An X-ray exposure apparatus for exposing a resist on a substrate to a pattern of an original includes a radiation source for providing X-rays; and an illumination system for irradiating the original and the substrate with the X-rays such that the resist of the substrate is exposed to the pattern of the original with the X-rays; wherein the illumination system has a convex mirror having a reflection surface of a shape like a cylindrical surface, for reflecting the X-rays from the radiation source to the original; and wherein the reflection surface of the mirror has such an aspherical surface shape that, with respect to a top of the reflection surface, a radiation source side and an original side are asymmetrical in shape, that, in the neighborood of the top, the radiation source side has a radius of curvature smaller than that of the original side, and that at a peripheral potion the reflection surface has a curvature of a radius larger than that at the top of the reflection surface.

FIELD OF THE INVENTION AND RELATED ART 
This invention relates to an X-ray exposure apparatus for use in the 
manufacture of semiconductor devices, for transferring a pattern of an 
original such as a reticle to a semiconductor substrate such as a wafer by 
using an X-ray source such as a synchrotron orbit radiation (SOR) source. 
In such an X-ray exposure apparatus, when an SOR source is used as an X-ray 
source, since the light from the SOR source consists of sheet-like 
electromagnetic waves having a large divergence angle in a direction 
parallel to the electron orbit plane, but having a small divergence angle 
in a direction perpendicular to the electron orbit plane, if the light 
from the SOR source is directly projected to an original, with respect to 
the aforementioned perpendicular direction only a limited area of the 
original can be illuminated. This necessitates some measures for expanding 
the SOR light (X-rays) in the perpendicular direction, when the X-ray 
exposure apparatus uses an SOR source as an X-ray source. 
An Example is shown in FIG. 1A wherein a grazing incidence mirror (flat 
mirror) 21 is disposed between an SOR source and an exposure area of a 
wafer 22, and the mirror 21 is oscillated by a small angle of a few 
milli-radians to expand the light from the SOR source, as discussed in 
"JVST", B1 (4), 1983, p. 1271. A second example is shown in FIG. 1B 
wherein a mirror 24 having a sectional shape which can be represented by 
an exponential function is provided to expand the SOR light having a 
Gaussian distribution, with respect to the perpendicular direction, and 
also to make the intensity distribution uniform, as disclosed in Japanese 
Laid-Open Patent Application, Laid-Open No. 60-226122. In FIG. 1A, the 
graph at the right-hand half depicts the intensity distribution of X-rays 
as absorbed by a resist applied to the wafer, in the first example. In 
FIG. 1B, the graph at the right-hand half depicts the intensity 
distribution of X-rays on the mask surface, in the second example. 
In the first method described above, at any moment only a part of the mask 
is irradiated. Thus, there is a high possibility of local thermal 
expansion of the mask during the exposure process, which leads to pattern 
transfer distortion. In order to avoid the affect of such thermal 
expansion, the oscillation period of the mirror 21 has to be made 
sufficiently small, and this requires use of a large driving power for 
oscillating the mirror 21. Also, the necessary mechanism of the driving 
means for the mirror 21 is complicated and, therefore, this method is not 
too practical. 
In the second method described above, non-uniformness in the intensity of 
the SOR light can be reduced by the reflection with the mirror 24. 
However, as the SOR light passing through the mask is absorbed by the 
resist, the absorption rate of the resist has wavelength-dependence and, 
generally, the SOR light is not a monochromatic light. Therefore, 
non-uniformness in exposure occurs in the resist itself. Further, the 
mirror 24 is equipped with only such a reflection surface which 
corresponds to a half of a cylindrical surface on one side of its top. As 
a result, only a portion of the SOR light which is at the upper side or 
lower side of the electron orbit plane can be used. Thus, the efficiency 
of utilization is bad. 
SUMMARY OF THE INVENTION 
It is accordingly, a primary object of the present invention to provide an 
X-ray exposure apparatus by which a resist on a substrate can be exposed 
with a small loss of energy, uniformly without non-uniformness in 
intensity. 
