WO2003007046A1 - Optical system and exposure apparatus having the optical system - Google Patents

Abstract

An optical system having a favorable optical performance without being substantially influenced by birefringence even if a birefringent crystal material such as fluorite is used. The optical system (100) comprises crystal optical elements composed of crystals of a cubic system. The crystal optical devices include crystal optical elements (105, 106) the first crystal axes of which are aligned with the optical axis and crystal optical elements (109, 110) the second crystal axes of which are aligned with the optical axis. In order to substantially avoid the influence of birefringence, a first total evaluation value ΣRj that is the total of first evaluation values Rj concerning the crystal optical elements is in a predetermined relation, about the light rays of the image forming light beam focused at least at a given point on the image plane of the optical system or on an object, with a second total evaluation value ΣSj that is the total of second evaluation values Sj concerning the crystal optical elements.

Description

 Description Optical system and exposure apparatus provided with the optical system

 The present invention relates to an optical system and an exposure apparatus provided with the optical system, and more particularly to a projection optical system suitable for an exposure apparatus used when a micro device such as a semiconductor device or a liquid crystal display device is manufactured by a photolithography process. It is. Background art

 When forming micropatterns of electronic devices (microdevices) such as semiconductor integrated circuits and liquid crystal displays, the pattern of the photomask (also called a reticle) drawn by enlarging the pattern to be formed by about 4 to 5 times is projected. A method of performing reduced exposure transfer onto a photosensitive substrate (substrate to be exposed) such as Jehachi using an exposure apparatus is used. In this type of projection exposure apparatus, the exposure wavelength keeps shifting to shorter wavelengths in order to cope with miniaturization of semiconductor integrated circuits.

At present, the exposure wavelength of 248 nm of KrF excimer laser is the mainstream. Ρ, but 19.3 nm of shorter wavelength ArF excimer laser is also entering the stage of practical use. Furthermore, the A r ₂ laser having a wavelength of 1 5 7 nm of F ₂ laser one and the wavelength 1 2 6 nm, proposed a projection exposure equipment that uses the light source for supplying light in a wavelength band so-called vacuum ultraviolet region Is being done. In addition, since high resolution can be achieved by increasing the numerical aperture (NA) of the projection optical system, not only development of a shorter exposure wavelength but also development of a projection optical system with a larger numerical aperture Has also been made.

Optical materials (lens materials) with good transmittance and uniformity for exposure light in the ultraviolet region having such a short wavelength are limited. In a projection optical system that uses an ArF excimer laser as a light source, synthetic quartz glass can be used as a lens material, but chromatic aberration cannot be sufficiently corrected with one type of lens material. Calcium fluoride crystals (fluorite) are used for the lenses. Meanwhile, projecting as a light source an F ₂ laser In shadow optics, the usable lens materials are effectively limited to calcium fluoride crystals (fluorite).

 Recently, it has been reported that birefringence occurs even in such cubic calcium fluoride crystals (fluorite) for ultraviolet rays having such a short wavelength. In an ultra-high-precision optical system such as a projection optical system used in the manufacture of electronic devices, the aberration caused by the birefringence of the lens material is fatal, and the effect of the birefringence is substantially avoided. It is indispensable to adopt the lens configuration and lens design that have been adopted. Disclosure of the invention

 The present invention has been made in view of the above-described problems. For example, even when a birefringent crystal material such as fluorite is used, good optical performance is obtained without being substantially affected by birefringence. It is an object of the present invention to provide an optical system that can be secured and an exposure apparatus including the optical system.

 Further, the present invention provides a micro device manufacturing apparatus capable of manufacturing a high performance micro device according to a high resolution exposure technology using an exposure apparatus equipped with an optical system having good optical performance using a crystalline material. It aims to provide a method.

 In order to solve the above problems, according to a first aspect of the present invention, there is provided an optical system including a plurality of crystal optical elements formed of crystals belonging to a cubic system,

 The plurality of crystal optical elements include: a crystal optical element having a first crystal axis set to substantially coincide with an optical axis of the optical system; and a second crystal axis different from the first crystal axis corresponds to the optical axis. With a crystal optical element set to substantially match,

 In the plurality of crystal optical elements Gj, a direction of a predetermined crystal axis in a plane perpendicular to the optical axis is an angle P about the optical axis with respect to a direction of a predetermined axis in the plane. j

For a specific light ray passing through the plurality of crystal optical elements Gj, an angle formed by the specific light ray with the direction of the optical axis is 0 j, and an angle formed by the specific light ray with the direction of the predetermined axis is Φ. j, and when the optical path length of the specific light beam is L j, The first constant for a first predetermined polarization determined by a sex constant, a crystal axis substantially coincident with the optical axis, the angle P j, the angle 0 j, the angle Φ ″ ′, and the optical path length L j. A first evaluation amount Rj and a second evaluation amount Sj for a second predetermined polarization, and a first total evaluation which is a total of the first evaluation amounts Rj for the plurality of crystal optical elements. The amount ∑R j and the second total evaluation amount ∑S j, which is the sum of the second evaluation amounts S j for the plurality of crystal optical elements, are on the image plane or the object plane of the optical system. Provided is an optical system characterized in that light rays in an image forming light beam condensed at at least one arbitrary point have a predetermined relationship.

 According to a preferred aspect of the first invention, the first evaluation amount Rj is optical path length change information for the first predetermined polarization, and the second evaluation amount Sj is the second evaluation amount Rj. This is optical path length change information for a fixed polarization. Further, the first predetermined polarized light is an R-polarized light having a polarization direction in a radial direction of a circle centered on the optical axis, and the second predetermined polarized light is a circular polarized light centered on the optical axis. It is preferably 0-polarized light having a polarization direction in the circumferential direction. Further, the predetermined relationship is a relationship in which the sum of the first evaluation amounts Rj is substantially equal for light rays in an imaged light beam condensed on at least any one point on an image plane or an object plane of the optical system. A relationship that the second total evaluation value ∑S j is substantially equal to a light ray in an imaged light beam converged on at least one arbitrary point on an image plane or an object plane of the optical system; The sum of the evaluation amounts Rj of the optical system and the second total evaluation amount ∑Sj are substantially equal to each other with respect to the light rays in the imaged light flux converged on at least one point on the image plane or the object plane of the optical system. It is preferred to include equal relationships.

 Further, according to a preferred aspect of the first invention, the crystal optical element G j is set such that the optical axis and the crystal axis [11 1] or the crystal axis and the optically equivalent crystal axis substantially coincide with each other. In the formula, the predetermined crystal axis is a crystal axis [−110] or a crystal axis optically equivalent to the crystal axis, and when ω j = φ j−pj, the first evaluation amounts R j and The second evaluation quantity S j is:

 Rj = CKXLjX [56X {l-cos (40 j)}

 -32V ~ 2Xsin (40 j) Xsin (3w j)] 192

Sj = aXLjX [32X {l-cos (20 j)} + 64 "2Xsin (29 j) Xsin (3coj)] Zl92

 Are represented by the following equations.

 Further, according to a preferred aspect of the first invention, in the crystal optical element G j set so that the optical axis and the crystal axis [001] or the crystal axis and the optical axis equivalent to the crystal axis substantially coincide with each other. The predetermined crystal axis is a crystal axis [1 10] or a crystal axis optically equivalent to the crystal axis, and when ω j == φ j−pj, the first evaluation amount R j and the crystal axis The second evaluation quantity S j is

Rj = CK XLj X {1-cos (0 j)} X {-84-12 Χοο8 (ω])} _/ ^/ 192

 S j = a X L j X {1-cos (2)} X {-48 + 48 Xcos (4ω j)} / 192

 Are represented by the following equations.

 According to a preferred embodiment of the first invention, in the crystal optical element Gj set so that the optical axis and the crystal axis [01 1] or the crystal axis that is optically equivalent to the crystal axis substantially coincide with each other. The predetermined crystal axis is a crystal axis [100] or a crystal axis optically equivalent to the crystal axis. When ω j = φ j — / 0 j, the first evaluation amounts R j and The second evaluation quantity S j is:

 Rj = a XLj X [U—cos (40j)} X {21-9Xcos (4 j) —84Xcos (2 oj)}

 + 96Xcos (2coj)] / 192

 S j = o; XLiX [{l-cos (20 j)} X {12 + 36Χο8 (4ωΐ) + 48Χοο8 (2ω))}

 One 96Xcos (2coj)] / 192

 Are represented by the following equations.

Further, according to a preferred aspect of the first invention, the physical property constant of the crystal is a crystal axis [01 1] or a crystal optically equivalent to the crystal axis in a crystal forming each crystal optical element Gj. Among the light traveling in the axial direction, the refractive index n100 of light having a polarization direction in the direction of the crystal axis [100 ° or a crystal axis optically equivalent to the crystal axis]; Or the difference from the refractive index _n 011 of light having a polarization direction in the direction of the crystal axis optically equivalent to the crystal axis. When the wavelength of light is λ, the absolute value of the difference between the first total evaluation amount ∑R j and the second total evaluation amount ∑S j is determined on the image plane or the object plane of the optical system. To focus on at least one arbitrary point It is preferable that the light ray in the image light beam is set to be smaller than λΖ2. According to a preferred aspect of the first invention, when a wavelength of light is λ, an absolute value of a difference between the first total evaluation amount ∑R j and a predetermined value is expressed on an image plane of the optical system. Alternatively, the value of λ 結 2 is set to be smaller than λ 中 2 for the light beam in the imaged light beam focused on at least one arbitrary point on the object surface. When the wavelength of light is λ, the absolute value of the difference between the second total evaluation amount ∑S j and a predetermined value is at least an arbitrary value on the image plane or the object plane of the optical system. It is preferable that the light beam in the imaging light beam condensed at one point is set to be smaller than λ Z 2.

 Further, according to a preferred aspect of the first invention, the optical system is set such that the optical axis substantially matches a crystal axis [111] or a crystal axis optically equivalent to the crystal axis. (Μ is an integer of 3 or more) crystal optical elements, wherein the 、 crystal optical elements have a crystal axis [1-10] in a plane perpendicular to the optical axis or an optical axis The directions of the crystal axes which are equivalent to the above have a rotational positional relationship about (120ZM) degrees apart from each other about the optical axis.

