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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 procedur es on April 22…

SEMI P35-0704 © SEMI 2000, 2004 6

dispersion of the values that could reasonably be

attributed to the pitch between two parallel lines (see

measurement uncertainty).

5.1.14.3.1 One option here is to choose inner and outer

linewidth bounding boxes so that there is a 95% chance

that the features’ true edges lie between their respective

inner and outer linewidth bounding boxes. Then the

pitch measurement uncertainty will be the combined

uncertainties of the measured distance between the

centroids of the feature mean linewidth bounding boxes

and the uncertainties of the differences of the positions

of the left edges and of the right edges within their

respective line edge bounding boxes. This option is the

default.

5.1.15 precision

5.1.15.1 static precision — repeatability

5.1.15.2 dynamic precision — reproducibility

5.1.16 reference plane — in the context of this

document, a user-defined plane approximating the

surface of a substrate and containing a coordinate

system.

NOTE 8: All dimensional measurement data are referred to

the reference plane coordinate system.

5.1.17 repeatability (of results of measurements) —

closeness of the agreement between the results of

successive measurements of the same measurand

carried out under the same conditions of measurement

[reference Section 6.1].

5.1.18 reproducibility (of results of measurements) —

closeness of the agreement between the results of

measurements of the same measurand carried out under

changed conditions of measurement. [reference Section

6.1]

5.1.19 resolution

5.1.19.1 measurement resolution — smallest difference

in the measurand that can be meaningfully

distinguished (usually limited by noise or quantization).

Adapted from [reference Section 6.1].

5.1.19.2 quantization resolution — smallest possible

change in indicated value of a measurement device

(e.g., the least significant bit of a digital instrument)

5.1.19.3 imaging resolution — qualitatively, the

smallest distance between two object points that allows

them to be distinguished in an image (limited, for

example, by λ/NA in an optical microscope, beam

shape in a scanning electron microscope, or tip shape in

a scanning probe microscope).

5.1.20 self calibration (coordinate) — set of operations

that establish, under specified conditions, the

relationship between relative values of quantities

indicated by a measuring instrument or measuring

system, using self-consistency techniques as a function

of the geometry’s group of motions, or one-to-one

mappings of a feature onto itself, that preserve the

geometrical properties of features in that geometry.

NOTE 9: Self calibration is a mapping of the coordinate

system of a measuring instrument or calibration artifact to an

ideal coordinate system using self-consistency techniques

(redundant measurements of the same object in different

orientations and different positions relative to the instrument

coordinate system, including reversal techniques)[reference

Sections 6.2, 6.3], requiring only a stable artifact and

instrument. This procedure can map errors in scale linearity

and orthogonality. A length standard is still required for

calibrating the length scale of the instrument or artifact in

order to measure feature size or placement.

5.1.21 traceability — property of the result of a

measurement or the value of a standard whereby it can

be related to stated references, usually national or

international standards, through an unbroken chain of

comparisons all having stated uncertainties [reference

Section 6.1].

5.1.22 true value — value consistent with the definition

of a particular quantity [reference Section 6.1].

6 Related Documents

6.1 ISO Document

International vocabulary of basic and general terms in

metrology, ISO, 1993, 60 p., ISBN 92-67-01075-1.

6.2 Chris Evans and Robert Hocken, “Self-

Calibration: Reversal, Redundancy, Error Separation,

and ’Absolute Testing’”, Annals of the CIRP, vol.

45/2/1996.

6.3 Raugh, Michael R., “Two-dimensional stage self-

calibration: Role of symmetry and invariant sets of

points,” Journal of Vacuum Science Technology B

15(6), (Nov/Dec 1997)

6.4 J. Potzick, “The problem with submicrometer

linewidth standards, and a proposed solution,”

Proceedings of SPIE 26th International Symposium on

Microlithography, vol. 4344-20 (2001).

2 International Organization for Standardization, ISO Central

Secretariat, 1, rue de Varembé, Case postale 56, CH-1211 Geneva 20,

Switzerland. Telephone: 41.22.749.01.11; Fax: 41.22.733.34.30,

Website: www.iso.ch

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

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].

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