WO2020207768A1 - Imaging optical unit for imaging an object field into an image field, and projection exposure apparatus comprising such an imaging optical unit - Google Patents

Abstract

An imaging optical unit (7) for a projection exposure apparatus is used to image an object field (4) into an image field (8). The projection exposure apparatus is embodied in such a way that a rectangular structuring field on an object to be imaged, which carries structures to be imaged, is imaged in the entirety thereof into an imaging field by displacement of the structuring field relative to the object field, said imaging field being displaced relative to the image field in a manner synchronized with the object displacement. The structuring field lies within a larger object specification field. The latter is defined by an object carrying the structures to be imaged and delimited by a rectangular specification field basic shape and convexly curved specification field corner regions. The object field (4) is spanned by two perpendicular field directions (x, y). The imaging optical unit (7) has a first reduction scale in the first field direction (x), which is given by a ratio of the extent in the first field direction (x) of, firstly, the structuring field and, secondly, the imaging field. The imaging optical unit (7) has a second reduction scale in the second field direction (y), which is given by a ratio of the extent in the second field direction (y) of, firstly, the structuring field and, secondly, the imaging field. The reduction scales and are chosen in such a way that an area of the structuring field is no more than 10% smaller than the area of the largest, rectangular Pareto structuring field which can be fitted into the object specification field. This results in an imaging optical unit with a well-corrected imageable field with, at the same time, a high imaging light throughput.

Description

Imaging optical unit for imaging an object field into an image field, and projection exposure apparatus comprising such an imaging optical unit

The content of the German Patent Application DE 10 2019 205 271.1 is incorporated by reference herein.

The invention relates to an imaging optical unit for a projection exposure apparatus for imaging an object field into an image field. Further, the invention relates to a method for designing such an imaging optical unit, an optical system of such an imaging optical unit and an illumination optical unit for illuminating the object field which is imageable with the imaging optical unit, a projection exposure apparatus comprising such an optical system, a method for producing a microstructured or nanostructured component using such a projection exposure apparatus and a microstructured or nanostructured component part produced by this method.

Projection optical units of the type set forth at the outset are known from US 2016/0085061 Al, DE 10 2012 202 675 Al, DE 10 2009 011 328 Al, US 8 027 022 B2 and US 6 577 443 B2. An illumination optical unit for a projection exposure apparatus is known from DE 10 2009 045 096 Al.

It is an object of the present invention to develop an imaging optical unit of the type set forth at the outset so that this results in a well-corrected imageable field with, at the same time, a high imaging light throughput.

According to the invention, this object is achieved by an imaging optical unit comprising the features specified in Claim 1.

According to the invention, it was recognized that an imaging optical unit or projection optical unit with specifiable reduction scales in the two field directions offers a degree of freedom which can be used to optimize the field dimensions ratios while taking account of, firstly, the actual area to be imaged on the object and, secondly, the field dimensions required on the image side. Here, it was recognized that, in particular, the form of an object specification field, including the rounded comer regions thereof, needs to be taken into account for the purposes of optimizing the imaging optical unit. The reduction scales of the imaging optical unit are specified with the aid of a Pareto criterion. It is possible to consider those field aspect ratios that can no longer be increased in one direction without having to accept losses in the other field direction. Perfect Pareto-optimality is not required in order to meet, where necessary, practical additional requirements, which may still be present; instead, all that is required is that the area of the structuring field deviates from a Pareto-optimized area by less than 10%. The deviation of the area of the structuring field from an area of a Pareto structuring field can be less than 8%, can be less than 5%, can be less than 3%, or else can be less than 2%.

The reduction scale specifies the factor by which the imaging optical unit reduces the image field, proceeding from the respective object field dimension. By way of example, in the case of a reduction scale of 4 in the first field direction, an object field that has an extent of 100 mm in this first field direction is imaged into an image field that has an extent of 25 mm in the same field direction.

The imaging optical unit is regularly embodied as an anamorphic optical unit.

The imaging optical unit can be embodied as a catoptric optical unit.

Integer reduction scale ratios according to Claim 2 render it possible to proceed from already known designs of imaging optical units and, for example, only adapt the imaging scale for one field direction.

Specifying a reduction scale ratio according to Claim 3 allows scaling of the imaging optical unit.

Embodiments of the imaging field according to Claim 4 and of the object specification field according to Claims 5 and 6 have proven their worth.

The advantages of a design method according to Claim 7 correspond to those that have already been explained above with reference to the imaging optical unit according to the invention. An inclusion of necessary auxiliary areas (Claim 8) and/or unavoidable stop-shadowed areas (Claim 9) according to Claims 8 and 9 improves the specification of the reduction scale ratio for the projection optical unit.

The advantages of an optical system according to Claims 10 to 12, a projection exposure apparatus according to Claim 13 or 14, a production method according to Claim 15 and a microstructured or nanostructured component produced therewith correspond to those which have already been explained above with reference to the imaging optical unit and the production method thereof.

In particular, a semiconductor component, for example a memory chip, can be produced using the projection exposure apparatus.

Exemplary embodiments of the invention are explained in greater detail below with reference to the drawing. In said drawing:

Fig. 1 schematically shows a projection exposure apparatus for EUV microlithography;

Fig. 2 shows, in a meridional section, an embodiment of an imaging optical unit which can be used as a projection lens in the projection exposure apparatus according to Figure 1, wherein an imaging beam path for chief rays and for an upper coma ray and a lower coma ray of three selected field points is depicted;

Fig. 3 shows a view of the imaging optical unit, as seen from the viewing direction III in Figure 2;

Fig. 4 shows a view of a first section of the imaging optical unit in the imaging beam path, as seen from the viewing direction IV in Figure 2;

Fig. 5 shows a view of a last section of the imaging optical unit in the imaging beam path, as seen from the viewing direction V in Figure 2; Fig. 6 to 15 show plan views of mirrors Ml to M10 of the imaging optical unit, illustrated in the sequence in which these mirrors reflect imaging light in the imaging beam path;

Fig. 16 to 85 show, in illustrations similar to Figures 2 to 15, further embodiments of imaging optical units that are usable in place of the imaging optical unit according to Figures 2 to 14 in the projection exposure apparatus according to Figure 1;

Fig. 86 shows a plan view of an embodiment of a reticle to be imaged by the projection exposure apparatus;

Fig. 87 to 91 show corresponding plan views of further embodiments of reticles to be imaged;

Fig. 92 shows a plan view of an imaging field of the projection exposure apparatus;

Fig. 93 to 95 show corresponding plan views of further embodiments of imaging fields of the projection exposure apparatus;

Fig. 96 shows a plan view of a used region of the reticle of one of the embodiments according to Figures 86 to 91 with different embodiments of object fields with different aspect ratios x/y inscribed in this used region;

Fig. 97 shows a diagram of a dependence between reduction scales b_c and b_n that are admissible for reticle imaging when an aspect ratio x/y of the used region of the reticle is taken into account, wherein Pareto-optimal reduction scales [b_c, b_n] assigned to one another are highlighted;

Fig. 98 shows, in a diagram similar to Figure 97, the Pareto-optimal reduction scales for various combinations of, firstly, reticle used regions and, secondly, imaging field dimensions; Fig. 99 shows, in an illustration similar to Figure 96, a plan view of a used region of a reticle to be imaged with an inscribed, rectangular object field and an additional illustration of the areas provided for the arrangement of auxiliary structures, which lie outside of the object field and within the used region;

Fig. 100, 101 show, in an illustration similar to Figure 99 in each case, further arrangement variants of the object field and of auxiliary areas for auxiliary structures within a reticle used region;

Fig. 102 shows, in an illustration similar to Figure 98, Pareto-optimal reduction scale assignments [b_c, b_n] for various combinations of object field aspect ratios and image field aspect ratios while taking account of area required for reticle auxiliary regions corresponding to those illustrated in Figures 99 to 101;

Fig. 103 shows a schematic plan view of a reticle to be imaged with an object field to be imaged that is defined by a stop boundary;

Fig. 104 shows the reticle with the object field to be imaged and the stops delimiting the latter (reticle masking stops), which act along the two object field dimensions x and y;

Fig. 105 shows a schematic section along a light path of the imaging light in the region of an edge portion of a reticle to be imaged, wherein beam-limiting and beam- influencing components for a light beam of the imaging light are shown schematically;

Fig. 106 schematically shows the consequences of the shadowing effect of the reticle masking stops for the reticle;

Fig. 107 shows, in an illustration similar to Figure 100, the used region of the reticle when the shadowing effect of the reticle masking stops are additionally taken into account; and Fig. 108 shows, in an illustration similar to Figures 98 and 102, Pareto-optimal pairs of reduction scales [b_c, b_n] for the respective combinations of, firstly, reticle embodiments and, secondly, image field dimension embodiments while the shadowing effect of the reticle masking stops is additionally taken into account.

A microlithographic projection exposure apparatus 1 comprises a light source 2 for illumination light or imaging light 3. The light source 2 is an EUV light source, which produces light in a wavelength range of, for example, between 5 nm and 30 nm, in particular between 5 nm and 15 nm. In particular, the light source 2 can be a light source with a wavelength of 13.5 nm or a light source with a wavelength of 6.7 nm. Other EUV wavelengths are also possible. In general, the illumination light 3 guided in the projection exposure apparatus 1 could even have any desired wavelength, for example visible wavelengths or else other wavelengths which may find use in microlithography (e.g. DUV, deep ultraviolet) and for which suitable laser light sources and/or LED light sources are available (e.g. 365 nm, 248 nm, 193 nm, 157 nm, 129 nm, 109 nm). A beam path of the illumination light 3 is illustrated very schematically in Figure 1.

An illumination optical unit 6 is used to guide the illumination light 3 from the light source 2 to an object field 4 in an object plane 5. Using a projection optical unit or imaging optical unit 7, the object field 4 is imaged into an image field 8 in an image plane 9 with a specified, possibly anamorphic reduction scale.

In order to facilitate the description of the projection exposure apparatus 1 and the various embodiments of the projection optical unit 7, a Cartesian xyz-coordinate system is indicated in the drawing, from which system the respective positional relationship of the components illustrated in the figures is evident. In Figure 1, the x-direction runs perpendicular to the plane of the drawing into the latter. The y-direction runs towards the left, and the z-direction runs upward.

The object field 4 and the image field 8 have a partial ring shape. Alternatively, it is also possible for the object field 4 and the image field 8 to have a different bent or curved embodiment, or else the rectangular embodiment. The object field 4 and the image field 8 have an x/y-aspect ratio of greater than 1. Therefore, the object field 4 has a longer object field dimension in the x-direction and a shorter object field dimension in the y-direction. These object field dimensions extend along the field coordinates x and y.

One of the exemplary embodiments depicted in Figures 2 et seq. can be used for the projection optical unit 7. The projection optical unit 7 according to Figures 2 to 15 has an anamorphic embodiment. In the yz-plane, i.e., in the meridional plane of the section according to Figure 2, the projection optical unit 7 has a reduction scale b_g of -8.10. In the meridional plane yz, the object field 4 is thus imaged onto the image field 8 with a reduction by a non-integer factor of 8.1 and, moreover, there is an image inversion on account of an even number of intermediate image planes between the object plane at 5 and the image plane 9 such that a negative value for p_y arises. A reduction scale b_c of the projection optical unit 7 is 4.00 in the sagittal plane xz, which is perpendicular to the meridional plane. In this plane xz, the object field 4 is thus imaged onto the image field 8 with a reduction by an integer factor of 4 and without an image inversion on account of an odd number of intermediate image planes between the object plane 5 and the image plane 9 such that a positive value for b_c arises. Other integer or non-integer reduction scales b_c, b_g are also possible, as will still be explained below on the basis of the further exemplary embodiments according to Figures 16 et seq.

The image field 8 has an x-extent of 26 mm and a y-extent of 1.6 mm. The image field has a partial ring shape, with field boundaries of the image field extending along the first field direction having a radius of curvature of 80 mm.

In the embodiments of the projection optical unit 7 according to Figures 2 and 5 et seq., the image plane 9 is arranged parallel to the object plane 5. What is imaged in this case is a portion of a reflection mask 10, also referred to as reticle, coinciding with the object field 4. The reticle

10 is carried by a reticle holder 10a. The reticle holder 10a is displaced by a reticle displacement drive 10b.

The imaging by way of the projection optical unit 7 is implemented on the surface of a substrate

11 in the form of a wafer, which is carried by a substrate holder 12. The substrate holder 12 is displaced by a wafer or substrate displacement drive 12a. Figure 1 schematically illustrates, between the reticle 10 and the projection optical unit 7, a beam 13 of the illumination light 3 that enters into said projection optical unit and, between the projection optical unit 7 and the substrate 11, a beam 14 of the illumination light 3 that emerges from the projection optical unit 7. An image field-side numerical aperture (NA) of the projection optical unit 7 is not reproduced to scale in Figure 1.

The projection exposure apparatus 1 is of the scanner type. Both the reticle 10 and the substrate 11 are scanned in the y-direction during the operation of the projection exposure apparatus 1. A stepper type of the projection exposure apparatus 1, in which a stepwise displacement of the reticle 10 and of the substrate 11 in the y-direction is effected between individual exposures of the substrate 11, is also possible. These displacements are effected synchronously or in synchronized fashion with one another by an appropriate actuation of the displacement drives 10b and 12a.

Figure 2 shows the optical design of a first embodiment of the projection optical unit 7. Figure 2 depicts the beam path of, in each case, three individual rays 15 emanating from three object field points which are spaced apart from one another in the y-direction in Figure 2. What is depicted are chief rays 16, i.e., individual rays 15 which pass through the centre of a pupil in a pupil plane of the projection optical unit 7, and, in each case, an upper coma ray and a lower coma ray of these two object field points. Proceeding from the object field 4, the chief rays 16 include an angle CRAO of 5.05° with a normal on the object plane 5.

The projection optical unit 7 has an image-side numerical aperture of 0.55.

The different object-side numerical apertures in the meridional section and in the sagittal section, which correlate with the different reduction scales b_c, b_n, can be gathered from a comparison of Figures 2 (meridional section) and 4 (sagittal view). In the sagittal view, the object-side numerical aperture is more than twice as large as in the meridional section.

The projection optical unit 7 according to Figure 2 has a total of ten mirrors, which are numbered consecutively by Ml to M10 in the order of the beam path of the individual rays 15, proceeding from the object field 4. An imaging optical unit 7 could also have a different number of mirrors, for example four mirrors, six mirrors or eight mirrors. An odd number of mirrors is also possible.

The calculated reflection surfaces of the mirrors Ml to M10 are depicted in some of Figures 2 to 15. As is evident from the illustration according to Figure 2, for example, only a portion of these calculated reflection surfaces is used. At least this actually used region of the reflection surfaces, shown in Figures 6 to 15, for example, is in fact present in the real mirrors Ml to M10. These used reflection surfaces are carried by mirror bodies in a manner known per se.

In the case of the projection optical unit 7 according to Figure 2, the mirrors Ml, M9 and M10 are embodied as normal incidence mirrors, i.e., as mirrors on which the imaging light 3 strikes with an angle of incidence of less than 45°. Overall, the projection optical unit 7 according to Figure 2 thus has three normal incidence mirrors Ml, M9 and M10.

The mirrors M2, M3, M4, M5, M6, M7 and M8 are mirrors for grazing incidence of the illumination light 3, i.e., mirrors on which the illumination light 3 is incident with angles of incidence of greater than 45° and, in particular, of greater than 60°. A typical angle of incidence of the individual rays 15 of the imaging light 3 on the mirrors M2 to M8 for grazing incidence lies in the region of 80°. Overall, the projection optical unit 7 according to Figure 2 has exactly seven mirrors M2 to M8 for grazing incidence.

The mirrors M2 to M8 reflect the imaging light 3 in such a way that the angles of reflection of the individual rays 15 at the respective mirrors M2 to M8 add up, i.e., lead to an amplification of the deflection effect thereof.

The mirrors M2 to M8 for grazing incidence each have large absolute values for the radius, i.e., they have a relatively small deviation from a plane surface. These mirrors M2 to M8 contribute to a specific imaging aberration correction and, in particular, to a local imaging aberration correction.

A deflection direction is defined below on the basis of the respectively depicted meridional sections for the purposes of characterizing a deflecting effect of the mirrors of the projection optical unit 7. As seen in the respective incident beam direction in the meridional section, for example according to Figure 2, a deflecting effect of the respective mirror in the clockwise direction, i.e., a deflection to the right, is denoted by the abbreviation“R”. By way of example, the mirror M2 of the projection optical unit 7 has such a deflecting effect“R”. A deflecting effect of a mirror in the anticlockwise direction, i.e., to the left as seen from the beam direction respectively incident on this mirror, is denoted by the abbreviation“L”. The mirror Ml of the projection optical unit 7 is an example for the“L” deflecting effect. A weakly deflecting effect, or an effect that does not deflect at all, of a mirror with a folding angle f, for which the following applies: -1° <f < 1°, is denoted by the abbreviation“0”. The mirror M9 of the projection optical unit 7 is an example for the“0” deflecting effect. Overall, the projection optical unit 7 for the mirrors Ml to M10 has the following sequence of deflecting effects: LRRRRRRROR.

In principle, all described exemplary embodiments of the projection optical units can be mirrored about a plane extending parallel to the xz-plane without this changing fundamental imaging properties in the process. However, this naturally then changes the sequence of deflecting effects, which has the following sequence in the case of a projection optical unit which emerges by appropriate mirroring from the projection optical unit 7: RLLLLLLLOL.

The mirrors Ml to M10 carry a coating that optimizes the reflectivity of the mirrors Ml to M10 for the imaging light 3. Here, this can be a ruthenium coating, a molybdenum coating, an alternating molybdenum-silicon coating, an alternating molybdenum-silicon coating with an uppermost layer made of ruthenium or a molybdenum coating with an uppermost layer made of ruthenium. A coating comprising for example a layer of molybdenum or ruthenium can be used in the case of the grazing incidence mirrors M2 to M8. These highly reflecting layers, in particular of the mirrors Ml, M9 and M10 for normal incidence, can be configured as multi-ply layers, wherein successive layers can be manufactured from different materials. Alternating material layers can also be used. A typical multi-ply layer can have fifty bilayers, respectively made of a layer of molybdenum and a layer of silicon. The bilayers may have an aperiodic and/or a spatially dependent embodiment. The multi-ply layer may also be provided with protective layers, e.g., to counter mechanical, optical and/or chemical damage, or with diffusion stop layers in addition to used layers, i.e., layers that contribute to the reflection of the imaging light 3. For the purposes of calculating an overall reflectivity of the projection optical unit 7, a system transmission is calculated as follows: A mirror reflectivity is determined at each mirror surface on the basis of the angle of incidence of a guide ray, i.e., a chief ray of a central object field point, and combined by multiplication to form the system transmission.

Further information concerning the system transmission can be found in US 2016/0085061 Al.

Further information concerning reflection at a GI mirror (grazing incidence mirror) can be found in WO 2012/126867 A. Further information concerning the reflectivity of NI mirrors (normal incidence mirrors) can be found in DE 101 55 711 A.

An overall reflectivity or system transmission of the projection optical unit 7, which emerges as a product of the reflectivities of all mirrors Ml to M10 of the projection optical unit 7, is R = 7.7%.

The mirror M10, that is to say the ultimate mirror upstream of the image field 8 in the imaging beam path, has a passage opening 17 for the passage of the imaging light 3 which is reflected from the antepenultimate mirror M8 toward the penultimate mirror M9. The mirror M10 is used in a reflective manner around the passage opening 17. None of the other mirrors Ml to M9 has a passage opening and said mirrors are used in a reflective manner in a continuous region without gaps.

A stop AS is disposed in the imaging beam path between the mirrors M9 and M10, said stop having both the function of an aperture stop and the function of an obscuration stop. Thus, the stop AS firstly specifies the image-side numerical aperture of the projection optical unit 7 and secondly specifies the size of an inner pupil obscuration. The stop AS may also have a non contiguous embodiment.

The mirrors Ml to M10 are thus embodied as free-form surfaces which cannot be described by a rotationally symmetric function. Other embodiments of the projection optical unit 7, in which at least one of the mirrors Ml to M10 is embodied as a rotationally symmetric asphere, are also possible. It is also possible for all mirrors Ml to M10 to be embodied as such aspheres.

A free-form surface can be described by the following free-form surface equation (Equation 1):

+ C_lx + C₂y

+ C₃x² + C₄xy + C₅y²

+ C₆x³ + ... + C₉y³

+ C₁₀x⁴ + ... + C₁₂x²y² + ... + C₁₄y⁴

+ Ci₅x⁵ + ... + C₂₀y⁵

+ C₂₁x⁶ + ... + C₂₄x³y³ + ... + C₂₇y⁶

+ ...

(1)

The following applies to the parameters of this Equation (1): Z is the sagittal height of the free-form surface at the point x, y, where x² + y² = r². Here, r is the distance from the reference axis of the free-form surface equation

(x = 0; y = 0).

In the free-form surface Equation (1), Ci, C2, C3... denote the coefficients of the free-form surface series expansion in powers of x and y.

In the case of a conical base area, c_x, c_y is a constant corresponding to the vertex curvature of a corresponding sphere or asphere. Thus, c_x = 1/R_X and c_y = 1/R_y applies. k_x and k_y each correspond to a conical constant of a corresponding asphere. Thus, Equation (1) describes a biconical free-form surface. An alternative possible free-form surface can be produced from a rotationally symmetric reference surface. Such free-form surfaces for reflection surfaces of the mirrors of projection optical units of microlithographic projection exposure apparatuses are known from

US 2007-0058269 Al.

Alternatively, free-form surfaces can also be described with the aid of two-dimensional spline surfaces. Examples for this are Bezier curves or non-uniform rational basis splines (NURBS). By way of example, two-dimensional spline surfaces can be described by a grid of points in an xy- plane and associated z-values, or by these points and gradients associated therewith. Depending on the respective type of the spline surface, the complete surface is obtained by interpolation between the grid points using e.g. polynomials or functions which have specific properties in respect of the continuity and the differentiability thereof. Examples for this are analytical functions.

The optical design data of the reflection surfaces of the mirrors Ml to M10 of the projection optical unit 7 can be gathered from the following tables.

The first of these tables indicates vertex radii (Radiusx = R_x, Radiusy = R_y) and refractive power values (Powerx, Powery) for the optical surfaces of the optical components. Negative radii values denote curves that are concave towards the incident illumination light 3 at the intersection of the respective surface with the considered plane (xz, yz) that is spanned by a surface normal at the vertex with the respective direction of curvature (x, y). The two radii Radiusx, Radiusy may explicitly have different signs.

The vertices at each optical surface are defined as points of incidence of a guide ray which travels from an object field centre to the image field 8 along a plane of symmetry x = 0, i.e., the plane of the drawing of Figure 2 (meridional plane).

The refractive powers Powerx (P_x), Powery (P_y) at the vertices are defined as: _p _ 2 cos AOI

-

R_x

P = _ ?

y R y cos AOI

Here, AOI denotes an angle of incidence of the guide ray with respect to the surface normal.

The second table specifies the absolute value along which the respective mirror, proceeding from a reference surface, was decentred (D_y) in the y-direction, displaced (D_z) in the z-direction and tilted (a_x, a _. a_z). This corresponds to a parallel shift and a tilting in the case of the free-form surface design method. Here, a displacement is carried out along the y-direction and in the z- direction in mm, and tilting is carried out about the x-axis, about the y-axis and about the z-axis. In this case, the angle of rotation is specified in degrees. Decentring is carried out first, followed by tilting. The reference surface during decentring is in each case the first surface of the specified optical design data. Decentring in the y-direction and in the z-direction is also specified for the object field 4 (reticle). In addition to values assigned to the individual mirrors Ml to M10, this table also tabulates the object plane (reticle) as a first surface, the image plane (wafer) as an ultimate surface and a stop surface (denoted“stop”) as an arrangement plane for an aperture or obscuration stop.

The third table (Tables 3a to 3d) specifies the free-from surface coefficients C_n, respectively assigned to the polynomials x^k, y¹, for the mirrors Ml to M10. Coefficients C_n not tabulated each have a value of 0.

The fourth table specifies a boundary of the stop AS as a polygonal chain with N corners in local coordinates xyz. As described above, the stop is still decentred and tilted. Each row of the table specifies the coordinates of two polygonal corners, specifically of the point i and of the point i+N/2; expressed differently, the table is constructed in such a way that the two front columns have to be read from top to bottom and subsequently the two back columns have to be read from top to bottom.

