AlllOl 110515

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( PUBLICATIONS

NBSIR 82-2458

Benefits and Costs of Improved

Measurements: The Case of

Integrated-Circuit Photomask

Linewidths

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Washington, DC 20234

March 1982

Issued May 1 982

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Prepared for: Planning Office

National Bureau of Standards

Washington, DC 20234
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ABSTRACT

Accurate dimensional measurements are vital to quality control in the semiconductor industry. This paper introduces an approach to estimating the dollar

cost-savings from improving measurements of integrated-circuit photomask linewidths. The approach is illustrated with a case study of a hypothetical semiconductor device manufacturer who uses a Standard Reference Material (SRM)

developed at the National Bureau of Standards to calibrate optical microscopes.

Benefits of investing in improved photomask linewidth measurements include

reducing disputes between mask maker and mask customer, reducing waste of good

photomasks, and increasing device yields. For the hypothetical manufacturer

described in the study, these benefits were much greater than costs of

implementing the new measurement procedures.

While the model is tailored to photomask linewidth measurements, many of its

concepts can be applied to other types of measurements.

iii
PREFACE

This research project was funded by the NBS Planning Office as part of its

efforts to develop and demonstrate methods of evaluating economic impacts of

NBS research. The topic chosen for study was NBS's research aimed at improving

the measurement of linewidths on integrated-circuit photomasks used in the

semiconductor industry.

This report is not intended to convey engineering information to those who make

linewidth measurements in industry . For scientific and engineering information

about linewidth measurements, see the publications by NBS scientists which are listed in appendix C to this report.

This study was based on published information, discussions with NBS scientists,

and discussions with 12 integrated circuit manufacturers, four independent

photomask producers, five measurement equipment and standards suppliers, six

consultants, and one manufacturer of photolithography equipment. Most data for

this study were collected during 1980.

The author is grateful for the information provided by individuals at various

semiconductor industry firms. In addition, the author is indebted to John Jerke,

Diana Nyyssonen, and Robert Scace of the National Bureau of Standards, Center for

Electronics and Electrical Engineering who provided valuable insight into many

aspects of linewidth measurements and helpful comments on the report draft.

Thanks are due to Steve Weber, Harold Marshall, Greg Tassey, and Pat Donvito

of NBS for their constructive criticism of the economic methodology used, and

to Carroll Croarkin of the NBS Center for Applied Mathematics for her helpful

comments. Credit is also due Mike Usle, now a graduate student at Brigham

Young University, who conducted most of the research for the chapter concerning

NBS research costs, and to Barbara Lippiatt, now a graduate student at American

University, who conducted a search of the economics and technical literature.

iv
TABLE OF CONTENTS

Page

EXECUTIVE SUMMARY vii

1. INTRODUCTION 1 2. MASK ACCEPTANCE MODEL 6

2.1 Costs of Measurement-Related Problems (Cl, C2 , C3) 6

2.2 Probabilities of Measurement-Related Problems (P 2 through P 5 ) 10

2.3 Implementation Costs (C4) 16

2.4 Discounting and Time Related Variables (UPW,SPW,r ,t,T,S) .... 18

2.5 Effects if NBS had not Done Research (B*, C4*) 18

Appendix 2A Assumptions 20

Appendix 2B Determining Alj^ and A2j^ 23

3. AN APPLICATION OF THE MASK ACCEPTANCE MODEL 27

3.1 Selection of the Base Case 27

3.2 Costs of Measurement-Related Problems (Cl, C2, C3) 30

3*3 Systematic Error (M and N) 31

3.4 Discounting and Time Related Variables (UPW,SPW,r ,t ,T,s

,

u,(i)) 33

3.5 Implementation Costs (C4) 34

3.6 Calculating the Cost Savings (B) 36

3.7 Sensitivity Analysis 41

4. NBS TECHNOLOGY: DIFFUSION AND QUALITATIVE IMPACTS 48

4.1 Transfer of NBS Results to Industry 48

4.2 Secondary Dissemination of NBS Research Results 49

4.3 Other Effects of NBS Linewidth Measurement Research 51

5. RESEARCH COSTS 54

6 . CONCLUSIONS 57

APPENDICES

A. GLOSSARY A-1

B. DISCOUNTING TECHNIQUES B-1

C. PUBLICATIONS RELATED TO NBS LINEWIDTH MEASUREMENT RESEARCH ... C-1

D. SELECTED BIBLIOGRAPHY D-1

V
LIST OF TABLES

Page

Table 2 . 1 Summary of Equations 7 Table 2.2 Formulas for Limits of Integration in Calculating Path

Probabilities 17

Table 2.3 Assumptions 20

Table 3.1 Values Used in the Model—Base Case 28

Table 3.2 Mask. Shop Implementation Costs 35

Table 3.3 Calculating Path Probabilities 37

Table 3.4 Gross Undiscounted Savings (Base Case) 40

Table 3.5 Values Used in Sensitivity Analysis of Implementation Costs .. 47

Table 4.1 Companies Participating in Interlab Tests, Attending

Seminars, or Ordering SRM 50

Table 5.1 NBS Research Expenditures 55

Table 6.1 Summary of Steps in the Analysis 60

Table B.l Discounting Factors for 10 Percent Discount Rate B-4

LIST OF FIGURES

Page

Figure 1.1 NBS Optical Microscope Linewidth Measurement Standard

(SRM 474) 3

Figure 1.2 Flow of Linewidth-Measurement Technology 5

Figure 2.1 Possible Outcomes of Mask Acceptance Measurements 11

Figure 2.2 Two Possible Distributions of Masks with Respect to Line

Dimensions 14

Figure 2.3 Path Probabilities 15

Figure 2.4 Conditions for Various Paths 24

Figure 2.5 Path Probabilities with Al^ and A2j[ 26

Figure 3.1 Probabilities of Various Mask Measurement Outcomes 39

Figure 3.2 Sensitivity Analysis; Benefits Due to NBS 42

Figure 3.3 Sensitivity Analysis: Total Benefits 44

VI
EXECUTIVE SUMMARY

Purpose

The purpose of this report is to introduce a rigorous approach to estimating

the cost savings from improved measurements of narrow lines on photomasks.

The approach uses a model which is based on many simplifying assumptions,

listed in table 2.3 on page 20.

The Model

The simplified model predicts the cost savings per photomask for a hypothetical

company which uses the Standard Reference Material SRM 474 and related measurement procedures. The National Bureau of Standards developed SRM 474 for calibrating optical microscopes which measure linewidths on integrated circuit (IC)

photomasks

Errors in mask measurements lead to the following problems: (1) mask waste if

a good mask is rejected; (2) disputes if the mask buyer and mask seller disagree

about whether the mask is within specifications; and (3) IC yield loss and

related costs if a bad mask is accepted for use in IC production.

The probabilities and costs associated with these problems are calculated for a single mask. Probabilities and costs are recalculated to reflect a reduction

in measurement error resulting from a company calibrating its microscopes with

the SRM 474 and adopting procedures recommended by NBS.

Results

The model is illustrated for a hypothetical company which produces photomasks

and IC devices with approximately 3 micrometer-wide lines. For masks costing

$1,000, the company would save $179 per mask by Implementing NBS procedures in

1980. NBS is credited with $82 or about half of these savings. (It is assumed

that companies would eventually improve measurements without NBS.) For masks

costing $100 each, the company would save $15 per mask, of which NBS is credited

with $7. Implementation costs are less than $2 per mask.

These results apply only for the valvies assumed for the hypothetical company.

(These values are listed in table 3.1 on page 28.) A sensitivity analysis suggests that for other values (listed in figure 3.3 on page 44), actual benefits

could be considerably higher or lower than the ones reported above. Benefits were strongly positive for most sets of values used in the sensitivity analysis.

1 The linewidths of interest are 0.5 to 10 micrometers wide. Photomasks are the

patterned glass plates used in producing semiconductor integrated circuits

(ICs).

2 "Yield" is the percent of units which are not defective. Terms are defined in

the glossary in appendix A.

vii
Other effects

Several Important benefits of the NBS research were not quantified for this

report, although they are discussed qualitatively. These include improved

measurement repeatability, improved measurement of linewidths on wafers, the

design and production of IC devices with narrower lines. Improved field reliability of IC devices, and improvements in the design and selection of linewidth

measurement equipment.

Use of the method

The method described in this report can aid NBS planners or individual

companies in understanding how improved measurements lead to cost savings.

Economic analysis using models of this type may be useful to NBS when the

industry involved is relatively homogeneous and good market data are available; and when considerable resources can be committed to the benefit-cost

study, perhaps including participation by NBS scientists in the study.

Those using the model should be aware that it represents only the specific

situation described by the assumptions on page 20. Many of these assumptions

may require modification before applying the model to additional situations

involving linewidth or other types of measurements.

viii
1 . INTRODUCTION

Purpose

The purpose of this report is to Introduce a rigorous approach to estimating

the cost savings from improved measurement of narrow lines (0.5 to 10 micrometers wide) on photomasks. Photomasks are the patterned glass plates used in

producing semiconductor integrated circuits (ICs). The approach uses a model

which is based on many simplifying assumptions, listed in table 2.3 on page 20.

Researchers in the NBS Semiconductor Technology Program have developed Standard

Reference Materials (SRMs) and improved measurement methods for use in measuring linewidths on photomasks used in the semiconductor industry. This research

is considered by NBS to be particularly successful.! An economic analysis

appeared feasible because a list of possible users (people requesting

information) was available.

Technical Background

This study is concerned with the measurement of narrow lines on photomasks,

patterned glass plates used by the semiconductor industry in manufacturing

integrated circuit (IC) devices. The IC manufacturing process can be compared

to the printing of photographs, with the photomask acting as a transparency.

The lines on the photomask — so minute they can be seen only with a powerful

microscope — serve as patterns for producing ICs on silicon wafers. The

wafers are later broken into tiny chips which are built into computers, instruments, automobiles, calculators, watches, and numerous other products.

Linewidths on photomasks must be within specified dimensional tolerances for

the mask to be acceptable to the IC manufacturer. Mask manufacturers can consistently ship masks within these tolerances only if they can make very

accurate llnewidth measurements. Generally these measurements are made using

optical microscopes fitted with micrometer attachments of various types.

Consequences of erroneous measurements

The industry has encountered difficulties in making sufficiently accurate

photomask measurements, leading to four costly consequences:

! It was one of several semiconductor projects highlighted in the NBS 1978

Annual Report, and in 1980 two researchers involved received Commerce Department silver medals for their work. In budget size it is typical of NBS

semiconductor research projects.

2 For more information on ICs, see Scientific American , September 1977 issue;

U.S. Department of Commerce, Industry and Trade Administration, A Report on

the U.S. Semiconductor Industry (Washington, D.C.: U.S. Government Printing

Office, 1979); and Robert I. Scace, Semiconductor Technology for the NonTechnologist , NBSIR 81-2197, (Washington, D.C.: National Bureau of Standards,

1981).

1
1 . Bad masks are sometimes accepted for use in IC manufacturing. Using such

masks to expose wafers results in incorrect line dimensions on the wafers.^

Incorrect wafer line dimensions reduce IC yield, may reduce reliability of

outgoing devices, and lead to other costs in IC manufacturing .2 Devices

which are outside of specifications must be scrapped or, at best, sold at a lower price for less demanding uses.

2. Good masks are sometimes rejected and scrapped, resulting in the cost of

remaking those masks.

3. Measurement discrepancies have led to numerous and sometimes costly

disputes between the mask manufacturer and the IC manufacturer concerning

whether masks shipped are within specified dimensional tolerances.

4. Inaccurate linewidth measurements slow the move toward production of

devices with smaller linewidths, thus deferring the benefits of these

improved products.

Scope

In response to the problems described above, NBS began research in 1973 aimed

at developing standards and procedures for accurate linewidth measurements on

IC photomasks. This research has resulted in: (1) improved industry measurements of linewidths on photomasks using existing measurement equipment; (2)

design changes in existing types of commercial linewidth measurement equipment

and development of new types of measurement equipment; (3) improved selection

of linewidth measurement equipment by mask houses and IC manufacturers; (4)

improved adjustment and characterization of equipment for producing photomasks

and IC devices; (5) measurement improvements in industries other than the semiconductor Industry; and (6) scientific Information useful in developing

improved methods of measuring linewidths on wafers.^

Resources were not available to quantify all these benefits. Therefore, only

the potential cost savings from Improved photomask measurements using existing

measurement equipment will be examined quantitatively in this report. The

NBS outputs responsible for this result are the Standard Reference Materials

(SRMs) 474 and 475 and related measurement procedures. These SRMs are used for

calibrating optical microscopes to measure chromium-on-glass photomasks. The

basic measurement pattern on the SRM 474 is shown in figure 1.1. The first

SRM 474 was sold to an industrial user in May 1980.

^ For definitions of engineering and economics terms, see the glossary in

appendix A.

2 For example, personnel from one company stated that measurement discrepancies

between their mask shop and IC production groups resulted in incorrect mask

linewidths and IC yield problems. They believe that standardizing linewidth

measurements between groups significantly improved yields for some IC

products.

^ These benefits were described by NBS scientists and industry personnel.

2
Figure 1.1 NBS Optical Microscope Linewidth Measurement Standard (SRM 474)

(A view of the basic measurement pattern)

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National Bureau of Standards, Standard Reference Material 474:

Optical Microscope Linewidth Measurement Standard (document

accompanying the SRM 474 artifact, June 9, 1980).

3
How NBS Results Reach Industry

The NBS linewidth measurement technology reaches industrial users through the

paths described in figure 1.2.

A handful of companies supply linewidth-measurement systems (typically, optical

microscopes fitted with a micrometer attachment). These companies transmit

NBS technology to their customers through equipment design, instruction manuals,

and personal contact. Some linewidth-measurement equipment manufacturers also

sell calibration standards traceable to the SRM 474. In addition, there is at

least one independent supplier of linewidth-measurement calibration standards

traceable to the SRM 474.

The two basic sources of IC masks are independent producers and in-house mask

shops in IC companies. These groups often provide standards, measurement procedures, and calibration services for their customers, thereby often transmitting NBS measurement technology.

IC producers also obtain NBS photomask-measurement technology either directly

from NBS or indirectly through other companies. In some cases they may transmit NBS technology to measurement equipment manufacturers by demanding features

recommended by NBS.

The equipment manufacturers and standards suppliers appear to be the primary

"leverage" points for disseminating NBS technology. By reaching the small number of companies in these groups, NBS can disseminate its technology to a large number of other organizations. Mask houses and inhouse mask shops are also leverage points for transmitting NBS technology.

In the future, standards-writing organizations (particularly, the American

Society for Testing and Materials) will also transmit NBS linewidth measurement technology through publication of standards documents based on the NBS

research.

The next two chapters examine the possible cost savings from using NBS

linewidth measurement technology.

4
Figure 1.2 Flow of Linewldth-Measurement Technology!

! In this figure, "standards" refers to photomask-like artifacts, not to

standards documents. In the future, standards-writing organizations

(particularly, the American Society for Testing and Materials) will also

transmit NBS linewidth measurement technology through publication of

standards documents based on the NBS research.

5
2. MASK ACCEPTANCE MODEL

This chapter describes a model for estimating the per-mask cost savings from

adopting improved methods of measuring linewidths on photomasks. The model

will be used in the next chapter to calculate cost savings for specified values

of model parameters.

The model is based on the assumptions listed and discussed in table 2.3 on page

20. It was not feasible within the available resources to explore a variety of

cases; thus, some assumptions were made to limit the scope of the analysis.

Many assumptions were made to simplify the analysis and are not strictly true,

although they may be good approximations for some situations. The assumptions

were made based on the author's judgment following discussions with NBS

scientists and industry personnel,

A major assumption used in this model is that the only error in measuring

linewidths is a systematic bias in measurements; i.e., there are no random

errors (measurements are perfectly consistent or repeatable) . ^ However, the

model could be modified to allow for random error as well.

Overview

The approach is to measure cost savings to the mask shop (or independent mask

producer) and the IC producer from measurement improvements which reduce the

frequency of buyer-seller disputes, reduce waste of good masks, and reduce use

of "bad" masks in IC production. Improved measurements can reduce both the

costs and frequency of these problems.

To find net benefits per mask, the cost of implementing improved measurement

procedures is subtracted from the cost savings,^ The equations used in the

model are summarized in table 2.1. Terms in the equations are discussed later

in this chapter.

2.1 COSTS OF MEASUREMENT-RELATED PROBLEMS (Cl, C2 , C3)

Erroneous measurements lead to three types of costs which can be quantified

using this model. The first is Cl, the cost of remaking a mask.

