0.45 **  ** ** ** * ** 2   **  **   **  * **   **  **

-0.45 to -0.40 * **   **  1 * **   **  «* **   **  **  

-0.40 to -0.35 **  * **   1 6 **  **   **  **   **  **   ** 

-0.35 to -0.30 «* **   **  7 ** 3 2 1 ** ** * * **   **  **

-0. 30 to -0. 25   **  ** ** 1 5 « ** 1 ** 1   **  **   **  **

-0.25 to -0.20 * * * ** ** 5 6 1 1 1 ** ** #* ** 1 1   **  **

-0.20 to -0. 1 5 ** 2 ** ** 1 7 2 4 2 3 2 2 «* 1 3 2 **   ** 

-0.15 to -0.10 ** 8   **  1 0 10 5 6 3 3 8 ** 4 1 2 9   **  6 -0.10 to -0.05 ** 1 1 * ** 2 8 1 14 1 1 1 1 4 9 6 9 1 6 15 ** 5 5 1 6 -0.05 to 0.00 I 1 3 30 26 5 1 4 * 22 27 26 8 15 6 13 9 12 ** 16 1 7 17

0.00 to 0.05 2 8 50 54 8 12 ** 10 9 14 12 21 10 22 1 0 10 ** 22 17 9 0.05 to 0.10 1 1 1 3   12 1 0 **  15 15 11 10 1

1

21 19 7 6 ** 16 9 9

0. 1 0 to 0. 1 5 1 3 5 * ** 7 2 ** 6 ** 2 1 3 7 15 3 7 9 ** 7 9 2 0.15 to 0.20 12 ** * ** 15 5 ** 2   1 1 3 13 2 4 5 1 1 2 2 ** 

0.20 to 0.25 8 ** ** 12 ** ** 1 * ** 7 1 3 6 ** «* 18 1 *# 1 0.25 to 0.30 13 ** ** ** 6 * **   **  3 2 3 1 ** ** 23 ** 1 *«

0.30 to 0.35 **   **  4 3 ** * ** ** 4 ** 3   **  12 1 ** **

0.35 to 0.40   **  ** 3   **  **   **  **   4 **  ** **

0.40 to 0.45 ** «* ** 1   **  ** 1   **  * **   **  **

0.45 to 0.50   **  1 **   **  ** 1   **  * * * 1 **  

0.50 to 0.55 **  ** * ** 2 1   **  **   **  **   **  ** ** * 0.55 to 0.60 **   I **  ** 1 1   **  ** ** * 1 * ** **

0.60 to 0.65 ** ** * **   **  **   **  ** ** ** * **   ** 

0.65 to 0.70 ** ** ** * 1 **   **  **   **  **   **  ** #* **

0.70 to 0.75   **  **   **  * **   **  **   **  **  

0.75 to 0.80 **  **   **  **   **  ** *« **   **  **   **  **

0.80 to 0.85   **  **   **  **   **  **   **  **   **  **

0.85 to 0.90   **  ** ** ** * ** ** * **   **  **   **  ** **

0.90 to 0.95   **  ** ** ** *« **   **  **   **  **  

0.95 to 1 .00 **  **   **  **   **  «* **   **  **   **  **

Number of Differences

Within ± 1.0 um 60 60 80 80 80 80 66 80 76 77 80 80 80 80 69 69 70 70 60 60

Number of Differences

Greater than + 1.0 ym 14

The left column (R) for each system contains the differences for the raw data, and the right

column (C) contains the differences for the corrected data. A double asterisk denotes the absence of a difference value.

79
Table 6 — Concluded

Number of Differences

System: 8P 8V 9W 101 IIF 111 13C 131 14C 15B

Difference

Intervals, ym R C R C R C R C R C R c R C R C R C R C

- 1 • 00 to -0. 95 * * **   **  ** * * * * * * ** * *

—— nu • to — 0» 90 * * ** * *

— n on to — 0. 85 **

—~ nU • fmO J to — 0 80 ** * * * *

— 0« 80 to -0. 7

* * * * * ** * * —u • / D to — u • / u * * ** ** ** * * ** ** *

— nu« 7/ nu to —— n A R U» O D * *

— U • DO to n An **   **  * * * **

— u%ov to — U« D -3 ** ** * * ** ** * * * * ** * * * *

— U • OD to — U • 3 u ** *=f> * ** * * * * * * ** * * ** * * * * **

to — 0» 4 5 1   **  ** * * * * * * ** * * * ** * * * * * ** * * _n At; to — Ci An 1 ** ** ** * * * * *

n A n to * * 1 * * * * 5 * * ** * *

— U • to _n n 1 1 * * 8 * * ** * *

to — n 9 R 1 * * * * * * 1 0 * * * 1 * * 1 — U • ZD to 3 * 1 7 2 1 1 1 n on to — U« 1 J 1

2 * * ** * * ** 1 9 7 1 1 3 *

— n 1 ^ U« 1 -5 to — U • 1 >J 1 ** ** ** * * * * 9 9 * * 6 1 2 8 ° 1 -0. 1 0 to -0. 05 1 5 6 4 2 3 * * * * 7 6 1 5 * * 1

7 * * 9 1 7 1 7 * * 1 0 -0.05 to 0.00 20 9 29 24 1 1 1 5 1 25 4 1 5 1 1

2 3

* * 20 1

20 * * 1 1 0.00 to 0.05 3 5 1 7 24 1 5 1 2 25 1 16 1 18 1 1 23 * * 38 1 8 1 1 5 1 7 0.05 to 0.10 ** 22   **  ** 30 5 ** 1 0 1 7 26 1 2 2 9 15 1 3 2 7

0. 1 0 to 0. 1 5 *« 13 **   **  14 6 1 2 1 1 1 1 22 4 1 2 1 4 5 9 4

0. 15 to 0.20 **   **  ** ** 8   3 14 1 12 1 25 **  2 1 10 **

0.20 to 0. 25   **  **   3 3 **  ** 19 ** 4 1 25 * ** ** 1 6 **

0.25 to 0. 30   **  ** *« ** 2   1 1 6 **  1 ** 1 4   **  7 1 0. 30 to 0. 35 **   **  *« * 1 ** ** *# 7 ** 2 ** 2 ** ** * 1 1 0.35 to 0.40 **   **  **   **  ** ** 1 0   **  **   **  1 1 0.40 to 0.45 **   **  **   2 **  ** * ** * ** * **  

0.45 to 0.50 **  ** * ** * ** * 1 ** * ** * * **   **  **  

0.50 to 0. 55 **  **   **  ** 3 1   **  **   **  ** ** 2 1 0.55 to 0.60   **  ** * * ** 4   **  ** ** ** * ** * ** 1 0.60 to 0.65   **  **   3 **  **   **  **   **  ** * *

0.65 to 0.70 *« **   **  ** 2   **  ** ** «* * * **   **  **

0.70 to 0.75 ** ** «* ** * ** * **   **  **   **  ** ** * 1 **

0.75 to 0.80 ** «* **   **  **   **  ** ** * ** ** * **   ** 

0.80 to 0.85 **   **  **   **  ** * **   **  ** ** * ** 1 0.85 to 0.90   **  **   **  **   **  * ** ** ** * **   ** 

0.90 to 0. 95 ** ** ** * **   **  **   **  * * **   **  ** * 0.95 to 1 .00 **   **  ** * * #* **   **  ** ** ** «* ** ** 1 **

Number of Differences

Within ± 1.0 urn 60 60 50 50 20 20 79 79 80 80 80 80 80 80 80 80 80 80 56 56

Number of Differences

Greater than ± 1.0 pm

80
T^ble 7 — Frequency of Differences Between Participant's Linewidth Measurements and NBS Values on Clear Lines (Row D)'*'

Number of Differences

System: II 3V 41 5U 5Z 6A 7A 7C 71 81

Difference

Intervals , ym

— 1 • 00 — 0. 95 ** 4c 4c * * 1 * * ** 1i * * ** ** * * * * ** * * * * * * * * -0. 95 to -0. 90 34c :4c * # ** 4c 4c * * J * * * * * * ** ** ** * * ** * * **  

-0. 90 to -0. 85 3tc:4c **  ** * * 4c 4c **   **  ** * * ** ** * * * * * * —0 .85 to -0. 80 4^ ** 4<# *4e X

4c 4c ** ** 4c 4c * * ** * * * * ** * * * * ** * *

— 0. 80 to -0. 75 3|c :tc ** 4c 4c * * -aJ * * ** ** * * * * * * * * * * * * ** * * * * * * —0. 75 to — 0. 70 :4c :4c ** 4c 4( 1 1 * * * * * * * * ** ** * * * * ** * * * * ** * * — 0« 7 0 to -0. 65 3^ ^ :4c :4c :^ :4i ** 4c 4c * * ^ * * ** * * * * ** * * * * * * ** * * * * * * —0. 65 to -0. 60 ** 1 * * a•3 ** ** 11 * * * * ** * * * * ** ** * * 1 * *

-0. 60 to -0. 55 ^ 4t ** * * ^ * * ** i * * * * * * * * * * ** * * ** * * —0. 55 to — 0. 50 4c# 4c ate ** 4^4 4r * f * * t1 * * * * c. ** * * * * * * * * * * * * * *

-0. 50 to -0. 45 :4t3)c 4c 4c ** * * 1 ** 1i * * 1 ** * * * * ** * * * * * *

—0» 45 to — 0. 40 # 4c 3^ 4c ** i

11 * * 1 ** * * ** * * * * ** * * * * o — 0. 40 to -0.35 4c 4c 4^^ ** 1

1 * * * * ** ** * * ** * * * * ** * * * * * *

4c 4c o 1

•aJ * * 1 * * * * * * * * * * ** * * 1 o * *

— 0. 30 to — 0. 2 5 ^ 4c 4e 3^ ** o

11 * * ** 1 * * 1 ** * * 1I ** 1 * * * *

uo 4^ 4c ^ ^ 1 A * * 1 oc. J

a ** * * 1 £. * * 11 c.9 1 — 0» 20 t-O — n 1 ^ 6 4c 4t 4e 4c * * J c.

11 * * o

aO f 1 O * *o -0. 15 to -0. 1 0 1 3 ** ** *4t 10 7 8 12 1 4 1 6 7 5 7 5 20 1 5 e -0. 1 0 to -0.05 18 12 4c* 4c 4c 1

1

9 6 1 0 2 1 1 3 8 9 6 1 0 6 24 2 5 8 -0.05 to 0.00 10 1 1 67 27 3 1 1 1 21 9 1 0 1 8 fi 21 1 3 13 6 1 8 1 8 0.00 to 0.05 e 14 1 3 52 4 14 9 1 4 12 15 1 15 20 15 1 1 14 1 1 8 1 1 3 0.05 to 0.10 5 1 4 ** 1 3 1 2 2 6 1 1 8 1 5 16 19 1 3 1 3 * * 25 #* 1 0 0.10 to 0. 1 5 ** 6 4c* ** 1 5 ** a 8 1 0 5 10 15 6 2 10 ** 5 ** 4

0.15 to 0.20 #* 3 ** 4c 4: 4c 4c 5 * 5 8 4 2 5 8 I ** 1   **  3 0.20 to 0.25 **   **  1 4 ** ** 10 2 1 2 3 1 1   **  * * ** 1 0.25 to 0. 30 * ** ** 4t4t 1 1   5 **  3 2 1 **   **  **  

0.30 to 0. 35 **  * **   **  ** 2 1 ** 16   **  ** «* ** ** ** *#

0.35 to 0.40 **   4c 4: 1 **  **   **  1 1 **   **  **   **  **

0.40 to 0.45   **  ** 4c* 2 **   1 7 **  * ** ** *« **   ** 

0.45 to 0.50 **   **  *4c **   **  ** 8   **  ** ** * **  

0.50 to 0.55 **  ** * * ** 4t4c 1   1 **  3 **   **  **   **  **

0.55 to 0.60   **  4t* 4t **   **  ** 1   **  **   **  ** **

0.60 to 0.65   **  4t* *4t **   **  ** 1   **  **   **  #* **

0.65 to 0.70 *« ** ** 4t* 4c 4t **   **  **   **  **   **  ** ** * * 0.70 to 0.75 ** ** ** 4t* 4c* **   **  **   **  **   **  **  

0.75 to 0.80 **  **   **  *4t ** ** ** * **   **  **   **  ** **

0.80 to 0.85   **  ** * **   **  **   **  **   **  **  

0.85 to 0.90 **  ** ** * **   **  **   **  ** *« ** * **   ** 

0.90 to 0.95 ** ** ** 4c 4c * **   **  **   **  **   **  ** ** **

0.95 to 1 .00 * **   **  **   **  **   **  ** ** ** *# ** **

Number of Differences

Within ± 1.0 ym 60 60 80 80 80 80 71 80 75 75 80 80 80 80 70 70 70 70 60 60

Number of Differences

Greater than ± 1.0 ym

The left column (R) for each system contains the differences for the raw data, and the right

column (C) contains the differences for the corrected data. A double asterisk denotes the absence of a difference value.

