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SEMI P25-94 © SEMI 1994, 2004 3 possible area at the correspo nding point in the optical image. It is always given as a numerical displacement of the optical image poi nt al ong the optical axis from some arbitrary refer…
SEMI P25-94 © SEMI 1994, 2004 2
5.1.3 standard coordinates — a system of Cartesian
coordinates with the z axis along the optical axis of the
system and with the x and y axes in the flat plane
perpendicular to the optical axis. The system user or the
supplier will specify the x and y directions in this plane
for any particular equipment studies.
NOTE 4: Upon occasion, cylindrical coordinates may be
used for special discussions, for example, mapping
astigmatism. The standard transform is used between the
Cartesian (x,y) and the cylindrical (r,ø) is used.
NOTE 5: The x and y coordinates are taken as displacements
from the optical axis along a flat plane. Thus, if the image
plane is curved, the x and y coordinates are taken from the
projection of the curved image plane onto a flat plane.
Consistently, r is taken as the distance along a perpendicular
to the optical axis.
NOTE 6: A displacement along the z axis (and hence the
optical axis) from a reference position will be negative for
displacements toward midpoint of the optical system and
positive for displacements away from the midpoint of the
optical system, regardless of whether the reference position is
on the object side or on the image side or coincident with
some portion of the optical system.
NOTE 7: For folded optical systems, the coordinate system is
allowed to rotate with position along the optical axis so that
the above definition holds at any given position along the
axis. Alternately, it may be assumed that for purposes of using
this coordinate system, all optical paths are represented as
unfolded.
5.1.4 image field — the extent of the image along the x
and y axes. It may be defined by the limits of image
quality, as a practical matter, for the intended
application.
NOTE 8: Definitions 5.1.1 and 5.1..2 in combination with
5.1.4 define the drafting image field, the optical image field,
the processed image field, etc. The term “image” refers to a
single geometrical form. The term “field” refers to the
complete set of forms.
5.1.5 practical use — the conditions of photoprocess,
image geometries, etc. that are required for the intended
use of the instrument. The practical use is specified by
the following:
process — photoresist type and chemical
processing, exposure conditions, and
environmental conditions (temperature and
humidty setpoints and stability).
pattern — description or diagram of the test
structures, including the choice geometrical
dimensions, orientations, positions.
substrate — the substrate quality and
specifications, including all pre-existing structures
and layers on the substrate.
leveling — the leveling mechanism used to hold
the substrate at the desired position and angle with
respect to the optical image plane.
site — list or map of the image sites in the
processed image field used for the tests.
criteria — the acceptance criteria used in the
evaluation of the processed images.
NOTE 9: Typically, the instrument vendor will indicate a
range of practical use parameters and the instrument user will
select from this range the actual conditions, as is appropriate
to the user’s needs.
5.1.6 resolution, practical — the minimum line width
that reproduces the mask (or drafting) dimensions
faithfully. [SEMI Micropatterning — Terms and
Definitions Relating to the Microlithography Industry]
NOTE 10: The practical resolution is a number specified by
the equipment vendor.
5.1.7 point-like object — A circular or square form in
the image where the diameter or width is equal to the
practical resolution.
5.1.8 evaluative line pattern — A pattern in the image
constructed of 3 to 5 straight parallel lines where the
lines are oriented at some specified angle with respect
to the standard coordinates and where the width of the
lines is equal to the practical resolution and the pitch of
the lines is twice the practical resolution. (See SEMI
P19.)
5.1.9 saggital lines — An evaluative line pattern where
the lines lie along a radius to the optical axis. (See
Figure 1.)
NOTE 11: Saggital lines are primarily formed from light rays
that do not lie in planes containing the optical axis. For optical
systems having cylindrical symmetry, such as some reduction
steppers, the saggital lines will be radial lines from some
particular point of the image field. For other systems the lines
may not be radial. For example, the saggital direction for
scanners is perpendicular to the direction of the scan
throughout the image field.
5.1.10 tangential lines — An evaluative line pattern
where the lines lie perpendicular to a radius to the
optical axis. (See Figure 1.)
NOTE 12: Tangential lines are primarily formed from light
rays that do lie in planes containing the optical axis. For
systems having cylindrical symmetry, tangential lines lie upon
circles about some particular point of the image field. For
other systems, the lines may not be so arranged. For example,
the tangential direction for scanners is parallel to the direction
of the scan throughout the image field.