Design data for the projection optical unit 7 with b_c = 4.00 and b_n = -8.10 Radii of the surfaces

RadiuS_x [mm] Power_x [1/mm] RadiuS_y [mm] Power_y [1/mm]

M01 -2155.29067785 0.00090708 -1360.16999579 0.00143734

M02 3088.63828999 -0.00011852 2632.04913940 -0.00013908

M03 2206.18993200 -0.00020553 -12503.78911686 0.00003626

M04 4094.16026291 -0.00009915 -8480.50613920 0.00004787

MO 5 -2112.63330655 0.00015809 -6112.82860111 0.00005464

M06 -930.07779041 0.00050052 -1837.61415658 0.00025333

M07 -759.40005725 0.00062139 18904.99392265 -0.00002496

MO 8 -1102.08162137 0.00048299 -5063.33369895 0.00010513

M09 1135.47023088 -0.00176138 314.39500683 -0.00636142

M10 -784.21274557 0.00253055 -718.88926505 0.00276049

Table 1 for Figure 2 Decentring (location, angle) the surfaces

D_x [mm] D_y [mm] l)_z [mm]

Reticle 0.000000000 2219.192642536 2300.991309649

M01 0.000000000 2072.094075772 619.646997872

M02 0.000000000 1779.251257647 1453.632551257

M03 0.000000000 1552.292739112 1719.915881109

M04 0.000000000 1192.846272958 1875.093827415

M05 0.000000000 799.725476332 1874.614838497

M06 0.000000000 166.006879888 1652.736739305

M07 0.000000000 -63.342524559 1413.441066080

M08 0.000000000 -129.812975755 1188.894098961

M09 0.000000000 147.735193235 106.368269562

Stop 0.000000000 109.604596583 256.158826042

M10 0.000000000 0.000000000 686.724695889

Wafer 0.000000000 0.000000000 0.000000000

Reticle 0.000000000 0.000000000 0.000000000

M01 7.174019540 180.000000000 0.000000000

M02 -60.105176620 0.000000000 0.000000000

M03 -36.454454545 0.000000000 180.000000000

M04 -11.640353045 0.000000000 0.000000000

MO 5 9.683012830 0.000000000 180.000000000 M06 32.756023490 0.000000000 0.000000000

M07 59.863005545 0.000000000 180.000000000

MO 8 88.945226730 0.000000000 0.000000000

M09 14.331060692 180.000000000 0.000000000

Stop 1.550202611 180.000000000 0.000000000

M10 7.140923508 0.000000000 0.000000000

Wafer 0.000000000 0.000000000 0.000000000

Table 2 for Figure 2

Free-form coefficients of the surfaces

Coefficient Formula M01 M02 M03

C7 x 2 y 1.7010571816e-08 -5.7421934582e-08 1.8511452905e-07

C9 3

y 1.5818583604e-09 -5.4479900983e-07 3.4637403526e-07

CIO X⁴ -6.7178934013e-12 2.7166871239e-10 7.3400243648e-10

C12 x² y² 3.5002224146e-l 1 -2.2400427398e-l 1 3.4713729577e-10

C14 y⁴ -1.2415798183e-10 2.0966593039e-09 -1.6478579447e-10

C16 x 4 y 7.6673982659e-16 -4.2008062875e-13 1.9292420047e-12

C18 x 2 y 3 8.7205577223e-14 1.3261388712e-12 3.7358191436e-13

C20 y -1.0583874588e-13 -9.7129821976e-12 2.8962356182e-12

C21 x⁶ -1.1549417272e-18 -3.6726340828e-17 5.0950634390e-16

C23 x⁴ y² -3.7362526432e-17 1.2842067865e-15 3.3515426307e-15

C25 x y⁴ -9.4246366936e-17 -8.0898345277e-15 1.0824010077e-15

C27 .6

y -4.6157931961e-16 4.7278561709e-14 -4.0950654427e-16

C29 x⁶ y 4.0170098189e-21 7.7046496902e-19 5.1154794745e-18

C31 x⁴ y³ -1.1138535602e-19 -2.6519581650e-18 6.6205074434e-18

C33 x² y⁵ -1.7291566060e-19 4.7339164059e-17 8.9670407205e-18

C35 y⁷ 6.4130942494e-19 -2.2749748482e-16 3.8142374390e-17

C36 x⁸ 7.4711889972e-24 -2.6081748965e-21 8.8503821496e-21

C38 x⁶ y² 9.9458447059e-24 6.6874958380e-21 1.4493124897e-20

C40 x⁴ y⁴ 5.6424490309e-22 2.562276948 le-20 1.4785866601e-20

C42 x² y⁶ 2.4928105523e-21 -2.3887468848e-19 2.6118610441e-20

C44 y⁸ -7.0275752780e-21 1.0397634858e-18 4.5570681700e-20

C46 x⁸ y 5.1131189353e-28 -4.1610273541e-23 -4.3922204289e-23

C48 x⁶ y³ 1.9225636966e-25 -3.7493504981e-22 -7.7643245004e-23

C50 x⁴ y⁵ -6.5804507949e-25 -5.7801737354e-22 -2.4772269939e-22

C52 x² y⁷ 2.7904407894e-23 8.1116914928e-22 -1.0097331743e-21

C54 9

y -9.5915218325e-24 -5.0922969220e-21 -5.2690508685e-23

C55 X¹⁰ -2.8693100147e-28 2.3371902724e-25 -7.4401731427e-25

C57 x⁸ y² -6.6138941956e-28 2.2754225124e-25 -1.2339758591e-24 C59 x⁶ y⁴ -3.9498024952e-26 1.9833396129e-26 -1.1231565864e-24

C61 x⁴ y⁶ -3.3357793308e-25 -1.5153075321e-25 -5.9639885400e-25

C63 x² y⁸ -4.073197621 le-25 -6.6097199039e-24 -1.7351524427e-24

C65 yio 1.0794966161e-24 3.5287209458e-23 -2.0970685903e-24

C67 x¹⁰ y -3 4906008288e-31 2.1022118653e-27 -2.2337530422e-27

C69 x⁸ y³ -9.6016929612e-30 2.3643642112e-26 1.1096397973e-26

C71 x⁶ y⁵ -7.9235313430e-30 5.8750544594e-26 1.7962573228e-26

C73 x 4 y 7 -5.4608206967e-28 5.4452321133e-26 6.5247652135e-26

C75 x 2 y 9 -4.713398926 le-27 1.0341914257e-25 1.9264569749e-25

C77 11

y -8.2439799454e-28 -2.4030017510e-25 1.0654164412e-25

C78 x¹² 5.483343143 le-33 -9.6973286792e-30 3.7771231463e-29

C80 x¹⁰ y² 8.0930393635e-33 -2.2335435165e-29 8.1601305406e-29

C82 x⁸ y⁴ 7.1531436188e-31 -4.4204429325e-29 1.3146746645e-28

C84 x⁶ y⁶ 1.0207667361e-29 2.5336276433e-29 1.2134343047e-28

C86 x⁴ y⁸ 4.2628507278e-29 -2.7924047093e-29 3.1041037656e-28

C88 x² y¹⁰ 1.7850310712e-29 -6.6200528532e-28 7.4931891293e-28

C90 y¹² -1.3382658524e-28 6.0287802684e-28 4.8181116069e-28

C92 x¹² y 1.5136653275e-35 -6.8749921124e-32 4.3723563283e-31

C94 x¹⁰ y³ 2.2480370978e-34 -9.2113221459e-31 -6.3791574381e-31

C96 x⁸ y⁵ 7.1776867460e-34 -3.2222103640e-30 -1.5996533573e-30

C98 x⁶ y⁷ 7.0664235987e-33 -5.2709952147e-30 -1.0376031741e-30

CIOO x⁴ y⁹ 8.7277851298e-32 -2.7747463548e-30 -8.6989798991e-30

C102 x² y^{1 1} 3.7088263456e-31 2.3400866736e-31 -1.6841078827e-29

C104 13

y -5.7722520790e-32 4.3896862438e-30 -6.4990529026e-30

C105 x¹⁴ -5.9357340457e-38 2.1781161018e-34 -6.9465402094e-34

C107 x¹² y² -9.1865231136e-38 9.7722048466e-34 -2.1787589763e-33

C109 x¹⁰ y⁴ -6.5339659731e-36 4.1408543527e-33 -7.7429651374e-33 cm x⁸ y⁶ -1.4200320685e-34 4.2432876918e-33 -8.1129856612e-33

Cl 13 x⁶ y⁸ -1.0083844464e-33 5.9430245922e-33 -1.001956371 le-32 Cl 15 x⁴ y¹⁰ -2.7303977530e-33 2.5405922762e-33 -4.7952010120e-32 Cl 17 x 2 y 12 6.3264291506e-37 1.0382175646e-32 -8.2767836596e-32 Cl 19 y¹⁴ 8.1220342923e-33 -1.9323344327e-32 -3.5695974450e-32 C121 x¹⁴ y -1.654055469 le-40 1.1359723695e-36 -1.6722263138e-35 C123 x¹² y³ -2.2613447234e-39 1.8248453168e-35 1.5040434535e-35 C125 x¹⁰ y⁵ -9.9981671970e-39 8.1654541562e-35 7.4234945440e-35 C127 x⁸ y⁷ -6.0948561388e-38 2.0445219427e-34 1.3666822151e-35 C129 x⁶ y⁹ -7.1324719765e-37 1.8528485174e-34 8.3226354269e-35 C131 x⁴ y^{1 1} -4.7139010347e-36 5.8742562556e-35 5.6970977505e-34 C133 x² y¹³ -1.3202567950e-35 4.2104541698e-35 7.6590166103e-34 C135 15

y 6.9831976310e-36 -2.1934609676e-34 2.5258918591e-34

C136 x¹⁶ 3.3467364619e-43 -2.4427341481e-39 -3.2843630009e-39

C138 x¹⁴ y² 8.7852957414e-43 -1.9972590380e-38 1.6413387542e-38

C140 x¹² y⁴ 2.9461102032e-41 -1.2581887687e-37 2.3658963787e-37

C142 x¹⁰ y⁶ 9.4427458519e-40 -2.9009537654e-37 3.8517841399e-37

C144 x⁸ y⁸ 9.3338923756e-39 -5.1275717140e-37 -3.9897248612e-39

C146 x⁶ y¹⁰ 4.3102127913e-38 -2.3969303198e-37 8.7082176158e-37

C148 x⁴ y 8.5752946584e-38 1.5351896021e-37 3.3476930080e-36

C150 x 2 y 14 -2.7916937622e-38 -7.8140936546e-37 4.3103138489e-36

C152 yl6 -2.5434092773e-37 2.0918439384e-36 1.4624401255e-36

C154 x¹⁶ y 5.9514085560e-46 -7.5237093735e-42 2.0428290895e-40

C156 x¹⁴ y³ 8.2825754628e-45 -1.4257550343e-40 -1.1242779842e-40

C158 x¹² y⁵ 4.2602157026e-44 -7.7884268616e-40 -1.1703720457e-39

C160 x¹⁰ y⁷ 2.7548643548e-43 -2.6699230707e-39 -3.985471651 le-40

C162 x⁸ y⁹ 2.2309519658e-42 -4.0907951551e-39 1.6782220829e-40

C164 x⁶ y^{1 1} 1.9391077974e-41 -3.7127016622e-39 -2.7712559844e-39

C166 x⁴ y¹³ 8.5698699286e-41 -2.3430466603e-39 -1.4253560159e-38

C168 x² y¹⁵ 1.7560184509e-40 3.1311771334e-39 -1.2880760133e-38

C170 17

y -1.6838979454e-40 -6.7218612334e-39 -3.3543050400e-39

C171 x¹⁸ -7.6505777723e-49 1.0611780850e-44 1.6220297530e-43

C173 x¹⁶ y² -3.4759169954e-48 1.5567037473e-43 1.5554472763e-43

C175 x¹⁴ y⁴ -5.0154497068e-47 1.2715585349e-42 -2.7842993659e-42

C177 x¹² y⁶ -2.4823542473e-45 4.5230227990e-42 -7.6231745892e-42

C179 x¹⁰ y⁸ -3.0397034102e-44 1.1005168599e-41 2.4217278415e-42

C181 x⁸ y¹⁰ -2.0090028875e-43 1.3913565114e-41 -2.4793432596e-42

C183 x⁶ y¹² -6.5778040458e-43 9.824908638 le-42 -2.5450810484e-41

C185 x⁴ y¹⁴ -1.0926346677e-42 4.7541557373e-42 -8.8582078606e-41

C187 x² y¹⁶ 6.7198733421e-43 -4.2696721110e-42 -7.9014463673e-41

C189 18

y 3.2613148198e-42 7.8387013954e-42 -2.1420888580e-41

Table 3 a for Figure 2

Coefficient Formula M04 M05 M06

C7 x 2 y 6.0341343808e-08 -8.5203527164e-08 2.0419794537e-07

C9 y 3 -6.3580458959e-08 -1.0167379181e-07 -1.9836055306e-08

CIO X⁴ 1.0026577731e-10 -1.3661478730e-10 -3.6302186255e-10

C12 x² y² 3.2596409071e-l 1 -1.7760997272e-10 3.9776648452e-l 1

C14 y⁴ -1.5858055519e-10 -7.8495552930e-l 1 -3.0188785500e-10

C16 x 4 y 1.5054235742e-13 -3.741670221 le-13 -2.4885844668e-13

C18 x 2 y 3^J 4.5683620837e-13 -5.6538020720e-14 3.5155340895e-14 C20 y -3.1874312473e-13 -9.1113788091e-14 1.2600547735e-12

C21 x⁶ -8.1848627831e-16 -6.9811117315e-16 -4.1239283734e-16

C23 x⁴ y² -4.5524269912e- 16 -1.4960955868e-16 -3.1490636056e-16

C25 x y⁴ 6.3192266919e-16 -5.2172377674e-17 -2.3207730308e-15

C27 y⁶ - 1.2209610740e- 15 1.7127008628e-16 -5.4410838424e-16

C29 x⁶ y 3.3108501819e- 18 -1.4803878632e-18 -3.3656376392e-19

C31 x⁴ y³ 5.1430394401e-20 -1.0541948277e-18 1.2212381781 e- 18

C33 x² y⁵ 4.9871935087e-18 1.2954515547e-18 -5.6937966717e-18

C35 7

y -4.0994128989e-18 1.3349430858e-18 9.6445459536e-18

C36 X 6.2084555126e-20 3.1278588157e-21 -5.8446421369e-21

C38 x⁶ y² -7.8564539750e-21 3.8087965223e-21 -1.2884164434e-20

C40 x⁴ y⁴ -1.8937319269e-20 8.4858388230e-21 3.1849601731e-21

C42 x² y⁶ -1.0558727153e-20 4.2228545052e-21 1.4400506882e-20

C44 y -3.8217868797e-20 -9.8504966838e-21 -8.7238650278e-20

C46 x⁸ y -4.8230289914e-23 3.2315949415e-22 7.6846667305e-23

C48 x⁶ y³ 2.9757811576e-22 1.2169225595e-22 1.8695663170e-22

C50 x⁴ y⁵ 2.9194844803e-22 6.2960743257e-23 2.8391982891e-22

C52 x² y⁷ 1.1110132296e-22 -7.4150823212e-23 1.2772848224e-21

C54 9

y 3.8453706796e-22 -1.5046784210e-22 3.6719189473e-23

C55 X¹⁰ -3.6546888678e-24 -4.4560152756e-25 4.4634377561e-25

C57 x⁸ y² 1.9150549716e-25 -6.2094140884e-25 6.3344928709e-25

C59 x⁶ y⁴ -2.0313342357e-25 -5.6278811763e-25 1.3201006014e-24

C61 x⁴ y⁶ 2.4357141550e-24 -1.3204079178e-25 -6.2424622070e-24

C63 x² y⁸ 5.8989961507e-25 -2.8502409723e-25 -7.4844629866e-24

C65 yio 3.0346126717e-24 1.566628700 le-24 -6.0532573605e-25

C67 x¹⁰ y 1.2130985426e-26 -2.4542519148e-26 -5.5404719543e-27

C69 x⁸ y³ -2.2987658166e-26 -1.3087625087e-26 -1.9320293801e-26

C71 x⁶ y⁵ -4.9931776085e-26 -3.9235774884e-27 -1.3051622341e-27

C73 x 4 y 7 -1.9804084178e-26 -1.260706533 le-26 -5.0280495962e-26

C75 x 2 y 9 -2.6040919705e-27 1.1178413574e-26 -1.1930427849e-25

C77 11

y -5.3382179389e-26 7.2758898590e-27 1.9109902289e-26

C78 x¹² 5.5835984399e-29 1.5020830077e-29 -2.0164590392e-29

C80 x¹⁰ y² -2.0328904626e-29 4.9788145366e-29 -3.0350282355e-30

C82 x⁸ y⁴ 1.4873783966e-28 4.4757878681e-29 -1.1034737240e-28

C84 x⁶ y⁶ -9.6430766058e-29 -1.1313899657e-29 2.6604598740e-28

C86 x⁴ y⁸ -2.2898887435e-28 -2.8445865107e-29 1.1819010246e-27

C88 x² y¹⁰ 1.7173111219e-29 1.8865397661e-30 8.6359397904e-28

C90 y¹² -2.4122665049e-28 -1.1087494422e-28 1.7190792446e-28

C92 x¹² y -9.6340701054e-31 1.1901845532e-30 2.5769726748e-31 C94 x¹⁰ y³ 8.6829254019e-31 8.4007341165e-31 1.3178120084e-30

C96 x⁸ y⁵ 3.5318027885e-30 1.4981111699e-32 -2.6039081605e-31

C98 x⁶ y⁷ 4.1390245010e-30 5.1554499498e-31 -3.2179540289e-30

CIOO x⁴ y⁹ 8.2406207493e-31 9.4116479671e-31 6.5089383430e-30

C102 x² y^{1 1} 4.9072633550e-31 -9.3509703779e-31 7.6766240802e-30

C104 13

y 4.1573906866e-30 -7.8783550268e-32 -1.8175443171e-30

C105 x¹⁴ 3.6908546879e-33 -4.8804466263e-34 6.0888241705e-34

C107 x¹² y² 2.4956067132e-33 -2.3773068238e-33 -1.6996027847e-33

C109 x¹⁰ y⁴ -1.3526587571e-32 -2.0020269554e-33 2.3484428805e-33 cm x⁸ y⁶ -6.3950662738e-33 -2.9590919344e-34 9.2450475366e-34

Cl 13 x⁶ y⁸ 3.3833129903e-33 3.6398007429e-33 -4.7956685585e-32 Cl 15 x⁴ y¹⁰ 9.0394454684e-33 1.6633589974e-33 -9.8387173791e-32 Cl 17 x 2 y 12 -4.5684487357e-33 1.3117510490e-33 -6.0986227418e-32 Cl 19 y¹⁴ 5.9350512022e-33 3.9641782220e-33 -1.3775337421e-32 C121 x¹⁴ y 3.4801802705e-35 -3.0350365762e-35 -6.0531148708e-36 C123 x¹² y³ -1.1371549397e-35 -2.7109215364e-35 -4.6587139561e-35 C125 x¹⁰ y⁵ - 1.0628477137e-34 -2.2480511955e-36 -2.3463817205e-35 C127 x⁸ y⁷ -1.9232693217e-34 2.5413494306e-36 3.0059399107e-34 C129 x⁶ y⁹ -1.6729724065e-34 -3.1568130749e-35 1.8448811292e-34 C131 x⁴ y^{1 1} 1.3342753546e-36 -3.0540126001e-35 -3.9042239852e-34 C133 x² y¹³ -2.3578434401e-35 3.9570249713e-35 -2.5284687381e-34 C135 15

y -1.7301634196e-34 -6.4073415882e-36 9.7627629609e-35 C136 x¹⁶ -1.8956574653e-37 1.5331747927e-38 -1.2343655712e-38 C138 x¹⁴ y² -1.4099492358e-37 6.1082739560e-38 7.4178896685e-38 C140 x¹² y⁴ 5.1124606346e-37 2.0473751463e-38 1.0869422872e-37 C142 x¹⁰ y⁶ 3.7662225187e-37 9.1246944167e-38 -3.0113199201e-37 C144 x⁸ y⁸ 5.2003842539e-37 -1.4793185822e-37 -2.6887380934e-37 C146 x⁶ y¹⁰ 5.4285572523e-38 -1.1114460864e-37 2.5353760690e-36 C148 x⁴ y -2.3048464363e-37 -2.3407654875e-38 4.1012561833e-36 C150 x 2 y 14 2.0528014110e-37 -9.9824185858e-38 2.2242246848e-36 C152 yl6 1.4307657768e-37 -5.3788497908e-38 5.4953584304e-37 C154 x¹⁶ y -4.7257358905e-40 3.1134715899e-40 5.6346915218e-41 C156 x¹⁴ y³ -3.1259455852e-41 3.3638899381e-40 6.2495386334e-40 C158 x¹² y⁵ 1.2231751625e-39 1.1508687091e-40 1.0759964071e-39 C160 x¹⁰ y⁷ 2.7297864877e-39 -2.1195040034e-40 -5.1397269669e-39 C162 x⁸ y⁹ 4.1149053670e-39 2.2178247336e-40 -1.2542643680e-38 C164 x⁶ y^{1 1} 2.7516933736e-39 4.555598743 le-40 -9.2448396932e-40 C166 x⁴ y¹³ -5.4470981989e-40 4.1655717207e-40 8.1191609651e-39 C168 x² y¹⁵ 5.7355620922e-40 -6.4848469755e-40 3.5147846664e-39 C170 17

y 2.9666257616e-39 1.7562008012e-40 -1.9605266157e-39

C171 x¹⁸ 2.6057955405e-42 -2.0327276126e-43 1.1679531016e-43

C173 x¹⁶ y² 2.7435302503e-42 -6.4286481304e-43 -9.6350975554e-43

C175 x¹⁴ y⁴ -7.5845817896e-42 2.4259459984e-43 -3.7733936384e-42

C177 x¹² y⁶ -4.2436257084e-42 -1.4320259515e-42 2.1328557630e-42

C179 x¹⁰ y⁸ -1.5344983693e-41 2.2536456688e-43 3.1566165152e-41

C181 x⁸ y¹⁰ -1.1245286809e-41 2.9837631195e-42 2.4795012140e-41

C183 x⁶ y¹² -6.4972621674e-42 1.0882633301e-42 -5.2394068784e-41

C185 x⁴ y¹⁴ 4.5929419759e-42 -3.3378252988e-43 -7.2968183762e-41

C187 x² y¹⁶ -3.9804401942e-42 2.2167054228e-42 -3.2149713453e-41

C189 18

y -7.4348868990e-42 -7.6657461128e-44 -1.0030776141e-41

Table 3b for Figure 2

Coefficient Formula M07 M08 M09

C7 x 2 y -1.4980098630e-07 2.6469813246e-07 1.5029816183e-06

C9 y 3 -4.3281552572e-07 -1.7411591110e-07 -8.026472128 le-07

CIO x⁴ 4.8598950600e-l 1 1.9356450688e-10 1.3104790693e-09

C12 x² y² -1.2394647234e-09 - 1.0447081821 e- 10 5.4506337450e-09

C14 y⁴ 2.3422570235e-09 -4.9611709777e-10 2.4158231622e-09

C16 x 4 y 4.1723748049e-13 6.1679291247e-13 8.1351144822e-12

C18 x 2 y 3^J -1.3813436729e-13 1.9004541505e-13 2.5169645914e-13

C20 y -4.519877931 le- 12 -2.3885478526e-12 -1.2145275471e-l 1

C21 x⁶ 1.5881692122e- 16 8.4049245781 e- 16 7.1897509291e-15

C23 x⁴ y² 2.7910318881e-15 3.2166200248e-15 4.6357596714e-14

C25 x y⁴ -2.8765055883e-14 -4.9874650813e- 16 9.0058955521e-14

C27 y⁶ 4.4759629640e-14 - 1.2954651676e- 14 1.3985464303e-13

C29 x⁶ y 2.6206404813e-18 8.6256863678e-18 5.7629354681e-17

C31 x⁴ y³ 5.4691792509e-17 2.0686813359e-17 1.2096289019e-16

C33 x² y⁵ -2.6648397103e- 16 -9.2339989533e-18 2.0451863373e-16

C35 y⁷ -8.6994736745e- 16 -7.4240359355e- 17 -7.4283563648e-16

C36 x⁸ 1.0030783487e-20 -8.4055387551e-20 3 4846478267e-20

C38 x⁶ y² -1.1276879423e-19 -3.0522408643e-19 5.0082790971e-19

C40 x⁴ y⁴ 2.1607163521e-18 -1.2728075115e-19 1.8460059532e-18

C42 x² y⁶ 6.7989686950e-18 -2.2492437270e-19 8.3809451304e-19

C44 y⁸ -2.9995669677e-17 -4.9706688506e-19 -2.1770027255e-18

C46 x⁸ y 1.1513290664e-22 - 1.2401734578e-21 5.0925189295e-22

C48 x⁶ y³ -8.7812569150e-21 -4.7332639845e-21 3.3525891351e-21

C50 x⁴ y⁵ -4.7301775959e-21 -1.0452472612e-21 8.2222628455e-21

C52 x² y⁷ 4.4278838843e-19 -4.4942014609e-21 -2.522509740 le-20 C54 9

y 3.3360645013e-19 -4.3768545597e-21 -1.7752544067e-20

C55 X¹⁰ -1.2094289571e-24 1.5465862891e-23 6.6516381385e-25

C57 x⁸ y² 9.5045625474e-24 9.0659624601e-23 2.1340031442e-24

C59 x⁶ y⁴ -2.4171560310e-22 7.1741275380e-23 9.3353026334e-24

C61 x⁴ y⁶ -2.4036396072e-21 1.6983960825e-23 2.1283359391e-23

C63 x² y⁸ -3.7302849965e-21 -2.6948334498e-23 4.2965186504e-22

C65 yio 2.9980085550e-20 -3.0809331544e-23 9.2430987794e-22

C67 x¹⁰ y -2.1532677603e-28 1.4172711108e-25 1.458793491 le-26

C69 x⁸ y³ 8.4257825961e-25 1.2077742773e-24 5.7571662973e-26

C71 x⁶ y⁵ 7.3790595984e-25 7.0690956072e-25 -6.7913923435e-25

C73 x 4 y 7 -2.7945200138e-24 1.5213236313e-25 -3.5833147159e-24

C75 x 2 y 9 -4.7076232072e-22 3.5420318951e-25 -2.9974026503e-25

C77 11

y 2.3438538378e-22 -6.2675163908e-26 5.4714156336e-24

C78 x¹² 6.5847917098e-29 -1.6573159205e-27 -8.2324373987e-30

C80 x¹⁰ y² 4.0224088390e-29 -1.3242664994e-26 4.8444684293e-28

C82 x⁸ y⁴ 1.8270199965e-26 -1.9851213322e-26 2.7733479198e-27

C84 x⁶ y⁶ 1.8109269376e-25 -1.2914225167e-28 -1.7410976703e-27

C86 x⁴ y⁸ 1.9795273135e-24 1.0601778558e-27 -4.0168770668e-26

C88 x² y¹⁰ -1.5811838950e-24 5.0835199082e-27 -1.0714716376e-25

C90 y¹² -1.2587218626e-23 2.7720178576e-28 -1.2180437487e-25

C92 x¹² y -7.3784737092e-31 -8.6661612275e-30 -5.6728270166e-31

C94 x¹⁰ y³ -4.6994999310e-29 -1.3502948674e-28 -3.9643174553e-30

C96 x⁸ y⁵ 5.8732290100e-29 -1.6967140008e-28 1.9748462012e-29

C98 x⁶ y⁷ -1.2800609274e-27 2.9885802863e-29 3.2106008091e-28

CIOO x⁴ y⁹ 1.1578415800e-26 -9.9606176662e-30 9.5898208683e-28

C102 x² y^{1 1} 2.4013413081e-25 -1.2702802775e-29 3.7550173150e-28

C104 13

y -2.8400731767e-25 -9.8582742961e-30 -1.1464312413e-27

C105 x¹⁴ -2.356084560 le-33 1.0757433378e-31 -4.1284274059e-34

C107 x¹² y² -4.0142746390e-32 1.0458338654e-30 -2.5264351334e-32

C109 x¹⁰ y⁴ -1.044489986 le-30 3.0162384552e-30 -2.3050975710e-31 cm x⁸ y⁶ -3.722972999 le-30 3.6833269289e-31 -4.3896621482e-31