 Further, according to a preferred aspect of the first invention, the optical system is set such that the optical axis substantially matches a crystal axis [001] or a crystal axis optically equivalent to the crystal axis. Ν is an integer of 3 or more). The 結晶 crystal optical elements have a crystal axis [100] in a plane perpendicular to the optical axis or an optically equivalent to the crystal axis. The directions of the crystal axes have a rotational positional relationship of about (90 °) degrees apart from each other about the optical axis.

 Further, according to a preferred aspect of the first invention, the optical system is configured such that the optical axis and the crystal axis [01 1] or a crystal axis optically equivalent to the crystal axis are set substantially equal to each other. (L is an integer of 3 or more) crystal optical elements, wherein the L crystal optical elements are a crystal axis [100] in a plane perpendicular to the optical axis or optically equivalent to the crystal axis. The directions of the various crystal axes have a rotational positional relationship about (180 / L) apart from each other about the optical axis.

Further, according to a preferred aspect of the first invention, the optical system is set such that the optical axis and a crystal axis [01 1] or a crystal axis optically equivalent to the crystal axis substantially coincide with each other. (P is an integer of 2 or more) crystal optical elements, and the P crystal optical elements have a crystal axis [100] in a plane perpendicular to the optical axis or the crystal axis and the optical axis. The directions of the crystal axes, which are equivalent to each other, have a rotational positional relationship about (90 / P) degrees apart from each other about the optical axis.

 According to a second aspect of the present invention, in an optical system including a plurality of crystal optical elements formed of crystals belonging to a cubic system,

 M (M is an integer of 3 or more) crystal optical elements set so that the optical axis and the crystal axis [1 11] or the crystal axis optically equivalent to the crystal axis substantially coincide with each other; In the M crystal optical elements, directions of crystal axes [1-10] lying in a plane perpendicular to the optical axis or crystal axes optically equivalent to the crystal axes are almost mutually centered on the optical axis. 120ZM) Provided is an optical system having a rotational positional relationship separated by degrees.

 According to a third aspect of the present invention, in an optical system including a plurality of crystal optical elements formed of crystals belonging to a cubic system,

 N (N is an integer of 3 or more) crystal optical elements set so that the optical axis and the crystal axis [001] or the crystal axis optically equivalent to the crystal axis substantially coincide with each other. ,

 The N crystal optical elements may have a crystal axis [100] in a plane perpendicular to the optical axis or a direction of a crystal axis optically equivalent to the crystal axis. (90 / N) An optical system characterized by having a rotational positional relationship separated by degrees.

 According to a fourth aspect of the present invention, in an optical system including a plurality of crystal optical elements formed of crystals belonging to a cubic system,

L (L is an integer of 3 or more) crystal optical elements set so that the optical axis and the crystal axis [0 11] or the crystal axis optically equivalent to the crystal axis substantially coincide with each other; The L crystal optical elements may have a crystal axis [100] in a plane perpendicular to the optical axis or a crystal axis optically equivalent to the crystal axis. / L) Provide an optical system characterized by having a rotational position Offer.

 The present invention provides, as a fifth invention, an optical system including a plurality of crystal optical elements formed of crystals belonging to a cubic system,

 P (P is an integer of 2 or more) crystal optical elements set so that the optical axis and the crystal axis [0 1 1] or a crystal axis optically equivalent to the crystal axis substantially coincide with each other, The P crystal optical elements may have a crystal axis [100] in a plane perpendicular to the optical axis or a crystal axis optically equivalent to the crystal axis. Almost

It is also possible to provide an optical system characterized by having a rotational positional relationship separated by (90 / P) degrees. In the first to fifth inventions, two or three or more crystal optical elements have a rotation error of ± 4 degrees or less, or an angle error between the crystal axis and the optical axis that should coincide with the optical axis. Is preferably ± 4 degrees or less.

According to a preferred embodiment of the first to fifth inventions, the crystal is preferably a calcium fluoride crystal or a barium fluoride crystal. Further, it is preferable to further include at least one concave reflecting mirror. Further, it is preferable that the optimally aberration correction with respect to A r F excimer laser optimally or are aberration correction with respect to the oscillation wavelength of, or F ₂ laser oscillation wave length.

 According to a sixth aspect of the present invention, there is provided an illumination system for illuminating a mask, and the optical system of the first to fifth aspects for forming an image of a pattern formed on the mask on a photosensitive substrate. An exposure apparatus is provided.

 In a seventh aspect of the present invention, an exposure step of exposing the pattern of the mask on the photosensitive substrate using the exposure apparatus of the sixth aspect, and a developing step of developing the photosensitive substrate exposed in the exposure step The present invention provides a method for producing microdeposits, comprising: BRIEF DESCRIPTION OF THE FIGURES

 FIG. 1 is a view schematically showing a configuration of an exposure apparatus having a projection optical system according to each embodiment of the present invention.

FIG. 2 is a diagram schematically showing a configuration of a projection optical system according to the first embodiment of the present invention. It is.

 FIG. 3 is a diagram for explaining names of crystal axes in a cubic crystal such as fluorite.

 4A to 4C are diagrams for explaining the definition of a rotation angle about the optical axis of the crystal lens.

 FIG. 5 is a diagram for explaining the definition of an angle 0 formed by the imaging light rays in the crystal lens G j with the Z-axis direction and an angle formed by the X-axis direction.

 FIG. 6 is a diagram schematically showing a configuration of a projection optical system according to a second embodiment of the present invention.

 FIG. 7 is a flowchart of a method for obtaining a semiconductor device as a micro device.

 FIG. 8 is a flowchart of a method for obtaining a liquid crystal display element as a micro device. BEST MODE FOR CARRYING OUT THE INVENTION

 An embodiment of the present invention will be described with reference to the accompanying drawings.

FIG. 1 is a view schematically showing a configuration of an exposure apparatus having a projection optical system according to each embodiment of the present invention. In each embodiment of the present invention, the present invention is applied to a projection optical system mounted on an exposure apparatus. Referring to FIG. 1, an exposure apparatus according to each embodiment includes a light source 1 such as an ArF excimer laser or a _two laser. The light beam supplied from the light source 1 is guided to the illumination optical system 3 via the light transmission system 2. The illumination optical system 3 is composed of bending mirrors 3a and 3b as shown, an optical integrator (not shown) (illuminance equalizing element), and the like, and illuminates the reticle (mask) 101 with substantially uniform illumination.

Reticle 101 is held by reticle holder 14 by, for example, vacuum suction, and is configured to be movable by the action of reticle stage 5. The light beam transmitted through the reticle 101 is condensed through the projection optical system 300 to form a projected image of the pattern on the reticle 101 on a photosensitive substrate such as a semiconductor wafer 102. .ゥ C 102 is also held by the wafer holder 7 by, for example, vacuum suction, and is configured to be movable by the action of the wafer stage 8. In this way, by performing the batch exposure while moving the wafer 102 in steps, the pattern projection image of the reticle 101 can be sequentially transferred to each exposure area of the wafer 102.

 Further, by performing scanning exposure (scan exposure) while relatively moving the reticle 101 and the wafer 102 with respect to the projection optical system 300, the reticle 101 is placed on each exposure area of the wafer 102. Can be sequentially transferred. When exposing a circuit pattern to an actual electronic device, it is necessary to accurately align and expose the pattern of the next step on the pattern formed in the previous step. An alignment microscope 10 for accurately detecting the position of the position detection mark on the device 102 is mounted.

When using a F ₂ laser one and A r F excimer laser (or the like A r ₂ laser having a wavelength of 1 2 6 eta m) as the light source 1, light transmitting system 2, the illumination optical system 3 and the projection optical science system 3 0 0 The light path is purged with an inert gas such as, for example, nitrogen. In particular, in the case of using the F ₂ laser, the reticle 1 0 1, the reticle holder one 4 and the reticle stage 5 is isolated from the outside atmosphere by the casing 6, the Ke - internal space also inert gas Thing 6 Has been purged. Similarly, the wafer 102, the wafer holder 17 and the wafer stage 8 are isolated from the outside atmosphere by a casing 9, and the internal space of the casing 9 is also purged with an inert gas. FIG. 2 is a diagram schematically showing a configuration of a projection optical system according to the first embodiment of the present invention. Note that in FIG. 2, the Z axis is parallel to the optical axis AX 100 of the projection optical system 100 (corresponding to the projection optical system 300 in FIG. 1), and in a plane perpendicular to the Z axis. The X axis is set parallel to the plane of FIG. 2 and the Y axis is set perpendicular to the plane of FIG. 2 in a plane perpendicular to the Z axis. The + Z axis is downward in the figure, the + X axis is rightward in the figure, the + Y axis is forward in the page, and the XYZ coordinate system as a whole is a right-handed coordinate system (hereinafter simply referred to as “hand system”). ").

In the first embodiment, the present invention is applied to a refractive projection optical system in which aberration correction is optimized for an ArF laser having a wavelength of 193 nm. Projection light of the first embodiment In the science system 100, a light beam emitted from one point on the reticle 101 is focused on one point on the semiconductor wafer 102 as a photosensitive substrate via lenses 103 to 110 arranged along the optical axis AX100. Collect light. Thus, a projected image of the pattern drawn on reticle 101 is formed on wafer 102.

 In the first embodiment, of the lenses 103 to 110, the lenses 105, 106, 109 and 110 are formed of calcium fluoride crystals (fluorite), and the other lenses are formed of synthetic quartz glass. Hereinafter, a lens made of fluorite is called a “crystal lens”. The pupil plane PP is almost an optical Fourier transform plane with respect to the reticle 101 and the wafer (photosensitive substrate) 102, and an aperture stop can be arranged here.

 As described above, fluorite has birefringence for short-wavelength light beams. However, birefringence (difference in refractive index between two light beams having orthogonal polarization planes) does not occur for light traveling in the directions of the crystal axes [100] and [11] of the fluorite crystal. Therefore, if the crystal axis [111] or [100] of the crystal lens (crystal optical element) is set to coincide with the optical axis AX 100 of the projection optical system 100 (therefore, the optical axis of the crystal lens). However, no birefringence occurs for the imaging light traveling parallel to the optical axis AX100. Conversely, for imaging light traveling along the crystal axis [01 1], the birefringence is maximized.

 By the way, in order to improve the resolution of the projection optical system 100, it is necessary to enlarge the image-side NA (image-side numerical aperture) which is a sine of the maximum incident angle 0100 (see FIG. 2) of the light beam on the wafer 102. . Incidentally, the imaging light flux emitted from one point on the reticle 101 and condensed on the wafer 102 is within the range of the imaging light flux defined by the maximum incident angle 100 on the wafer 102 (in FIG. (The range from L to 100 R) and passes through lenses 103 to 110 constituting the projection optical system 100.

