Patent Number: 051270293
Section: description

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIGS. 1A and 1B are schematic views, respectively, showing an X-ray exposure apparatus according to an embodiment of the present invention. In FIG. 1A the apparatus includes an X-ray directing means 20, and in FIG. 1B one component of the directing means 20 is illustrated in detail. In FIGS. 1A and 1B, denoted at 1 is an emission point of a SOR source 10; at 2 is a cylindrical mirror having a convex surface, which is one component of the directing means 20; at 3 is a mask; and at 4 is a semiconductor wafer. In this embodiment, the SOR source 10 and the directing means 20 cooperate to provide an illumination system. The mask 3 has a semiconductor circuit pattern formed thereon, which pattern is at the surface 3a to be exposed. In a zone at the peripheral part of this surface 3a, one or more alignment marks are formed. The mask 3 is supported by a mask stage 30. On the other hand, the wafer 4 has a surface which is coated with a resist, and the wafer 4 is placed on a wafer stage 40. Each of the mask stage 30 and the wafer stage 40 is movable vertically and horizontally as viewed in FIG. 1A, as well as in a direction perpendicular to the sheet of the drawing. With the displacement of the stages 30 and 40, the mask 3 and the wafer 4 can be aligned into a predetermined positional relationship. The apparatus of the present embodiment is an exposure apparatus of proximity type. In the present embodiment, an X-ray beam emitted from the emission point 1 of the SOR source 10 is received by the directing means 20 which serves to adjust the sectional shape of the received X-ray beam and to correct the intensity distribution thereof. The directing means 20 directs the X-ray beam to the mask 3 and irradiates the pattern 3a of the mask 3 with this X-ray beam. Then, the X-ray beam is projected to the wafer 4 through the mask 3, by which the pattern of the mask 3 is transferred to the resist on the wafer 4. The mirror 2 of the directing means 20 serves to expand the diameter of the X-ray beam, obliquely incident on the reflection surface thereof, with respect to a sectional plane perpendicular to the generating line of the mirror 2. Also, the mirror 2 serves to reduce non-uniformness in intensity distribution of the X-ray beam on the mask 3 surface. Further, the mirror 2 is disposed so that its generating line extends substantially in parallel to the horizontal orbit plane of the SOR source 10. While in FIG. 1B only the mirror 2 is illustrated as a component of the directing means 20, actually the directing means 20 include some other components. Examples are: a beryllium (Be) window provided to shield the inside of the exposure apparatus against the outside atmosphere to allow that the inside of the apparatus is maintained at a vacuum or it is filled with an He gas; a stop member for determining the size of the X-ray beam in accordance with the size of the pattern 3a region of the mask 3; a shutter mechanism for controlling the amount of exposure by the X-ray beam. FIG. 2 is a sectional view of the illumination system shown in FIGS. 1A and 1B, taken on a plane including the optical axis thereof and along the vertical direction (direction y.sub.a), as viewed in FIG. 1B. Like numerals as in FIGS. 1A and 1B are assigned to the elements corresponding to those of FIGS. 1A and 1B. In FIG. 2, denoted at d.sub.1 is the distance from the emission point 1 of the SOR source 10 to the center of effective X-ray beam diameter on the reflection surface of the mirror 2; at d.sub.2 is the distance from the center of effective X-ray beam diameter on the reflection surface of the mirror 2 to the mask 3; at R is the radius of curvature of the mirror 2 in a sectional plane perpendicular to the generating line of the mirror; at .alpha. is the angle defined at the center of effective X-ray beam diameter on the reflection surface of the mirror 2, between the reflection surface and the X-ray beam projected thereto from the SOR source 10; at .sigma.' is a standard deviation (angle: rad) of a distribution of intensities of X-rays from the SOR source 10, having different emission angle, in