Cl 13 x⁶ y⁸ -1.4796162278e-28 -1.2230166578e-31 3.2544266349e-30 Cl 15 x⁴ y¹⁰ -6.4951433758e-28 -3.7629537828e-31 1.3914733138e-29 Cl 17 x 2 y 12 1.9969491162e-27 -6.0393719510e-31 2.0078594150e-29 Cl 19 y¹⁴ 1.4560741818e-27 -1.9108989726e-31 1.5647775551e-29 C121 x¹⁴ y 4.0005818647e-35 3.0081860540e-34 2.0847058316e-35 C123 x¹² y³ 1.4103155934e-33 7.0930058017e-33 2.5639335291e-34 C125 x¹⁰ y⁵ -5.9397937696e-33 1.5936433953e-32 7.0388022575e-34 C127 x⁸ y⁷ 4.1338002978e-32 1.8066231390e-34 -9.3000503001e-33 C129 x⁶ y⁹ 2.1673891205e-31 -7.5489310260e-33 -5.2474560862e-32

C131 x⁴ y^{1 1} -5.5175575275e-30 -1.2028000036e-33 -1.1884261080e-31

C133 x² y¹³ -5.9377090314e-29 -4.4244264612e-33 -6.2921630741e-32

C135 15

y 9.9491097684e-29 -1.3892754945e-33 9.9151546329e-32

C136 x¹⁶ 5.9367921705e-38 -3.9086954302e-36 3.6329466957e-38

C138 x¹⁴ y² 1.8976437184e-36 -4.0451692540e-35 8.5468148430e-37

C140 x¹² y⁴ 3.5151371590e-35 -2.1405687091e-34 1.0585778930e-35

C142 x¹⁰ y⁶ -1.8316637013e-35 -7.6884844109e-35 4.3624777450e-35

C144 x⁸ y⁸ 3.2270129032e-33 -1.8447784938e-36 -1.6342541582e-35

C146 x⁶ y¹⁰ 4.3044774475e-32 -2.7904315078e-35 -6.7987598347e-34

C148 x⁴ y 7.2570491167e-32 2.3163712124e-35 -1.6097820672e-33

C150 x 2 y 14 -6.4687202284e-31 -1.3333424159e-35 -1.6118012545e-33

C152 yl6 4.5344808377e-31 -5.195789673 le-36 -1.1983990815e-33

C154 x¹⁶ y -6.6264507430e-40 -4.9794816089e-39 -2.3464519916e-40

C156 x¹⁴ y³ -1.7410292873e-38 -1.3987824925e-37 -4.2720727668e-39

C158 x¹² y⁵ 1.3773673673e-37 -5.1265638169e-37 -3.0755990155e-38

C160 x¹⁰ y⁷ -4.9189261656e-37 -1.7512245875e-37 6.9924646229e-38

C162 x⁸ y⁹ -2.6640577835e-36 3.8528501056e-37 9.7477696086e-37

C164 x⁶ y^{1 1} -2.0391086112e-35 1.3369205398e-37 3.0735516765e-36

C166 x⁴ y¹³ 8.8874281456e-34 1.8412399524e-37 6.0237312343e-36

C168 x² y¹⁵ 5.5058449350e-33 -1.2094752114e-38 3.7504230635e-36

C170 17

y -1.1770314976e-32 -9.9269678282e-39 -3.3500707128e-36

C171 x¹⁸ -7.5562867445e-43 6.1671204254e-41 -5.9574078217e-43

C173 x¹⁶ y² -2.8449309406e-41 5.6390122836e-40 -1.0888720256e-41

C175 x¹⁴ y⁴ -4.8188730677e-40 5.6774018316e-39 -1.7750493757e-40

C177 x¹² y⁶ 8.5604731416e-40 3.5644673045e-39 -1.0762569406e-39

C179 x¹⁰ y⁸ -1.8612269583e-38 1.0632555615e-39 -1.8087723428e-39

C181 x⁸ y¹⁰ -5.3757808576e-37 1.7279617198e-39 6.4783855619e-39

C183 x⁶ y¹² -4.3424625115e-36 6.260967535 le-40 4.2322993908e-38

C185 x⁴ y¹⁴ 2.3285538399e-36 3.8566171091e-40 5.7867732944e-38

C187 x² y¹⁶ 6.7999660807e-35 9.4531088469e-42 3.9370084467e-38

C189 18

y -1.0260980068e-34 -7.6043594479e-42 3.8220262598e-38

Table 3 c for Figure 2

Coefficient Formula M10

C7 x 2 y -1.2073199536e-08

C9 y 3 8.7782631399e-09

CIO X⁴ -2.1135859437e-l l

C12 x² y² -5.9834662932e-l 1 C14 y⁴ -1.3443430600e-l 1

C16 x 4 y -2.9899827344e-14

C18 x 2 3 -7.7448726568e-15

C20 y 1.2440729856e-14

C21 x⁶ -4.4201857012e-17

C23 x⁴ y² -1.7313252068e-16

C25 x y⁴ -1.5606453698e-16

C27 y⁶ -3.5492462087e- 17

C29 x⁶ y -5.2425950879e-20

C31 x⁴ y³ -6.0978501628e-20

C33 x² y⁵ -2.5207395989e-22

C35 7

y 1.9021989274e-20

C36 X -8.4617143390e-23

C38 x⁶ y² -3.9214991493e-22

C40 x⁴ y⁴ -6.0342325722e-22

C42 x² y⁶ -3.6677879525e-22

C44 y -6.1826088446e-23

C46 x⁸ y -7.6533590184e-26

C48 x⁶ y³ -2.0917182905e-25

C50 x⁴ y⁵ -1.5388135872e-25

C52 x² y⁷ 1.8107516367e-26

C54 9

y 5.103484904 le-26

C55 X¹⁰ -1.0798352267e-28

C57 x⁸ y² -1.0006063556e-27

C59 x⁶ y⁴ -2.2510577007e-27

C61 x⁴ y⁶ -2.2611988333e-27

C63 x² y⁸ - 1.0213726748e-27

C65 yio -1.7451446659e-28

C67 x¹⁰ y -2.5053804319e-31

C69 x⁸ y³ -3.3639027166e-31

C71 x⁶ y⁵ -2.3000585068e-31

C73 x 4 y 7 4.6317972303e-31

C75 x 2 y 9 2.6835066549e-31

C77 11

y -7.582766784 le-32

C78 x¹² -3.1957253510e-34

C80 x¹⁰ y² 2.1076467863e-34

C82 x⁸ y⁴ 2.5118635339e-33

C84 x⁶ y⁶ 4.0800565250e-33

C86 x⁴ y⁸ 2.4148743334e-33 C88 x² y¹⁰ 6.7649691548e-34

C90 y¹² -7.3285702529e-35

C92 x¹² y 4.1657376875e-37

C94 x¹⁰ y³ -2.3864950004e-36

C96 x⁸ y⁵ -3.4192095510e-36

C98 x⁶ y⁷ -6.7106223870e-36

CIOO x⁴ y⁹ -6.7653046130e-36

C102 x² y^{1 1} -4.7693438708e-37

C104 13

y 8.0612200336e-37

C105 x¹⁴ -5.0147801591e-40

C107 x¹² y² -1.7146117047e-38

C109 x¹⁰ y⁴ -7.7170881957e-38 cm x⁸ y⁶ -1.5311406942e-37

Cl 13 x⁶ y⁸ -1.4636329649e-37 Cl 15 x⁴ y¹⁰ -7.5885325789e-38 Cl 17 x 2 y 12 -2.1535993122e-38 Cl 19 y¹⁴ -1.4838695167e-39 C121 x¹⁴ y -2.4269767687e-42 C123 x¹² y³ 4.794340969 le-42 C125 x¹⁰ y⁵ - 1.7838892399e-42 C127 x⁸ y⁷ 4.9226302038e-42 C129 x⁶ y⁹ 3.6310829513e-41 C131 x⁴ y^{1 1} 3.1353343502e-41 C133 x² y¹³ 1.5961567122e-43 C135 15

y -2.3278985886e-42 C136 x¹⁶ 7.3524059733e-46 C138 x¹⁴ y² 4.8410529570e-44 C140 x¹² y⁴ 2.8284757370e-43 C142 x¹⁰ y⁶ 7.4368326210e-43 C144 x⁸ y⁸ 9.5483041876e-43 C146 x⁶ y¹⁰ 6.4376977153e-43 C148 x⁴ y 2.4364807196e-43 C150 x 2 y 14 5.2354676832e-44 C152 yl6 1.6845564149e-45 C154 x¹⁶ y 1.1016160767e-48 C156 x¹⁴ y³ -2.5273940801 e-47 C158 x¹² y⁵ -3.6737179978e-47 C160 x¹⁰ y⁷ -3.3476988649e-47 C162 x⁸ y⁹ -8.5930637599e-47 C164 x⁶ y^{1 1} -1.2641835179e-46

C166 x⁴ y¹³ -5.9732349227e-47

C168 x² y¹⁵ 8.3341314710e-48

C170 17

y 4.6335184158e-48

C171 x¹⁸ -4.9179114747e-51

C173 x¹⁶ y² -1.1208115428e-49

C175 x¹⁴ y⁴ -6.7377189315e-49

C177 x¹² y⁶ -2.0781632568e-48

C179 x¹⁰ y⁸ -3.4411161488e-48

C181 x⁸ y¹⁰ -3.2793070904e-48

C183 x⁶ y¹² -1.8142307618e-48

C185 x⁴ y¹⁴ -5.999574359 le-49

C187 x² y¹⁶ - 1.1594044702e-49

C189 18

y -5.9942768045e-51

Table 3d for Figure 2

Coordinate of the stop edge

Xi [mm] yi [mm] Xi+N/2 [mm] yi+N/2 [mm]

-98.425261 152.247682 104.405530 169.191778

-77.494319 160.719730 91.448280 174.175335

-63.042003 165.204932 70.517339 180.653960

-48.589686 168.693422 47.094619 185.637518

-31.147234 171.683557 24.170254 188.627652

-16.196562 173.178624 4.734380 189.624364

-5.731091 173.676980 -5.232735 189.624364

7.226158 173.676980 -24.170254 188.627652

27.160388 172.181912 -33.639013 187.630941

43.606128 169.690134 -55.566666 184.142450

61.048580 165.703287 -66.530493 181.650672

74.504185 161.716441 -82.477877 177.165470

82.976233 158.726307 -105.402242 168.693422

96.431838 153.244394 -123.343049 160.221374

107.894020 147.762480 -139.788788 150.752615

126.333183 137.297010 -147.264125 145.769057

137.297010 129.821673 -162.214797 134.306875

152.247682 118.359491 -170.188489 127.329895

166.201643 105.402242 -177.663826 119.854558

178.162181 -92.444992 -186.135873 110.385799

189.624364 -77.494319 -194.109565 99.920328 195.604633 -68.523916 -203.079969 85.468011

201.086546 -59.055157 -207.565171 76.995964

206.070103 -49.088042 -212.548728 65.035426

212.050372 -34.635725 -214.542151 59.055157

216.037218 -21.678475 -218.030641 46.097907

218.030641 -13.704783 -220.522420 30.648879

219.525709 -5.232735 -221.020776 23.173542

221.020776 9.717937 -221.020776 10.714649

221.020776 22.675187 -220.024064 -1.245889

219.525709 38.124215 -218.528997 -11.213004

217.532286 48.091330 -214.043795 -28.655456

214.043795 60.550224 -209.558594 -41.114350

208.561882 74.504185 -205.571748 -50.084753

201.086546 88.956502 -197.099700 -66.032137

191.617787 103.408819 -187.132585 -80.982810

186.135873 110.385799 -178.162181 -92.444992

179.158893 118.359491 -169.191778 102.412107

170.686845 126.831539 -162.713153 108.890732

159.224663 136.798654 -153.244394 117.362780

150.752615 143.277279 -137.297010 129.821673

133.310164 154.739461 -121.349626 140.287144

115.369357 164.208220 -113.375934 144.772346

Table 4 for Figure 2

The mirrors Ml, M5, M6, M8 and M10 have negative radius values, i.e., are concave mirrors as a matter of principle. The mirrors M2 and M9 have positive radius values, i.e., are convex mirrors as a matter of principle. The mirrors M3, M4, M7 have R_x, R_y radius values with differing signs in each case, i.e., are each saddle-shaped as a matter of principle.

A boundary of a stop surface of the stop (cf , also, Table 4 for Figure 2) emerges from

intersection points on the stop surface of all rays of the illumination light 3 which, on the image side, propagate at the field centre point in the direction of the stop surface with a complete image-side telecentric aperture. When the stop is embodied as an aperture stop, the boundary is an inner boundary. The stop AS can lie in a plane or else have a three-dimensional embodiment. The extent of the stop AS can be smaller in the scan direction (y) than in the cross-scan direction (x).

Further data of the projection optical unit 7 arise from Table 5 below:

Further design data for the projection optical unit 7 according to Figure 2

Wavelength 13.5 nm

NA 0.55

4.00

bg 8.10

Chief ray angle (CRA) 5.05°

Etendue 12.58 mm²

Mean wavefront aberration RMS 7.32 m l

System transmission 7.68 %

Position of the entry pupil EP (x) -2377.91 mm

Position of the entry pupil EP (y) -2678.36 mm

Object-image offset 2219.19 mm

Working distance between M9 and

81 mm

image field

Reticle tilt 0 0

Installation length 2300.99 mm

Obscuration 18.4 %

Installation space cuboid (790 x 2561 x 1819) mm

Table 5 for Figure 2

The projection optical unit 7 is designed for a wavelength of the illumination light 3 of 13.5 nm.

The value of the etendue arises as the product of the field dimensions of the image field 8 in the two field directions x and y and the square of the image-side numerical aperture.

The mean wavefront aberration RMS is a measure for the imaging quality of the projection optical unit 7.

The negative values for the positions of the entry pupil in Table 5 mean that the entry pupil lies upstream of the object field 4 in the imaging light beam path, both in the xz-plane (EP (x) value) and in the yz-plane (EP (y) value). A positive value for EP(x) or for EP(y) would mean that the entry pupil lies downstream of the object field 4 in the respective plane in the imaging light beam path.

The object-image offset is the y-distance between the centre of the object field 4 and the centre of the image field 8. The corresponding dimension of the object-image offset, dois, is plotted in Figure 2. The object-image offset, dois, is at least approximately identical to the decentring of the reticle relative to the wafer as specified in Table 2; in the case of object and image fields with a partial ring shape, in particular, the exact value of dois depends on the definition of which point of the object field 4 and which point of the image field 8 are considered.

The working distance between the mirror M9 closest to the wafer and the image plane 9 specifies the distance between the used reflection surface of the mirror M9 and the image plane 9.

A reticle tilt of 0° arises on account of the object plane 5 being parallel to the image plane 9.

The installation length is the distance between the object plane 5 and the image plane 9 in the z- direction.

In a system pupil of the projection optical unit 7, an area that cannot be illuminated due to the obscuration by the obscuration stop AS is less than 0.184² of the area of the overall system pupil.

Less than 3.4% of the numerical aperture is obscured as a result of the passage opening 17.

The non-illuminated area within the system pupil can have a different extent in the x-direction than in the y-direction. The non-illuminated area in the system pupil can be round, elliptical, square or rectangular. Moreover, this area in the system pupil which cannot be illuminated can be decentred in the x-direction and/or in the y-direction in relation to a centre of the system pupil.

The mirrors Ml to M10 can be housed in an installation space cuboid with the extents in the x-, y- and z-direction as specified in Table 5. A telecentricity value of the projection optical unit 7, measured in the y-direction over the image field 8, is less than 0.4 mrad.

The projection optical unit 7 is approximately telecentric on the image side.

Further mirror data emerge from the following Table 6.

Ml M2 M3 M4 M5

Maximum angle of 13.9 84.5 80.1 80.6 83.4

incidence [deg]

Minimum angle of incidence [deg] 10.5 74.1 74.2 76.0 77.5

Mirror extent (x) [mm] 640.8 410.7 341.1 294.8 324.8

Mirror extent (y) [mm] 272.2 299.7 265.2 296.8 364.2

Maximum mirror diameter 641.1 355.2 378.2 425.6

[mm] 410.9

Table 6a for Figure 2

M6 M7 M8 M9 M10

Maximum angle of incidence 79.9 81.8 78.0 20.4 8.4

[deg]

Minimum angle of incidence [deg] 73.7 72.2 70.3 0.0 5.1

Viirror extent (x) [mm] 349.7 306.2 234.3 292.1 789.9

Viirror extent (y) [mm] 260.6 119.9 264.3 155.7 767.9

Maximum mirror diameter 351.3 306.3 291.2 292.2 790.2

[mm]

Table 6b for Figure 2

Again, the angles of incidence are specified for the chief rays 16 in each case. For the NI mirrors, the mirror M9 has the largest maximum angle of incidence. It is less than 21°. For the GI mirrors, the mirror M8 has the smallest minimum angle of incidence of 70.3°. Thus, in the projection optical unit 7, the minimum angle of incidence for the chief rays is greater than 70° in each case.

The ultimate mirror M specifying the image-side numerical aperture is the largest, both in the x- and in the y-extent, with both extents in the x and y of the mirror M10 being less than 800 mm. Accordingly, the maximum diameter of the mirror M10 is also less than 800 mm and represents the largest maximum mirror diameter of the projection optical unit 7.

The plan view according to Figure 3 elucidates that the complete reflection surface of the mirror Ml lies at greater y-coordinates than the object field on account of the chief ray angle of 5.05° at the object field. Advantageously, this allows a better separation of illumination optical unit 6 and projection optical unit 7. The reflection surfaces of mirrors M7 and M8 lie at greater y- coordinates than the image field 8. The mirrors Ml and M2 do not overlap in the plan view according to Figure 3.

Figure 4 shows a lateral view of the projection optical unit 7 in the region of a first section of the imaging beam path containing the mirrors Ml to M4. Figure 5 shows, in turn, a lateral view of the last section of the imaging beam path of the imaging optical unit 7, comprising mirrors M6 to M10, as seen from the opposite direction of Figure 4.

Using dashed lines, Figure 5 shows the edge contours of the aperture/obscuration stop AS with a stop body OS and an outer edge. A ring-shaped passage region of the stop AS is present between this inner stop body OS and the outer edge, the inner edge of said passage region specifying the obscuration of the projection optical unit 7 and the outer edge of said passage opening specifying the image-side numerical aperture of the projection optical unit 7.

Figures 6 to 15 show edge contours of the surfaces in each case impinged upon by the illumination light 3 on the mirrors Ml to M10 of the projection optical unit 7, i.e., the so-called footprints of the mirrors Ml to M10. These edge contours are in each case depicted in an x/y- diagram, which corresponds to the local x- and y-coordinates of the respective mirror Ml to M10. Mirrors M4, M5, M8 and M10 have an x/y-aspect ratio that does not deviate, or only deviates slightly, from a value of 1. The mirror M7 has the largest x/y-aspect ratio of

approximately 2.55. Accordingly, none of the mirrors Ml to M10 has an x/y-aspect ratio that is greater than 2.6.

Figure 86 shows a plan view of a first embodiment of a reticle 10 that is imageable by the projection optical unit 7. Figure 86 and the following illustrations of further embodiments of the reticle in Figures 87 to 91 are provided with dimensions, just like the imaging field illustrations (Figures 92 to 95). Here, an inch (”) corresponds to 2.54 cm, i.e., 25.4 mm.

The reticle 10 according to Figure 86 comprises a square substrate 18 with an edge length of 1524 mm (6 inches, 6”). A used region, also referred to as object specification field 19, which is available for imaging structures of the reticle 10 lies within the square boundary of the substrate 18. The object specification field 19 is delimited by a square specification field basic shape and convexly curved specification field corner regions 20.

The reticle 10 according to Figure 86 is also referred to as a standard reticle.

Figures 87 to 91 show further size variants of the reticle 10, which are likewise provided with dimensions. Components and functions corresponding to those which have already been explained above with reference to Figure 86, in particular, bear the same reference signs and will not be discussed in detail again.

The reticle 10 according to Figure 87 has a square substrate, the external dimensions of which matching those in Figure 86. The object specification field 19 in the reticle 10 according to Figure 87 is smaller than in the embodiment according to Figure 86. This is due to the fact that the distance in the y-dimension between the specification field basic shape of the object specification field 19 and the outer edge of the substrate 18 is greater than in the embodiment according to Figure 86.

The embodiment according to Figure 88 corresponds to that of Figure 86.

The reticle 10 according to Figure 89 has a substrate 18 two times larger in the x-dimension than the embodiments according to Figures 86 to 88. Thus, the x/y-dimensions in the reticle 10 according to Figure 89 are 12 inches/6 inches. Accordingly, the object specification field 19 in the reticle 10 according to Figure 89 is also correspondingly larger in the x-dimesion and has a rectangular specification field basic shape, likewise with an x/y-aspect ratio of approximately 2/1 and convexly curved specification field corner regions 20. The reticle 10 according to Figure 89 is also referred to as a reticle with twice the size in the horizontal direction.

The reticle 10 according to Figure 90 corresponds to that of Figure 89, rotated through 90° about the z-axis (axis perpendicular to the plane of the drawing according to Figures 86 to 91).