Therefore, it is impossible to set any traveling direction of 100 m of the imaging light beam in the imaging light flux (100 L to 10 OR) to be parallel to the optical axis AX 100 at all. In fact, for any imaging ray 10 Om, the optical path 1 in the crystal lens 105 05m, the optical path 106m in the crystal lens 106, the optical path 109m in the crystal lens 109, and the optical path 110m in the crystal lens 110 are not parallel to the optical axis AX100.As a result, for the imaging ray 10 Om, It is subject to optical path length fluctuation (optical path length change) due to birefringence of fluorite crystals.

 Other imaging light rays in the imaging light flux (100L to 100R) also undergo optical path length fluctuations due to the birefringence of the fluorite crystal when passing through the crystal lens 105, 106, 109, 110 . In this case, the optical path length in each crystal lens and the angle formed with the optical axis AX100 for the other imaging light rays are different from the case of the imaging light ray 10 Om in general. The optical path length will be affected. As described above, each of the imaging light beams in the imaging light flux (100 L to 100 R) undergoes a different optical path length variation, that is, a wavefront aberration occurs in the imaging light flux, and the solution of the projection optical system 100 This leads to lower image performance.

 Such a birefringence amount can be accurately determined based on the exposure wavelength λ, the relationship between the crystal direction of the fluorite and the traveling direction of the light beam, and the polarization direction of the light beam. However, it can only be obtained by using a second-order tensor determined by the crystal direction of the fluorite and the traveling direction of the luminous flux, and a number of rotation matrices for rotating the tensor in three-dimensional space. However, it was an extremely complicated calculation method to use as an index for optical design. The present inventor has found that the above-mentioned birefringence amount can be represented by a simple formula described below. Then, they have found that by performing optical design so as to satisfy this equation, it is possible to design an optical system in which the adverse effect of birefringence does not substantially occur even if a crystal lens is used.

The formula for calculating the amount of birefringence differs depending on which crystal axis of the crystal lens substantially coincides with the optical axis of the optical system (hereinafter, also referred to as “axis”). The names of crystal axes in cubic crystals such as fluorite will now be described with reference to FIG. The cubic system is a crystal structure in which unit cells of a cube are periodically arranged in the direction of each side of the cube. Each side of the cube is orthogonal to each other, and these are defined as Xa axis, Ya axis, and Za axis. At this time, the + direction of the Xa axis is the direction of the crystal axis [100], the + direction of the Ya axis is the direction of the crystal axis [010], and the + direction of the Za axis is the crystal. Direction of axis [001].

 More generally, when the azimuth vector (xl, y1, zl) is taken in the above (Xa, Ya, Za) right-handed coordinate system, the direction is the crystal axis [X1, y1, z1]. ] Direction. For example, the orientation of the crystal axis [1 1 1] matches the orientation of the azimuth vector (1, 1, 1). Also, the direction of the crystal axis [1 1 1 2] coincides with the direction of the azimuth vector (1, 1, -2). Of course, in a cubic crystal, the Xa axis, the Ya axis, and the Za axis are completely equivalent optically and mechanically to each other, and cannot be distinguished in actual crystals. Also, the crystal axes [01 1], [0- 1 1],

The sequence of three numbers and the crystal axes with different signs, such as [1 10], are completely equivalent (equivalent) both optically and mechanically.

 In the present invention, when it is necessary to strictly define the relative crystal axis orientation, for example, a plurality of crystal axes optically equivalent to the crystal axis [01 1] are represented by [01 1], [0- 11],

Notation (listing) by changing the code and array position, such as [1 10]. However, if it is not necessary to define the relative crystallographic axis strictly, the notation [01 1], [0—11], [1 10], etc. Here, a plurality of optically equivalent crystal axes are collectively represented. The same applies to other crystal axes other than the crystal axis [01 1] such as the crystal axis [001] and [11 1].

 In the case of an optical system that requires high resolution, in the crystal lens, the crystal axis [001], the crystal axis [01 1], or the crystal axis' [1 1 1] should almost coincide with the optical axis (Z axis). It is good to set. This is because by making these crystal axes coincide with the optical axis, the rotational symmetry of the birefringence with respect to the optical axis can be set optimally. When the crystal axis [00 1] is made to coincide with the Z axis, the crystal axes [100], [010], [1 10], [1] are in a plane perpendicular to the Z axis (XY plane). -1 10] and so on. When the crystal axis [01 1] is made to coincide with the Z axis, the crystal axes [100], [-100], [01-1], etc. exist in the XY plane. Furthermore, when the crystal axis [1 1 1] is made to coincide with the Z axis, the crystal axes [1 10], [1 1 -2], etc. exist in the XY plane.

Therefore, among the three crystal axes [001], [Oil], and [1 1 1], Even if the crystal axis of the crystal is made to coincide with the optical axis (Z axis), the degree of freedom of the rotation angle remains as to how many times the crystal lens is rotated around the optical axis. Will change. In the first embodiment, in the crystal lenses 105 and 106, the crystal axis [001] coincides with the optical axis AX 100 of the projection optical system 100. In the crystal lenses 109 and 110, the crystal axis [11 1] coincides with the optical axis AX 100 of the projection optical system 100.

 4A to 4C are diagrams for explaining the definition of a rotation angle about the optical axis of the crystal lens. In FIGS. 4A to 4C, the + Z axis is directed toward the front of the drawing and coincides with the optical axis AX100 of the projection optical system 100. As shown in FIG. 4A, for the crystal lens G j (one of the crystal lenses 105 and 106) whose crystal axis [00 1] coincides with the optical axis (Z axis), Let pj be the amount of rotation (rotation angle) from the X-axis direction to the Y-axis direction around the Z-axis of the crystal axis [100] in the XY plane.

 Also, as shown in FIG. 4B, in the crystal lens Gj (one of the crystal lenses 109 and 110) whose crystal axis [1 1 1] coincides with the optical axis (Z axis), the XY The amount of rotation of the crystal axis [1-11] in the plane from the X-axis direction to the Y-axis direction around the Z-axis is defined as <0 j. Further, although not used in the present embodiment, the crystal lens G j in which the crystal axis [01 1] coincides with the optical axis (Z axis) is, as shown in FIG. Let pj be the amount of rotation from the X-axis direction to the Y-axis direction around the Z-axis of the crystal axis [100].

FIG. 5 is a diagram for explaining the definition of an angle 0 formed by the imaging light rays in the crystal lens G j with the Z-axis direction and an angle formed by the X-axis direction. In other words, FIG. 5 shows that the angle 0 formed by the imaging optical path (105m, 106m, 109m, 110m) in the crystal lens G j (crystal lens 105, 106, 109, 110) with the Z axis direction and the X axis direction The angle Φ is shown. The vector L jm in FIG. 5 is a direction vector parallel to the imaging optical path (105 m, 106 m, 109 m, 110 m) in each crystal lens G j, its starting point is Z, and the point on the axis is I match. The Z and Z axes are axes that are parallel-shifted from the optical Z axis to the position of the starting point I of the vector L jm, and the direction is naturally While equal to the direction of the Z axis.

 At this time, the angle between the vector L j m and the Z axis is defined as 0. For the j-th crystal lens Gj, this angle is 0 j. The position at which the end point P of the vector L j m is projected on the Z ′ axis is defined as the origin 、, and the angle between the line segment extending from the origin O to the end point P and the X ′ axis is defined as Φ. Also in this case, the angle is <i> j for the j-th crystal lens Gj. Here, the X and X axes are also obtained by shifting the X axis in parallel, and the direction is naturally equal to the direction of the X axis. As a result, the Y 'axis is also a parallel shift of the Y axis, and its direction is naturally equal to the Y axis direction.

 Hereinafter, polarized light having an electric field plane in a plane including the vector L jm representing the traveling direction of the light beam and the Z ′ axis is referred to as “R-polarized light”, and a plane including the vector L jm and orthogonal to the R-polarized plane. Polarized light with an electric field is called "0 polarized light". In a broader sense, R-polarized light represents polarized light whose polarization direction is substantially coincident with the radial direction of a circle centered on the optical axis AX100. The 0-polarized light represents polarized light whose polarization direction is substantially coincident with the circumferential direction of a circle centered on the optical axis AX100.

 Based on the above assumptions, the above-described equation for calculating the amount of birefringence will be described again. The evaluation amount representing the effect of the amount of birefringence on the light flux in the j-th crystal lens G j is an evaluation amount R j (first evaluation amount) representing the amount of change in the refractive index of R polarized light, and the refractive index of Θ polarized light. The evaluation amount S j (the second evaluation amount) representing the variation amount. These two evaluation amounts R j and S j are the physical constant α of the crystal forming the crystal lens Gj, the optical path length L j of each light beam in the crystal lens G j, and the three angles 0 j, The present inventor's analysis has made it clear for the first time that φ j, pj and the angle pattern oj (= φ j — P j) are expressed by the following simple formula.

 That is, in a crystal lens (crystal optical element) G j set so that the optical axis coincides with the crystal axis [1 1 1], the first evaluation amount R j and the second evaluation amount S j are Equations (1) and (2) respectively.

 Rj = aXLjX [56X {l-cos (40j)}

 — 32V ~ 2Xsin (40 j) Xsin (3 oj)] Zl92 (1)

Sj-aXLjX [32X {l-cos (20 j)} + 64 / ~ 2Xsin (20 j) Xsin (3c j)] Zl92 (2) In the crystal lens Gj set so that the optical axis and the crystal axis [001] coincide, the first evaluation amount R j And the second evaluation quantity S j are expressed by the following equations (3) and (4), respectively.

 Rj = Q! XLjX {l-cos (40 j)} X {-84-12 Χοο8 (4ωΐ)} / 192 (3)

 Sj = aXLjX {l-cos (20 ϊ)} Χ {-48 + 48Χο8 (4ωί)} / 192 (4) Further, a crystal lens G set so that the optical axis and the crystal axis [01 1] coincide. In j, the first evaluation value R j and the second evaluation value S j are expressed by the following equations (5) and (6), respectively.