81
Table 7 — Concluded

Number of Differences

System: 8P 8V 9W 101 IIF 111 13C 131 14C 15B

Difference

Intervals, ym R C R C R C R C R C R C R C R c R C R C

-1. 00 to -0.95 ** *« * * **   **  ** ** * ** ** * **   **  ** * **

-0.95 to -0.90   **  ** ** ** * **   **  **   **  **

-0. 90 to -0. 85   **  **   **  * ** ** * ** * ** ** * **  

-0.85 to -0.80 **  **   **  #* ** ** * ** ** * * ** ** * ** **

-0.80 to -0.75   **  #* ** * ** ** * **   **  ** * ** **

-0.75 to -0.70   **  ** * ** ** ** * * **   **  **   **  **

-0.70 to -0,65   **  *« **   **  ** ** * **   **  ** ** ** *

-0.65 to -0.60 **   **  * * **   **  * **   **  **   ** 

-0.60 to -0.55 ** *# ** ** ** * **   **  ** * ** ** * ** ** *

-0.55 to -0.50 ** 1   **  * ** * ** ** 1   **  ** ** * **

-0. 50 to -0.45 1   **  **   **  **   **  ** ** ** * ** ** ** *

-0.45 to -0.40 **   **  **   **  ** ** 1 ** * **   **  **

-0. 40 to -0. 35   **  ** ** * * ** ** * 1 ** 3 1   **  * ** **

-0.35 to -0.30   **  ** «* ** 1 ** * ** 3 1 6   **  ** 1  

-0. 30 to -0.25 **  **   **  ** 1   **  4 ** 1 3   **  **  

-0.25 to -0.20 **  ** * ** ** 10 ** ** 1 8 1 4 8 1 3 * ** 2  

-0.20 'to -0. 1 5 **  ** ** «* ** ** 1 9 1 ** 2 14 2 1 1 7 4 1   8 **  2 -0. 15 to -0.10 ** 1 ** ** #* ** 19 3 ** 7 18 4 6 1 1 5 ** ** 5 2 1 -0. 1 0 to -0.05 1 I 4 * 6 * ** 15 13 ** 10 21 8 7 1 3 1 0 4 1 1 1 1 5 -0.05 to 0.00 1 1 21 8 24 ** 1 2 13 22 ** 1 6 7 1 1 8 8 1 24 ** 1 4 7 1 4

0. 00 to 0.05 23 3 27 18 ** 6 2 24 ** 19 3 20 8 2 ** 44 2 9 4 1 6 0.05 to 0. 1 0 4 1 1 3 1 12 1 ** 13 2 6 ** 21 9 8 ** 6 6 1 2 7 7

0. 1 0 to 0. 1 5 ** 7 1 1 5 1 ** 3 2 5 ** 10 2 10 ** 2 6 9 1 3 3 0.15 to 0.20 7 4 1 ** 2 ** 1 10 9 ** 2 7 8 ** * 1 2 6 9 3 0.20 to 0.25 5 4 ** * 1 **   16 3 **  * 3 3 ** ** 13 2 7 1 0.25 to 0.30 4 1 ** ** * ** ** * 19 1 ** ** 4 7 ** 8 ** 1 0.30 to 0.35 1 2 ** ** * **   1 1 1 **  * ** 1 ** 13 1 I **

0.35 to 0.40 2 ** ** * **   **  6 **   **  * * ** * 1 0 ** 1 1 0.40 to 0.45 ** 1   **  **   7 **  **   **  ** ** 4   1 0.45 to 0.50 1 **  **   **  ** ** 3 * **   **  ** * 4 ** 1 **

0. 50 to 0.55   **  **   **  ** 3   **  **   **  ** ** 1 **

0.55 to 0.60   **  **   **  **   **  **   **  1 ** 1 **

0.60 to 0.65   **  **   **  ** 1   **  **   **  **   ** 

0.65 to 0.70 ** * «* **   **  **   **  ** * ** * * * ** * ** **

0. 70 to 0.75   **  ** «   **  **   **  **   **  ** ** * **

0.75 to 0.80   **  **   **  ** * ** ** * * **   **  ** * **

0.80 to 0.85   **  ** ** ** *« **   **  **   **  **   ** 

0.85 to 0.90 **   **  ** ** * ** *>« **   **  **   **  ** 1 0.90 to 0.95   **  ** * **   **  ** ** * * **   2 1 0.95 to 1 .00 **  ** *« **   **  **   **  ** «* **   **  **

Number of Differences

Within ± 1.0 ym 60 60 50 50 20 20 80 80 80 80 80 80 80 80 80 80 80 80 57 57

Number of Differences

Greater than ± 1.0

32
I^ble 8 - Random Error Limits for Linewidth Measurements Corrected by Linear

Calibration Curve, Process Standard Deviations, and Degrees of

Freedom

Row A Row B

Measurement (opaque lines) (clear lines)

System

E (vim) s ( ym) v E ( ym) s ( ym)

Li Li

10. 2o r\ AO O U. Uo2 bo 0.21 0, oby C Q bo

3V U. U4 U. 01 J / / U. 21 U. Ul 4 /o

A T n "J U • OD U. 1 UD 1 1 U. 4 1 U . 122 1 1 C n U, j2 u . u /y 1 1 n A"? U. 4 / n 1 1 Q U * 1 1 7 / / 5Z O.J/ 0.1 Oo c o DO 0. J J A AAA 0. uyy C A bU

6A 0.37 0.105 78 0.35 0.105 68

7A 0. 15 0.045 68 0.27 0.082 77

70 0.32 0.094 68 0.37 0.111 68

71 0. 18 0.054 67 0.15 0.046 68

81 0.31 0.090 58 0.31 0.089 58

BP 0.21 0.060 55 0.22 0.066 58

9V 0.1 1 0.030 48 0. 1 3 0.037 48

9W 0.11 0.026 18 0.17 0.039 18

101 0.14 0.041 78 0.17 0.051 77

1 1F 0.32 0.096 78 0.32 0.099 78

1 1

0.25 0.076 78 0.25 0.074 78

13C 0. 13 0.040 68 0.56 0. 169 78

131 0.14 0.043 11 0.16 0.048 78

14C 0.28 0.084 78 0.37 0.111 78

1 5B 0.24 0.066 48 0.34 0.094 48

83
T^ble 9 - F Statistics for Detecting Between-Day Differences in Linewidth

Calibration Curves, Degrees of Freedom, and Pooled Standard

Deviations^

Operator A Operator B Measurement

System F v, v„ s F v, v„ s

1 2 P 1 2 p

1A 2.

4 24 0.054 5.2* 4 24 0.044

B 1.5 4 24 0.033 1.5 4 24 0.036

C 0.8 4 24 0.059 16.4* 4 24 0.037

D 2.7 4 24 0.040 3.2 4 24 0.026

3V A 0.6 6 32 0.01

1.8 6 32 0.015

B 0.3 6 32 0.013 2.9 6 32 0.01 2 C 0.2 6 32 0.012 1.5 6 32 0.018

D 0.4 6 32 0.012 3.2 6 32 0.015

41 A 0.6 6 32 0. 1 43 6. 3* 6 32 0. 068

B 0.3 6 32 0.172 5.8* 6 32 0.075

C 9.8* 6 32 0.116 2.8 6 32 0.101 D 5.3* 6 32 0.156 1.7 6 32 0.094

5U A 2.7 6 32 0. 070 3.1 6 32 0. 070 B 1.6 6 32 0.078 12.2* 6 31 0.081

C 0.8 6 32 0.079 1.7 6 32 0.071 D 0.9 6 32 0.075 10.4* 6 32 0.061

5Z A 1 .4 6 32 0. 1 15 47. 0* 6 32 0. 1 59 B 5.4* 6 32 0.082 336.9* 6 32 0.068

C 4.1 6 32 0.059 11.9* 6 32 0.280

D 2.8 6 32 0. 103 1 10.6* 6 32 0.126

6A A 4.8* 6 32 0.081 2.2 6 32 0.084

B 2.7 6 32 0.079 21 .5* 6 32 0.096

C 4.6* 6 32 0.065 1 .4 6 32 0.087

D 3.2 6 32 0. 1 1 2 39.5* 6 32 0.077

7A A 43.4* 6 32 0.039 2.9 6 32 0.038

B 9.3* 6 32 0.057 18.6* 6 32 0.039

C 32.2* 6 32 0.038 3.7* 6 32 0.054

D 13.2* 6 32 0.055 16.3* 6 32 0.040

70 A 19.4* 4 24 0.053 2.4 6 32 0.076

B 9.7* 4 24 0.065 5.8* 6 32 0.062

C 12.1* 4 23 0.065 4.4* 6 32 0.069

D 8.9* 4 24 0.054 6.3* 6 32 0.056

71 A 3.1 4 24 0.039 2.0 6 32 0.041

B 1.9 4 24 0.043 1.5 6 32 0.045

C 9. 3* 4 24 0.045 5.2* 6 32 0.036

D 0.6 4 24 0.050 4.6* 6 32 0.060

'Insufficient data to determine statistics for measurement systems 9V and 9W. *Significant at the 0.99 probability level.

84
T^ble 9 — Concluded

Measurement

System Row

Operator A Operator B

81 A 8.8* 4 24 0.068 0.2 4 24 0.059

B 1.6 4 24 0.086 0.9 4 24 0.052

C 5.9* 4 24 0.056 1.2 4 24 0.048

D 4.2* 4 24 0. 107 1.4 4 24 0.050

8P 7.2*

21 .9*

6.5*

16.0*

24

2424

24

0.076

0.030

0.081

0.074

1 .

0.4

2.9

0.3

24

2424

24

0.083

0.026

0.026

0.101

101 A 1.7 6 32 0.034 1.9 6 32 0.044

B 4.9* 6 32 0.038 4.0* 6 32 0.048

C 0.6 6 32 0. 163 0.0 6 31 0. 192

D 3.5* 6 32 0.049 4.7* 6 32 0.050

11F A 2.2 6 32 0.092 1 .6 32 0.092

B 0.3 6 32 0.115 2.8 6 32 0.049

C 1.1 6 32 0.115 2.4 6 32 0.057

D 1.4 6 32 0.110 1.8 6 32 0.064

111 A 0.4 6 32 0.081 6.5* 6 32 0.055

B 2.1 6 32 0.068 5.2* 6 32 0.054

C 1.1 6 32 0.097 2.1 6 32 0.064

D 3.0 6 32 0.073 2.6 6 32 0.082

13C 41 .6*

33.7*

18.7*

69.6*

32

3232

32

0.029

0.081

0.035

0.057

2.9

44.5*

2.0

36.5*

32

32

32

32

0.038

0.037

0.039

0.039

131

14C

15B

A 8.8* 6 32 0.031 2.3 6 32 0.025

B 2.5 6 32 0.050 0.8 6 32 0.042

C 11.3* 6 32 0.034 5.5* 6 32 0.029

D 2.6 6 32 0.040 1.9 6 32 0.028

A 2.8 6 32 0.083 10.9* 6 32 0.043

B 2.4 6 32 0.110 9.6* 6 32 0.055

C 6.9* 6 32 0.066 4.7* 6 32 0.050

D 6.0* 6 32 0.098 11.8* 6 32 0.062

A 3.5 6 32 0.057 656.7* 6 32 0.046

B 16.2* 6 32 0.051 203. 3* 6 32 0.081

C 2.0 6 32 0.065 162.7* 6 32 0.093

D 2.2 6 32 0.061 282.8* 6 32 0.064

* Significant at the 0.99 probability level.

85
Table 10 - Standard Deviations of Repetition, Process Standard Deviations,

Degrees of Freedom, and F Statistics for Testing Linearity

of Linewidth Calibration Model'*'

M A ^ 1 1 v~ mi"i t-i t- rl e ao u r mt= 1

System

Row

Repetitions Linear Fit

F

Sj^ (Urn) V V

11 A 0 0803 50 0.0815 58 1.2 B 0.0565 50 0. 0589 58 1 .

3V A 0 0083 69 0.0126 77 13.8* B 0.0097 70 0.01 37 78 10.5*

41 A 0. 1 009 69 0.1 051 77 1.8 B 0.1211 69 0. 1 225 77 1 .

5U A f) 0861 69 0.0895 77 1.8 B 0.1 322 69 0.1 345 77 1 . 3 5Z A n 1 n7Q 6Q 0. 1 082 68 0.0

B 0.0987 69 0.0993 68 0.0

A 0. 0961 70 0. 1 050 78 3.0* B 0.1080 60 0. 1 050 68 0.6

7A A \j % *j J ^ 60 0.0452 68 1.5 B 0.0856 69 0.0819 77 0.2

7C A 0.0941 60 0.091 7 68 0.6 B 0. 1 149 60 0. 1 1 02 68 0. 3 71 A 0 0594 59 0.0543 67 1.6 B 0.0427 60 0.0457 68 2.2

81 A 0 0868 50 0.0898 58 1.5 B 0.0844 50 0.0887 58 1 .8 8P A 0.0632 47 0.0602 55 0.4

B 0.0701 50 0.0658 58 0.

