U.S. patent application number 10/114112 was filed with the patent office on 2002-08-22 for method of adjusting projection optical apparatus.
This patent application is currently assigned to NIKON CORPORATION. Invention is credited to Chiba, Hiroshi.
Application Number | 20020113953 10/114112 |
Document ID | / |
Family ID | 11727134 |
Filed Date | 2002-08-22 |
United States Patent
Application |
20020113953 |
Kind Code |
A1 |
Chiba, Hiroshi |
August 22, 2002 |
Method of adjusting projection optical apparatus
Abstract
This invention relates to an adjusting method for correcting the
random component of distortion of a projection optical apparatus
without performing complicated assembly and adjustment. This
adjusting method has the first step of measuring the residual
distortion component of a projection optical system having a
predetermined target member in its optical path, the second step of
calculating, based on the measurement result of the first step, the
surface shape of the target member to cancel the residual
distortion component, the third step of removing the target member
from the projection optical system and machining the target member
so as to have the surface shape calculated in the second step, and
the fourth step of inserting the target member machined in the
third step into the optical path of the projection optical
system.
Inventors: |
Chiba, Hiroshi;
(Yokohama-shi, JP) |
Correspondence
Address: |
OLIFF & BERRIDGE, PLC
P.O. BOX 19928
ALEXANDRIA
VA
22320
US
|
Assignee: |
NIKON CORPORATION
Tokyo
JP
|
Family ID: |
11727134 |
Appl. No.: |
10/114112 |
Filed: |
April 3, 2002 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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10114112 |
Apr 3, 2002 |
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09536691 |
Mar 28, 2000 |
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09536691 |
Mar 28, 2000 |
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08581016 |
Jan 3, 1996 |
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6268903 |
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Current U.S.
Class: |
355/52 ;
355/53 |
Current CPC
Class: |
G03F 7/70308 20130101;
G02B 27/0025 20130101; G03F 7/706 20130101 |
Class at
Publication: |
355/52 ;
355/53 |
International
Class: |
H01L 021/027; G03F
007/20 |
Foreign Application Data
Date |
Code |
Application Number |
Jan 25, 1995 |
JP |
009687/1995 |
Claims
What is claimed is:
1. A method of adjusting a projection optical apparatus that
projects an image of a first object on a second object, comprising:
the first step of measuring a distortion component of said
projection optical apparatus having a projection optical system and
a correction optical member which is arranged at a predetermined
position with respect to said projection optical system; the second
step of calculating, based on a measurement result of the first
step, a surface shape that said correction optical member should
have, the distortion component of said projection optical apparatus
being canceled to zero when said correction optical member has the
surface shape that said correction optical member should have; the
third step of removing said correction optical member from said
projection optical apparatus and machining said correction optical
member so that the surface shape of said correction optical member
coincides with the surface shape calculated in the second step; and
the fourth step of re-arranging said correction optical member
machined in the third step at a position where said correction
optical member has been arranged in the first step.
2. A method according to claim 1, further comprising the step,
executed prior to the first step, of correcting components of
various aberrations of said projection optical apparatus that are
symmetric with respect to an optical axis of said projection
optical system.
3. A method according to claim 1, wherein said projection optical
system sequentially has a front group, an aperture stop, and a rear
group in an order named from a side of said first object, and a
distance between one of said front and rear groups through which a
beam having a smaller numerical aperture passes and said correction
optical member is smaller than a distance between the other of said
front and rear groups through which a beam having a larger
numerical aperture passes and said correction optical member.
4. A method according to claim 1, wherein said projection optical
system sequentially has a front group, an aperture stop, and a rear
group in the order named from the side of said first object, and
said correction optical member is arranged at a position close to
said front or rear group and farthest from said aperture stop.
5. A method according to claim 4, wherein an
inequalityd/f<0.07is satisfied where f is the focal length of
one of said front and rear groups which is closer to said
correction optical member, and d is a distance between, of optical
members belonging to said group closer to said correction optical
member, one closest to said correction optical member and said
correction optical member.
6. A method according to claim 1, wherein an
inequality-0.005<.PHI.<- 0.005is satisfied where .PHI. is the
refracting power of said correction optical member.
7. A method according to claim 6, wherein the refracting power
.PHI. of said correction optical member is substantially zero.
8. A method according to claim 7, wherein said correction optical
member is a plane-parallel plate.
9. A method according to claim 1, wherein said correction optical
member arranged in the first step is a dummy and is different from
said correction optical member machined in the third step.
10. A method according to claim 1, wherein the second step
comprises: the step of calculating a normal vector at a first point
of a surface shape that said correction optical member should have;
the step of calculating a tangential vector at the first point that
concerns a predetermined direction perpendicular to a direction of
an optical axis of said projection optical system; the step of
setting a point remote from the first point in the predetermined
direction by a predetermined distance as a second point, and
calculating a product of an angle defined by the predetermined
direction and the tangential vector and the predetermined distance;
and the step of adding the product to a height at the first point
in the direction of the optical axis of the surface shape that said
correction optical member should have, thereby obtaining a height
in the direction of the optical axis of the surface shape at the
second point.
11. A method according to claim 10, wherein a height is set at a
predetermined value at the beginning at a point through which the
optical axis of said projection optical system passes, in the
direction of the optical axis of the surface shape that said
correction optical member should have.
12. A method according to claim 10, wherein a height in the
direction of the optical axis of the surface shape that said
correction optical member should have is obtained by a plurality of
manners by changing the predetermined direction, and a plurality of
obtained values are averaged.
