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Description  |
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BACKGROUND OF THE INVENTION
The present invention relates to a method of forming a fine pattern for
various types of solid state devices. This invention also relates to a
projection exposure apparatus and a projection exposure mask used for the
fine pattern formation, a method of fabricating the mask and a method of
layout designing of the mask pattern. This invention further relates to an
optical lens used for all optical apparatuses and an optical filter
installed in the optical lens.
In order to improve the degree of integration and the operation speed of
solid state devices such as LSI, circuit patterns have been miniaturized
more and more. At present, a reduction projection exposure method superior
in mass productivity and resolution capability is widely used for forming
such circuit patterns. The resolution limit of this method is proportional
to the exposure wavelength and inversely proportional to the numerical
aperture (NA) of the projection lens. The depth of focus, on the other
hand, is proportional to the exposure wavelength and inversely
proportional to the square of NA. As a result, with the improvement in the
resolution limit (increase in NA and shortening of wavelength), the depth
of focus is greatly reduced.
Conventionally, there has been suggested a phase-shifting method for
reversing the phase of light transmitted through an adjacent aperture on
the mask as a method for remarkably improving the resolution of the
projection exposure. Also, a FLEX (Focus Latitude Enhancement Exposure)
method for effecting exposure by the use of images of the same mask
pattern formed at a plurality of positions along the light axis has been
suggested as a method for remarkably improving the depth of focus in the
conventional projection exposure method. The phase-shifting method is
discussed in Levenson, et al, IEEE Trans. Electron Devices, Vol. ED-29,
pp. 1828-1836 (1982), and the FLEX method in Fukuda, et al, IEEE Electron
Device Letters Vol. EDL-8, pp. 179-180 (1987), for example.
A method of changing the imaging characteristics by changing the
distribution of amplitude or phase in a lens pupil, on the other hand, is
generally known as an apodisation or an optical filtering. Further, the
double diffraction method is known as a method for restoring the reduced
contrast of an image. These methods are discussed in, for example,
Tsujiuchi, Progress in Optics, Vol. 2, pp. 133-152 (1983), North-Holland
Publishing Co.
SUMMARY OF THE INVENTION
In recent years, the circuit pattern has been more and more miniaturized
with the increase in the degree of large scale integration, while
electronic device structures of DRAM, a typical LSI, and the like are
increasingly formed in three dimensions. As a result, the projection
surface of a mask pattern on the LSI surface is undesirably affected by
the ever-reducing depth of focus, thereby making it increasingly difficult
to form a fine pattern on the whole surface of an LSI chip. It is
therefore necessary to secure a high resolution with the required depth of
focus.
If the above-mentioned phase-shifting method is applied to repetitive
patterns such as an LSI wiring pattern under the illumination condition of
about 0.3 in coherence factor, not only the resolution but also the depth
of focus is improved greatly by a factor of two or more. In the
conventional applications to hole patterns or other isolated patterns,
however, both the resolution and the depth of focus are improved only by
about 20%. Also, a transfer pattern identical to the mask shape cannot be
obtained due to an increased proximity effect in the case of a pattern of
complicated shape.
According to the above-mentioned FLEX method, on the other hand, the depth
of focus of an isolated pattern like a hole pattern is improved greatly by
a factor of two or three. In this method involving a plurality of
exposures effected while moving the substrate stage mainly along the light
axis, however, the exposure control is complicated and mechanical
operation of the substrate stage is required during exposure of the chip.
Another problem is that the image contrast is deteriorated in patterns
having a comparatively large proportion of exposure area, or especially,
repetitive patterns of LSI wirings or the like.
An object of the present invention is to provide a novel method of forming
patterns, a projection exposure apparatus, a mask, a mask fabrication
method and a pattern layout method which are capable of maintaining a
large depth of focus in spite of a larger NA and a shorter wavelength to
improve the resolution limit without posing any of the problems mentioned
above.
In the references cited above, a multiple-foci filter is suggested by Dr.