9V A 0 0946 40 0.0298 48 3.8* B 0.0363 40 0.0366 48 1 .1 9W A n n 9 "5 7 1 u 0.0259 18 1.4

B 0.0486 10 0.0386 1 8 0.2

101 A 7nt\j 0.041 3 78 9.5* B 0.0521 69 0.051

77 0.6

11F A 70 0.0960 78 4.0*

B 0.0934 70 0.0985 78 2.1 111 A 0.0770 70 0.0755 78 0.6 B 0.0734 70 0.0745 78 1 .

13C A 0.0389 60 0.0395 68 1.3 B 0.1743 70 0.1675 78 0.3

131 A 0.0355 69 0.0382 77 2.5 B 0.0373 70 0.0485 78 7.6*

14C A 0.0835 70 0.0835 78 1.0 B 0.1 1 27 70 0.1111 78 0.7

15B A 0.0669 40 0.0666 48 0.9 B 0.1019 40 0.0956 48 0.3

t Outliers are excluded from measurement data.

* Significant at the 0.99 probability level.

86
Table 11 — Frequency of Differences Between Participant's Linewidth Measurements and NBS Values for Two Operators on Each of Three Measurements Systems'''

(a) Row C (opaque lines)

Number of Differences

System II System 81 System 8P

Operator: 12 12 12

Difference

IntejTval , ym R C R C R c R C R c K

/-«

- 1.00 to -0-.' J ** * ** *

-0.95 to -0.90 ** ** * * ** * * i(e ^ -0-50 CO -0.85 ** ** ** * -0.85 to -0.80 * **  

-0.80 to -0.75 **  ** ** * * ** * * -0.75 to -0.70 ** * ** * * *

-0. 70 to -0.65

* ** ** ** * * * * -0.65 to -0.60 * * ** * * * -0.60 to -0.55 ** ** ** * ^ 4t -0.55 to -0.50 **   **  WW i^i^ -0.50 to -0.45

* ** ** * * 1 -0.45 to -0.40 ** ** * 1

ate 4t -0.40 to -0.35 ** * ** * * ifc # ifc ^ -0.35 to -0.30

* ** * ** 11

1 -0.30 to -0.25   **  * *

11 1 -0.25 to -0.20 ** ** * * -0.20 to -0.15 ** 1 ** ** 1 1

1 -0.15 to -0.10

* 2 * * 2 * 3 1 1

4c 4c -0.10 to -0.05 ** 7 ** 5 1 10 4 6 6 3 0 *4t -0.05 to 0.00 8 1 1 2 5 5 1 2 10 2 1 1

1I A0 e. 0.00 to 0.05 ** 9 2 5 1 0 6 7 6 1 3 2 8 0.05 to 0.10 1 3 10 3 4 6 5 ** 6 * 17

0. 1 0 to 0. 1 5 4 9 2 9 ** 1 ** 2 ** 3

0.15 to 0.20 7 ** 5 1 1 1 1   1 **  **

0.20 to 0.25 6 * 2 ** ** * ** * * * 0.25 to 0.30 12 ** 1 ** 1 ** * * ** ** *

0. 30 to 0. 35 # # ^ ^ ** * * i|<* ** **

0.35 to 0.40   **  **   **  * ** * **

0.40 to 0.45   **  **   **  * ** **

0.45 to 0.50   **  **   **  * * * ** **

0.50 to 0.55 ** * **   **  * ** * **  

0.55 to 0.60 **  ** ** * ** *« ** ** ** * ** **

0.60 to 0.65 * **   **  ** ** ** * **  

0.65 to 0.70 **  **   **  ** ** * ** * * *

0.70 to 0.75 * * **   **  **   **  **

0.75 to 0.80

* * ** ** * **   **  ** * **

0.80 to 0.85   **  ** ** * ** * #*

0.85 to 0.90 **   **  ** ** ** * **   ** 

0.90 to 0.95 ** ** ** * **   **  ** ** * *

0.95 to 1 .00 ** ** * * ** * ** ** *

Number of Differences

30 30 Within ± 1.0 pm 30 30 30 30 30 30 30 30 30 30

Number of Differences

Greater than ± 1.0 ym 0 0 0 0 0 0 0 0 0 0 0 0

'•' The left column (R) for each operator contains the differences for the raw data, and the right

column (C) contains the differences for the corrected data. The same two operators did not make

the measurements on all three systems. A double asterisk denotes the absence of a difference

value. 87
Table 11 (Concluded)

(b) Row D (clear lines)

Number of Differences

System II System 81 System 8P

Operator

1 2 1 2 1 2

Difference

Interval, \im R c R C R c R C R C R C

-1.00 to -0.95 * * * **   **  **   ** 

-0.95 to -0.90 ** ** * **   **  **   ** 

-0.90 to -0.85 **   **  * * **   **  **

-0.85 to -0.80   **  **   **  * ** * ** **

-0.80 to -0.75   **  ** ** * * **   **  *# * -0.75 to -0.70 ** ** ** * **   **  **   ** 

-0.70 to -0.65 **   **  1 **   **  ** ** **

-0.65 to -0.60 * **   1 **  ** ** * ** **

-0.60 to -0. 55   **  * **   **  * ** * **

-0.55 to -0.50 ** ** * ** * ** ** * **  

-0.50 to -0.45 **  ** ** * ** ** «* **   1 1 -0.45 to -0.40 **  ** ** * 2 1 ** * ** ** * **

-0.40 to -0. 35 ** # ** * 4 1 **   **  **

-0.35 to -0.30   **  * 8 ** ** ** * ** * **

-0. 30 to -0.25   **  ** 5   **  * **  

-0.25 to -0.20 **  ** ** 6 * « 6 * ** * **

-0.20 to -0. 1 5   6 **  1 1 14 ** * ** ** * -0.15 to -0.10 ** ** 1 3 ** 1

•3 4 ** * 2 ** **

-0.10 to -0.05 e ** 1 0   7 5 4 7 1 1 -0.05 to 0.00 9 10 1 I 1 **  8 1 8 2 1 9 12

0.00 to 0.05 8 8 ** 1 3 1 4 * 1 1 6 1 17 1 4 0.05 to 0.10 5 8 ** e ** 3 ** 4 2 7 2 2

0. 1 0 to 0. 1 5 ** 3 ** * ** 1 ** 3 * 4 * **

0.15 to 0.20 ** 1   **  * * * 7 4 ** **

0.20 to 0.25   **  **   **  ** 5 1 ** **

0.25 to 0.30 * ** * * ** 1   4 2 **  **

0.30 to 0.35 * # ^ ^ J ^ ifr 0.35 to 0.40 **   **  ** ** ** 2 1 * **

0.40 to 0.45 * **   **  ** ** ** * **  

0.45 to 0.50 **  **   **  **   1 **  **

0.50 to 0. 55   **  **   **  **   ** 

0.55 to 0.60 ** ** ** * **   **  ** **

0.60 to 0. 65   **  ** ** * ** * * ** * **

0.65 to 0.70   **  **   **  ** * ** **

0.70 to 0.75 ** * * * ** * « ** * **  

0.75 to 0.80 **  ** ** ** * **   **  * **

0.80 to 0.85 * ** * **   **  ** **

0.85 to 0.90   **  **   **  * ** * **

0.90 to 0.95 * **   **  ** ** ** * **  

0.95 to 1 .00 **  ** * **   **  **   **  **

Number of Differences

Within ± 1.0 ym 30 30 30 30 30 30 30 30 30 30 30 30

Number of Differences

Greater than ± 1.0 ym 0 0 0 0 0 0 0 0 0 0 0 0

83
APPENDIX A

Reprinted from Vol. 21, Solid State Teahnology (January 1978)

Design of a Pattern on a

Photomask-Like Physical Standard

for Evaluation and Calibration of

Linewidth-Measuring Systems*

Dennis A. Swyt

National Bureau of Standards

Optics and Micronnetrology Section Washington, D.C.

A pattern for a photomask-like physical standard, having among its elements lines of widths and spacings in the 1-to-lO micrometer (Am) range, has been developed to be used by the

integrated circuit industry to calibrate lirewidth-measuring optical microscopes. In order

to meet the special requirements of a National Bureau of Standards (NBS) measurement

transfer program, the pattern has been designed with some essential metrological and

statistical principles in mind. The resulting unusual and functionally important features

are intended first, to test the ability of an optical system to perform proper linewidth measurements; second, to expose or counteract instrument and operator biases in the measurement process; and third, to allow a transfer of linewidth calibration values with a

built-in test of the accuracy and precision of the transfer. The basic pattern can be scaled

to micrometer and submicrometer sizes, formed on transmitting photomasks and opaque

substrates, and used with linewidth-measuring devices of imaging or non-imaging, re- flecting or transmitting, optical or electron types.

Introduction At stages in the manufacture of inregrated circuit ±\. devices during which measurements of the smallest

circuit elements on photomasks, substrates-in-process,

and finished devices are made, linewidth measurement

problems are often acute. These can be problems of re- peatability (precision) within individual production

houses, or they can be problems of agreement (accuracy) between producers of masks or devices and their consumers.* For example, a mask maker, using a commercial

microscope calibrated with a line scale, measures the width of a specific photomask line, obtaining a result which is clearly within specification. Using a similar microscope calibrated with the identical linescale, the IC manufacturer buying the mask measures a width for the same line which is clearly outside specification. Measurement problems such as this, characterized by

serious discrepancies in numerical results, occur when

the measurements are not, in a special sense of the word,

"proper." The term proper can be used to describe both

the numerical result of a measurement process and the process itself. Referring to the numerical result, a proper measurement is one which, by definition, results when

the prescribed operations which constitute a measure-

•This effort was conducted as part of the Micrometrology Pro- gram and of the Semiconductor Technology Program at the National Bureau of Standards and was funded by the National Bureau of Standards and by the Defense Advanced Research

Projects Agency Order 2397. Contribution of the National Bureau of Standards and not subject to copyright.

ment process satisfy certain essential conditions. Referring to the process, a proper measurement is one which, because it fulfills certain conditions, predictably yields

(within a known uncertainty) a number which is characteristic of a given system; furthermore, the process

yields that number whenever and wherever it is per- formed on the system.^-^ There are rules (axioms) which must be operationally defined if proper measurements are to be made. Within

the philosophical framework described by Rudolf Carnap,2 five such rules in turn define a logically complete measurement system of the type appropriate to line- widths. The means by which these five axioms are to be

defined is a prescription which tells in detail how to make the measurements. At present, however, there is in industry, no generally accepted, empirically validated

prescription for making proper measurements of the property "photomask linewidth." One effect of this absence is reflected in the example

of the mask maker and his customer cited above; they

tacitly and erroneously assumed that proper calibration

for linespacings would lead to proper measurement of

linewidths. Linewidths and linespacings are, however,

separate and distinct measurement properties, each re- quiring its own valid prescription for proper measurement. Now a National Bureau of Standards (NBS) program'

has generated a prescription, which by specifying equip- ment and procedures, operationally defines the measure- ment property "photomask linewidth." The prescription

defines the linewidth in terms of the distance between 89
two well-defined points in a microscope image of the material photomask line; these two points are at one level on an intensity' profile of the line's optical (or electron) image.

Some of the elements in the prescription derive from

the logical necessity to define the five rules, some derive from the nature of the physical phenomena of optical or

electron imagery, some derive from convention. Detailed

specifications cover, for example: an optical system's imaging quality, resolving power, numerical apertures, focus settings, illumination type and wavelength; as well

as a detection system's calibration, linearity and thresh- old or, for a visual microscope, the eyepiece configuration and optical performance.' Such a prescription, however, is not in itself a complete solution to the linewidth measurement problem. Measurements should not only be proper but should be demonstrated to be so. A completely specified measure- ment system should contain, then, a second important

element: procedures to statistically determine how well

the necessary axioms have been realized at the level at which the measurements are made. Procedures such as these make it possible to judge the statistical significance of differing measurements, such as those the mask maker

encounters. Recognition of the importance of such pro- cedures has lead to the formulation by workers at NBS

of a "measurement assurance" approach to calibrations and measurements.® The purpose of this paper, then, is to describe a pattern for a photomask linewidth standard which is de- signed to be a means to measurements which are both proper and demonstrably so. This linewidth standard, upon direct calibration by NBS and subsequent use with NBS-prescribed procedures and instrument parameters,

will allow the evaluation and transfer calibration of optical systems for the proper measurements of photomask

linewidths. The paper is divided into four parts: one describes

briefly the pattern as it appears on the photomask-like

standard; the second discusses the axioms of Carnap

which formed the conceptual foundation for the general

design; the third discusses the "measurement assurance"

principles which formed the basis for the aetailed design; and the last major section of this paper describes

the configuration and dimensions of the design in the context of the thinking that went into it.