 R j = a X L j X [{l-cos (40 j)} X {21-9 X cos (4 oj) -84X cos (2ω] ')}

 + 96Xcos (2coj)] 192 (5)

 S j = a X L j X [{l-cos (20 j)} X {12 + 36Xcos (4ω j) + 48Xcos (2ω j)}

 One 96Xcos (2 oj)] Zl92 (6)

The physical property constant a of a crystal represents the birefringence generated for light traveling in the direction of the crystal axis [01 1], and the refractive index n of light having a polarization direction (electric field direction) in the direction of the crystal axis [100]. It is the difference between 100 and the refractive index n 0 11 of light having a polarization direction in the direction of the crystal axis [0-11]. Physical constants a, if crystal fluorite is 3. about 6 X 1 CI- ⁷ for A r F laser beam having a wavelength of 193 nm, with respect to F ₂ laser light having a wavelength of 157 nm the Te is about 6. 5 X 10_ ^7. The optical path length L j is the length of the imaging optical path in the crystal lens Gj (eg, the optical path 105 m). The terms including cos and sin after that are dimensionless, and the evaluation quantities R j and S j represent the change in the optical path length of the transmitted light (optical path length information) due to birefringence.

Thus, a plurality of (four in the present embodiment) crystal lenses Gj are present on the imaging light beam 100m from one point on the reticle 101 to one point on the wafer 102. S j is obtained for each of the plurality of crystal lenses G j. Then, the first total evaluation amount ∑R j (∑ is a multiplication symbol representing the integration for different j), which is the sum total of the first evaluation amounts R j, and the second total evaluation amount S j is the sum total of the second evaluation amounts S j The total evaluation amount 2 S j of 2 is obtained. The total evaluation quantities ∑ R j and ∑ S j are the imaging rays It is an index indicating the effect of birefringence of the entire projection optical system 100 on 100 m (change in the optical path length of transmitted light due to birefringence). That is, if the value of the total evaluation amount ∑Rj is equal to the value of the total evaluation amount ∑Sj, the change in the optical path length between the R-polarized light and the zero-polarized light is equal, and accordingly, the wavefronts also match.

 More specifically, since the crystal axis [001] of the crystal lenses 105 and 106 coincides with the optical axis AX100, the optical path length L j and the angles 0 j and φ of the imaging optical paths 105 m and 106 m are determined. j, and substituting them into equations (3) and (4), the evaluation quantities R j and S j of each crystal lens 105, 106 are obtained, respectively. Since the crystal axis [111] of the crystal lenses 109 and 110 coincides with the optical axis AX100, the optical path length Lj and the angles 0j and φj of the imaging optical paths 109m and 11Om are calculated. Then, by substituting them into equations (1) and (2), the evaluation amounts R j and S j of each crystal lens 109 and 110 are obtained, respectively. Then, the total evaluation amounts ∑R j and ∑ S j, which are the sum of the evaluation amounts R j and S j for all the crystal lenses 105, 106, 109 and 110, are obtained.

 To determine the wavefront aberration in the imaged light flux (100L to 10OR) from one point on the reticle 101 to one point on the wafer 102, that is, the optical path length difference between the imaged light beams, It is necessary to determine ∑Rj and ∑Sj for each of the imaging light rays passing through different positions on the pupil plane PP. Then, if ∑R j and ∑S j are constant for all the imaging rays, and if ∑R j and ∑S j are equal to each other for all the imaging rays, the imaging luminous flux (100L ~ 10 OR) has no wavefront aberration.

The projection optics is such that ∑R j and ∑ S j are constant for all imaging rays and ∑R j and ∑S j are equal to each other for all imaging rays. By optimizing the design of the system 100, that is, optimizing the thickness, radius of curvature, and spacing of each lens, and optimizing the rotation angle of the crystal lens around the optical axis, the wavefront aberration due to birefringence It is possible to realize an optical system without any trouble. It should be noted that 結 R j and ∑ S j are applied to all imaging rays. It is difficult to make them completely constant and make ∑R j and ∑S j completely equal to each other for all imaging rays.

 In practice, an optical system which is not practically affected by birefringence can be realized by suppressing the range of variation of ∑R j and ∑S j to about 1/2 or less of the exposure wavelength λ. In other words, the absolute value of the difference between ∑R j and the predetermined value and the absolute value of the difference between ∑S j and the predetermined value are focused on at least one arbitrary point on the image plane or the object plane. For the middle ray, keep it smaller than λ Ζ 2 and calculate the absolute value of the difference between ∑R j and ∑ S j in at least one point on the image plane or object plane. By keeping the light beam smaller than λ / 2, it is possible to realize an optical system that is not substantially affected by birefringence.

 However, this reference value person 2 does not significantly affect the imaging characteristics, assuming a pattern with a fineness of kl factor 1 = 0.35 (line width = kl XA ZNA). This is an acceptable value, and stricter standards are required when the pattern size to be exposed is smaller. For example, when using a phase shift reticle to expose a pattern with a fineness of about 0.2 kl facsimile = 0.2, the entire range of variation of 」1” and ぉ 3 ”is required. It is difficult to obtain good imaging characteristics unless the image forming light beam is suppressed to about 1/20 or less of the exposure wavelength.

 Actually, it is difficult to realize the above-described R-polarized light and> polarized light over the entire surface (the entire surface of the pupil plane P P) in the imaging light flux. However, considering that each part of the imaged light beam (part of the pupil plane PP) is divided, such R-polarized light and 0-polarized light are converted from the actual X-polarized light and the Y-polarized light by using a rotation matrix as a conversion relation. Polarized light that is tied. Therefore, an optical system that assumes R-polarized light and 0-polarized light and has no wavefront aberration in this polarization state also has a wavefront aberration for realistic X-polarized light and Y-polarized light flux that are connected by the relationship between the polarization state and the rotation matrix. Since there is no optical system, there is no particular problem in using the evaluation index based on the R polarization and the 0 polarization as described above.

By the way, in the above equations (1) to (6), the existence of the term including j (= φ j -pj), that is, the term including Φ j depends on the angle Φ j between the light flux and the X-axis direction. Means that the effect of fluctuates. That is, the values of these terms are By changing the angle ιο j in one night ω j, that is, the rotation angle of the crystal lens G j with respect to a predetermined axial direction, it is possible to change the angle.

 In a crystal lens with the crystal axis [1 1 1] as the optical axis, the scale! 'Pobi 3' 'has a term proportional to sin (3 ω j), so it rotates three times with respect to the rotation of the lens. Has symmetric values. This means that the amount of change in the optical path length given by R j and S j fluctuates with a cycle of 120 degrees of lens rotation. Therefore, if two lenses with the crystal axis [11 1] as the optical axis are used, the other lens rotates relative to one lens by 60 or 180 degrees (= 60 + 120) around the optical axis. However, if both crystal axes [1-10] are set to be angularly separated by 60 or 180 degrees in the XY plane, the three-fold rotationally symmetric components of both lenses cancel each other out, and ∑R It can be seen that it is convenient to make j and ∑S j equal.

 Similarly, in a crystal lens with the crystal axis [001] as the optical axis, R j and S j have a term proportional to cos (4 ω j), so the value is four times rotationally symmetric with respect to the rotation of the lens. have. In this case, the angle 3 fluctuates with a cycle of 90 degrees of the lens rotation. Therefore, if two lenses with the crystal axis [001] as the optical axis are used, the other lens rotates relative to one lens by 45 or 135 degrees (= 45 + 90) about the optical axis. If both crystal axes [100] are set to be angularly separated by 45 or 135 degrees in the XY plane, the four-fold rotationally symmetric components of both lenses cancel each other out, and 結 R j and ∑ This is convenient for making S j equal.

 Further, in a crystal lens having the crystal axis [011] as the optical axis, R j and S j have both a term proportional to cos (4 ω j) and a term proportional to cos (2 ω j). In this case, four lenses with the crystal axis [01 1] as the optical axis are used, and each lens is rotated by 45 degrees around the optical axis, and each crystal axis [100] is 45 degrees in the XY plane. Setting them apart from each other cancels the rotational asymmetry of each lens, which is convenient for equalizing ∑R j and ∑ S j for each imaging light flux.

Of course, the rotational symmetric component cancellation by the two lens pairs and the rotational asymmetric cancellation by the four lens pairs described above are limited to application to two lenses ゃ four lenses. Not only. Therefore, while adjusting the rotation angle, thickness, radius of curvature, spacing, etc. of the plurality of crystal lenses around the optical axis, and the thickness, radius of curvature, spacing, etc. of the other lenses, as a whole, ∑R j and 全体It goes without saying that S j should be set to be equal.

 For example, it is possible to cancel rotationally asymmetric components of birefringence by using three lenses of approximately equal thickness with the crystal axis [1 1 1] as the optical axis. In this case, the rotationally asymmetric period of one lens is 120 degrees as described above. Therefore, the three lenses have a rotational positional relationship of 40 degrees apart from each other about the optical axis, that is, the direction of the crystal axis [1-10] in the plane perpendicular to the optical axis is centered on the optical axis. By setting them so as to have a rotational positional relationship of 40 degrees apart from each other, the rotational asymmetries of the three lenses overlap each other with a positional shift of 1/3 cycle.

 At this time, in the three lenses, the direction of the crystal axis [1-10] of the second lens is a predetermined direction about the optical axis with respect to the direction of the crystal axis [1-10] of the first lens. And the direction of the crystal axis [1-10] of the third lens is the same as the direction of the crystal axis [1-10] of the second lens around the optical axis. It has a positional relationship rotated by 40 degrees in a predetermined direction. In other words, the rotation angle of the crystal axis [1-10] of each lens is 0 degrees, 40 degrees, and 80 degrees with respect to one of the three lenses (20 degrees).

 If the refracting power of each of the three lenses is weak and the traveling direction of the light beam in each lens is almost constant, sin (3ωj) in the above equations (1) and (2) becomes Equations (21), (22), and (23) are given for the following lens. Here, the unit of the argument of sin is [degree].

 sin (3col) (21)

 sin {3 (o) l 0)} = sin (3c l + 120) (22)

 sin {3 (l + 80)} = sin (3 l + 240) (23)

Furthermore, equations (22) and (23) can be transformed as shown in the following equations (22 ') and (23'). sin (3col) Xcos (120) + cos (3cl) X sin (120) (22,)

 sin (3 ol) X cos (240) + cos (3ω 1) Xsin (240) (23,)

 Therefore, the sum of equations (21), (22), and (23) is expressed by the following equation (24).