Tsujiuchi, et al. Such a filter, however, is intended for setting the
focal point to a plurality of mutually-distant planes in a system having a
large aberration, and fails to take into full consideration the phase
relation between a plurality of images formed at the focal points. It is
therefore not always possible to assure the desired effect in a
diffraction limited optical system. Further, the spatial distribution of
the transmittance (transmission) and phase of the filter for securing a
uniform light intensity along the light axis in accordance with various
patterns are not defined clearly.
Another object of the present invention is to provide a projection exposure
apparatus using a novel optical filter, an optical lens and the
above-mentioned lens which is capable of maintaining a large depth of
focus and a resolution capability in a diffraction limited optical system
of a projection exposure apparatus for LSI or the like.
A large depth of focus is required in various fields of optics in addition
to the reduction projection exposure described above. More specifically,
an optical microscope for observing objects having a three-dimensional
structure such as living creatures and the surfaces of LSI, a microlens
for an optical disk head, and general optical devices including cameras
and telescopes are expected to find applications in wider areas and may be
improved in capacity by increasing the depth of focus. As the second
object, the present invention provides a novel optical lens capable of
maintaining a large depth of focus also in such general optical devices,
and an optical filter used for such a purpose.
According to one aspect of the present invention, when projection exposure
is effected through a mask pattern on a predetermined region of a
photoresist layer formed on a substrate having a topography in the surface
thereof, images of the mask pattern having substantially the same
amplitude are formed simultaneously at mutually-distant first and second
positions having different distances from the reference level of the
substrate along the light axis, and the phase correlation between the
images formed at the two positions satisfies a predetermined condition,
whereby the sum of exposure amounts in the region interposed between the
first and second positions is equal to or more than the exposure amount
capable of forming a pattern of the photoresist layer by development.
According to another aspect of the present inventions, when projection
exposure of a mask is effected on a substrate through a projection lens by
use of light, the distribution of the complex amplitude transmittance of
the mask pattern or the pupil (or an aperture stop plane at a position
conjugate therewith) of the projection lens or the illuminance
distribution of an effective light source is set in such a manner that the
amplitude distribution of the light transmitted through the pupil of the
projection lens is equal or appropriately approximate to the amplitude
distribution of the light obtained on the pupil when a mask having the
desired design pattern is illuminated with a normal partially spatial
coherent light or a spatial coherent light, multiplied by cos
(2.pi..beta.r.sup.2 -.theta./2) (r: pupil radius coordinate, .beta.,
.theta.: appropriate real number).
According to still another aspect of the present invention, an optical
filter having the distribution of complex amplitude transmittance
expressed by
T(r)=cos (2.pi..beta.r.sup.2 -.theta./2).times.circ(r)
(.beta., .theta.: appropriate constant), or the distribution of complex
amplitude transmittance with an appropriate discrete function of T(r), is
disposed substantially at a pupil plane of the lens, a plane conjugate
with the pupil plane or an aperture stop position determining the
numerical aperture of the lens.
According to a further aspect of the invention, the Fourier transform of
the layout pattern drawn on the LSI is obtained, the pattern data obtained
after Fourier transform are multiplied by cos (2.pi..beta.f.sup.2
-.theta./2) (f:spatial frequency), and the inverse Fourier transform of
the resulting product is taken, so that the pattern thus obtained or a
solution approximate thereto is used as a mask pattern to fabricate an LSI
by exposure.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram typically showing the principle of the present
invention.
FIGS. 2A to 2D are other diagrams typically showing the principle of the
present invention and a process for producing a modified mask pattern from
a designed mask pattern, FIG. 2E is a diagram showing the distribution of
light intensity by a modified mask, and FIG. 2F is a diagram showing the
distribution of light intensity by a conventional mask.
FIG. 3A is a diagram showing the phase-amplitude distributional of a
projected image of a linear aperture pattern according to the prior art
(conventional exposure method), FIG. 3B is a diagram showing the light
intensity distribution of a projected image of a linear aperture pattern
according to the prior art, FIG. 3C is a diagram showing the
phase-amplitude distribution of a projected image of a linear aperture
pattern according to the present invention, and FIG. 3D is a diagram
showing the light intensity distribution of a projected image of a linear
aperture pattern according to the present invention.
