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Claims  |
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What is claimed is:
1. A pattern forming method of projecting a pattern on a mask, having a top
surface, onto a substrate through a projection lens in order to transfer
the pattern onto the substrate, comprising the steps of:
illuminating the pattern on the mask in a direction almost perpendicular to
the top surface of the mask, with a pupil filter having a first pupil
function disposed between the mask and the substrate, the pupil filter
defining a pupil plane;
changing the pupil filter with a first pupil function to a pupil filter
with a second pupil function; and
continuing illuminating the pattern on the mask,
wherein at least one of the first and second pupil functions has an
amplitude transmittance distribution that is asymmetric with respect to a
pupil center.
2. The pattern forming method according to claim 1, wherein the pupil
functions include pupil function A.sub.1 and pupil function A.sub.2
satisfying the following relations:
A.sub.1 (X, Y)=A.sub.1 (-X, Y)=A.sub.1 (X, -Y)=A.sub.1 (-X, -Y),
and
A.sub.2 (X, Y)=-A.sub.2 (-X, Y)=-A.sub.2 (X, -Y)=A.sub.2 (-X, -Y),
where X and Y denote orthogonal axes in the pupil plane and having an
optical axis defined by the projection lens as an origin.
3. The pattern forming method according to claim 2, wherein the pupil
function A.sub.1 (X, Y) takes a value 1 in an entire pupil area, the pupil
function A.sub.2 (X, Y) takes any one of values 1, 0, and -1 in the pupil
plane, and the area for which A.sub.2 (X, Y)=0 has approximately the shape
of a cross, covering an image of an effective source in the pupil plane.
4. The pattern forming method according to claim 1, wherein the pupil
functions include pupil function B.sub.1 and pupil function B.sub.2
satisfying the following relations:
B.sub.1 (X, Y)=B.sub.1 (Y, X)=B.sub.1 (-Y, -X),
and
B.sub.2 (X, Y)=B.sub.1 (-Y, X),
where X and Y denote orthogonal axes in the pupil plane with an optical
axis defined by the projection lens as an origin.
5. The pattern forming method according to claim 4, wherein the pupil
function B.sub.1 (X, Y) takes any one of values 1, 0.5, and 0 and an area
for which B.sub.1 (X, Y)=0.5 covers an image of an effective source in the
pupil plane.
6. The pattern forming method according to claim 5, wherein the pupil
function B.sub.1 (X, Y) takes a value 1 or 0 in a pupil area and an area
for which B.sub.1 (X, Y)=0 is arranged symmetrically with respect to the
pupil center.
7. The pattern forming method according to claim 1, further comprising the
steps of:
changing the pupil filter with the second pupil function to a pupil filter
with a third pupil function; and
continuing illuminating the pattern on the mask,
wherein the pupil functions include pupil functions C.sub.1, C.sub.2, and
C.sub.3 meeting the following relations:
C.sub.1 (X, Y)=C.sub.1 (-X, Y)=C.sub.1 (X, -Y)=C.sub.1 (-X, -Y),
C.sub.2 (X, Y)=-C.sub.2 (-X, Y)=C.sub.2 (X, -Y),
and
C.sub.3 (X, Y)=C.sub.2 (-Y, X),
where X and Y denote orthogonal axes in the pupil plane with the optical
axis as the origin.
8. The pattern forming method according to claim 7, wherein the pupil
function C.sub.1 (X, Y) takes a value 1 in an entire pupil area, the pupil
function C.sub.2 (X, Y) takes any one of values 1, 0, and -1, and an area
for which C.sub.2 (X, Y)=0 has a shape of a stripe, which covers an image
of an effective source in the pupil plane.
9. The pattern forming method according to claim 1 further comprising the
steps of:
changing the pupil filter with the second pupil function with a pupil
filter with a third pupil function;
continuing illuminating the pattern on the mask;
changing the pupil filter with the third pupil function with a pupil filter
with a fourth pupil function; and
continuing illuminating the pattern on the mask,
wherein the pupil functions include pupil functions D.sub.1, D.sub.2,
D.sub.3, and D.sub.4 meeting the following relations:
D.sub.1 (X, Y)=D.sub.1 (Y, X),
D.sub.2 (X, Y)=D.sub.1 (-Y, X),
D.sub.3 (X, Y)=D.sub.1 (-X, -Y),
and
D.sub.4 (X, Y)=D.sub.1 (Y, -X),
where X and Y denote orthogonal axes in the pupil plane with an optical
axis of the projection lens as an origin.