 {1 + cos (120) + cos (240)} Xsin (3col) + {sin (120) + sin (240)} Xcos (3col) (24) In equation (24), Hcos (120 cos (240) and sin (120) + sin (240) are both 0. Therefore, the sum of Equations (21), (22) and (23), that is, the value of Equation (24), is 0. In other words, By setting the three lenses whose optical axis is the crystal axis [1 1 1] to have a rotational positional relationship of 40 degrees apart from each other about the optical axis, the birefringence is reduced by the canceling action. The rotationally asymmetric component can be removed, and it can be seen that using such a set of three lenses is advantageous for equalizing ∑Rj and ∑Sj for each imaging light flux.

 Similarly, it is possible to cancel the rotationally asymmetric component of birefringence by using three lenses of approximately the same thickness with the crystal axis [001] as the optical axis. In this case, the period of the rotational asymmetry in one lens is 90 degrees as described above. Therefore, the three lenses have a rotational positional relationship of 30 degrees apart from each other about the optical axis, that is, the directions of the crystal axes [100] in a plane perpendicular to the optical axis are alternated about the optical axis. By setting them so that they have a rotational positional relationship separated by 30 degrees each other, the rotational asymmetry of the three lenses will be displaced by 1 to 3 periods and overlap each other.

 The cos (4ωj) in the above equations (3) and (4) is expressed by the following equations (31), (32), and (33) for three lenses. Here, the unit of the argument of cos is [degree].

 cos (4o) l) (31)

 cos {4 (oH + 30) cos (4 ol + 120) (32)

 cos {4 (ol + 60)} = cos (4 ol + 240) (33)

Furthermore, equations (32) and (33) can be transformed as shown in the following equations (32 ') and (33,). cos (4o> l) Xcos (120) — sin (4col) X sin (120) (32,)

 cos (4c l) Xcos (240) — sin (4col) Xsin (240) (33,)

 Therefore, the sum of Equations (31), (32), and (33) is expressed by the following Equation (34).

 {l + cos (120) + cos (240)} Xcos (4col) — {sin (120) + sin (240)} Xcos (4col) (34) In equation (34), l + cos (120) + cos (240) and sin (120) + sin (240) are both zero. Therefore, the sum of equations (3 1), (32), and (33), that is, the value of equation (34) is zero. In other words, by setting the three lenses with the crystal axis [00 1] as the optical axis so as to have a rotational positional relationship of 30 degrees apart from each other about the optical axis, the birefringence of the two lenses is canceled out by the canceling action. The rotationally asymmetric component can be removed. Then, it can be seen that even if such a set of three lenses is used, it is convenient to make ∑Rj and ∑Sj equal for each imaging light flux.

 The method of reducing rotationally asymmetric birefringence for the lens having the crystal axis [111] as the optical axis and the lens having the crystal axis [001] as the optical axis is based on the above two lenses or three lenses. The present invention is not limited to cancellation of rotationally asymmetric components due to mutual rotation of the lenses. For example, if the above method is further developed, if the crystal lens has a rotational asymmetry with a period of 3 degrees, Q lenses (Q is Q) having a rotational positional relationship of () 3 / Q) degrees apart from each other about the optical axis By using a crystal lens of (an integer of 2 or more), a rotationally asymmetric component of birefringence can be removed by its canceling action.

 In other words, when using M (M is an arbitrary integer of 3 or more) crystal lenses having the crystal axis [1 1 1] as the optical axis, the M lenses are mutually (1207 M) centered on the optical axis. By setting so as to have a rotational positional relationship separated by degrees, the rotationally asymmetric component of birefringence can be removed by the canceling action. Specifically, for example, when five crystal lenses with the crystal axis [1 1 1] as the optical axis are used, the five lenses are separated from each other by 24 (= 120/5) degrees about the optical axis. By setting so as to have the rotational positional relationship described above, it is possible to cancel the rotationally asymmetric component of birefringence.

In addition, N (N is an arbitrary integer of 3 or more) crystals whose optical axis is the crystal axis [00 1] When lenses are used, the N lenses are set so as to have a rotational positional relationship separated by (90 ZN) degrees about the optical axis, so that the birefringent rotationally asymmetric component is canceled out by the canceling action. Can be removed. Specifically, for example, when six crystal lenses having the crystal axis [001] as the optical axis are used, the six lenses have a rotational positional relationship of 15 (= 90/6) degrees apart from each other about the optical axis. By setting so as to have, it is possible to cancel the rotationally asymmetric component of birefringence. It is to be noted that the rotation angle of each crystal lens may be a value obtained by adding the rotation asymmetric period 3 to each of the above values (120 / M, 90 / N), as in the above-described embodiment. In general, the number of lenses for canceling the birefringent rotationally asymmetric component may be two, but in the above method, any three or more lenses are used to cancel the birefringent rotationally asymmetric component. Therefore, the restriction on the lens design is reduced compared to the case of two lenses, which is convenient. That is, a lens group including a large number of crystal lenses can be used to make ∑Rj and ∑Sj equal for each imaged light beam. As described above, when the refractive power of each lens is weak and the traveling direction of the luminous flux in each lens is almost constant, the above-described cancellation effect is most effectively obtained. It goes without saying that an offset effect can be obtained.

By the way, in the case of a lens with the crystal axis [011] as the optical axis, as shown in the above equations (5) and (6), the term proportional to cos (4o) j) There is a term proportional to cos (2c j). Among these two terms, the term proportional to cos (2c j) is a component having a rotation period of 180 degrees. Therefore, as described above, two lenses of approximately the same thickness with the crystal axis [01 1] as the optical axis must be rotated by 90 degrees around the optical axis center (two-lens group rotated by 90 degrees). It is possible to cancel the rotationally asymmetric component by Furthermore, from the same considerations as above, it is also possible to cancel the rotationally asymmetric birefringent component by using three lenses of approximately equal thickness with the crystal axis [0 1 1] as the optical axis. In this case, the three lenses have a rotational positional relationship of 60 degrees apart from each other about the optical axis, that is, the direction of the crystal axis [100] in a plane perpendicular to the optical axis points to the optical axis. Rotate 60 degrees apart from each other as center By setting it to have a positional relationship (a three-lens group rotated by 60 degrees), it is possible to cancel the rotationally asymmetric component of birefringence.

 More generally, to remove the rotationally asymmetric term proportional to cos (2coj), use L (L is an arbitrary integer of 3 or more) crystal lenses with the crystal axis [01 1] as the optical axis. Then, the L lenses may be set so as to have a rotational positional relationship of (180 / L) degrees apart from each other about the optical axis. According to this method, in the lens having the crystal axis [01 1] as the optical axis, the number of lenses for canceling the rotationally asymmetric term proportional to cos (2c j) can be selected to an arbitrary value. This is convenient because the restrictions on the lens design are reduced.

 The rotationally asymmetric term proportional to cos (4 j) uses two lenses that are rotated 45 degrees about the optical axis, similar to a lens that uses the crystal axis [00 1] as the optical axis. It is possible to offset by. Furthermore, from the same considerations as above, it is possible to cancel out the rotationally asymmetric birefringent component by using three lenses of approximately equal thickness with the crystal axis [01 1] as the optical axis. In this case, the three lenses have a rotational positional relationship of 30 degrees apart from each other about the optical axis, that is, the direction of the crystal axis [100] in the plane perpendicular to the optical axis is the center of the optical axis. It is possible to cancel the rotationally asymmetric component of birefringence by setting the rotation position relationship so as to be 30 degrees apart from each other (30-degree rotation three-lens group).

 More generally, in order to remove the rotationally asymmetric term proportional to cos (4 j), we need to use P (P is an arbitrary integer of 2 or more) crystal lenses with the crystal axis [01 1] as the optical axis. In this case, the P lenses may be set so as to have a rotational positional relationship of (907P) degrees apart from each other about the optical axis. According to this method, in a lens having the crystal axis [0 11] as the optical axis, the number of lenses for canceling the rotationally asymmetric term proportional to cos (4c j) can be selected to an arbitrary value. This is convenient because the restrictions on the lens design are reduced.

Note that, in the case of a lens having the crystal axis [011] as the optical axis, in order to actually cancel the rotationally asymmetric component proportional to cos (2c j), the above L lenses arranged close to each other along the optical axis are used. Prepare at least P sets of lenses or a lens group consisting of two lenses. So Then, it is desirable to remove a term proportional to cos (4 oj) by giving a relative rotation of (90 ZP) degrees around the optical axis between each lens group. Also in this method, the number of lens groups for canceling the rotationally asymmetric term proportional to cos (4o) j) is not limited to two, and three or more lens groups can be used. This is convenient because the restrictions on the lens design are reduced. In the present embodiment, the number of lenses for canceling the rotationally asymmetric component of birefringence may be two, but in the above method, three or more arbitrary lenses are used. Since the rotationally asymmetric component of refraction can be canceled out, the restriction on the lens design is reduced as compared with the case of two lenses, which is preferable.

 As described above, in order to eliminate the effect of birefringence by rotating the multiple lenses around the optical axis, the rotation direction of each of the multiple lenses should be within ± 4 degrees with respect to the predetermined angle. It is desirable to suppress it. If the rotation angle setting error is larger than the allowable value, there is a problem that the effect of eliminating birefringence according to the present invention is reduced, and the residual birefringence deteriorates the imaging performance. It is also desirable that the direction error of the specified crystal axis, which should be substantially coincident with the optical axis, with the optical axis be kept within about ± 4 degrees. If the setting error of the angle between the specified crystal axis and the optical axis becomes larger than this allowable value, there is a problem that the imaging performance is deteriorated due to the residual birefringence, as in the case described above.

The same applies to the case where birefringence is eliminated using a lens group including three or more lenses, and the case where birefringence is eliminated using a lens group including two lenses. However, the angle error range within the ± 4 degrees, like the above-mentioned reference, the allowable angular error range in which it is assumed kl factor = _0.35 approximately fineness of a pattern (line width = kl XA / NA) In an optical system that needs to transfer a finer pattern than this, the directional error between the specified crystal axis and the optical axis needs to be smaller than the above-mentioned angle error range. For example, in the case of exposing a pattern with a fineness of about KL factor ₌ 0.2 using a phase shift reticle, it is desirable that both of these angle errors be ± 2 degrees or less.

Conversely, if the optical system targets a pattern with a k 1 factor of about 0.5, Even if both of these angle errors are reduced to about ± 6 degrees, practically sufficient imaging performance can be obtained. As described above, in order to strictly control the direction of the crystal axis, the crystal lattice constants in the manufacturing process of the crystal material, which is the material of the crystal lens, and the processing (grinding and polishing) of the crystal lens are required. It is preferable to irradiate the crystal with X-rays having a near wavelength and measure the diffraction pattern to confirm the crystal axis direction, that is, to provide crystal axis direction confirmation means.