The reticle 10 according to Figure 90 is also referred to as a reticle with twice the size in the vertical direction.

The reticle 10 according to Figure 91 has a square substrate 18 with x/y-dimensions of respectively 12 inches. The object specification field 19, which has a square specification field basic shape and convexly curved specification field corner regions 20, lies within this substrate 18 of the reticle 10 according to Figure 91.

In the reticle embodiments according to Figure 86 and Figures 88 to 91, the edge distances between the object specification field 19 and the outer edge of the substrate 18 are always the same, both in the region of the rectangular specification field basic shape and in the region of the specification field corner regions 20.

The reticle 10 according to Figure 91 is also referred to as a reticle with twice the size in both directions.

Figure 92 shows an entire imaging field 21 with dimensions in exemplary fashion, said imaging field being exposed in contiguous fashion on the wafer 11 during a scanning procedure within the scope of the projection exposure. The imaging field 21 according to Figure 92 has an extent of 26 mm in the x-dimension; this corresponds to the x-extent of the image field 8. The imaging field 21 has an extent of 33 mm in the y-dimension. With the aid of the image field 8 with an extent of 1.6 mm in the y-dimension, the entire y-extent of the imaging field 21 is illuminated during the scanning process by way of the scanning movement of the wafer 11 in the y-direction with the aid of the substrate displacement drive 12a. The imaging field 21 according to Figure 92 is also referred to as a full field. Figures 93 to 95 show further embodiments of imaging fields 21 with dimensions. Components and functions which have already been explained above with reference to Figure 92, in particular, bear the same labels and will not be discussed in detail again.

The imaging field 21 according to Figure 93 has an extent of 13 mm in the x-dimension and an extent of 33 mm in the y-dimension. The x-extent thus corresponds to half the x-extent of the image field 8 of the projection optical unit 7. The y-extent corresponds to that of the imaging field 21 according to Figure 92. The imaging field 21 according to Figure 93 has exactly half the area of the full field according to Figure 92 and is also referred to as a rotated half field.

Figure 94 shows an embodiment of the imaging field 21 with an x-extent of 26 mm and a y- extent of 16.5 mm. The x-extent of the imaging field 21 according to Figure 94 is therefore just as large as that of the embodiment according to Figure 92, and the y-extent has half the size. The imaging field 21 according to Figure 94 is also referred to as a half field.

In comparison with the imaging field according to Figure 92, the imaging field 21 according to Figure 95 has half the x-extent of 13 mm and half the y-extent of 16.5 mm. The imaging field 21 according to Figure 95 is also referred to as a quarter field.

Using the example of an object specification field 19 with a square specification field basic shape corresponding to the object specification field of the reticle 10 according to Figure 86, 88 or 91, for example, Figure 96 shows arrangement options of structuring fields 4i (4a, 4b, 4c, 4d) with different x/y-aspect ratios, which use the area of the object specification field 19 in Pareto- optimal fashion.

The respective rectangular structuring field 4i is illuminated within the scope of a scanning operation of the projection exposure apparatus 1 by way of a relative displacement of the reticle 10 with respect to the object field 4. This is illustrated in Figure 96 using the example of the arcuate object field 4, the x-extent of which corresponds to that of a Pareto-optimal structuring field 4c. The object field 4 is scanned relative to this structuring field 4c along the field direction y, i.e., along the object displacement direction, during the scanning operation of the projection exposure apparatus 1 until the entirety of the structuring field 4c has been illuminated. In this way, the respective structuring field 4i overall is imaged into the imaging field 21 associated with the imaging optical unit by way of the imaging scales b_c, b_n. The imaging field 21 is displaced relative to the image field 8 in a manner synchronized to the object displacement by way of an appropriate synchronization of the drives 10b and 12a.

A Pareto-optimal use of the object specification field 19 by the structuring field 4i inscribed therein is present if a magnification of the respective structuring field 4i along an object field dimension is possible only to the detriment of a reduction in the extent of this structuring field along the structuring field dimensional orthogonal thereto.

In respect of the theory surrounding Pareto-optimality, reference is made to the German

Wikipedia page“Pareto-Optimum”, retrievable on 18 July 2018, and the references specified therein.

In order to elucidate this specification of the Pareto-optimality, Figure 96 also plots, in exemplary fashion two fields 22 (dotted) and 23 (dashed) that are not inscribed in Pareto- optimal fashion. The field 22 has not been inscribed into the object specification field 19 in Pareto-optimal fashion since it could have a greater extent in the x-dimension without the y- dimension of the field 22 having to be reduced. Accordingly, the field 23 is not inscribed into the object specification field 19 in Pareto-optimal fashion either since it could be increased in the y- dimension without the field 23 having to be reduced in terms of its x-dimension in this case.

Examples of structuring fields inscribed in the object specification field 19 in Pareto-optimal fashion are the structuring fields 4a (dash dotted), 4b (dashed), 4c (dotted) and 4d (dashed with a greater spacing). In all of these Pareto-optimally inscribed structuring fields 4a to 4d or 4i (i = a...d), the comers of these rectangular structural fields 4a to 4d lie on the convexly curved boundary lines of the specification field corner regions 20. Such structuring fields 4a to 4d are also referred to as Pareto-structuring fields.

The corners of the Pareto-optimally inscribed structuring fields 4i, which follow this boundary line of the specification field corner regions 20, each have a defined x/y-aspect ratio, which follows the curve following the form of the specification field corner regions 20 in a diagrammatic representation. Accordingly, the admissible, absolute bc/b_n-ratios of the reduction scales, which the projection optical unit 7 may have for Pareto-optimal imaging of the respective structuring field 4i into an image field 8 of specified dimensions, also follow a corresponding curve. The sign of b_c or b_n is not important when forming this ratio b_c/b_n; all that matters is the absolute value.

Figure 97 elucidates this result in a diagram, which plots the reduction scale b_c along the abscissa and the reduction scale b_n along the ordinate. Pareto-optimal, absolute reduction scale ratios are reproduced by a scale ratio curve 24. Proceeding from this curve, smaller assigned absolute reduction scales b_g or b_c are possible in each case - illustrated using hatching - in the case of respectively set absolute reduction scale b_{c 0G} b_n; this would lead to non-Pareto-optimal inscribed structuring fields, for example structuring fields of types 22, 23 in Figure 96.

With the aid of, firstly, the various combinations of object specification fields 19 according to Figures 86 or 88 to 91 and, secondly, imaging fields 21 according to Figures 92 to 95, Figure 98 shows ascertained scale ratio curves 24i. In the key on the right-hand side of Figure 98, each of the scale ratio curves 24i (i = 1, 2... 16) is assigned to a combination of reticle size according to Figures 88 to 91 and an imaging field size according to Figures 92 to 95. Moreover, Figure 98 highlights, inter alia, the scale ratio b_c/ b_n = 4/8.1 of the projection optical unit 7.

A scale ratio curve 24i for the combination of a standard reticle according to Figure 86 and a half field according to Figure 94 lie close to this scale ratio 4/8.1 of the projection optical unit 7.

Apart from the combinations of“standard reticle and full field” (scale ratio curve 24₂),“standard reticle and rotated half field” (scale ratio curve 24₃),“reticle with twice the size and horizontal format and full field” (scale ratio curve 24₄) and“reticle with twice the size and horizontal format and rotated half field” (scale ratio curve 24s), all other combinations of, firstly, reticles according to Figures 86 to 91 and imaging fields according to Figures 92 to 95 can be imaged using the projection optical unit 7 and the scale ratio 4/8.1. The associated scale ratio curves for these admissible combinations of reticles and imaging fields are denoted by 24₆ to 24i₆ in Figure 98 and in addition to the scale ratio curve 24i already discussed at the outset. In an illustration comparable to Figure 96, Figure 99 once again shows an object specification field 19 with a Pareto-optimally inscribed structuring field 4a. Additionally, usable auxiliary areas 25, 26, 27, 28 are plotted in the surface regions, which lie, firstly, within the object specification field 19 and, secondly, outside of the structuring field 4a. The auxiliary areas 26 to 28 are each rectangular and represent spatial requirements of sensors or markings, which serve to align the reticle, for example. By way of example, such auxiliary areas have dimensions of 3250 pm x 160 pm, of 9636 pm x 1750 pm and of 4000 pm x 4000 pm.

Figures 99 to 101 show, not entirely true to scale, three different arrangement variants of auxiliary areas 25 to 28 between the respective structuring field 4a, 4b and 4c, each inscribed in Pareto-optimal fashion with a different x/y-aspect ratio, and the edge contour of the object specification field 19.

What ultimately arises on account of the extent of auxiliary areas 25 to 28 is that the play for the Pareto-optimal inscription of the structuring field 4i within the edge contour of the object specification field 19 is restricted in comparison with the entirely free inscription according to Figure 96, and so the corners of the Pareto-optimally inscribed structuring field 4i, in particular, cannot come to rest near the ends of the specification field corner regions 20, i.e., not near the transitions between the rounded specification field corner regions 20 and the specification field basic shape boundaries running in a straight line.

The effect on the scale ratio curves 24i arising as a result thereof is illustrated in Figure 102. There has been no change in the basic position of the respective scale ratio curves 241 to 24i₆ in the illustration 102, which takes account of the auxiliary areas 25 to 28, in comparison with the illustration according to Figure 98, which does not take account of the auxiliary areas. Only in the region of the extremal values of the respective scale ratio curves 24i, i.e., in the region of the respective start and/or in the region of the respective end of the scale ratio curve 24i, is there shortening in the illustration according to Figure 102 and hence a corresponding reduction in the admissible scale ratio values b_c, b_g below the respective scale ratio curve 24i. Even when the auxiliary areas 25 to 28 are considered, the projection optical unit 7 with its scale ratio of 4/8.1 remains admissible for the same scale ratio curves 24i, as explained above in conjunction with Figure 98.

A shadowing effect as a further influencing quantity for the profile of the scale ratio curves 24i is explained below on the basis of Figures 103 to 108. Components and functions which have already been explained above bear the same labels and will not be discussed in detail again.

Figure 103 schematically shows an embodiment of the reticle 10 together with a region 29, in which reticle structures to be imaged are present. This region 29 is spaced apart from an outer edge contour of the substrate of the reticle 10 on all sides of the square or rectangular reticle 10.

Figure 104 shows, very schematically, an arrangement of shadowing stops of the projection exposure apparatus 1, which are also referred to as reticle masking (ReMa) stops. Two x-ReMa stops 30, 31, which are spaced apart from one another in the x-direction, and two y-ReMa stops 32, 33, which are spaced apart from one another in the y-direction, are present. Between them, these ReMa stops 30 to 33 delimit the region 29 to be imaged on the reticle 10.

Figure 105 shows, very schematically, those components of the projection exposure apparatus 1 that influence the illumination or imaging light 3 in the region of a reflection at the reticle 10.

In the illumination beam path towards the reticle 10, an entire light beam of the illumination light 3 initially passes energy sensors 34 that are located at the edge, said sensors measuring the energy and, optionally, a directional stability of the illumination light 3. Subsequently, the illumination light 3 passes a field intensity specification device with finger stops 35 in the style of a Unicom. By way of example, such a Unicom is described in DE 10 2017 206 541 A1 and DE 10 2012 208 016 Al. This field intensity specification device serves to specify a defined illumination intensity curve over the x-coordinate of the object field 4.

Subsequently, the illumination light 3 passes the y-ReMa stops 32 and 33. The back ReMa stop 33 of Figure 105 is illustrated in the section of Figure 5. Subsequently, the illumination light 3 passes the x-ReMa stops 30, 31, the left x-ReMa stop 30 of which is illustrated in Figure 105.

Subsequently, the illumination light 3 passes an optional pellicle 36, which protects a surface of the reticle 10, before the illumination light 3 strikes the object structures of the reticle 10.

Like the reticle 10, the pellicle 36 is carried by the reticle holder 10a.

Figure 106 schematically shows a shadowing effect caused by the ReMa stops 30 to 33, which occurs at the edge of the region 29 to be imaged in each case. In Figure 106, the reticle 10 is illustrated with a break in the central portion such that the edge regions are illustrated with great magnification in Figure 106. The illumination light 3 passes through the ReMa stops 30 to 33 with a respective object-side numerical aperture, which is indicated at NA in Figure 106.

Depending on this object-side numerical aperture and the distance d of the ReMa stops 30 to 33 from the reticle 10, half-shadow regions or stop-shadowed areas D arise on the reticle 10, in which some of the illumination light 3 is shadowed by the respective ReMa stop 30 to 33 in each case. Depending on the combination of object-side numerical aperture NA and distance d between the ReMa stops 30 to 33 and reticle 10, the half shadow regions D have a value ranging from 1 mm to 3.5 mm.

In an illustration similar to Figure 100, Figure 107 shows the relationship between the usable structuring field 4i and the shape of the object specification field 19, wherein, firstly, the auxiliary areas 25 to 28, in particular for the alignment sensors and alignment markings, and, secondly, the half-shadowed regions D are additionally taken into account. This yields a corresponding reduction in the usable structuring field 4i in both object field dimensions x and y.

Figure 108 shows the influence that this taking account of, firstly, the auxiliary areas and, secondly, the half-shadowed regions has on the curve of the scale ratio curves 24i. When taking this half shadow into account according to Figure 108, the scale ratio curves 24i are shifted to smaller b_c values and to smaller b_n values in comparison with the case where only the auxiliary areas according to Figure 102 are taken into account. The reduction scale ratio value 4/8.1 of the projection optical unit 7 still lies just below the scale ratio curve 24i and the projection optical unit 7 still satisfies the scale ratio criterion for the same scale ratio curves 24i, as explained above on the basis of Figures 98 and 102.

The following procedure is undertaken when designing an imaging optical unit if an optimization of the reduction scale ratio is taken into account:

A shape of the object specification field 19, which is bounded by the rectangular specification field basic shape and the convexly curved specification field comer regions 20, and the dimensions of the image field 8 in both field directions x and y are included when ascertaining a reduction scale ratio to be specified from a first reduction scale b_c of the imaging optical unit 7 in the first field direction x and the second reduction scale b_n of the imaging optical unit 7 in the second field direction y. Then, an arrangement of optical components of the imaging optical unit 7, for example the arrangement described above in conjunction with Figures 2 to 15, is specified, by means of which the specified imaging scale ratio between the object field 4 and the image field 8 is generated.

As explained above, an auxiliary area need can also be included in the ascertainment of the reduction scale ratio b_c/b_g to be specified. No structures to be imaged are present on the respective auxiliary area 25 to 28, and so the structuring field 4i must not overlap with the auxiliary area 25 to 28.

As likewise described above, the need for at least one stop-shadowed area D on the object specification field 19 can be included in the ascertainment of the reduction scale ratio b_c/ b_g to be specified.

No structures to be imaged are allowed to be present on the stop-shadowed areas D, and so the structuring field 4i must not overlap with the stop-shadowed area D.

Figures 16 to 29 show a further embodiment of a projection optical unit 37, which can be used instead of the projection optical unit 7 in the projection exposure apparatus 1. Components and functions corresponding to those which were already explained above with reference to Figures 1 to 15, in particular, are denoted by the same reference signs and are not discussed in detail again. The projection optical unit 37 has an integer reduction scale b_c in the xz-plane of 4.00 and a reduction scale b_g in the yz-plane of -8.80. In terms of its basic design, the projection optical unit 37 corresponds to the projection optical unit 7.

The optical design data emerge from following Tables 1 to 6, which, in turn, correspond in terms of the basic structure to Tables 1 to 6 relating to the embodiment according to Figure 2.

Radii of the surfaces

RadiuS_x [mm] Power_x [1/mm] RadiuS_y [mm] Power_y [1/mm]

M01 -2149.74307520 0.00090990 -1362.27734550 0.00143587

M02 2951.01744024 -0.00012502 2712.04344590 -0.00013603

M03 2191.51476631 -0.00020518 -11642.78088155 0.00003862

M04 4303.80775718 -0.00009566 -8301.25656720 0.00004960

M05 -2107.30064397 0.00015821 -6172.35866799 0.00005401

M06 -932.82274076 0.00049065 -1858.97453141 0.00024621

M07 -763.03971988 0.00062902 36508.86814551 -0.00001315

M08 -1095.26826407 0.00048573 -5537.85564012 0.00009607

M09 1134.00647010 -0.00176366 315.29960114 -0.00634317

M10 -784.04106832 0.00253122 -718.87542257 0.00276067

Table 1 for Figure 16

Decentring (location, angle) the surfaces

D_x [mm] D_y [mm] l)_z [mm]

Reticle 0.000000000 2210.981916717 2301.547066942

M01 0.000000000 2063.733100150 618.485392066

M02 0.000000000 1775.827961535 1451.540846742

M03 0.000000000 1550.505676179 1717.000095488

M04 0.000000000 1196.044970849 1872.526464812

M05 0.000000000 798.146061456 1872.043574818

M06 0.000000000 168.387727608 1651.981239302

M07 0.000000000 -61.812466046 1415.923766055

M08 0.000000000 -129.367296140 1187.996276842

M09 0.000000000 147.308716142 106.028755734 Stop 0.000000000 109.279602567 255.875038017

M10 0.000000000 0.000000000 686.469933215

Wafer 0.000000000 0.000000000 0.000000000

« [°] «y P °]

Reticle 0.000000000 0.000000000 0.000000000

M01 7.032610840 0.000000000 0.000000000

M02 -60.305060791 180.000000000 0.000000000

M03 143.317140055 0.000000000 0.000000000

M04 -11.810421261 180.000000000 0.000000000

M05 189.665478733 0.000000000 0.000000000

M06 32.490576806 180.000000000 0.000000000

M07 239.605285876 0.000000000 0.000000000

M08 88.917443106 180.000000000 0.000000000

M09 14.292174071 -0.000000000 0.000000000

Stop 1.508659025 180.000000000 0.000000000

M10 7.120151714 180.000000000 0.000000000

Wafer -0.000000000 -0.000000000 0.000000000

Table 2 for Figure 16

Free-form coefficients of the surfaces

Coefficient Formula M01 M02 M03

C7 x 2 y 1.7432098326e-08 -4.4623820617e-08 1.7051619165e-07

C9 3

y 3.3715366275e-09 -5.2811768454e-07 3.2939519637e-07

CIO X⁴ -6.6297473048e-12 2.6173508552e-10 7.0663063675e-10

C12 x² y² 4.0146454028e-l 1 1.7456806714e-l 1 3.1842507927e-10

C14 y⁴ -1.4499155377e-10 2.0351988517e-09 -2.0197542726e-10

C16 x 4 y - 1.7300235249e- 16 -4.057473421 le-13 1.8373474415e-12

C18 x 2 y 3 9.6045073382e-14 1.3179582488e-12 2.8100631490e-13

C20 y -5.5746703360e-14 -9.5457119369e-12 2.7320887718e-12

C21 X .6 -1.3081768504e-18 1.3616950321e-17 5.204007106 le- 16

C23 x 4

4 y 2 -4.4191928350e-17 1.400624420 le- 15 2.9530268958e-15

C25 x 2 y 4

4 -1.1020038744e- 16 -8.1353284898e-15 9.3041533968e-16

C27 .6

y -3.7417779508e-16 4.5503290830e-14 -1.0317672036e-15

C29 x⁶ y 5.5066724659e-21 7.6289840190e-19 4.7794423107e-18

C31 x⁴ y³ -1.3355143656e-19 -2.4221367844e-18 5.3581493413e-18

C33 x² y⁵ 4.8085026762e-20 4.9612594964e-17 7.0830887456e-18

C35 7

y 1.1494003337e-18 -2.1427657968e-16 3.7319240299e-17 C36 x 7.8328753569e-24 -3.2738672783e-21 1.2368178276e-20

C38 x⁶ y² -5.6374986327e-23 6.5002024356e-21 1.4551762271e-20

C40 x⁴ y⁴ -6.3981724492e-23 3.3387704514e-20 2.9977044125e-20

C42 x² y⁶ 1.6713426747e-21 -2.3026370522e-19 4.2253280691e-20

C44 y -2.204147113 le-20 1.0557874204e-18 7.6780588488e-20

C46 x⁸ y 1.4089754984e-26 -4.7587057940e-23 -3.5112434259e-25

C48 x⁶ y³ -2.2082137927e-25 -5.1585739640e-22 -5.3019449696e-23

C50 x⁴ y⁵ -1.2254116954e-23 -1.0828586769e-21 -6.0079209117e-23

C52 x² y⁷ -2.2549362896e-24 -7.5584008603e-23 -7.2999984203e-22

C54 9

y -6.5947900176e-23 -5.8325914144e-21 -4.7689171293e-22

C55 X¹⁰ -3.0438454151e-28 2.7417781952e-25 -9.8475237058e-25

C57 x⁸ y² 1.6914763581e-27 3.6936149946e-25 - 1.1066430236e-24

C59 x⁶ y⁴ -1.4874645734e-26 3.6904296120e-25 -2.8884711468e-24

C61 x⁴ y⁶ -2.9669764509e-25 -1.000267805 le-24 -4.0023016323e-24

C63 x² y⁸ -4.7441792653e-25 -4.1167728125e-24 -2.8122115967e-24

C65 yio 3.2329528401e-24 3.3951708574e-23 -9.2186988033e-24

C67 x¹⁰ y -8.1193570438e-31 2.4227453180e-27 -6.2483814368e-27

C69 x⁸ y³ -6.8069472809e-30 3.2749135078e-26 1.0483788387e-26

C71 x⁶ y⁵ 2.9038584527e-28 1.0986313185e-25 4.7343307374e-27

C73 x 4 y 7 1.5550905816e-27 1.5095743767e-25 2.6136501715e-26

C75 x 2 y 9 -2.1385660939e-27 2.2382121323e-25 1.5961797117e-25

C77 11

y 9.5009245151e-27 -1.7910258171e-25 1.5392586815e-25

C78 x¹² 5.7921118982e-33 -1.0913956487e-29 4.2996197743e-29

C80 x¹⁰ y² -3.1540236857e-32 -3.2630531779e-29 6.0518395154e-29

C82 x⁸ y⁴ 1.1202578335e-31 -1.0585946372e-28 2.2975793259e-28

C84 x⁶ y⁶ 7.9887456083e-30 -5.6152559781e-29 4.0648598893e-28

C86 x⁴ y⁸ 4.5241059787e-29 -7.1528187213e-29 5.5073759204e-28

C88 x² y¹⁰ 2.4949076389e-29 -1.4682423383e-27 6.7073694500e-28

C90 y¹² -3.9413917460e-28 4.6207474676e-28 1.1551929898e-27

C92 x¹² y 2.1495703723e-35 -7.6901083550e-32 6.0518219551e-31

C94 x¹⁰ y³ 2.8898576184e-34 -1.2265484660e-30 -7.1955828081e-31

C96 x⁸ y⁵ -2.4177077459e-33 -5.6720292940e-30 -9.5973789473e-31

C98 x⁶ y⁷ -3.9269124909e-32 -1.2342281999e-29 2.8872128360e-31

CIOO x⁴ y⁹ -7.0824577793e-32 -1.1232183288e-29 -4.6775445520e-30

C102 x² y^{1 1} 3.2714084788e-31 -6.6283207466e-30 -1.5061190382e-29

C104 13

y -1.0494099888e-30 3.2562367950e-30 -1.0489397807e-29

C105 x¹⁴ -6.1915065482e-38 2.3514671742e-34 -6.0547869016e-34

C107 x¹² y² 2.7112774517e-37 1.3320931815e-33 -1.2334342497e-33

C109 x¹⁰ y⁴ 1.2699232433e-36 7.3741185564e-33 -1.1561907828e-32 cm x⁸ y⁶ -9.5089221315e-35 1.4680349874e-32 -1.7442247332e-32