10. The pattern forming method according to claim 9, wherein the pupil
function D.sub.1 (X, Y) takes any one of values 1, 0.5, and 0 and the area
for which D.sub.1 (X, Y)=0.5 covers an image of an effective source in the
pupil plane.
11. The pattern forming method according to claim 1, wherein the pupil
functions are realized using patterned opaque layers, partially absorbing
layers and phase-retarding layers on a transparent substrate.
12. The pattern forming method according to claim 11, wherein the step of
changing a pupil filter with a first pupil function to a pupil filter with
a second pupil function involves physically replacing a first pupil filter
with a second pupil filter.
13. The pattern forming method according to claim 1, wherein the step of
changing a first pupil filter with a first pupil function to a second
pupil filter with a second pupil function is accomplished by rotating the
pupil filter.
14. The pattern forming method according to claim 1, wherein the step of
changing a pupil filter with a first pupil function to a pupil filter with
a second pupil function involves physically replacing a first pupil filter
with a second pupil filter.
15. The pattern forming method according to claim 1, wherein the different
pupil functions are realized using a patterned opaque layer, a partially
phase-retarding layer on a transparent substrate and a stencil mask opaque
to light.
16. The pattern forming method according to claim 15, wherein the step of
changing a first pupil filter with a first pupil function to a second
pupil filter with a second pupil function is accomplished by rotating the
stencil mask.
17. The pattern forming method according to claim 1, wherein the pupil
filter having the first pupil function and the pupil filter having the
second pupil function are formed from by a patterned opaque, partially
absorbing and phase-retarding layer on an optically birefringent
substrate, and wherein a polarization of light used in the step of
illuminating is changed during the step of continuing illuminating.
18. A method for forming a pattern onto a substrate comprising the steps
of:
providing a mask having a predetermined pattern formed thereon;
providing a pupil filter between the mask and the substrate, the pupil
filter having a center and a pupil function with an asymmetric or
anti-symmetric phase transmittance distribution with respect to its
center;
illuminating the mask in a substantially perpendicular direction.
19. The method according to claim 18, wherein the pupil filter has a
transparent substrate that is partially covered by a phase retarding
layer, and wherein the method further comprises the step of laterally
translating the transparent substrate in order to illuminate different
portions of the transparent substrate.
20. A method for forming a pattern onto a substrate comprising the steps
of:
providing a mask having a predetermined pattern formed thereon;
providing a pupil filter between the mask and the substrate, the pupil
filter having a center and a pupil function with an anti-symmetric
amplitude transmittance distribution with respect to its center;
illuminating the mask and changing filters as necessary to form the pattern
desired. |
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Claims |
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Description |
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FIELD OF THE INVENTION
The present invention relates to a pattern forming method, a projection
exposure system, and a semiconductor device fabrication method. In
particular, the present invention relates to a pattern forming method for
forming fine patterns of various types of solid-state devices, a
projection exposure system used for the pattern forming method, and a
semiconductor device fabrication method employing the pattern forming
method.
BACKGROUND OF THE INVENTION
In general, improvement of the integration density of semiconductor
integrated circuits in recent years has been achieved mainly through a
reduction in size of the various circuit patterns. These circuit patterns
are presently formed mainly by optical lithography processes using a wafer
stepper.
FIG. 1 shows the structure of such a prior art stepper. Mask 14 is
illuminated by the light emitted from illumination system 11. An image of
mask 14 is projected onto a photoresist film coated on wafer 19 which is
the substrate to be exposed through projection system 15. As shown in FIG.
1, illumination system 11 includes a source 10, condenser lens 12, and
aperture 13 for specifying the shape and size of the effective source.
Projection system 15 includes a projection lens 16, pupil filter 17, and
aperture 18 arranged in or near the pupil plane of projection lens 16 to
set the numerical aperture (NA) of the lens.
The minimum feature size R of patterns transferable by an optical system is
approximately proportional to the wavelength .lambda. of the light used
for exposure and inversely proportional to the numerical aperture (NA) of
the projection optical system. Therefore, size R is expressed as R=k.sub.1
.lambda./NA, where k.sub.1 is an empirical constant and k.sub.1 =0.61 is
referred to as the Rayleigh limit.