1 See the glossary in appendix A for definitions of measurement terms. For a discussion of measurement errors, see Ku, Harry, "Statistical Concepts in

Metrology," in Handbook of Industrial Metrology , American Society of Tool and

Manufacturing Engineers (New York: Prentice-Hall, 1967), pp. 20-50.

2 Net benefits per mask are based on the number of masks which are good with

respect to non-linewidth aspects (and may or may not be good with respect to

linewidths). If the number of masks originally manufactured or the number

shipped to customers were used instead, the per-mask benefits would be

different

6
Table 2.1 Summary of Equations^

Number

( 1 ) B = (C'-C")

Equation

UPW(t-s)

(SPWg) - C4

See Report

Section

2.4

( 2 ) B* = (C'-C") -^-*2 (SPW*) - C4*

T s 2.5

( 3 ) C'= C1'(P2'+P3'+P5'+P6')

+C2’(P2'+P5')+ C3'(P4')

B

B*

C

Definitions

= Total net benefits

per mask with NBS

= Total net benefits

per mask without NBS

= Per-mask cost of

measurement error (before)^

C" = Per-mask cost of

measurement error (after)^

UPW(t_g) = Uniform Present Worth

discounting factor

for time period "t-s"

t = life of measurement

procedures (number of

years before obsolescence) as of base

year (e.g. 1980)

s = number of years after

base year that the

procedures are adopted

at a particular company, with NBS ("t-s"

Is the number of years

the procedures are useful at a particular

company)

,

s* = number of years after

base year that the

procedures are adopted

at a particular company, without NBS

T = analysis period

SPWg = Single Present Worth

discounting factor for

time period "s"

C4 = per-mask cost of Implementing new procedures

(with NBS)

C4* = per-mask cost of Implementing new procedures

(without NBS)

2.1 Cl’ = Mask remake cost (before)

and C2' = Dispute cost (before)

2.2 C3' = Yield loss and related

costs (before)

7
Table 2.1 Summary of Equations^ (continued)

Equation Section Definitions

(4) C"= C1”(P2"+P3"+P5"+P6")

+C2'’(P2’’+P5") + C3"(P4")

A2i’

(5)

Pj^* = J f(x)dx

All'

A2i”

( 6 ) P^" = / f(x)dx

All"

(7)

C4 = ^

{ C5 + C 6 UPW. . kT (b-s)

j

+ Z C7± SPWu(i) } SPWg

i=l

2.1 P2

* = Probability of good mask

and

2.2

P3

’

rejected by IC mfr., with

dispute (before)^

Prob. of good mask

P4

'

rejected by mask shop

(before)^

Prob. of bad mask

P 5

’ accepted (before)^

Prob. of bad mask

Pe’

accepted by mask shop/

rej . by IC mfr. /dispute

(before)^

Prob. of bad mask

Cl"

rejected (before

through C3" and P2" through P6

"

Pi' s

have similar definitions

for after improving measurements

Probabilities of paths

2.2

f(x)

described in figure 2.1

(before)

Probability density funcAli’

tion of a mask with

respect to linewldths

Lower and upper limits of

and •H <CM range in which a mask

2.2

Pi’’> Ali"

linewidth must be for

path "i" in figure 2.1 to occur (before)

and A2 i" have similar

k

definitions for after

improving measurements

Number of masks measured

2.3

C5

annually at one company

(kT is the total number

measured over the analysis period)

Initial cost of Improving

C6 — measurements

Equal annual costs of

improving measurements

8
Table 2.1 Sunrmary of Equations^ (continued)

Equation Section Definitions

( 8 ) C4* { C5 + C6 UPW

kT '

+ Z C7*^ } SPWg

i=l

(9) A B = B - B*

2.5

2.5

j = Number of "other” cost

items

C7i = Other costs of improving

measurements

u(i) = Number of years before

cost item C7*^ occurs u(i)* = Number of years before

cost item C7*j^ occurs.

If u(i)* = s then

C7*i = 0.

A B = Benefits credited to NBS

research

B* = Benefits per mask that

would occur even without

NBS research

^ Variables with a prime (') are before adopting improved measurement procedures;

variables with a double prime (") are after adopting improved procedures. Variables

with an asterisk * are for the hypothetical situation in which NBS did not conduct

its measurement research.

^ See figure 2.1.

9
The second, C2, is the cost of resolving measurement disagreements between the

IC manufacturer and the mask shop. Costs of resolving disputes may include

remeasurement by both parties at their respective sites, travel to the other

site to remeasure masks, and management time.

The third, C3, is the cost if a bad mask is used in IC production. This is the

most difficult cost to estimate. The average cost of using a bad mask is used

rather than the catastrophic cost that might occasionally occur.

There are at least four sources of cost C3: (1) loss of IC device yield. The

full value of the rejected devices may be lost, or substandard devices may be

sold for less demanding applications at a lower price; (2) the cost of identifying the source of IC yield loss and correcting the problem. If the cause

is not correctly traced, much engineering time may be lost trying to improve

yields by adjusting other aspects of the manufacturing process; (3) there may

be costs associated with field failure of IC devices with incorrect linewldths^; and (4) if IC yield losses are traced to the bad mask, then the mask

itself will need to be replaced.

Improved measurements may reduce the costs, C2 and C3, that result ^ a measurement-related problem occurs. As the next section describes, improved

measurements may also reduce the probabilities that Cl, C2, and C3 will occur.

2.2 PROBABILITIES OF MEASUREMENT-RELATED PROBLEMS (^2 THROUGH ^6)

This section explains how to estimate the probabilities ?2 through Pg that

measurement-related problems will occur.

Decision tree

Figure 2.1 shows the different possible events involving mask production and

measurement. For example, consider the path marked by the heavy line in figure

2.1. First (column A), a mask is manufactured which is good with respect to

all non-linewidth characteristics. It may or may not be good with respect to

linewidths. For the path marked by the heavy line, the mask is assumed to be

good with respect to linewidths (column B). That is, its use will not lead to

yield losses due to faulty mask line dimensions. (For certain other paths in

figure 2.1, the mask is bad with respect to linewidths.) The entry in column B

shows whether a mask is actually good or bad. Entries in later columns show

whether the mask is thought to be good or bad as a result of measurements.

1 Many companies responding to a survey conducted by Charles River Associates

for the National Bureau of Standards reported that better llnewidth measurements led to Improved product reliability (in addition to reducing yield loss).

Charles River Associates, Productivity Impacts of NBS R&D; A Case Study of

the Semiconductor Technology Program , Summary Volume, June 1981.

2 Replacing a bad mask creates a cost, although presumably it is less costly

than the alternative of continuing to use the bad mask.

10
Figure 2.1 Possible Outcomes of Mask Acceptance Measurements^

Mask Manufactured

(A)

Is mask

good/line

widths^

(B)

Mask

shop

(C)

IC

mfr.

(D)

ProbaL- Cost of

Outcome bility outcome

Good

Mask

Accepted

Pi’

Pi"

or No cost^

Good Mask P2' or Mask remake—Cl'

Rejected,

Dispute

P2" or Cl"

Dispute—C2' or C2"

Good Mask P3

' or Mask remake—Cl'

Rejected P3" or Cl"

Bad Mask P4

’ or Yield loss and

Accepted P4" related costsC3' or C3"

Dispute

,

P5' or Dispute cost —C2

Bad Mask

Rejected

P5" or C2"

Mask remake—Cl' or Cl"

Bad Mask Pe’ or Mask remake—Cl'

Rejected Pe" or Cl"

^ Prime (') refers to before adopting improved measurements; probabilities

and costs must be recalculated after adopting improved measurements (").

^ Mask is assumed to be good with respect to defects, registration, and other

non-linewldth specifications.

c Is mask good with respect to linewidth specifications?

^ Cost of path 1 is the baseline for measuring other costs and so equals zero.

11
Continuing to follow the path marked by the heavy line in figure 2.1, the mask

is measured by the mask shop and found to be acceptable for shipment to the IC

manufacturer (column C) . At the IC manufacturer, the mask is erroneously measured as being outside specifications and is rejected (column D). The returned

mask is remeasured by both the mask manufacturer and the IC manufacturer, and

rejected again by the IC manufacturer. This path occurs with a probability ?2

for a single mask.

The last column in figure 2.1 shows the costs that arise if path "i” occurs.

For example, with the path "good/accept/reject" (path 2), a dispute occurs with

cost C2 and the mask must be remade at cost Cl.l Thus, the cost of the

"good/accept/reject path" is Cl + C2.2

Calculating path probabilities

The path probabilities P2 through P5 must be determined in order to find the

cost of measurement error.

Often, the probabilities of paths in decision trees are determined by

calculating the probabilities of each step in the path and then multiplying

along the path. However, in this case, calculating probabilities of each step

would be complicated. A simpler approach is used here. It involves identifying the range of actual mask linewidths for which all steps in a path can occur,

and then figuring out the likelihood that a mask will have linewidths in this

range, based on knowledge of the mask production process.

For example, to calculate P2 , first we must determine the range of mask

linewidths (from AI 2 to A22 ) for which a mask will be good, accepted by the

mask manufacturer, and rejected by the IC manufacturer. Methods for determining the limits Al^ and A2 ^ for each path in figure 2.1 are described in

appendix 2B to this chapter.

Probability of linewidths between Alj[ and A2^

To determine the probability that mask linewidths will be in the range Al^ to

A2 ^, we must estimate (or assume) the distribution of actual mask linewidths,

after eliminating masks which have non-linewidth defects. By normalizing the

^ We assume disputes are won by the IC manufacturer. See the assumptions in

table 2.3.

3 The baseline against which costs of various outcomes are determined is the

situation in which a good mask is accepted (path 1). By definition, the

costs of path 1 are zero.

3 A path probability is the probability that the sequences of events described

by the path will occur.

12
curve so that the area under the curve equals one, the curve is converted to a probability density function. ^ Figure 2.2 shows two possible probability density functions which reflect the distribution of masks with respect to actual

linewidths.

The reader should keep two points in mind: ( 1 ) these curves are based on the

distribution of actual linewidths, not the distribution of measurements; and

(2) they are based on the distribution of linewidths among masks, not within a single mask. (Linewidths are assumed to be uniform within a mask.) 2

The probability that a mask will have linewidths between Al^ and A2 j^ (i.e., the

probability of path "i") is the area under the curve between Al^ and A2j^, as shown in appendix 2 A-figure 2 . 3 . The mathematical expression for this is:

A2i

= / f(x) dx. (10)

All

where:

= the probability of a path described in figure 2.1,

Ali and A2^ = lower and upper limits of range in which mask linewidths

must lie for path "i" in figure 2.1 to occur, and

f(x) = probability density function of a mask with respect to linewidths.

By varying "i" from two to six, the formula gives probabilities P2 through P5

(It is not necessary to compute the zero-cost path probability, Pi«)

For example, the probability of good/accept/reject, P2, is given by the formula

A2z

P2 = / f(x) dx. (11)

AI2

The area P2 is shown in figure 2 . 3 . The curve in figure 2.3 is drawn for the

situation where the IC producer's bias, N, is greater than the mask shop's bias

M, and both M and N are positive.

^ For an explanation of the concept of probability density functions, refer to

any good statistics textbook, such as Mills, Frederick C., Statistical

Methods (New York: Holt, Rinehart and Winston, various editions).

^ See table 2.3 with assumptions.

13
Figure 2.2

Two Possible Distributions of Masks with Respect to Line Dimensions^

Probability

Density Function

of Mask

Linewidths

f(x)

Normal

• • •

• •

/

• •

• // •

• /// •

• /// • A] ,• A2 4 X

(linewidth)

f(x)

I /// I probability a mask will have line dimensions

between Alj^ and A2^

^ f (x) is based on the distribution of actual linewidths among masks, not

measured linewidths or linewidths on a single mask.

14
Figure 2.3 Path Probabilities where N>M>0^

f(x)

bad/

reject

I . ///

LJIUbJL

• /.

• //. <-—good/

• ////.

• /////.

• ///////.» bad/ , good/accept /////// /.

accept/ Pi / / ///. <- accept / / ?2 / /////.

+ //// / / / //

.// / /////// / P3 //

// P4 / /////// / //

// // //////./ ///////-

/ . <—bad/reject

P6 • miuu

AI5 A25=Al4 A24=A1 i A2i=Al2 A22=Al3 A23=Al6* A2g*

specified tolerances (good masks)

W1 W2

P 3 (bad/accept/reject) = 0

f(x) = probability density function for a mask with respect to linewidths

^ This example assumes that the IC producer's measurement bias, N, is greater

than the mask shop's measurement bias, M, and that both are positive.

15
In this example, P5 is represented by two separate areas, so that the formula

is;

A26 A2*e

P5 = / f(x)dx + / f(x)dx. ( 12 ) Ale A1*5

Table 2.2 gives formulas for computing Al^ and A2j, given the measurement

biases of the mask shop and IC producer, and the distribution of mask linewidths. The method for computing these limits is explained in appendix 2B to

this chapter.

Improving measurement methods affects the probabilities Pj through P5 and

involves a movement between paths. For example, with better measurements

there would be more good masks accepted (an increase in Pj) and fewer good

masks rejected by the IC manufacturer (a decrease in P2 )»

Computing Costs of Measurement Errors

To find "before" and "after" costs of measurement error, ^ the values for P2

' through P^' and P2

" through Pg" and the values for Cl’ through C3’ and Cl"

through C3" are substituted into equations (3) and (4) in table 2.1. Other

terms in equation 1 are discussed in the following sections.

2.3 IMPLEMENTATION COSTS (C4)

The costs of implementing new measurement procedures are found by adding up

costs that have been discounted to their present values, according to

equation 7 in table 2.1.

The factor "two" is used in equation 7 because the new procedures must be

implemented by both the mask shop and IC producer, doubling the cost. It is

divided by "k" (the number of masks measured per year) and "T" (the number of

years in the analysis period) to put costs on a per-mask basis.

Equal annual future costs are discounted to their present value using a Uniform

Present Worth (UPW) discounting factor. One-time future costs are discounted

using Single Present Worth (SPW) factors. Discounting is discussed in

appendix B. Individual cost items are discussed below.

Startup costs (C5)

Management time is needed to become familiar with improved procedures, to

determine what changes are needed to adopt them, and to coordinate implementation, including conducting any needed training sessions. Training costs for

operators, technicians and engineers are estimated using number of hours

and costs per hour.

^ C and C" in equation 1 of table 2.2.