Cl 13 x⁶ y⁸ -9.7102114465e-34 2.1707965628e-32 -3.4498266381e-32 Cl 15 x⁴ y¹⁰ -3.3363424403e-33 2.2609910146e-32 -4.4565703791e-32 Cl 17 x² y¹² 1.3892885170e-34 9.8636301467e-32 -7.1044595266e-32 Cl 19 y¹⁴ 2.8039623317e-32 -2.1257256935e-32 -7.9017977402e-32 C121 x¹⁴ y -2.0548112895e-40 1.2408473059e-36 -2.0067332102e-35 C123 x¹² y³ -3.1722027237e-39 2.333158333 le-35 1.9965414657e-35 C125 x¹⁰ y⁵ 9.6758103876e-40 1.3525511163e-34 5.7930245024e-35 C127 x⁸ y⁷ 3.5126320558e-37 4.3260561031e-34 -1.4873239302e-35 C129 x⁶ y⁹ 1.9700401102e-36 5.8429821840e-34 1.1760562147e-35 C131 x⁴ y^{1 1} 2.3640569867e-37 3.6356868375e-34 3.5073579071e-34 C133 x² y¹³ -1.5868284671e-35 -4.7102756998e-35 7.3980367777e-34 C135 15

y 5.8406929219e-35 -1.9425891669e-34 4.2319792703e-34 C136 x¹⁶ 3.4420345971e-43 -2.5295366363e-39 -8.7502549109e-39 C138 x¹⁴ y² -8.1590702694e-43 -2.5870417384e-38 -1.8296885153e-39 C140 x¹² y⁴ -2.1128276500e-41 -1.9801069084e-37 3.3864931426e-37 C142 x¹⁰ y⁶ 5.2470831128e-40 -6.5234269435e-37 4.879082351 le-37 C144 x⁸ y⁸ 7.9743132003e-39 -1.4573753605e-36 7.2493547762e-37 C146 x⁶ y¹⁰ 4.6690947865e-38 -1.4301005432e-36 1.5947845063e-36 C148 x⁴ y 1.2064790126e-37 -1.0748199680e-36 2.2650199163e-36 C150 x 2 y 14 -7.456842579 le-38 -3.5789633920e-36 3.9564885833e-36 C152 yl6 -1.0747936572e-36 2.5458854599e-36 3.0185283116e-36 C154 x¹⁶ y 6.9096923519e-46 -8.0894874728e-42 2.2978234583e-40 C156 x¹⁴ y³ 1.1514098771e-44 -1.7571261957e-40 -1.8987889326e-40 C158 x¹² y⁵ 4.7809247668e-44 -1.2177267903e-39 -1.0293442762e-39 C160 x¹⁰ y⁷ -9.0351418638e-43 -5.215886791 le-39 -8.4778485534e-42 C162 x⁸ y⁹ -1.1496817573e-41 -1.0790789473e-38 3.3402110734e-40 C164 x⁶ y^{1 1} -3.1546044294e-41 -1.1721845279e-38 -5.9065154284e-40 C166 x⁴ y¹³ 4.0472798226e-41 -4.2578318863e-39 -9.8100163066e-39 C168 x² y¹⁵ 2.4721170568e-40 1.8348597385e-38 -1.3481495938e-38 C170 17

y -1.2322983262e-39 -1.0274081794e-38 -6.4710389422e-39 C171 x¹⁸ -7.7696354769e-49 1.0478428070e-44 2.2586751994e-43 C173 x¹⁶ y² -3.3602432929e-49 1.9346324756e-43 2.8327161576e-43 C175 x¹⁴ y⁴ 8.0541368165e-47 1.8591575941e-42 -4.0397845563e-42 C177 x¹² y⁶ -1.1630920478e-45 8.5533249427e-42 -7.7899331700e-42 C179 x¹⁰ y⁸ -2.2217127589e-44 2.6283154180e-41 -3.3319414778e-42 C181 x⁸ y¹⁰ -1.9140790346e-43 4.4420274832e-41 -2.0359168269e-41 C183 x⁶ y¹² -7.7217979784e-43 3.9454747793e-41 -2.4226283961e-41 C185 x⁴ y¹⁴ - 1.8269249335e-42 1.522210928 le-41 -5.8047204225e-41 C187 x² y¹⁶ 2.2341278320e-42 -2.9268822501e-41 -7.9280898085e-41

C189 y¹⁸ 1.7185164667e-41 1.4784334892e-41 -4.6267408488e-41

Table 3a for Figure 16

Coefficient Formula M04 M05 M06

C7 x 2 y 5.7630260309e-08 -8.2466913454e-08 2.0753059829e-07

C9 y 3 -6.388299237 le-08 -1.0109001182e-07 -2.6624852147e-08

CIO X⁴ 1.1740810333e-10 -1.2714745137e-10 -3.6018874805e-10

C12 x² y² 3.7723403261e-l 1 -1.8108395179e-10 5.2705851210e-l 1

C14 y⁴ -1.5533643419e-10 -8.3008278320e-l 1 -2.988531141 le-10

C16 x 4 y 1.2940323056e-13 -3.9114017276e-13 -2.4930123708e-13

C18 x 2 3 4.6228262860e- 13 -9.0446836128e-14 9.1595798092e-15

C20 y -3.5009214697e-13 -7.9467335826e-14 1.2876369865e-12

C21 x⁶ -8.4733462550e-16 -6.8813776839e-16 -4.0273110102e-16

C23 x⁴ y² -4.9919173867e-16 -2.3159160364e-16 -2.4547875449e-16

C25 x y⁴ 7.2975604296e-16 2.7327436674e-17 -2.4320208775e-15

C27 y⁶ -1.3342532005e-15 1.1846297505e-16 -4.4631817054e-16

C29 x⁶ y 3.1569935186e-18 -1.9278717303e-18 -4.7751067293e-19

C31 x⁴ y³ -2.2038517130e-19 -3.5089118995e-19 1.4070408757e-18

C33 x² y⁵ 5.2182592804e-18 1.2661920948e-18 -6.8848644921e-18

C35 y⁷ -5.4913395057e-18 1.0391579235e-18 8.3922774213e-18

C36 x⁸ 7.0956068088e-20 3.4388795801e-23 -6.0726694777e-21

C38 x⁶ y² -2.9298997772e-21 5.7481253498e-21 -1.7285222723e-20

C40 x⁴ y⁴ -1.3200525254e-20 5.4023731342e-21 -1.474409581 le-20

C42 x² y⁶ 4.9449176869e-21 4.0379726885e-21 9.1298484539e-22

C44 y⁸ -3.7106440250e-22 -3.8805689553e-21 -1.0356309959e-19

C46 x⁸ y -3.2135160667e-23 3.7129353542e-22 1.0008309255e-22

C48 x⁶ y³ 3.0552124665e-22 6.2459143209e-23 2.8937391423e-22

C50 x⁴ y⁵ 2.4171868505e-22 -1.1988586492e-23 3.8645583434e-22

C52 x² y⁷ 4.980906821 Oe-24 -9.6622768618e-23 1.9538765909e-21

C54 9

y 4.7541929665e-22 -1.0182867764e-22 3.0675099285e-22

C55 X¹⁰ -4.6729345526e-24 -2.3381244105e-25 4.9453926249e-25

C57 x⁸ y² -5.0637351779e-25 -8.5946014553e-25 8.0624575677e-25

C59 x⁶ y⁴ -8.2814264566e-25 -5.5959528621e-25 3.7439362401e-24

C61 x⁴ y⁶ 1.4464529023e-24 2.2229010662e-25 -3.3091058056e-24

C63 x² y⁸ -1.9367545012e-24 -2.9729560962e-25 -5.0971015105e-24

C65 yio -2.5292458227e-24 6.2511503369e-25 1.106267953 le-24

C67 x¹⁰ y 1.0745421654e-26 -2.9318586757e-26 -7.4021657978e-27

C69 x⁸ y³ -2.5188207293e-26 -9.2230412465e-27 -3.3260583257e-26 C71 x⁶ y⁵ -4.4357706790e-26 4.6262218163e-27 -2.6268931975e-26

C73 x 4 y 7 -1.2151663050e-26 -5.9359324747e-27 -8.9395815179e-26

C75 x 2 y 9 1.8392975172e-26 1.0571302499e-26 -2.5797542321e-25

C77 11

y -5.6668257627e-26 5.0559064774e-27 -1.8427728365e-26

C78 x¹² 1.2428752271e-28 4.6975507713e-30 -2.4999219433e-29

C80 x¹⁰ y² 4.6907549546e-29 7.0218513460e-29 6.6819884154e-30

C82 x⁸ y⁴ 1.8113119128e-28 5.6909221993e-29 -2.1838907388e-28

C84 x⁶ y⁶ -1.2630695435e-29 -2.1266924333e-29 -4.6342534983e-29

C86 x⁴ y⁸ -1.4519324228e-28 -3.7269577987e-29 1.0675725927e-27

C88 x² y¹⁰ 2.8408441208e-28 1.1614756733e-29 7.2314927648e-28

C90 y¹² 2.0297200756e-28 -3.8611013126e-29 1.2843664979e-28

C92 x¹² y -8.8170327781e-31 1.4393031944e-30 3.3307445809e-31

C94 x¹⁰ y³ 1.0615320319e-30 6.9418613200e-31 2.1164631909e-30

C96 x⁸ y⁵ 3.2019965018e-30 -3.9521068894e-31 2.3001057315e-30

C98 x⁶ y⁷ 3.4205063801e-30 5.1988795085e-33 -4.3016436296e-31

CIOO x⁴ y⁹ 1.7198183617e-31 5.5905531972e-31 1.2808295012e-29

C102 x² y^{1 1} -2.0626142072e-30 -6.8914717850e-31 2.1213166618e-29

C104 13

y 3.6939177301e-30 -1.1544854800e-31 3.8853076387e-31

C105 x¹⁴ 1.0333993829e-33 -1.9066963077e-34 8.6227993826e-34

C107 x¹² y² -1.1658147670e-33 -3.3850149492e-33 -2.7452830970e-33

C109 x¹⁰ y⁴ -1.4413923415e-32 -2.3474309637e-33 2.6682419133e-33 cm x⁸ y⁶ -8.828728141 le-33 -1.7685359006e-33 7.9143887319e-33

Cl 13 x⁶ y⁸ -7.501774433 le-34 4.355124115 le-33 -3.4948278680e-32 Cl 15 x⁴ y¹⁰ 6.2880902836e-33 8.4990265868e-34 -1.1297615227e-31 Cl 17 x 2 y 12 -1.6306540531e-32 3.7218392838e-34 -6.1091600355e-32 Cl 19 y¹⁴ -1.2183133295e-32 1.2084745603e-33 -1.8592498867e-32 C121 x¹⁴ y 3.1841051194e-35 -3.6796685847e-35 -7.6011715904e-36 C123 x¹² y³ -1.9046287559e-35 -2.4620383097e-35 -6.8114162348e-35 C125 x¹⁰ y⁵ -9.6853455100e-35 8.2045557766e-36 -1.2093362300e-34 C127 x⁸ y⁷ -1.6481783363e-34 1.7366348188e-35 1.2574029671e-34 C129 x⁶ y⁹ -1.3238875290e-34 -1.6760830373e-35 1.7543993598e-35 C131 x⁴ y^{1 1} 3.8137604915e-35 -1.5530725806e-35 -8.2668265888e-34 C133 x² y¹³ 1.2735101028e-34 2.2538044113e-35 -8.9296362969e-34 C135 15

y -1.3276679506e-34 2.0346404134e-37 4.5550650949e-35 C136 x¹⁶ -1.3425890565e-37 1.0123846145e-38 -1.8921742915e-38 C138 x¹⁴ y² -3.5093987868e-38 8.6335276240e-38 1.0656943241e-37 C140 x¹² y⁴ 5.3445973824e-37 2.3997094830e-38 1.9973024491e-37 C142 x¹⁰ y⁶ 3.6200655433e-37 1.2474117815e-37 -9.9942018121e-38 C144 x⁸ y⁸ 6.0385849370e-37 -7.0913491183e-38 -2.0261413189e-37 C146 x⁶ y¹⁰ 7.5123785473e-38 -1.3142077459e-37 2.6089077643e-36

C148 x⁴ y¹² -2.4624143440e-37 7.0634414265e-39 5.8243685957e-36

C150 x 2 y 14 2.5061157530e-37 -4.0580444298e-38 2.5518695629e-36

C152 yl6 4.4215281039e-37 -1.5027994928e-38 9.8751012698e-37

C154 x¹⁶ y -4.2905800862e-40 3.7753203617e-40 6.9034708736e-41

C156 x¹⁴ y³ 8.8924683674e-41 3.2821831162e-40 8.5304751687e-40

C158 x¹² y⁵ 1.0845496010e-39 -1.9591001233e-41 2.3371158506e-39

C160 x¹⁰ y⁷ 2.4716300085e-39 -2.9364409696e-40 -1.7602989150e-39

C162 x⁸ y⁹ 3.2178839273e-39 -1.0584977571e-40 -8.6263426012e-39

C164 x⁶ y^{1 1} 2.2544021341e-39 3.7800236337e-40 3.3733169079e-39

C166 x⁴ y¹³ -1.6447488816e-39 1.1343195468e-40 1.8991775123e-38

C168 x² y¹⁵ -2.8187774036e-39 -2.7619104495e-40 1.5280672906e-38

C170 17

y 2.0291936895e-39 2.0683162323e-41 -1.7939075427e-39

C171 X¹⁸ 2.1406116989e-42 -1.5783619353e-43 1.8307655802e-43

C173 x¹⁶ y² 1.4544200669e-42 -8.9277299667e-43 -1.3137336866e-42

C175 x¹⁴ y⁴ -7.9638434091 e-42 2.0550014451e-43 -5.5117990139e-42

C177 x¹² y⁶ -2.9980621319e-42 -1.4406938597e-42 -4.0640284629e-42

C179 x¹⁰ y⁸ -1.6441770385e-41 -1.1910787171e-42 1.8414102010e-41

C181 x⁸ y¹⁰ -8.1194783968e-42 2.3075581349e-42 1.8406372377e-41

C183 x⁶ y¹² -6.9458206074e-42 8.3832784295e-43 -6.8856791973e-41

C185 x⁴ y¹⁴ 8.883142373 le-42 -1.4645907564e-43 -1.2379886339e-40

C187 x² y¹⁶ 3.3538544962e-42 7.4865970668e-43 -4.0731532460e-41

C189 18

y -7.5231261356e-42 1.6355008700e-44 -2.0905561441e-41

Table 3b for Figure 16

Coefficient Formula M07 M08 M09

C7 x 2 y -1.4328785010e-07 2.8767253989e-07 1.4861984149e-06

C9 y 3 -5.0169931316e-07 -1.3673179784e-07 -9.0960929799e-07

CIO X⁴ 4.5861551563e- 11 1.8562300088e-10 1.3501177015e-09

C12 x² y² -1.1682449229e-09 -1.1660213469e-l l 5.2914315907e-09

C14 y⁴ 2.3507310171e-09 -3.3546685877e-10 3.3851271001e-09

C16 x 4 y 4.2331709604e-13 7.6472271672e-13 7.9072510176e-12

C18 x 2 y 3^J 4.0783744014e-13 6.5508852064e-13 9.0514131518e- 13

C20 y -6.3103383842e-12 -1.5394651345e-12 -1.6887332773e-l 1

C21 x⁶ 1.2981329783e-16 8.4037528212e-16 7.2107631023e-15

C23 x⁴ y² 2.3336753317e-15 3.7329072350e-15 4.6681543919e-14

C25 x y⁴ -2.5040064399e-14 2.7933218218e-15 9.3348554853e-14

C27 y⁶ 3.6798674820e-14 -8.1297329369e-15 1.3121337944e-13

C29 x⁶ y 3.8540260826e-18 1.2572398416e-17 5.8133594592e-17 C31 x⁴ y³ 2.8605894623e-17 2.7461366369e-17 1.2188167650e-16

C33 x² y⁵ -3.1365465880e-16 1.2165589942e-17 4.8907260615e-17

C35 7

y -9.4196117825e-16 -4.4438125095e-17 -7.3101936159e-16

C36 X 1.2130847401e-20 -7.8121196796e-20 3.2880788939e-20

C38 x⁶ y² -4.0477441689e-20 -3.3433773563e-19 4.9488647036e-19

C40 x⁴ y⁴ 1.3368086795e-18 -1.1578625157e-19 1.6898169526e-18

C42 x² y⁶ 5.0229156393e-18 -5.7586348020e-20 1.6053934236e-18

C44 y -1.4299745509e-17 -2.9939120845e-19 5.7197404980e-18

C46 x⁸ y -1.7131516043e-22 -2.6472162835e-21 4.9227686968e-22

C48 x⁶ y³ -5.3062884486e-21 -5.7392662954e-21 3.3942789526e-21

C50 x⁴ y⁵ 2.6872940949e-20 -6.4399118956e-22 8.5379414586e-21

C52 x² y⁷ 4.2438502446e- 19 -2.9150646324e-21 1.0354587430e-20

C54 9

y 4.8263330164e-19 -3.1065275121e-21 -2.5866833420e-20

C55 X¹⁰ -1.5665336455e-24 1.3702715576e-23 9.6118653479e-25

C57 x⁸ y² -1.7788957963e-24 1.0041128835e-22 3.3558687581e-24

C59 x⁶ y⁴ -1.0666066376e-22 8.3298494480e-23 1.3850777996e-23

C61 x⁴ y⁶ - 1.1674984718e-21 3.1193496910e-23 7.4537855035e-23

C63 x² y⁸ -3.1990424375 e-21 -2.2356873305e-23 3.4911065912e-22

C65 yio 1.6610294210e-20 -2.3059787191e-23 -4.4812268605e-22

C67 x¹⁰ y 2.8986830212e-26 4.2559392155e-25 1.5705432425e-26

C69 x⁸ y³ 5.8431490750e-25 1.5558110747e-24 2.4485669501e-26

C71 x⁶ y⁵ -2.8346748342e-24 8.2431835962e-25 -7.1797130033e-25

C73 x 4 y 7 -2.2783042969e-23 1.3631669397e-25 -3.6176816402e-24

C75 x 2 y 9 -3.782408802 le-22 2.6902742256e-25 -9.7568022868e-24

C77 11

y -9.8169138776e-23 -8.8584403712e-27 1.9803110241e-24

C78 x¹² 1.0515631485e-28 - 1.4699192196e-27 -1.8387157035e-29

C80 x¹⁰ y² 1.0578545655e-27 -1.5116495075e-26 3.7649308065e-28

C82 x⁸ y⁴ 8.7536944166e-27 -2.1905816952e-26 1.7195829581e-27

C84 x⁶ y⁶ -6.1452527112e-27 -3.0515546486e-27 1.3160065932e-27

C86 x⁴ y⁸ 1.2302421136e-24 -5.3310599240e-28 -4.2672410302e-26

C88 x² y¹⁰ -7.6651186577e-25 5.6702933403e-27 -7.0053665046e-26

C90 y¹² -7.7071633787e-24 6.1851018785e-28 1.1419825266e-25

C92 x¹² y -2.3999788804e-30 -4.0026016120e-29 -5.9571046460e-31

C94 x¹⁰ y³ -3.6864354446e-29 -1.8836150912e-28 -1.7026919053e-30

C96 x⁸ y⁵ 2.5768979675e-28 -1.9215227260e-28 3.8003219664e-29

C98 x⁶ y⁷ 3.0911056035e-28 5.1504094185e-30 3.2095252975e-28

CIOO x⁴ y⁹ 1.7764954193e-26 9.1710811970e-30 9.8284188370e-28

C102 x² y^{1 1} 1.6973302169e-25 1.2741831096e-29 2.0860727965e-27

C104 13

y -3.4482809553e-26 -8.9758944290e-30 -3.4691991449e-28 C105 x¹⁴ -4.7555314742e-33 1.0223306131e-31 -3.4966949517e-34

C107 x¹² y² -9.1543968626e-32 1.2767803423e-30 -2.0867698540e-32

C109 x¹⁰ y⁴ -7.8609717752e-31 3.2291048341e-30 -1.2649353958e-31 cm x⁸ y⁶ 8.2697172220e-30 7.8280571976e-31 -3.9097645121e-31

Cl 13 x⁶ y⁸ -6.3589745294e-29 2.3856359226e-32 1.3615177354e-30 Cl 15 x⁴ y¹⁰ -4.0687799390e-28 1.3803626616e-32 1.2785899962e-29 Cl 17 x 2 y 12 1.1465446480e-27 -4.8700438753e-31 1.0571075292e-29 Cl 19 y¹⁴ 1.6348207683e-27 -1.9555184235e-31 -1.2186751538e-29 C121 x¹⁴ y 8.9912938867e-35 2.1250867785e-33 2.0613856930e-35 C123 x¹² y³ 1.2472998107e-33 1.1113583540e-32 1.8866522077e-34 C125 x¹⁰ y⁵ -1.2408223447e-32 1.7406973513e-32 -2.5495192789e-34 C127 x⁸ y⁷ 6.6819235542e-33 4.4299289167e-33 -1.2325093570e-32 C129 x⁶ y⁹ -3.0055081032e-31 -7.1679907255e-33 -5.1084942405e-32 C131 x⁴ y^{1 1} -5.5447717859e-30 -6.1971448133e-34 -1.3076897479e-31 C133 x² y¹³ -3.8135133137e-29 -5.6186581996e-33 -2.4897122838e-31 C135 15

y 1.8102255806e-29 -1.4170055402e-33 1.1131588419e-32 C136 x¹⁶ 1.3579993736e-37 -4.3103108901e-36 4.1183568175e-38 C138 x¹⁴ y² 3.2250043184e-36 -5.6781254721e-35 7.8086717774e-37 C140 x¹² y⁴ 3.6265972778e-35 -2.2604205659e-34 6.6247158056e-36 C142 x¹⁰ y⁶ -3.7980428592e-34 -1.0711901569e-34 2.7273639869e-35 C144 x⁸ y⁸ -4.2263572962e-35 1.8798442078e-36 4.1139198075e-35 C146 x⁶ y¹⁰ 2.2386306228e-32 -4.8862260013e-35 -3.4688676332e-34 C148 x⁴ y 4.6251726119e-32 5.8632096300e-36 -1.3677886726e-33 C150 x 2 y 14 -3.6380356475e-31 -2.7473908504e-35 -3.5242476834e-34 C152 yl6 -9.4689815552e-32 -5.1477537813e-36 8.2942106360e-34 C154 x¹⁶ y - 1.2702143905e-39 -4.8220668395e-38 -2.1864146233e-40 C156 x¹⁴ y³ -1.7288176372e-38 -2.5981349705e-37 -3.5206404396e-39 C158 x¹² y⁵ 2.2924099326e-37 -5.4113072019e-37 -1.4069263475e-38 C160 x¹⁰ y⁷ -2.3449874018e-37 -3.5625756332e-37 1.576242921 le-37 C162 x⁸ y⁹ 3.1330521236e-36 3.2509299724e-37 1.1199804619e-36 C164 x⁶ y^{1 1} 3.5910568620e-35 -7.2194470264e-39 2.9629731827e-36 C166 x⁴ y¹³ 7.0550002441e-34 8.2664446432e-38 7.1869528674e-36 C168 x² y¹⁵ 3.2080231474e-33 -6.5392935648e-38 1.2245936062e-35 C170 17

y -1.9703142266e-33 -9.3347129176e-39 3.8844972846e-37 C171 x¹⁸ -1.7342115756e-42 8.3401397595e-41 -6.8644820970e-43 C173 x¹⁶ y² -4.1979733557e-41 1.0429593783e-39 -1.0638346724e-41 C175 x¹⁴ y⁴ -5.9988344258e-40 6.0087467082e-39 -1.2431441492e-40 C177 x¹² y⁶ 4.9843433085e-39 4.3561227842e-39 -6.4320671245e-40 C179 x¹⁰ y⁸ 2.6898460596e-38 8.2976611230e-40 -1.7056592226e-39 C181 _c8 ylO -1.7035559562e-37 1.6139057810e-39 -4.5690444894e-40