As shown by the above expression, the resolution (minimum feature size R)
can be increased by decreasing wavelength .lambda. or by increasing the
numerical aperture NA. In the past, both approaches have been taken.
However, it has recently become difficult to decrease the wavelength
further, because of the limited availability of optical materials. Also,
lens design issues set a limit to further increases in the numerical
aperture. Therefore, pattern dimensions of integrated circuits are now at
or near the limit of resolution of the projection exposure system used to
define them.
In general, when the pattern dimensions approach the Rayleigh limit, the
projected image is no longer a faithful reproduction of the mask pattern
shape. This phenomenon is known as optical proximity effects and results
in corner rounding, line-end shortening, and line width errors, among
other things. To solve this problem, algorithms have been proposed that
can be used to pre-distort the mask pattern so that the shape of a
projected image takes on the desired shape.
Moreover, approaches have been described which improve the resolution limit
of a given optical system, resulting effectively in a decreased value of
k.sub.1. Adoption of a phase shifting mask is a typical example of this
approach. A phase shifting mask is used to provide a phase difference
between adjacent apertures of a conventional mask. Examples of this
technique are shown by Mark T. Levenson et al. in an article entitled
"Improving Resolution in Photolithography with a Phase-Shifting Mask" in
IEEE, Trans. on Electron Devices, Vol. ED-29, No. 12, pp. 1828-1836
(1982)".
A chromeless phase shifting mask method is known as a phase shifting method
suitable for the transfer of a fine isolated opaque line pattern, which is
needed, for example, for the gate pattern of a logic LSI. A mask used
according to this method uses a transparent layer to provide a phase
difference of 180.degree. in a transparent area. A very narrow dark line
on a bright background is formed along the outline of the transparent
layer. This chromeless phase shifting mask method is taught by Toh et al
in an article entitled "Chromeless Phase-Shifted Masks: A New Approach to
Phase-Shifting Masks" in SPIE vol. 1496 10th Annual Symposium on
Microlithography, pp. 27-53 (1990).
An off-axis illumination method and a pupil filtering method are also known
methods for improving images. According to the off-axis illumination
method, the transmittance of aperture 13 is modified in the illumination
system 11 of FIG. 1. One particular embodiment of this method changes the
illumination intensity profile so that the transmittance at the margin
becomes larger than that of the central portion, which is particularly
effective to improve the resolution of a periodic pattern and the depth of
focus. The pupil filtering method is a method of performing exposure
through a filter (pupil filter) located at the pupil position of a
projection lens to locally change the amplitude and phase of the
transmitted light. For example, this approach makes it possible to greatly
increase the depth of focus of an isolated pattern. The off-axis
illumination method is, for example, discussed by Noguchi et al. in an
article entitled "Resolution Enhancement of Stepper by Complementary
Conjugate Spatial Filter" in SPIE vol. 1674 Optical/Laser Microlithography
V, pp. 662-668 (1992). The pupil filtering method is disclosed by Fukuda
et al. in the Jpn. J. Appl. Phys. 32 (1993) pp. 5845-5849. Furthermore, it
is shown in an article by Orii et al., entitled "Quarter Micron
Lithography System with Oblique Illumination and Pupil Filter", SPIE vol.
2197 pp. 854-868 (1994), and shown in European Patent Publication No.
0562133 A1 (1993), that the resolution of a periodic pattern can further
be improved by combining the off-axis illumination method and the pupil
filtering method.
SUMMARY OF THE INVENTION
The present inventors have recognized that in order to apply optical
proximity effect correction to an actual pattern, large amounts of
calculation time are required for complex circuit patterns. Moreover,
typically a large number of correction patterns are necessary, thereby
greatly increasing the amount of pattern data required for making a mask.
The chromeless phase shifting method increases the complexity of the
exposure process, because dark lines are formed along the outline of the
shifter areas. Therefore, exposure must be performed twice with different
masks in order to form only the desired line pattern. Image improving
methods combining the off-axis illumination method and the pupil filtering
method have been proposed by Orii et al. and EP 0562133 A1 to Sandstrom,
as mentioned above in the Background section. In the case of the method
proposed by Orii et al., however, the number of patterns to be accurately
transferred is limited because imaging properties are asymmetric. The
method proposed by Sandstrom has practical problems in that not only is
the image contrast low, but it is also necessary to rotate the pupil
filter during exposure.