16
Path

probabilities

are

calculated

using

the

formula

Pi= /

f(x)dx

where

Ali

and

A2i

have

the

following

values 8 2 II

II •KO VO o 2 CM <

•H 1 f

<3 CM 2 2 CM CM 2

TJ <! <3

O 2 1 d II II CM

CO •H 2 o 2 o < CM

PM IIVO

II •JC vO

V 2 2 CM 2 2 <3 <3 2 8 •H 2 1 II o CM 1 •JC vO V CM 2 CM 2 2 2 2 II <3 vO

TO CM CM d <3 O <!

cO 2 II II 2 CM

•H 1 -<J- 1 o 2 o CM PM II II <3 2 2 <! 2 vO ^C vO s C <38 2 2 2 2 II •H 1 1 1 II •JC vO

CM CM vO CM

<3 2 2 2 in CM <3 o CM <3 V <3 o 2 II II 2 V UO m 1 2 2 r—

PM CM

•H 1 <3 o 2 r-H CM II II <3 2 2 2 vO * VO

<3 <3 2 2 1 8

T-C 1 II CM CvJ CM 2 •JC vO o <3 2 2 2 lO II CM

CM vO <3 2 <3 O CM

II II <3 2 m in CM

•H 2 2 2 PM o 2 1 1 1 <3 II II <3 CM CM vO 1C vO 2 2 2

<3 <3

rW 8 2 2 2 2 II •H 1 1 1 II •K vO

CM CM CM vO CM

O <3 2 2 2 CM < V CM <3 2 CM 2 y < o 1 2 II II 2 CM

•H Csl CM 1 o 2

PM CM CM II II <3 <3 2 2 2 vO •1C vO

<3 <3 2 •H 1 CM 2 r-H 8

<3 1 2 II CM CM II * vO o CM O 2 2 2 VO CM

<3 II CM •< 2 II CM <3 CM PM 2 2 2 CM t4 <3 1 1 o 2

CM l> II <3 2 2 2 VO •1C vO ^ ! <c <3 Uo 2 CM CM CM

f-i 1 Ml 2 2 2 2 2 2 4J CM J-i O 1 1 /^ 1 nv

cO CM 2 O CM

X CM CM

X CM MlX -1 2 , V 2 , 2 2 2 2 . 2 O 0

bOV

X 2 2 V 1 Ml

VV MlV Ml

(UX

V 1 1 X CM

O

X

X

O

X 2 2 0 2 2

iJ

V 2 -H CM 2 2 V

V

y 1 1 1 d 1 2 2 1-H V /\ 2 2 CM -4 CM • • •H 2 V 2 X X 2 1 1 2 1 2 2 2 2 2

CO 2 X

X

V —1V —1

V

V

V

n

d 4-1X 2 2 X 2 X

XX

X

X o o

•H TO TJ 4J CO o 4-) 4-J O 4-1 4J

u TO 4J 4J TJ 4J

•H 4J o cx o O o CO CM Cu CO PX CJ CO CJ TO •H o (U (U o 0) PO OJ <V 03 CU CU PQ OJ d E 1 o •r-) 1 •r-) 1 u u 1 u •rn *1“) o •H cs: o (U CO OJ Ml- O u in o CU VO CU o PM cO Ml PM Ml PM (0 cd PM CO Ml PM

UC • B 3

<u I • 3 S , <U w V >

ta

— o 0) s ^ S 

u x) c

(V c e P rt 3 3 rH

4J •>

O o —< o

cC 12

l4-( I 4J 3 CM W C S. J-I CO V "H e—M. u— <u M •> JC

-H 4-1 -a 13 c I c

CO CM av

X o s

x: I c

CO ^ o

CO 4J

CO CO S ^4J

ID JC <U *H

4J

a «-i 3 -tJ 0) CO CO

(-1 CO 0)

CO CO 2; CO <u

CO -C

-a iH

CO

a >% U JD 5 o

cw TOC

CO (U CO O CO

OJ 0) -H a.,c CM

CO t-i <;V ^ X

4J • V »-H 1-4 •H • *-H 6 CM <3

<v3 <U

C

•H iH

O

H ^ *H

CO 4J T3 -W -H C TO 3 C d O -H O

rO

V

T3

M 0) (U

CU

C J3 CL>H 4J CXU-i 3 0) TO JO T3C 0) TO

CO

M

CO

(U CO ^ I—

o o

<H tJ3a

d

d TO ^ CO 4J 0)

>-l >-l (U <U CO

j:: CO 4-1 *H O CM

CM <;dd

•HE

<u

4-) • TO TJ CO d d 0) CO

cO CO

*-H «H

CO

17
Improving measurement procedures may involve acquiring new measurement systems

or retrofitting existing systems. Time spent selecting equipment should be

included here if it was not included under management time. The cost of buying,

or manufacturing and measuring, calibration standards is also included. If

standards must be replaced during the analysis period "T," the replacement

cost is included.

If the calibration process uses a computer program, its development time is

included as a startup cost. The cost of using the program is included under

ongoing costs, discussed below.

Time needed to adjust and calibrate measurement systems—in excess of what

was needed under the old procedures —is included.

Ongoing costs (C6 and C7)

The cost of any additional time needed to periodically check, adjust, and

calibrate equipment is included. Any Increase or decrease in the time to make

routine measurements is also included,

2,4 DISCOUNTING AND TIME-RELATED VARIABLES (UPW, SPW, r, t, T, s)

Two discounting factors are used in the net benefits equation (1) in table 2,1

to adjust for the time value of money.

The factor UPW(j-_g)/T is a Uniform Present Worth factor divided by the analysis

period, T, It adjusts for the fact that benefits occur over a period of time

and puts them on a per-mask basis. This is explained further in appendix B,

The Single Present Worth factor SPWg adjusts for the fact that improved

measurement procedures are implemented in a future year,

"r" is the real discount rate, used in selecting UPW and SPW factors, "s" is

the number of years after the base year (e.g., 1980) that the procedures are implemented. It is also used in selecting UPW and SPW factors, "t" is the

assumed life of the measurement procedures at the company being analyzed. It

is used in selecting UPW factors.

Discounting is discussed further in appendix B,

2,5 EFFECTS IF NBS HAD NOT DONE RESEARCH ( B* , C4*)

The costs savings in equation (1) and the costs in equation (7) in table 2,1 were calculated assuming that, without the NBS technology, firms would have

made no progress toward improving linewidth measurements. However, this is

unrealistic. Even without NBS, firms will improve their measurement methods.

Therefore, to avoid exaggerating the value of NBS’s contribution, we need to

compare what does happen with v;hat probably would have happened if NBS had not

conducted its research.

18
It seems likely that NBS work affected both the nature and timing of linewidth

measurement advances. However, to simplify the analysis, this model considers

only NBS's effect on timing of advances.

The values used in calculating net benefits reflect the situation that would

prevail if NBS had not conducted its research. This model assumes that, without NBS, companies would adopt measurement Improvements later so that "s" is

changed to "s*." We also assume that costs of implementing measurement improvements are essentially the same except that they are incurred later. Finally,

we assume that the technology becomes obsolete in a certain year regardless of

whether it is from NBS or another source, so that the value for "t" does not

change

The net cost savings, B-B* , are the cost savings with NBS less the cost savings

that would have been realized even without NBS, Both types of cost savings are averaged over the number of masks produced during the analysis period, T,

1 This approach was used by Marshall and Ruegg in estimating benefits of NBS

efforts to develop a new type of roofing shingle. Marshall, Harold and

> Rosalie, Efficient Allocation of Research Funds; Economic Evaluation

Methods with Case Studies in Building Technology , National Bureau of Standards Special Publication 558 (Washington, D.C.: U.S. Government Printing

Office, 1979), p. 20.

19
APPENDIX 2A: ASSUMPTIONS

Table 2.3 Assumptions

Assumption Discussion

There Is an unknovm measurement

difference between mask buyer

and mask supplier.

Mask design and specifications

are not changed as a result of

Improved measurements.

The specifications state that

all lines must fall between

certain limits. Masks measured

as being outside these specs are rejected by whoever Is doing the

measuring; masks measured as being Inside are accepted.

Masks measured are used In

IC production.

Any delays In mask delivery

due to measurement error do not

Increase costs.

The measurement differences

between mask buyer and mask

supplier are stable.

Many suppliers try to keep track of measurement discrepancies with customers

and adjust mask dimensions accordingly.

But even for these companies, measurement

discrepancies with customers are probably

unknown at least some of the time. If

untrue, the assumption may overstate

benefits of Improved measurements.

Actually, Improved ability to measure

frequently leads to a further shrinking

of circuits, resulting In higher performance

and/or lower cost devices. If untrue, this

assumption may significantly understate

economic benefits of improved measurements.

In fact, the mask shop may give the benefit

of the doubt to the IC manufacturer on marginal masks (or vice versa). Also, the

mask shop may purposely build in a margin for error by rejecting masks barely within the

specifications. Finally, It is possible that

people sometimes bias their measurements so

as to get the "right" number.

A small percentage of masks are used to make

other masks, so are not used directly in

IC production.

The startup of a new wafer fabrication

process might conceivably be delayed if

a needed mask is not available on time.

This assumption may sometimes understate

the benefits from Improved measurements.

Many measurement systems "drift" from

day to day so that the difference from

other firms will change over time.

20
Table 2.3 Assumptions C continued)

Assumption Discussion

There Is no random error. Measurements are perfectly

repeatable. (The standard

deviation a of the measurement distribution Is zero.)

Some spread of measurements within an organization Is likely, and this spread

may be significant. This assumption probably understates the benefits of Improved

measurement procedures, since NBS methods

are designed to reduce random error.

Measurement bias Is the same

for all mask shop measurement

systems.

The bias typically varies between production

and quality control groups In the mask shop,

whether they are using similar or different

measurement systems.

Any deviation of actual

llnewldths from specifications

Is uniform across the mask.

The amount of deviation of actual dimensions

from specified dimensions actually may vary

across a mask. The wlthln-mask variation In

this deviation may be significant at some llnewldths, but Is thought to be Insignificant at the llnewldth target values (3 micro

meters) used In chapter 3 In applying the

present model.

Masks cause yield losses If and

only If llnewldths are outside

specified tolerances. Masks

Inside this range never cause yield losses due to line dimensions.

Actually, some masks outside of specifications may be completely adequate for IC

production, and some masks within

specifications may lead to yield losses,

depending on other factors In the IC

manufacturing process.

Disputes are always won by the

IC manufacturer.

More likely, disputes are sometimes won

by one party and sometimes by another.

Lines measured are of one polarity (all clear or all

opaque)

Masks always have both clear and opaque

lines, but for some devices dimensions

may be critical only for clear, or only

for opaque, lines.

Mask Inspection and measurement

for features other than line

dimensions Is 100 percent

accurate.

Actually, some error Is likely to exist

In non-llnewldth-related aspects of

Inspection and measurement.

No masks are rejected for nonllnewldth defects by the IC

producer

Actually, some masks will be rejected

for other reasons, such as pinholes or ragged line edges.

21
Table 2.3 Assumptions (continued)

Assumption Discussion

There are no costs to shipping

masks

If NBS had not conducted its

research, companies would have

obtained the same measurement

technology later from other

sources

Costs of implementing the hypothetical non-NBS technology would

be the same, but incurred later,

as costs for implementing NBS

technology.

NBS and non-NBS technology would

become obsolete in the same year.

The fact that such costs exist introduces a very minor error into the

model

Most likely, measurement technology

acquired from sources other than

NBS would be different in nature as well as in timing from NBS technology.

This is likely to be true only if

the two types of technology are

the same (see preceding assumption).

This is likely to be true only if

the two types of technology are

the same (see preceding assumptions).

22
APPENDIX 2B: DETERMINING All AND A2i

This appendix explains how the limits Alj^ and A2^ are selected for calculating

the probabilities of the paths described in section 2.2. The reader will

recall that Pj^ is the probability that all conditions describing path "i” in

figure 2.4 will hold, i.e., it is the probability the mask will have line

dimensions between Ali and A2i where All and A2i are determined by the particular path being studied. P^ is calculated from the expression

A2i

P^ = / f(x)dx, (13)

Ali

where f(x) is the probability density function of masks with respect to line

dimensions. (Examples of f(x) are shown in figure 2.2.)

To find the limits Al^ and A2i, first we determine the conditions for each step

in a path shown in figure 2.4 (similar to figure 2.1) to take place. For

example, consider path 2, marked by the heavy line in figure 2.4.

Example for path 2

Column B; Conditions for mask to be "good." Let "x" be the actual mask

linewidth, assumed to be the same for all lines on a mask. By assumption,

masks are good only if their lines are within specified dimensional tolerances

W1 and W2. Thus, a mask will be good if WKx^W2 and the mask will be bad if

x<Wl or x>W2. For path 2, the mask is good so that Wl^x^W2 is written in

column B in figure 2.4.

Column C; Conditions for acceptance by the mask shop . Let "y" be the line

dimension as measured by the mask shop. This model assumes that the mask shop

will accept masks for shipment to its customers if and only if the linewidths

are measured as being within specifications. Thus, the mask is accepted by the

mask shop if WK y<W2. The mask is rejected if y<Wl or y>W2. But since y

= x + M, where M is the mask shop’s measurement bias, the acceptance condition can

be rewritten: WKx+M ^ W2, or Wl-M^x^W2-M. The mask will be rejected if x<Wl-M

or x>W2-M. For path 2, the mask is accepted by the mask shop, so that Wl-M<x^

W2-M is written in column C.

Column D: Conditions for rejection by the IC manufacturer . Where ”z" is the

value measured by the IC manufacturer , a mask is accepted by the IC manufacturer if WKz^W2, and it is rejected if z<Wl or z>W2. Since z=y+N, the IC

manufacturer will accept the mask if Wl-N^x^W2-N, where N is the IC manufacturer’s measurement bias. The mask will be rejected if x<Wl-N or x>W2-N. For

path 2, the mask is rejected so that x<Wl-N or x>W2-N.

These conditions are written for path 2 in the appropriate columns in figure

2.4. All the conditions on path 2 must hold for the complete path to occur with probability ?2

. Similar restrictions are also written for paths 3, 4, 5,

and 6.

23
Figure 2.4 Conditions for Various Paths^

Mask

mfr’d^

(A)

Is mask

good/ linewidths^

(B)

Mask

shop

(C)

IC

mfr.

(D)

Accept

Outcome

Good

Mask

Accepted

Good Mask

Rejected,

Dispute

Good Mask

Rejected

Bad Mask

Accepted

x<Wl-M or x>W2-M

Dispute

,

Bad Mask

Rejected

Bad Mask

Rejected

Path

probability

Pi'

Pi

P2'

P2"

^3.’. P3

or

or

or

P4

' or

P4

”

P

5

' or

Pa’ or

P6

"

Cost of

outcome

No cost^

Mask Remake—Cl or Cl"

Dispute—C2' or

f

C2"

Mask Remake—C 1

’ or Cl"

Yield Loss and

related costs

C3’ or C3"

Dispute Cost—C2’ or C2"

Mask remake—Cl' or Cl"

Mask remake—Cl’ or Cl"

a Prime (') refers to before adopting improved measurements; probabilities and

costs must be recalculated after adopting Improved measurements, represented

by a double prime (").

b Mask is assumed to be good with respect to defects, registration, and other

non-llnewidth specifications.

c Is mask good with respect to linewidth specifications?

d Cost of path 1 is the baseline for measuring other costs and so equals zero

24
Next we determine the limits AI 2 and A22 which are consistent with all the

restrictions on x shown in figure 2.4. Continuing with the example of

path 2, we ask; For what range of line dimensions will masks be good masks

(column B) , accepted by the mask shop (column C) , and rejected by the IC

manufacturer (column D)? I.e., for what AI 2 and A22 do the following hold:

mask is between AI 2 and A22 » i.e.... Al 9 <x<A22

mask is good, i.e Wlj<x^W2

accepted by mask shop, i.e Wl-M£^x^W2-M, and

rejected by IC manufacturer, i.e,,., W2-N<x or x<Wl-N.

One method of finding the limits Al^ and A2i is to draw a graph showing the

relative positions of the values Wl-N, Wl-M, Wl, W2, W2-N and W2-M, and to find

by inspection the range Alj^—A2j^ which satisfies the conditions listed above.

For example, if the IC producer’s measurement bias (N) is greater than the mask

shop’s bias and both are positive (N>M>0) , the relative locations of Wl-M, Wl-N,

etc., are as shown in figure 2.5.

The limits Al^ and A2j used in calculating probabilities P£ are shown in

figure 2,5. For example, for path 2 (good/accept/reject) , the restrictions

Wl<x^2,

Wl-M£x^W2-M, and

W2-N<x or x<Wl-N

are satisfied if Al= W2-N and A2=W2-M so that for all masks on this path,

W2-N<x£W2-M.

The formulas for Al^ and A2i for all paths are summarized in table 2.2. The

table assumes that measurement biases M and N are small relative to the

specified range of linewidths; specifically, |m|+| n|^ W2-W1

,

25
Figure 2.5 Path Probabilities with and A2j^

f(x)

bad/ . good/ accept /////// /.

accept/ Pi / / ///. <-- bad/ accept / / P2 / /////.

reject ^ nil / / / //

1 .// / /////// / P3 //

1 . /// II P4 / /////// / //

/// Pfi // II II /////// ///////

/.

//. < good/accept/reject

I/ll.

/////.

///////.

/ . <—bad/ reject

P6 • ///////.

Wl-M W1

Al6 A2e=Al4 A24=A1 i

W2-N W2-M W2

A2i=Al2 A22=Al3 A23=Al5* A26*

specified tolerances (good masks)

W1 W2

P 5 (bad/accept/reject) = 0

f(x) = probability density function for mask with respect to linewidths

^ This example assumes that the IC producer’s measurement bias is greater than

the mask shop's measurement bias and that both are positive (N>M>0).

^ This graph is the same as figure 2.3, but the values for Al^ and A2j^ are shown on the x-axis.

26
3. AN APPLICATION OF THE MASK ACCEPTANCE MODLl

This chapter illustrates an application of the model developed in chapter 2.

It estimates how per-mask costs of erroneous photomask measurements would change

as a result of measurement Improvements, given certain assumptions about the

measurement system, products, production levels, and other factors. Effects are estimated for several sets of assumptions.

Table 2.1 in the preceding chapter summarizes the formulas that will be used.

The derivation of these formulas was explained in chapter 2. Values for various parameters are given in table 3.1. These values were selected to describe

a situation that might plausibly occur in industry, based on discussions with

Industry and NBS scientists.

3.1 SELECTION OF THE CASE

This section discusses the values given in table 3.1. The case analyzed was chosen to be compatible with the intended use of the SRM 474 and to be reasonably representative of many firms, although it does not represent a statistically average case. It was determined through conversations with semiconductor

industry firms and NBS scientists, reading, the trade literature, and other

sources.