13. An exposure apparatus for transferring an image on an original
plate onto a photosensitive substrate, comprising: an illumination
optical system for supplying light to said original plate; a first
stage for supporting said original plate; a second stage for
supporting said photosensitive substrate; and a projection optical
apparatus, having a projection optical system and a correction
optical member arranged at a predetermined position with respect to
said projection optical system, for causing a position of said
original plate supported by said first stage and a position of said
photosensitive substrate supported by said second stage to be
conjugated, wherein said projection optical apparatus is adjusted
by a method comprising: the first step of measuring a distortion
component of said projection optical apparatus; the second step of
calculating, based on a measurement result of the first step, a
surface shape that said correction optical member should have, the
distortion component of said projection optical apparatus being
canceled to zero when said correction optical member has the
surface shape that said correction optical member should have; the
third step of removing said correction optical member from said
projection optical apparatus and thereafter machining said
correction optical member so that the surface shape of said
correction optical member coincides with the surface shape
calculated in the second step; and the fourth step of re-arranging
said correction optical member machined in the third step at a
position where said correction optical member has been arranged in
the first step.
14. An exposure apparatus according to claim 13, wherein said
projection optical system sequentially has a front group, an
aperture stop, and a rear group in the order named from a side of
said original plate, and a distance between one of said front and
rear groups through which a beam having a smaller numerical
aperture passes and said correction optical member is smaller than
a distance between the other of said front and rear groups through
which a beam having a larger numerical aperture passes and said
correction optical member.
15. An exposure apparatus according to claim 13, wherein said
projection optical system sequentially has a front group, an
aperture stop, and a rear group in the order named from the side of
said original plate, and said correction optical member is arranged
at a position close to said front or rear group and farthest from
said aperture stop.
16. An exposure apparatus according to claim 15, wherein an
inequalityd/f<0.07is satisfied where f is the focal length of
one of said front and rear groups which is closer to said
correction optical member, and d is a distance between, of optical
members belonging to said group closer to said correction optical
member, one closest to said correction optical member and said
correction optical member.
17. An exposure apparatus according to claim 13, wherein an
inequality-0.005<.PHI.<0.005is satisfied where .PHI. is the
refracting power of said correction optical member.
18. An exposure apparatus according to claim 17, wherein the
refracting power .PHI. of said correction optical member is
substantially zero.
19. An exposure apparatus according to claim 18, wherein said
correction optical member is a plane-parallel plate.
Description
BACKGROUND OF THE INVENTION
[0001] 1. Field of the Invention
[0002] The present invention relates to a projection optical
apparatus for projecting and exposing the pattern of a first object
on a second object and, more particularly, to a method of adjusting
the projection optical apparatus.
[0003] 2. Related Background Art
[0004] A projection optical system used in an exposure apparatus
that prints a precision circuit pattern on a substrate (wafer,
plate, or the like) coated with a photosensitive material requires
very high optical performance. For this purpose, optical members
used in the projection optical system are manufactured with an
ultimately high manufacturing precision.
[0005] When manufactured optical members are combined to assemble a
projection optical system, very fine adjustment is performed such
as adjusting the distances between the respective optical members
by changing the thicknesses of washers between lens barrels holding
the respective optical members, tilting the optical members
(rotating the optical members about, as an axis, a direction
perpendicular to the optical axis), or shifting the optical members
(moving the optical members in a direction perpendicular to the
optical axis), while actually measuring the aberration of the
projection optical system. This adjustment minimizes degradation in
optical performance which is caused by the manufacturing error of
the optical members or which occurs during assembly of the optical
members.
SUMMARY OF THE INVENTION
[0006] According to the present invention, there is provided an
adjusting method having the first step of measuring the residual
distortion component of a projection optical system having a
predetermined target member in its optical path, the second step of
calculating, based on the measurement result of the first step, the
surface shape of the target member which cancels the residual
distortion component, the third step of removing the target member
from the projection optical system and machining the target member
so as to have the surface shape calculated in the second step, and
the fourth step of inserting the target member machined in the
third step into the optical path of the projection optical
system.
[0007] The present invention will be more fully understood from the
detailed description given hereinbelow and the accompanying
drawings, which are given by way of illustration only and are not
to be considered as limiting the present invention.
[0008] Further scope of applicability of the present invention will
become apparent from the detailed description given hereinafter.
However, it should be understood that the detailed description and
specific examples, while indicating preferred embodiments of the
invention, are given by way of illustration only, since various
changes and modifications within the spirit and scope of the
invention will be apparent to those skilled in the art from this
detailed description.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] FIGS. 1 and 2 are views for explaining the principle of an
adjusting method according to the present invention, in which FIG.
1 shows the state of a beam before adjustment, and FIG. 2 shows the
state of a beam after adjustment;
[0010] FIG. 3 shows the schematic arrangement of an exposure
apparatus to which the adjusting method of the present invention is
applied;
[0011] FIG. 4 shows the arrangement of a holding member that holds
a distortion correction plate;
[0012] FIG. 5 is a plan view showing the arrangement of a test
reticle used for measuring various aberrations other than
distortion;
[0013] FIG. 6 is a plan view showing the arrangement of a test
reticle used for measuring distortion;
[0014] FIG. 7 shows the state of a pattern on a wafer which is
formed by using the test reticle shown in FIG. 6;
[0015] FIGS. 8 and 9 are graphs for explaining a curved surface
interpolation equation of this embodiment, in which FIG. 8 shows a
case wherein a conventional curved surface interpolation equation
is used, and FIG. 9 shows a case wherein a curved surface
interpolation equation of this embodiment is used;
[0016] FIGS. 10 to 14 show a curved surface interpolation method of
this embodiment;
[0017] FIG. 15 shows the arrangement of an apparatus that machines
the distortion correction plate;
[0018] FIG. 16 briefly shows the adjusting method according to the
present invention; and
[0019] FIG. 17 briefly shows a method of calculating the shape of
the distortion correction plate from distortion data.