It is the first object of the present invention to solve the
above-mentioned problems of the prior art and provide a novel pattern
forming method capable of forming a projected image or resist pattern very
close to the shape of a circuit design pattern even when using a
conventional mask having the same pattern as the circuit design pattern
without performing complex mask correction. This object also includes
improving the fidelity of the pattern shape with respect to corner
rounding and line width errors and providing a projection exposure system
used for this pattern forming method.
It is another object of the present invention to provide a novel pattern
forming method capable of forming a very fine pattern with a high accuracy
without using a phase shifting mask or multiple exposure using two or more
different masks and to provide a projection exposure system used for this
pattern forming method.
It is still another object of the present invention to provide a
semiconductor device fabrication method capable of forming various
patterns with a high accuracy and without increasing the number of process
steps.
In order to solve the above-mentioned problems and satisfy the
above-mentioned objects, the present invention uses a method of exposing a
mask pattern onto a substrate through a projection lens and transferring
the pattern onto the substrate. The mask is illuminated almost
perpendicularly from the top and exposure of the same pattern to the same
position on the substrate surface is performed by changing the
transmittance of the pupil filter located at the pupil position of the
projection lens. At least one of the pupil functions has an amplitude
transmittance distribution that is asymmetric with respect to the pupil
center.
A preferred embodiment is obtained when the pupil functions include pupil
function A.sub.1 and pupil function A.sub.2 which satisfy the following
relations.
A.sub.1 (X, Y)=A.sub.1 (-X, Y)=A.sub.1 (X, -Y)=A.sub.1 (-X, -Y)
A.sub.2 (X, Y)=-A.sub.2 (-X, Y)=-A.sub.2 (X, -Y)=A.sub.2 (-X, -Y)
(In the above expressions, X and Y denote orthogonal axes in the pupil
plane with the optical axis as the origin.)
A satisfactory result is obtained when the pupil function A.sub.1 (X, Y)
takes the value 1 in the whole pupil area, the pupil function A.sub.2 (X,
Y) takes any one of values 1, 0, and -1 in the pupil plane of the
projection lens, and the area for which A.sub.2 (X, Y)=0 has approximately
the shape of a cross, covering the image of the effective source in the
pupil plane.
A preferred embodiment is obtained when the pupil functions include pupil
function B.sub.1 and pupil function B.sub.2 satisfying the following
relations.
B.sub.2 (X, Y)=B.sub.1 (Y, X)=B.sub.1 (-Y, -X)
B.sub.2 (X, Y)=B.sub.1 (-Y, X)
(In the above expressions, X and Y denote orthogonal axes in the pupil
plane with the optical axis as the origin.)
A satisfactory result is obtained when the pupil function B.sub.1 (X, Y)
takes any one of the values 1, 0.5, and 0 in the pupil plane and the area
for which B.sub.1 (X, Y)=0.5 covers the image of the effective source in
the pupil plane.
A satisfactory result is also obtained when the pupil function B.sub.1 (X,
Y) takes the value 1 or 0 in the pupil area and the area for which B.sub.1
(X, Y)=0 is arranged symmetrically with respect to the pupil center.
A preferred embodiment is obtained when the pupil functions include pupil
functions C.sub.1, C.sub.2, and C.sub.3 satisfying the following relations
.
C.sub.1 (X, Y)=C.sub.1 (-X, Y)=C.sub.1 (X, -Y)=C.sub.1 (-X, -Y)
C.sub.2 (X, Y)=-C.sub.2 (-X, Y)=C.sub.2 (X, -Y)
C.sub.3 (X, Y)=C.sub.2 (-Y, X)
(In the above expressions, X and Y denote orthogonal axes in the pupil
plane with the optical axis as the origin.)
A satisfactory result is obtained when the pupil function C.sub.1 (X, Y)
takes the value 1 in the whole pupil area, the pupil function C.sub.2 (X,
Y) takes any one of values 1, 0, and -1, and the area for which C.sub.2
(X, Y)=0 has the shape of a stripe, covering the image of the effective
source in the pupil plane.
A preferred embodiment is obtained when the pupil functions include pupil
functions D.sub.1, D.sub.2, D.sub.3, and D.sub.4 satisfying the following
relations.
D.sub.1 (X, Y)=D.sub.1 (Y, X)
D.sub.2 (X, Y)=D.sub.1 (-Y, X)
D.sub.3 (X, Y)=D.sub.1 (-X, -Y)
D.sub.4 (X, Y)=D.sub.1 (Y, -X)
(In the above expressions, X and Y denote orthogonal axes in the pupil
plane with the optical axis as the origin.)