 As described above, when the lens group having the same crystal axis as the optical axis is relatively rotated around the optical axis to cancel out the rotationally asymmetric component, if the cancellation is completely achieved, Only the terms that do not include ω j in Equations (1) to (6) affect ∑R j and ∑S j.

 In a crystal lens Gj set so that the optical axis coincides with the crystal axis [1 11], if only the term that does not include ω j is affected, the first evaluation amount R j ′ and the second evaluation amount The quantity S j 'is expressed by the following equations (7) and (8), respectively.

 Rj '= a XLj X56X {1-cos (40 j)} / 192 (7)

 S j "= a XLj X32X {l-cos (20 j)} / 192 (8)

 Also, in the crystal lens Gj set so that the optical axis and the crystal axis [001] coincide with each other, when only the term that does not include ω j is affected, the first evaluation amount Rj ′ and the second evaluation amount Sj j, is represented by the following equations (9) and (10), respectively.

 Rj "= a XLj X-84X {1-cos (40 j)} / 192 (9)

 S j "= a XLj X-48X {1-cos (20 j)} / 192 (10)

 Further, in the crystal lens G j set so that the optical axis and the crystal axis [01 1] coincide with each other, when only the term not including ω j is affected, the first evaluation amount R j ′ and the second The evaluation quantity S j ′ is expressed by the following equations (11) and (12), respectively.

 Rj '= a XLj X21X {l-cos (40 j)} / 192 (1 1)

 Sj "= aXLjX12X {l-cos (20 j)} / 192 (12)

As described above, no matter which crystal axis is the optical axis, the coefficient of the term including {1-cos (40 j)} in R j ′ and the {l-cos (20 j)} in S j, There is a 7: 4 relationship with the coefficient of the term containing. In addition, a crystal lens whose crystal axis [1 1 1] is the optical axis Between the crystal lens whose crystal axis [001] is the optical axis and the crystal lens whose crystal axis [01 1] is the optical axis, both the values of R j ′ and S j ′ : The relationship of 1 2: 3 is established.

 Therefore, when the lens group having the same crystal axis as the optical axis is relatively rotated around the optical axis to cancel out the rotationally asymmetric component, the crystal axis [11 1] is within the lens group having the optical axis. The sum of the optical path lengths ∑L 11 1 of the lens group, the sum of the optical path lengths ∑L 001 in the lens group whose crystal axis [001] is the optical axis, and the optical path in the lens group whose crystal axis [01 1] is the optical axis When the relationship shown in the following expression (13) is satisfied with the sum of lengths ∑L 011, both ∑Rj and ∑S j can be set to 0.

 8 X∑L 11 1 -12 X∑L 001 +3 X∑L 01 1 = 0 (13) In the case of the projection optical system 100 according to the first embodiment, the crystal lens (where the crystal axis [001] is the optical axis) 105, 106) and a crystal lens (109, 110) whose crystal axis [1 11] is the optical axis, but does not include a crystal lens whose crystal axis [01 1] is the optical axis. Therefore, the thickness of the crystal lens 105 and the thickness of the crystal lens 106 are made substantially equal to each other, and both the lenses are relatively rotated by 45 degrees or 135 degrees about the optical axis. Further, the crystal lens 109 and the crystal lens 110 have substantially the same thickness, and both lenses are relatively rotated by 60 degrees or 180 degrees about the optical axis.

 Then, the birefringent rotation anti-pair between the lens group (105, 106) whose crystal axis [001] is the optical axis and the lens group (109, 110) whose crystal axis [1 1 1] is the optical axis. When canceling the nominal component, the following equation is used between the sum of the optical path lengths of the imaging optical paths 105m and 106m ∑L 001 and the sum of the optical path lengths of the imaging optical paths 109m and 110m ∑L 1 1 1 When the relationship shown in (14) is satisfied, both ∑R j and ∑ S j can be set to 0.

 8 X∑L 1 1 1-12 X∑L 001 = 0 (14)

That is, if the ratio of the sum of the thicknesses of the crystal lenses 105 and 106 to the sum of the thicknesses of the crystal lenses 109 and 110 is set to approximately 2: 3, the influence of birefringence can be minimized. . Note that, in the above example, for each imaging light ray in the imaging light flux, ∑ R j and ∑ S j are both equal to 0. However, it is not always necessary to make ∑R j and ∑S j always equal to 0, and it is sufficient to make ∑R j and ∑ S j substantially equal to predetermined values for each imaging ray. Then, as described above, the crystal axis and rotation of each crystal lens are adjusted so that the variation of ∑ R j and ∑ S j falls within the range of λ Ζ 2 or λ Ζ 20 as described above. By setting the angle | 0 j and the thickness, radius of curvature, and spacing of all lenses, it is possible to realize an optical system that minimizes the adverse effects of birefringence.

 Note that, as in the first embodiment described above, a method of removing the adverse effect of birefringence in the entire optical system by a combination of lens groups in which rotational asymmetry is canceled is a method of reducing the adverse effect of birefringence in the present invention. Needless to say, this is only an example. That is, the first total evaluation amount 組 み 合 わ せ R j and the second total evaluation amount ∑S j of the optical system as a whole are not limited to the combination of the rotating lens groups as described above. It goes without saying that any other method may be used as long as the light flux condensed at any one of the above points is set to be equal.

FIG. 6 is a diagram schematically showing a configuration of a projection optical system according to a second embodiment of the present invention. In the second embodiment, the wavelength is applying the present invention to 1 5 7 nm of F ₂ catadioptric projection optical system is aberration correction is optimized for laser scratch. In the projection optical system 200 (corresponding to the projection optical system 300 in FIG. 1) of the second embodiment, one point on the reticle 201 (corresponding to the reticle 101 in FIG. 1) is emitted. The light beam enters a mirror block 203 as an optical path changing means via a lens 204 arranged along an optical axis AX200a.

The light beam reflected by the mirror 203 of the mirror block 203 is passed through the lenses 205 and 206 arranged along the optical axis AX200b to form the concave M mirror 2 It is incident on 20. The light beam reflected by the concave reflecting mirror 220 enters the mirror block 203 again through the lenses 206 and 205. The luminous flux reflected by the flat mirror 203 b of the mirror block 203 is transmitted to the wafer 2 via the lenses 207 to 212 arranged along the optical axis AX200a. 0 2 (corresponding to wafer 102 in Fig. 1) Focus on one point above. Thus, on wafer 202, reticle 201 is drawn The projected image of the pattern is formed. In the second embodiment, all the lenses 204 to 212 are formed of calcium fluoride crystals (fluorite).

 Even in such a catadioptric optical system, the influence of the birefringence of the projection optical system 200 can be calculated by the total evaluation amounts 評 価 R j and ∑ S j of the present invention. Based on the amounts ∑R j and ∑S j, it is possible to minimize the adverse effect of the birefringence of the projection optical system 200. However, in the reflection refractive optical system according to the second embodiment, some crystal lenses are arranged on an optical axis different from the other crystal lenses, and the plane mirrors 203 a and 203 b and concave surfaces Due to the reflection action of the reflector 220, the direction of the X axis, which is the reference for the rotation angle around the optical axis of each crystal lens, also fluctuates, and the crystal lenses 205, 206 form an image. The difference between the first embodiment and the first embodiment is that the light path reciprocates in the path.

 Hereinafter, the setting of the XYZ axes in the catadioptric projection optical system 200 will be described. First, as shown in FIG. 6, for the crystal lens 204 arranged along the optical axis AX 200 a in the vicinity of the reticle 201, as in the first embodiment, X 0 Y 0 The Z0 coordinate system is set. That is, the downward direction along the optical axis AX200a, which is the traveling direction of the exposure light, is defined as the direction of the + Z0 axis, the horizontal rightward direction is defined as the direction of the + X0 axis on the plane of FIG. The forward direction is set as + Y0 axis direction. In this case, the X0Y0Z0 coordinate system is a right-handed system. Thus, for the crystal lens 204, the above-mentioned angles 0j, pj, and φj are obtained with reference to the X0Y0Z0 coordinate system, and these are substituted into equations (1) to (6). Thus, the evaluation amounts R j and S j are calculated.

Next, after the imaging light beam is reflected by the plane mirror 203a, the traveling direction of the light beam is rightward in the figure, so that the traveling direction of this light beam is the + Z1 axis and the X1Y1Z1 coordinate is used. Set the system. In this case, the X 1 Y 1 Z 1 coordinate system is transformed into a left-handed coordinate system (hereinafter simply referred to as “left-handed system”) by the reflection effect of the plane mirror 203 a. That is, the rightward direction along the optical axis AX200b, which is the traveling direction of the exposure light, is the direction of the + Z1 axis, the downward direction in the figure is the direction of the + X1 axis, and the forward direction of the drawing is the + Y1 axis direction. Set the direction. Thus, for the imaging light flux passing through the crystal lenses 205 and 206 to the right, The evaluation values Rj and Sj are calculated by obtaining the above-mentioned angles 0j, pj, and φ with reference to the XIYlZ1 coordinate system and substituting them into equations (1) to (6). However, in this case, since the XIYlZ1 coordinate system is a left-handed system, it is necessary to pay attention to the sign of the angles pj and φj shown in FIGS. 4 and 5. In other words, in the case of the left-handed X1Y1Z1 coordinate system, if the X-axis, Z-axis, X'-axis, and Z'-axis are fixed according to Figs. 4 and 5, respectively, the Y-axis And the Y 'axis is opposite to the direction in FIGS. 4 and 5. Since the definition of the rotation angle pj and the angle φj is defined as the positive direction of rotation from the X axis (X 'axis) to the Y axis (Υ' axis), in the left-handed X 1 Υ 1 系 1 coordinate system , The forward direction of rotation is also opposite to the direction shown in FIGS. 4 and 5. However, the rotation direction from the X1 axis to the Υ1 axis direction is still positive.

 Next, when the image-forming light beam is reflected by the concave reflecting mirror 220, the traveling direction of the light beam is directed leftward in the figure, so that the 方向 2Υ2Ζ2 coordinate system is set with the traveling direction of this light beam as the + Ζ2 axis. In this case, the {2} 2 ^ 2 coordinate system returns to the right-handed system due to the reflecting action of the concave reflecting mirror 220. That is, the leftward direction along the optical axis ΑΧ200b, which is the direction of travel of the exposure light, is set as the + Z2 axis direction, the upward direction in the figure is set as the + X2 axis direction, and the depth direction of the paper is set as the + Y2 axis direction. I do. Thus, for the imaging luminous flux passing through the crystal lenses 205 and 206 to the left, the above-mentioned angles 0 j, P j,} are obtained with reference to the X2Y2Z2 coordinate system, and these are calculated by the equations (1) to (6). ), The evaluation amounts R j and S j are calculated.