DESCRIPTION OF THE PREFERRED EMBODIMENT
[0020] In the conventional projection optical system, distortion
components are present that cannot be corrected even by assembly
adjustment as described above. Of all the distortion components,
regarding in particular a random component (asymmetric distortion)
not having a directionality with respect to an optical axis serving
as the reference, no effective correcting method is conventionally
available for such a random component, and this random component
interferes with an improvement in total overlay of a precision
printing exposure apparatus.
[0021] On the other hand, in the present invention having the above
arrangement, as the surface of a target member serving as an
optical member partly constituting the projection optical system is
machined, a beam that passes through this target member can be
deflected by refraction. Thus, an imaging position at a
predetermined point on the surface of an object is deflected on an
image surface in a direction perpendicular to the optical axis, so
that a residual magnification component and a residual distortion
component in the projection optical system can be corrected.
[0022] Assuming an ideal imaging position of a projection optical
system which is an ideal optical system having no aberration, a
residual distortion component is a shift amount between the actual
imaging position of a beam formed through a target member and a
projection optical system, and an ideal imaging position.
[0023] The principle of the present invention will be described
with reference to the accompanying drawings. FIG. 1 is a view
showing a target member 10 before machining arranged between a
reticle R and a wafer W. In FIG. 1, the projection optical system
is omitted. Referring to FIG. 1, a beam emerging from a point O on
the reticle R forms an image on the wafer W through the target
member 10 and the projection optical system (not shown). When the
projection optical system (not shown) has distortion, the beam
emerging from the point O on the reticle R is focused on a point
P.sub.1 to form the image of the point O at the point P.sub.1. When
the projection optical system (not shown) is an ideal imaging
optical system, a beam emerging from the point O on the reticle R
is focused on a point P.sub.0 to form the image of the point O at
the point P.sub.0. At this time, the shift between the points
P.sub.0 and P.sub.1 within the surface of the wafer W corresponds
to the distortion of the projection optical system.
[0024] In the present invention, as shown in FIG. 2, the surface of
the target member 10 present in the optical path of the projection
optical system is machined so that it is changed from a surface 10a
before machining to a surface 10b. Then, the beam emerging from the
point O on the reticle R is refracted by the surface 10b of the
target member 10, and is thus focused on the point P.sub.0 on the
wafer W. Hence, the distortion of the projection optical system is
corrected.
[0025] In the present invention, it is desirable that the various
aberrations that occur symmetrically with respect to the optical
axis are corrected before correction by means of the target member
is performed. Then, the machining amount of the target member can
be decreased, so that machining becomes easy, and the influence of
machining on other aberrations can be prevented.
[0026] In the present invention, it is preferable that the
projection optical system is constituted to sequentially have a
front group, an aperture stop, and a rear group in this order from
the object side. At this time, it is preferable that the target
member be arranged in one of the front and rear groups, through
which a beam having a smaller numerical aperture passes. With this
arrangement, the target member is arranged at a position where the
beam has a small spot size for the purpose of imaging. Therefore,
the control precision of the residual magnification component and
the residual distortion component can be further improved.
Furthermore, with this arrangement, the influence of the adjusting
method of the present invention on other aberration components can
be decreased.
[0027] The present invention is preferably arranged such that the
target member is located in the front or rear group and farthest
from the aperture stop. With this arrangement, the target member is
provided at a position where the beam has a small spot size for the
purpose of imaging. Therefore, the control precision of the
residual magnification component and the residual distortion
component can be further improved. Furthermore, in this
arrangement, since the target member is located at the outermost
position (closest to the object or the image) of the projection
optical system, the arrangement of the lens barrels of the
projection optical system can be simplified, thereby facilitating
removed and insertion of the target member in the third and fourth
steps.
[0028] The present invention preferably satisfies an
inequality:
d/f<0.07 (1)
[0029] where d is the distance between an optical member adjacent
to a target member and this target member, and f is the focal
length of the group in which the target member is located.
[0030] This conditional inequality (1) defines the appropriate
arrangement of the target member. When this conditional inequality
(1) is not satisfied, the operational distance of the projection
optical system cannot be sufficiently maintained, which is not
preferable. In the conditional inequality (1), it is preferable
that the lower limit of d/f be set to 0.001 to satisfy
0.001<d/f. If d/f exceeds this lower limit, it may cause
interference between a holding member that holds the target member
and a holding member that holds an optical member adjacent to the
target member. Then, the degree of freedom in design of the holding
members is decreased, which is not preferable.
[0031] The present invention preferably satisfies an
inequality:
-0.005<.PHI.<0.005 (2)
[0032] where .PHI. is the refracting power of the target member.
The refracting power .PHI. of the target member is expressed by
.PHI.=1/fa where fa is the focal length of the target member.
[0033] This conditional inequality (2) defines the range of
appropriate refracting powers .PHI. of the target member so that
the target member can be easily mounted. If the target member has a
refracting power exceeding the range of the conditional inequality
(2), the decentering allowed for the target member becomes strict.
Then, the target member must be positioned (the optical axis of the
target member must be adjusted) at high precision, which is not
preferable. If the refracting power .PHI. of the target member
falls within the range of the conditional inequality (2), the
influence of aberrations caused by the mounting error of the target
member can be decreased, and the positioning precision of the
target member can be set to almost equal to the machining precision
of the holding member of the target member. When these points and
easy machinability are considered, the target member is preferably
constituted by a plane-parallel plate having no refracting
power.