In accordance with a first aspect of the present invention, to achieve this 
object, there is provided an X-ray exposure apparatus for exposing a 
resist on a substrate to a pattern of an original, comprising: a radiation 
source for providing X-rays; and an illumination system for irradiating 
the original and the substrate with the X-rays such that the resist of the 
substrate is exposed to the pattern of the original with the X-rays; 
wherein said illumination system has a convex mirror having a reflection 
surface of a shape like a cylindrical surface, for reflecting the X-rays 
from said radiation source to the original; and wherein said reflection 
surface of said mirror has such an aspherical surface shape that, with 
respect to a top (vertex) of said reflection surface, a radiation source 
side and an original side are asymmetrical in shape, that, in the 
neighborhood of said top, the radiation source side has a radius of 
curvature smaller than that of the original side, and that at a peripheral 
portion said reflection surface has a curvature of a radius larger than 
that at said top of said reflection surface. 
In accordance with a second aspect of the present invention, to achieve the 
above object, there is provided an X-ray exposure apparatus for exposing a 
resist on a substrate to a pattern of an original, comprising: a radiation 
source for providing X-rays; and an illumination system for irradiating 
the original and the substrate with the X-rays such that the resist of the 
substrate is exposed to the pattern of the original with the X-rays; 
wherein said illumination system has a convex mirror having a convex 
reflection surface of a shape like a cylindrical surface, for reflecting 
the X-rays from said radiation source to the original; wherein said 
reflection surface of said mirror has such an aspherical surface shape 
that, with respect to a top of said reflection surface, a radiation source 
side and an original side are asymmetrical in shape; wherein, in the 
neighborhood of said top, said reflection surface has a particular radius 
of curvature; wherein a particular quantity is set with respect to an 
X-ray beam reflected by said top and then absorbed by the resist; wherein, 
when a y coordinate is defined along an axis corresponding to a tangent to 
said top while taking said top as an origin, the surface shape of said 
reflection surface is represented by a function Z(y); and wherein specific 
conditions are satisfied with regard to the surface shape of the 
reflection mirror so as to ensure substantially uniform distribution of 
the X-ray absorption quantity of the resist on the substrate. 
In accordance with a third aspect of the present invention, to achieve the 
above object, there is provided an X-ray exposure apparatus for exposing a 
resist on a substrate to a pattern of an original, comprising: a 
synchrotron radiation source for providing X-rays; and an illumination 
system for irradiating the original and the substrate with the X-rays such 
that the resist of the substrate is exposed to the pattern of the original 
with the X-rays; wherein said illumination system has a convex mirror 
having a reflection surface of a shape like a cylindrical surface, for 
reflecting the X-rays from said radiation source to the original; wherein 
said reflection surface of said mirror has such an aspherical surface 
shape that, with respect to a top of said reflection surface, a radiation 
source side and an original side are asymmetrical in shape; wherein, in 
the neighborhood of said top, said reflection surface has a particular 
radius of curvature; wherein a particular quantity is set with regard to 
an X-ray beam reflected by said top and then absorbed by the resist; 
wherein, when a y coordinate is defined along an axis corresponding to a 
tangent to said top while taking said top as an origin, the surface shape 
of said reflection surface is represented by a function Z(y); and wherein 
specific conditions, different from those mentioned above, are 
substantially satisfied so as to ensure sufficiently uniform distribution 
of the X-ray absorption quantity of the resist on the substrate. 
In the second and third aspects, the reflection surface of the reflection 
mirror is shaped so that the radius of curvature at a peripheral portion 
(a portion off the optical axis and spaced from the top) is larger than 
that in the neighborhood of the top (adjacent to the optical axis). As a 
result, a beam of a peripheral part of the X-ray flux which impinges on a 
peripheral portion of the mirror can be directed to the original and the 
substrate with good efficiency. Namely, it is possible to use, for the 
exposure, such a peripheral part of the beam which could not be used for 
the exposure in an arrangement wherein a simple cylindrical reflection 
surface is used to reflect the X-rays to the original and the substrate. 
As for the structure of such a mirror, a substrate of SiC, a substrate of 
SiO.sub.2 or a substrate of SiO.sub.2 with Au deposition or, 
alternatively, a substrate of SiO.sub.2 with Pt deposition, can be used. 
Thus, with the present invention, it becomes possible to expose a resist on 
a substrate uniformly, while reducing the loss of X-ray energy and, 
therefore, it is possible to accurately transfer a pattern of an original 
onto the resist of the substrate. Additionally, it is possible to reduce 
the exposure time. 