The Basic Pattern The pattern described in this report is designed to be formed on a substrate by conventional IC artwork generation and lithographic transfer. The finished artifact, after subsequent calibration, is to be used as a photomask linewidth standard by the microelectronics in- dustry in its mask metrology. In this paper, the pattern

will be described in its application to optical microscopes measuring 1 to 10 micrometers (fjn) wide lines on light-transmitting photomasks. However, the pattern dimensions can be scaled to sub-micrometer sizes, it can

be formed on opaque substrates, and it can be used to

-l-l-lHiiHH"!-

Fig. 1 —Elements of a photomask pattern for the evaluation and calibration of linewidth-measuring optical microscopes:

(top row) isolated opaque lines and (second row) isolated clear spaces for linewidth measurements; (third row) bracketed line pairs for spacing measurements; and (bottom row)

combined isolated and bracketed pairs for image polarity- proximity effect studies.

characterize linewidth-measuring devices of the imaging

or non-imaging, reflecting or transmitting, optical or elec- tron types. There are three major types of features within the pattern, the first two being of most direct importance to the user of the calibrated target. In Figure 1 are shown the three types of features: isolated lines, both opaque on

clear fields and clear on opaque fields; linespacing pairs;

and bracketed-unbracketed pairs. Figure 2 shows the individual elements of the pattern arranged within the

grid of a 6 X 10 array, the six rows being lettered A

through F and the ten columns being numbered zero through 9. Figure 3 shows characteristic dimensions of

these individual pattern elements. Rows A through D contain forty isolated lines whose

individual widths, in the range 1 to 1 1 ^m, are their most important dimension. The lines are grouped ten per horizontal row of like-polarity: rows A and C contain opaque lines on clear fields, while rows B and D

contain clear spaces on opaque fields. Although there are forty lines in the pattern, there

are only twenty different linewidths. The group in Row

B is specified to contain the same nominal widths as the group in Row A, although in reversed order; in a like manner, the group in Row D is specified to contain the same nominal widths as the group in Row C.

90
Row E contains ten pairs of lines of equal widths whose center-to-center spacinp (pitch), also in the range 1 to 11 nm, are their most important dimension. Each pair of lines is bracketed by another pair, such that

the three spaces defined by the four lines in a group are equal in width. The lines themselves are equal in width,

their values being 1.0, 1.5, or 2.0 >im. Row F contains five pairs of opaque lines, each partially bracketed by another pair, where the nominal

equality of the lines and spaces is the most important

feature of the pattern element. The characteristic widths

of the individual elements are 1, 2, 3, 5, and 10 /*m,

respectively.

PtiUosphfcai Framaworic of the Unewidth Pattern Design

The essential feature of a linewidth standard is some

nimiber of lines which can aa as "knowns" in a calibration scheme. The pattern described has that feature and

more. Much of what is included in the variety of ele- ments on the pattern is there to provide a means to at- taining proper measurements. According to Camap,^ there is a minimum number

of logical axioms which must be operationally defined in order to obtain proper measurements of a specific quantity; the number of axioms required depends on the nature of the physical system. For an extensive quantity (that is, one for which a

satisfactory addition or "joining" operator can be defined), three axioms are needed: one axiom defines an

equality operator by which one measured quantity can be

said to equal another; a second axiom defines an ordering operator by which one measured quantity can be

said to be greater or less than another; and a third defines the dimensional unit of the quantity to be measured. For an intensive quantity (that is, one for which no satisfactory addition operator can be defined), five axioms are needed. To the first three are added a fourth which defines a zero, either explicitiy or impiicity, and a

fifth axiom which defines a way to generate a continuous

scale by which to interpolate between the unit of the

third axiom and tiie zero of the fourth. This "zero" can

be interpreted as a second unit since it may have a mathematically non-zero value. Since the concept of "linewidth" may be a somewhat

unfamiliar one to some readers, the meaning of each axiom and their relationships to each other will be dis- cussed first in terms of the more familiar quantities, mass and temperature. The first two of the axioms, those of the equality operator and of the ordering operator, taken together de- termine "what" is being measured by defining "how * to measure it For example, what is meant by the property of matter "mass" depends on whether one uses a pan balance and

Newton's law of universal gravitation or an "inertial bal- ance" and Newton's second law of motion to say that

"this body has greater, less or the same amount of mass

as that body." Operationally defined by these two means,

gravitational mass and inertial mass can be two inde01234 56789

A -l-l-l-l-l —l-H

c-l-l-l-l-I—

E H„HiiHHiiHMiiHHHiiH<ih

HHiHiihFig. 2—Scale drawing of linewidth-artifact pattern in' corporating basic elements: Rows A and C—isolated clear

lines on opaque field; Rows B and C—isolated opaque lines on clear field. Row E—bracketed line pairs of various spacings; Row F—combined bracketed and isolated pairs.

7.0 10.

Fig. 3—Map of linewidth artifact pattern showing (in di- mensions of jxm): the widths of opaque (WJ arui clear (W^) isolated lines for linewidth measurements; the spacings

of bracketed line pairs (S) for linespacing measurements; and the widths of lines and spaces in combination bracketed

(P) and isolated (F) pairs for image polarity-proximity

effect studies. Please note that the linewidth values quoted,

while representative of, are not equal to those on the physical standard since it must act as an "unknown" in a current NBS-industry study.

pendentiy proper measurement properties of the same

body.

The other three axioms, those of the unit, the zero, and the scale, taken together determine how numerical

values are assigned to observed states of the property

which is being measured.

91
For example, temperature is a property which requires

the operational definition of these additional three axioms

for its proper measurement. One way to convert the subjective impressions of hotter, colder, same "temperature,"

into objective observations is by using a liquid-in-glass tube thermometer as the equality-ordering operators. Then the height of the liquid column when the thermo- meter is in contact with boiling water can define a unit (212 degrees), similarly the height of the column when

the thermometer is in contact with freezing water can

define a "zero" (32 degrees). And the prescription for forming the bore in the tube and ruling the graduations can define the means for dividing the nimierical differ- ence between the unit (212) and the zero (32) into 180

equal divisions. Like temperature, the measurement quantity "photomask linewidth" is an intensive one; tne prescription tell- ing how to perform the measurement must operationally

define five axioms. Specifically, this prescription must

tell what things to manipulate and what actions to per- form in order to give meaning to the abstract idea: "the width of a material line on a photomask is the perpendicular distance between its two (parallel) edges." The

NBS prescription defines this width as the distance be- tween the two points at a certain intensity level on the

intensity profile of the optical (or electron) microscope

image of that photomask line, when the microscope itself meets certain requirements and is operated under specified conditions.' The most basic function of a prescription such as this one is to define the "what" of the measurements, photomask linewidth, by first of all defining the ordering and

equality axioms. Errors arising from absent, incomplete

or faulty definitions of these two axioms are not diflScult to observe. For example, there is evidence that the commonly used linespacing-calibrated filar and image-shearing eyepieces can perform ordering-equality operations with opposite results: a filar showing line A wider than

line B, an image-shearing showing line B wider than line A.* Other types of photomask linewidth measurement

errors occur because of the faulty and incomplete reali- zation of unit, zero and scale-generation axioms.

Figure 4 shows the results of different types of pure and combination axiom errors. In a proper measurement

system the observed values are correct at all points along

a linear interpolation between the defined values of the unit and the zero. Pure errors in either the unit (Figure

4a) or the zero (Figure 4b) yield observed values which

are correct at one end of the range but in maximum er- ror at the other end. A scale-generation error gives correct observed values at the unit and zero values, but

deviations of some type between them (Hgs. 4c and 4f). Experience at NBS with optical-microscope linewidth measurements, both empirical and analytical,^ * leads to the expectation that a common form of error in the measurement of photomask linewidths can be described by

Fig. 5. In region I. the dominant error is the unit-zero combination of the incremental type; not sho'.vn. but

III inOK OF «*UHt 111 IMOI Of ««UIII ID |»tl 0> tUU

or ui(T tiD aao or oarr au (iiiMTtM

iMOfO rrpfi iiKMMiri tthi iphimk ttmi

Fig. 4—Examples of Types of fundamental measurement

errors within five-<jxiom scheme for extensive physical

quantities described by Rudolf Carnap^. Pure forms of

errors in: (A) realized value of unit; (B) realized value of

zero: (C) and (F), continuously generated scale; and mixed

forms of errors in realized values of unit and zero of (D)

general and (E) special, incremental types.

likely to be present, is some degree of scale-generation

error of either (or both) the non-linear or periodic types. In region U, a strong scale-generation error, which arises as the resolution limit of the measuring instnmient is approached, is linked with zero and unit errors. At the industrial user's level, these unit-zero errors can occur because the required prescription for measurement, conventionally accepted and based on the physics

of image formation, is absent. Due to this absence, the

unit, zero and scale generation of a completely different physical quantity, line-spacing, are usually carried over

tacitiy to linewidth measurements. While the scale generation scheme can be carried over, the unit and zero

fail; these failures occur because the ordering equality

operators for linespacing and linewidth differ in a funda- mental way. A measurement of a linespacing is a "symmetric"

one, while a measurement of a linewidth is "asymmetric."

Linespacings are measured center-to-center, left-edgeto-left-edge, or right-edge-to-right-edge of two different

lines. The "handedness" of the detection at each line is the same; hence, "synounetric." Linewidths, however, are measured left-edge-to-right-edge of the same line; the "handedness" of the detection at one edge is the opposite of the handedness at the other edge; hence, "asymmetric." The effect of the presence or absence of symmetry in the measurement can be described in the language of

optics. If X represents the location of a line's edge in object space and y represents the location of the same line edge in image space, for a microscope which linearly

maps the object into the image, then:

y = ax b A linespacing raefl^ rement with such a system is the

92
difference of two y coordinates which, because the detector in effect approaches each of two lines from the same direction, have the same origin:

5(spacing) = y,„ - y^g = [ ax, + b^] - [ojc, + ba] — a[x, - Xt\. (1)

Since the two intercepts, bn, are of the same "handedness," they cancel. A linewidth measurement with the same system, however, is the difference of two y coordinates which, because the detector in effect ap- proaches the two sides of the same line from opposite

directions, have different origins:

(width) = y„i - y,L= ^ax, + b,t\ - iaxt + fej = a[x, - x,] + Ibn - bi]. (2)

The intercepts, bn and bi., being of different "handedness," do not cancel. This equation exemplifies the form

of the unit-zero error of the incremental type shown in Fig. 4E and region I of Fig. 5. Phenomenologically, the b intercepts can be inter- preted as image "edge shifts" which prevent one-to-one correspondence of object and image dimensions. They

are complex functions of, for example, the imaging sys- tem's optics and illumination, the object polarity (clear or opaque), the illumination polarity (reflection or

transmission), and the detailed operation of the measuring device (visual filar or image-shearing eyepiece, CRT

scan. etc). These "edge shifts" and their resulting offset- type errors are not "constants" but vary among instru- ments, among operators on the same instrument (especially visual eyepiece systems), and between times on

the same instrument-operator system.^ Even with explicit "edge shift" effects present, there

are, however, no scale-generation errors in the example

cited above; and the same scale applies to both the line- spacing and linewidth measurement. The test of a scale- generation operation is that intervals in different regions

along the scale are equal. Formally, this is stated as: For the line spacings, if certain conditions are met,

5, - 5, = S, - 5, . (3) For the linewidths, if certain conditions are met, W, - W, — W: - W,. (4)

On inspection of equations (2) and (4), it can be

seen that the difference between two linewidths is free of the "handedness" constants and has only the multiplicative constants of the linespacings. Therefore, the pitch of a micrometer screw or the linear timebase of a CRT sweep can be used to generate a scale for either linespacing or hnewidth measurements; however, with- out a proper realization of their own unit and zero, line- width measurements cannot be made correctly on a line- spacing-calibrated device. The fact that linespacing and linewidth measurements

can naturally share a scale-generation operation has led to one of the design features of the pattern. Since line-

"region II REGION 1 /

_ ////

_ //

/

/

/

7l 1 1

1 1 1 1 1 1

PROPER LINEWIDTH

Fig. 5—Forms of errors anticipated to be encountered in industrial photomask linewidth measurements for linewidths below 10 fim; in Region I, the combined unit-zero error of

the incremental type; in Region II, the combined unit-zeroscale generation error.

spacing measurements can, in general, be done more

precisely than linewidth measurements, a spectrum of

linespacings has been included in the pattern to test the

ability of the operator-instrument system to generate a proper linewidth scale.