[0034] The preferred embodiment of the present invention will be
described in detail with reference to the accompanying drawings.
FIG. 3 is a diagram schematically showing an arrangement of an
exposure apparatus suitably applied to a projection optical
apparatus of the present invention. The coordinate system is set as
shown in FIG. 3.
[0035] Referring to FIG. 3, an illumination optical unit IS
uniformly illuminates a reticle R placed on a reticle stage RS with
exposure light, e.g., a 365-nm i line, a 248-nm KrF excimer laser,
and a 193-nm ArF excimer laser. A distortion correction plate 10
serving as the target member, a holding member 11 for placing the
distortion correction plate 10 thereon, and a projection objective
lens (projection optical system) PL having a predetermined
reduction magnification and substantially telecentric on its two
sides are provided below the reticle R. The projection objective
lens PL sequentially has a front group G.sub.F of positive
refracting power, an aperture stop AS, and a rear group G.sub.R of
positive refracting power in this order from the reticle R side,
and the ratio in refracting power of the front group G.sub.F to the
rear group G.sub.R corresponds to the reduction magnification of
the projection objective lens PL. In this embodiment, the
projection objective lens PL is optically designed such that its
aberration is corrected including that of the distortion correction
plate 10. Accordingly, light from the reticle R illuminated by the
illumination optical unit IS reaches a wafer W placed on a wafer
stage WS through the distortion correction plate 10 and projection
objective lens PL, and forms a reduced image of the reticle R on
the wafer W. This wafer stage WS is movable in the X, Y, and Z
directions. In this embodiment, the distortion correction plate 10
is constituted by a plane-parallel plate made of a material, e.g.,
silica glass, that transmits exposure light therethrough.
[0036] As shown in, e.g., FIG. 4, the holding member 11 on which
the distortion correction plate 10 is placed has an opening for
passing exposure light therethrough, and pins 11a to 11c for
regulating the distortion correction plate 10 are provided on part
of the holding member 11. Accordingly, when the distortion
correction plate 10 is abutted against the pins 11a to 11c, the
distortion correction plate 10 is positioned.
[0037] In this embodiment, of the various aberrations of the
projection objective lens PL, symmetrical components are corrected
prior to the random component of the distortion. First, a test
reticle TR.sub.1 formed with a predetermined pattern is placed on
the reticle stage RS. As shown in, e.g., FIG. 5, the test reticle
TR.sub.1 has a pattern area PA.sub.1 provided with a plurality of
marks and a light-shielding band LST surrounding the pattern area
PA.sub.1. The test reticle TR.sub.1 is subjected to Koehler
illumination with the exposure light emerging from the illumination
optical unit IS. Light emerging from the illuminated test reticle
TR.sub.1 reaches the wafer W coated with a photosensitive material,
e.g., a resist, through the distortion correction plate 10 and
projection objective lens PL, and forms the pattern image of the
test reticle TR.sub.1 on the wafer W. Thereafter, the wafer W is
developed, and the resist pattern image obtained by this
development is measured by a coordinate measuring machine. The
distances between the optical members and the tilt shift of the
optical members are adjusted based on the information on the
measured resist pattern image, thereby correcting the various
aberrations other than the random component of the distortion.
[0038] After the various aberrations other than the random
component of the distortion are corrected, the random component of
the distortion is corrected.
[0039] A test reticle TR.sub.2 as shown in FIG. 6 is placed on the
reticle stage RS in place of the test reticle TR.sub.1 used for
above correction. The test reticle TR.sub.2 has a plurality of
cross marks M.sub.0,0 to M.sub.8,8 arranged in a matrix form, i.e.,
arranged on the lattice points of square lattices, within a pattern
area PA.sub.2 surrounded by a light-shielding band LST that shields
exposure light. The cross marks M.sub.0,0 to M.sub.8,8 of the test
reticle TR.sub.2 may be formed on the pattern area PA.sub.1 of the
test reticle TR.sub.1. In other words, both the test reticles
TR.sub.1 and TR.sub.2 may be employed simultaneously.
[0040] As shown in FIG. 3, the test reticle TR.sub.2 on the reticle
stage RS is illuminated with the exposure light of the illumination
optical unit IS. Light from the test reticle TR.sub.2 reaches the
exposure area on the wafer W whose surface is coated with the
photosensitive material, e.g., the resist, through the distortion
correction plate 10 and projection objective lens PL, and forms the
latent images of the plurality of cross marks M.sub.0,0 to
M.sub.8,8 of the test reticle TR.sub.2 on the wafer W. The exposed
wafer W is developed, and the plurality of exposed cross marks
M.sub.0,0 to M.sub.8,8 are patterned.
[0041] FIG. 7 shows the plurality of patterned cross marks in an
exposure area EA on the wafer W. In FIG. 7, ideal imaging positions
where images are formed when the projection optical system is an
ideal optical system (an optical system having no aberrations) are
expressed by intersection points of broken lines. In FIG. 7, a
cross mark P.sub.0,0 corresponds to the image of the cross mark
M.sub.0,0 on the reticle R, a cross mark P.sub.1,0 corresponds to
the image of the cross mark M.sub.1,0 on the reticle R, and a cross
mark P.sub.0,1 corresponds to the image of the cross mark M.sub.0,1
on the reticle R. Any other cross mark M.sub.i,j and cross mark
P.sub.i,j correspond to each other in the same manner.
[0042] The X- and Y-coordinates of each of the plurality of cross
marks P.sub.0,0 to P.sub.8,8 formed on the wafer W are measured by
the coordinate measuring machine.