A satisfactory result is obtained when the pupil function D.sub.1 (X, Y)
takes any one of values 1, 0.5, and 0 and the area for which D.sub.1 (X,
Y)=0.5 covers the image of the effective source in the pupil plane.
The exposure can be performed by using a variable off-axis illuminator
capable of producing a different effective source distribution for each
pupil function.
The pupil functions can be set by providing a pupil filter in which a film
selected out of a group of a film opaque to the light, a film for
partially absorbing the light, and a film for phase-retarding the light is
locally set on a transparent substrate almost on the pupil plane of the
projection lens.
The projection exposure can be performed by changing the pupil filters
having amplitude transmittance distributions different from each other
during a plurality of exposures or during a single exposure applied to the
same position on the substrate surface. Also, the projection exposure can
be performed by rotating the pupil filter having one amplitude
transmittance distribution during a plurality of exposures or during a
single exposure applied onto the same position on the substrate surface.
The different pupil functions can be set by providing a filter in which a
film selected out of a group of a film opaque to the light, a film for
partially absorbing the light, and a film for phase-retarding the light is
locally set on a transparent substrate and a stencil mask opaque to the
light is provided near the pupil plane of the projection lens.
The projection exposure can be performed by rotating the stencil mask
during a plurality of exposures or during a single exposure onto the same
position on the substrate surface.
Since a filter in which a film selected out of a film opaque to the light,
a film for partially absorbing the light, and a film phase-retarding the
light is locally set onto an optically birefringent substrate and is
formed almost on the pupil plane of the projection lens, projection
exposure can be performed by rotating the direction of polarization of the
light during a plurality of exposures or during a single exposure onto the
same position on the substrate surface.
Moreover, the above-mentioned objects of the present invention can be
achieved by a projection exposure system having a source, a mask stage for
mounting a mask, an illumination optical system for applying the light
emitted from the source onto the mask, a wafer stage for mounting a wafer,
a projection optical system for projection-exposing the light passing the
mask to the wafer, a pupil filter or stencil filter arranged almost nearby
the pupil of the projection optical system, and means for replacing or
rotating the pupil filter or stencil filter during a plurality of
exposures during a single exposure onto the same position on the surface
of the wafer.
Furthermore, in a method for projection-exposing a predetermined pattern
formed on a mask to a principal plane of a semiconductor substrate through
a projection lens and transferring the pattern to the principal plane of
the semiconductor substrate, a semiconductor device can be fabricated by
illuminating the mask from a direction almost perpendicularly above the
mask and arranging pupil filters having a plurality of pupil functions
different from each other on the pupil plane of the projection lens and
performing the exposure onto the same position of the same pattern on the
substrate surface.
In this case, the mask pattern can be used as a contact-hole or via-hole
pattern of a MOS LSI and therefore, a preferable result can be obtained.
It should be noted that other objects, features and advantages of the
present invention will be readily apparent in view of the following
detailed description of the preferred embodiments.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is an illustration showing the basic structure of a projection
exposure system;
FIG. 2(a) to 2(d) are illustrations showing basic pupil functions used in
the present invention;
FIGS. 3(a) to 3(d) are illustrations showing qualitative amplitude
distributions of point images obtained by using the pupil functions shown
in FIG. 2;
FIGS. 4(a) to 4(d) are illustrations explaining the shape of the projected
images when transferring dark-field patterns using the present invention;
FIGS. 5(a) to 5(e) are illustrations explaining the shape of the projected
images when transferring bright-field patterns by the present invention;
FIGS. 6(a) and 6(b) are illustrations showing pupil function of the present
invention;
FIGS. 7(a) to 7(c) are illustrations showing the structure of pupil filters
for realizing a pupil function of the present invention;
FIGS. 8(a) to 8(c) are illustrations showing the structure of pupil filters
for realizing another pupil function of the present invention;
FIG. 9 is an illustration showing the structure of a stepper used for the
present invention;
FIG. 10 is a chart showing the flow of an exposure process of the present
invention;
FIGS. 11(a) and 11(b) are illustrations showing mask patterns;
FIGS. 12(a) to 12(e) are process diagrams showing a case of applying the
present invention to the fabrication of a semiconductor integrated circuit
device;
FIG. 13(a) and 13(b) are illustrations showing a layout of a mask pattern
for fabricating a semiconductor integrated circuit device;
FIGS. 14(a) and 14(b) are illustrations of contours of formed resist
patterns;
FIG. 15 is an illustration showing the concept of exposure superposition
using different pupil filters;
FIGS. 16(a) to 16(c) illustrate the implementation of pupil functions A, C
and D of FIG. 2; and
FIGS. 17(a) to 17(d) illustrate various mask pattern layouts according to
the present invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
The present invention will now be described in conjunction with the
accompanying drawings.
