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SEMI P35-0704 © SEMI 2000, 2004 8 can be made con sistent with the ultimate purpo se of the measurements. A1-4 The inner and oute r linewidth bounding boxes need not have the sam e shape, but their widths must be unambig…

SEMI P35-0704 © SEMI 2000, 2004 7

APPENDIX 1

SOME GENERAL NOTES ON LINEWIDTH METROLOGY

NOTICE: The material in this appendix is an official part of SEMI P35 and was approved by full letter ballot

procedures on April 22, 2004.

A1-1 A metrology process can be represented by the

operation

process model ⊕ feature model → output model.

A1-1.1 Here the process model represents the

metrology process. These models are abstractions of the

complex realities they represent, a simplification

usually required in order to make the modeling tractable

and the measurement practical. The output model of

this metrology process is the feature model (Section

5.5.4) with the metrology results attached, including the

associated measurement uncertainty. Measurement

uncertainty arises from inevitable differences between

both the process and feature models and their respective

realities. The measurement error (Section 5.10) is the

difference between the measurement result and the

unknown true value, and the measurement uncertainty

(Section 5.11) is expressed as a confidence interval

representing the variance of the measurement errors.

The measurement uncertainty includes components

from model infidelity in addition to scale calibration,

repeatability, environmental factors, etc. A confidence

interval of 95% (or 2σ for normally distributed errors)

is used in the examples, in accordance with

international custom. That is, the likelihood that the true

value of the measurand (Section 5.9) lies within the

range (measurement result ± measurement uncertainty)

is 95%.

A1-1.2 A manufacturing process can be represented in

a similar manner. In particular, if that process is wafer

exposure, then the same feature model for the

photomask features can be used for both the mask

metrology and exposure processes:

exposure model ⊕ photomask feature model

→ wafer feature model.

A1-1.3 Errors and uncertainties in the photomask

feature model propagate through the exposure model to

become manufacturing errors—differences between a

wafer feature’s size or placement and its target value—

and manufacturing uncertainties. In analogy with

measurement uncertainty, tolerances on wafer features

encompass mask measurement uncertainties, including

differences between the models and their respective

realities, as well as the effects of tolerances for

exposure parameters and photomask features. The mask

error enhancement factor (MEEF) and other optical

proximity effects are good examples of the wafer

exposure model operating on photomask feature size

and placement variations to produce nonlinear

variations in wafer feature size and placement under

some conditions.

A1-2 Real microlithographic features (Section 5.5)

often have irregular shapes and rough edges; it is

neither possible nor necessary to know the exact shape

of a feature to be measured. The purpose of the feature

bounding boxes (Section 5.1) defined here is to account

for such edge details as top-to-bottom runout and along-

the-line irregularities that are often observed. In such

cases the bounding boxes help define the measurand

(Section 5.9). To the extent that such details are not

known, not relevant, or too complex to be considered,

the bounding boxes represent the feature with a simpler

geometry and mix these disregarded details into the

measurement uncertainty. For the ideal line with known

edge geometry and no edge irregularities, the inner,

mean, and outer linewidth bounding boxes (Sections

5.8.3–5.8.5) can be identical and the line edge bounding

box (Section 5.6) can have zero width. The bounding

box approach simplifies metrology issues for the quasi-

thin-film features often encountered in

microlithography. Extension of the concept to

structures with nonplanar top surfaces or extending

below the reference plane (Section 5.14) becomes more

complicated.

A1-3 A great deal of flexibility has been incorporated

into some of these definitions. This is because the

definition of a measurand (Section 5.9) can depend on

the purpose for which a measurement is made, and the

measurement error depends on the definition of the

measurand. It is up to the user to specify or define the

measurand in a way that suits his present purpose and in

an unambiguous way. Otherwise interpretation of the

measurement result may be in error and the

measurement uncertainty may be meaningless or

impossible to ascertain. In other words, the “true

values” of feature edge positions, centerline (Section

5.3), centroid (Section 5.4), and linewidth (Section

5.8.1), can depend on the purpose to which the

corresponding measurement results are put. The

definitions given here allow for some flexibility so they

SEMI P35-0704 © SEMI 2000, 2004 8

can be made consistent with the ultimate purpose of the

measurements.

A1-4 The inner and outer linewidth bounding boxes

need not have the same shape, but their widths must be

unambiguously defined. A rectangular shape for both

will result in a centerline, centroid, and linewidth

independent of height above the substrate, but may also

result in a larger interval between the inner and outer

linewidth bounding boxes. The figure 95% represents 2

standard deviations of the Gaussian probability

distribution of possible values for the linewidth. The

multiplier value of 2 (the “coverage factor”) is also

often used even if the distribution is not Gaussian

[reference Section 3.2], but then the interpretation of

95% confidence no longer applies. Three standard

deviations or some other multiple may be used if so

specified.