FIG. 4A is a diagram showing the complex amplitude transmittance of a
filter according to the present invention, and FIG. 4B is a diagram
showing the focus dependence of the light intensity distribution with a
filter according to the present invention applied to a hole pattern.
FIG. 5A is a diagram showing the complex amplitude transmittance in a pupil
according to the prior art, and FIG. 5B is a diagram showing the focus
dependence of the light intensity distribution according to the prior art.
FIG. 6A is a plan view showing a contact hole pattern, FIG. 6B is a diagram
showing the light intensity distribution under a just-focused condition
without using any filter according to the present invention for the
contact hole pattern shown in FIG. 6A, FIG. 6C is a diagram showing the
light intensity distribution without using the filter according to the
present invention with the contact hole pattern defocused by 1 .mu.m, FIG.
6D is a diagram showing the light intensity distribution in the case where
the filter according to the present invention is used with the contact
hole pattern according to the present invention just focused, and FIG. 6E
is a diagram showing the light intensity distribution in the case where
the filter according to the present invention is used for the contact hole
pattern of FIG. 6A with the contact hole pattern defocused by 1 .mu.m.
FIG. 7A is a diagram showing the complex amplitude transmittance of another
filter according to the present invention, and FIG. 7B is a diagram
showing the focus dependence of the light intensity distribution in the
case where another filter according to the present invention is applied to
the hole pattern.
FIG. 8A is a diagram showing the complex amplitude transmittance of still
another filter according to the present invention, FIG. 8B is a diagram
showing the relation between the depth of focus and size when no filter is
used, and FIG. 8C is a diagram showing the relation between the depth of
focus and size in the case where a filter is used.
FIG. 9A is a diagram showing an example of a wiring pattern of an LSI
circuit, FIGS. 9B to 9E are diagrams showing the light intensity
distribution under various conditions when the conventional method is
applied to the wiring pattern shown in FIG. 9A, and FIGS. 9F and 9G are
diagrams showing the light intensity distribution under various conditions
when the present invention is applied to the wiring pattern shown in FIG.
9A.
FIG. 10A is a diagram showing the complex amplitude transmittance of a
filter, FIG. 10B is a diagram showing the Al layer thickness distribution
on a filter, and FIG. 10C is a diagram showing the SiO.sub.2 layer
thickness distribution on a filter.
FIG. 11A is a diagram showing the radial distribution of the thickness of
an absorber formed on a filter according to the present invention, FIG.
11B is a diagram showing the radial distribution of thickness of an
MgF.sub.2 layer formed on a filter according to the present invention, and
FIG. 11C is a diagram showing the complex amplitude transmittance of a
filter according to the present invention.
FIG. 12 is a diagram showing the complex amplitude transmittance of an
optical filter according to the present invention.
FIG. 13 is a diagram showing the complex amplitude transmittance of another
optical filter according to the present invention.
FIG. 14A is a diagram showing the radial distribution of the thickness of
an annular absorber pattern formed on a filter according to the present
invention, FIG. 14B is a diagram showing the light transmittance
distribution of the same filter, FIG. 14C is a plan view of the phase
filter pattern of the filter, and FIG. 14D is a diagram showing the
complex amplitude transmittance of the filter.
FIG. 15A is a diagram showing an aperture pattern, FIG. 15B is a diagram
showing the amplitude transmittance along line A--A' in FIG. 15A, FIG. 15C
is a contour map showing the amplitude transmittance distribution of a
mask obtained on the basis of the aperture shown in FIG. 15A, and FIG. 15D
is a diagram showing the amplitude transmittance along line A--A' in FIG.
15C.
FIG. 16A is a diagram showing the focus dependence of the light intensity
distribution according to the prior art, and FIG. 16B is a diagram showing
the dependence of the light intensity distribution on the focal point
according to the present invention.
FIGS. 17A to 17D are diagrams showing the light intensity distribution for
various coherence factors using a mask according to the present invention.