Application of Measurement Assurance Principles to the Design

The previous section has dealt with the requirements

which must be satisfied for measurements to be proper. Also discussed were the types of errors which arise if these requirements are not met. This section will deal with a technique for determining whether or not a functioning measurement system is yielding proper measure- ments by looking for error. The technique, developed at NBS with contributions by a nimiber of workers, is called "measurement assur- ance". '•'^ Its formulation was guided by an analogy be- tween manufacturing processes (which generate product) and measurement processes (which generate numbers). By the analogy, quality assurance procedures apply to both processes. A manufacturing process is considered to be in "quality control" if the product being

generated is within tolerances; similarly, a measurement

process is considered to be in "statistical control" if the numbers generated and their variations lie within acceptable limits. This statistical control is a sign that the measurements are proper, a demonstration that in fact the necessary axioms have been realized. For many of the most economically important measurements in an industrial society, such as the accept-orreject linewidth measurements on the mask maker's

product, two complete sets of axioms must be realized and tested, one set at each of two levels or stages of the measurement process. At the first stage are the direct or primary measurements. These yield numbers from a fundamental realiza- tion of the defined property, such as linewidth values

93
which are derived from the analysis of a properly formed

image profile. Such measurements can be complex and

expensive to make. At the second stage are the transfer or secondary measurements. These yield numbers from

a comparison of an unknown with a known, such as linewidth values which are derived from a comparison

of lines of unknown widths with lines for which widths have been measured directly. The added complexity of this two-stage process is justified when the comparison-transfer measurement is significantly easier and more economical than the di- rect-calibration measurement. In the real world, this is usually the case; for many smaller manufacturing firms, transfer measurements are the only ones practically

attainable. In the context of this paper, the two levels of the process are the calibration stage which takes place in an NBS laboratory and the transfer stage which takes place in an industrial plant. The pattern described here has been tailored to meet the special needs of this system. In particular, a sufficient number of elements of the

right kind have been included in the pattern to make

possible a statistically-engineered test of the basic axioms

of linewidth measurement. With a calibrated physical standard bearing such a pattern in hand, a user can fol- low prescribed directions, perform repeated measure- ments and obtain a well-defined curve of observed-versus- proper (calibrated) linewidth values, a curve such as one of those in Figs. 4 or 5. This curve can be analyzed

for slope, intercept and deviations from linearity to de- termine the errors present: both fundamental axiom er- rors as well as "random" scatter errors. Since the goal of the program for which the pattern was designed is to attain accurate linewidth measure- ments at the industrial user's level, a collaborative inter- laboratory study of linewidth measurements is being

made between individual microelectronics industry firms and NBS." What follows is a sketch of the manner in which the pattern-bearing physical standard is to be used

in that study.

With the pattern formed by conventional lithography on a substrate, linewidths and linespacings on the re- sulting photomask-like object are to be measured at NBS.

Some or all, as deemed necessarj', of the linewidths

are to be measured by a combination of electron micro- scope/photometric optical microscope procedures; these measurements constitute a fundamental realization of the physical quantity "photomask linewidth".^ Some or

all of the linespacings, again as deemed necessary, are

to be calibrated on the NBS linespacing interferometer.'" The physical standard, bearing lines of calibrated widths, is then supplied to a user within the microelectronics industry.

Designated linewidths and linespacings on the cali- brated standard are to be measured by such participants

in the study without, however, their having knowledge

of the calibration values. The procedure for the measurements is prescribed by NBS; included in it are details of the instrument set-up, the specific lines to measure,

the sequence in which to measure them, and the number

of repeated measurements. Completed data sheets and the physical standard are then returned to NBS.

In broad terms, analysis of the data performed by

NBS is to determine how well the necessary axioms are

realized at the NBS-calibration stage and at the usertransfer stage of the two-stage measurement process. In more specific terms, the data will be used to assess:

( 1 ) the integrity and completeness of the prescribed

procedure, (2) the suitability of the calibrated artifact standard, and (3) the precision and accuracy attainable and attained by the user of the physical standard. At present, one of the working assumptions of the ex- periment is that, since most linewidth measuring instru- ments operate as comparators, the common linewidth

error of Fig. 4 (Region I) can be eliminated by proper

two-point calibration. Deviations from this expected be- havior in the results of the study of the measurement

process are to be judged within the "model ambiguityalgorithm error-unit error" scheme formulated among

Cameron, Eisenhart, Pontius and Simpson and described by Pontius.* Within this scheme, the measurement system is considered to include these elements: (1) an object—which

is the physical thing with a property to be measured; (2)

a model—which is the conception of the object and its properties; (3) an algorithm—which is the instrumentation, manipulative procedures, computations, etc, taken

together; and (4) a unit—which is the defined value of measurable quantity, having zero error by definition. From the inter-relationships of these elements origi- nate three sources of error, two more important than the

third. "Model ambiguity" causes "perfect" measurements

to disagree because the real object behaves differently than the conceptual model predicts. "Algorithm error" causes measurements of "perfect" objects to disagree be- cause the measurements are not proper. "Unit error," the least significant error of the three, is the disagree- ment between the unit as locally realized and the unit as expresed by the assigned number (e.g., the number as- signed the international SI unit of length). Besides providing a framework for error analysis, the model-algorithm concept has influenced the specification

for manufacture of the physical standard being discussed. In order to focus on algorithm errors by reducing model

ambiguity to a minimum, the object is to be refined to

fit the existing conceptual model. In practice, this means

that the physical standard will be "idealized," having

properties such as line straightness and edge acuity more

akin to best-effort output of the industry than to the

typical photomasks to be measured. To the extent that the standard is "idealized" and

used for this initial study outside the stream of e^'ery- day production measurements, the study contains deviations from an end-form which is being sought.

94
Configuration and Dimensions of Elements Apart from the general design considerations dis- cussed, certain more specific "measurement assurance"

principles have been applied in the design of the pattern. One such principle is that the objects to be measured

should have attributes in themselves which tend to counteract and eliminate biases and errors in the measure- ment process. Application of this principle has deter- mined how the lines of measured widths and the lines of measured spacings are grouped, how the lines of dif- ferent widths and spacings are located relative to each

other within groups, how the values of widths and spacings are distributed over the range of values, and finally, how the linespacing pairs are bracketed.

The Linewidth Groups

The range of linewidths (1 to 11 /^m) included in the pattern covers the region in which the measurement problems addressed by the NBS photomask program lie.'' Within this range, the number, distribution, and sequence

of linewidths in the pattern have been chosen for statisti- cal purposes.

In order to adequately cover the range of interest, ten

lines of various widths, distributed over the range, were

chosen for a single group. Ten other lines of the same

polarity (opaque or clear) in a distribution of similar but slightly different values of linewidth became a sec- ond group. Inclusion of two distinct groups allows one

group to be treated as a calibration or control group and the other as an unknown in an approximation of an

instrument calibration-photomask inspection process.

See, for example. Rows A and C of Figs. 2 and 3. either of which may be the control for that polarity. Both of the distributions were derived from a single, starting distribution of linewidths (in ixm): 1.0, 1.5, 2.0. 2.5. 3.5, 4.5, 5.5, 7.0, 8.5, 10.0. The important properties of the basic distribution are: (1) the intervals are non-uniform to avoid the possibility of being in phase

with the type of periodic errors shown in Fig. 4F; and

(2) the distribution has more points at its low end be- cause of the anticipated behavior of systems shown in region II of Fig. 5. The two distributions associated with the control and unknown groups were generated from the basic distri- bution given above by a "coin-toss" incrementing tech- nique. For each linewidth of the basic distribution, an

increment of either 0% or (approximately) 10% of its value was chosen for it by coin toss; if the non-zero

value were indicated, a second coin-toss determined the sign of the increment. In such manner, each linewidth value in the basic distribution was incremented. The entire procedure was then repeated and two distinct but

similar distributions obtained. The presence of two such distributions on one pattern provides a number of pairs of lines: (1) lines which

are of like polarity; (2) lines which are similar, sometimes nearly equal but non-identical in width; and (3)

lines which are somewhat physically removed from each

other. Interromparison of measurements made on respective members of such pairs allows some estimate of the resolution of the ordering-equality operations of the measurement process. In Fig. 3, an array map of the entire pattern, a simulation of these distributions of linewidth values is given. Actual values are not reported in order to preclude current and future participants in the NBS-industry study from obtaining foreknowledge of what are supposed to be, for them, unknowns.

The order in which lines of various widths appear in the pattern is not one of ascending or descending values

of linewidth, but a randomized one. This implied se- quence of measurements is to counteract operator bias

in the anticipation of values and to prevent the cumulative effects of hysteresis and "memory"-type effects in instruments. Two minor details of the design of the lines as they appear in rows A through D of Fig. 1 are worth mention: the lines were made long enough to give a moderately high aspect ratio for the widest one; and horizontal

orientation lines, run between the isolated lines to lo- cate points half-way down their lengths, are kept far enough away to prevent the sheared images in an imageshearing visual eyepiece from overlapping them.

The Linespacing Group

Although linespacings are a distinctly different measurement quantity from linewidths, lines of known spacings have a place in the pattern: they can function as a highprecision check of the lin;\»idth scale-generation. There

are design features of these line pairs which give them

special advantages as linespacing standards in themselves. These features are related to principles of symmetry, in- dependence of measurements, disorder, and pattern rec- ognition.

The basic configuration of the linespacing element is shown in the third row of Figure 1; it consists of a pair of short lines bracketed by a longer pair. The distance from a point on one of the short lines along a horizontal

axis to a similar point on the other short line is the dimension of interest, the line spacing. Since the two

short lines are specified to be equal in width, the left- edge-to-left-edge, right-edge-to-right-edge and center-to- center distances are nominally equal; this distance is the linespacing or pitch. The linespacing values are 2.0, 3.0, 4.0, 4.8, 6.2, 7.0. 7.8, 9.2, 10.0, and 10.8 micrometers. In all the line- spacing elements but two, the width of the lines is 2 /^m. The spaces are of various widths. For reasons related to the lithography of photomasks and to imaging phenomena, the two elements having the lowest linespacing val- ues are formed with lines and spaces equal in width;

these widths are 1.0 and 1.5 /^m respectively for these two elements. The lines of the outer pair bracketing the inner pair are of fundamental importance: they add a necessary symmetry to each line of the inner, linespacing pair. With

95
an isolated pair of lines, ones without the bracketing

pair, each line has one "interior" and one "exterior""

edge. Asymmetries in the material profiles of the lines

as well as in the intensity profiles of their optical or elec- tron images can make measurements of their spacing

biased. Addition of the bracketing pair, as dummy lines, makes all edges in the linespacing pair "interior" edges, thus eliminating an asymmetry and a potential source of measurement error. The brackets are made longer for two reasons: ( 1

) to differentiate them from the Unespacing pair and thus to avoid confusion during measure- ment (this is especially useful for image-shearing eyepiece measurements where the presence of many lines in

the sheared images causes confusion), and (2) to create

a clearly identifiable configuration having a "pattern- recognition" quality which separates the linespacing group from the one below it on the overall pattern. The linespacing elements have three other properties usuallv absent from linescale standards. First, each line- spacing value is defined by a single pair of lines which

are phvsically independent of the lines which define other

values. Thus, measurements are decoupled from each

other: S, = A', — X = X:, — X^, S3 — X^ - Xr„

not 5, = A'j - X„ S,-X, - A-,, S, = X, - X,. Sec- ond, the linespacing values are of non-equal intervals; and, third, they occur in a randomized order of relative values. The purposes of the latter two properties have

been discussed above in their application to linewidth

values.

The Bracketed-Unbracketed Pair Group These elements (bottom row. Fig. 1 ) are designed to have a pair of lines which are bracketed about the central portion of their lengths and unbracketed about their ends. The clear spaces separating the opaque lines within

the elements are specified to be equal in width to each

other and the lines; the basic dimensions of the group

are 1, 1, 3, 5 and 10 micrometers. All horizontal lines attached to the elements are orientation reference marks. The purpose of the elements is primarily to provide,

when necessary, information on the imaging properties

of the lithography which forms the pattern on the substrate and on the imaging properties of the optical or

electron system which views the pattern. These pattern elements may also be used to set the controls of systems such as TV-microscopes which require for calibration an image having known line-to-space ratios.

Conclusion

Explicitly, this report describes the thought processes behind the design of a pattern for a photomask-like physical standard for linewidths; implicitly, it describes an at- tempt to make abstract measurement philosophy pay off in the marketplace.

The thought processes reflect an attempt to apply to a new and evolving measurement system the synthesis of two important measurement ideas; the one which asserts

that proper measurements require the operational defi- nition of essential axioms and the other which asserts that proper measurements require demonstration of the

realization of those axioms. The pattern described in this report has been designed, then, not only as a calibration standard, but as

a tool to examine the measurement process. Such an ex- amination is about to take place in a hmited study. Because of the design features of the basic pattern, the details of the measurement procedure specified, and

the structure of the overall measurement repetition

scheme, statistically reliable results on the soundness of

the entire measurement process at the user's level are expected. Such information is important to the user because it can become a means to attaining accurate and precise

photomask linewidth measurements on the production

line.

Acknowledgements

The author thanks Dr. J. A. Simpson both for his timely introduction of the author to Camap's philosophical framework of measurements and for his contribution

of ideas to this paper; Mr. Paul Pontius for his counsel on the means to serve an end-user by a measurement as- surance program; Mr. John Jerke for his labor and planning on the lay-out of a practical photomask pattern; Mr.

John Heine for his drafting; and the NBS Ofl&ce of Measurement Services for guidance in tailoring the pattern to achieve a statistically sound experiment.

References

1. Jerke, J., "Semiconducior Measurement Technology: Optical and Dimensional Measurement Problems with Photomasking in Microelectronics", NBS Special Publication 400-20,

available frofn U.S. Government Printing Office, Washington,

D.C. 20402, DC Catalogue No. C13. 10:400-20.

2. Camap, Rudolf, "Philosophical Foundations of Physics," Basic Books, New York and London, 1966, pp. 51-95.

3. Simpson, J. A., "On the Dialectic of Measurement," Unpublished talk given at the National Bureau of Standards, Mechanics Division Seminar, Nov. 1975.