a sectional plane perpendicular to the generating line of the mirror 2 and including the center 1a of the effective diameter, at the gravity center wavelength of the X-ray beam in the used wavelength region. Here, in a sectional plane (x.sub.a -y.sub.a plane) perpendicular to the horizontal orbit plane of the SOR source 10 (x.sub.a -z.sub.a plane in FIG. 1B), the rays of the X-ray beam from the SOR source 10 having different emission angles have a distribution of intensity which is usually in the form of a Gaussian distribution. In FIGS. 1A, 1B and 2, the X-ray beam emitted from the emission point 1 of the SOR source 10 goes along a path in the neighborhood of a plane parallel to the horizontal orbit plane of the SOR source 10, and impinges on the convex mirror 2 having a cylindrical shape. Since the mirror 2 has a curvature with respect to the plane of vertical section (x.sub.a -y.sub.a plane), it serves to reflect the received X-ray beam so as to expand the angle of divergence of the X-ray beam in the vertical direction (y.sub.a direction). As a result, on the mask 3 surface, an X-ray beam expanded sufficiently in the vertical direction, is obtainable. Further, in the present embodiment, the mirror 2 is structured so as to satisfy equations to be set forth below, to thereby reduce the non-uniformness in intensity distribution (Gaussian distribution) of the X-ray beam on the mask 3 surface, with respect to the vertical (y.sub.a) direction. EQU R=(2d.sub.1 d.sub.2 .sigma.')/{[.DELTA.-(d.sub.1 +d.sub.2).sigma.'].multidot..alpha.} . . . (1--1) where d.sub.1 : the distance from the emission point of said X-ray source to the center of effective X-ray beam diameter on said reflection surface; PA0 d.sub.2 : the distance from the center of effective X-ray beam diameter on said reflection surface to the center of effective X-ray beam diameter on the surface to be exposed; PA0 .alpha.: the angle defined at the center of effective X-ray beam diameter on said reflection surface, between the X-ray beam and said reflection surface; PA0 .sigma.': a standard deviation of a distribution of intensities of the X-rays having different angles of emission from said X-ray source, in a sectional plane perpendicular to a generating line of said mirror, at the gravity center wavelength of the X-ray beam from said X-ray source; PA0 .DELTA.: 0.43a.ltoreq..DELTA..ltoreq.4.0a (1-2); and PA0 a: the length of the surface to be exposed, with respect to a direction which is substantially perpendicular to the generating line of said mirror. EQU R=(2d.sub.1 .multidot.d.sub.2)/{[.DELTA.'-(d.sub.1 +d.sub.2)].multidot..alpha.} (2-1) where EQU 4.3.times.10.sup.2 a.ltoreq..DELTA.'.ltoreq.4.0.times.10.sup.4 a (2--2) Next, description will be made of the significance and the derivation of equations (1-1), (1-2), (2-1) and (2-2) that determine an appropriate curvature radius R of the cylindrical convex mirror 2. First, the focal length f of the mirror 2 in the sectional plane (x.sub.a -y.sub.a plane) perpendicular to the generating line of the mirror 2 is given by: EQU f=-Rsin .alpha./2.perspectiveto.-R.alpha./2 (3) where EQU R&gt;0, .alpha.&gt;0 and f&lt;0 Approximating the mirror 2 as a thin lens, examination will now be made as to the degree of expansion, on the mask 3 surface, of the paraxial rays emitted from an object point on the axis (SOR emission point 1). FIG. 3 illustrates the paraxial relation of the thin lens. In this Figure, denoted at 1' is the center position of the emission point 1 of the SOR source 10; at 2' is a thin lens which is an approximation of the mirror; at 3' is a surface that corresponds to the mask 3; at .phi. is the refracting power (=1/f) of the thin lens (i.e. the mirror); d.sub.1 is the distance from the emission point center position 1' to the thin lens 2'; at d.sub.2 is the distance from the thin lens 2' to the surface 3'; at u.sub.1 and u.sub.2 are half angles of divergence of the X-ray beams just emitted from the emission point center position 1' and the thin lens 2', respectively; at h.sub.1 and h.sub.2 are the radii (heights of incidence) of the X-ray beams, in the y.sub.a direction, incident on the thin lens 2' and the surface 3', respectively. The