C183 x⁶ y¹² -2.3976006216e-36 3.8148901906e-40 2.3124667582e-38

C185 x⁴ y¹⁴ 1.2456084555e-36 2.1914578407e-40 4.1766450391e-38

C187 x² y¹⁶ 3.5839617512e-35 -6.1943173661e-41 -2.5645755876e-38

C189 18

y -5.982440098 le-36 -6.5541945691e-42 -2.8783972585e-38

Table 3c for Figure 16

Coefficient Formula M10

C7 x 2 y -1.1619556735e-08

C9 y 3 9.6267535999e-09

CIO X⁴ -2.1724936213e-l l

C12 x² y² -5.9884146205e-l 1

C14 y⁴ -1.4309946983e-l 1

C16 x 4 y -2.868705766 le- 14

C18 x 2 y 3^J -5.4800436499e- 15

C20 y 1.3922478017e-14

C21 x⁶ -4.5292421127e-17

C23 x⁴ y² -1.7435062351e-16

C25 x y⁴ -1.5873033837e-16

C27 y⁶ -3.5692678948e-17

C29 x⁶ y -5.0417764698e-20

C31 x⁴ y³ -5.5113782291e-20

C33 x² y⁵ 7.0094510892e-21

C35 7

y 2.244365428 le-20

C36 X -8.6423630967e-23

C38 x⁶ y² -3.9626818889e-22

C40 x⁴ y⁴ -6.1157378107e-22

C42 x² y⁶ -3.7171875916e-22

C44 y -7.6132006529e-23

C46 x⁸ y -7.3841318863e-26

C48 x⁶ y³ -2.0248611745e-25

C50 x⁴ y⁵ -1.3635832446e-25

C52 x² y⁷ 2.777326999 le-26

C54 9

y 3.6883888148e-26

C55 X¹⁰ -1.0527226907e-28

C57 x⁸ y² -1.0082114660e-27

C59 x⁶ y⁴ -2.2626738145e-27

C61 x⁴ y⁶ -2.2706354017e-27

C63 x² y⁸ -1.0825148907e-27 C65 ylO -1.0981947524e-28

C67 x¹⁰ y -2.4569304874e-31

C69 x⁸ y³ -1.9665576727e-31

C71 x⁶ y⁵ 8.2032192594e-34

C73 x 4 y 7 5.6097593847e-31

C75 x 2 y 9 3.2922913244e-31

C77 11

y 9.4787672714e-32

C78 x¹² -3.9893531144e-34

C80 x¹⁰ y² 1.3609035454e-34

C82 x⁸ y⁴ 2.3437368815e-33

C84 x⁶ y⁶ 3.5712114995e-33

C86 x⁴ y⁸ 2.1593599710e-33

C88 x² y¹⁰ 1.0521003819e-33

C90 y¹² -4.8696810122e-34

C92 x¹² y 4.4454812756e-37

C94 x¹⁰ y³ -3.2791419250e-36

C96 x⁸ y⁵ -5.5151065625e-36

C98 x⁶ y⁷ -8.0374905597e-36

CIOO x⁴ y⁹ -6.2640221789e-36

C102 x² y^{1 1} -4.1483325549e-37

C104 13

y -1.6999668152e-37

C105 x¹⁴ -2.8581665631e-41

C107 x¹² y² -1.6610779258e-38

C109 x¹⁰ y⁴ -7.6444036777e-38 cm x⁸ y⁶ -1.4907775962e-37

Cl 13 x⁶ y⁸ -1.4323789196e-37 Cl 15 x⁴ y¹⁰ -7.7581165704e-38 Cl 17 x 2 y 12 -2.5380651079e-38 Cl 19 y¹⁴ 3.1621427266e-41 C121 x¹⁴ y -2.5893948454e-42 C123 x¹² y³ 8.8855722212e-42 C125 x¹⁰ y⁵ 1.1642580099e-41 C127 x⁸ y⁷ 2.1345230441e-41 C129 x⁶ y⁹ 4.0247239518e-41 C131 x⁴ y^{1 1} 2.6373581198e-41 C133 x² y¹³ -5.8301508333e-43 C135 15

y 9.5872967943e-43 C136 x¹⁶ -7.2031404258e-46 C138 x¹⁴ y² 4.5466456847e-44 C140 x¹² y⁴ 2.7738070182e-43

C142 x¹⁰ y⁶ 7.2352098423e-43

C144 x⁸ y⁸ 9.1727615866e-43

C146 x⁶ y¹⁰ 6.4674973671e-43

C148 x⁴ y 2.6521873613e-43

C150 x 2 y 14 7.0631405299e-44

C152 yl6 -2.0282010420e-45

C154 x¹⁶ y 1.5910138418e-48

C156 x¹⁴ y³ -3.1565522043e-47

C158 x¹² y⁵ -6.3192786148e-47

C160 x¹⁰ y⁷ -7.8923511646e-47

C162 x⁸ y⁹ -1.1147703000e-46

C164 x⁶ y^{1 1} -1.1046319988e-46

C166 x⁴ y¹³ -3.8070948186e-47

C168 x² y¹⁵ 1.2792397916e-47

C170 17

y 2.9656508890e-49

C171 x¹⁸ -3.3430171036e-51

C173 x¹⁶ y² -1.0720497036e-49

C175 x¹⁴ y⁴ -6.616603113 le-49

C177 x¹² y⁶ -2.0451246296e-48

C179 x¹⁰ y⁸ -3.3493623262e-48

C181 x⁸ y¹⁰ -3.2223386958e-48

C183 x⁶ y¹² -1.9037914200e-48

C185 x⁴ y¹⁴ -6.7370152882e-49

C187 x² y¹⁶ -1.5421651631e-49

C189 18

y -1.7271699427e-51

Table 3d for Figure 16

Coordinates of the stop edge

Xi [mm] yi [mm] ¾+N/2 [mm] yi+_N/2 [mm]

-208.379236 74.438939 204.893801 -51.534650

-211.864671 65.974310 208.877155 -42.572102

-215.350106 55.518004 212.860510 -32.115796

-217.341784 48.049215 217.839703 -13.692781

-219.333461 37.592909 220.329300 2.738556

-220.827219 23.153248 220.827219 11.203185

-220.827219 10.207346 220.827219 20.663652

-219.831380 -1.742718 219.333461 37.592909

-217.839703 13.194862 217.839703 46.057537 -214.852187 -25.642845 216.345945 52.032569

-209.872994 -40.082505 212.860510 63.484713

-203.400043 -54.522166 210.868833 68.463907

-197.922930 -64.480552 207.881317 75.434777

-191.449979 -74.936858 202.902123 85.393164

-184.977028 -83.899406 193.441656 100.330743

-176.014480 -94.853631 185.474947 110.787049

-172.031126 -99.334905 178.006157 119.251677

-158.089385 -113.276646 172.031126 125.226709

-143.151805 -125.724629 162.072739 134.189257

-129.707983 -135.185096 147.633079 145.143482

-122.737113 -139.666370 130.205903 156.097707

-108.297452 -147.633079 111.782888 165.558174

-91.368195 -155.599788 93.359873 173.026964

-79.916051 -160.081062 78.422293 178.006157

-68.961826 -163.566497 58.505520 182.985351

-60.497198 -166.056094 48.547134 184.977028

-47.551295 -169.043610 35.601231 186.968705

-33.609554 -171.533206 12.696943 188.960382

-13.692781 -173.524883 -11.701104 188.960382

13.194862 -173.524883 -20.663652 188.462463

29.626200 -172.031126 -35.601231 186.968705

42.572102 -170.039448 -56.513843 183.483270

62.488875 -165.558174 -69.459745 180.495754

83.899406 -158.587304 -81.409809 177.010319

103.318259 -150.122675 -101.326582 170.039448

112.280807 -145.641401 -113.774565 164.562336

121.741274 -140.164289 -125.724629 158.587304

139.168450 -128.712145 -138.670531 151.118514

145.143482 -124.230871 -154.603949 140.164289

154.603949 -116.264162 -165.558174 131.201741

159.583142 -111.782888 -176.014480 121.243355

173.026964 -98.339066 -181.989512 114.770404

179.997835 -90.372357 -190.952060 103.816178

186.470786 -81.907728 -195.931253 96.845308

194.935414 -69.459745 -200.910446 88.

Table 4 for Figure 16 Wavelength 13.5 nm

NA 0.55

b^c 4.00

Py -8.80

Chief ray angle (CRA) 5.06°

Etendue 12.58 mm²

Mean wavefront aberration RMS 7.87 ihl

System transmission 7.68 %

Position of the entry pupil EP (x) -2380.34 mm

Position of the entry pupil EP (y) -2679.38 mm

Object-image offset 2210.98 mm

Working distance between M9 and

81 mm

image field

Reticle tilt 0.0°

Installation length 2301.55 mm

Obscuration 18.5 %

Installation space cuboid (789 x 2546 x 1817) mm

Table 5 for Figure 16

Ml M2 M3 M4 M5

Maximum angle of 13.7 84.2 80.4 80.4 83.4

incidence [deg]

Minimum angle of incidence [deg] 10.4 74.1 74.3 75.8 77.6

Mirror extent (x) [mm] 641.5 409.5 341.1 294.8 324.3

Mirror extent (y) [mm] 257.0 276.8 262.7 290.8 369.8

Maximum mirror diameter 641.6 409.6 356.9 377.9 433.3

[mm]

Table 6a for Figure 16

M6 M7 M8 M9 M10

Maximum angle of incidence 80.3 81.4 77.9 20.3 8.4

[deg]

Minimum angle of incidence [deg] 73.9 72.1 70.5 0.0 5.1

Viirror extent (x) [mm] 348.0 306.2 234.0 292.0 789.4

Viirror extent (y) [mm] 255.4 123.4 264.0 155.7 767.9

Maximum mirror diameter 349.8 306.3 291.5 292.0 790.0

[mm]

Table 6b for Figure 16 On account of the greater reduction in the yz-plane, the corresponding scale ratio of the projection optical unit 37 is shifted upward to greater b_n values in comparison to that according to Figure 7. Hence, in comparison with the projection optical unit 7, the projection optical unit 37 no longer satisfies the allowed scale ratios of the scale ratio curves 24i, 247, 24io and 24n. The scale ratio curves for which the projection optical unit 7 was unsuitable are not satisfied by projection optical unit 37 either. The projection optical unit 37 is suitable for the scale ratio curves 24₆, 24s, 24₉, 2412 to 24 ½ if all that is taken into account is the Pareto-optimal inscription of rectangular structuring fields 4i into the object specification field 19.

There is no change in the result of the admissible scale ratio curves 24i in the projection optical unit 37 if the auxiliary areas 25 to 28 are additionally taken into account. What emerges if the shadowing region D is additionally taken into account is that the scale ratio curves 24₆, 24s, 24₉ and 24i₂ are also eliminated from the admissible scale ratio curves 24i. All that remains as admissible scale ratio curves in the projection optical unit 37 are the scale ratio curves 24n to 24i6.

Figures 30 to 43 show a further embodiment of a projection optical unit 38, which can be used instead of the projection optical unit 7 in the projection exposure apparatus 1. Components and functions corresponding to those which were already explained above with reference to Figures 1 to 15, in particular, are denoted by the same reference signs and are not discussed in detail again.

The projection optical unit 38 has a reduction scale b_c in the xz-plane of 4.70 and a reduction scale p_y in the yz-plane of -8.80.

In terms of its basic design, the projection optical unit 38 corresponds to the projection optical unit 7.

The mirrors Ml and M2 overlap in the plan view according to Figure 3.

The optical design data emerge from following Tables 1 to 6, which, in turn, correspond in terms of the basic structure to Tables 1 to 6 relating to the embodiment according to Figure 2. Radii of the surfaces

RadiuS_x [mm] Power_x [1/mm] RadiuS_y [mm] Power_y [1/mm]

M01 -2139.90455825 0.00092764 -1373.11977394 0.00144565

M02 2582.32095828 -0.00016825 3348.09694670 -0.00012977

M03 1832.86151821 -0.00026833 -262737.81292930 0.00000187

M04 3695.54455200 -0.00011887 -6162.06096652 0.00007129

MO 5 -2153.25960440 0.00017981 -4412.62305237 0.00008774

M06 -882.16332363 0.00053588 -1899.40653934 0.00024888

M07 -694.05381126 0.00066078 40178.56498808 -0.00001141

MO 8 -902.11305413 0.00057442 -5798.78102485 0.00008936

M09 1131.39037185 -0.00176774 315.29483148 -0.00634326

M10 -784.57643539 0.00252929 -719.07853325 0.00275967

Table 1 for Figure 30

Decentring (location, angle) the surfaces

D_x [mm] D_y [mm] l)_z [mm]

Reticle 0.000000000 1834.113580290 2312.048676749

M01 0.000000000 1684.187265100 598.383052570

M02 0.000000000 1549.068060009 1449.681805403

M03 0.000000000 1371.318189813 1712.099290804

M04 0.000000000 1082.201722234 1862.070558573

M05 0.000000000 738.525366001 1874.311017579

M06 0.000000000 147.580015498 1655.890535477

M07 0.000000000 -62.261412411 1425.850465480

M08 0.000000000 -127.329396917 1196.791838022

M09 0.000000000 148.326521489 105.401883054

Stop 0.000000000 110.051063873 255.419876855

M10 0.000000000 0.000000000 686.757366877

Wafer 0.000000000 0.000000000 0.000000000

ax [°] ay [°] az [°]

Reticle -0.000000000 0.000000000 0.000000000

M01 2.009412367 180.000000000 0.000000000

M02 -68.434609348 0.000000000 0.000000000

M03 -41.652418444 0.000000000 180.000000000

M04 -14.728295691 0.000000000 0.000000000

M05 9.122559278 0.000000000 180.000000000

M06 33.956999305 0.000000000 0.000000000

M07 60.885493189 0.000000000 180.000000000 MO 8 89.158413816 0.000000000 0.000000000

M09 14.243979417 180.000000000 0.000000000

Stop 7.156517725 180.000000000 0.000000000

M10 7.156517725 0.000000000 0.000000000

Wafer 0.000000000 0.000000000 0.000000000

Table 2 for Figure 30

Free-form coefficients of the surfaces

Coefficient Formula M01 M02 M03

C7 x 2 y 1.7426878325e-08 -6.5178691072e-08 2.6835734080e-07

C9 3

y -6.6077346227e-09 -3.8821297444e-07 3.7729483337e-07

CIO X⁴ -6.5515572520e-12 1.6320428899e-10 8.9525960742e-10

C12 x² y² 4.5903363770e-l 1 -2.4785872529e-l 1 7.0365174648e-10

C14 y⁴ -1.1922758913e-10 1.3401644995e-09 -1.2960644957e-10

C16 x 4 y -7.2476667576e-15 1.8947341630e-14 3.1204533391e-12

C18 x 2 y 3 6.1901613041e-14 2.2563270123e-12 -6.1748295267e-14

C20 y 2.0001661605e-14 -6.0673766748e-12 3.5706035244e-12

C21 x⁶ -1.2920097328e-18 2.9456035020e-16 2.5901148302e-16

C23 x⁴ y² -3.6476053184e-17 1.2354164776e-15 2.1471396790e-15

C25 x y⁴ -1.1810601392e-16 -1.2022816213e-14 1.1114483505e-15

C27 .6

y -1.5203113365e-16 2.6693657963e-14 1.0329823262e-15

C29 x⁶ y 2.0802977069e-21 -1.7385871642e-18 6.6042918364e-18

C31 x⁴ y³ - 1.8474904647e- 19 -1.1737178674e-17 1.4144658923e-17

C33 x² y⁵ -3.2756705624e-19 6.4671009105e-17 1.9421373406e-17

C35 y⁷ 3.3185857361e-18 -9.5778779803e-17 1.7088481198e-16

C36 x⁸ 1.2782281420e-23 -1.4568858470e-21 2.7774822661e-20

C38 x⁶ y² 1.5216967939e-23 2.7278820391e-20 1.2772764458e-19

C40 x⁴ y⁴ 1.2938097467e-21 8.8740828054e-20 2.7978434552e-19

C42 x² y⁶ 1.1674479894e-20 -3.1123618188e-19 4.6044904015e-19

C44 y⁸ 3.6741320793e-20 4.6939452318e-19 8.7141571203e-19

C46 x⁸ y 2.9708245590e-25 -7.2956377844e-24 -8.4929243345e-22

C48 x⁶ y³ 2.0820324994e-24 -1.6253227122e-23 -5.7169612413e-21

C50 x⁴ y⁵ -7.7820665726e-24 -3.9374876656e-22 -1.0684311797e-20

C52 x² y⁷ -5.4913952653e-23 6.5027406704e-22 -1.1329965307e-21

C54 9

y -2.5286385054e-22 -4.0777332819e-21 -1.0362875697e-20

C55 X¹⁰ -5.5910460048e-28 1.5515233413e-25 - 1.722182674 le-24

C57 x⁸ y² -1.9563253726e-27 -5.7125466006e-25 -2.9769220952e-23

C59 x⁶ y⁴ -5.9549523053e-26 -1.7487775923e-24 -8.2887135800e-23

C61 x⁴ y⁶ -8.0986030379e-25 1.1876875223e-24 -1.4576599193e-22 C63 x² y⁸ -3.5613943677e-24 -3.6236768591e-24 -1.0665642394e-22

C65 yio -6.6378117804e-24 2.5270468502e-23 -1.3003317765e-22

C67 x¹⁰ y -5.6057283203e-30 -9.3114425900e-28 9.5179289762e-26

C69 x⁸ y³ -6.7875509534e-29 -5.9330779624e-27 6.2213954914e-25

C71 x⁶ y⁵ -2.1418877683e-28 -2.4313343540e-26 2.0958905274e-24

C73 x 4 y 7 1.8943789222e-27 9.6144045223e-27 1.8725521528e-24

C75 x 2 y 9 1.1218812820e-27 1.3595380847e-25 -2.7842281485e-25

C77 11

y 2.5769518506e-26 -1.0596842190e-25 1.2958346246e-24

C78 x¹² 1.1401952144e-32 -6.8967779571e-30 6.4910042326e-29

C80 x¹⁰ y² 6.8379386233e-32 3.0709029780e-29 2.8916929019e-27

C82 x⁸ y⁴ 1.1577401480e-30 2.3728273309e-28 8.4595970127e-27

C84 x⁶ y⁶ 2.1532489351e-29 3.7000735485e-28 2.2402346985e-26

C86 x⁴ y⁸ 1.4734155975e-28 5.6129999308e-29 2.3775952715e-26

C88 x² y¹⁰ 4.4717070497e-28 -8.5361931098e-28 1.6797305281e-26

C90 y¹² 6.7569435968e-28 3.9450041045e-29 1.9445069842e-26

C92 x¹² y 6.4787771876e-35 7.3229292234e-32 -5.6719262544e-30

C94 x¹⁰ y³ 1.1150524699e-33 1.6232470024e-31 -3.7133404049e-29

C96 x⁸ y⁵ 9.0232110404e-33 1.6005337931e-30 -1.8429814281e-28

C98 x⁶ y⁷ -5.9702868130e-33 -8.1745518229e-31 -3.2761208236e-28

CIOO x⁴ y⁹ -1.3881804814e-31 -3.9646165913e-30 -1.6213783449e-28

C102 x² y^{1 1} 2.1379044547e-31 -5.1986539648e-30 1.0039834100e-28

C104 13

y -1.7226884530e-30 6.6618182214e-30 -7.2773663383e-29

C105 x¹⁴ -1.3437730198e-37 2.0435086024e-34 -1.2597987623e-33

C107 x¹² y² -1.3100347172e-36 -7.5204158295e-34 -1.6237444587e-31

C109 x¹⁰ y⁴ -1.2452130637e-35 -1.2056306328e-32 -5.0158343359e-31 cm x⁸ y⁶ -3.0941833103e-34 -2.8170544082e-32 -1.7822207380e-30

Cl 13 x⁶ y⁸ -2.7371807875e-33 -2.3485799792e-32 -2.9690666445e-30 Cl 15 x⁴ y¹⁰ -1.3038379774e-32 9.5982975983e-33 -2.0416162990e-30 Cl 17 x 2 y 12 -3.3095767428e-32 6.1396868068e-32 -1.2542209748e-30 Cl 19 y¹⁴ -4.1049963216e-32 -4.8022076570e-32 -1.5969936273e-30 C121 x¹⁴ y -4.1869507876e-40 -1.9107523075e-36 1.6073492697e-34 C123 x¹² y³ -9.5684481148e-39 5.0089878790e-37 1.0827951000e-33 C125 x¹⁰ y⁵ -1.0234469199e-37 -3.4229212685e-35 7.4506274487e-33 C127 x⁸ y⁷ -3.9912185498e-37 2.5499431902e-35 1.9260916369e-32 C129 x⁶ y⁹ 1.5386513298e-36 3.1662444779e-34 2.2909121177e-32 C131 x⁴ y^{1 1} 2.3010578573e-36 1.7006679323e-34 5.2765883859e-33 C133 x² y¹³ -2.1666529459e-35 7.8480448801e-35 -9.7107544578e-33 C135 15

y 6.8523780149e-35 -6.4708292966e-35 2.8447829420e-33 C136 16

X 8.3836661951e-43 -2.9361486264e-39 -1.2005149446e-38 C138 x 14 2

1 y 1.2495461791e-41 4.0446757730e-39 4.6934231802e-36

C140 x¹² y⁴ 8.2825546155e-41 2.4354266225e-37 1.6284108024e-35

C142 x¹⁰ y⁶ 2.3753792190e-39 8.0310793376e-37 7.1348066396e-35

C144 x⁸ y⁸ 2.4310948042e-38 8.6586823142e-37 1.6730096419e-34

C146 x⁶ y¹⁰ 1.5087109592e-37 -4.4166548670e-37 1.8829043058e-34

C148 x⁴ y 5.7874281161e-37 -4.4891097981e-38 7.8757592046e-35

C150 x 2 y 14 1.3048559061e-36 -3.0371904664e-36 3.7193735641e-35

C152 yl6 1.3722358402e-36 2.0537960824e-36 7.4267332410e-35

C154 x¹⁶ y 1.1628582951e-45 1.6872905751e-41 -1.7500234054e-39

C156 x¹⁴ y³ 3.3472954979e-44 -4.4006420188e-41 -1.2418380787e-38

C158 x¹² y⁵ 3.8586274398e-43 2.0913818849e-40 -1.1546997293e-37

C160 x¹⁰ y⁷ 3.4112763307e-42 -3.7835574685e-40 -3.8405639209e-37

C162 x⁸ y⁹ -1.7451105599e-42 -7.2324901234e-39 -6.9471751713e-37

C164 x⁶ y^{1 1} -2.2625390237e-41 -9.8899125234e-39 -5.8425013643e-37

C166 x⁴ y¹³ 3.7607050984e-41 -7.3920269742e-39 -5.9137950757e-38

C168 x² y¹⁵ 6.1971201298e-40 1.3766109023e-38 3.8149383042e-37

C170 17

y -1.1625740147e-39 -8.6195153446e-39 -7.5076582033e-38

C171 x¹⁸ -2.1302070623e-48 1.3888098448e-44 6.055500945 le-43

C173 x¹⁶ y² -4.4929070879e-47 5.9907239150e-44 -5.4165139736e-41

C175 x¹⁴ y⁴ -2.7543673863e-46 -1.5499279349e-42 -2.2267625954e-40

C177 x¹² y⁶ -8.0554616747e-45 -8.1782490417e-42 -1.1691375917e-39

C179 x¹⁰ y⁸ -8.2456119456e-44 -6.0672809045e-42 -3.4448843864e-39

C181 x⁸ y¹⁰ -6.5744543913e-43 2.2393137325e-41 -5.6750926308e-39

C183 x⁶ y¹² -2.9039002857e-42 3.5210776589e-41 -4.5933148985e-39

C185 x⁴ y¹⁴ -1.0776617680e-41 2.1436301163e-41 -1.2068371748e-39

C187 x² y¹⁶ -2.094306281 Oe-41 -2.0658026914e-41 4.9859670720e-40

C189 18

y -1.9383776928e-41 1.1985345912e-41 -1.5849807288e-39

Table 3a for Figure 30

Coefficient Formula M04 M05 M06

C7 x 2 y 4.9044547045e-08 -1.2254048421e-07 1.4188281251e-07

C9 y 3 -5.8551961877e-08 -1.6355534836e-07 -1.6676901346e-08

CIO X⁴ 2.2293183396e-10 -8.0243321377e-l 1 -4.3095674155e-10

C12 x² y² 6.7595463166e-l l -2.7465511006e-10 3.4554684261e-l 1

C14 y⁴ -2.9515361697e-10 -4.3613974817e-l 1 -3.4420202998e-10

C16 x 4 y 4.2322013280e-13 -4.3265721858e-13 -2.1939484758e-13

C18 x 2 y 3^J 1.0114823935e-12 3.3018278158e-13 1.9651118091 e- 13

C20 y -3.0610157497e-13 -2.5398756527e-13 9.3245321856e-13

C21 6

X -2.6497746461 e- 16 -3.3200765770e-16 -7.0052255642e-16 C23 x 4 y 2 -1.1522579767e-15 8.2663345626e-16 1.9440757616e-16