4. Swyt, D., "NBS Program in Photomask Linewidth Measurements," Solid State Technology. April 1976.

5. Jerke, J. M., Nyyssonen, D., Rosberry, R. W., Scire, F. E., Swing, R. E., Swyi, D. A., and Young, R. D., "Semiconductor Measurement Technology: Accurate Linewidth Measurements on Integrated Circuit Photomasks," NBS Special Publication 400-43, available from U.S. Government Print- ing Office, Washington. D.C. 20402.

6. Cameron, J. M., "Measurement Assurance," National Bureau

of Standards, NBSIR 77-1240, available from U.S. Govern- ment Printing Office, Washington, D.C. 20402.

7. Pontius, Paul, "Notes on the Fundamentals of Measure- ment and Measurement as a Production Process", National Bureau of Standards, NBSIR 75-545, available from National Technical Information Service, Springfield, Va. 22151.

8. Swyt, D. A. and Rosberry, F. W., "A Comparison of Some

Optica! Microscope Measurements of Photomask Linewidths," Solid State T£chnology, August 1977.

9. Swyt, D. A., Rosberry, F. W., and Nyyssonen, D., "Calibration of Optical Microscopes for Photomask Linewidth Measurements." Talk given at Interface 77, Kodak Seminar, Monterey. California, Oct. 5-7, 1977.

10. Gilliand, K. E., Cook, H. D., Mielenz, K. D. and Stephens, R. B. "Use of a Laser for Length Measurements by Fringe

Counting," Metrologia vol. 2, 95-98 (1966).

96
APPENDIX B

NBS Linewidth and Line-Spacing Values for Artifacts

The mean values for linewidths and line spacings assigned to each of the

nine artifacts used in the inter laboratory study are given in table B-1

.

Each line of data in this table corresponds to one row of patterns on the

artifact; for example, the first line of data corresponds to linewidth values

for lines A-0 through A-9 and the fifth line of data corresponds to line

spacings for line pairs E-0 through E-9. (See sec. 2.1, fig. 3.) The

letters and numbers in the right-hand column are a code used to identify the

line of data. The first letter in this code is the row on the artifact, the

next three letters identify the data as coming from NBS, the first two numbers identify the artifact, and the last number is the particular pattern

group on the artifact that was measured by NBS.

Table B-1 — Mean Values of Linewidths and Line Spacings

Assigned to Artifacts by NBS

Mean Values, Code

2.54

6.46

*.77

7,05

6.19

1 .99

1 .47

1 . 78 2.33

9.16

0. 79 7.88

8.29

3.54

2.00

4.31 3.93

0.30

1.45 7.78

10. eo 5.58

8.92

5.60 4.00

5.34

10.89

5.27

9. 35 10.76

3. 72 4.56

1.28

0.92

4.77

7.47

0.67

3.31

3.60

3.00

32

24

120599

6.18

2.73

6.78

4.96

9. 99

ANBSS2-1

BNeS52-l

CNBS52-1

0NBS52-1

eN8S52-l

2.48

6.48

4.69

7.09

6.16

1.91

1 .51

1 .70 2.36

9.15

0. 72 7.91

8.23

3.57

1.97

4.24

3.98

0.73

1.49 7.76

10.51

5.58

e.85

5.62 3.98

5.27

10.95

5.23 9.37

10.75

3.67

4.58

1 .24 0.93

4-75

7.42

0.7 1 3.27

8.62

2 .97

24

26

060699

6. 1 1 2.76

6.72

4 .99 9.97

ANBS53-3

BNBS53-3

CNBSE3-3

DNBS53-3

eNBSS3-3

2.29

6.77

4.56

7.31 6.19

1 .75

1 .79

1 .52 2.62

9.17

0.53

8.18

8.07

3.81

1.99

4 .04 4.24

0.55

1 .76 T. 78

1 0.35

5. 87 e.67

5.92

4. CO

5.08

11.19

5.0 1 9.64

10.76

3.49

4.85

1.03 1.25

4.78

7.25

1 .04 3.07

8.90

3.00

1052

8734

99

5. 90 3.03

6.5C

5.26

9.99

ANBS54-1

eNBS54-l

CNaS54-l

DNeS54-l

ENBS54-1

2.40

6. 54 4.66

7.17

6.18

1 .84 1.58

1 .63 2.44

9 .19

0.64

7.95

8.16

3. 63 1.98

4.19

3.98

0.68

1.57 7.77

10.44

5.66

e.78

5.70 3.99

5.19

11.01

5. 15 9.44

10.77

3. 60 4.65

1.13

1.0 1 4.77

7.33

0.70

3.17

8.70

2 .98

193198

I 2 SS

6.02

2.85

6.64

5. 06 9.98

ANeS55-6

BNBSE5-6

CNBS5S-6

DNaS£S-6

ENBS55-6

2.42

6.60

4.64

7.18

6.18

1 .66

1 .60 1.63 2.46

9. 17

0.65

8.00

8. 16 3.66

2.00

4.20

4.06

0.68

1.57 7.78

10.50

5.70

8.77

5.73

4.00

5.21 11.03

5. 1 5 9.45

10.76

3. 62 4.66

1.17

0.98

4.77

7.37

0.66

3.19

8.73

3.00

213602

1599

6. 06

2. 86

6 .65 5.09

9.99

ANBS5e-5

BNBS5e-5

CNBS56-5

DNaS56-5

ENBS5e-S

2.52

6.51 4.76

7.08

6.19

1 .94

1 .50 1.74 2.37

9. 17

0.78

7.91

6.29

3.55

1.99

4.32

3<94

0.76

1 .46 7.78

10.61

5.61 8.93

5.62

4.00

5.33

10.94

5.30

9.37

1 0.77

3.71

4.59

1.29

0.89

4.78

7.46

0.62

3.28

8.63

3.01

32

25

09

05

00

6.19

2.75

6.79

4.97

9 .99

AN0S57-4

BNBS57-4

CNBS57-4

DNBS57-4

ENBS57-4

2.45

6.56

4.68

7.12

6.18

1 . 89

t .56

1 .68 2.42

9.17

0.69

7.96

8.21

3.61 2.00

4.22

4.03

0.69

1.55 7.77

1 0.55

5.66

8.83

5.68

4 .00

5.25

10.98

5. 18 9.43

10.78

3.65

4.64

1.19

0.98

4.77

7.41

0.74

3.24

8.67

3 .00

24

33

03

1 1 99

6.12

2 .83 6.69

5.07

9.99

ANBS58-3

BNBS5a-3

CN8S5a-3

0NflS58-3 ENBS58-3

2.63

6.37

4.88

6.97

6.18

2.05

I .39

1 .88 2.26

9.17

0. 88 7.77 8.40

3.44

1.99

4 .39 3.84

0.90

1.39 7.77

10.71 5.48 9.02

£.51 4.00

5.42

10.79 5.36

9.26

10.77

3. 83 4.48

1.41 0.84

4.78

7.57

0.62

3.41

8 .52 3.01

48

1 5 23

9499

6.25

2.68

6.92

4.85

9. 99

ANBS59-2

BNBS59-2

CNBSS9-2

DNBS59-2

ENBS59-2

2.50 6.50

4.71 7.08

6.19

1 .94 1.52

1 .72 2.37

9.17

0. 74 7.91 8.24

3.57

1.99

4.25

3.97

0.76

1 .49 7.77

1 0.56

5.61 8.89

5.64

4.00

5.29

10.93

5.23

9.38

10^77

3. 67 4.59

1.24 0.97

4.78

7.45

0.72

3.29

8.63

2.99

3027

0806

98

6.14

2.80

6. 74 4.98

9.98

ANBS60-1

ONBS60-t

CNBS60-1

DNBS6Q-1

ENeS60-l

*The NBS values are provided by Arie W. Hartman, Fred W. Rosberry (retired),

and Dennis A. Swyt, Center for Manufacturing Engineering, NBSt

97
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123
ATTACHMENT F

INFORMATION SHEET AND DATA SHEETS

124
INFORMATION SHEET

Company Name:

Company Mailing Address:

Company Phone Number:

Company Contact Name:

Phone Number:

Operators' Names:

Date

NBS Target Number:

Microscope Data

Instrument Brand Name:

Model Name or Number:

Objective Lens:

Brand Name:

Type

Numerical Aperture

Cover Glass Required No D YesD Thickness

Tube Length: ' mm Condenser Lens:

Brand Name

Type

Numerical Aperture

Built-in Condenser with Unknown N.A.

Measuring Device:

Type: FilarQ Image-shearing^ TV Q

Read-out: Digital Display O Vernier ScaleD

Barrel Monocular^ BinocularQ

Eyepiece Magni fi cation

O

Overall Magnification Computation for Visual Systems:

Objective Lens Magnification: X Additional Magnification 1: X Eyepiece (or viewing screen): X Overall Magnification X X X =

125
DATA SHEET 1

LINEWIDTH MEASUREMENTS

Target # Pattern Group ^

Date \ ^^^^ \ When you begin to take measurements

Your Name Company

Pattern Type . Measurement

A-0 Opaque Line

A-1 "

A-2 II

A-3 II

A -4 II

A -5 II

A-6 II

A-7 II

A -8 It

A-9 "

B-0 Clear Line B-1 II

B-2 11

B-3 II

B-4 II

B-5 II

B-6 II

B-7 II

B-8 II

B-9 II

C-0 Opaque Line C-1 ri

C-2 II

C-3 II

C-4 "

C-5 II C-6

C -7 H C-8 II C-9 D-0 Clear Line D-1 II

D-2 II D-3 II

D-4

D-5 II

D-6

D-7 II

D-8 D-9 II

126
DATA SHEET 2

LINE-SPACING MEASUREMENTS

FILAR, TV, OR PHOTOMETRIC SYSTEM

Pattern Method Measurement

E-0

Left edge of line A to left edge of line B

Right edge of line A to right edge of line B

E-1

Left edge of line A to left edge of line B

Right edge of line A to right edge of line B

E-2

Left edge of line A to left edge of line B

Right edge of line A to right edge of line B

E-3

Left edge of line A to left edge of line B

Right edge of line A to right edge of line B

E-t

Left edge of line A to left edge of line B

Right edge of line A to right edge of line B

B-5

Left edge of line A

to left edge of line B

Right edge of line A to right edge of line B

E-6

Left edge of line A to left edge of line B

Right edge of line A to right edge of line B

E-7

Left edge of line A to left edge of line B

Right edge of line A to right edge of line B

B-8

Left edge of line A to left edge of line B

nignc eage oi iine a to right edge of line B

E-9

Left edge of line A to left edge of line B

Right edge of line A to right edge of line B

Date \

\ When you finish taking measurements.

Time )

Your Name /Company

127
DATA SHEET 3

LINE-SPACING MEASUREMENTS

IMAGE-SHEARING SYSTEM

NOTE: USE ONLY THE SHEAR TECHNIQUE AS DESCRIBED IN ATTACHMENT D.

Pattern Method Reading Measurement

(Difference in Readings

Right edge of Bj^ against left edge of A2

E-0

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Left edge of A-^ against right edge of B2

Left edge of h-^ )

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Right edge of B-^ affain*^t" IpTt" pdtzp of* A«

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Right edge of B^

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Left edge of A^^ 1

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Right edge of Bj^

1

E-2

Right edge of B^^ against left edge of B2

Left edge of Aj^ against right edge of B2

Left edge of k-^ I

Right edge of B-^ against left edge of A2

1

E-3

Right edge of B^

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Left edge of A-j^ j

3g3inst fight edge of A2

Right edge of Bj^ against left edge of Aj

E-l»

Right edge of B-^ against left edge of B2

Left edge of k^ against right edge of B2

Left edge of Aj^ against right edge of A2

128
DATA SHEET 3 Concluded)

Pattern Method Reading Measurement

(Difference in Readings)

E-5

Right edge of Bj^ against left edge of A2

Right edge of B-^ against left edge of B2

Left edge of Aj^ against right edge of 82

Left edge of against right edge of A2

E-6

Right edge of B-^ against left edge of A2

Right edge of Bj^ against left edgs of B2

Left edge of k-^ against right edge of B2

Left edge of A-^ against right edge of A2

E-7

Right edge of B^^ against left edge of Ag

Right edge of B^^ against left edge of Bj

Left edge of A-^ against right edge of B2

Left edge of A-^ against right edge of A2

E-8

Right edge of Bj^ against left edge of A2

Right edge of B^ against left edge of 82

Left edge of Aj^ against right edge of 82

Left edge of A-^ against right edge of A2

E-9

Right edge of B^ against left edge of A2

Right edge of A-^ against left edge of 82

Left edge of A-^ against right edge of B2

Left edge of Aj^ against right edge of A2

Date

When you finish taking measurements.

Time

Your Name/Company

129
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130
Eyepiece

Lamp Diffuser

Figure 1. Schematic of an optical microscope. The labelled parts are defined

and discussed in Attachment A, This schematic is not intended to

represent the microscope of any particular manufacturer. The Wratten

60 filter is provided by NBS and should be placed at the location

designated in this schematic.

131
Figure 2. An overall view of the NBS target. The horizontal and vertical lines serve as an aide- for locating the eight pattern groups in the center

of the target.