5.1.11 focus — a condition of geometric adjustment of
the lens’s object, the optical system and the image plane
such that the optical image rays originating from a
given point in the object converge to the smallest
SEMI P25-94 © SEMI 1994, 2004 3
possible area at the corresponding point in the optical
image. It is always given as a numerical displacement
of the optical image point along the optical axis from
some arbitrary reference such as an optical exit surface,
optical center, conjugate plane, etc. Focus may vary
across the image field and is properly given as a z axis
value for a specified image site in the image field. (See
the definition for Focal Surface.)
NOTE 13: Point-like objects will have the sharpest optical
image at this z-axis position. The z-axis position for the
sharpest processed image of point-like objects will usually
have a constant offset from the z-axis position for the sharpest
optical image for point-like objects. (See “mean focus” and
“best focus” definitions that follow in the text.)
NOTE 14: This is also the position which yields the highest
contrast in the photon flux at the given point in the optical
image.
5.1.12 line focus — the z axis position where for
evaluative lines in the image, the optical image has the
highest contrast and the evaluative line pattern will
consequently appear with the correct width and pitch.
Line focus may vary across the image field and is
properly given as a z axis value for a specified image
site in the image field. It also varies with the line angle,
and the line focus must, therefore, include a
specification of the angle (e.g., saggital, tangential, or
some other angle).
5.1.13 focal surface — the surface determined by
finding the focus for each point-like object in the
optical image field, with the object fixed with respect to
the lens. The focal surface is then the map of z axis
displacements for the highest contrast at each point in
the optical image field as a function of the (x,y) or (r,
ø)
coordinates.
NOTE 15: It is important to remember that the unqualified
focal surface is determined using point-like objects, not lines
or gratings. Separate determinations must be made for non-
point-like objects.
5.1.14 field flatness — the difference between the
maximum and the minimum z axis positions over the
focal surface.
5.1.15 saggital focal surface — the focal surface
determined by examining only saggital lines.
5.1.16 tangential focal surface — the focal surface
determined by examining only the tangential lines.
5.1.17 normal astigmatism — the difference in z axis
position at each image site between the saggital focal
surface and the tangential focal surface. Astigmatism is
a map of scalar values over the (x,y) coordinates of the
image field.
5.1.18 rotated astigmatism — at each image site, the z
axis difference for the line focus of two evaluative line
sets, oriented at right angles to each other and at some
specified angle to the coordinate system, where the
specified angle is selected so that the z axis focus
difference is a maximum at the given image site. The
specified angle may vary from image site to image site.
NOTE 16: This is called “rotated” astigmatism because the
specified angle is not necessarily the saggital or tangential
direction.
5.1.19 mean focus — the z axis position representing
the area average focal surface for point-like objects in
the optical image.
5.1.20 best focus — a position of the processed image
surface such that the best compromise of focus across
the whole of the processed image is obtained, as
defined by the application requirements upon the
processed image. The best focus is a single numerical
value for the processed image surface displacement.
The best compromise may be such as to optimize the
possible defocus range or may optimize the line width
variations or may minimize the deviation from some
target width or may relate to some other processed
image parameter.
NOTE 17: Because of processing effects, this may or may
not correspond to an optical conjugate plane coincident with
the photoresist film or other processed layer — top, middle, or
bottom.
NOTE 18: Because the processed image surface will
generally have a curvature that is not adjustable, it is not usual
for the processed image surface to fully correspond to any of
the focal surfaces. Focal surfaces are defined by determining
the z-axis position for a given focus condition, as a function
of the image position. A processed image surface is therefore
set at a z axis position that provides the best compliance to the
focal surface.
5.1.21 defocus — the distance, perpendicular to the
image plane, between the processed image plane and
the plane of best focus.
NOTE 19: A defocus of zero is the best focus position, a
positive defocus places the optical image plane further from
the lens, a negative defocus places the optical image plane
closer to the lens.
5.1.22 focal range — depth of focus — the total
distance of defocus where over the whole of the
processed image field, the processed image is
sufficiently resolved for practical use.
5.1.23 depth of focus map — a plot, for each position
in the image field, of the greatest defocus in the positive
direction and the greatest defocus in the negative
direction, where the processed image is sufficiently
resolved for practical use.