C25 x 2 y 4

4 8.6156654725e-16 -5.3154423859e-16 -1.0350128899e-15

C27 y⁶ -5.4094576217e- 15 9.4323666792e-16 -3.4732517609e-15

C29 x⁶ y 9.3785147124e-18 -1.633824521 le-18 -9.1915349362e-19

C31 x⁴ y³ 8.5962184370e-18 -6.7719425436e-18 -3.1811637383e- 18

C33 x² y⁵ 2.8839814733e-17 1.0407984737e-17 1.0035980597e-17

C35 7

y -4.5258879086e-17 -2.0635841621e-18 5.1238777608e-17

C36 X 7.1585237245e-20 -3.8881955432e-20 -2.5526685494e-21

C38 x⁶ y² 3.9928010539e-21 -1.7922282448e-20 -8.9166478202e-20

C40 x⁴ y⁴ 1.3227274710e-20 -8.4948473200e-20 -2.9777820410e-19

C42 x² y⁶ 1.5383699718e-19 -1.1320127204e-19 -4.4074935146e-19

C44 y 3.8918980138e-19 5.5829115865e-20 1.6249087635e-20

C46 x⁸ y 3.0342591227e-22 9.6547378316e-22 1.1847963269e-22

C48 x⁶ y³ -6.4569844579e-22 1.0285077169e-21 8.2988568727e-22

C50 x⁴ y⁵ -1.4779944302e-21 4.8246509578e-22 2.086029483 le-21

C52 x² y⁷ -5.3558349589e-22 -5.9603582667e-22 -4.2415321917e-22

C54 9

y 1.2482188813e-20 1.3540748521e-22 -2.7796812589e-21

C55 X¹⁰ -9.4874235962e-24 8.5342385375e-25 2.7347110906e-25

C57 x⁸ y² -1.1335744237e-24 2.7807589755e-24 7.8179638514e-24

C59 x⁶ y⁴ -4.1494205898e-24 1.3585049470e-23 3.6848113120e-23

C61 x⁴ y⁶ 5.925750081 le-24 1.8612044652e-23 5.7114037659e-23

C63 x² y⁸ -4.3140612220e-23 7.4304562012e-24 5.0004570042e-23

C65 yio -1.0195794955e-22 -7.4438587864e-24 -1.7464983412e-23

C67 x¹⁰ y -8.3620661605e-26 -7.1243723293e-26 -5.6550316934e-27

C69 x⁸ y³ 1.5365679961e-25 -1.4501890056e-25 -7.7607085552e-26

C71 x⁶ y⁵ 1.3564449801e-25 -2.3258016184e-25 -2.9988673556e-25

C73 x 4 y 7 3.6501094907e-25 -8.0792190164e-26 -3.8247064080e-25

C75 x 2 y 9 -1.3555040847e-25 6.7167105724e-26 2.3182336151e-25

C77 11

y -2.0694131967e-24 -3.4103121573e-26 1.7707514958e-25

C78 x¹² 7.2624419233e-28 1.9520095056e-29 -1.7185048222e-29

C80 x¹⁰ y² 3.2908352672e-28 -5.4316538529e-28 -3.8060001116e-28

C82 x⁸ y⁴ -2.776728975 le-28 -1.2730986662e-27 -2.3955259270e-27

C84 x⁶ y⁶ -3.538474298 le-28 -2.4636342422e-27 -5.0268838155e-27

C86 x⁴ y⁸ -1.9145997541e-27 -1.1874988347e-27 -5.7837527099e-27

C88 x² y¹⁰ 7.5511935389e-27 -5.0746748116e-28 -4.522273472 le-27

C90 y¹² 1.4324256907e-26 8.4861245535e-28 1.2650575685e-27

C92 x¹² y 8.5617194406e-30 3.4546747274e-30 1.8583824227e-31

C94 x¹⁰ y³ -1.5948765804e-29 1.0771752118e-29 4.0713977710e-30

C96 x⁸ y⁵ -1.4440690956e-29 1.8689476188e-29 2.0720077629e-29 C98 x⁶ y⁷ -1.5746739713e-29 2.6812223039e-29 4.6762808316e-29

CIOO x⁴ y⁹ -3.5427908079e-29 -4.1559522242e-31 3.4017118583e-29

C102 x² y^{1 1} 4.2202776657e-29 6.9004693660e-32 -2.5942152370e-29

C104 13

y 1.9736149377e-28 1.3594277319e-30 -4.4368899660e-30

C105 x¹⁴ -2.9624860104e-32 -2.3141254413e-33 4.6123723024e-34

C107 x¹² y² -4.9781847707e-32 4.3638818097e-32 9.6097543935e-33

C109 x¹⁰ y⁴ 7.6402356483e-32 8.0179931665e-32 7.5211547315e-32 cm x⁸ y⁶ 3.3964800074e-32 1.7866857649e-31 1.9966270932e-31

Cl 13 x⁶ y⁸ 1.1792871634e-31 1.5780526497e-31 2.4225615480e-31 Cl 15 x⁴ y¹⁰ 1.8587187146e-31 5.3504133979e-32 3.1450424630e-31 Cl 17 x 2 y 12 -8.0034542128e-31 5.5689769219e-33 2.6231877007e-31 Cl 19 y¹⁴ -1.2686780720e-30 -4.5481597303e-32 -4.4628180955e-32 C121 x¹⁴ y -4.0014067345e-34 -9.2799503276e-35 -3.6455146015e-36 C123 x¹² y³ 7.4025166652e-34 -3.9781912207e-34 -1.1872076997e-34 C125 x¹⁰ y⁵ 1.0283374990e-33 -7.3237387512e-34 -6.8443400665e-34 C127 x⁸ y⁷ 2.5991863225e-34 -1.2484560280e-33 -2.0327751700e-33 C129 x⁶ y⁹ 1.3445063474e-33 -1.2670294228e-33 -3.0682515916e-33 C131 x⁴ y^{1 1} 1.4332459575e-33 3.3517721056e-34 -1.2289713871e-33 C133 x² y¹³ -3.5017840974e-33 -2.2172033346e-34 1.3617011916e-33 C135 15

y -9.9728526205e-33 8.3776140520e-36 -8.0176477156e-36 C136 x¹⁶ 5.3101677178e-37 8.8933166273e-38 -6.4713827830e-39 C138 x¹⁴ y² 3.1597109694e-36 -1.5762798614e-36 -1.0603028315e-37 C140 x¹² y⁴ -4.2657554292e-36 -3.4568453471e-36 -8.5379335633e-37 C142 x¹⁰ y⁶ -5.7802237243e-36 -4.9586437614e-36 -3.1598241898e-36 C144 x⁸ y⁸ 1.7222327695e-36 -1.1430213062e-35 -1.7510466473e-36 C146 x⁶ y¹⁰ -1.4751199638e-35 -3.0863836471e-36 -2.2529051585e-36 C148 x⁴ y -4.2122399287e-36 -2.4101776492e-36 -9.5378524753e-36 C150 x 2 y 14 4.4588112986e-35 9.5474526371e-37 -9.7663973696e-36 C152 yl6 6.2502154310e-35 1.0843967254e-36 3.1149530600e-37 C154 x¹⁶ y 7.2795880481e-39 9.9981615893e-40 3.3985458469e-41 C156 x¹⁴ y³ -1.239520501 le-38 5.6095761702e-39 1.5227869428e-39 C158 x¹² y⁵ -2.7449067544e-38 1.2604150888e-38 9.4885499299e-39 C160 x¹⁰ y⁷ 4.6773018281e-40 1.6771936806e-38 3.0434789266e-38 C162 x⁸ y⁹ -1.8392052807e-38 3.5415378549e-38 6.7691275982e-38 C164 x⁶ y^{1 1} -3.0311868420e-38 1.5987969751e-38 6.7440591056e-38 C166 x⁴ y¹³ -1.5591926185e-38 -9.6416452987e-39 1.4372615084e-38 C168 x² y¹⁵ 1.0062648317e-37 7.6990819647e-39 -2.6128678682e-38 C170 17

y 2.0735141183e-37 -1.3901671532e-39 1.6577373639e-39 C171 18

X -3.2266407102e-42 - 1.2748604721 e-42 3.2220609631 e-44 C173 x¹⁶ y² -6.9400268388e-41 2.0914817123e-41 1.5652175238e-43

C175 x¹⁴ y⁴ 6.9779372892e-41 6.6556382376e-41 -3.6441085312e-42

C177 x¹² y⁶ 2.1073006405e-40 4.5709931328e-41 4.5526659303e-42

C179 x¹⁰ y⁸ -1.1169724755e-40 2.1212129889e-40 -6.6711185255e-41

C181 x⁸ y¹⁰ 1.9367369422e-40 1.7518613708e-40 -1.6145779366e-40

C183 x⁶ y¹² 3.0422155161e-40 2.4477362423e-41 -9.6696970342e-41

C185 x⁴ y¹⁴ -3.3706562710e-41 5.3717046134e-41 1.3766540516e-40

C187 x² y¹⁶ -1.0312017747e-39 -3.8411401401e-41 1.7194670824e-40

C189 18

y -1.3068506882e-39 -5.6376968234e-42 7.0037358232e-42

Table 3b for Figure 30

Coefficient Formula M07 M08 M09

C7 x 2 y -4.2199123517e-08 3.7858844158e-07 1.4387266454e-06

C9 y 3 -1.6536295577e-07 -2.1014199184e-07 -9.1191091762e-07

CIO X⁴ 3.4371960184e-l 1 2.2715641934e-10 1.4749280691e-09

C12 x² y² -1.3413443399e-09 -5.2557655318e-10 5.0527124367e-09

C14 y⁴ 1.5115560000e-09 -6.0485840887e-10 2.1024662286e-09

C16 x 4 y -1.8309829720e-13 7.2436355895e-13 6.4286572276e-12

C18 x 2 y 3^J 8.9389758201e-13 -1.5610150402e-13 -4.3629294781e-12

C20 y -3.1074413581e-12 -3.0377012351e-12 -1.3806612685e-l 1

C21 x⁶ 2.2871144053e-16 9.5559207163e-16 7.0711038669e-15

C23 x⁴ y² -1.0328916552e-15 -6.1318457574e-16 4.2513882354e-14

C25 x y⁴ 2.1078567173e-14 -6.6853430734e-15 7.3312833004e-14

C27 y⁶ 1.8464145453e-13 -1.8102924646e-14 8.2164954357e-14

C29 x⁶ y 1.1908225322e-17 2.2475187218e-17 5.5486099607e-17

C31 x⁴ y³ -1.1642440634e- 16 1.9840787095e-17 5.7932606833e-17

C33 x² y⁵ -5.7476067787e-16 -2.0582086784e-17 -8.3188796284e-17

C35 y⁷ 2.8768882968e-15 -1.0549654648e-16 -7.5956455942e-16

C36 x⁸ -6.5138943691e-21 -1.1910842415e-19 3.1849124369e-20

C38 x⁶ y² -1.0000774392e-19 6.6116414464e-19 3.9801092548e-19

C40 x⁴ y⁴ -1.0305195177e-17 9.4940158150e-19 1.0485960708e-18

C42 x² y⁶ -9.9702705983e-17 3.2856429666e-19 6.9017409899e-19

C44 y⁸ -1.5550656290e-16 -3.5600487918e-19 -1.9726873160e-18

C46 x⁸ y -1.2830777309e-21 -5.3755682334e-21 6.7267138619e-22

C48 x⁶ y³ 1.3279820395e-20 -9.7655357918e-21 2.7909082415e-21

C50 x⁴ y⁵ 1.0830820952e-19 1.3273968721e-21 3.5953113164e-21

C52 x² y⁷ 3.5931792005e-20 -1.8844656328e-20 3.466109441 le-21

C54 9

y -4.9910472804e- 18 -4.1465567345e-21 -2.3453463064e-20

C55 10

X 2.4054899661e-25 3.2110194905e-23 9.9686498624e-25 C57 x⁸ y² 1.422415638 le-23 -1.3319598251e-22 1.0041219912e-23

C59 x⁶ y⁴ 1.2943078377e-21 -3.9723055988e-22 6.0406491007e-23

C61 x⁴ y⁶ 1.8258315233e-20 -2.4989303339e-22 1.1649230484e-22

C63 x² y⁸ 1.0009545562e-19 -4.5447075661e-22 -3.3831100672e-22

C65 yio 5.7360063013e-20 -1.2229099588e-22 1.2188729200e-21

C67 x¹⁰ y 1.3024986420e-25 8.7867723634e-25 -1.8011881632e-26

C69 x⁸ y³ -7.5489261598e-25 2.3059282823e-24 -1.5169570301e-25

C71 x⁶ y⁵ -1.2712644192e-23 -7.2628087777e-25 -8.0566184448e-25

C73 x 4 y 7 2.6850866921e-24 -1.4341350985e-24 -4.2930123980e-24

C75 x 2 y 9 4.5052621647e-22 1.3613329410e-24 -8.3135847265e-24

C77 11

y 3.7915593409e-21 -1.4877136348e-24 5.6039837172e-24

C78 x¹² 7.7720905965e-30 -5.0733760903e-27 -2.0770542126e-29

C80 x¹⁰ y² -1.2113381735e-27 1.3455123451e-26 -5.4677671675e-28

C82 x⁸ y⁴ -1.0198160426e-25 6.9787006799e-26 -6.2191935877e-27

C84 x⁶ y⁶ -1.5415270243 e-24 7.4713582272e-26 -3.3952900766e-26

C86 x⁴ y⁸ -1.3922552790e-23 3.4326839199e-26 -1.3389117766e-26

C88 x² y¹⁰ -5.2336254256e-23 1.0073016289e-25 2.1818357825e-25

C90 y¹² 1.7048905096e-23 -9.4477754939e-27 -1.0451074806e-25

C92 x¹² y -7.5370053560e-30 -7.9774913998e-29 1.5600549122e-30

C94 x¹⁰ y³ 1.8593234120e-29 -2.5418246964e-28 1.4067495023e-29

C96 x⁸ y⁵ 5.2552802658e-28 -9.2421023315e-29 8.4782290040e-29

C98 x⁶ y⁷ 5.6561839745e-27 7.8404548464e-28 3.3108404577e-28

CIOO x⁴ y⁹ -7.0569242124e-26 6.6031105343e-29 1.6942578207e-27

C102 x² y^{1 1} -4.2418409627e-25 4.4618878535e-28 2.3040538502e-27

C104 13

y - 1.2591405827e-24 -5.3398381181e-29 -6.3918263678e-28

C105 x¹⁴ -9.3303924014e-34 4.5426141530e-31 3.5046263445e-34

C107 x¹² y² 4.9815005165e-32 -6.4954628056e-31 3.7610060081e-32

C109 x¹⁰ y⁴ 5.2930089600e-30 -5.7849445805e-30 4.6375890219e-31 cm x⁸ y⁶ 6.992260781 le-29 -1.0491677722e-29 3.5509887424e-30

Cl 13 x⁶ y⁸ 8.5166946683e-28 -3.3246233966e-30 9.9849567667e-30 Cl 15 x⁴ y¹⁰ 4.8736619355e-27 -6.5539204242e-30 -5.3604259143e-30 Cl 17 x 2 y 12 1.3586730354e-26 -9.2031782636e-30 -4.7406311087e-29 Cl 19 y¹⁴ -1.9329753797e-26 -4.3192258952e-31 -1.7471472919e-30 C121 x¹⁴ y 2.2724358872e-34 3.9123136595e-33 -4.8441914262e-35 C123 x¹² y³ -4.4298561543e-35 1.2951865424e-32 -5.2658058251e-34 C125 x¹⁰ y⁵ -6.7641214114e-33 1.9196598630e-32 -4.2534579191e-33 C127 x⁸ y⁷ -2.0830127398e-31 -5.6784766772e-32 -1.8423599269e-32 C129 x⁶ y⁹ -4.4876940900e-31 -1.0226497074e-31 -7.1087942029e-32 C131 x⁴ y^{1 1} 4.3028469140e-29 -2.2795459173e-32 -3.0434137025e-31 C133 x 2 y 13 1.5744538975e-28 -1.2021052105e-31 -3.1508039746e-31

C135 15

y 7.0125098133e-29 -2.6699667053e-33 3.1115800209e-32

C136 X¹⁶ 3.3940091527e-38 -2.1434715567e-35 9.7683483273e-39

C138 x¹⁴ y² -6.9838303510e-37 1.1570604249e-35 -1.1869926267e-36

C140 x¹² y⁴ -1.6116320294e-34 2.1383224297e-34 -1.6494336450e-35

C142 x¹⁰ y⁶ -1.8072079470e-33 6.353500643 le-34 -1.5981836143e-34

C144 x⁸ y⁸ -2.2653748130e-32 3.2180561018e-34 -7.2635127591e-34

C146 x⁶ y¹⁰ -2.1426316242e-31 -3.7816216691e-34 -1.1068516289e-33

C148 x⁴ y -5.5331080288e-31 6.1532835307e-34 1.9301399708e-33

C150 x 2 y 14 -1.3277939014e-30 -5.5905588588e-34 5.3044679989e-33

C152 yl6 3.9847569878e-30 -7.9228995884e-36 9.4236333082e-34

C154 x¹⁶ y -2.7517362399e-39 -7.9592487860e-38 6.5213020906e-40

C156 x¹⁴ y³ -5.2483430390e-39 -2.4019470457e-37 8.4325697525e-39

C158 x¹² y⁵ 7.9559349285e-38 -7.5491247707e-37 8.0499713973e-38

C160 x¹⁰ y⁷ -1.3765228774e-36 8.9723027412e-37 4.4907119904e-37

C162 x⁸ y⁹ 7.1725776381e-35 5.0215604481e-36 1.4970803156e-36

C164 x⁶ y¹¹ -5.7607381301e-34 2.0591751453e-36 6.0342273374e-36

C166 x⁴ y¹³ -6.3530280703e-33 5.4036363271e-36 2.0229448026e-35

C168 x² y¹⁵ -2.4845058236e-32 -1.0146517706e-36 1.6082603006e-35

C170 17

y 3.5490341420e-32 -5.7258815276e-39 -1.4134207528e-36

C171 X¹⁸ -4.0436538836e-43 4.1427230340e-40 -2.3241569178e-43

C173 x¹⁶ y² -3.2988108139e-42 -9.5444511601 e-42 1.6295694202e-41

C175 x¹⁴ y⁴ 2.0535415531e-39 -2.5338943718e-39 2.4189829544e-40

C177 x¹² y⁶ 2.3990296362e-38 -1.3999973916e-38 2.7089834086e-39

C179 x¹⁰ y⁸ 1.8190815639e-37 -1.0016490514e-38 1.6429876492e-38

C181 x⁸ y¹⁰ 3.5335522295e-36 1.8917979854e-38 4.7615437482e-38

C183 x⁶ y¹² 1.1467647111e-35 1.1249049880e-38 3.0136699870e-38

C185 x⁴ y¹⁴ -3.9745195587e-36 1.2760236382e-38 -1.6243720729e-37

C187 x² y¹⁶ -8.6759892693e-35 -2.9308500771e-40 -2.3678147952e-37

C189 18

y 1.0575439753e-34 1.0698752583e-41 -3.6948489454e-38

Table 3c for Figure 30

Coefficient Formula M10

C7 x 2 y -9.3479519329e-09

C9 y 3 1.0030003070e-08

CIO X⁴ -2.2276966215e-l 1

C12 x² y² -5.8456897718e-l 1

C14 y⁴ -1.2468906159e-l 1

C16 x 4 y -2.3354834733e-14 C18 x 2 3 4.4940020685e-16

C20 y 1.4894553686e-14

C21 x⁶ -4.7975060368e-17

C23 x⁴ y² -1.7261750961e-16

C25 x y⁴ -1.4933461801e-16

C27 y⁶ -3.0106711938e-17

C29 x⁶ y -3.9498375489e-20

C31 x⁴ y³ -3.7813299375e-20

C33 x² y⁵ 2.1516541218e-20

C35 7

y 2.6431238423e-20

C36 X -8.4835205260e-23

C38 x⁶ y² -4.0516138664e-22

C40 x⁴ y⁴ -5.9844485385e-22

C42 x² y⁶ -3.4822727100e-22

C44 y -5.7610349727e-23

C46 x⁸ y -6.815163041 le-26

C48 x⁶ y³ -1.5227335878e-25

C50 x⁴ y⁵ -7.5124040802e-26

C52 x² y⁷ 2.4152259923e-26

C54 9

y 6.1704342346e-26

C55 X¹⁰ -1.3743942369e-28

C57 x⁸ y² -8.4089353136e-28

C59 x⁶ y⁴ -1.8375694963e-27

C61 x⁴ y⁶ -1.8339060459e-27

C63 x² y⁸ -7.046472053 le-28

C65 yio -5.5287117125e-29

C67 x¹⁰ y -8.1292483029e-32

C69 x⁸ y³ -1.3707237742e-31

C71 x⁶ y⁵ -3.1863352435e-32

C73 x 4 y 7 7.8442623922e-31

C75 x 2 y 9 1.2175886968e-30

C77 11

y 7.8519187583e-32

C78 x¹² -3.7592370205e-34

C80 x¹⁰ y² -2.1039416634e-33

C82 x⁸ y⁴ -4.5395863218e-33

C84 x⁶ y⁶ -3.8333894777e-33

C86 x⁴ y⁸ -2.9006605495e-33

C88 x² y¹⁰ -2.5462117883e-33

C90 12

y -1.2734046610e-33 C92 x¹² y -4.8080050475e-37

C94 x¹⁰ y³ -3.2094979729e-36

C96 x⁸ y⁵ -4.2227695119e-36

C98 x⁶ y⁷ -5.2203983499e-36

CIOO x⁴ y⁹ -9.4881212778e-36

C102 x² y^{1 1} -8.5611174483e-36

C104 13

y -9.2384991148e-37

C105 x¹⁴ 2.7670836087e-40

C107 x¹² y² 6.1328990230e-41

C109 x¹⁰ y⁴ -8.1489904906e-39 cm x⁸ y⁶ -4.4669886003e-38

Cl 13 x⁶ y⁸ -6.2937582037e-38 Cl 15 x⁴ y¹⁰ -2.8311368828e-38 Cl 17 x 2 y 12 2.5370973656e-39 Cl 19 y¹⁴ 6.4126626237e-39 C121 x¹⁴ y 9.9015018098e-43 C123 x¹² y³ 1.2145891024e-41 C125 x¹⁰ y⁵ 1.8366746833e-41 C127 x⁸ y⁷ 1.5842347005e-41 C129 x⁶ y⁹ 3.7362009257e-41 C131 x⁴ y^{1 1} 6.4812451567e-41 C133 x² y¹³ 4.3250646081e-41 C135 15

y 7.2076923209e-42 C136 x¹⁶ -2.3636426603 e-45 C138 x¹⁴ y² -2.0702018365e-44 C140 x¹² y⁴ -5.3912349594e-44 C142 x¹⁰ y⁶ 5.2994160668e-44 C144 x⁸ y⁸ 2.6031702359e-43 C146 x⁶ y¹⁰ 2.5283242192e-43 C148 x⁴ y 6.4380076792e-44 C150 x 2 y 14 -2.6437236406e-44 C152 yl6 -2.1744996396e-44 C154 x¹⁶ y -3.5462956348e-48 C156 x¹⁴ y³ -3.8527039339e-47 C158 x¹² y⁵ -8.7396993445e-47 C160 x¹⁰ y⁷ -9.1988392396e-47 C162 x⁸ y⁹ -6.9951200608e-47 C164 x⁶ y^{1 1} -1.1660753751e-46 C166 x⁴ y¹³ -1.4460940134e-46 C168 x² y¹⁵ -7.5293474807e-47

C170 17

y -1.3522332498e-47

C171 x¹⁸ -9.4076845388e-52

C173 x¹⁶ y² -2.3595185722e-52

C175 x¹⁴ y⁴ -2.4024140922e-50

C177 x¹² y⁶ -4.1090574900e-49

C179 x¹⁰ y⁸ -1.2021621503e-48

C181 x⁸ y¹⁰ -1.6472529567e-48

C183 x⁶ y¹² -1.0973691375e-48

C185 x⁴ y¹⁴ -3.3722116578e-49

C187 x² y¹⁶ -1.5714862072e-50

C189 18

y 1.9633472375e-50

Table 3d for Figure 30

Coordinates of the stop edge

Xi [mm] yi [mm] ¾+_N/2 [mm] yi+_N/2 [mm]

-207.881317 73.941019 200.412527 -60.497198

-214.354268 57.011762 207.881317 -45.061699

-217.839703 43.567941 214.354268 -27.136603

-219.333461 34.605393 217.341784 -15.186539

-220.329300 24.647006 219.831380 0.248960

-220.329300 6.223992 220.329300 7.219830

-219.831380 0.248960 220.329300 24.647006

-217.341784 -15.186539 219.333461 34.107474

-212.860510 -32.115796 216.843864 47.551295

-205.391720 -50.538811 212.860510 61.493036

-200.910446 -59.501359 207.881317 73.941019

-192.943737 -72.945181 201.906285 85.891083

-182.985351 -86.886922 198.918769 90.870276

-172.031126 -99.832824 191.947898 101.326582

-158.587304 113.276646 186.968705 107.799533

-150.620595 120.247516 178.006157 118.255839

-143.151805 126.222548 170.039448 126.222548

-132.695499 133.691338 162.072739 133.193418

-120.745435 141.160128 152.114353 141.160128

-110.289130 147.135159 145.143482 146.139321

-92.364034 155.599788 131.699660 154.603949

-73.941019 162.570658 114.770404 163.566497

-52.530488 168.545690 98.836985 170.537368 -42.572102 -170.537368 90.870276 173.524883

-25.642845 -173.026964 75.434777 178.504077

-12.199023 -174.022803 57.011762 182.985351

13.194862 -174.022803 37.094989 186.470786

25.144926 -173.026964 16.182378 188.462463

36.597070 -171.533206 -15.186539 188.462463

47.551295 -169.541529 -27.634522 187.466624

60.497198 -166.554013 -40.580425 185.972867

75.434777 -162.072739 -49.542972 184.479109

86.389002 -158.089385 -65.974310 180.993673

102.322421 -151.118514 -87.882760 174.520722

122.737113 -140.164289 -107.301614 167.051932

132.695499 -133.691338 -121.741274 160.081062

143.649724 -125.724629 -139.168450 150.122675

154.106030 -117.260000 -156.097707 138.172612

159.583142 -112.280807 -170.039448 126.222548

172.529045 -99.334905 -182.487431 113.276646

179.001996 -91.866115 -190.454140 103.318259

187.964544 -80.413970 -200.412527 88.380680

196.429172 -67.468068

Table 4 for Figure 30

Wavelength 13.5 nm

NA 0.55

b^c 4.70

Py -8.80

Chief ray angle (CRA) 5.18°

Etendue 12.58 mm²

Mean wavefront aberration RMS 16.17 mk

System transmission 7.15 %

Position of the entry pupil EP (x) -2380.86 mm

Position of the entry pupil EP (y) -2185.04 mm

Object-image offset 1834.11 mm

Working distance between M9 and

80 mm

image field

Reticle tilt 0.0°

Installation length 2312.05 mm

Obscuration 18.4 % Installation space cuboid (790 x 2167 x 1810) mm

Table 5 for figure 30

Ml M2 M3 M4 M5

Maximum angle of incidence 8.7 82.6 79.1 80.0 82.2

[deg]

Minimum angle of incidence [deg] 5.4 72.3 72.6 74.6 75.9

Mirror extent (x) [mm] 611.8 368.5 304.5 261.3 284.0

Mirror extent (y) [mm] 258.7 282.0 213.0 239.4 284.0

Maximum mirror diameter 612.2 369.4 306.7 314.7 345.3

[mm]

Table 6a for Figure 30

M6 M7 M8 M9 M10

Maximum angle of incidence 79.5 81.9 78.4 20.2 8.4

[deg]

Minimum angle of incidence [deg] 73.7 72.9 70.8 0.0 5.1

Mirror extent (x) [mm] 329.1 298.1 233.3 291.1 789.9

Mirror extent (y) [mm] 264.4 113.9 228.3 155.7 768.4

Maximum mirror diameter 331.0 298.2 266.8 291.2 790.5

[mm]

Table 6b for Figure 30

In the projection optical unit 38, the mirror M7 has the largest x/y-aspect ratio of approximately 2.62. None of the mirrors Ml to M10 of the projection optical unit 38 has an x/y-aspect ratio that is greater than 2.65.