In the crystal lenses 205 and 206, the crystal axis [0 0 1] (or the crystal axes [1 1 1] and [0 1 1]) coincides with the traveling direction of the light flux. It should be noted that the sign of each crystal axis is reversed between the case where the light beam travels rightward and the case where it travels leftward in the lenses 205, 206. In other words, the crystal axis that was [1 1 1] when the light beam travels to the right is treated as the crystal axis [1-1-1-1] when the light beam travels to the left. Similarly, the crystal axis [100] is treated as the crystal axis [_100], and the crystal axis [1-100] is treated as the crystal axis [-110]. Finally, after the imaging light beam is reflected by the flat mirror 203b, the traveling direction of the light beam Returning to the downward direction in the figure, the X3 Y3 Z 3 coordinate system is set with the traveling direction of this light beam as the + Z 3 axis. In this case, the X3Y3Z3 coordinate system is converted again into a left-handed system by the reflection operation of the plane mirror 203b. That is, the downward direction along the optical axis A X200a, which is the traveling direction of the exposure light, is defined as the direction of + Z3 axis, the rightward direction in the figure is defined as the direction of + X3 axis, and the depth direction of the paper is defined as the direction of + Y3 axis. Set. In this way, for the crystal lenses 207 to 212, the angles 0 j, pj, and j are determined with reference to the X 3 Y 3 Z 3 coordinate system, and are substituted into the equations (1) to (6). Calculate the quantities R j and S j. Since the X 3 Y 3 Z 3 coordinate system is a left-handed system, the method of calculating the angle and Φ j is the same as the case of the light beam transmitted right through the crystal lenses 205 and 206.

 The total evaluation amounts ∑Rj and ∑Sj obtained by adding the evaluation amounts Rj and Sj of the respective crystal lenses obtained in this manner are respectively calculated as the influence of the birefringence in the catadioptric projection optical system 200. What can be used as an index is the same as in the case of the refraction type projection optical system 100 according to the first embodiment. Also, for all the imaging rays in the imaging luminous flux that emits one point on the reticle 201 and converges to one point on the wafer 202, the predetermined values of the total evaluation amounts ∑R j and ∑ S j are centered. The crystal axis and the rotation angle of each crystal lens are adjusted so that the variation within the range falls within the range of λ / 2 or λ / 20, for example. oj, by setting the thickness, radius of curvature, spacing, etc. of all lenses, it is possible to realize an optical system that minimizes the adverse effects of birefringence. This is the same as the case of the refraction type projection optical system 100.

 In the projection optical system 200 according to the second embodiment, for the crystal lenses 205 and 206 arranged near the concave reflecting mirror 220, the crystal axis [1 1 1] of fluorite is made to coincide with the optical axis AX200b. And the crystal axis [1-10] is arranged to be rotated relative to the optical axis by 60 degrees or 180 degrees. For the crystal lenses 204, 207, 208, and 209, the crystal axis [01 1] of the fluorite is aligned with the optical axis AX 200a, and the crystal axis [100] is 45 degrees around the optical axis. Rotate them relative to each other.

Furthermore, for the crystal lenses 21 1 and 212, the fluorite crystal axis [001] is Align with the axis AX 200a and the direction of the crystal axis [100]. For the crystal lens 210, the crystal axis [001] of the fluorite is made to coincide with the optical axis AX200a, and the direction of the crystal axis [100] is changed to the crystal axis of the crystal lenses 211 and 212.

 It is rotated relative to the direction of [100] by 45 or 135 degrees around the optical axis. Thus, for all the imaging rays in the imaging luminous flux that emits one point on the reticle 201 and converges to one point on the wafer 202, the values of the total evaluation amounts ∑R j and ∑ S j are set within a predetermined range. Setting is easy.

 In the above-described first and second embodiments, in order to simplify the description of the present invention, attention is paid only to an image forming light beam emitted from one point on the reticle 101 (201). However, in order to obtain good imaging performance, reticle 101

It goes without saying that the above relationship of the present invention should be satisfied with respect to the imaged light flux that reaches the effective exposure area on the wafer 102 (202) from all points in the effective illumination area on (201).

In each of the above embodiments, calcium fluoride crystal (fluorite) is used as the birefringent optical material. However, the present invention is not limited to this, and other uniaxial crystals, for example, barium fluoride may be used. crystal (B aF _2), lithium fluoride crystals (L i F), fluoride kana thorium crystals (NaF), strontium fluoride crystal (S r F _2), fluoride base Lili © beam crystals (B e F ₂₎ For example, other crystal materials that are transparent to ultraviolet light can be used. Of these, barium fluoride crystals have already been developed for large crystal materials exceeding 200 mm in diameter, and are promising as lens materials. In this case, it is preferable that the crystal axis orientation such as parium fluoride (BaF ₂ ) is also determined according to the present invention.

Further, in each of the above-described embodiments, the present invention is applied to the projection optical system. However, the present invention is not limited to this, and may be applied to an optical system for inspecting the projection optical system, for example, an optical system for measuring aberration. Can also be applied. Also, depending on the type of optical system to which the present invention is applied, unlike the optical system that forms an image from the object plane to the image plane as in the above embodiment, the optical system from the object plane to the pupil plane and the parallel light beam are different. In some cases, the configuration of an optical system for condensing light on the image plane is used. In this case, the reticle 101 (20 1) An imaging light flux from one point on the wafer 102 to one point on the wafer 102 (202) cannot exist, but this imaging light flux is focused from one point on the object plane to the pupil plane. It is apparent that the present invention can be applied in the same manner as in the above-described embodiment by treating it as an image light beam or an image light beam condensed at one point on the image plane.

 In the exposure apparatus of each of the above-described embodiments, the reticle (mask) is illuminated by the illumination device (illumination step), and the transfer pattern formed on the mask is exposed on the photosensitive substrate using the projection optical system. By doing so, a micro device (semiconductor element, imaging element, liquid crystal display element, thin film magnetic head, etc.) can be manufactured. Hereinafter, refer to the flowchart of FIG. 7 for an example of a technique for obtaining a semiconductor device as a microdevice by forming a predetermined circuit pattern on a wafer or the like as a photosensitive substrate using the exposure apparatus of each embodiment. I will explain.

 First, in step 301 of FIG. 7, a metal film is deposited on one lot of wafers. In the next step 302, a photoresist is applied on the metal film on the one lot of wafers. Then, in step 303, using the exposure apparatus of each embodiment, the pattern image on the mask is sequentially exposed and transferred to each shot area on the single wafer through the projection optical system. Is done. Then, in step 304, after the photoresist on the one lot of wafers is developed, in step 305, etching is performed on the one lot of wafers using the resist pattern as a mask. As a result, a circuit pattern corresponding to the pattern on the mask is formed in each shot area on each wafer.

Thereafter, a device such as a semiconductor element is manufactured by forming a circuit pattern of an upper layer and the like. According to the above-described semiconductor device manufacturing method, a semiconductor device having an extremely fine circuit pattern can be obtained with high throughput. In steps 301 to 305, a metal is vapor-deposited on the wafer, a resist is applied on the metal film, and the respective steps of exposure, development, and etching are performed. Prior to forming a silicon oxide film on the wafer in advance, it is needless to say that a resist may be applied on the silicon oxide film, and each step of exposure, development, etching and the like may be performed. Further, in the exposure apparatus of each embodiment, a liquid crystal display device as a micro device can be obtained by forming a predetermined pattern (circuit pattern, electrode pattern, etc.) on a plate (glass substrate). . Hereinafter, an example of the technique at this time will be described with reference to the flowchart in FIG. In FIG. 8, in a pattern forming step 401, a so-called photolithography step is performed in which a pattern of a mask is transferred and exposed to a photosensitive substrate (a glass substrate coated with a resist or the like) using the exposure apparatus of each embodiment. Is executed. By this photolithography process, a predetermined pattern including a large number of electrodes and the like is formed on the photosensitive substrate. Thereafter, the exposed substrate is subjected to various processes such as a developing process, an etching process, a resist stripping process, etc., so that a predetermined pattern is formed on the substrate, and the process proceeds to the next color filter forming process 402. Next, in the color filter forming step 402, a large number of sets of three dots corresponding to R (Red), G (Green), and B (Blue) are arranged in a matrix, or R, G , B. A plurality of sets of three stripe filters are arranged in the horizontal scanning line direction to form a color filter. Then, after the color filter forming step 402, a cell assembling step 403 is performed. In the cell assembling step 403, the substrate having the predetermined pattern obtained in the pattern forming step 401, the color filter obtained in the color filter forming step 402, and the like are used. Assemble the liquid crystal panel (liquid crystal cell). In the cell assembling step 403, for example, between the substrate having a predetermined pattern obtained in the pattern forming step 401 and the color filter obtained in the color forming step 402, for example. Injects liquid crystal to manufacture liquid crystal panels (liquid crystal cells).

 Thereafter, in a module assembling step 404, components such as an electric circuit and a pack light for performing a display operation of the assembled liquid crystal panel (liquid crystal cell) are attached to complete a liquid crystal display element. According to the above-described method for manufacturing a liquid crystal display element, a liquid crystal display element having an extremely fine circuit pattern can be obtained with high throughput.

In each of the above embodiments, the present invention is applied to the projection optical system mounted on the exposure apparatus. However, the present invention is not limited to this, and may be applied to other general optical systems. The present invention can also be applied. Further, in the embodiments described above, but using a 1 9 3 nm F ₂ laser primary light source for supplying wavelength light A r F excimer laser primary light source and 1 5 7 nm supplying wave wavelength light of which However, the present invention is not limited to this. For example, an Ar laser light source that supplies light having a wavelength of 126 nm can be used. Industrial applicability; As described above, according to the present invention, even when a birefringent crystal material such as fluorite is used, good optical performance is obtained without being substantially affected by birefringence. It is possible to realize an optical system having Therefore, by incorporating the optical system of the present invention into an exposure apparatus, a good microdevice can be manufactured by high-precision projection exposure through a high-resolution projection optical system.