[0043] In this embodiment, beams emerging from the plurality of
cross marks M.sub.0,0 to M.sub.8,8 and focused on the plurality of
cross marks P.sub.0,0 to P.sub.8,8 are shifted to ideal imaging
positions by machining the surface of the distortion correction
plate 10. The calculation of the surface shape of the practical
distortion correction plate 10 will be described.
[0044] As shown in FIG. 3, the distortion correction plate 10 of
this embodiment is arranged in the optical path between the
projection objective lens PL and the reticle R. This position is a
position where a beam having a comparatively smaller numerical
aperture (N.A.) passes. Thus, in shifting the imaging positions by
the distortion correction plate 10, only shifting of the principal
ray of the beam shifted by changing the surface shape of the
distortion correction plate 10 need be representatively
considered.
[0045] A relationship expressed by an equation:
w=.beta..multidot.L.sub.R.multidot.(n-1).multidot..theta. (3)
[0046] is established where w is a distortion amount which is a
shift amount between the ideal imaging positions and the plurality
of cross marks P.sub.0,0 to P.sub.8,8 shown in FIG. 7, and .theta.
is the change amount of angle of the normal to the surface of the
distortion correction plate 10 at a principal ray passing point
where each of the principal rays from the plurality of cross marks
M.sub.0,0 to M.sub.8,8 passes through the distortion correction
plate 10. The angle change amount .theta. concerns the normal to
the surface of the distortion correction plate 10 in a reference
state before machining, .beta. is the lateral magnification of the
projection optical system, L.sub.R is a distance between the
reticle R and the machining target surface of the distortion
correction plate 10 along the optical axis, and n is the refractive
index of the distortion correction plate 10. In equation (3), the
machining target surface of the distortion correction plate 10 is
on the wafer W side.
[0047] When the distortion correction plate 10 is located in the
optical path between the projection objective lens PL and wafer W,
a relationship satisfying an equation:
w=L.sub.w.multidot.(n-1).multidot..theta. (4)
[0048] is established where L.sub.w is a distance between the wafer
W and the machining target surface of the distortion correction
plate 10 along the optical axis.
[0049] Therefore, the plane normals at principal ray passing points
on the surface of the distortion correction plate 10 can be
obtained from the distortion amount as a shift amount between the
coordinates of the plurality of cross marks P.sub.0,0 to P.sub.8,8
measured by the coordinate measuring machine described above and
the ideal imaging positions.
[0050] Although the plane normals at the respective principal ray
passing points of the distortion correction plate 10 are determined
by the above procedure, the surface of the distortion correction
plate 10 cannot be obtained as a continuous surface. Therefore, in
this embodiment, a continuous surface shape is obtained from the
plane normals at the principal ray passing points of the distortion
correction plate 10 that are obtained by the equation (3) or (4),
by using a curved surface interpolation equation.
[0051] Various types of curved surface interpolation equations are
available. In this embodiment, since plane normals are known and
the tangential vectors of the surface at the principal ray passing
points can be calculated from the plane normals, as the curved
surface interpolation equation used in this embodiment, the Coons'
equation is suitable which extrapolates a curved surface with the
coordinate points and tangential vectors of these coordinate
points. For example, however, if the tangential vectors
.theta..sub.0 and .theta..sub.1 of adjacent coordinate points
Q.sub.0 and Q.sub.1 are equal, as shown in FIG. 8, the extrapolated
curved line (curved surface) may wave.
[0052] In this embodiment, when the distortion amounts caused by
the principal rays that pass through adjacent principal ray passing
points are equal, it is effective to equalize the distortion
amounts of these adjacent principal ray passing points. If the
extrapolated curved line (curved surface) waves, as shown in FIG.
8, the amounts and directions of distortion at adjacent principal
ray passing points change over time. Then, not only the random
component of the distortion cannot be corrected, but also a random
component of this type might be further generated undesirably.
[0053] Hence, in this embodiment, in order to equalize the
distortion amounts of adjacent principal ray passing points as
well, as shown in FIG. 9, the vector component in the Z direction
of a tangential vector .theta..sub.0 at the coordinate point
Q.sub.0 is added, as a height Z.sub.1 in the Z direction, to the
coordinate point Q.sub.1 adjacent to the coordinate point Q.sub.0.
Then, even if the tangential vectors of the adjacent coordinate
points Q.sub.0 and Q.sub.1 are equal, the extrapolated curved line
becomes almost linear between these coordinate points Q.sub.0 and
Q.sub.1, and the principal rays passing between these coordinate
points Q.sub.0 and Q.sub.1 are refracted at almost the same angles.
Accordingly, when the distortion amounts of the adjacent principal
ray passing points are equal, the distortion amounts can be
equalized between these points as well.
[0054] The procedure of curved surface complement of this
embodiment will be described in detail with reference to FIGS. 10
to 14. An X-Y-Z coordinate system is set as shown in FIGS. 10 to
14.
[0055] [Step 1]
[0056] As shown in FIG. 10, an X-Y-Z coordinate system is defined
on a target surface 10a of the distortion correction plate 10. In
FIG. 10, principal ray passing points Q.sub.0,0 to Q.sub.8,8,
through which the principal rays of the beams propagating from the
plurality of cross marks M.sub.0,0 to M.sub.8,8 shown in FIG. 6
toward the plurality of cross marks P.sub.0,0 to P.sub.8,8 shown in
FIG. 7 pass, are expressed by intersection points of broken lines.