A1-5 The probability distribution and expectation

value for the position of an edge within the line edge

bounding box are determined as described in ANSI

Z540-2 [reference Section 3.2]. Default values for these

assume the edge is equally likely to be anywhere inside

the line edge bounding box. In that case the expectation

value of the line edge location is the center of the line

edge bounding box (i.e., the linewidth is the width of

the mean linewidth bounding box [Section 5.8.3]), and

the edge position uncertainty (at the 95% confidence

level) is 0.577 × width of line edge bounding box. The

corresponding linewidth measurement uncertainty

(Section 5.8.7) component is 0.816 × width of line edge

bounding box if the right and left edge location

uncertainties are uncorrelated, and 1.154 × width of line

edge bounding box if they are mirror-image correlated

(as is often approximately the case). See reference

Section 3.2, page 13.

A1-6 In most cases, the width or centroid or edge

positions of the bounding box is measured from its

image in a metrology tool; inferring the width of the

bounding box from this image usually requires

modeling of the image-forming process. The bounding

box should be constructed so that its image in the

metrology tool can be modeled with the modeling tools

available. If the image is not modeled accurately,

additional measurement uncertainty will accrue

[reference Section 6.4].

NOTICE: SEMI makes no warranties or

representations as to the suitability of the standards set

forth herein for any particular application. The

determination of the suitability of the standard is solely

the responsibility of the user. Users are cautioned to

refer to manufacturer' s instructions, product labels,

product data sheets, and other relevant literature,

respecting any materials or equipment mentioned

herein. These standards are subject to change without

notice.

By publication of this standard, Semiconductor

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mentioned in this standard. Users of this standard are

expressly advised that determination of any such patent

rights or copyrights, and the risk of infringement of

such rights are entirely their own responsibility.

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the contents in whole or in part is forbidden without express written

consent of SEMI.

SEMI P36-0600 © SEMI 20001

SEMI P36-0600

GUIDELINE OF MAGNIFICATION REFERENCE FOR CRITICAL

DIMENSION MEASUREMENT SCANNING ELECTRON MICROSCOPES

(CD-SEMS)

This guideline was technically approved by the Global Metrology Committee and is the direct responsibility

of the Japanese Metrology Committee. Current edition approved by the Japanese Regional Standards

Committee on March 1, 2000. Initially available at www.semi.org May 2000; to be published June 2000.

1 Purpose

1.1 The purpose of this guideline is (1) to define

common and important specifications of magnification

references which are used for calibrating magnifications

of critical dimension measurement scanning electron

microscopes (CD-SEMs), and as the result (2) to

provide magnification references which are easy for

anyone to use.

2 Scope

2.1 It is preferable that design, manufacture and

purchase specifications for CD-SEM magnification

references conform to this guideline.

2.2 This standard does not purport to address safety

issues, if any, associated with its use. It is the

responsibility of the users of this standard to establish

appropriate safety and health practices and determine

the applicability of regulatory limitations prior to use.

3 Referenced Standards

3.1 None.

4 Terminology

4.1 CD-SEM magnification refere nce



a CD-SEM

magnification reference is defined as a standard for

calibrating magnifications of a said CD-SEM through

mounting the standard on the specimen stage,

measuring the dimensions of reference patterns formed

on the standard, determining the difference between the

measurement value and the true or reference value of

the reference patterns, and adjusting the CD-SEM

parameters to bring the difference zero.

4.1.1 There are two types of CD-SEM magnification

references: one is a wafer on which reference patterns

are formed; another is a chip on which reference

patterns are formed. Hereinafter, the former will be

referred to as “wafer-type magnification reference,” and

the latter will be referred to as “chip-type magnification

reference.”

4.2 edge roughness  Edge rough ness refers to edge

variations seen in the SEM images, and is defined as

the distance, within a field of view, between the peak

line and the valley line, where the peak line means the

line which runs through the highest peak and is parallel

to the pattern-edge mean line, the valley line means the

line which runs through the lowest valley and is parallel

to the pattern-edge mean line, and the pattern-edge

mean line conforms to the expected pattern-edge line.

Here, a peak is the tip of a convex section, and a valley

is the deepest part of a concave section (See Figure 1).

5 Ordering Information

5.1 Specify whether a said CD-SEM magnification

reference is a wafer-type magnification reference or a

chip-type magnification reference.

6 Requirements

6.1 CD-SEM Magnification References and Their

Structure

6.1.1 CD-SEM Magnification References are either

wafer type or chip type. Chip types are composed of a

chip (or chips) and a stub to hold the chip (or chips).

Wafer type include a 'drop-in' wafer which is a wafer

with a thinned section where a die with the reference

calibration pattern can be dropped in.

6.2 Shape, Size and Mounting Method of CD-SEM

Magnification References

6.2.1 Shape and size of wafer-type magnification

references, and method of mounting them on the

specimen stages in CD-SEMs must follow the shape,

size and mounting method of product wafers.

6.2.2 Shape and size of chip-type magnification

references, and method of mounting them on the

specimen stages of CD-SEMs are defined as follows:

6.2.2.1 Size and shape of chip-type magnification

references: See Figure 2.

6.2.2.2 Mounting method of chip-type magnification

references:

6.2.2.2.1 A magnification reference should be

mounted on a specimen stage as markers made on the

stub fit in markers made on the specimen stage, and be

fixed by using a screw. The markers made on the stub

should show the direction of reference patterns at an

accuracy of within ± 1°.