Masks per year (k) . We assume that the hypothetical company being analyzed

measures 10,000 masks per year which are used in wafer fabrication. These may

Include masks for both contact and projection printing of wafers.

Linewidths target value (W) . More than half of IC devices produced in 1980 had

linewidths from 2 to 5 ym.l The base case in this study assumes that target

values (W) for photomask linewidths are 3 ym. This is a conservative assumption, since measurement errors are more costly at the smaller linewidths that

will become common in the future. (Smaller linewidths are assumed in the

sensitivity analysis.)

Tolerances (W1 and W2 ) . Companies interviewed for this study mentioned

linewidth tolerances of +10 percent or in the 0.1 to 0.3 ym range for chromium

masks. It is likely that tolerances on photomasks will decline to +0.1 or +

0.2 ym. A tolerance of + 0*25 ym is assumed here, so that the base case mask

specifications are Wl=2.75 ym and W2=3.25 ym. (Smaller tolerances are used in

the sensitivity analysis.)

^ Bossung, J.W. and E.S. Muraskl , "Advances in Projection Microlithography,"

Solid State Technology , August 1979, pp. 109-112; Jerke, John M. , ed.. Semiconductor Measurement Technology; Accurate Linewidth Measurements on Integrated Circuit Photomasks , National Bureau of Standards Special Publication

400-43 (Washington, D.C.: U.S. Government Printing Office, 1980), pp. 3 and

113; and Burggraaf, Pieter, "Photomask Making: Issues vs. Equipment,"

Semiconductor International, March 1981, p. 30.

27
Table 3.1 Values Used in the Model - Base Case

(See section)

Selection of the case 3.1

Lower bound specification for linewidths

Upper bound specification for linewidths

Target Value

W1 = 2.75 ym

W2 = 3.25 ym

W = 3 ym

Mask probability density function^

Number of masks measured annually

f(x): normally distributed

mean (W) = 3 ym

st’d dev. (ox)=0.1 ym

k = 10,000

Costs of measurement

related problems

Masks for pro- Masks for

j action printing contact print.

Mask remake cost (before better meas.) Cl’ = $1,000 $100

Mask remake cost (after better meas.) Cl" = $1,000 $100

Costs of resolving dispute (before) C2’ = $100 $ 0

Costs of resolving dispute (after) C2" = $ 50 $ 0

Costs if a bad mask is used (before) C3’ = $2,000 $ 30

Costs if a bad mask is used (after) C3" = $2,000 $ 30

Systematic error

Mask shop measurement bias: before M

after

IC manufacturer measurement bias : before N

after

= 0.12 ym

= 0.08 ym

= 0.2 ym

= 0.1 ym

Discounting and time-related variables

Real discount rate

Useful life of procedures

Years before procedures implemented (with NBS)

(without NBS)

Analysis period

r = 10%

t = 6 years

s = 1 year

s*= 3 years

T = 5 years

Single present worth discounting factors

for discount rate "r"

Uniform present worth discounting factors

for discount rate "r"

SPWi = .9091 SPW3 = .7513

SPW2 = .8264 SPW4 = .6830

UPW 3 = 2.487

UPW5 = 3.791

3.2

3.3

3.4

28
Table 3.1 Values Used in the Model - Base Case

(Cont .)

Implementation costs

Added initial implementation cost

Added annual implementation cost

Other added implementation costs

(* indicates wlthout-NBS situation)

Timing of other added costs

(* indicates without-NBS situation)

C5 = $13,460

C6 = $ 6,600

C7i = $ 6,600 C7i* = $6

on

= $ 6,600

u(l) = 2 u(D* = 2

u(2) = 4

^ Based on the frequency distribution of masks produced with respect to

linewidths

600

29
Mask production function [f(x) and Ox] « We assume that the distribution of

masks with respect to linewldths can be approximated by a normal curve with a mean of W = 3ym and a standard deviation o The formula for such a normal

X curve is as follows:

f(x)

A 1979 conference paper described a method of producing high quality masks

which gave a three-sigma variability of 0.35 pm.^ In the absence of good

information about mask variability, a one-sigma variability (a^) of 0.1 pm

is assumed for the base case study and varied in the sensitivity analysis.

(14)

3.2 COSTS OF MEASUREMENT RELATED PROBLEMS (Cl, C2 , C3)

Erroneous measurements lead to several types of costs. This section assigns

values to costs of disputes, costs of remaking masks, and costs arising from a bad mask being put into use.

Remake cost (Cl* and Cl") . The mask remake cost used in the base case study is

$1,000 for masks intended for projection printing of wafers, both before and

after improving measurements. Masks intended for contact printing of wafers

are assumed to cost $100. These values were selected based on information from

mask producers and other sources concerning typical mask sales prices, but they

do not represent statistical averages of mask prices. Projection and contact

printing are the most widely used methods for printing wafers. Values were

chosen assuming that the masks were chromium because the SRM is designed to

improve measurements of antireflective chromium masks.

Dispute resolution cost (C2* and C2'') One company Interviewed estimated that

resolving disputes involving measurements of submicrometer lines probably cost

$3,000 to $4,000 per dispute. However, disputes concerning less costly masks,

and disputes between divisions of the same company, are likely to cost less to

resolve. At $40 per hour, a dispute whose resolution takes one hour of management time each from the mask shop and the mask user would cost $80. For masks

intended for projection printing, this is rounded up to C2' = $100 per dispute

to account for other expenses such as operator measurement time.

Several companies mentioned that the introduction of the SRM would make

disputes easier to resolve. Presumably companies would be able to detect the

reason for measurement discrepancies more quickly if they can check their

equipment using standardized procedures and NBS standards or secondary

^ The method described here could also be used for non-normal distributions.

We chose the normal distribution due to lack of data about actual

distributions, and to simplify the analysis.

2 Dan, M.; I. Tanabe ; M. Hoga; and S. Torisawa, "Fabrication System of High

Duality Hard-Surface Masks for LSI's," Proceedings of Kodak Microelectronics

Seminar: Interface *79 (San Diego, October 25-26, 1979).

30
standards measured on equipment calibrated using NBS standards. This source of

cost savings Is difficult to quantify. We attribute a savings of $50 per dispute to the availability of the NBS SRM and procedures, so that C" Is $50 for

masks Intended for projection printing. In the sensitivity analysis, this cost

saving Is reduced.

For masks used In contact printing of wafers, dispute costs are assumed to be zero "before" and "after."

Yield loss cost (C3)

We were not able to obtain adequate data on the costs due to yield loss and

other effects of using a bad mask In wafer fabrication. It appears that the

effect on yield loss can be substantial; It ranges widely, from almost nothing

to a complete loss of yield until the source Is detected. The causes of yield

loss may be detected and corrected Immediately, or the yield loss may persist

for months, until the mask Is replaced for other reasons. This Is especially

likely for very slight yield losses.

In the absence of good data, the base case assumes a yield loss cost of $2,000.

This would correspond, for example, to a decline In yield from 16 percent to

15 percent for ten days on IC devices valued at $3,200 per day. Such a yield

loss due to Incorrect mask measurements appears plausible, based on conversations with Industry.

The cost of measurement error Is lower for masks for contact printing because

of the lower costs and reduced use of each mask. The yield loss cost for such

masks was assumed to be $30.

3.3 SYSTEMATIC ERROR (M and N)

Since the model In this report assumes perfectly repeatable measurements (no

random error) , the measurement bias Is simply the discrepancy between the true

and measured llnewldth.l The size of bias can be reduced by calibrating to a standard such as the SRM 474.

Bias before calibrating

NBS conducted an Interlaboratory test of the NBS calibration procedures. 2 The

ten companies Involved In the study Included mask houses, device manufacturers.

1 If there ^ random error, then the bias or systematic error Is the difference

between the true llnewldth value and the limiting mean of the llnewldth measurements, l.e., the mean to which the sample mean approaches as the number

of measurements Increases. See Ku, Harry, "Statistical Concepts In Metrology,"

p. 299-23.

2 Results will be published In Semiconductor Measurement Technology;

Interlaboratory Study of Llnewldth Measurements for Antlreflectlve Chromium

Photomasks , J.M. Jerke, M. Carroll Croarkln, and Ruth N. Varner (Washington,

D.C.: National Bureau of Standards, in preparation).

31
and equipment suppliers. NBS sent mask-like artifacts to the participants for

measurement and, later, compared the linewldth measurements reported by industry

with the NBS values.

Several types of measurement systems were Involved. For opaque lines near 3 ym

measured on one widely used type of system, the average offset from the NBS

values was 0.16 ym. There were also differences between systems of this type

in the amount of offset, averaging .08 ym for opaque 3 ym lines.

Biases and discrepancies in industry before calibrating with the SRM 474 may

be greater than those in the interlaboratory study, for three reasons:

(1) in the interlab test, company data were edited for "outliers"—occasional

extreme measurements—before determining offsets. For data that had not been

edited, average offsets from the true value would frequently be greater; (2)

the interlab studies involved firms who were relatively advanced in their

linewidth measurement practices; and (3) the companies in the test followed

NBS procedures in making the measurements. Even without the SRM, following

these procedures would tend to reduce bias.

These data are for a type of linewidth measurement system which is widely used

in Industry and appears to be intermediate in its accuracy between other types

of systems. Therefore, the data for this system are used in selecting the

values for measurement bias used in the base case.

Based on the above discussion, we assume that the average offset from NBS is

0.16 ym, and that .08 ym is the difference between the mask shop and IC producer. Thus, the assumed offsets for a mask shop and IC producer are

[0.16 - 1/2 (.08)]yra and [0.16 + 1/2 (.08)]ym. Since mask shops tend to be the

leaders in mask measurement technology in their organizations, the mask shop

is assumed to have the lower offset, M=0.12 ym. For the IC producer, the offset, N, is assumed to be 0.20 ym.^

Bias after calibrating

The case example in this report concerns a company which has purchased an SRM 474, Most companies will calibrate one microscope with the SRM and then

measure secondary standards on this calibrated microscope. From discussions

with firms, it appears that few companies followed statistically-based calibration procedures for calibrating their linewidth measurement equipment before

1 Croarkin, Carroll; John Jerke; and Ruth Varner, Results of Interlaboratory

Study: Lecture Notes (presented at the NBS Training Seminar, "Linewidth

Measurement on Integrated Circuit Photomasks and Wafers," July 15-18, 1980).

2 The assumption that both supplier and customer use the same type of system

is a conservative assumption; measurement discrepancies may be larger where

measurements are made with different types of systems.

32
NBS made Its recommendations. NBS researchers believe that following these

procedures may significantly reduce companies' measurement biases.!

However, the biases will probably not be reduced to zero, for several reasons:

(1) the SRM itself has an inherent uncertainty of +.05 ym; (2) in-house standards measured on equipment calibrated with the SRM 474 will have uncertainties

greater than that of the SRM; and (3) the calibration curve itself has uncertainty attached to it. Based on discussions with NBS scientists, this paper assumes that offsets are reduced to 0.08 ym for M and 0.1 ym for N.2

3.4 DISCOUNTING AND TIME-RELATED VARIABLES (UPW, SPW, r, t, T, s, u(i))

The base case uses a real discount rate, r, of 10 percent, the rate specified

for Federal agency use by the Office of Management and Budget. 3 With 10 percent inflation, this would be the equivalent of a 21 percent market rate.^

Effects of changing the discount rate are shown in the sensitivity analysis.

Useful life and analysis period

The Uniform Present Worth (UPW) factors for discounting equal annual costs and

benefits were selected from the table in appendix B for 10 percent and the

remaining useful life, "t-s". The factors for discounting other cost and

benefit items — the Single Present Worth (SPW) factors — were selected from

table B.l for 10 percent and the number of years ”u(i)" or "s". These factors

are shown in table 3.1.

It is very difficult to predict the useful life of the measurement procedures.

A new measurement approach may eventually supersede the NBS approach, or new

technologies such as direct writing on wafers with an electron beam may make

photomasks less widely used. This study assumes that the NBS results will be

useful for six years after 1980 before they become obsolete. Thus, the useful

life, t, is six years. It assumes that the company adopts the new procedures

in 1981 so that the number of years after 1980 that the new procedures are implemented, s, is one. The analysis period, T, equals ”t-s" or 5 years.

1 Jerke, J. M. ; Croarkln, M. C.; and Varner, R. N. , Semiconductor Measurement

Technology; An Interlaboratory Study of Linewidth Measurements for Antireflective Chromium Photomasks (Washington, D.C.: National Bureau of

Standards, in preparation).

2 We assume the company keeps the same measurement system, thus neglecting any

benefit from NBS Influence on choice of system.

^ U.S. Office of Management and Budget, "Circular No. A-94 Revised," March 27,

1972.

^ Market rate = (1 + real rate) (1 + inflation rate) - 1.

33
3.5 IMPLEMENTATION COSTS (C4)

Some costs of implementing NBS results, such as the SRM cost, are relatively

easy to determine. Other costs, such as of management planning time, may be

difficult to estimate. However, the sensitivity analysis in section 3.8 suggests that the uncertainty connected with the estimates of implementation

costs is not of great concern because net benefits predicted from adopting the

SRM and NBS procedures appear to be fairly insensitive to Implementation costs,

at least for the assumptions and parameter values used in this paper. The

various costs are discussed below.

Costs of implementing NBS results are calculated for a hypothetical mask shop

which measures 10,000 masks per year using 10 measurement systems. Other

assumptions describing the hypothetical mask shop are listed in table 3,2. The

assumptions were made based on information from two mask houses and from other sources. Implementation costs would probably be different for companies not

fitting these assumptions.

Fourteen cost items are listed in table 3,2. Several of them are briefly

discussed below.

Startup costs (C5)

The figures in table 3.2 for management time assume that a manager from

California attends a week-long training seminar on the East Coast, ^ Other

startup costs listed in table 3,2 are management time to train others, operator

training, engineer training, and initial equipment calibration.

Hardware changes . No major equipment changes are needed to implement the NBS

results on many systems. This case assumes that the hardware cost for implementing the NBS procedures is $16/system, the cost of adding a green filter.

Computer program development . Some companies have spent money writing a computer program to carry out the calibration calculations. However, since

NBS provides the listing for such a program, this cost is excluded from the

estimates

SRM . Most companies are likely to purchase only one SRM 474, at a cost of $3,600.

A simpler SRM (475) is also being sold for $2,500, but the $3,600 figure is used

for this study. It is assumed that the SRM requires replacement every two years

due to damage. Its actual life could be much longer with careful handling.

Secondary standards . Most companies will use standards traceable to the SRM

474 for their routine calibrations. Some companies will manufacture or purchase

new secondary standards; others will simply remeasure existing standards. We

assume the company obtains and measures one new standard for each measurement

system, and that standards are replaced every two years.

1 Costs would be reduced for companies attending West Coast seminars, which

were initiated by NBS in 1981.

34
Table 3.2 Mask Shop Implementation Costs

Assumptions

10 measurement systems 1 SRM

1,000 masks measured/ system/ year $40/hour management cost

3 operators/ system ($10/hour/operator) 10% real discount rate

2 engineers ($20/hour/englneer)

1 secondary standard/ system

Added Cost

Item Added Cost /Unit per Company ($

Startup Costs (C5)

Mgt . learning & planning Travel $1,000 1 60 hours X $40/hour

3,400

Mgt. time to train others 20 hours X $40/hour 800

Hardware 10 systems X $16/system 160

SRM 3,600

Computer program 0 hours 0

Operator training 5 hours X $10/hour X 30 oper. 1,500

Engineer training 20 hours X $20/hr. X 2 engrs. 800

Mfrg. in-house standards 10 standards X $100/standard 1,000

Measuring in-house stds. 10 standards X $200/standard 2,000

Initial equip, calibrat. 10 systems X $20/system 200

Subtotal (C5) 13,460

Equal annual costs (C6)

Production meas. 10,000 masks X .05 hrs./mask X $ 10/hr. 5,000/yr.

Checking and adjusting equipment:

engineer: 10 syst. X 2 hrs/syst. X $20/hr. 400/yr

oper.: 10 syst. X 12 hrs/syst, X $10/hr. 1,200/yr.

Subtotal (C6) 6 ,600/yr

Other ongoing costs (C?i)

SRM replacement 3, 600/ two yrs

Stds replacement 10 stds!. X $300/std ./ two years 3, 000/ two yrs

Subtotal (C7) 6,600/two yrs.

35
Ongoing costs (C6 and C7)

Production measurements . This case assumes a few extra minutes per mask are needed to measure according to NBS procedures. This figure is subject to much

uncertainty. It is also relatively important, since it is a cost which

continues over the life of the procedures.

Other ongoing costs are for SRM and secondary standards replacement. These are listed in table 3.2.