signs are such as those illustrated in the drawing. From the paraxial relationship, the following relations are established: EQU h.sub.1 =-d.sub.1 .multidot.u.sub.1 (4) EQU u.sub.2 =u.sub.1 +h.sub.1 4 (5) EQU h.sub.2 =h.sub.1 -d.sub.2 u.sub.2 (6) By erasing h.sub.1 and u.sub.2 in equations (4)-(6), h.sub.2 is expressed as follows: EQU h.sub.2 =-u.sub.1 (d.sub.1 +d.sub.2)+d.sub.1 d.sub.2 u.sub.1 4 (7) Further, by substituting the relation of equation (3) into equation (7), then EQU h.sub.2 =-u.sub.1 (d.sub.1 +d.sub.2)-2u.sub.1 d.sub.1 d.sub.2 /R.alpha. (8) This is the paraxial relation that represents the expansion of the X-ray beam upon the surface 3', in the vertical (y.sub.a) direction. Accordingly, if a standard deviation of a distribution of intensities of the rays having different emission angles, in the vertical direction, at the gravity center wavelength in the used wavelength region of the X-ray beam is denoted by .sigma.' (&gt;0), the height (radius) h'.sub.2 from the optical axis and on the surface 3' of the X-ray beam as emitted from the center position 1' at an angle substantially corresponding to this standard deviation .sigma.', can be determined by substituting u.sub.1 =-.sigma.' into equation (8), as follows: EQU h'.sub.2 =.sigma.'(d.sub.1 +d.sub.2)+2.sigma.'d.sub.1 d.sub.2 /R.alpha. (9) By taking the height h'.sub.2 in equation (9) as an effective radius .DELTA. nd by solving the equation with respect to R, then equation (1-1) is obtained. Also, as will be understood from the foregoing description, equation (1-2) is the one that defines the range for the position of the X-ray beam that determines the standard deviation. With smaller .DELTA., a beam of a small expansion is obtainable, and with larger .DELTA., a beam of large expansion is obtainable. Next, the range of the value .DELTA. suitable for the exposure will be explained. FIG. 4 is a graph showing the relationship between (i) a/.DELTA. (the ratio of the length a (exposure area) of the surface 3a, to be exposed, in the y.sub.a direction, to the effective radius .DELTA. of the X-ray beam on the surface 3' in the y.sub.a direction) in an occasion where, in the x.sub.a -y.sub.a plane, the rays of the X-ray beam having different emission angles have a distribution of intensity which is a Gaussian distribution, and (ii) the non-uniformness on the surface 3a, to be exposed, in the y.sub.a direction (i.e. the value of "(maximum exposure strength - minimum exposure strength)/maximum exposure strength)" on the surface 3a to be exposed, with respect to the y.sub.a direction). Here, it is assumed that there is no variation in intensity (i.e. non-uniformness in exposure) with respect to the z.sub.a direction. It is seen from this graph that, in order to maintain the non-uniformness in exposure not higher than 50%, it is necessary to keep the ratio a/.DELTA. within a range not greater than about 2.3. In other words, unless .DELTA. is made not less than about 0.43a, the magnitude of the difference between the maximum exposure strength and the minimum exposure strength on the surface 3a to be exposed (exposure area), with respect to the maximum exposure strength, is reduced to a half or less. As a result, large non-uniformness in exposure is produced on the surface 3a to be exposed, which is not proper for use in an exposure apparatus. FIG. 5 is a graph showing the relationship between (i) the ratio a/.DELTA. as described which is under the same condition as FIG. 4, and (ii) the ratio of used light quantity (the ratio of the amount of exposure on the surface 3' to the total quantity of the X-ray beam emitted from the light source). Here, it is assumed that the length of the surface 3a to be exposed, in the z.sub.a direction is substantially equal to the width of the X-ray beam in the z.sub.a direction and that it is unchangeable. In other words, this graph is one that shows to what extent the X-ray beam from the SOR source is effectively used in exposure, in dependence upon the value a/.DELTA.. If, in this graph, the ratio of used light quantity is less than 1/10, the efficiency is too low for use in an exposure apparatus. It is seen from this graph that, in order to make