FIGS. 2(a) to 2(d) show four different pupil functions A, B, C, and D. FIG.
2(a) shows a four-fold symmetric pupil function A having a positive
transmittance everywhere within the pupil area 20.
In the case of pupil function B shown in FIG. 2(b), the top-left and the
bottom-right quadrants 21 have a positive transmittance and the top-right
and the bottom-left quadrants 22 have a negative transmittance in a bright
background. Cross-shaped area 23 in the middle is completely opaque and
its width corresponds to the diameter of the image of the effective source
in the pupil plane. Pupil function B is symmetric with respect to axes
obtained by rotating the X and Y axes by 45.degree. about the center of
the pupil plane and it is anti-symmetric with respect to the X and Y axes.
In the case of pupil function C shown in FIG. 2(c), upper-half area 24 has
a positive transmittance and lower-half area 25 has a negative
transmittance. Stripe-shaped area 26 in the middle is completely opaque
and its width is equal to or larger than the diameter of the image of the
effective source in the pupil plane. Pupil function C is symmetric with
respect to the Y axis and anti-symmetric with respect to the X axis.
Finally, pupil function D shown in FIG. 2(d) is obtained by rotating pupil
function C by 90.degree. about the pupil center.
Amplitude point spread functions obtained by using pupil functions A to D
shown in FIGS. 2(a) to 2(d) are shown schematically in FIGS. 3(a) to 3(d).
Because the amplitude point spread functions are obtained via a
two-dimensional Fourier transform of the pupil function, they have the
same symmetry as the pupil functions. The amplitude point spread function
corresponding to pupil function A, as shown in FIG. 3(a), consists
primarily of a bright spot 30 of uniform phase in a dark background 31.
In the case of the amplitude point spread function corresponding to pupil
function B, as shown in FIG. 3(b), four peaks 32 and 33 appear which are
separated by dark lines along the X and Y axes. In FIG. 3(b), peaks 32
shown at the top left and the bottom right of the figure are opposite in
phase to peaks 33 shown at the top right and the bottom left.
In the amplitude point spread function corresponding to pupil function C,
two peaks 34 and 35 separated by a horizontal dark line appear, as shown
in FIG. 3(c). In FIG. 3(c), upper peak 34 is opposite in phase to lower
peak 35.
The amplitude point spread function corresponding to pupil function D, as
shown in FIG. 3(d), is the same as that obtained by rotating the
distribution shown in FIG. 3(c) by 90.degree. about the pupil center. In
FIG. 3(d), left peak 34 is opposite in phase to right peak 35.
Therefore, by properly combining and using pupil functions A, B, C, and D,
it is possible to image various fine patterns with a high degree of
accuracy.
FIG. 4(a) illustrates the case of imaging a mask pattern consisting of a
bright horizontal line segment 40 onto an opaque background 41 by
combining and using pupil functions A and B as described below. By using
pupil function A in which the whole pupil area 20 has positive
transmittance for the pattern shown in FIG. 4(a), the projected image
shown qualitatively in FIG. 4(b) is obtained. This projected image is an
image in which bright line image 42 is in dark area 43. When the width of
image 42 becomes close to the resolution limit of a protection optical
system, resulting image 42 will suffer from line-end shortening and its
corners will be rounded compared to the mask-pattern outline 44.
By using pupil function B, the projected image shown qualitatively in FIG.
4(c) is obtained. In this case, because cross-shaped opaque area 43 is
present in the pupil plane, the light transmitted through the central
portion of the mask feature and the light diffracted by the edge of the
feature are blocked by the pupil filter and only the light diffracted by
the corners of the pattern passes through the pupil plane and reaches the
image plane. However, as shown in FIG. 3(b), in the case of pupil function
B, the amplitude point spread functions are anti-symmetric. Therefore,
light spots 45a produced at the top right and the bottom left are opposite
in phase to light spots 45b produced at the top left and the bottom right.