132
Figure 3. A view of the center of the NBS target. The basic pattern is repeated

eight times, and each pattern group is numbered. (The specific pattern

group on which you will make your measurements is identified in the

instructions,

)

133
0 12 3 4 5 6 7 8 9

-i-i— i-i-i-i-iB

-l-l-l-l-l-l-l-l-l-lpattern for checking

microscope resolution

pattern for adjusting

length scale

H"Hi'hHiiHMiiHiHH"H'i|-

pattern for adjusting

TV -measurement system

Figure 4. A view of the basic pattern group on the NBS target. The lines and

line-spacings to be measured are located by reference to an alphanumeric

grid with the letters A through F identifying the row and the numbers

0 through 9 identifying the colimm. The pattern E-2 is used to check

the resolution of the microscope objective. The pattern E-5 is used

to adjust the measurement system for the NBS-furnished length scale.

The pattern F-5 is used for adjusting the ratio of a linewidth to the

width of an adjacent space en TV -measurement systems.

134
0 12 3 4 5

t

right

edge

right

edge

left left

edge edge

Figure 5. Four-line pattern for pitch measurements. These patterns are E-0 through E-9 on the target. Pitch measurements are made only

on the interior line pair (A and B). The specific pattern represented here is E-5 which is used to adjust the measurement system

or correct the data for the NBS-furnished length scale. Note the

orientation of the left edges of lines A and B with reference to the letters and numbers that mark the row and column location.

135
0 12 3 4 5

t

left

edge

left

edge

Figure 6. Four -line pattern for adjusting the LINE -SPACE control on TV measurement

systems. The NBS value for the ratio of the width of line C to the width

of space D is used for this adjustment. The letters and numbers, which

mark the row and column location of the pattern, are shown to help identify

the left edges of line C and space D.

136
APPENDIX D

Participants' Linewidth and Line-Spacing Measurements

The raw data from the participants in the study are given in table D-1

This table consists of 705 lines of information representing the twenty mea- surement systems included in the study. Data from some companies or groups

within a company that did not follow instructions or did not furnish requested data are not included in this table. (See table 2, sec. 2.4.) In each

case where the participant furnished all the requested measurements on one measurement system there are forty lines of information; eight of these lines

represent the four sets of independent measurements made by each of two operators for each measured linewidth or line spacing on the artifact. In those cases where the participants did not furnish all of the requested data, there are less than forty lines of information. The data are sorted by company/

measurement system, row on the artifact (A, B, C, D, or E) , operator, and

chronological order of the measurements. Any obvious transcription error in

the raw data was corrected, and the corrected value is included in table D-1,

Each line in the data listing contains the following information: ten

measurements; a character A, B, C, D, or E denoting the row measured on the

artifact; a seven-character code uniquely identifying each line of data; a conversion factor for converting the data to micrometers; and a set of ten

digits denoting the presence or absence of outliers in the data. The ten

measurements are recorded from left to right in accordance with the pattern

on the artifact; for example; A-0 thru A-9 on row A. (See fig. 3, sec. 2.1.)

The first three characters of the code are used to identify the measurement

system. (See table 2, sec. 2.4.) The fourth and fifth characters of the

code are the initials of the operator. The sixth character denotes the

chronological order of the data. The seventh character designates the units

of the data; (I - microinch, M - micrometer, and A - arbitrary units). For

example, the first three lines of the listing represent the three sets of

measurements on the ten opaque lines in row A made by the first operator with

initials BE for the measurement system designated as II.

The set of ten digits used to denote outliers in the data corresponds to

the ten measurements on a row. Each digit has a value of 0, 1, or 2. A

value of 1 denotes that the measurement is included in the data analysis. A

value of 0 denotes that the measurement is considered to be an outlier and

is not used in the analysis. Two of the recorded measurements are considered

to be transcription errors and are also flagged with a zero. (See lines with

codes C 7CMB1M and C10INO2M.) In cases where the ten digits are all two's,

an entire day's measurements are considered outliers. (See sec. 3.3.2.)

Table D-2 gives linewidth data for rows C and D that have been corrected

based on linewidth calibration curves derived from rows A and B, respectively.

In some cases, these linewidth data have also been corrected based on a linespacing calibration curve derived from row E. The data for rows A and B in

this table are the same data as that given in table D-1 except for the cases

in which a line-spacing correction was applied. (See table 4.) The format

for data in table D-2 is the same as that described for data in table D-1.

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175
APPENDIX E

(Rejninted from INDUSTRIAL QUALITY CONTROL, Vol. XV, No. 11, May 1959)

Graphical Diagnosis

of Interlaboratory

Test Results

^^^^^^^^^^^^^^^^^^^^^^^^

W. J. YOUDEN

National Bureau of Standards, Washington, D. C.

Introduction Interlaboratory or round robin programs to evaluate

the performance of test procedures will always be with

us. New materials require new tests. New, and hopefully better, test procedures are developed for old products. Test procedures are used to ascertain whether a product meets the specification set down for the product. A double problem confronts the producer. There is boimd to be a certain amount of variation in his product. And there is bound to be variation in the test results made on a given sample of the product. The impact of the errors of measurement associated with the

test procedure is obvious because half the tests made on

a product that just meets specification will rate the product below specification.

Test Procedures and Production Costs

It is customary to manufacture purposely a product

that exceeds specification in order to allow for testing

errors. The larger these testing errors, the greater the excess quality that must be buUt into the product to in- sure the acceptance of nearly all lots that are in fact equal to or better than the specification. The manufacturer already has to contend with variation in the

process. Considerable saving in manufacturing costs can be affected by reducing the margin between the

quality level set for production and that called for in the

specification. The savings attainable with improved test procedures are a strong inducement for the improve- ment of test procedures. Interlaboratory test programs

of varying degrees of thoroughness are frequently used

to establish the performance of existing procedures.

Missed Opportunities in Interlaboratory Test Programs

Strangely enough modem statistical tests such as the

analysis of multifactor studies and the isolation of components of variance have not made the contribution expected of them. Part of this no doubt comes about because these more sophisticated statistical techniques are not too well understood by some of those in the laboratories that run the tests. It is all very well for someone

with statistical skill to set up an intricate interlaboratory

test program and analyse the data but this still leaves the problem of interpreting the statistical jargon to those

directly concerned. Even when this interpretation is undertaken the report is apt to read somewhat along

these lines. "Duplicates run by the same operator in the

176
same laboratory show excellent agreement. Agreement

between different operators in the same laboratories is not quite so good, and very poor between results from

different laboratories. Results on different days do not agree as weU as those obtained on the same day." This

is a brief summary of the interpretation that is made

after the statistical analysis shows that practically all the F-tests are significant. Unhappily almost all con- cerned were already aware of the state of affairs just described and want to know what can be done to improve matters. It is just here that statisticians have not

risen to the opportunities presented by interlaboratory

test programs. When all is said and done, what we want is rather

simple. We want to know whether the test procedure as

set forth is capable of yielding acceptable agreement

among residts from different laboratories. If the results are not acceptable, we would like some specific indication of what is wrong with the procedure. If the pro- cedure appears to be reasonably good but there are some disturbing discrepancies, we would like to know

which laboratories are having trouble and if possible

why they are having trouble. And most important we

should be able to get this information back to the laboratories concerned in such a form that the diagnosis is beUeved. For only so will these laboratories take any

action to correct the difficulties.

Graphical Representation of Results The graphical procedure is based upon a very simple

interlaboratory program. Samples of two different materials, A and B, are sent to a number of laboratories which are asked to make one test on each material. The

two materials should be similar and be reasonably close

in the magnitude of the property evaluated. This will avoid complications that may arise from differentiaJ behavior of the two test materials. A second pair of samples are circulated at a later time if there are only a few

participating laboratories. The pairs of results that are reported by the laboratories are used to prepare a graph.

The graph is prepared by drawing the customary xaxis at the bottom of the paper and laying off on this axis a scale that covers the range of results for material A. At the left the y-axis is provided with a scale in the same units that includes the range of results reported

for material B. The pair of results reported by a laboratory are then used to plot a point. There will be as many points as there are reporting laboratories. After

the points are plotted a horizontal median line is drawn

parallel to the x-axis so that there are as many points above the line as there are below it. A second median

line is drawn parallel to the y-axis and so placed that there are as many points on the left as there are on the

right of this line. Figure 1 shows the seven-day tensile strengths reported by 25 laboratories on two cement

samples. Two of the laboratories are so patently separated from the other 23 that they are not used in deter- mining the position of the median lines.

Diagnosis of the Configuration of Points The two median lines divide the graph pai)er into four quadrants. In the ideal situation where only random

errors of precision operate the points are expected to be

equally numerous in all quadrants. This follows because

plus and minus errors should be equally likely. In any

existing test procedure that has come to my attention the points tend to concentrate in the upper right and

lower left quadrants. This means that laboratories tend

to get high results on both materials or low results on

both materials. Here is evidence of individual laboratory

450 -

400 -

350

« •

J_ 300 350 400

Figure 1 —Tensile Strength

450

biases. There is evidence of this state of affairs in Fig.

1. The more pronounced this tendency to individual

bias the greater the departure from the expected circulcir distribution of points about the intersection of the median lines. Figure 2 shows 15 points plotted from phthalic

anhydride determinations on two paint samples. The

points tend to scatter more or less closely along a line approximately bisecting the upper right and lower left quadrants. There is reason to expect the line to make a

45 degree angle with the axes when the same scale is used for both axes and the two materials are sufiBciently similar so that the dispersion of the results is about the same for each material. A test procedure that yields results like those in Fig.

2 is probably in need of more careful description. In its present form the procedure apparently is open to indi- vidual modifications that do have an effect upon the

results. The procedure rather than the laboratories should be considered as a possible source of the diffi- culty even though the difficulty is exhibited by a large

scatter among the results from the different laboratories. When the points lie closely along the 45 degree line the conclusion may be drawn that many of the laboratories

7 -

6 -

5 -

6 7 8

Figure 2—Percent Phthalic Anhydride

177
are following rather carefully their own versions of the

test procedure.

Checking on Sample Variation There is no possibility of the distribution of points in

Fig. 2 arising from lack of uniformity among the samples distributed from each material. If the stock is heterogeneous, some samples wiU be high, some low, and this will be true for both materials. The pairs of samples distributed to the laboratories will be of four

kinds: high in A, high in B

high in A, low in B

low in A, high in B

low in A, low in B

The four possible combinations have the same probability of occurrence and would result in the test results being nearly equally divided among the four quadrants. Concentration of the points in two quadrants rules out

questions of sampling heterogeneity.

On the other hand if there is a roughly circular dis- tribution of points but with a disappointingly widespread scatter, the diagram does not reveal whether this arises from sampling difficulties or poor precision of the

test results. If sampling is considered a possible source

of difficulty the following modification in the assignment

of samples should be tried. If there are 2N laboratories, prepare N douhle-size samples for each, material. Carefully mix and divide each double-size sample into two

usual size samples.

Double size sample

2N

Laboratory

12

34 I2N-1

12N

Samples

A B

lA IB

lA' IB' 2A 2B

2A' 2B' NA NB

NA' NB' The samples are assigned to laboratories as shown

above. It should be possible to mix and divide each

double-size sample into two closely matching regular

samples. These samples are assigned to a pair of laboratories. If there are sampling difficulties the plotted

points should tend to occur in doublets. Two laboratories getting the two carefully mixed halves should check each other and have their points close together. This involves a little extra work in getting out the samples and no extra work for the participating laboratories. If the pouits corresponding to the two halves

of a double-size sample are separated as much, on the average, as points from different double samples, the

dispersion cannot be ascribed to sampling. In addition

to noting the spacial distribution the projections of the

points on the axes may also be used to see whether just one of the materials was heterogeneous.

Interpretation of Out-of-Line Results So far the large aspects of the diagram have been

examined. The individual points can now be consid- ered and in particular those points most distant from

the intersection of the median lines. Almost always one

or more points are so far out of the picture that it is better not to compress the scale in order to show them. Such points should be ignored in locating the median

lines. (See Fig. 1.) The more distant points tend to fall into one or the other of two categories. Either the point

is far out and remote from both axes or far out and

fairly close to one or the other axis. In the latter case, the result is fairly good on one material and very bad

on the other. Examples of such points Eire found in Figures 2 and 3. Often the explanation is simple—a mistake in typing, or calculation, or some simple blvmder

that sometimes can be corrected by going back to the

records. If the same laboratory shows up in such a meinner on succeeding pairs of materials, this implies

carelessness on the part of the laboratory. The laboratory can do good work but often does not. Occasionally a laboratory has difficulty with one material and not with the other but this is not likely to occur with similar materials. Points in the upper right or lower left quadrants that are far removed from the intersection of the median

lines and that are not near either axis reflect a tendency

to get either high results on both materials or low re- sults on both materials. There are examples in all the

figures. The more consistent a laboratory is in its work

the more likely its point will lie in the proximity of the 45 degree line. A point far out along this line suggests

the possibility that the laboratory concerned has intro- duced some modification into the test procedure. A laboratory finding itself in this situation should check carefully the prescribed procedure for performing the test and endeavor to locate the cause of the large bias. All of the above interpretation can be made while keeping anonymous the identity of the plotted points. When circulating a report of the interlaboratory test it might be helpful to circle in red the point belonging to the laboratory in the copy going to that laboratory. That would save the laboratory from consulting its files to locate itself and would display prominently just where the laboratory stood in reference to the whole

group. This vivid picturing of a laboratory's position should stimulate the laboratory to some self examination that could hardly avoid having beneficial results.

