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SEMI P35-0704 © SEMI 2000, 2004 5 5.1.9 measur and — particular quantity subject to measurement [reference Section 6.1]. 5.1.10 measure ment error — result of a measurem ent minus a true value of th e measurand [referenc…
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Figure 4
Examples of inner, outer, and mean linewidth
bounding boxes, and the corresponding default
linewidth and pitch. Line edge asperities at the
substrate were judged not to be relevant to the
function of this feature and were excluded from the
outer linewidth bounding box.
5.1.6 line edge bounding box — (a) the region, for each
edge, between specified inner and outer linewidth
bounding boxes encompassing the edge of the feature.
(b) user-specified bounding box intended to encompass
the feature edge. See Figure 3.
NOTE 5: The underlying concept here is the same as for a
feature bounding box; only the perspective is different. If a
feature is described using a pair of inner and outer linewidth
bounding boxes, then the widths of the corresponding line
edge bounding boxes illustrate the component of the linewidth
measurement uncertainty arising from the definition of the
feature’s edge, and “the linewidth bounding box” describing
the feature is taken to mean the mean linewidth bounding box
by default.
5.1.7 line edge position — expectation value of the
position of the edge within the line edge bounding box
used to define the linewidth. If the probability
distribution of the edge within the line edge bounding
box is symmetric, this will be at the center of the line
edge bounding box.
5.1.8 linewidth bounding box — (a) if the feature
height is unambiguous, a specified rectangular
bounding box constrained to the line height and
bounding a specified line length segment; (b)
appropriate parameters describing a different bounding
box. Additional constraints, such as orientation parallel
to a defined length direction, may be placed on the
bounding box. See Figure 4.
5.1.8.1 linewidth — (a) width of a specified linewidth
bounding box. See Figures 3 and 4. (b) distance
between the two opposing line edge positions of a
feature. See Figures 5, 6, and 7.
NOTE 6: Linewidth is sometimes referred to as critical
dimension or CD.
5.1.8.2 best fit linewidth — width of constrained best
fit linewidth bounding box.
5.1.8.3 mean linewidth bounding box — a bounding
box between inner and outer linewidth bounding boxes,
whose right and left edge positions at any height above
the substrate are the means of the edge positions of the
inner and outer linewidth bounding boxes at that height.
See Figues 4 and 5.
5.1.8.4 inner bound linewidth — width of largest
linewidth bounding box entirely inside the line segment.
Its width is the smallest linewidth that is ordinarily
associated with the feature.
Figure 5
Example of using rectangular and trapezoidal
linewidth bounding boxes to describe Line A in
Figure 4. The trapezoidal case requires an
additional specification for the linewidth, such as at
the distance h above the reference plane, but it
probably better represents the real feature and the
width of its line edge bounding box is smaller.
5.1.8.5 outer bound linewidth — width of smallest
linewidth bounding box encompassing the line segment.
Line edge asperities may reasonably be excluded. Its
width is the largest linewidth that is ordinarily
associated with the feature.
5.1.8.6 section linewidth — width of the planar
rectangle defining the intersection of a linewidth
bounding box and a plane parallel to and a specified
distance from the reference plane.
5.1.8.7 linewidth measurement uncertainty —
parameter that characterizes the dispersion of the values
that could reasonably be attributed to the linewidth of
an object (see measurement uncertainty).
5.1.8.7.1 One option here is to choose inner and outer
linewidth bounding boxes so that there is a 95% chance
that the line’s true edges lie between them. Then the
linewidth measurement uncertainty will be the
combined uncertainties of the measured width of the
mean linewidth bounding box and of the positions of
the line’s edges between these linewidth bounding
boxes, taking into account possible right-left edge
correlations. This option is the default.
SEMI P35-0704 © SEMI 2000, 2004 5
5.1.9 measurand — particular quantity subject to
measurement [reference Section 6.1].
5.1.10 measurement error — result of a measurement
minus a true value of the measurand [reference Section
6.1].
NOTE 7: The measurement error is unknown because the
true value is unknown. Otherwise there would be no need to
measure.
Figure 6
Example of linewidth (and spacewidth) after the
definition in SEMI P19. Since the intention in this
case is to conform to the irregular shape of the edge,
the generalized linewidth bounding box definition (b)
is used. The inner, outer, and mean linewidth
bounding boxes coincide, and the linewidth is defined
to be the width of the mean linewidth bounding box
at a specified distance h above the substrate.
Alternatively, the line edge bounding box approach
can be used here, giving the same results.
5.1.11 measurement uncertainty — parameter,
associated with the result of a measurement, that
characterizes the dispersion of the values that could
reasonably be attributed to the measurand [reference
Section 6.1]. Numerically, it is the square root of the
sum of the variances of the probability distributions of
all the possible errors (both random and systematic),
multiplied by a stated factor chosen to represent the
desired confidence interval (usually 2 for 95% or 3 for
99% for normally distributed errors), as described in
ANSI/NCSL Z540- 2-1997 [reference Section 3.2].
Figure 7
Example of stacked-rectangle linewidth feature
model for a chrome photomask line, consistent with
common imaging models. For an optical metrology
system the stacked rectangles may have different
complex indices of refraction. For an SEM they may
have different atomic numbers. The edge bounding
box will have some additional width to account for
line edge roughness.
5.1.12 overlay — vector distance between the feature
placements of two corresponding features created at
different processing levels, in the reference plane
coordinate system.
5.1.13 pattern — set of one or more features.
5.1.13.1 pattern placement — coordinates describing
the centroid of the set of features comprising the
pattern in the reference plane relative to a coordinate
system in that plane.
5.1.14 pitch
5.1.14.1 pitch in general — the centroid-to-centroid
distance between the feature models describing two
features, i.e., the distance between the two feature
placements.
5.1.14.2 pitch between parallel lines — (a) the
centroid-to-centroid distance between the linewidth
bounding boxes describing two parallel lines, over a
specified length segment common to both, and
perpendicular to their edges. (b) right edge to right-edge
or left-edge to left-edge distance between
corresponding line edge bounding boxes, or the
centerline-to-centerline (preferred) distance, can also be
used where appropriate, if so specified.
5.1.14.3 pitch measurement uncertainty (between
parallel lines) — parameter that characterizes the
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
2
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