Therefore, adjacent corners are always separated by a dark area.
Therefore, by adding the exposure with pupil function B to the exposure
with pupil function A, the image shown in FIG. 4(d) is obtained whose
corners 46 are highlighted. The same effect is obtained for a line pattern
in the perpendicular direction or a square pattern.
Conversely to FIG. 4(a), FIG. 5(a) illustrates a mask pattern in which an
opaque line segment 50 is formed in a bright background 51, by using mask
patterns A, C, and D. By performing an exposure with pupil function A, the
projected image in which dark image 52 is formed in bright area 53 is
obtained as shown in FIG. 5(b). If the line width is close to the
resolution limit of the projection system and image 52 is formed by
adjusting the exposure dose so that the width of the projected image is
equal to the width of the original pattern outline 54 shown by a broken
line, the line ends of image 52 will be shortened and the corners will be
rounded. When exposure is performed so that the length of image 52 becomes
equal to original pattern outline 54, an image 55, having a width larger
than the width of the original pattern outline 54, is formed.
Therefore, it is difficult to form a pattern whose width and length are
equal to design dimensions and whose corners are not rounded. However, if
it is possible to decrease the line width while keeping the length
constant it is clear that line ends of an image can be prevented from
shortening.
When exposure is performed using pupil function C, narrow bright lines 56a
and 56b are formed along the horizontal edges as shown in FIG. 5(c). This
is because, as shown in FIG. 2(c), stripe-shaped opaque area 26 is present
in the pupil plane of pupil function C and therefore, the undiffracted
background component and the light diffracted at the vertical edges of the
pattern do not pass through the pupil but only the light diffracted at the
horizontal edges and pattern corners reaches the image plane. Thus,
background 57 becomes dark.
Because a print image obtained by pupil function C has the anti-symmetry
shown in FIG. 3(c), the upper bright line (edge image) 56a shown in FIG.
5(c) is opposite in phase to lower bright line (edge image) 56b and these
bright lines 56a and 56b are separated from each other. Therefore, by
adding the exposure using pupil function C to the exposure using pupil
function A, it is possible to decrease the line width while keeping the
length constant.
However, to obtain the same effect also for a vertically-oriented line
pattern, an exposure using pupil function D, obtained by rotating pupil
function C by 90.degree. must be performed. In this case, the projected
image according to pupil function D consists of bright lines 58a and 58b
along the vertical edges of the line pattern as shown in FIG. 5(d).
However, when forming a horizontally-oriented line pattern whose line width
is close to the resolution limit of a projection optical system, the
maximum light intensity of the projected image shown in FIG. 5(d) is very
small compared to the case of FIG. 5(c) because vertical edges are very
short. Therefore, by performing the exposure using pupil function C and
the exposure using pupil function D with an equal exposure value and
adding both types of exposure to the image obtained by pupil function A,
contraction of line ends of the line image is decreased and the width of
the line image can be decreased. Therefore, as shown in FIG. 5(e), summed
image 59 can be obtained whose length and width coincide with the length
and width of original feature outline 54. It is needless to say that the
same can be applied to a vertically-oriented opaque pattern.
When an L-shaped opaque line is present in the bright background, the added
light intensity of the inside corner of the L-shaped opaque pattern is
larger than at the outside convex corner of the pattern when images
obtained by using pupil functions C and D are added to an image obtained
by pupil function A to form a summed image. Therefore, also in this case,
a summed image with a high pattern fidelity is obtained.
By summing images obtained by using pupil functions A, C, and D, it is
possible not only to moderate the optical proximity effect but also to
greatly improve the resolution of a dark line on a bright background. For
example, when considering a light intensity profile perpendicular to the
direction of a dark line pattern, the light intensity distribution
obtained by pupil function A is shown by curve 150 in FIG. 15 and a dark
region wider than the pattern width is obtained. However, the distribution
obtained by pupil function C consists of bright lines at the edges of the
original line as shown by curve 151 in FIG. 15. In this case, distribution
152 obtained by pupil function D does not contribute. Therefore, a more
faithful light intensity distribution 153 is obtained by superposing light
intensity distributions 150, 151, and 152 onto each other.