Estimating the Precision of the Test Procedure The above discussion does not exhaust the information to be gleaned from this graphical representation.

Assuming that the two materials are similar in type and

nearly equal in magnitude for the property the dispersion among the results reported for A should be about

the same as the dispersion of the B results. In that event the 45 degree line through the intersection of the medians makes possible an estimate of the precision of the data. Often an interlaboratory test imdertakes to dif- ferentiate among the laboratories in respect to precision. Not only does this require large numbers of measure- ments from each laboratory but differences in precision

usually turn out to be unimportant in comparison with

bias errors and careless errors. No violence at this stage seems to be done by assuming about the same precision

for all the laboratories. The perpendicular distance from each point to the 45 degree line can be used to form an estimate of the precision. The estimate of the standard deviation of a single

result is obtained by multiplying the average length of the perpendiculars by ^/u/2 or 1.2533. These perpendiculars need not be mesisured on the graph paper. Instead, write d wn for each laboratory the difference (A—B) keeping track of the signs. Call these differ- ences di, d2, ... dn. Calculate d, the algebraic average

difference. Subtract d from each difference and obtain

a set of corrected differences di', dj', . . . dn'. The aver- age of the absolute values of these differences when

multiplied by \/:k/2 or 0.886 gives an estimate of the standard deviation.

178
TABLE I —Data and Calculations on Percent Insoluble Residue

In Cement Reported by 29 Laboratories

Labor- Percent Besldne A —

(A—B) — 0.095 atory A B

1 n 99 0.09 —0.005

2 0.08 0.12 —0.04 -0.135

0.24 o!i4 0.10 0 14 0 07 0 07

o!52 0I37 6 0.38 0.19 0.19 0.095 7 0.22 0.14 0.08 —0.015

g 0.46 o'.23 g 0^26 0.05 0.21 0.115 10 0.28 0.14 0.14 0.045

11 0.10 0.18 —0.08 —0.175

12 0.20 0.09 0.11 0.015 13 0.26 0.10 0.16 0.065 14 0.28 0J4 0.14 0.045 15 0.25 0.13 0.12 0.025

16 0.25 0.11 0.14 0.045 17 0.26 0.17 0.09 —0.005

18 0.26 0 18 0.08 0.015 19 0.12 0.05 0.07 —o!025 20 0.29 0.14 0.15 0.055 21 0.22 0.11 0.11 0.015 22 0.13 oao 0.03 —0.065

23 0.56 0.42 24 0.30 OJO 0.00 —0.095

25 0.24 0.06 0.18 0.085 26 0.25 0.35 27 0.24 0.09 0.15 0.055 28 0.28 0.23 0.05 —0.045

29 oa4 0.10 0.04 -0.055 Average 0.229 0.134 0.095 0.053

The data on percent insoluble residues reported by 29

laboratories are given in Table I and plotted in Fig. 3. There are three points far out along the 45 degree line and one far out on the y-axis. These laboratories were

excluded from the calculations shown in Table I. The last column shows the differences between the two results diminished by the difference between the two sample

averages. The average, 0.053, shown at the bottom of

this column is the average of the absolute values, i.e., ignoring the signs. Multiplying 0.053 by 0.886 gives 0.047 as the estimate for the standard deviation of a single

result. Probably this is inflated by leaving in the two

laboratories turning in the very low results for sample A. This estimate of the standard deviation for precision leads to the construction of circles (centered on the in- tersection of the median lines) within which any given

percentage of the points can be expected to fall should

the laboratories be able to eUminate all bias or constant

errors. The multiples of the standard deviation that include various percents of the points are given in Table H. Thus a circle whose radius is about 2.5 to 3.0 times

the standard deviation gives a fair idea of the smallest

circle that could be expected to contain nearly eiII points

after the eUmination of the constant errors that are causing the points to congregate in the upper left and

lower right quadrants. Generally a fair number of points

will lie outside such a circle. The laboratories responTABLE II—Probability Table for Circular Normal Distribution

Percent of the Points Within Circle Multiple b of the Standard Deviation

10 0.459 20 0.668 25 0.759 30 0.845 40 1.011 50 1.177 60 1.350 70 1.552 75 1.665 80 1.794 90 2.146 95 2.448 99 3.035

Note: Percent = 100(1 — exp{—b2/2)l

0.4 •

< «

0.3 - •

• 02 -

• /

1 * *

•

0.1

0

-

1 1

• y

1 1 1 0.1 0.2 0.3 04 0.5

Figure 3—Percent of Insoluble Residue

sible for these points almost certainly have somehow got

substantial systematic errors incorporated in their techniques. Multiplying the standard deviation obtained above by 2.45 gives the radius of the circle that should

include 95 percent of the laboratories if individual constant errors could be eliminated. This circle is drawn

in Fig. 3. Seven further laboratories are outside the

circle including the two who got the benefit of the doubt and were retained in the computation. This ex- amination has directed attention to at least six of the

laboratories that might well go over their method of making this determination of insoluble residue.

If the number of laboratories in the program is rather

small, the way to accumulate more points is to send the

laboratories additional pairs of samples from different materials. A chart is prepared for each pair of materials and the median lines drawn in. The charts are now superimposed so that the points of intersection of the median lines coincide and, of course, the median

lines Eilso. All points are then transferred to one sheet

of paper with one pair of median lines. As there are only a few laboratories each can be assigned an identi- fying symbol.

Figure 4 shows the reports made by eight laboratories determining CaO in cement. The laboratories are

V

•

0

0

Q ^

I

D

1

1

Figure 4—CaO in Cement (interval equals one percent)

179
identified by sjrmbols. The hollow symbols show the

results for the first pair of samples. The corresponding

solid symbols show the work of these same laboratories on a second pair of samples. Few as these data are they

serve to indicate the things that we want to know about

the test procedure and about the laboratories. Clearly

this procedure is one that is vulnerable to individual

bias. Two of the eight laboratories appear in the same

region for both pairs. The circle laboratory is very consistent—and gets the highest results. The square lab- oratory gets very low results and is not very precise as shown by the fact that the two squares are separated

by a much greater distance than any of the other seven

pairs. Using this chart some possibly helpful suggestions could be passed along.

Discussion The two materials used in this double-sample pro- gram were specified to be similar in type and in the magnitude of the property measured. Sometimes the measurement errors are proportional to the magnitude

under measurement and this will show up in a greater

/scatter of the points along one of the axes. Particular

types of samples may give trouble in just some of the

laboratories. The thorough study of a test method must

include consideration of these possible complications.

Naturally a more comprehensive interlaboratory test program wUl be required to explore these aspects of the test procedure. A thorough study in one laboratory

usually reveals these complications.

Summary of Advantages of Graphical Diagnosis

The double-sample, graphic analysis scheme described

in this article offers a number of advantages.

(1) An unusually light burden is imposed on each lab- oratory

(2) The graphical procedure greatly facilitates presentation of the results in a convincing manner

(3) No statistical background is required to follow the reasoning and no computations are required to demonstrate the general presence of constant errors and the gross deviations of individual laboratories

(4) A minimum of computation is imposed upon the in- dividual collating the results

(5) The use of a circle of 2.5 or 3.0 a radius shows the

individual laboratories whether or not their method

of carrying out the test has in some way become

saddled with a substantial constant error

(6) Most important the direction for improvement is clearly indicated

a. A long, narrow ellipse directs attention to a more

careful description of the procedure or even to the need for modification

b. Wild points far out near either axis indicate erratic work

c. Wild points far out along the 45 degree line are strong evidence of substantial deviations from the

specified procedure

d. General prevalence of constant errors is indicat- ed by a substantial proportion of the points lying outside the 2.5 a circle Experience has already indicated that a certain few laboratories are found too frequently in the most distant positions from the intersection of the median. Improved performance from these few laboratories may go far to restore confidence in a test procedure. There is no substitute for careful work

in the laboratory.

180
APPENDIX F

Calibration Curve from Method of Least Squares

For the measurements y^-; ^ given line where i denotes the ith

repetition and j identifies the jth line in a row, the calibration curves are

of the form

y. . = a + gx. i = 1,...,w. (F-1

)

3 = i/...,m

where Wj is the number of repetitions for the jth line, and Xj is the NBS

linewidth value for the jth line.

Let m

j = 1 '

and

m w.

j=1 i = 1 (F-3)

mS^j

(F-4) m

The least-squares estimates of the intercept a and slope 3 are given by

A A

a = y - 3 X (F-5)

• • • where

m w

.

3 = 3 ^ ^ ^ (F-6) m

/ . w. (x. - X )

The standard deviations of the estimates of the intercept and slope are given

by

181
m

1/2

s = s a

5Z w. X . 1=1 ' ' (F-7) m

n yi w. (x. - X ) 3=1 ^ ^

•

and

s „ = — ^ w. (x . - X )

where the residual standard deviation is given by

m

1/2

(F-8)

s =

m w

X; (y.. - a - ex ) j=1 i=1 -*

n-2

1/2

(F-9)

and V = n-2 are the degrees of freedom associated with s,

182
APPENDIX G

Standard Deviation of the Residual

The definition of the standard deviation of a residual is facilitated by

matrix notation. For n measurements consisting of k repetitions on m

linewidths, the model

Y = X $

corresponds to the model in section 3.3.1 where Y is the (nxl) matrix of

measurements, $ is the {1+k+m) x 1 natrix of unknown coefficients

*' = CY'«1 ^m)

and X is an n by (1+k+m) matrix of ones and zeroes. For the ith repetition

on the jth linewidth, the corresponding row of the matrix is as follows: The

first element is one, the (1+i)th element is one, the (1+k+j)th element is

one, and all other elements are zero.

The least-squares estimate of the coefficient matrix is

4 = (X'X)"1 X'

Y

and a residual from the least-squares fit is defined by

A = (I - X (X'X)~1 X') Y

where A is an (nxl ) natrix.

The covariance of the residual matrix is the (nxn) matrix

V(A) = (I - X (X'X)"1 X')

where the estimate of is given by

2 Y'(I - X (X' X)"1 X') Y

s = • n - p

Thus the standard deviation of any residual, referred to as sg^. in section

3.3.1, is the square root of the diagonal element of the [k •( j-i )+i] th row of

the matrix V(A) where s^ is substituted for a^.

183
NBS-IMA (REV. 2-80) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

Spec. Publ. 400-74

2. Performing Organ. Report No 3. Publication Date

October 1982

4. TITLE AND SUBTITLE

Semiaonduotov Measurement Teehnology: Interlaboratory Study on Linewidth Measurements for Anti reflective Chromium Photomasks

5. AUTHOR(S)

John Jerke, M. Carroll Croarkin, and Ruth N. Varner

6. PERFORMING ORGANIZATION f/f joint or other than N6S. see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

ARPA Order 2397

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

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

Defense Advanced Research Projects National Bureau of Standards

Agency Washington, DC 20234

1400 Wilson Boulevard

Arlington. VA 22209

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-v/ord or less factual summary of most si gnifi cant information. If document includes a si gnificant

bi bliography or literature survey, mention it here)

Optical microscopes fitted with a micrometer attachment are commonly used to measure small llnewldths and

other critical dimensions on Integrated-clrcult ( IC) photomasks. In the absence of calibrated linewidth standards, users have experienced systematic measurement errors much larger than required manufacturing tolerances. As IC llnewldths approach 1 \in with a 10 percent tolerance, the need for calibration standards and

Improved measurement procedures becomes even more important.

This report discusses the results of an Interlaboratory study to evaluate a National Bureau of Standards (NBS)

prototype calibration standard for linewidth measurements on IC photomasks and procedures for adjusting and

calibrating opt lea I -microscope systems In the 0,5- to 12-vm measurement range. Using procedures furnished by

NBS, industrial participants measured line spacings and llnewldths on NBS anti reflective-chromium artifacts,

A comparison of NBS linewidth values with participants' measurements showed that most differences were less

than ±0,3 ]sn. A linewidth calibration significantly reduced systematic errors for most systems. Outliers In the data showed the need for measurement-control procedures. The standard deviation of the measurement process was ±0.1 \sn or larger for about half of the systems. For some systems, there were significant day-to-day

differences and operator differences.

The study showed that the NBS artifact and recommended procedures were adequate for calibrating sr. opticalmicroscope system which was In a state of statistical control. This study led to the Issuance of Ni3S Standard

Reference Material 474 (Optical Microscope Linewldth-f^teasurement Standard),

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

dimensional measurements; filar micrometer; Image-shearing micrometer; Integrated circuits; interlaboratory

study; Kohler Illumination; line-spacing nneasurements; linewidth calibration; linewidth measurements; measure- ment uncertainty; micrometre logy; optical microscope; photomask; semiconductor technology; statistical tests.

13. AVAILABILITY

Unlimited

Q For Official Distribution. Do Not Release to NTIS

1"^ Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. ^ 20402.

1^31 Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

191

15. Price

$7.00

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List of Publications 72 - 1962-1981

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Washington, DC 20234

Dear Mrs. Cohen:

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