The normal vectors at the respective principal ray passing points
Q.sub.0,0 to Q.sub.8,8 obtained by the above equation (3) are
expressed as .theta..sub.i,j (note that in this embodiment i=0 to 8
and j=0 to 8, that is, .theta..sub.0,0 to .theta..sub.8,8, and that
the X-and Y-components of vector .theta..sub.i,j are defined as
zero when the direction of the normal vector .theta..sub.i,j is
equal to the direction of the optical axis), and the heights of the
normal vectors in the Z direction at the respective principal ray
passing points Q.sub.0,0 to Q.sub.8,8 are expressed as Z.sub.i,j
(note that in this embodiment i=0 to 8 and j=0 to 8, that is,
Z.sub.0,0 to Z.sub.8,8).
[0057] [Step 2]
[0058] As shown in FIG. 11, of the principal ray passing points,
the principal ray passing point Q.sub.0,0 at the end point of the
Y-axis is defined as the reference in the Z-axis direction, and is
set as Z.sub.0,0=0.
[0059] [Step 3]
[0060] The height Z.sub.0,1 in the Z direction of the tangential
vector at the principal ray passing coordinate point Q.sub.0,1
adjacent to the principal ray passing point Q.sub.0,0 on the Y-axis
is calculated, based on the normal vector .theta..sub.0,0 of the
principal ray passing point Q.sub.0,0, by the following equation
(5):
Z.sub.0,j=Z.sub.0,j-1+.theta.y.sub.0,j-1.multidot.(y.sub.0,j-y.sub.0,j-1)
(5)
[0061] where .theta.y.sub.0,j: the vector component in the Y-axis
direction of the normal vector .theta..sub.0,j at the principal ray
passing point Q.sub.0,j
[0062] y.sub.0,j: the component in the Y-axis direction of the
coordinates of the principal ray passing point Q.sub.0,j obtained
when the principal ray passing point Q.sub.0,0 is set as the
origin
[0063] In step 3, the height Z.sub.0,1 in the Z direction of the
tangential vector at the principal ray passing point Q.sub.0,1 is
calculated based on the above equation (5) as follows
Z.sub.0,1=Z.sub.0,0+.theta.y.sub.0,0.multidot.(y.sub.0,1-y.sub.0,0)
[0064] [Step 4]
[0065] The heights Z.sub.0,2 to Z.sub.0,8 in the Z direction of the
tangential vectors at the principal ray passing points Q.sub.0,2 to
Q.sub.0,8 on the Y-axis are calculated based on the above equation
(5) in the same manner as in step 3.
[0066] [Step 5]
[0067] The height Z.sub.1,0 in the Z direction of the tangential
vector at the principal ray passing coordinate point Q.sub.1,0
adjacent to the principal ray passing point Q.sub.0,0 on the X-axis
is calculated, based on the normal vector .theta..sub.0,0 of the
principal ray passing point Q.sub.0,0, by the following equation
(6):
Z.sub.i,0=Z.sub.i-1,0+.theta.x.sub.i-1,0.multidot.(x.sub.i,0-x.sub.i-1,0)
(6)
[0068] where .theta.x.sub.i,0: the vector component in the X-axis
direction of the normal vector .theta..sub.i,0 at the principal ray
passing point Q.sub.i,0
[0069] x.sub.1,0: the component in the X-axis direction of the
coordinates of the principal ray passing point Q.sub.i,0 obtained
when the principal ray passing point Q.sub.0,0 is set as the
origin
[0070] In step 5, the height Z.sub.1,0 in the Z direction of the
tangential vector at the principal ray passing point Q.sub.1,0 is
calculated based on the above equation (6) as follows
Z.sub.1,0=Z.sub.0,0+.theta.x.sub.0,0.multidot.(x.sub.1,0-x.sub.0,0)
[0071] [Step 6]
[0072] The heights Z.sub.2,0 to Z.sub.8,0 in the Z direction of the
tangential vectors at the principal ray passing points Q.sub.2,0 to
Q.sub.8,0 on the X-axis are calculated based on the above equation
(6) in the same manner as in step 5.
[0073] [Step 7]
[0074] As shown in FIG. 12, the heights Z.sub.i,j in the Z
direction of the tangential vectors at the principal ray passing
points Q.sub.1,1 to Q.sub.8,8 located between the X- and Y-axes are
sequentially calculated starting with the one closer to the origin
Q.sub.0,0 based on the following equation (7):
Z.sub.i,j={[Z.sub.i-1,j+.theta.x.sub.i-1,j.multidot.(x.sub.i,j-x.sub.i-1,j-
)]+[Z.sub.i,j-1+.theta.y.sub.i,j-1.multidot.(y.sub.i,j-y.sub.i,j-1)]}/2
(7)
[0075] In step 7, first, the height Z.sub.1,j in the Z direction of
the tangential vector at the principal ray passing point Q.sub.1,1
closest to the origin Q.sub.0,0 is calculated. Z.sub.1,1 is
calculated based on the equation (7) as follows
Z.sub.1,1={[Z.sub.0,1+.theta.x.sub.0,1.multidot.(x.sub.1,1-x.sub.0,1)]+[Z.-
sub.1,0+.theta.y.sub.1,0.multidot.(y.sub.1,1-y.sub.1,0 )]}/2
[0076] In step 7, as shown in FIG. 13, after the height Z,.sub.1,1
in the Z direction of the tangential vector at the principal ray
passing point Q.sub.1,1 is calculated, the heights Z.sub.1,2,
Z.sub.2,1, Z.sub.2,2, . . . , Z.sub.i,j, . . . , and Z.sub.8,8 in
the Z direction of the tangential vectors at the principal ray
passing points Q.sub.1,2, Q.sub.2,1, Q.sub.2,2, . . . , Q.sub.i,j,
. . . , and Q.sub.8,8 are sequentially calculated starting with the
one closer to the origin Q.sub.0,0 based on the above equation
(7).