FIG. 18A is a plan view of a mask according to the present invention, FIG.
18B is a diagram showing the amplitude transmittance of the mask shown in
FIG. 18A, and FIG. 18C is a diagram showing the focus dependence of the
light intensity distribution when the mask shown in FIG. 18A is used.
FIG. 19A is a plan view showing an example of the mask for the contact
hole, and FIG. 19B is a plan view of the mask for the contact hole
according to the present invention.
FIG. 20A is a diagram showing the light intensity distribution for 0 .mu.m
defocus when the mask shown in FIG. 19A is used, FIG. 20B is a diagram
showing the light intensity distribution for 1 .mu.m defocus when the mask
shown in FIG. 19A is used, FIG. 20C is a diagram showing the light
intensity distribution for 0 .mu.m defocus when the mask shown in FIG. 19B
is used, FIG. 20D is a diagram showing the light intensity distribution
for 1 .mu.m defocus when the mask shown in FIG. 19B is used, FIG. 20E is a
diagram showing the light intensity distribution for 0 .mu.m defocus when
the mask is used with the interference between patterns suppressed, and
FIG. 20F is a diagram showing the light intensity pattern for 1 .mu.m
defocus when the same mask is used with the interference between patterns
suppressed.
FIG. 21A is a partial plan view of a conventional mask for the hole
pattern, FIG. 21B is a partial plan view of a mask for the hole pattern
according to the present invention, and FIG. 21C is a partial plan view of
another mask for the hole pattern according to the present invention.
FIG. 22A is a plan view showing the light intensity distribution for 0
.mu.m defocus when the mask shown in FIG. 21A is used, FIG. 22B is a plan
view showing the light intensity distribution for 1 .mu.m defocus when the
mask shown in FIG. 21A is used, FIG. 22C is a plan view showing the light
intensity pattern for 0 .mu.m defocus when the mask shown in FIG. 21B is
used, FIG. 22D is a diagram showing the light intensity distribution for 1
.mu.m defocus when the mask shown in FIG. 21B is used, FIG. 22E is a plan
view showing the light intensity distribution for 0 .mu.m defocus when the
mask shown in FIG. 21C is used, and FIG. 22F is a plan view showing the
light intensity distribution for 1 .mu.m defocus when the mask shown in
FIG. 21C is used.
FIG. 23A is a diagram showing a mask for the hole pattern according to the
present invention, FIG. 23B is a diagram showing the amplitude
transmittance of the mask, FIG. 23C is a diagram showing the light
intensity obtained when the same mask is used, FIG. 23D is a diagram
showing another mask for the hole pattern according to the present
invention, FIG. 23E is a diagram showing the amplitude transmittance of
the same mask, FIG. 23F is a diagram showing the light intensity obtained
when the same mask is used, FIG. 23G is a diagram showing another mask for
the hole pattern according to the present invention, FIG. 23H is a diagram
showing the amplitude transmittance of the same mask, and FIG. 23I is a
diagram showing the light intensity obtained when the same mask is used.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
In order to facilitate a better understanding of the present invention,
there will first be described the principle of the present invention with
reference to FIGS. 1, 2A to 2F and 3A to 3D.
The amplitude distribution U.sub.0 of an image projected by coherent light
is written as shown below as a function of the defocus z and the position
vector x within the plane perpendicular to the light axis.
U.sub.0 (x,z)=exp(i.phi.).intg.a(f).multidot.p.sub.0
(.vertline.f.vertline.z).multidot.exp(2.pi.ix.multidot.fl)df p.sub.0
(r,z)=circ(r).multidot.exp((2.pi.izr.sup.2) (1)
where a(f) is the Fourier spectrum of the mask pattern, p.sub.0 (r,z) the
pupil function, f the spatial frequency vector normalized by NA/.lambda.,
and r the radial coordinate of the pupil plane normalized by the maximum
aperture radius. The amplitude transmittance distribution of the pupil
plane of the projection lens is assumed to be a two-dimensional function
circ(r) which becomes 1 when 0.ltoreq.r.ltoreq.1 and 0 when 1<r. The
defocus z holds the relation D=2z.lambda./NA.sup.2 with the defocus amount
D of real dimensions on the light axis. The term exp(i.phi.) represents
the light please and .phi. is regarded as equal to
2.pi.D/.lambda.=4.pi.z/NA.sup.2.