These and other objects, features and advantages of the present invention 
will become more apparent upon a consideration of the following 
description of the preferred embodiments of the present invention taken in 
conjunction with the accompanying drawings.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring to FIGS. 2A and 2B showing an X-ray exposure apparatus according 
to an embodiment of the present invention, denoted at 1 is a synchrotron 
which is adapted to emit synchrotron radiation light (SOR light). The 
synchrotron 1 has a horizontal orbit plane which is parallel to the X-Y 
plane. The synchrotron 1 emits, toward a mirror 2, a sheet-like flux 6 of 
X-rays having a small width with respect to the Z direction and a large 
width with respect to a direction parallel to the X-Y plane. The mirror 2 
is a convex mirror, the reflection surface of which has an aspherical 
surface shape and is based on a cylindrical reflection surface, to be 
described below. 
The mirror 2 has a generating line which extends in the X direction. A 
perpendicular to the top (vertex) of the reflection surface of the mirror 
2, extends in the Z direction. In the section along the Z-Y plane, the 
mirror 2 has a predetermined shape deformed slightly from a cylindrical 
shape. More particularly, with respect to the top of the reflection 
surface, the synchrotron 1 side and a side opposite thereto (i.e. the mask 
3 side) are asymmetrical in shape. Further, in the neighborhood of the 
top, the radius of curvature at the synchrotron 1 side is set to be 
smaller than that at the mask side. 
The reflection surface of the mirror 2 reflects the X-rays 6 from the 
synchrotron 1, and while expanding the beam diameter and transforming the 
sectional intensity distribution thereof into a predetermined 
distribution, the mirror 2 directs the X-rays to the mask 3. The X-rays 6 
from the mirror 2 pass through a shutter 5 and illuminate a circuit 
pattern of the mask 3. Those of the X-rays passing through the circuit 
pattern of the mask impinge on a wafer 4. By those X-rays 6, a resist 
applied to the wafer 4 surface is exposed in accordance with the circuit 
pattern of the mask 3. The surfaces of the shutter 5, the mask 3 and the 
wafer 4, receiving the X-rays, are placed substantially parallel to the 
Z-Y plane. The mirror 2 may comprise a substrate of SiC having a machined 
convex reflection surface, a substrate of SiO.sub.2 having a machined 
convex reflection surface, a substrate of SiO.sub.2 having a machined 
convex reflection surface on which Au is deposited, a substrate of 
SiO.sub.2 having a machined convex reflection surface on which Pt is 
deposited, or the like. 
Referring to FIG. 3, a solid line depicts the X-ray absorption distribution 
(a distribution of the quantity (intensity) X-ray absorption per unit 
time), with respect to the Z direction, of the resist on the wafer 4 as 
the wafer 4 is exposed by using the exposure apparatus of FIGS. 2A and 2B. 
Also, in FIG. 3, a broken line depicts the X-ray absorption distribution 
with respect to the Z direction, as a wafer 4 is exposed by using a mirror 
having a cylindrical reflection surface, in place of the mirror 2. 
Referring to FIG. 4, a solid line depicts the sectional shape of the mirror 
2 of the exposure apparatus of FIGS. 2A and 2B. Also, a broken line 
depicts the sectional shape of the aforementioned mirror having the 
cylindrical reflection surface. 
If such a mirror having a cylindrical reflection surface is used for 
exposure, as depicted by the broken line in FIG. 3, the X-ray absorption 
distribution obtained is non-uniform. In order to correct such 
non-uniformness, it is necessary to use some measures to block the X-rays 
corresponding to the hatched area in FIG. 3. If such a method for 
partially blocking the X-rays is used, the quantity of X-ray absorption 
per unit time is reduced to a lower level, such as Ic shown in FIG. 3. 
With the mirror 2 of the present embodiment, as compared therewith, it is 
possible to attain the quantity of X-ray absorption per unit time, of a 
high level Ia which is higher than Ic. Additionally, over the whole 
exposure region on the resist, the X-ray absorption distribution is 
uniform. Thus, with the exposure apparatus of the present embodiment, it 
is possible to accomplish uniform exposure in a reduced time. 
Details of the mirror 2 of the present embodiment will be explained below. 
The quantity I(z) of X-ray absorption of the resist on the wafer 4, at a 
certain portion along the Z direction, can be expressed by the following 
equation: 
##EQU1## 
where .lambda. is the wavelength of the X-rays 6; I.sub.1 (.lambda.) is 
the intensity of the X-rays 6 impinging on the mirror 2; R(.lambda.) is 
the reflectivity of the mirror 2; Tw(.lambda.) is the transmittance as 
provided when a beryllium window or a filter is used; T.sub.3 (.lambda.) 
is the transmittance of the mask 3; A.sub.4 (.lambda.) is the absorption 
rate of the resist 4; and C is the expansion rate of the X-ray 6 (i.e., 
"beam area on the wafer 4"/"beam area on the mirror 2", of the mirror 2, 
as determined by the curvature radius .rho. at each point on the mirror 2 
surface, the distance l.sub.12 between the light emission center of the 
synchrotron 1 and each point on the mirror 2, the distance l.sub.23 
between each point on the mirror 2 and each corresponding point (z) on the 
resist of the wafer 4, and the angle of incidence (.theta.) of an X-ray 
beam impinging on each point on the mirror 2. 