NOTE 20: As stated previously, the focal range or the depth
of focus are dependent on the process, upon the image
geometries (especially the line width), and upon the
SEMI P25-94 © SEMI 1994, 2004 4
permissible deviations. The depth of focus maps may be
dependant, among other things, on the process, line width,
and image geometry, especially the choice of point-like
patterns or line-like patterns along the saggital, tangential, or
other directions. Several maps may be produced as part of a
test, covering these variations.
6 Procedure
6.1 Pattern — See SEMI P19. A pattern and pattern
dimensions are to be selected in accordance with the
most reasonable correspondence to the intended
application of the equipment. Typically, the pattern will
consist of two sets of evaluative lines. A sequence of
patterns of varying line widths may also be employed,
in which case the depth of focus may be reported as a
function of the line width. The pattern selection and
dimensions must be included as part of the report.
6.2 Test Sites — The pattern is to be repeated at least
nine times over the image field. The minimum of nine
sites will include the four corners of the image, the four
edge midpoints of the image field and the center of the
image field. Whichever many sites are used, the sites
must be distributed symmetrical and uniformly over the
image field, giving no special weight to any portion of
the image field. For examples, see Figure 2.
6.3 Process — A test image will be printed under the
same conditions and processes to be used in the
practical application (see Section 2) of the instrument
(stepper, scanner, etc.). The process description will be
included in the depth of focus and best focus report.
6.4 Focus Steps — The image will be printed several
times, varying the defocus by a fixed amount between
each print. The amount of variation of defocus between
steps and the limits of the defocus will be selected so as
to bracket the expected best focus position and to reach
beyond the depth of focus at the extremes of the image
series, as best as can be determined. The number and
size of the defocus steps must be specified in the report.
6.5 Image Array — These multiple images can be a
row of separate exposure fields on one substrate,
multiple stepped displaced exposures of the test
geometry within one image field region, or even
exposures on entirely separate substrates. The particular
strategy is usually constrained by the functions of the
instrument under test.
6.6 Test Measurements — For each image site for both
test pattern orientations and at each value of defocus,
the processed image geometries will be examined and
either accepted or rejected on the basis of image
sharpness, image size or some related image
characteristic. Usually this examination will use the line
width as the acceptance criteria. The total number of the
measurements will be twice the number of sites times
the number of defocus steps.
6.7 Quantitative Image Evaluation — The photoresist
image patterns will be examined or measured for
deviation from the target, in a manner specified by the
vendor or user of the instrument. An acceptable image
is where the variation of the pattern is not outside the
permissible deviation under the conditions of the
intended use of the equipment. The defocus values for
which the image is usable will be determined at each
image site within the image field.
6.8 Depth of Focus and Best Focus Determination —
The defocus variation over which there are usable
images at simultaneously every test site within the field,
by the above criteria, will be reported as the practical
focal range. In accordance with the definition, the best
focus will be the z axis position where some target
specification is met or the possible defocus is
maximized or the line deviation minimized, etc. If there
is no common range of usable defocus across the field,
the depth of focus is zero and the best focus is
undetermined. This can occur due to, among other
things, a large plane tilt of substrate to the optical axis,
high aerial image focus surface curvature, high
astigmatism, and auto focus system instabilities.
6.9 Focal Astigmatism Determination — The test
measurements are separated into two groups, one group
for each of the two different orthogonal orientations of
the test pattern. These groups are referred to as the “S”
and “T” groups, however the saggital and tangential
orientations have not necessarily been used in
accordance with the definition of “rotated astigmatism.”
6.9.1 For each group separately, the focal surface is
determined by using for each site the midpoint of the
defocus values where the processed image is found to
be acceptable, in accordance with Section 6.7.
6.9.2 The difference in z position between these
surfaces for each image site is calculated. These
differences are plotted as a function of image position.
This map of values is the astigmatism.
6.9.3 The maximum of the absolute values is the
maximum astigmatism.
6.9.4 The average of the absolute values is the mean
astigmatism.
6.10 Field Flatness Determination — Two alternative
but essentially equivalent methods of determining the
focal surface are allowed:
a. The focal surface which is the midpoint of the S and
T focal surfaces is calculated.