Now, when the image plane of the original image is moved in parallel to the
light axis (z) by +.beta. with the phase thereof displaced by
+.DELTA..phi., the amplitude distribution thereof is given as U.sub.0 (x,z
- .beta.)exp(i.DELTA..phi.). Therefore, the amplitude distribution U'
(x,z) of a composite image composed of an image formed at z=+.beta. with
the phase displaced by +.DELTA..phi. and an image formed at z=-.beta. with
the phase displaced by -.DELTA..phi. is given as
U'(x,z)=[U.sub.0 (x,z-.beta.)exp (i.DELTA..phi.)+U.sub.0 (x,z+.beta.)
exp(-i.DELTA..phi.]/2 (2)
Substituting Equation (1) into Equation (2),
U'(x,z)=exp(i.phi.)x.intg.a(f).multidot.cos (2.pi..beta.f.sup.2
-.theta./2).multidot.p.sub.0
(.vertline.f.vertline.,z).multidot.exp(2.pi.ix.multidot.f)df(3)
where .theta.=2.DELTA..phi.-8.pi..beta./NA.sup.2, which is equivalent to a
net phase difference as expressed by the difference between the phase
difference of the two images and the phase change caused by the change in
the distance between the image planes. Comparison of Equations (1) and (3)
shows that the amplitudes of the two images (with a distance 2.beta.
between the image planes) formed at different positions along the light
axis may be superimposed while controlling the phase difference (.theta.)
of each image, by introducing cos (2.pi..beta.f.sup.2 -.theta./2) in the
amplitude integration. In the case where the light source has a finite
magnitude (partially coherent illumination), "a(f)" in Equation (3) may be
changed to [.intg. S(s). a(f-s)ds] with S(s) as an effective light source.
The term cos (2.pi..beta.f.sup.2 -.theta./2) may be introduced into the
integral of Equation (3) by either of the two methods mentioned below.
A first method consists in changing the pupil function to
p'(.vertline.r.vertline.,z)=cos (2.pi..beta.r.sup.2
-.theta./2).multidot.p.sub.0 (.vertline.r.vertline.,z) (4)
The pupil function can be regarded as a complex amplitude transmittance
distribution of the pupil of the projection lens (or the aperture stop at
a position conjugate therewith). As a result, in order to obtain the
above-mentioned pupil function p', the amplitude transmittance
distribution of the pupil or the aperture stop is set to cos
(2.pi..beta.r.sup.2 -.theta./2). An outline of this method is shown as a
model in FIG. 1. If a spatial filter expressed by a complex amplitude
transmittance distribution
T(r)=cos (2.pi..beta.r.sup.2 -.theta./2).multidot.circ(r) (5)
is provided in the pupil or the aperture stop, it is possible to combine
the amplitudes UI and UII of two images I and II formed at different
positions along the light axis while controlling the phase difference
between the two images. The distance between two image planes and the
phase difference may be set as desired depending on the values .beta. and
.theta. in Equation (5).
A second method of introducing the term cos (2.pi..beta.f.sup.2 -.theta./2)
in the integral of Equation (3) consists in using a new mask pattern whose
Fourier transform a'(f) becomes
a'(f)=a(f).times.cos (2.pi..beta.f.sup.2 -.theta./2) (6)
This method is briefly shown as a model in FIG. 2. The Fourier transform
a(f) (See FIG. 2B) of the complex amplitude transmittance distribution
A(x) of the designed mask pattern shown in FIG. 2A is determined, and the
result is multiplied by cos (2.pi..beta.f.sup.2
-.theta./2).multidot.circ(r) as a'(f) (FIG. 2C). Further, the complex
amplitude transmittance distribution A'(x) (See FIG. 2D) of a new mask
pattern is determined by the inverse Fourier transform of a'(f). More
specifically, when a mask with the amplitude transmittance distribution
thereof is expressed as
A'(x)=F.sup.-1 [F{A(x)}.times.cos (2.pi..beta.f.sup.2
-.theta./2).multidot.circ(.vertline.f.vertline.)] (7)
the composite amplitude distribution of Equation (3) is obtained. Here,
F[f(x)] and F.sup.-1 [g(t)] represent the Fourier transform of f(x) and
the inverse Fourier transform of g(t), respectively. The distance between
image planes and the phase difference can be set as desired by the values
of .beta. and .theta. in Equation (7).