[0077] [Step 8]
[0078] Based on the heights Z.sub.0,0 to Z.sub.8,8 at the principal
ray passing points Q.sub.0,0 to Q.sub.8,8 obtained through steps 1
to 7, the X- and Y-coordinates of the principal ray passing points
Q.sub.0,0 to Q.sub.8,8, and the tangential vectors at the principal
ray passing points Q.sub.0,0 to Q.sub.8,8 obtained from the plane
normal vectors .theta..sub.0,0 to .theta..sub.8,8 at the principal
ray passing points Q.sub.0,0 to Q.sub.8,8, a curved surface is
formed in accordance with the Coons' patching method. More
specifically, the control points of the Coons' patching method are
determined as the X-, Y-, and Z-coordinates of the principal ray
passing points Q.sub.0,0 to Q.sub.8,8, and the tangential vectors
of the control points are determined as the tangential vectors
calculated from the plane normal vectors .theta..sub.0,0 to
.theta..sub.8,8 at the principal ray passing points Q.sub.0,0 to
Q.sub.8,8.
[0079] A curved surface as shown in, e.g., FIG. 14, can be obtained
by curved surface interpolation in accordance with the Coons'
patching method of step 8.
[0080] In above steps 1 to 8, the height Z.sub.0,0 in the Z
direction of the tangential vector at the point Q.sub.0,0 located
at the edge of the target surface 10a is set as 0 (step 2), the
heights Z.sub.0,1 to Z.sub.0,8 and Z.sub.1,0 l to Z.sub.8,0 in the
Z direction of the tangential vectors at the points Q.sub.0,1 to
Q.sub.0,8 and the points Q.sub.1,0 to Q.sub.8,0 on the Y- and
X-axes, respectively, present at the edges of the target surface
10a are calculated (steps 3 to 6), and thereafter the heights
Z.sub.i,j (i.noteq.0, j.noteq.0) in the Z direction of the
tangential vectors at points other than the points on the Y- and
Z-axes are calculated (Steps 7 and 8). Thus, farther from the point
Q.sub.0,0, the larger the error in the calculated value, and the
sizes of the errors of the calculated values are not symmetric with
respect to the central point Q.sub.4,4 of the target surface 10a
through which the optical axis of the projection objective lens PL
passes.
[0081] For this reason, the heights Z.sub.i,j may be calculated in
the accordance with the following procedure. First, in step 2, the
height Z.sub.4,4 in the Z direction of the tangential vector at the
point Q.sub.4,4 located at the center of the target surface 10a is
defined as 0. In steps 3 to 6, the heights Z.sub.4,0 to Z.sub.4,3,
Z.sub.4,5 to Z.sub.4,8, and Z.sub.0,4 to Z.sub.3,4, Z.sub.5,4 to
Z.sub.8,4 in the Z direction of the tangential vectors at the
points Q.sub.4,0 to Q.sub.4,3, Q.sub.4,5 to Q.sub.4,8, Q.sub.0,4 to
Q.sub.3,4, and Q.sub.5,4 to Q.sub.8,4 on axes extending through the
central point Q.sub.4,4 and parallel to the Y- or Z-axis are
calculated. Thereafter, in steps 7 and 8, the heights Z.sub.i,j
(i.noteq.4, j.noteq.4) in the Z direction of the tangential vectors
at points other than the points on the axes extending through the
point Q.sub.4,4 and parallel to the Y-or X-axis are calculated.
[0082] When the distortion measurement points, i.e., the marks on
the test reticles, are not arranged on the lattice points of the
square lattices, the heights in the Z direction and the plane
normal vectors at lattice points on square lattices located between
the respective measurement points are interpolated. More
specifically, the height in the Z direction and the plane normal
vector at a lattice point can be obtained by summing the heights in
the Z direction and the plane normal vectors at a plurality of
measurement points surrounding these lattice points while weighting
them with the distances between the measurement points and the
lattice points.
[0083] In above steps 1 to 8, only information inside the
distortion measurement points is used. However, in order to further
smooth the surface of the distortion correction plate 10 serving as
the target member, the lattice points may be set on the outer side
(a side remote from the optical axis) of the principal ray passing
points corresponding to the distortion measurement points, and the
heights in the Z direction and the plane normal vectors at these
lattice points may be extrapolated from the height in the Z
direction and the plane normal vector at the outermost principal
ray passing point.
[0084] The distortion correction plate 10 is removed from the
projection optical apparatus shown in FIG. 3, and the surface of
the removed distortion correction plate 10 is machined based on
surface shape data of the distortion correction plate 10 which is
calculated through steps 1 to 8. The distortion correction plate 10
of this embodiment has a random surface that waves irregularly, in
order to correct the random component of the distortion.
Accordingly, in this embodiment, a polishing machine as shown in
FIG. 15 is used. A coordinate system as indicated in FIG. 15 is
employed.
[0085] Referring to FIG. 15, the distortion correction plate 10 is
placed on a stage 21 movable in the X and Y directions, and the end
portion of the distortion correction plate 10 is abutted against a
pin 21a on the stage 21. A driver 22 for moving the stage 21 in the
X and Y directions is controlled by a controller 20. A detector 30
comprising an encoder, an interferometer, and the like is provided
to the stage 21 to detect the position of the stage 21 in the X and
Y directions when the stage 21 is moved. A detection signal output
from the detector 30 is transmitted to the controller 20.