Table 3.2 summarizes the breakdown of costs. The total initial cost is $13,460.

Ongoing costs are $1,600 per year for periodic recalibration and adjustment,

$6,600 every two years for replacement of standards, and $5,000 per year for

added time for routine mask measurements.

Calculating implementation costs (C4)

Implementation costs (C4) are calculated using equation (7) in table 2.1 and

the values in table 3.1. For a company implementing in 1981, the analysis

period is 1981-1985. The total costs of about $88,000 (present value) are averaged over 50,000 masks (five years X 10,000 masks/year) to get the

discounted average cost per mask of $1.76.^

Had NBS results not been available, this company would implement new

measurement procedures in 1983, according to an assumption discussed in section

3.7. However, the relevant analysis period is still 1981-1985, and costs are averaged over the 50,000 masks that are produced in this period. Costs per

mask would be about $1.06.2

3.6 CALCULATING THE COST SAVINGS (B)

We have now assigned values to all the variables in the model and calculated

implementation costs, C4 , for the hypothetical company. The values assigned

are shown in table 3.1. To determine benefits per mask for an IC company with

an in-house mask shop, the next step is to calculate the path probabilities ?2

through using the formulas for Alj^ and A2^ from table 2.2 for N>M>0, the

equation for in table 2.1, and the parameter values in table 3.1.

Calculations for P2 through Pg , before and after improving measurements, are shown in table 3.3. For example, the probability of good/accept/reject (P2 ) is .21174 or 21 percent before improving measurements, but falls to .02224 or

2 percent after improving measurements. These probabilities are illustrated

in figure 3.1.

1 C4 = 2 [$13, 460+$6, 600(3. 791)+$6,600(. 8264 )+$6,600(. 6830)] .9091=$!. 76.

10,000 (5)

2 C4* = 2 [$13, 460+$6, 600(2. 487)+$6,600( .8264)1 .7513=$!. 06.

10,000 (5)

36
Table 3.3 Calculating Path Probabilities®

W2-M

P

2

' - / f(x)dx = W2-N

W2

P

3

' = / f(x)dx = W2-M

W1

P4

' = / f(x)dx = Wl-M

P 5

’ = 0

Wl-M

P6

* = / f(x)dx +

0

W2-M

P

2

" = / f(x)dx = W2-N

W2

Po" = / f(x)dx = W2-M

W1

P 4

" = / f(x)dx = Wl-M

3.13

f f(x)dx = .21174

3.05

3.25

/ f(x)dx = .09059

3.13

2.75

/ f(x)dx = .00610

2.63

2.63

f f(x)dx +

0

3.17

/ f(x)dx = .02224

3.15

3.25

/ f(x)dx = .03836

3.17

2.75

/ f(x)dx = .00573

2.67

/ f(x)dx = W2

J f(x)dx

3.25

.00632

P5"

P6"

Wl-M

/ f(x)dx + f f(x)dx =

0 W2

2.67

/ f(x)dx + / f(x)dx

0 3.25

.00669

® The limits of integration come from table 2.2 for N>M>0 and parameter values

come from table 3.1. In this example, f(x) is a normal curve with standard

deviation Ox = 0.1 ym and mean W = 3 pm, A slight variation on the formula

given in table 2.1 for Pj^ is needed to compute Pg since it equals the sum

of two sections under the probability density function. For the method of

calculating areas under a normal curve, see a statistics text such as Mills,

Frederick C., Statistical Methods , third edition (New York: Hold, Rinehart,

and Winston), 1955, pp. 157-159.

37
For the base case, as table 3.4 shews, the gross undiscounted cost savings

(before subtracting implementation costs) per mask due to improved measurements

are $262.16 per mask. For the less expensive masks for contact printing, the

savings are $24.15 per mask.

Discounted net benefits per mask for a company measuring 10,000 masks/year were computed using equation (1) in table 2.1. The savings are $178.94 for masks

intended for projection printing of wafers and $14.88 for masks used in contact

printing.

These estimates of savings do not take into account progress that might have

been made in the absence of the NBS research. Cost savings that might have

occurred had NBS not conducted its research, also shown in table 3.4, are discussed in the next section.

Comparison with the "without NBS” situation

The net benefits calculated so far show the savings when companies adopt

Improved measurement technology. However, even without NBS, companies would

eventually adopt Improved measurement technologies. Therefore, costs and

benefits if companies had acquired improved measurement technology from some other source were calculated.

Values are assigned to s*, C7*, and u(i)* to reflect the "without NBS"

situation. Without NBS, improved methods would have been available three

years later than they actually were so that s* = 3. This assumption, which is

thought to be conservative, was based on comments by an industry metrologist.

Without NBS, cost item C7i* is the same as cost item C7i, but there is no C72*.

This is because C72* would occur in four years, one year after the end of the

useful life of the measurement procedures. Similarly, u(l)* = 2 but there is no u(2)*.

Implementation costs and net benefits were computed using equations 8 and 2 in

table 2.1 and values for s*, C?i* and u(i)* in table 3.1. Other values were unchanged. Implementation costs without NBS (C4*) were $1.06 per mask. Net

benefits per mask without NBS (B*) were $96.91 for masks for projection

printing and $7.96 for masks for contact printing.

For companies who would adopt NBS procedures in 1981, the wlthout-NBS

alternative would have been to adopt new procedures in 1983. Therefore, the

cost savings for adoption in 1983 are subtracted from cost savings for adoption

in 1981. The added cost savings per mask due to NBS for masks for projection

printing are $82.03.2

1 B = ($342.02 - $79.86) 3.791 (.9091) - $1.76 = $178.94.

5

B = ($31.05 - $6.90) 3.791 (.9091) - $1.76 = $14.88.

5

2 B-B* = $178.94 - $96.91 = $82.03.

38
Figure 3.1

PROBABILITIES OF VARIOUS MASK MEASUREMENT OUTCOMES

BEFORE IMPROVED MEASUREMENTS

f(x)

2.63 W1-M2.75 W1

3.05 W2-N3.13 W2-M3.25 W2

•SPECIFIED LINEWIDTH TOLERANCES

AFTER IMPROVED MEASUREMENTS

f(x)

SPECIFIED LINEWIDTH TOLERANCE

39
Table 3.4 Gross Undiscounted Savings (Base Case)^

Masks for projection printing

G’ = Cl’ (P 2

* + P3 '+ P 5

’ + P6’) + C2’ (P2* + P5

') + C 3 ’P4

'

= 1,000 (.21174 + .09059 + 0 + .00632) + 100 (.21174 + 0) + 2,000 (.0061)

= $342. 02/mask

C" = Cl" (P2

" + P3" + P 5" + P6") + C2" (P2" + P5 ") + C 3 '*P4

"

= 1,000 (.02224 + .03836 + 0 + .00669) + 50 (.02224 + 0) + 2,000 (.00573)

= $79. 86 /mask

C' - C" = $262. 16/mask

Masks for contact printing

C’ = 100 (.21174 + .09059 + 0 + .00632) +0+30 (.0061)

= $31. 05 /mask

C" = 100 (.02224 + .03836 + 0 + .00669) +0+30 (.00573)

= $6. 90/mask

C’ - C" = $24. 15/mask

^ Savings before discounting or subtracting implementation costs. Values

are from tables 3.2 and 3.8. The formulas are from table 3.1.

40
(The company saves the full $178.94, of course, but only part of this Is

credited to NBS, since some savings would have been realized even without

NBS.) For contact printing, the added cost savings are $6.92.1

It is important to remember that these figures do not necessarily represent

the cost savings for any particular company, or the average savings from using

NBS procedures. Rather, they are examples of the amount of savings that might

occur in a specific hypothetical situation. The model used is in some ways a simplification of the real world, and in any case it only shows what would

happen for a particular situation. Also, the NBS linewidth measurement research

has major effects which are outside the scope of this study. Thus, the kinds

of cost savings estimated here may well represent only a fraction of the

overall benefits from the NBS research.

3.7 SENSITIVITY ANALYSIS

Benefits credited to NBS

The amount of benefits attributed to NBS was sensitive to the assumed lag by

industry behind NBS. Results of the sensitivity analysis are illustrated in

figure 3.2.

In the base case, NBS technology is available three years earlier than similar

technology would be available from other sources, i.e., in 1980 rather than

1983. In this case, net benefits credited to NBS were $82 per mask. If NBS

technology were available only two years earlier, net benefits credited to NBS

would decrease to $43 per mask. If NBS technology were available four years

earlier, the benefits attributed to NBS would increase to $117 per mask. If

NBS technology were available six years earlier, the entire $179 of per-mask

benefits would be attributed to NBS since the life of the procedures is assumed

to be six years.

The amount of benefits credited to NBS was sensitive to the selection of other

variables. This is illustrated in figure 3.2. For example, under a "pessimistic" case involving 3 ym lines, the net benefits due to NBS fell to $25 per

mask. 2 in an "optimistic" case involving 3 ym lines, the net benefits increased

to $153 per mask. For cases involving 2 ym and 1 ym lines, benefits due to NBS were $219 and $339 per mask, respectively.

1 B-B* = $14.88 - $7.96 = $6.92.

2 In this context, the "pessimistic" case is the one likely to result in small

benefits from improved measurements. Thus, smaller variability in masks

with respect to linewidths would be part of the "pessimistic" case even though it is a desirable result for the manufacturer.

41
Figure 3.2 Sensitivity Analysis: Benefits due to NBS (B-B*)

Benefits due to NBS (B-B*)

0 $100 $200 $300 $400

Variations ^

in lag

behind NBS 2 years

3 years (base case)

4 years

Different

cases

3 ym pessimistic^

3 ym base case^

3 ym optimistic^

2 ym case*^

1 ym case® l$339

a

b

cd

e

Ox=.05, M'=.09, N’=.15, Cl=500, C2"=90, C3»200

W2-W1=.5, Ox=.l, M’=.12, M"=.08, N'=.2, N"=.l, Cl=1000,

C3=2,000

W2-W1=.4,

W2-W1=.4,

W2-W1=.2,

N'=-.2, N"=-.l, C2=0, 03=2,000

Oj^=.05, C2’=500, C2"=250, 03=5,000

a^=.05, 01=2,000, 02'=500, 02"=250, 03=5,000

02 ’= 100 , 02”=50,

42
Total benefits including those not credited to NBS

We also calculated the sensitivity of the benefits from improved measurements

to changes in assumed values without subtracting out the benefits that would

have occurred even without NBS. Figure 3.3 shows the results. The letters

below refer to parts of figure 3.3.

A. Measurement bias (M, N)

As is shown in part A of figure 3.3, the net benefits per mask were very

sensitive to changes in the amount by which measurement bias is reduced. Where

biases were opposite in sign, improved measurements were particularly beneficial (benefits rose to $220) because they substantially reduced measurement

differences between companies.

A few combinations of initial errors and improvements gave very slightly

negative results. For example, net benefits per mask were very slightly negative (-$2) in a case where there was an improvement for the IC producer but

not for the mask maker. Also, where there was a high level of bias to start

with, e.g., around 0.5 ym, a reduction in bias led to very slightly negative

benefits per mask of -$2.

In certain situations, improving measurements may reduce one kind of cost but

increase another. For example, companies may reduce the number of bad masks

accepted, but increase the number of disputes. The net Impact depends on which

kind of problem is most costly.

B. Tolerances (Wl, W2 , and W) ; standard deviation of mask distribution (Oy)

Part B of figure 3.3 shows that the effects of improved measurements varied

with the tolerance range W2-W1 but not with the absolute level of the target

value, W. As the spread W2-W1 narrowed from 0.5 ym to 0.2 ym, the benefits of

improved measurements increased from $179 to $264 per mask for mask variability

standard deviation (a^) of 0.1 ym. For Oj^=.05 ym, the relationship was not as clearcut, as figure 3.3 part B shows.

The degree of control of between-mask linewidth variability (the one-sigma of

the mask distribution, o^) was very significant. Improving production control

by changing from 0.3 ym to 0.1 ym made it more cost-effective to improve

measurements, increasing savings from $109 to $179 per mask. This may be

because where control is relatively poor (o^ is large), many masks are so far out of spec that they are correctly determined to be out of spec even with

measurement error. But where control is better, more masks are close to the

tolerance limits, so that there may be more acceptance mistakes due to measurement error. On the other hand, where control is extremely good, most masks

may be so far within specs that even with measurement error they are accepted.

C. Discount rate (r)

Figure 3.3 part C shows that changing the discount rate had a significant

effect on net benefits. For example, reducing the real rate of return from

43
Figure 3.3 Sensitivity Analysis: Total Benefits

A, Measurement

Biases (ym)

B. Tolerances,

Standard

Deviation

of Mask

Distributlon(ym)

C. Discount

Rate

Total Benefits per Mask (B)

0 $100 $200 $300

M» M" N' N’

.12 .08 -.2 -.1

.12 .03 .2 .05

0 0 .2 .1

.12 .08 .2 .1

.2 .1 .12 .08

.4 .36 .48 .38

.12 .08 0 0

.12 .11 .2 .19

.12 . 08 . 2 .2

.2 .2 .12 .08

.5 .46 .58 .48

W2-'W1 ax

.5 .05

.4 .05

.2 .05

.5 .1

.4 .1

.2 .1

.5 .05

.5 .1

.5 .2

.5 .3

.2

.2

.2

.05

.1

.2

l$34A

5%

10%

20 %

100%

44
Figure 3.3 Sensitivity Analysis: Total Benefits (Continued)

Total Benefits per Mask (B)

0 $100 $200 $300 $400

D. Implemen- C4

tation

Costs Pessimistic

Base Case

Optimistic

E. Mask

Cost

Cl C2 C3

$ 2,000

$ 1,000

$ 500

$ 200

$ 100 $ 0 $30

TM base CASE!

I$15

$179

l$345

F. Dispute C2* C2"

Cost

$ 100 $ 90

$ 100 $ 50

$ 100 $ 0

$ 1,000 $500 $303

G. Yield ^ W2-W1

Loss

Cost $ 0 .5

$ 2,000 .5

$20,000 .5

$ 0 . 2 ym

$ 2,000 .2 ym

$20,000 .2 ym

l$234

H$264

H. Groups

of

Variables^

3 ym “pessimistic"

3 ym base case

3 ym "optimistic"

2 ym case

1 ym case

1$54

BASE CASE! i$179

l$335

l$473

l$741

^ See figure 3.2 for parameter values.

45
10 to 5 percent (5 percent is equivalent to a 15.5 percent market rate if there

is 10 percent inflation) increased net benefits per mask from $179 to $214

because it did not discount future benefits so heavily. However, even at very

high rates of discount (100 percent), net benefits were still positive.

D. Implementation costs (C4)

The sensitivity to implementation costs was analyzed for an optimistic and

pessimistic set of assumptions, listed in table 3.5. As figure 3.3 part D

illustrates, the net benefits were very insensitive to implementation costs,

since implementation costs were very small relative to benefits.

E. Mask cost (Cl)

Increasing the mask cost from $1,000 to $2,000 significantly increased the net

benefits of improved measurements, from $179 to $345 per mask. This is illustrated in figure 3.3 part E.

F. Dispute cost (C2)

The results are sensitive to changes in the reduction of dispute costs (C2'-C")

only when the magnitude of reduction is large. If improving measurements

reduces dispute costs from $1,000 to $500, net benefits are $303 per mask.

G. Yield loss cost (C3)

Figure 3.3 part G shows that changes in yield loss had remarkably little effect

on measured net benefits when the tolerance range (W2-W1) was 0.5 ym. However,

narrowing the tolerance range to 0.2 pm (e.g., a range of 1.9 to 2.1 pm) made

the benefits much more sensitive to the estimate of yield loss cost. In this

case, increasing the yield loss cost from $2,000 to $20,000 Increased benefits

from $264 to $537 per mask.

H. Groups of variables

Variables were also changed several at a time. For example, for a tolerance

range of +.25 pm, such as might apply to a 3 pm mask, a pessimistic set of

assumptions (described in figure 3.2) gave net benefits of $54 per mask, still

very good. An optimistic set of assumptions for the "3 pm case" gave benefits

of $335 per mask. Tifhen values were selected for a hypothetical device with

2 pm lines, net benefits increased greatly, to $478 per mask. This is shown

in figure 3.3 part H.