In this case, to obtain the minimum line width, it is preferable to make
the exposure values when using pupil functions C and D larger than the
exposure value when using pupil function A. However, because this method
causes a larger side lobe, it is preferable to increase the interval
between dark patterns to a distance for which no interference is produced
between adjacent patterns. Many patterns for logic LSI satisfy this
criterion.
A method for realizing multiple exposure in which pupil functions are
different from each other will now be described below. The most direct
method for performing the multiple exposure involves preparing a plurality
of pupil filters with pupil functions different from each other and
changing the pupil filters for each exposure. This method makes it
possible to achieve an effect equivalent to multiple exposure without
changing different pupil filters as described below.
That is, the multiple exposure performed by using pupil functions A.sub.A
and .alpha.A.sub.B different from each other is equivalent to the multiple
exposure using pupil function A.sub.1 =(A.sub.A +.alpha.A.sub.B)/.sqroot.2
and pupil function A.sub.2 =(A.sub.A -.alpha.A.sub.B)/.sqroot.2. FIG. 6(a)
shows an example of pupil function A.sub.1, in which symbol 60 denotes an
area with a transmittance of 1, 61 denotes an opaque area, and 62 denotes
a cross-shaped area with a transmittance of 0.5. The above a is a value
showing the relative weights of the two types of exposure.
When pupil functions A.sub.A and A.sub.B have the same symmetry as pupil
functions A and B shown in FIG. 2, pupil function A.sub.1 and pupil
function A.sub.2 become the same pupil function by rotating them through
90.degree.. Therefore, only by rotating a single-pupil filter during
exposure, it is possible to obtain the same effect as double exposure
using two pupil functions A and B.
When pupil function A has a completely clear pupil (transmittance is 1 for
the whole surface) and pupil function B has only transmittance values of
-1, 0, and 1, pupil functions A.sub.1 and A.sub.2 have only transmittances
of 0, 0.5, and 1 for .alpha.=1. Moreover, in the central area with a
transmittance of 0.5, A.sub.1 and A.sub.2 are common.
When rotating a pupil filter, the same problem as that when replacing pupil
filters occurs. However, as described later, the same effect as that when
rotating the whole pupil function is obtained by rotating only a stencil
mask combined with a pupil filter instead of rotating the whole pupil
filter. In this case, the above problem due to replacement or rotation of
pupil filters will not occur. The above stencil mask can be rotated or
secured on a filter.
The exposure using three types of pupil functions A.sub.A, .alpha.A.sub.C,
and .alpha.A.sub.D is equivalent to the multiple exposure using pupil
functions A.sub.1 =(A.sub.A +.alpha.A.sub.C +.alpha.A.sub.D)/2, A.sub.2
=(A.sub.A +.alpha.A.sub.C -aA.sub.D) /2, A.sub.3 =(A.sub.A -.alpha.A.sub.C
+.alpha.A.sub.D)/2, and A.sub.4 =(A.sub.A -.alpha.A.sub.C
+.alpha.A.sub.D)/2.
When pupil functions A.sub.A, A.sub.C, and A.sub.D have the same symmetry
as pupil functions A, C, and D shown in FIG. 2 and A.sub.D is a function
obtained by rotating A.sub.C through 90.degree., pupil functions A.sub.1
to A.sub.4 are obtained in order by rotating the same pupil filter
incrementally through 90.degree.. Therefore, by rotating a single pupil
filter during exposure, the result same as that of the triple exposure
using three types of pupil functions A, C, and D is obtained.
Pupil function A.sub.1 shown in FIG. 6(b) comprises area 63 with a
transmittance of 1, opaque area 64, and a square area 65 with a
transmittance of 0.5. When pupil function A is a clear area (transmittance
is 1 for the whole surface) and pupil functions C and D have only
transmittances of -1, 0, and 1, transmittances of pupil functions A.sub.1
to A.sub.4 are only 0, 0.5, and 1 for .alpha.=1. In the case of a pupil
filter having pupil functions A.sub.1 to A.sub.4, however, areas with a
transmittance of 0.5 are all common.
In both pupil functions shown in FIG. 6 the area occupied by the image of
the effective source in the pupil plane is attenuated. Such pupils have
the property of decreasing the intensity of the undiffracted light
relative to the various diffraction orders, and are sometimes referred to
as conjugate filters.
We also observe that in FIG. 6b a relatively large fraction of the pupil
area is opaque and therefore unused. This suggests shifting the pupil
filter sideways towards the opaque side of the pupi | | |