As shown in FIG. 2E, when a mask satisfying Equation (7) is used, it is
possible to realize a satisfactory light intensity distribution with a
large depth of focus as compared with the prior art (FIG. 2F). The term
"circ(.vertline.f.vertline.)" in Equation (7) may be eliminated. Further,
the area given as .vertline.f.vertline.>1 of the function a'(f) subjected
to inverse Fourier transform may substantially take any value.
In the case of a light source having a finite capacity (partially coherent
illumination), "a(f)" in Equation (1) or (3) is changed to
[.intg.S(s).multidot.a(f-s)ds] with S(s) as an effective light source. In
applying the present invention under (spatially) partially coherent
illumination, therefore, it is necessary to determine a mask pattern whose
Fourier transform a"(f) satisfies
.intg.S(s).multidot.a"(f-s)ds=.intg.S(s).multidot.a(f-s).multidot.cos
(2.pi..beta.f.sup.2 .theta./2 )ds (8)
The amplitude transmittance distribution A"(x) of a desired mask pattern is
given below with the equation above solved as to inverse Fourier
transform.
A"(x)=F.sup.-1 [F{A(x).multidot.F.sup.-1 [S(f)]}.times.cos
(2.pi..beta.f.sup.2
-.theta./2).multidot.circ(.vertline.f.vertline.)]/F.sup.-1 [S(f)](9)
In this equation, the convolution theorem relating to Fourier integration
is used. By using a mask whose designed pattern is changed according to
Equation (9), it is possible to obtain an effect under (spatially)
partially coherent illumination similar to the one under spatially
coherent illumination. Nevertheless, in the case of using Equation (9),
there exists a singular point expressed as F.sup.-1 [S(f)]=0. In the case
of almost coherent illumination, the singular point is situated far away
from the main pattern and therefore the effect thereof may be ignored.
With the decrease in spatial coherency, on the other hand, the singular
point approaches the main pattern, with the result that the mask pattern
becomes considerably complicated. Even when Equation (7) is used, a
sufficient effect is obtained as long as the coherence of illumination is
high to some degree. Desirable coherence conditions in such a case will be
described later with reference to particular embodiments.
A similar effect is obtained in the case of a light source having a finite
capacity by using an effective light source having an illumination
distribution S' (s) satisfying
.intg.S'(s).multidot.a(f-s)ds=.intg.S(s).multidot.a(f-s).multidot.cos
(2.pi..beta.f.sup.2 -.theta./2)ds (10)
as against the ordinary effective light source of partially coherent
illumination.
Now, the depth of focus and the improvement in resolution by amplitude
superposition described above will be explained with reference to FIG. 3.
The phase/amplitude distribution U.sub.0 and the light intensity
distribution which is the square of the absolute value of the
phase/amplitude distribution U.sub.0 of a projected image of a linear
aperture pattern according to the prior art undergo a change in the manner
shown in FIGS. 3A and 3B. This indicates that the image disappears by
defocus.
On the other hand, FIGS. 3C and 3D show a similar result for the phase
amplitudes U.sub.I, U.sub.II and the composite amplitude U.sub.I +U.sub.II
of two images formed at z=.+-..beta. and having phases substantially
opposite to each other. The phase change of the wavelength period,
however, is not included.