Conclusion

The sensitivity analysis suggests that for the underlying model described in

chapter 2, the benefits of Improved measurements are strongly positive, and even large errors in estimating many variables would probably not make the

net effects negative. Sensitivity to changes in the underlying model (e.g.,

modifying the model to allow for random error) was not tested. ^

1 See suggestions for further research in chapter 6.

46
Table 3 .

Values Used in Sensitivity Analysis of Implementation Costs

Pessimistic Optimistic

Cost Item Base Case ($) Case ($) Case ($)

Management learning & planning 3,400 4,000 1,000

Management time to train others 800 1,600 400

Hardware 160 160 160

SRM 3,600 3,600 3,600

Computer program 0 5,000 0

Operator training 1,500 3,000 300

Engineer training 800 800 800

Standards manufacturer 1,000 1,000 500

Standards measurement 2,000 2,000 1,250

Initial calibration 200 2,000 200

TOTAL INITIAL COSTS (C5) 13,460 23,160 8,210

Periodic checking of equipment

Routine measurement

Secondary standards replacement

1,600/yr.

5,000/yr.

1,600/yr.

10,000/yr.

3 ,000/yr

750/yr.

0

TOTAL ANNUAL COSTS (C6) 6,600/yr

14,600/yr. 750/yr.

OTHER COSTS [C7(l)]:

SRM replacement

SRM replacement

Secondary standards replacement

Secondary standards replacement

3,600^

3,600l^

3,000^

3,000^

3,600^

3,600^5

3,000^

3,000b

3,600^

3,600^

1,750^

^ Two years after implementating new procedures.

^ Four years after implementing new procedures,

c Three years after implementing new procedures.

47
4. NBS TECHNOLOGY: DIFFUSION AND QUALITATIVE IMPACTS

The first part of this chapter presents evidence on the extent to which the

SRM 474 and NBS procedures for measuring photomask linewidths are used in the

U.S. semiconductor industry. The second part qualitatively describes some effects of the NBS research which were not quantified for this report.

4.1 TRANSFER OF NBS RESULTS TO INDUSTRY

The NBS "Market"

It was not feasible within the resources available for this study to estimate

dollar values for aggregate national impacts of NBS linewidth measurement research.

However, some data on diffusion of results and the number of masks shipped may

help put the per-mask benefits mentioned earlier into perspective.

The potential market for the NBS photomask linewidth measurement results depends

on the number of photomasks measured each year. (Wafer measurement applications

are not considered here.) The NBS SRM 474 and procedures are intended to apply

to chromium masks. Inforaation from Dataquest Inc. suggests that, for 1979, the

number of chromium masks used in projection printing of wafers was about 25,000

and the number of chromium masks used for contact printing was about 2.6 million.

NBS data suggests that the majority of companies in relevant parts of the

semiconductor industry make at least some use of NBS’s linewidth research results.

At yearend 1980, companies accounting for roughly 85 percent of mask manufacturing, including IC manufacturers, were known to make some use of NBS results,^

Undoubtedly many other companies also use the NBS results.

NBS has transferred research results to users in the following ways:

SRM 474 sales . As of yearend 1980, NBS had received orders for linewidth SRMs

from 16 IC manufacturers, four independent photomask manufacturers, three

linewidth measurement equipment and standards manufacturers, and one firm

1 Dataquest provided us with values of 1979 silicon consumption for companies

with captive IC manufacturing facilities. Based on their workshop attendance, interlaboratory study participation, and SRM purchases, companies

which account for about 90 percent of the value of silicon purchases are known to make some use of NBS linewidth measurement results. (Some others

probably also use NBS results.) In addition, out of ten leading merchant IC

manufacturers, nine are known to make some use of the NBS results.

Twenty-three percent of masks are manufactured by independent mask houses.

The rate of NBS research use by mask houses is not known; therefore, we con- servatively assume a rate of only 50 percent. Using these figures, the proportion of companies, by mask volume, known to be using NBS linewidth measurement techniques would be at least 50 percent X 13 percent + 90 percent X

87 percent = 85 percent. This assumes that mask volume is proportional to

silicon volume for the IC manufacturers.

48
outside the semiconductor industry.^ Out of 13 companies contacted which have

received or ordered the SRM, 11 said they would standardize on the SRM companywide and two (both large companies) said they will standardize at some, but not

necessarily all, company locations.

Seminars and interlaboratory studies . From 1977 through 1980, NBS conducted

four seminars for industry concerning procedures for setting up and calibrating

linewidth measurement equipment. 2 Also, ten companies were exposed to NBS

linewidth measurement technology when they participated in two interlaboratory

studies in the 1977-1980 period.

The list of SRM purchasers, seminar attendees, and interlaboratory study

participants shows some of the companies who make use of NBS linewidth measurement results. At yearend 1980 there were about 66 companies at 87 locations

involved with NBS in one or more of these ways. Table 4.1 shows the types of

organizations involved.

Publications . Over 700 people at 189 organizations have asked specifically to

receive publications related to NBS linewidth research, including 59 IC manufacturers and/or buyers, 22 independent photomask manufacturers, 17 microscope

and measurement systems manufacturers, 11 government agencies, 25 foreign

organizations, 9 universities, and 46 others (including organizations whose

activities were not determined).

Other methods of direct transfer to Industry . NBS scientists have also

transferred linewidth measurement results to industry through phone calls,

talks presented at conferences, industry visits to NBS, visits by NBS people

to companies, and interactions at meetings of American Society for Testing

and Materials (ASTM) standards committees. (NBS research will be the basis

for three ASTM standards related to linewidth measurements.)

4.2 SECONDARY DISSEMINATION OF NBS RESEARCH RESULTS

Companies also learn about NBS linewidth measurement technology indirectly, as was illustrated in figure 1.3 in chapter 1. For example, linewidth measurement

systems manufacturers frequently recommend NBS practices to their customers.

One part of a company may share NBS technical findings with other parts of the

company. Photomask suppliers often share NBS recommendations with their customers. And information moves among companies through mobility of people

familiar with NBS research results.

In addition, non-NBS authors reference IJBS findings in articles and conference

papers. Although a computerized search^ turned up only ten citations to NBS

^ As of January 6, 1981, NBS had sold 58 linewidth SRMs.

2 Two more seminars were held in 1981. Ninety-four different organizations

have been represented at all the seminars through 1981.

^ Science Citation Index (Philadelphia: Institute for Science Information).

49
Table 4 .

Companies Participating in Interlab Tests, Attending Seminars,

or Ordering SRM (through 1980)

Companies Company Locations

Represented Represented

Type of Firm Number Percent Number Percent

IC device manufacturer 34 52 51 59

Measurement systems supplier 10 15 12 14

Mask house 6 9 6 7 Other, including government 16 24 18 20

Total 66 100% 87 100%

Source: Computed from CEEE lists of seminar attendees, companies ordering

SRMs , and companies participating in interlaboratory tests. Many

companies were involved in more than one way. The number of company locations represented is greater than the number of companies

because some companies sent employees from plants at several

locations

50
linewidth articles by non-NBS authors through October 1980, this is probably

a very Incomplete reflection of the extent to which NBS linewidth research is

referenced. For example, several conference papers which reference the NBS

work were not listed in the Science Citation Index .

Secondary standards

NBS results are transmitted indirectly to industry through the use of secondary

standards which are related to an SRM 474 through direct calibration. One company may have a dozen or more such secondary standards related to the SRM 474.

There are also a few commercial suppliers of linewidth measurement standards

to the semiconductor industry. As of January 1981, the major independent

supplier had shipped about 100 standards related to an SRM 474, and had recalibrated 20 standards for customers who returned standards previously purchased.

In addition, at least one manufacturer of linewidth measurement equipment supplies standards related to the SRM 474 to customers, and as of yearend 1980,

at least one other equipment manufacturer was planning to do so.

4.3 OTHER EFFECTS OF NBS LINEWIDTH MEASUREMENT RESEARCH

NBS linewidth measurement research has had many effects which are not quantified

in this report. Some of these "other effects” may involve far greater economic

benefits than the effects quantified . These other effects are summarized in

this section.

Repeatability . In addition to reducing measurement bias, NBS measurement

procedures are designed to Improve the repeatability or consistency of linewidth

measurements

Discussions with industry Indicate that at a number of companies, NBS has had

a significant effect on measurement practices related to repeatability such as use of Kohler illumination, filtered green light, a two-thirds condenser-toobj active numerical aperture ratio, and other practices.

However, we were not able to determine quantitative effects of NBS

recommendations on repeatability. NBS researchers believe that following the

NBS procedures may Improve "3-sigma repeatability" by as much as 1 ym for

image-shearing systems. 2 One company suggested that improvements might be

large (e.g., a decrease in variability from 0.5 ym to .05 ym) for companies

which previously had poor measurement practices but slight for companies with

^ Kohler Illumination is a type of illumination for optical microscopes which

provides uriform Illumination, reduces stray light, and results in bright

Images with good contrast. A condenser is a microscope lens which collects

light to illuminate the object being measured. An objective is a lens which

forms an image of the object. The numerical aperture is a computed value

used to describe the resolving power of the microscope.

2 Nyyssonen, Diana, November 21, 1980 conversation.

51
previously good practices. Generally, the companies queried did not appear to

have collected and analyzed measurement data in a way that would show the

repeatability effects of adopting NBS recommendations.

Wafer linewidths . Some of NBS’s photomask linewidth measurement research has

also helped improve measurements on wafers. (Current NBS research is

specifically concerned with wafer linewidth measurements.)

Better wafer measurements can provide substantial cost savings through improved

yields and other benefits. For example, one company responding to a survey

conducted for NBS by Charles River Associates reported benefits of $200,000 for

1980 as a result of improved linewidth measurements on wafers due to NBS

research.

Product performance . Improved measurements reduce the barrier to production of

IC devices with finer lines. For example, one company told us it was able to

produce IC devices for research purposes with finer geometries as a result of

better linewidth control on photomasks due to applying NBS measurement procedures. Shrinking circuits improves device performance in several important

ways. Including Increasing speed, reducing the space required for a device,

reducing energy required to operate the device, and reducing IC manufacturing

costs

Product reliability . NBS researchers believe that improved linewidth

measurements also lead to better field reliability of IC devices. This view

is corroborated by companies responding to the survey mentioned above conducted

by Charles River Associates.

Measurement equipment design . NBS work has affected the design of commercially

marketed linewidth measurement systems. According to NBS scientists involved

in the project, NBS work has stimulated several major changes in design of some measurement systems, including adjustable threshold for line edge, fine focus

control, mercury arc lamps, and use of CRT output in setting video levels for

video image scanning systems. 2 For example, one equipment manufacturer

referenced NBS work as the basis for the method of line edge selection used in

its scanning system.

Measurement equipment selection . NBS work has affected measurement equipment

selection. For example, one company told us it avoided a $300,000 expenditure for new measurement equipment because NBS research helped them to make

adequate measurements with existing systems.

1 Results were reported in Productivity Impacts of NBS R&D; A Case Study of

the Semiconductor Technology Program by Charles River Associates (National

Bureau of Standards: Washington, D.C., 1981).

2 Nyyssonen, Diana, January 26, 1981 conversation.

3 Coates, Vincent, "Computerized Optical System for Precision Line Width

Measurements," paper presented at the Microelectronics Measurement Technology

Seminar, San Jose, CA, February 7, 1979.

52
In other cases, companies have decided to replace their equipment with more advanced measurement systems as a result of NBS work, and some companies have

used the SRM 474 in evaluating competing systems.

International competitiveness . Better llnewidth measurements resulting from

NBS research are likely to Improve the International competitiveness of U.S.

semiconductor firms. Although foreign organizations have access to NBS

research results, e.g., through publications and through their American subsidiaries, it seems likely that dissemination of NBS results will be more

rapid among U.S. firms.

Other benefits . Other benefits of NBS research within the semiconductor

industry include better ability to tune and characterize photolithography

equipment used to produce ICs and photomasks. Potential applications outside

the semiconductor industry include measurements of the following: computer

magnetic tape head gaps; metal fatigue; scratches and digs in optical glass;

reticles of various types such as those used for star tracking; laser

recordings; and medical and biological specimens.

^ Nyyssonen, D. and R. E. Swing, Theory and Use of Optical Microscopes for

Llnewidth Measurements on IC Photomasks and Wafers , July 15, 1980 (draft

paper presented at the July 1980 llnewidth measurement workshop held at

National Bureau of Standards, Gaithersburg, Md.), p. 1-1.

53
5. RESEARCH COSTS

This chapter presents estimates of NBS's cost of conducting its linewidth

measurement research. As table 5.1 shows, the estimated present value of NBS

photomask linewidth measurement expenditures for FY 1974 through FY 1980 was about $2.2 million. This was derived as follows;

1. Data were obtained on actual NBS expenditures for research related to both

photomask and wafer linewidth measurements. The primary source of data on expenditures from FY 1974, when the project began, through FY 1978 was

files maintained by a scientist involved in the project.

For FY 79 and 80, direct labor and overhead charges were found by contacting

scientists who had worked on the project to determine the percent of their

time spent on this project. Capital equipment and other expenditures for

FY 79 and 80 were obtained from financial ledgers of the Center for Electronics and Electrical Engineering.

Some NBS expenses were recovered through fees to industry and so are not

included in research costs. For example, the SRM 474 is sold for $3,600,

which covers direct costs of producing and measuring an individual SRM.

It does not include any margin to repay NBS for the measurement research.

Cost data are also available from NBS computerized accounting records.

However, securing accurate cost data through the NBS accounting system was difficult because of problems in identifying the appropriate cost centers.

In some cases, linewidth project costs were combined in one cost center

with expenditures on other projects. Also, the change in cost centers over

time made the "audit trail" more intricate. Had data been available by

project areas, it would have been much easier to estimate research costs.

2. The percent of total linewidth measurement research which was related to

photomask mesurements (as opposed to wafer measurements) was estimated by

the linewidth measurement research project leader. For example, in FY 80,

20 percent of the research was related to photomasks with the rest being

related to wafer measurements. Multiplying by these figures showed

photomask-related expenditures of $1,335,756 for the seven-year period.

3. All amounts in column 5 have been expressed in 1980 dollars to adiust for

inflation since 1973. Inflation factors for labor and overhead were

obtained from the U.S. Office of Personnel Management. Inflation factors

for "measuring and Integrating instruments" were obtained from the Bureau

of Labor Statistics and applied to expenditures on equipment and other

items.

^ The research for this chapter was conducted primarily by Michael Usle,

presently a graduate student at Brigham Young University.

54
Table 5.1 NBS Research Expenditures

Fiscal

Year

(1)

Linewidths

research

spending^ ($)

(2)

Percent for

photomask

research^ (%)

(3)

Dollars for

photomask

research ($)

(4)

Inflated

to 1980

dollars^

(5)

Compounding

Factor^

(6)

Present

Value ($)

(7) = (5)x(6)

1974 16,082 100 16,082 22,736 1.7716 40,279

1975 193,500 100 193,500 258,415 1.6105 416,177

1976 338,000 100 338,000 429,101 1.4641 628,247

1977 426,000 88 374,880 454,969 1.3310 605,564

1978 262,500 70 183,750 209,751 1.210 253,799

1979 305,526 50 152,763 164,831 1.10 181,314

1980 383,903 20 76,781 76,781 1.0 76,781

Totals 1,925,511 1 ,335,756 1, 616,584 2,202,161

^ See text for source.

^ Percentages are based on conversation with Diana Nyyssonen, January 26, 1981.

^ Costs for salaries + overhead and costs for equipment + other items were

separately estimated. Inflation factors from the U.S. Office of Personnel

Management were applied to salaries + overhead. Inflation factors from the

Bureau of Labor Statistics for "measuring and integrating instruments" were applied to the cost of equipment + other items.

^ Single Compound Amount factors were selected for a 10 percent discount rate

from the table in appendix B.

55
Photomask-related research expenditures adjusted for inflation amounted to

$1,616,584.

4, Expenditures expressed in 1980 dollars were compounded at a rate of 10

percent per year to find their present (1980) value. The compounding was necessary to adjust for the opportunity cost of money—the net benefits

that would have been realized if the money had been spent for something

other than the linewldths measurement project. We used a compounding rate

of 10 percent per year, which is the rate specified for federal use by the

Office of Management and Budget.! Compounding is discussed in appendix B.

After compounding, the present value of photomask-related linewidth expenditures in 1980 dollars (col. 7) amounted to about $2.2 million for the

seven-year period.

Industry costs

There are other costs of developing the SRM and procedures which were not borne

by NBS but may be considered costs of the research. These other costs were not

quantified for this report. They include: (1) the costs incurred by firms to

cooperate in two interlaboratory studies in the 1977-1980 period and (2) industry costs of loaning a number of linewidth measuring systems to NBS for use in

its workshops.

Costs to individual firms of implementing NBS results were estimated in chapters

2 and 3 and are not included in research costs.

! U.S. Office of Management and Budget, "Circular No. A-94 Revised," March 27,

1972.