Here, the quantity (intensity) of X-ray as absorbed per unit time by the 
resist of the wafer 4 is determined as Ia, on the basis of the nature of 
the resist used and the intensity of the X-rays 6. For example, based on 
the X-ray absorption distribution such as depicted by the broken line in 
FIG. 3 which is obtainable when the resist is exposed by using a mirror 
having a cylindrical reflection surface, the quantity of X-rays absorbed 
by the resist is integrated, with respect to the Z direction, from an end 
of the illumination region to the other end, and an integrated level Ir is 
obtained. Then, the integrated level Ir is divided by the length Ar of the 
illumination region in the Z direction, by which Ia can be determined as 
Ia=Ir/Ar. Here, if the length of the exposure area in the Z direction is 
denoted by Dr, it is necessary that the length Ar of the illumination 
region is made larger than the length Dr of the exposure area. Also, if 
the former is too large, the intensity of X-rays (the X-ray quantity to be 
used for the exposure) decreases. In consideration of these points, 
preferably the structure is arranged to satisfy the relation that 
Dr&lt;Ar&lt;3Dr. 
After the quantity Ia of X-ray absorption per unit time is determined, the 
curvature radius .rho..sub.0 (unknown quantity) of the mirror 2 at a 
portion adjacent the top (vertex) thereof is determined. To this end, I=Ia 
and .rho.=.rho..sub.0 are substituted into equations (1) and (2), and 
calculations are made in accordance with these equations. If Ia and 
.rho..sub.0 are determined in this manner and the quantity I.sub.0 of 
X-rays reflected by the top of the mirror 2 and absorbed by (the center of 
) the exposure area of the resist is determined as I.sub.0 =Ia, then the 
curvature radius .rho.=.rho.(y) at each point on the reflection surface of 
the mirror 2 can be determined in accordance with the following equation: 
##EQU2## 
where l.sub.12, l.sub.23 and .theta. are those corresponding to the 
variables in equations (1) and (2), and I is the quantity of X-ray 
absorption per unit time at each point (z) on the resist of the wafer 4, 
as the resist is exposed with an X-ray beam reflected at each point (y) on 
the mirror with a cylindrical reflection surface having a curvature radius 
.rho..sub.0. 
In the present embodiment, I.sub.0 and .rho..sub.0 are set beforehand and, 
in accordance with equations (3) and (4), the curvature at each point (y) 
of the reflection surface of the mirror 2 is determined successively, in 
an order from the vertex of the mirror 2 to the end, so as to assure that 
the X-ray absorption distribution of the resist in the exposure area 
becomes uniform such as depicted by the solid line in FIG. 3. FIG. 5 shows 
the change in the curvature .rho.(y), wherein .rho..sub.0 /.rho.(y) is 
taken on the axis of the ordinate. In FIG. 5, the sign of the curvature 
.rho.(y) is illustrated as being positive (.rho.(y)&gt;0) when the curvature 
center is below the mirror 2 surface, while the sign of the curvature 
.rho.(y) is illustrated as being negative (.rho.(y)&lt;0) when the curvature 
center is above the mirror 2 surface. However, it will be readily 
understood from the drawing that in the present embodiment the shape of 
the reflection surface of the mirror 2 is determined in accordance with a 
range - 0.5&lt;.rho..sub.0 /.rho.(y)&lt;1.5 and, additionally, .rho..sub.0 
/.rho.(y)&gt;0 is satisfied. 
In the present embodiment, the reflection surface of the mirror 2 has such 
a shape that, with spacing from the top of the mirror 2, the surface 
gradually shifts from a cylindrical reflection surface having the same 
curvature radius as the curvature radius (.rho..sub.0 at the portion 
adjacent the top (vertex) of the mirror 2). The curvature radius at a 
point off the optical axis and sufficiently spaced from the vertex, is 
larger than the curvature radius .rho..sub.0 in the neighborhood of the 
vertex. Also, in order to ensure uniform X-ray absorption distribution of 
the resist in the exposure area, the left-hand and right-hand sides of the 
vertex of the reflection surface have asymmetrical shapes. 