The fact that follows becomes known from FIGS. 3C and 3D. First, a uniform
amplitude distribution having a substantially opposite phase of an image
defocused by (-)28 is superposed on a mount-shaped amplitude distribution
of a focused image in the vicinity of each image plane. As a result, the
amplitudes offset each other near the periphery of the pattern, thereby
reducing the FWHM (full width at half maximum) of the amplitude (light
intensity) distribution. In the neighborhood of an intermediate point
between two image planes, in contrast, the amplitudes of the images
defocused by .+-..beta. are superposed one on the other. Although the
absolute value of amplitude remains substantially uniform, the phase is
turned by about .+-.45 degrees at the center of the pattern while
remaining almost unchanged at the periphery thereof. The amplitudes of the
two images are thus superposed with a phase difference of about 90 degrees
at the pattern center, whereas the composite amplitude is zero as
substantially opposite phases are offset by each other at the periphery of
the pattern. The result is that an image is formed with a smaller
expansion of light intensity distribution than the original image. As a
consequence, the effects of the focus latitude enhancement of the FLEX
method and the phase-shifting method using a peripherally-added subphase
shifter are obtained at the same time, thereby improving the depth of
focus and the resolution. This is almost the case with other patterns.
The values of .beta. and .theta. (in radians) in the various equations
shown above are preferably in the ranges set below.
0.3<.beta.<0.7
10.beta.-5<.theta.<10.beta.-2
Further, the desirable values of .beta. and .theta. are dependent on the
pattern transferred. In the case of a periodic pattern, for example, the
sign of the amplitude transmittance is preferably constant except for the
outermost periphery of the pupil. This does not apply to the hole pattern
or the like whose Fourier transform represents a continuous spectrum.
Preferable values of .beta. and .theta. according to the pattern may be
considered about those shown in the embodiments described below, for
example.
The amplitude superposition described above is the simplest case. The
number and the positions of planes of images to be superposed and the
phase relation therebetween may be variously considered. In the case where
three or more images are superposed by the use of a pupil filter, for
instance, the cosine function in Equation (5) is changed to the sum of two
or more distribution functions in the form of Equation (5) with an
appropriate weight and having different values of .beta. and .theta.. More
specifically, a general formula of the complex amplitude transmittance for
securing amplitude superposition of a plurality of images is given as
##EQU1##
In view of the fact that the light intensity of an image decreases
extremely while the depth of focus increases with the increase in the
number of image planes, however, the number of image planes is preferably
two or three. In order to increase the transmittance of the optical
filter, on the other hand, the value of each C.sub.i is preferably set in
such a manner that the maximum value of T(r) (0.ltoreq.r.ltoreq.1) is
about unity.
When the mask is illuminated with a point light source, the Fourier
spectrum of the mask pattern is formed on the pupil plane. As a result,
the amplitude transmittance T(r) of the pupil is equal to the coherent
transmission function regarding r as the spatial frequency. An optical
filter having a frequency smaller at the center than at the periphery
functions as a high frequency-enhancing filter or a low
frequency-suppressing filter for reducing the transmittance of lower
spatial frequencies of an optical system. Depending on how to select
.beta. and .theta., therefore, the imaging characteristics are affected.
In the case of a multi-focal filter in which the transmittance decreases
with the increase in r, the high frequency transmission characteristics of
the optical system are deteriorated, so that the contrast of a fine
pattern is decreased. When a low frequency-suppressing filter having a
proper transmittance distribution with the transmittance thereof smaller
at the center than at the periphery is disposed at the position of the
pupil in superposition with the multi-focal filter, it is possible to
suppress the decrease in the image contrast while maintaining the FLEX
effect.
A comparatively satisfactory result is obtained, for instance, when a low
frequency-suppressing filter satisfying the relationship
T'(r)=a(r/r')+(1-a)(12)
where 0.7<a<1.0 and 0.5<r'<1.0, is superposed on a multi-focal filter
satisfying the relationship T(r)=C.multidot.cos
(2.pi..multidot.0.3.multidot.r.sup.2). In this case, the value C is
preferably set in such a manner that the maximum value of the product of
T(r) and T' (r) (0.ltoreq.r.ltoreq.1) is almost unity. Instead of
superposing a low frequency-suppressing filter on a multi-focal filter, it
is of course possible to use a filter having a complex amplitude
transmittance equal to the product of the respective amplitude
transmittances.