[0086] A polisher 23 is attached to one end of a rotating shaft 25
through a holding portion 24 and is rotatable about the Z direction
in FIG. 15 as the rotation axis. A motor 26 controlled by the
controller 20 is mounted to the other end of the rotating shaft 25.
A bearing 27 that rotatably supports the rotating shaft 25 is
provided to a support portion 28 fixed to a main body (not shown)
to be movable in the Z direction. A motor 29 controlled by the
controller 20 is mounted to the support portion 28. When the motor
29 is operated, the bearing 27 is moved in the Z direction, and
accordingly the polisher 23 is moved in the Z direction. The
holding portion 24 for holding the polisher 23 is provided with a
sensor (not shown) which detects a contact pressure between the
abrasion tray 23 and the distortion correction plate 10. An output
from this sensor is transmitted to the controller 20.
[0087] The operation of the polishing machine shown in FIG. 15 will
be briefly described. Surface shape data obtained through steps 1
to 8 is input to the controller 20. Thereafter, the controller 20
moves the stage 21 in the X and Y directions through the driver 22
while it rotates the polisher 23. More specifically, the polisher
23 is moved on the target surface 10a of the distortion correction
plate 10 in the X and Y directions. At this time, the amount of
abrasion of the target surface 10a of the distortion correction
plate 10 is determined by the contact pressure between the target
surface 10a and the polisher 23 and the residence time of the
polisher 23.
[0088] An anti-reflection film is coated, by vapor deposition, on
the distortion correction plate 10 machined by the abrading machine
shown in FIG. 15, and the machined distortion correction plate 10
is placed on the holding member 11 of the projection optical
apparatus shown in FIG. 3. In the polishing machine of FIG. 15, the
polisher 23 is fixed in the X and Y directions. However, the
polisher 23 may be moved in the X and Y directions in place of
moving the stage 21 in the X and Y directions. Alternatively, a
small tool (see FIG. 16) may be used in place of the polisher
23.
[0089] With this embodiment described above, correction of the
random component of distortion, which has conventionally been
impossible only with adjustment of the respective optical members
constituting the projection optical system, can be performed
easily.
[0090] In the above embodiment, as the plane-parallel plate having
no refracting power is used as the distortion correction plate 10,
the decentering precision of the distortion correction plate can be
moderated. Then, even if positioning is performed by the holding
member 11 as shown in FIG. 4, i.e., even if positioning is
determined by the machining precision of the holding member 11,
sufficiently high optical performance can be achieved. As the
distortion correction plate 10 is a plane-parallel plate, it can be
machined easily. When a lens having a predetermined curvature is
used as the distortion correction plate 10, this lens preferably
has a low refracting power due to the reason described above.
[0091] In the above embodiment, as the distortion correction plate
10 is arranged on the reticle R side (enlargement side) where the
beam has a smaller numerical aperture, only shift of the principal
ray is considered. However, when the distortion correction plate 10
is arranged on the wafer W side (reduction side), the machining
amount of the distortion correction plate 10 is preferably
determined by considering the influence of the size of the beam on
the distortion correction plate 10. Also, in order to further
improve the precision of distortion correction, even if the
distortion correction plate 10 is arranged on the reticle R side,
the machining amount is preferably determined by considering the
influence of the size of the beam size on the distortion correction
plate 10.
[0092] In the above embodiment, the distortion correction plate 10
is mounted in the optical path for measurement to decrease the
adverse influence caused by the parts precision of the distortion
correction plate 10. However, for measurement, a dummy component
different from the distortion correction plate as the target member
may be mounted in the optical path. In this case, however, the
parts precision of the dummy component must be high.
[0093] In the above embodiment, since the distortion correction
plate 10 is an optical member which is placed closest to the
reticle of all the optical members constituting the projection
objective lens PL, the operation of mounting and removing the
distortion correction plate 10 in and from the optical path of the
projection objective lens PL can be performed easily.
[0094] In the above embodiment, the distortion correction plate 10
is positioned with precision which is determined by the machining
precision of the holding member 11. In order to perform
higher-precision correction, a predetermined mark may be provided
to part of the distortion correction plate 10, so that the location
of the distortion correction plate 10 with respect to the holding
member 11 (with respect to the projection objective system PL) is
optically detected. At this time, the mark is desirably provided to
the distortion correction plate 10 at a position through which
exposure light does not pass.
[0095] FIG. 16 briefly shows the adjusting method of the present
invention that has been described so far. In FIG. 16, the
distortion correction plate 10 is mounted in the optical path of
the projection objective system PL, and the distortion is measured.
Subsequently, the shape of the distortion correction plate 10 is
calculated based on this measured distortion by using software that
calculates an aspherical shape. Thereafter, the distortion
correction plate 10 is machined by using a small tool or the like
so that it has the calculated shape. When the distortion correction
plate 10 machined in this manner is mounted in the optical path of
the projection objective system PL again, the distortion on the
surface of the wafer W is almost 0.
[0096] FIG. 17 briefly shows how to calculate the shape of the
distortion correction plate 10 from distortion data. In FIG. 17,
the amounts with which the plane normals at the respective points
on the distortion correction plate 10 must be controlled are
calculated based on the distortion data obtained by measurement.
Subsequently, the shape of a curved surface that the machining
target should have is calculated such that it satisfies the control
amounts calculated in this manner.
[0097] From the invention thus described, it will be obvious that
the invention may be varied in many ways. Such variations are not
to be regarded as a departure from the spirit and scope of the
invention, and all such modifications as would be obvious to one
skilled in the art are intended for inclusion within the scope of
the following claims.
[0098] The basic Japanese Application No. 009687/1995 (7-009687)
filed on Jan. 25, 1995 is hereby incorporated by reference.
* * * * *