The mirror 2 so shaped has a function for collecting peripheral portions of 
the X-ray flux from the synchrotron 1, which portions are off the axis and 
which cannot be used for the exposure conventionally, toward the wafer 4 
as well as a function for providing uniform X-ray absorption distribution 
of the resist on the wafer 4. As a result, it is possible to reduce the 
exposure time and also to assure uniform exposure, that is, accurate 
pattern transfer. As regards the uniformness of the X-ray absorption 
distribution, desirably it is such that the non-uniformness is not greater 
than 2%, preferably, not greater than 0.2%. 
Advantageous effects of the present embodiment will be explained by using 
specific numerical values. 
For determination of the intensity Ia of resist absorption, the integrated 
intensity Ir' as absorbed by the resist is determined as 23 mW/cm.sup.3. 
Here, the mirror material is SiO.sub.2, the mask material is Si.sub.3 
n.sub.4, the resist material is PMMA and the angle of incidence of the 
center beam is 10 mrad. 
Here, if the exposure area has a size of 3 cm square while the illumination 
area has a size of 6 cm square, then the quantity Ia of X-ray absorption 
can be determined by: 
EQU Ia=I.sub.0 =24/6=4.0 (mW/cm.sup.2) 
Here, the curvature radius .rho..sub.0 of the mirror 2 in the neighborhood 
of the top thereof is 50 m, for example, and the shape of the reflection 
surface can be determined in accordance with equations (3) and (4). As 
compared therewith, if a mirror with a cylindrical reflection surface 
having a curvature radius of 50 m is used, at the opposite ends of the 
exposure area, the quantity Ic of X-ray absorption was 3.5 mW/cm.sup.2. 
As described, with the mirror 2 of the present embodiment, as compared with 
a mirror having a cylindrical reflection surface of the same curvature 
radius, the quantity of X-ray absorption is increased by 15%. Thus, with a 
simple comparison with respect to the intensity, the exposure time can be 
reduced to 87% of that as required by a mirror having a cylindrical 
reflection surface. 
FIG. 6 illustrates the results of comparison, with respect to the X-ray 
absorption distribution, between the resist used in this embodiment and a 
different type resist. In FIG. 6, a broken line depicts the distribution 
as obtained with the resist (resist 1) used in the present embodiment, 
while a solid line depicts the distribution as obtained with a different 
type resist (resist 2). It is seen from the drawing that, with a different 
resist, a different distribution is provided, and there is a possibility 
of non-uniformness (hatched area). However, as shown in FIG. 7, the 
non-uniformness resulting from the different resist (resist 2) is 3% at 
the maximum, and this is very small as compared with the non-uniformness 
of 15% in the case using a mirror having a cylindrical reflection surface. 
Thus, with a simple comparison with respect to the intensity, the exposure 
time can be reduced to 89% of that as required when the mirror with a 
cylindrical reflection surface is used. 
The concept of increasing the intensity and resultant reduction of exposure 
time, based on use of an aspherical surface shape of the reflection 
mirror, is not limited to a form satisfying equations (3) and (4). There 
is a certain effective range. That is, when the surface shape of the 
mirror that satisfies equations (3) and (4) is denoted by Z.rho.(y) and 
the surface shape of a mirror with a cylindrical reflection surface having 
a curvature radius .rho..sub.0, which is a basic curved surface on which 
the mirror of the present embodiment is based, is denoted by Z.sub.0 (y), 
then the effective surface shape Z(y) can be represented by: 
EQU Z(y)=Z.sub.0 (y)+K(Z.sub..rho. (y)-Z.sub.0 (y)) (5) 
wherein 
EQU 0&lt;K.ltoreq.1.5 (6) 
FIG. 8 shows the quantity (intensity) distribution of X-rays that are 
absorbed by the resist, with different values for "K". "K=0" corresponds 
to the cylindrical reflection surface, while "K=1" corresponds to the 
surface shape of the mirror. It is to be noted here that Z.sub.0 (y) can 
be expressed, while taking the origin on the vertex, as follows: 
##EQU3## 
While the invention has been described with reference to the structures 
disclosed herein, it is not confined to the details set forth and this 
application is intended to cover such modifications or changes as may come 
within the purposes of the improvements or the scope of the following 
claims.