Claims

The scope of the claims 1. In an optical system including a plurality of crystal optical elements formed of crystals belonging to the cubic system,  The plurality of crystal optical elements include: a crystal optical element having a first crystal axis set to substantially coincide with an optical axis of the optical system; and a second crystal axis different from the first crystal axis corresponds to the optical axis. With a crystal optical element set to substantially match,  In the plurality of crystal optical elements Gj, a direction of a predetermined crystal axis in a plane perpendicular to the optical axis is an angle P about the optical axis with respect to a direction of a predetermined axis in the plane. j  For a specific light ray passing through the plurality of crystal optical elements Gj, an angle formed by the specific light ray with the direction of the optical axis is 0 j, and an angle formed by the specific light ray with the direction of the predetermined axis is Φ. j, and when the optical path length of the specific light beam is L j, the physical property constant α of the crystal, a crystal axis substantially coincident with the optical axis, the angle pj, the angle 0 j, and the angle Φ j and a first evaluation amount R j for a first predetermined polarization determined from the optical path length L j and a second evaluation amount S j for a second predetermined polarization are defined, and the plurality of crystal optics A first total evaluation amount ∑R j, which is a total sum of the first evaluation amounts R j for the elements, and a second total sum, which is a total sum of the second evaluation amounts S j for the plurality of crystal optical elements. The evaluation amount ∑S j is a result of focusing on at least one arbitrary point on the image plane or the object plane of the optical system. Optical system, characterized in that the light in the light beam in a predetermined relationship. 2. In the optical system according to claim 1,  The first evaluation amount Rj is optical path length change information for the first predetermined polarization, and the second evaluation amount Sj is optical path length change information for the second predetermined polarization. An optical system characterized by the above. 3. In the optical system according to claim 1 or 2, The predetermined relationship is such that the sum of the first evaluation amounts Rj is substantially equal to light rays in an imaged light beam condensed on at least any one point on the image plane or the object plane of the optical system. A relationship that the second total evaluation value ∑S j is substantially equal for light rays in an imaged light beam converged at at least one point on the image plane or the object plane of the optical system; and The sum of the evaluation amounts Rj and the second total evaluation amount ∑Sj are substantially equal to each other with respect to the light rays in the imaged light flux converged on at least any one point on the image plane or the object plane of the optical system. An optical system characterized by including at least one of equal relationships. 4. In the optical system according to any one of claims 1 to 3, wherein the optical axis is substantially equal to a crystal axis [1 1 1] or a crystal axis optically equivalent to the crystal axis. In the crystal optical element Gj set to match, the predetermined crystal axis is a crystal axis [110] or a crystal axis optically equivalent to the crystal axis, and co j = (i) j — ί) j, the first evaluation amount R j and the second evaluation amount S j are  R j = a X L j X [56X {l-cos (40 j)}  -32AT2Xsin (40 j) X sin (3 ω])] No 192  S j = a X L j X [32X {l-cos (20 j)}. 5. The optical system according to any one of claims 1 to 4, wherein the optical axis substantially matches the crystal axis [001] or a crystal axis optically equivalent to the crystal axis. In the crystal optical element Gj set as above, the predetermined crystal axis is a crystal axis [110] or a crystal axis optically equivalent to the crystal axis, and when ω〗 = φ〗 1 pj, The first evaluation amount R j and the second evaluation amount S j are  Rj = aXLjX {卜 cos (40j)} X {-84—12Xcos (4coj)} / 192  S j = a X L j X {l-cos (20 j)} X {-48 + 48 X cos (4ω))} / 192 An optical system represented by the following formulas: 6. The optical system according to any one of claims 1 to 5, wherein the optical axis substantially matches a crystal axis [01 1] or a crystal axis optically equivalent to the crystal axis. In the crystal optical element Gj set to perform the above, the predetermined crystal axis is a crystal axis [100] or a crystal axis optically equivalent to the crystal axis. The first evaluation amount R j and the second evaluation amount S j are:  R j = a X L j X [{l-cos (40 j)} X {21-9Xcos (4ω j) -84Xcos (ω] ')}  + 96Xcos (2coj)] / 192  Sj = aXLjX [U—cos (20j)} X {12 + 36Xcos (4 oj) + 48Xcos (2coj)}  — 96Xcos (2 j)] / 192  An optical system represented by the following formulas: 7. The optical system according to any one of claims 1 to 6, wherein the physical property constant of the crystal is a crystal axis in a crystal forming each crystal optical element Gj. 11] Or, of light traveling in the direction of the crystal axis optically equivalent to the crystal axis, refraction of light having a polarization direction in the direction of the crystal axis [100] or the crystal axis optically equivalent to the crystal axis. the difference between the rate _n 100, the a crystal axis [0 1 1] or refractive index n 0 1 1 light is the refractive index of the light having the polarization direction in the direction of the crystal axis and optically equivalent to the crystal axis An optical system, characterized in that: 8. In the optical system according to any one of claims 1 to 7, wherein the wavelength of light is λ, the first total evaluation amount ∑ R j and the second total evaluation The absolute value of the difference from the quantity ∑S j is set to be smaller than λ Z 2 with respect to the light beam in the imaging light beam condensed at least at any one point on the image plane or the object plane of the optical system. An optical system characterized in that: 9. In the optical system according to any one of claims 1 to 8, when a wavelength of light is λ, a difference between the first total evaluation amount ∑R j and a predetermined value Is focused on at least one point on the image plane or object plane of the optical system. An optical system, wherein light rays in an image forming light beam are set to be smaller than λ / 2. 10. In the optical system according to any one of claims 1 to 9, when a wavelength of light is λ, a difference between the second total evaluation amount ∑S j and a predetermined value The absolute value of is set to be smaller than λΖ2 for a light ray in an imaged light beam converged on at least one arbitrary point on an image plane or an object plane of the optical system. 1 1. In an optical system including a plurality of crystal optical elements formed of crystals belonging to the cubic system,  光 (と is an integer of 3 or more) crystal optical elements set so that the optical axis and the crystal axis [1 1 1] or a crystal axis optically equivalent to the crystal axis substantially coincide with each other, The crystal optical elements have a crystal axis in a plane substantially perpendicular to the optical axis. [0] An optical system characterized in that directions of crystal axes optically equivalent to the crystal axes have a rotational positional relationship about (120 / Μ) degrees apart from each other about the optical axis. 12. In the optical system according to claim 11,  Further comprising Ν (Ν is an integer of 3 or more) crystal optical elements set so that the optical axis and the crystal axis [001] or a crystal axis optically equivalent to the crystal axis substantially coincide with each other,  The three crystal optical elements may have a crystal axis [100] in a plane perpendicular to the optical axis or a direction of a crystal axis optically equivalent to the crystal axis, which is substantially (互 い に) relative to the optical axis. 90ZN) An optical system characterized by having a rotational positional relationship separated by degrees. 13. In the optical system according to claim 11 or 12, The optical axis and the crystal axis [01 1] or the crystal axis optically equivalent to the crystal axis are substantially Further including L (L is an integer of 3 or more) crystal optical elements set to match,  The L crystal optical elements may have a crystal axis in a plane perpendicular to the optical axis or a crystal axis optically equivalent to the crystal axis. 180 / L) An optical system characterized by having a rotational positional relationship separated by degrees. 14. In the optical system according to any one of claims 11 to 13,  Further comprising P (P is an integer of 2 or more) crystal optical elements set so that the optical axis and the crystal axis [011] or the crystal axis optically equivalent to the crystal axis substantially coincide with each other;  The P crystal optical elements may be arranged such that directions of crystal axes in a plane perpendicular to the optical axis [100] or crystal axes optically equivalent to the crystal axes are substantially equal to each other about the optical axis. (90ZP) An optical system having a rotational positional relationship separated by degrees. 15. In an optical system including a plurality of crystal optical elements formed of crystals belonging to the cubic system,  N (N is an integer of 3 or more) crystal optical elements set so that the optical axis and the crystal axis [001] or the crystal axis optically equivalent to the crystal axis substantially coincide with each other. ,  The N crystal optical elements may have a crystal axis [100] in a plane perpendicular to the optical axis or a direction of a crystal axis optically equivalent to the crystal axis. 90ZN) An optical system characterized by having a rotational positional relationship separated by degrees. 16. In the optical system according to claim 15, L (L is an integer of 3 or more) crystal optical elements further set so that the optical axis and the crystal axis [011] or the crystal axis optically equivalent to the crystal axis are further included, The L crystal optical elements may have a crystal axis in a plane perpendicular to the optical axis or a crystal axis optically equivalent to the crystal axis. 180 / L) An optical system characterized by having a rotational positional relationship separated by degrees. 17. In the optical system according to claim 15 or 16,  P (P is an integer of 2 or more) crystal optical elements further set so that the optical axis and the crystal axis [01 1] or the crystal axis optically equivalent to the crystal axis are further included. ,  The P crystal optical elements may have a crystal axis [100] in a plane perpendicular to the optical axis or a direction of a crystal axis optically equivalent to the crystal axis. 90 / P) An optical system having a rotational positional relationship separated by degrees. 18. In an optical system including a plurality of crystal optical elements formed of crystals belonging to the cubic system,  L (L is an integer of 3 or more) crystal optical elements set so that the optical axis and the crystal axis [01 1] or the crystal axis optically equivalent to the crystal axis substantially coincide with each other; The L crystal optical elements may have a crystal axis [100] in a plane perpendicular to the optical axis or a crystal axis optically equivalent to the crystal axis. / L) An optical system characterized by having a rotational positional relationship separated by degrees. 19. The optical system according to claim 18, wherein  P (P is an integer of 2 or more) crystal optical elements further set so that the optical axis and the crystal axis [01 1] or the crystal axis optically equivalent to the crystal axis are further included. ,  The P crystal optical elements may be arranged such that directions of crystal axes in a plane perpendicular to the optical axis [100] or crystal axes optically equivalent to the crystal axes are substantially equal to each other about the optical axis. (90 / P) An optical system having a rotational positional relationship separated by degrees. 20. The optical system according to any one of claims 1 to 19, wherein the crystal is a calcium fluoride crystal or a barium fluoride crystal. 2 1. An illumination system for illuminating the mask,  An optical system according to any one of claims 1 to 20 for forming an image of a pattern formed on said mask on a photosensitive substrate. Exposure equipment. 22. An exposure step of exposing the pattern of the mask to the photosensitive substrate using the exposure apparatus according to claim 21,  A developing step of developing the photosensitive substrate exposed in the exposing step.