As an alternative to disposing a low frequency-suppressing filter at the
pupil position of the projection optical system in superposition with a
multi-focal filter, a low-contrast image that has been formed may be
reproduced by the double diffraction method through the filter mentioned
above.
Apart from the suppression of the low frequency components of the Fourier
transform of a pattern in combining two or more images described above
mainly with reference to the pupil filtering method, the same can be said
of a method of modulating the phase amplitude transmittance of a mask.
First embodiment
A filter having a complex amplitude transmittance distribution (FIG. 4A)
with .beta.=0.65 and .theta.=260.degree. in Equation (5) is inserted at
the stop position (conjugate plane of the entrance pupil) determining the
numerical aperture of a projection lens of a KrF excimer laser reduction
projection exposure apparatus (coherence factor .sigma.=0.5) having a
numerical aperture of 0.5. As a result, the focus dependence of the light
intensity distribution shown in FIG. 4b is obtained for a 0.3 .mu.m hole
pattern corresponding to the Rayleigh's resolution limit. A similar result
obtained when lacking a filter is shown in FIGS. 5A and 5B for comparison.
Comparison between FIGS. 4 and 5 shows that the insertion of the filter
more than triples the depth of focus while reducing the FWHM of the light
intensity distribution at the resolution limit by about 20%. The light
intensity, however, decreases to one fifth of the normal level.
The above-mentioned pattern was transferred by the use of a positive-type
chemically-amplified resist having a sensitivity of about 10 mJ/cm.sup.2.
By regulating the exposure time, a hole pattern having a diameter of 0.22
.mu.m to 0.35 .mu.m was formed with a satisfactory section over the focal
range of .+-.1.5 .mu.m. In spite of the fact that the light intensity
decreased to one fifth, the exposure required only about 0.2 to 0.4
seconds.
Actual LSI contact hole patterns as shown in FIG. 6A were exposed by the
use of the above-described optical system. (The numerical aperture was
changed to 0.45) The resulting light intensity distributions are shown in
FIGS. 6B to 6E. The insertion of a filter enables a pattern to be resolved
even in the case of 1 .mu.m defocus. When the filter is lacking, on the
other hand, a 1-.mu.m defocus causes the image to disappear almost
entirely.
The wavelength of the exposure apparatus, the numerical aperture, the
coherence conditions, the resist process used, the mask pattern feature
size, etc. are not limited to those shown in the embodiments described
herein. Also, the values of .beta. and .theta. are not confined to those
used above. When .beta.=0.55 and .theta.=140.degree., for instance, the
FWHM of the intensity profile is almost equal to the value obtained
according to the prior art, while the FWHM of the intensity profile
increases by about 30% when .beta.=0.35 and .theta.=0.degree.. In either
case, the depth of focus increases as according to the present embodiment.
Second embodiment
A filter similar to that used for the first embodiment was fabricated as
shown by a thick solid line in FIG. 7A. This filter was disposed at the
conjugate plane of the entrance pupil of a projection lens as in the first
embodiment to expose a mask pattern. The approximate complex amplitude
transmittance distribution T'(r) shown by the solid line is given as
T=1.0 (when cos (2.pi..beta.r.sup.2 -.theta./2).gtoreq.0) or -0.6 (when cos
(2.pi..beta.r.sup.2 -.theta./2)<0)
As a result, the focus dependence of the light intensity distribution as
shown in FIG. 7B is obtained, thereby producing the same effect as in the
first embodiment. In addition, the light intensity is increased by a
factor of 1.5 as compared with the first embodiment, thus saving exposure
time. In this way, Equation (5) may be appropriately subjected to discrete
approximation.
There are various methods of approximation in addition to the one shown
above.
In the case where a(f) (or .intg. S(s)a(f-s)ds | | |