the ratio of used light quantity not less than 1/10, it is necessary to keep a/.DELTA. not less than 0.25. Namely, .DELTA..ltoreq.4a is the condition for an X-ray exposure apparatus. As will be understood from the foregoing, the condition for .DELTA. in an X-ray exposure apparatus is determined, in consideration of the length a of the surface 3a, to be exposed, with respect to the X-ray beam expanding direction (y.sub.a direction in FIG. 1), as depicted by equation (1-2), and it is determined as follows: EQU 0.43a.ltoreq..DELTA..ltoreq.4.0a Accordingly, as showed by equation (1-1), the radius of curvature of the mirror 2 is expressed as follows: EQU R=(2d.sub.1 .multidot.d.sub.2 .multidot..sigma.')/{[.DELTA.-(d.sub.1 +d.sub.2).multidot..sigma.'].multidot..alpha.} where EQU 0.43a.ltoreq..DELTA..ltoreq.0.40a Namely, the condition is ##EQU2## On the other hand, if .DELTA.'=.DELTA./.sigma.', as showed by equation (2-1), equation (1-1) can be rewritten as follows: EQU R=(2d.sub.1 .multidot.d.sub.2)/{[.DELTA.'-(d.sub.1 +d.sub.2)].multidot..alpha.} where .DELTA.'=.DELTA./.sigma.' Generally, in a SOR light source, the value .sigma.' is in the range of EQU 0.1.times.10.sup.-3 .ltoreq..sigma.'.ltoreq.1.0.times.10.sup.-3 (rad) (11) Therefore, from equations (1-2) and (11), as showed by equation (2-2), the following relation is obtained: EQU 4.3.times.10.sup.2 a.ltoreq..DELTA.'.ltoreq.4.0.times.10.sup.4 a Thus, equations (2-1) and (2-2) can be rewritten as follows: ##EQU3## From these equations, the following relation is determined: ##EQU4## Examples will now be described in detail. The parameters in equation (1-1) were set as follows: EQU d.sub.1 =5000 (mm) EQU d.sub.2 =5000 (mm) EQU .sigma.'=5.0.times.10.sup.-4 (rad) EQU .alpha.=1.0.times.10.sup.-2 (rad) EQU a=30 (mm) By setting the parameters in this manner, from equation (10) the following relation is obtained: EQU 2.2.times.10.sup.4 .ltoreq.R.ltoreq.3.2.times.10.sup.5 (13) (unit:mm) With the parameters set in accordance with the above-described described conditions, the relationship between the surface 3' to be exposed (exposure area) and the X-ray exposure strength was examined by using cylindrical convex mirrors of R=250 m (.DELTA.=a/2), R=100 m(.DELTA.=a) and R=45.5 m (.DELTA.=2a), respectively. The results are illustrated in FIG. 6. In this Figure, the axis of abscissa depicts the position in the y.sub.a direction with the origin being at the center of the surface 3' to be exposed, while the axis of ordinate depicts the X-ray intensity at each point (relative value of the X-ray intensity at each point, relative to the value of the intensity of the X-ray beam emitted from the cylindrical convex mirror as integrated with respect to the area on the surface 3' to be exposed). As a comparative example, FIG. 7 shows a graph of the X-ray intensity distribution which was obtained in a similar manner as in FIG. 6, but with use of a cylindrical convex mirror of R=8.5 m (.DELTA.=10a) and a mirror R=.infin.(.DELTA.=a/6), namely, a flat mirror, which were out of the range of the curvature radius as determined in accordance with the present invention. As will be understood from these Figures, if R is within the range as defined in accordance with the present invention, the non-uniformness in exposure can be kept within a tolerable range (the light quantity at the peripheral portion is not less than a half of that of the central portion). Also, the proportion of the quantity of used light to the total quantity is not too small. With the X-ray exposure apparatus of the present embodiment, as described hereinbefore, the whole surface to be exposed can be exposed at a time. This avoids the possibility of local thermal distortion of the mask due to displacement of the X-ray beam. Further, the apparatus includes a mirror having a radius of curvature which is suitable for ensuring the amount of exposure as required in a practical exposure apparatus, and also which is effective to reduce the non-uniformness in intensity distribution of the X-ray beam. Therefore, the present invention is effective to make it easier to provide a practical X-ray exposure apparatus. 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.