56
6. CONCLUSIONS

Summary

This report has estimated the costs and benefits of using the NBS-developed

Standard Reference Material 474 and related procedures for measuring linewidths

on photomasks. We used a model to estimate the net benefits per mask for a hypothetical IC manufacturer with inhouse mask-making facilities. Steps in the

analysis are summarized in table 6,1 at the end of this section.

For masks used in projection printing of wafers, benefits net of implementation

costs were $179 per mask. However, NBS gets credit for only $82 of these benefits since presumably the industry would have eventually improved measurements

on its own. For masks Intended for contact printing of wafers, the benefits

are $15 per mask, with NBS getting credit for $7.

Implications of the study

The results of applying the model to a particular case and the sensitivity

analysis suggest that many companies are likely to realize substantial net

benefits from improving their photomask linewidth measurements. Most combinations of values used in the model yielded positive net benefits and many benefits of improved photomask measurements were not quantified at all, so that

actual benefits were probably understated.

However, the reader should be aware that the numbers estimated in this report

are based on many assumptions which were not altered in the sensitivity analysis. Further study might show that some assumptions require modification in

order to produce reliable upper- and lower-bound estimates of the cost savings,

A subjective impression, based on discussions with industry, is that industry

managers consider the NBS photomask and wafer linewidth measurement research

very Important, They respect NBS as being a competent. Impartial, authoritative source of measurement technology. However, some in industry feel that NBS

research proceeds too slowly.

NBS linewidth measurement research has many impacts beyond the measurement of

photomask linewidths. An extremely important example is the effects on measurement of linewidths on wafers. Many in industry believe that NBS impacts

on wafer linewidths will be far more important than its effects on photomask

linewidths. Including these other benefits would substantially increase the

estimated economic benefits of NBS’s research.

Uses of the model

NBS and industry can use models such as the one developed for this report in

several ways.

1. NBS managers and researchers can use them to help estimate the overall

benefits of NBS research, to help plan NBS research directions, to

demonstrate benefits of improved measurement technology in terms meaningful

57
to corporate managers, and to help in deciding how to disseminate research

results.

2.

Company quality control managers can use such models to determine the

payoff from investing in improved measurements and to demonstrate these

payoffs to higher management. They can also use them to help choose among

alternative strategies for investing in improved measurements. By doing a sensitivity analysis, companies can determine which statistics to collect

to improve estimates of cost-savings.

Further research

This study has suggested several topics for further research:

1. Alter the assumptions in table 2.3, e.g., allow for random as well as systematic measurement error, additional measurements in the mask shop, and

gradual improvements in yield as linewidths become closer to target value;

2. Analyze the benefits of improved measurements of linewidths on wafers ;

3. Estimate industry-wide impacts of the photomask linewldth research and

estimate impacts after there has been time for results to disseminate

further in industry; and

4. Develop a guide for benefit-cost analysis of improved measurements for NBS

managers. Such a guide would identify the general kinds of data needed for

the analysis, suggest alternative methods of collecting this data, explain

basic economic tools, and show how to determine aggregate benefits and

costs. Worksheets could be included to help readers follow the method.

Economic research at NBS

In the past two years, the NBS Planning Office has funded two approaches to

estimating benefits and costs of a NBS semiconductor research effort.

First , the approach used in this paper relies on a model of the acceptance

measurement process. The model and the values used in illustrating it were based on discussions with NBS researchers and industry managers.

This approach helps in understanding how improved measurements benefit industry

and lets NBS managers simulate effects of various types of measurement improvements under various conditions. This should be useful in planning directions

for NBS measurement research and in showing individual companies how they may

benefit from Improved measurements, given their particular situation.

However, it can be very time consuming and difficult to develop such a model.

For a heterogeneous industry, it can also be difficult to gather the data

needed to apply the model for the various situations found in industry.

Also, aggregating may require hard-to-get data on diffusion of NBS results

within companies and the mix of product sales.

58
Second, the Planning Office also funded a study, by Charles River Associates,

of NBS impacts on productivity which included case studies of three NBS semiconductor research efforts. For the case studies, companies using NBS technology were surveyed by mail to directly obtain their estimates of dollar

benefits

This approach obtains inputs from a large number of companies at relatively low

cost. Even if some responses are "guesstimates," they may be the best data

available. This appears to be a less expensive way of getting dollar estimates

than the modeling approach, and it may avoid the need to collect additional

data for aggregating, since total reported effects can be used as a lower-bound

estimate of aggregate effects and survey responses will automatically reflect a variety of situations.

A disadvantage of the survey approach is that, unless the questionnaire is very

detailed, NBS may not know how companies arrived at their dollar estimates and

it may not know just which aspects of improved measurements were responsible

for the Impacts.

Both of these approaches are likely to be useful to NBS in its future efforts

to understand the economic effects of its research, A combination of the two

approaches might be to develop a somewhat detailed model for estimating benefits and costs, and to use surveys to get data on steps in the measurement

process as well as dollar benefits. This would help in evaluating the quality

of the model and in Interpreting company responses.

No matter which approach is used, there will be several problems in getting

accurate information. For one, companies often do not know how improved measurements affect yields and other parameters. Also, it may be difficult for

industry managers to trace particular technical advances to NBS, especially if

NBS results have filtered out to industry over a long period. Companies may

also be reluctant to reveal proprietary Information, such as yield data.

However, because industry perceives NBS research as being quite useful, many

companies are very willing to help by providing non-sensitive information for

the benefit-cost analysis. This greatly aids NBS*s ability to conduct studies

of the economic impacts of its research.

59
Table 6.1 Summary of Steps in the Analysis

1. Determine values for all parameters listed in tables 3.1 and 3.2.

2. Determine the form of the probability density function f(x) describing

mask linewidths. II” ” 3. Calculate the limits of Integration for f(x) (A1 A2 A1 ^ and A2

using table 2.2.

I I

•• •• 4. Calculate probabilities ?2 through and ?2 through using equations

(5) and (6) in table 2.1.

5. Calculate costs of measurement error before and after improving procedures,

using equations (3) and (4) in table 2.1.

6. Calculate implementation costs C4 for the "with NBS" situations using

equation (7) in table 2.1.

7. Calculate implementation costs C4* for the "without NBS" situation using

equation (8) in table 2.1.

8. Calculate benefits for the "with NBS" situation using equation (1) in

table 2.1.

9. Recompute benefits for the "without NBS" situation using equation (2)

in table 2.1.

10.

Subtract the "without NBS" benefits from the "with NBS" benefits to find

the benefits credited to the NBS research (equation [9] in table 2.1).

60
APPENDICES

A. GLOSSARY

B. DISCOUNTING TECHNIQUES

C. PUBLICATIONS RELATED TO NBS LINEWIDTH MEASUREMENT

RESEARCH

D. SELECTED BIBLIOGRAPHY
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(3
APPENDIX A

GLOSSARYl

ACCEPTANCE MEASUREMENT - measurement of characteristics of incoming products

to make sure they meet specifications.

ACCURACY - (in length metrology) closeness to the true length as defined by

the national standard of length.

CALIBRATION CURVE - for linewidths , formula for correcting knovm systematic

errors in llnewidth measurements.

CHIP - see Die.

COMPOUNDING - increasing the value of a dollar amount to find its value at a later time. (This can be done using a Single Compound Amount factor.)

CONTACT PRINTING - printing masks or wafers from a photomask by placing the

photomask in contact with the photoresist-coated surface to be exposed.

DEVICE - a unit containing a functionally complete integrated circuit pattern.

DIE - the portion of a wafer bearing an individual circuit or device. (One

wafer has an array of such circuits.)

DISCOUNT RATE - the interest rate reflecting the time value of money that is

used to convert benefits and costs occurring at different times to equivalent

values at a common time

DISCOUNTING - a technique for converting future cash flows to equivalent

amounts at an earlier point in time.

INTEGRATED CIRCUIT (IC) - an interconnected group of circuit elements such

as resistors and transistors on a single tiny chip of semiconductor material,

where each chip comprises a complete operable electronic circuit.

LINE - a single feature of the pattern on a wafer or photomask.

^ In some cases the definitions given here are simplified and tailored to this

report. For more generally applicable and exact definitions of engineering

terms, see American National Standard ANSI/ASTM F 127-74, Standard Definitions

of Terms Relating to Photomasking Technology for Microelectronics , and "Procedures for Using SRM 474,” National Bureau of Standards, June 9, 1980,

pp. A-4 through A-7. For standard definitions of economics terms, see Marshall, H.E.; Ruegg , R.T.; and Petersen, S.R., Recommended Practice for

Measuring Life-Cycle Costs of Buildings and Building Systems , NBSIR 80-2040

(Washington, D.C.: National Bureau of Standards, 1980).

A-1
LINEWIDTH - the width of a line as measured between its two edges.

MARKET INTEREST RATES - interest rates actually paid by borrowers. Market

rates generally include a premium to compensate for inflation,

MICROMETER (pm) - one millionth of a meter.

PHOTOMASK - a glass plate with a pattern used for exposing photoresist-coated

wafers in the fabrication of integrated circuits (analogous to a transparency

in a photographic process),

PHOTORESIST - a radiation-sensitive substance used to coat wafers in IC

fabrication. Exposed and developed photoresist masks the wafer in a way useful

for creating patterns on the substrate,

POLARITY - for a photomask, whether a line is opaque or transparent.

PRESENT VALUE - the value of a benefit or cost at the present time (i.e., as of the base period) , found by discounting future cash flows or compounding past

cash flows to the present.

PROJECTION PRINTING - printing wafers by projecting an optical image of the

photomask on the photoresist-coated wafer.

RANDOM ERROR - in measurements , the component of measurement error which

increases the spread of measured values about the mean, but does not affect

the mean. (An increase in random error reduces measurement repeatability.)

REAL INTEREST RATE - the interest rate expressed in constant dollars, i.e.,

dollars which do not reflect price inflation. (If there is inflation, the

real rate is less than the market rate.)

REPEATABILITY - a measure of the ability to make consistent measurements within

a single organization.

RESIST - see photoresist.

SEMICONDUCTORS - materials which conduct electricity better than insulating

materials but not as well as metals.

SINGLE PRESENT WORTH (SPW) FACTOR - a discount factor by which a value may be

multiplied to find its value at an earlier point in time.

SINGLE COMPOUND Af'IOUNT ( SCA) FACTOR - a factor by which a value may be

multiplied to find its value at a later point in time.

STANDARD REFERENCE MATERIALS (SRMs) - physical calibration standards sold by

the National Bureau of Standards. The SRM 474 and SRM 475 are coated glass

plates with line patterns used in calibrating optical microscopes.

A-2
STEP AND REPEAT - a method for exposing photomasks and wafers which involves

making an exposure and then stepping the image to the next position to create

an identical pattern.

SYSTEMATIC ERROR - in measurement, the measurement bias; the difference between

the true linewidth value and the limiting mean of the linewidth measurements.

(The limiting mean is the mean which the sample mean approaches as the number

of measurements Increases.)

TARGET VALUE - for linewidths, the desired linewidth.

UNIFORM PRESENT WORTH (UPW) FACTOR - a discount factor for converting a series

of recurring sums to their value at an earlier point in time.

WAFER - a crystal slice used in fabricating semiconductor devices.

WORKING PLATE - a photomask (usually made from a master or sub-master mask)

used in wafer fabrication.

YIELD - the percent of product which meets acceptance standards during

measurement and testing.

A-3
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APPENDIX B. DISCOUNTING TECHNIQUES

This appendix explains how to discount or compound to accurately calculate

the costs and benefits of research.

A one-dollar cost or benefit is worth less today if it will occur in the

future than if it occurs in the present, even in the absence of inflation.

This is because money received now can be invested at a profit which is lost

if the money is not received until later. Similarly, a one-dollar cost or benefit is worth more if it occurred in the past than if it occurs in the

present. Therefore, future dollar effects must be discounted (reduced) to

find their present value, and past dollar effects must be compounded (increased)

to find their present value.

A project which has zero net benefits (i.e., benefits equal costs) when all

amounts are discounted at 10 percent is the equivalent of a project which

returns 10 percent when evaluated without discounting. It is important to

remember this when comparing projects.

In this report , for the purpose of discounting or compounding we assume that

all amounts occur at the end of the year.

Compounding past sums

In table 5.1 in chapter 5, 1974 research costs were compounded to find their

1980 value. Original research expenditures were $16,082. Adjusting for inflation increased the amount to $22,736. This amount was then compounded at a rate of 10 percent over the six-year period through 1980, using the following

formula

Present Value (1980) = Original Sum X SCA

= $22,736 X 1.7716

= $40,279

The Single Compound Amount factor (SCA) was chosen from table B.l in appendix B

for a period of six years. All factors in table B.l are for a 10 percent discount rate, but the SCA can be computed for other discount rates using the

formula:

SCA = (1 + r)t

where "r" is the discount rate and "t" is the number of years.

Discounting future sums

Equations (7) and (8) in table 2.1 discount future implementation costs to

their present value. The equation for implementation costs is:

B-1
j

C4 = ^[C5+C6 UPW, . + I C7. SPW SPW

kT (t-s) ±=i 1 u(i) s

The discount factors are underlined. The expression inside the brackets shows

implementation costs discounted to the implementation year. The SPWg factor

further discounts from the implementation year "s" to the present. The discount

factors are discussed some more below.

Uniform Present Worth (UPW)

Costs which are the same each year (C6) can be discounted using a Uniform

Present Worth (UPW) factor for the number of years (t-s) over which the cost occurs. The UPW factor can be selected from table B.l or computed using the

following formula:

UPW = (i+r)t - 1

r(l+r)t

Single Present Worth (SPW)

Future costs which are not the same each year (C7;j^) are each discounted using a Single Present Worth (SPW) factor for the year in which the cost occurs. The

Single Present Worth factor can be selected from table B.l or computed using

the formula:

SPW = 1

. (l+r)t

The entire expression inside the brackets is also discounted by a Single Present

Worth factor. This is because if the implementation year is in the future (e.g.,

1981 for a base year of 1980), costs must be further discounted to adjust for

this delay.

An Example

For the values:

C5 = C6 = C7i = C72 =

r = kT =

$13,460 (initial cost)

$6, 600/year (equal annual costs for 5 years)

$6,600 (2 years after implementation)

$6,600 (4 years after implementation)

10 percent (real discount rate)

50,000 (number of masks measured over five years)

Discounted costs C4 would be:

C4 = 2 [$13,460+$6, 600(3. 791)+$6,600(.8264)+$6,000(.6830)](. 9091)

50,000

= $1. 76/mask

B-2
where

3.791 is a UPW factor from table B.l for a 5-year period

.8264 is a SPW factor from table B.l for 2 years

.6830 is a SPW factor from table B.l for 4 years

.9091 is a SPW factor from table B.l for 1 year

Average benefits over analysis period

Benefits (C - C") in equation (1) in table 2.1 are benefits/mask in a single

year, e.g., 1980. However, these benefits are repeated over the period (t-s).

For example, benefits of (C’-C") might occur each year for five years. To find

the average benefits per mask over the analysis period, discounted to the

implementation year, we multiply the one-year benefits (C*-C") by the factor

UPW(t-s). This averages the higher per-mask benefits of earlier years with

T

the lower per-mask benefits of later years (benefits of later years are lower

due to discounting). The following section explains how t-s) was obtained.

T

The benefits per mask in the year after the procedures are implemented are (C'-C) X SPW]^, where (C'-C") is the per-mask benefits before discounting and

SPWj^ is the Single Present Worth discounting factor for one year. The benefits

per mask in the second year are (C’-C") x SPW2 , and so on. Assuming masks are produced at a constant rate over the analysis period, average benefits per

mask are:

(C'-C") X SPWx + (C'-C") X SPW2 + ... + (C'-C") X SPW(t-s)

(C’-C") UPW(^_3)

T

(14)

where T is the analysis period, (t-s) is the period over which benefits occur

and UPW is the Uniform Present Worth factor. UPW can be found in table B.l in

appendix B, or calculated from the formula in appendix B, for time period (t-s).

B-3
APPENDIX B

Source

Table B.l Discounting Factors for 10 Percent Discount Rate

Gonpound Prcaect sinking Capital Compound Freaent •ount voith fund recovery amount worth

factor factor factor factor factor factor

fi SCA 8PW OSF OCR UCA UFW

1 2 3 4 5 6 7 Q

X 1.1000 0.9091 1 .00000 1.10000 1.000 0.909 1 2 1.2100 0.8264 0.47619 0.57619 2.100 1.736 2 3 1.3310 0.7513 0.30211 0.40211 3.310 2.487 3 4 1.4641 0.6830 0.21547 0.31547 4.641 3.170 4

S 1.6105 0.6209 0.16380 0.26380 6.105 3.791 5

6 1.7716 0.5645 0.12961 0.22961 7.716 4.355 6

7 1.9487 0.5132 0.10541 0.20541 9.487 4.868 7 8 2.1436 0.4665 0.08744 0.18744 11.436 , 5.335 8

9 2.3579 0.4241 0.07364 0.17364 13.579 5.759 9 10 2.5937 0.3855 0.06275 0.16275 15.937 6.144 10

11. 2.6531 0.3505 0.05396 0.15396 18.531 6.495 11 12 3.1384 0.3186 0.04676 0.14676 21.384 6.814 12

13 3.4523 0.2897 0.04078 0.14078 24.523 7.103 13

14 3.7975 0.2633 0.03575 0.13575 27.975 7.367 14 15 4.1772 0.2394 0.03147 0.13147 31.772 7.606 15

16 4.5950 0.2176 0.02762 0.12782 35.950 7.824 16

17 5.0545 0.1978 0.02466 0.12466 40.545 8.022 17 18 5.5599 0.1799 0.02193 0.12193 45.599 8.201 18 19 6.1159 0.1635 0.01955 0.11955 51.159 8.365 19 20 6.7275 0.1486 0.01746 0.11746 57.275 8.514 20

21 7.4002 0.1351 0.01562 0.11562 64.002 8.649 21 22 8.1403 0.1228 0.01401 0.11401 71.403 8.772 22

23 8.9543 0.1117 0.01257 0.11257 79.543 8.883 23 24 9.8497 0.1015 0.01130 0.11130 88.497 8.985 24 25 10.8347 0.0923 0.1017 0.11017 98.347 9.077 25

26 11.9162 0.0639 0.00916 0.10916 109.182 9.161 26

27 13.1100 0.0763 0.00826 0.10826 121.100 9.237 27 28 14.4210 0.0693 0.00745 0.10745 134.210 9.307 28 29 15.8631 0.0630 0.00673 0.10673 148.631 9.370 29 30 17.4494 0.0573 0.00609 0.10608 164.494 9.427 30

31 19.1943 0.0521 0.00550 0.10550 181.943 9.479 31 32 21.1138 0.0474 0.00497 0.10497 201.138 9.526 32 33 23.2252 0.0431 0.00450 0.10450 222.252 9.569 33

34 25.5477 0.0391 0.00407 0.10407 245.477 9.609 34 35 28.1024 0.0356 0.03369 0.10369 271.024 9.644 35

40 45.2593 0.0221 0.00226 0.10226 442.593 9.779 40

45 72.8905 0.0137 0.00139 0.10139 718.905 9.863 45

50 117.3909 0.0085 0.00086 0.10086 1163.909 9.915 50

55 189.0591 0.0053 0.00053 0.10053 1880.591 9.947 55 60 304.4816 0.0033 0.00033 0.10033 3034.816 9.967 60

65 490.3707 0.0020 0.00020 0.10020 4893.707 9.980 65 70 789.7470 0.0013 0.00013 0.10013 7887.470 9.987 70

75 1271.8952 0.0008 0.00008 0.10008 12708.954 9,992 75 80 2048.4002 0.0005 0.00005 0.10005 20474.002 9.995 80

85 * 3298.9690 0.0003 0.00003 0.10003 32979.690 9.997 65

90 5313.0226 0.0002 0.00002 0.10002 53120.226 9.998 90

95 8556.6760 0.0001 0.00001 0.10001 85556.760 9.999 95 100 13780.6123 0.0001 0.00001 0.10001 137796.123 9.999 100

Marshall, H. E . & Ruegg , R. T .

,

Energy Conservation in Buildings

Economics Guidebook for Investment Decisions, NBS Handbook 132,

(Washington, D.C.: U.S. Government Printing Office, 1980).

B-4
APPENDIX C. PUBLICATIONS RELATED TO NRS LINEWIDTH MEASUREMENT RESEARCH

Source

Ciarlo, D. R. , Schultz, P. A., and Novotny, D. B. , Automated Inspection of

ic Photomasks, Proa. Soc. Photo-Optical Inetrum. Engre. Photofabrication Imagery, 84-89 (1975).

Jerke, J. M. , Semiconductor Measurement Technology

Optical and

Dimensional-Measurement Problems with Photomasking in Microelectronics,

NBS Spec. Publ. 400-20 (October 1975). (GPO, NTIS]

Swyt, D. A., NBS Program in Photomask Linewidth Measurements, Solid State

Technology 19 (4), 55-61 (April 1976). [NTIS]

Kasdan, H. L. , and George, N. , Linewidth Measurement by Diffraction Pattern

Analysis, Proc. Soc. Photo-Optical Inetrum. Engre. Developments

in Semiconductor Microlithography, 54-63 (1976).

Swing, R. E. , The Theoretical Basis of a New Optical Method for the Accurate

Measurement of Small Line-Widths, Proc. Soc» Photo-Optical Inetrum.

Engre. Developments in Semiconductor Microlithography, 65-77

(1976).

Jerke, J. M. , Hartman, A. W. , Nyyssonen, D. , Rosberry, F. W. , Swing, R. E.

,

Swyt, D. A. , and Young, R. D. , Accurate Line-Width Measurements at the

National Bureau of Standards, Proc. Microelectronics Seminar - Inters

face '76, Monterey, California, October 3-5, 1976, pp. 51-59.

Jerke, J. M. , Hartman, A. W. , Nyyssonen, D. , Swing, R. E. , Young, R. D. , and

Keery, W. E. , Comparison of Linewidth Measurements on an SEM/Interferometer System and an Optical Linewidth-Measuring Microscope, Proc. Soc.

Photo-Optical Inetrum. Engre. 100 , Developments in Semiconductor Microlithography II, 37-45 (1977).

Nyyssonen, D. , Optical Linewidth Measurements on Silicon and Iron-Oxide Photomasks, Proc. Soc. Photo-Optical Inetrum. Engre. 100 , Developments

in Semiconductor Microlithography II, 127-134 (1977).

Young, R. D. , Length Calibrations in the Micrometer and Sub-Micrometer

Range, >lnn. CIRP 25, 245-250 (1977).

Nyyssonen, D. , Linewidth Measurement with an Optical Microscope: The Effect

of Operating Conditions on the Image Profile, Appl. Optics _1j6, 2223-

2230 (1977).

Swyt, D. A. , and Rosberry, F. W. , A Comparison of Some Optical Microscope

Measurements of Photomask Linewidths, Solid State Technology 20 (8),

70-75 (August 1977).

National Bureau of Standards, Semiconductor Measurement Technology , NBS

List of Publications 72 (Washington, D.C.: National Bureau of Standards, revised December 1981).

C-1
Swyt, D. A., Rosberry, F. W. , and Nyyssonen, D, , Calibration of Optical Microscopes for Photomask Linewidth Measurements, Pvoc. MicvoetectvonicB Seminar - Interface '77, Monterey, California, October 5-7, 1977,

pp. 131-144.

Swyt, D. A., An NBS Physical Standard for the Calibration of Photomask Linewidth Measuring Systems, Proc, Soc, Photo-Optical Instmm. Engrs. 129,

Effective Utilization of Optics in Quality Assurance, 98-105 ( 1977)

Swyt, D. A., Design of a Pattern on a Photomask-Like Physical Standard for

Evaluation and Calibration of Linewidth-Measuring Systems, Solid

State Technology _21 ( 1 ) , 35-42 (January 1978).

Novotny, D. B. , and ciarlo, D. R. , Semiconductor Measurement Technology:

Automated Photomask Inspection, NBS Spec. Publ. 400-46 (April 1978).

[GPO, NTIS]

Nyyssonen, D. , Optical Linewidth Measurements on Wafers, Proc* Soc. PhotoOptical Instrum. Engrs. 135 , Developments in Semiconductor Microlithography III, 115-119 (1978).

Novotny, D. B. , and Ciarlo, D. R., Automated Photomask Inspection, Solid

State Technology 2^ (5), 51-59, 76 (May 1978) and 21_ (6), 59-67

(June 1978). (Based on 15f) [Reprint supply exhausted]

Scire, F. E. , and Teague, E. C. , Piezodriven 50-pm Range Stage with Subnanometer Resolution, ReV. Sci. Instrur. _49, 1735-1740 (1978).

Swyt, D. A., Rosberry, F. W., and Nyyssonen, D. , Photomask Linewidth Measurement, Circuits Manufacturing 1 8 (9), 20 ff (September 1978). [No

reprints available]

Kintner, E. C. , Method for the Calculation of Partially Coherent Imagery,

Appl. Optics 21' 2747-2753 (1978).

Nyyssonen, D. , and Jerke, J. M. , Linewidth Measurement; From Fine Art to

Science, Tech. Digest, 1978 Intemat. Electron Devices Meeting, Washington, D. C. , December 4-6, 1978, pp. 437-440.

Nyyssonen, D. , and Jerke, J. M. , Optical Linewidth Measurement— A Basic Understanding, Proc. Microelectronic Measurement Technology Seminar,

San Jose, California, February 6-7, 1979, pp. 251-266.

Nyyssonen, D. , Spatial Coherence: The Key to Accurate Optical Micrometrology, Proc. Soc. Photo-Optical Instrum. Engrs. 1 94 , Applications

of Optical Coherence, 34-44 (1979).

Jerke, J. M. , Ed., Semiconductor Measurement Technology: Accurate Linewidth Measurements on Integrated-Circuit Photomasks, NBS Spec. Publ.

400-43 (February 1980). [GPO, NTIS]

C-2
Nyyssonen, D. , Linewidth Measurement Spotlight, Semiconductor International

3 (3), 39-56 (March 1980).

Kasdan, H. L. , Linewidth Measurement by Diffraction Pattern Analysis, NBS

rA.K-79-175 (April 1980). [NTIS]

Nyyssonen, D. , Cali’'>ration of Optical Systems

Wafers, Proc* 3oc» Photo—Optical Insururrim

Microlithography V, 119-126 (1980).

for Linewidth Measurements on Engre, 221 , Semiconductor

Addenda

Bullls, M. and Nyyssonen, D. , "Optimal Linewidth Measurements on Photomasks and

Wafers," Microstructure Science and Engineering , Vol, 2, Norman G. Einspruch,

ed., (New York: Academic Press, forthcoming).

Croarkin, M. C. and Varner, R. N. , "Measurement Assurance for Dimensional

Measurements on Integrated - Circuit Photomasks," to be published as an NBS

Tech Note (Washington, DC: National Bureau of Standards, forthcoming).

Jerke, John M. , M. C. Croarkin, and R. N. Varner. Semiconductor Measurement

Technology: Interlaboratory Study of Linewidth Measurements for Antireflective Chromium Photomasks . Washington, D.C.; National Bureau of Standards (in preparation).

C-3
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T* -
APPENDIX D. SELECTED BIBLIOGRAPHY

1. American National Standards Institute. Standard Definitions of Terms

Relating to Photomasking Technology for Microelectronics , ANSl/ASTM F

127-74.

2. Bossung, J.W. and E.S. Muraski. "Advances in Projection Microlithography,"

Solid State Technology , August 1979, pp. 109-112.

3. Burggraaf, Pieter. "Photomask Making: Issues vs. Equipment," Semiconductor

International , March 1981, pp. 27+.

4. Bullis, W. Murray, and Diana Nyyssonen. "Optical Linewidth Measurements

on Photomasks and Wafers," in Microstructure Science and Engineering , Vol. 2, Norman G. Einspruch, ed. (New York: Academic Press, forthcoming).

5. Charles River Associates, Productivity Impacts of NBS R&D: A Case Study

of the Semiconductor Technology Program , Summary Volume. Washington, D.C.:

National Bureau of Standards, June 1981.

6. Coates, Vincent. "Computerized Optical System for Precision Line Width

Measurements," paper presented at the Microelectronics Measurement

Technology Seminar, San Jose, Ca., February 7, 1979.

7. Croarkin, Carroll, John Jerke, and Ruth Varner. Results of Interlaboratory

Study: Lecture Notes (presented at the NBS Training Seminar, "Linewidth

Measurements on Integrated Circuit Photomasks and Wafers," July 15-18,

1980).

8. Dan, M. , I. Tanabe , M. Hoga, and S. Torisawa. "Fabrication System of

High Quality Hard-Surface Masks for LSI’s," Proceedings of Kodak

Microelectronics Seminar: Interface *79 (San Diego, Oct, 25-26, 1979).

9. Jerke, John M, , ed. Semiconductor Measurement Technology: Accurate

Linewidth Measurements on Integrated Circuit Photomasks , National Bureau

of Standards Special Publication 400-43. Washington, D.C.: U.S.

Government Printing Office, 1980.

10. Jerke, John M., M.C. Croarkin, and R. N, Varner. Semiconductor

Measurement Technology: Interlaboratory Study of Linewidth Measurements

for Anti-reflective Chromium Photomasks . Washington, D.C.: National

Bureau of Standards (in preparation),

11, Ku, Harry. "Statistical Concepts in Metrology," in Handbook of Industrial

Metrology, American Society of Tool and Manufacturing Engineers (New York:

Prentice-Hall, 1967), pp. 20-50.

D-1
12 . Marshall, H.E. and R.T. Ruegg. Efficient Allocation of Research Funds:

Economic Evaluation Methods with Case Studies In Building Technology , National Bureau of Standards Special Publication 558. Washington, D.C.:

U.S. Government Printing Office, 1979.

13. Marshall, H.E., R.T. Ruegg, and S.R. Petersen. Recommended Practice for

Measuring Life-Cycle Costs of Buildings and Building Systems , NBSIR 80-

2040. Washington, D.C.: National Bureau of Standards, 1980.

14. Mills, Frederick C., Statistical Methods , 3^^ ed. New York: Holt,

Rinehart and Winston, 1955.

15. National Bureau of Standards. Standard Reference Material 474; Optical

Microscope Linewidth Measurement Standard (written procedures accompanying

SRM 474). Washington, D.C.: National Bureau of Standards, June 9, 1980

(unpublished)

16. National Bureau of Standards. "Procedures for Using SRM 474,"

June 9, 1980, in Standard Reference Material 474; Optical Linewidth

Measurement Standard (written procedures accompanying SRM 474). Washington, D.C.: National Bureau of Standards, June 9, 1980 (unpublished).

17. Nyyssonen, D. and R.E. Swing. Theory and Use of Optical Microscopes for

Linewidth Measurements on IC Photomasks and Wafers , July 15, 1980 (draft

paper presented at the July 1980 linewidth measurement workshop held at

National Bureau of Standards, Gaithersburg, Md.).

18. Scace, R.I. Semiconductor Technology for the Non-Technologist , NBSIR 81-

2197. Washington, D.C.: National Bureau of Standards, 1981

19. Science Citation Index . Philadelphia; Institute for Science Information.

20. Scientific American . September 1977 issue.

21. U.S. Department of Commerce, Industry and Trade Administration. A Report

on the U.S. Semiconductor Industry . Washington, D.C.: U.S. Government

Printing Office, 1979.

22. U.S. Office of Management and Budget. "Circular No. A-94 Revised,"

March 27, 1972.
NBS-114A iREv. 2 -ac) U.S. CF-PT. OF COMM.

BIBLIOGRAPHIC DATA

1, PUBLICATION OR

REPORT NO.

2. Perforr ng Organ. Report No. 3. Publication Date

SHEET (See instructions) NBSIR 82-2458 May 1982

4. TITLE AND SUBTITLE

BENEFITS AND COSTS OF IMPROVED MEASUREMENTS: THE CASE OF INTEGRATED-CIRCUIT

PHOTOMASK LINEWIDTHS

5. AUTHOR(S)

Carol Chapman Rawie

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions)

national bureau of STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8 . Type of Report & Period Covered

Final

9.

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

Planning Office

National Bureau of Standards

Washington, D.C. 20234

10.

SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here)

Accurate dimensional measurements are vital to quality control in the semiconductor

industry. This paper presents a method for estimating the dollar cost-savings

from improving integrated-circuit photomask linewidth measurements. The method

is illustrated with a case study of a hypothetical semiconductor device manufacturer who uses a Standard Reference Material (SRM) developed at the National

Bureau of Standards for optical microscope calibration.

Benefits of investing in improved photomask linewidth measurements include

reducing disputes between mask maker and mask customer, reducing waste of good

photomasks, and Increasing device yields. For the hypothetical manufacturer

described in the study, these benefits were much greater than costs of

implementing the new measurement procedures.

While the model is tailored to photomask linewidth measurements, its concepts

can be applied to many other types of measurements.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

accurate measurements; benefit-cost analysis; cost savings; economic analysis;

photomask linewidth measurements; semiconductors

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