On account of the greater reduction in the yz-plane, the corresponding scale ratio of the projection optical unit 38 is shifted upward to greater b_n values in comparison to that according to Figure 7. Hence, in comparison with the projection optical unit 7, the projection optical unit 38 no longer satisfies the allowed scale ratios of the scale ratio curves 24i, 24₆, 24₇, 24io and 24ii. The scale ratio curves for which the projection optical unit 7 was unsuitable are not satisfied by projection optical unit 38 either. The projection optical unit 38 is suitable for the scale ratio curves 24s, 24₉, 24i₂ to 24₁₆ if all that is taken into account is the Pareto-optimal inscription of rectangular structuring fields 4i into the object specification field 19. A further embodiment of the projection optical unit, which has a reduction scale b_c in the xz- plane of 4.60 and a reduction scale b_g in the yz-plane of -8.80 and otherwise corresponds to the structure of the projection optical unit 38 according to Figures 30 to 43, is additionally suitable for the scale ratio curve 24₆ of Figure 98.

There is no change in the result of the admissible scale ratio curves 24i in the projection optical unit 38 if the auxiliary areas 25 to 28 (Figure 102) are additionally taken into account.

What emerges if the shadowing region D (Figure 108) is additionally taken into account is that the scale ratio curves 24₆, 24s, 24₉ and 24i₂ are also eliminated from the admissible scale ratio curves 24i. All that remains as admissible scale ratio curves in the projection optical unit 38 are the scale ratio curves 24n to 24i_6.

Figures 44 to 57 show a further embodiment of a projection optical unit 39, which can be used instead of the projection optical unit 7 in the projection exposure apparatus 1. Components and functions corresponding to those which were already explained above with reference to Figures 1 to 15, in particular, are denoted by the same reference signs and are not discussed in detail again.

The projection optical unit 39 has a reduction scale b_c in the xz-plane of 4.70 and an integer reduction scale b_g in the yz-plane of -8.0.

In terms of its basic design, the projection optical unit 39 corresponds to the projection optical unit 7.

The optical design data emerge from following Tables 1 to 6, which, in turn, correspond in terms of the basic structure to Tables 1 to 6 relating to the embodiment according to Figure 2.

Radii of the surfaces

RadiuS_x [mm] Power_x [1/mm] RadiuS_y [mm] Power_y [1/mm]

M01 -2146.55520611 0.00092427 -1373.48065079 0.00144450

M02 2670.34363441 -0.00016054 3402.46869819 -0.00012600

M03 1740.48606941 -0.00027921 19419.34177163 -0.00002502

M04 3286.81628892 -0.00013482 -5601.02971169 0.00007912 MO 5 -2030.97492965 0.00019630 -4241.39850662 0.00009400

M06 -865.61775732 0.00054641 -1882.70121751 0.00025122

M07 -694.18431263 0.00065049 36391.71605146 -0.00001241

MO 8 -928.95349426 0.00054895 -5894.39247609 0.00008651

M09 1129.26772053 -0.00177106 315.99587854 -0.00632919

M10 -784.78674282 0.00252918 -719.36876887 0.00275918

Table 1 for Figure 44

Decentring (location, angle) the surfaces

D_x [mm] D_y [mm] l)_z [mm]

Reticle 0.000000000 1860.595258076 2319.315179189

M01 0.000000000 1710.018371031 598.213484681

M02 0.000000000 1567.122002664 1451.555525145

M03 0.000000000 1385.421129065 1718.307843287

M04 0.000000000 1100.381298430 1867.412015638

M05 0.000000000 724.558212645 1880.613163188

M06 0.000000000 144.771435379 1658.230934640

M07 0.000000000 -62.121336224 1425.663180023

M08 0.000000000 -125.779135276 1197.030536677

M09 0.000000000 146.335536214 104.444993291

Stop 0.000000000 108.590196947 254.671161423

M10 0.000000000 0.000000000 686.859333548

Wafer 0.000000000 0.000000000 0.000000000

ax [°] ay [°] az [°]

Reticle 0.000000000 0.000000000 0.000000000

M01 2.253131245 180.000000000 0.000000000

M02 -68.116315896 0.000000000 0.000000000

M03 -41.676467261 0.000000000 180.000000000

M04 -14.812891259 0.000000000 0.000000000

MO 5 9.486502794 0.000000000 180.000000000

M06 34.664193974 0.000000000 0.000000000

M07 61.392466223 0.000000000 180.000000000

MO 8 89.213301718 0.000000000 0.000000000

M09 14.044652724 180.000000000 0.000000000

Stop 1.372349973 180.000000000 0.000000000

M10 7.051997188 0.000000000 0.000000000

Wafer 0.000000000 0.000000000 0.000000000

Table 2 for Figure 44 Free-form coefficients of the surfaces Coefficient Formula M01 M02 M03

C7 x 2 y 1.9402150523e-08 -1.2495046419e-07 3.3503969534e-07

C9 3

y -8.8767311629e-09 -3.7762659954e-07 3.9798202347e-07

CIO X⁴ -6.4951289600e- 12 1.5956709901e-10 8.5486852771e-10

C12 x² y² 3.7788256379e-l 1 7.1674867826e-l l 7.5629574578e-10

C14 y⁴ -1.1446357086e-10 1.2740083385e-09 -3.7064672869e-l 1

C16 x 4 y -4.4682011902e-15 -5.0626859160e-14 3.0226707580e-12

C18 x 2 y 3 5.7859090898e-14 1.6252499605e-12 2.3630076819e-13

C20 y -4.2598202624e-14 -5.3326066064e-12 3.8301551162e-12

C21 X .6 -1.0971315354e-18 1.8235234876e-16 -1.8654563002e-17

C23 x 4

4 y 2 -2.8118766971e-17 8.7362852296e-16 2.3941067717e-15

C25 x 2 y 4

4 -8.4976714477e-17 -8.3868931174e-15 1.944071841 le-15

C27 .6

y -9.8888652205e-17 2.3577129563e-14 -3.6425045161e-16

C29 x⁶ y 1.1298822299e-21 -1.0132456143e-18 4.9313100210e-18

C31 x⁴ y³ -9.1954645496e-20 -8.0026012122e-18 1.3135279171 e- 17

C33 x² y⁵ -1.9667975247e-19 4.9826237404e-17 4.4190503539e-17

C35 7

y 2.2617484119e-18 -1.1386481213e-16 2.1408532305e-16

C36 X 2.1756063463e-24 1.8843420388e-22 3.1152192276e-20

C38 x⁶ y² -7.9853593540e-23 1.7815660146e-20 9.6896460699e-20

C40 x⁴ y⁴ 1.5750147450e-21 4.699877935 le-20 1.9832664526e-19

C42 x² y⁶ 1.1151596614e-20 -3.1060444428e-19 3.9139014460e-19

C44 y⁸ 3.3852664024e-20 6.0662775005e-19 1.8689789160e-18

C46 x⁸ y 2.0506675377e-25 -4.1805519085e-23 -7.5341752436e-22

C48 x⁶ y³ -1.5981785388e-25 -6.8073979616e-23 -6.0237485819e-21

C50 x⁴ y⁵ -1.229116690 le-23 -5.3087860294e-23 -1.1958702917e-20

C52 x² y⁷ -3.7990749193e-23 9.7280970727e-22 -1.0326925944e-20

C54 9

y -1.3362313607e-22 -3.1164692563e-21 -1.2235654053e-20

C55 X¹⁰ -2.3371581369e-28 -4.2238868692e-26 -8.3334687285e-25

C57 x⁸ y² 3.2074710187e-27 -8.7032095669e-26 -2.5662466824e-23

C59 x⁶ y⁴ -4.2360541238e-26 7.6687396152e-26 -6.8355413149e-23

C61 x⁴ y⁶ -7.322489449 le-25 1.8919308287e-24 -1.2375987086e-22

C63 x² y⁸ -2.8296971688e-24 9.5397358409e-25 -1.0176492704e-22

C65 yio -5.3867342722e-24 1.9854936033e-23 -2.4095181824e-22

C67 x¹⁰ y -3.7098267252e-30 1.6976171991e-27 9.4308152846e-26

C69 x⁸ y³ -8.5719507001e-30 6.2485793994e-27 6.7413152916e-25

C71 x⁶ y⁵ 2.0466765522e-28 -1.7843933212e-26 2.1492086018e-24

C73 x 4 y 7 1.4405687334e-27 -4.2459912385e-26 2.4496492158e-24

C75 x 2 y 9 -1.5592360161e-28 2.9969276318e-26 2.1086437216e-24

C77 11

y 1.1724940522e-26 -1.2782086679e-25 1.1792636552e-24 C78 x¹² 5.9431702506e-33 2.4183434222e-30 -5.9154135072e-30

C80 x¹⁰ y² -6.5569369173e-32 -4.7731175193e-31 2.6651783666e-27

C82 x⁸ y⁴ 1.8732496669e-31 6.4341769019e-29 6.8989916093e-27

C84 x⁶ y⁶ 1.6470892959e-29 2.2632603525e-28 1.8031026829e-26

C86 x⁴ y⁸ 1.1285474442e-28 8.4023382522e-29 2.2022418077e-26

C88 x² y¹⁰ 3.0749035741e-28 -5.5856836978e-28 2.1692996439e-26

C90 y¹² 4.6562383279e-28 -1.1782314027e-28 2.7865914794e-26

C92 x¹² y 4.2744537152e-35 -4.1419403509e-32 -5.7350818564e-30

C94 x¹⁰ y³ 2.6084830772e-34 -4.9999691135e-31 -4.1719527783e-29

C96 x⁸ y⁵ -1.7713879819e-33 -6.5240926515e-31 -1.9124779846e-28

C98 x⁶ y⁷ -2.5184069698e-32 8.3171403934e-31 -3.3796668414e-28

CIOO x⁴ y⁹ -4.7048085148e-32 2.1495099372e-30 -3.1225668750e-28

C102 x² y^{1 1} 2.1442905001e-31 1.6624861577e-30 -2.2368185298e-28

C104 13

y -7.3379885985e-31 8.2710526023e-30 1.7085327846e-30

C105 x¹⁴ -8.2060713293e-38 -3.0214483458e-35 1.2409976767e-33

C107 x¹² y² 5.4281842440e-37 4.1875102894e-34 -1.5707534156e-31

C109 x¹⁰ y⁴ 6.3120725074e-36 -1.6741554773e-33 -4.4219209053e-31 cm x⁸ y⁶ -1.7803380067e-34 -1.1870268992e-32 -1.4240974463e-30

Cl 13 x⁶ y⁸ - 1.9416792429e-33 -2.4754976044e-32 -2.5468192618e-30 Cl 15 x⁴ y¹⁰ -8.6034638985e-33 -1.0489457033e-32 -2.4971142030e-30 Cl 17 x 2 y 12 -1.9130288013e-32 6.8165752844e-33 -2.3737287292e-30 Cl 19 y¹⁴ -2.388823721 le-32 -3.3187630401e-32 -1.6465394317e-30 C121 x¹⁴ y -2.9218915240e-40 5.4495202027e-37 1.6053485431e-34 C123 x¹² y³ -3.2247057307e-39 1.6096968470e-35 1.2777167654e-33 C125 x¹⁰ y⁵ 8.6565775941e-39 5.7670350053e-35 7.9886089452e-33 C127 x⁸ y⁷ 1.8091290017e-37 1.0743972689e-34 1.9589770749e-32 C129 x⁶ y⁹ 8.5867214884e-37 6.9479333151e-35 2.5354102254e-32 C131 x⁴ y^{1 1} -1.3475373052e-36 -5.2841855924e-35 2.1862106178e-32 C133 x² y¹³ -1.5229526148e-35 4.5971087785e-36 1.2627607654e-32 C135 15

y 2.6729606030e-35 -1.7039567719e-34 -4.9790511102e-33 C136 x¹⁶ 5.6980679444e-43 2.8930318503e-40 -6.3338749765e-38 C138 x¹⁴ y² -8.942179653 le-43 -1.7311670878e-38 4.6740658303e-36 C140 x¹² y⁴ -8.0986140095e-41 -4.4200698523e-38 1.6170235702e-35 C142 x¹⁰ y⁶ 7.9786626045e-40 3.8457359974e-38 6.0695092772e-35 C144 x⁸ y⁸ 1.5555343662e-38 3.3042401084e-37 1.4198029163e-34 C146 x⁶ y¹⁰ 9.4926396632e-38 7.5159746169e-37 1.8450240940e-34 C148 x⁴ y 3.2995150786e-37 6.7127031917e-37 1.6185101184e-34 C150 x 2 y 14 6.2090769492e-37 -4.9750166241e-37 1.3875289272e-34 C152 16

y 6.7469733795e-37 1.7809036739e-36 3.9604831751e-35 C154 x¹⁶ y 9.0378512589e-46 -3.4223014882e-42 -1.6753978321e-39

C156 x¹⁴ y³ 1.4095879522e-44 -1.8359768475e-40 -1.5645493550e-38

C158 x¹² y⁵ -8.5057034236e-45 -9.3300931129e-40 -1.2826694957e-37

C160 x¹⁰ y⁷ -4.5253515381e-43 -3.0073019764e-39 -4.0362539635e-37

C162 x⁸ y⁹ -4.6413569509e-42 -5.1407389660e-39 -7.1011116174e-37

C164 x⁶ y^{1 1} 1.8229888273e-42 -5.2617699313e-39 -7.4283964354e-37

C166 x⁴ y¹³ 7.1705961959e-41 -2.5589502440e-39 -7.5488833214e-37

C168 x² y¹⁵ 3.4012475843e-40 2.2485475042e-39 -1.9856797718e-37

C170 17

y -4.1157345838e-40 -5.4287621563e-39 1.9871581084e-37

C171 x¹⁸ -1.5527350800e-48 -6.1250561856e-45 1.1663632101e-42

C173 x¹⁶ y² -5.4739239154e-48 2.1511165003e-43 -5.4777860578e-41

C175 x¹⁴ y⁴ 2.6224616804e-46 1.2800386523e-42 -2.4815270737e-40

C177 x¹² y⁶ -9.0941127235e-46 3.9443858008e-42 -1.0992862127e-39

C179 x¹⁰ y⁸ -4.3790559513e-44 9.3828285268e-42 -3.0720122129e-39

C181 x⁸ y¹⁰ -3.9315288336e-43 1.2056244312e-41 -5.2162473561e-39

C183 x⁶ y¹² -1.6493308387e-42 9.5767165088e-42 -5.4738296579e-39

C185 x⁴ y¹⁴ -5.1829043793e-42 3.6031856158e-42 -5.4278669395e-39

C187 x² y¹⁶ -8.1297508468e-42 -3.1155754692e-42 -2.6302067986e-39

C189 18

y -8.1196105262e-42 5.8808993882e-42 1.3598608941e-41

Table 3a for Figure 44

Coefficient Formula M04 M05 M06

C7 x 2 y 7.9488243132e-08 -1.3678302663e-07 1.4224260430e-07

C9 y 3 -6.7894770438e-08 -1.7683091393e-07 -2.8831402337e-08

CIO X⁴ 1.6376453507e-10 -1.4309405819e-10 -4.2467395275e-10

C12 x² y² 8.8445181956e-l 1 -2.7629344162e-10 1.1812792578e- 11

C14 y⁴ -3.2634191471e-10 -3.4715533685e-l 1 -3.1816123040e-10

C16 x 4 y 5.2374044279e-13 -3.4923229804e-13 -1.690178271 le-13

C18 x 2 y 3^J 1.0706095726e-12 4.2806959668e-13 7.7804803645e-14

C20 y -5.0556229898e-13 -2.0556905630e-13 7.8328694995e-13

C21 x⁶ -1.1915817694e- 15 -1.3301624277e-16 -7.4665243830e-16

C23 x⁴ y² -1.1127245781 e- 15 9.2605871247e-16 3.0263759818e-16

C25 x y⁴ 1.3806017853e-15 -6.1035430837e-16 -3.7533897334e-16

C27 y⁶ -5.8877618037e-15 7.4730757433e-16 -1.4243676117e-15

C29 x⁶ y 1.3635807883e-17 -2.8074440492e-18 -1.0734339475e-18

C31 x⁴ y³ 1.1687036843e-17 -5.5271370742e-18 -6.1636780277e-18

C33 x² y⁵ 2.8072700174e- 17 1.1396965450e-17 -8.3190878420e-19

C35 7

y -2.7089468556e-17 -1.2324940985e-17 6.4714857658e-17

C36 X 9.7985811386e-20 -4.2015608986e-20 -3.4122390046e-21 C38 x⁶ y² 3.2314182516e-21 -2.2844307707e-21 -8.4766121490e-20

C40 x⁴ y⁴ -1.8353650448e-20 -5.3027382860e-20 -2.7158280738e-19

C42 x² y⁶ 1.8018627654e-19 -1.3678265273e-19 -5.0211952705e-19

C44 y 5.2664983302e-19 1.6399718481e-19 -2.7527182113e-19

C46 x⁸ y -2.4960788400e-22 9.4181247724e-22 1.0508231013e-22

C48 x⁶ y³ -1.2460631040e-21 5.0203542992e-22 1.0821992275e-21

C50 x⁴ y⁵ -2.4213177528e-21 -4.1631373945e-22 3.0914227159e-21

C52 x² y⁷ -1.8093116899e-22 -4.7226544202e-22 1.9254774793e-21

C54 9

y 5.4717371780e-21 2.3436718381e-21 -4.5395008219e-21

C55 X¹⁰ -7.5921537710e-24 6.7891706644e-25 5.9911614878e-25

C57 x⁸ y² -2.1615897784e-24 1.0375387887e-24 7.6575454855e-24

C59 x⁶ y⁴ 4.0593309833e-24 6.2860475837e-24 3.1436051937e-23

C61 x⁴ y⁶ 9.4008716253e-24 1.7086771049e-23 4.9097200308e-23

C63 x² y⁸ -4.1534363143e-23 1.1872448818e-23 5.9673444707e-23

C65 yio -1.2141388520e-22 -3.3105262529e-23 7.8212783728e-24

C67 x¹⁰ y -2.6347911247e-26 -6.2852173634e-26 -2.3735842275e-27

C69 x⁸ y³ 1.7846904840e-25 -8.5667462614e-26 -9.1046938598e-26

C71 x⁶ y⁵ 3.4563462465e-25 -1.4424513392e-25 -3.7680088551e-25

C73 x 4 y 7 3.8578227607e-25 7.8452530849e-26 -5.6525801996e-25

C75 x 2 y 9 - 1.2892123060e-25 -4.2703751544e-26 -5.3903682728e-26

C77 11

y -8.4106590479e-25 -2.6175630360e-25 3.5329728841e-25

C78 x¹² 4.1770098975e-28 3.0785383524e-29 -3.9875935487e-29

C80 x¹⁰ y² 4.5164435087e-28 -4.1341581702e-28 -4.0428831759e-28

C82 x⁸ y⁴ -7.5072017673e-28 -6.4778291056e-28 -1.8851025743e-27

C84 x⁶ y⁶ -2.3220276410e-27 -1.5062485600e-27 -3.9639495686e-27

C86 x⁴ y⁸ -1.0644481319e-27 -1.5613428313e-27 -4.4408031229e-27

C88 x² y¹⁰ 6.4555946584e-27 -5.4709235792e-28 -5.3850683559e-27

C90 y¹² 1.4996548571e-26 3.9113383512e-27 -9.3077745393e-29

C92 x¹² y 4.5923673145e-30 2.8655281322e-30 -3.9362878985e-32

C94 x¹⁰ y³ - 1.4741737082e-29 7.5067063938e-30 4.2104200589e-30

C96 x⁸ y⁵ -2.6709910102e-29 1.2518021436e-29 2.3879003509e-29

C98 x⁶ y⁷ -3.9250350903e-29 2.0751882740e-29 5.3969885217e-29

CIOO x⁴ y⁹ -2.1149583538e-29 -1.7128878140e-29 4.9325150274e-29

C102 x² y^{1 1} 2.6039195543e-29 1.9436476129e-29 -6.7123304621e-30

C104 13

y 7.3265152999e-29 1.1887189515e-29 -1.491735243 le-29

C105 x¹⁴ -1.1765428804e-32 -2.0984358985e-33 1.2320790070e-33

C107 x¹² y² -5.5217998391e-32 3.5702117826e-32 1.2469940716e-32

C109 x¹⁰ y⁴ 6.5022251930e-32 5.2601801308e-32 5.3719688973e-32 cm x⁸ y⁶ 1.9011888704e-31 1.1227217355e-31 1.3159164191 e-31 Cl 13 x⁶ y⁸ 2.5749256828e-31 1.0062288158e-31 1.5810812158e-31 Cl 15 x⁴ y¹⁰ 1.0658092864e-32 1.2137507826e-31 1.879833331 le-31 Cl 17 x² y¹² -5.8934672281e-31 -5.4057422230e-32 3.0978251822e-31 Cl 19 y¹⁴ -1.1100115944e-30 -2.3393977954e-31 -6.0867690100e-33 C121 x¹⁴ y -2.4144748536e-34 -7.4926591670e-35 3.0724245233e-36 C123 x¹² y³ 6.1702758483e-34 -3.1719547262e-34 -1.0613278305e-34 C125 x¹⁰ y⁵ 1.2228652351e-33 -4.9565521237e-34 -7.3597394416e-34 C127 x⁸ y⁷ 1.5776309750e-33 -1.0873431089e-33 -2.2012931327e-33 C129 x⁶ y⁹ 1.9620860728e-33 -1.0627842306e-33 -3.1653564819e-33 C131 x⁴ y^{1 1} 1.7376556132e-34 1.2983826573e-33 -1.8749043299e-33 C133 x² y¹³ -1.7074498668e-33 -1.6611483837e-33 7.2791327436e-34 C135 15

y -3.3869390528e-33 -4.3968351717e-35 3.0793961289e-34 C136 x¹⁶ -4.2028896354e-38 6.5782707666e-38 -1.9874552200e-38 C138 x¹⁴ y² 3.1939444062e-36 -1.2520228838e-36 -2.1606351439e-37 C140 x¹² y⁴ -2.3033035059e-36 -2.8664271444e-36 -4.9416465482e-37 C142 x¹⁰ y⁶ -1.0042023954e-35 -2.7901523465e-36 -1.2081349452e-36 C144 x⁸ y⁸ -9.4374801539e-36 -9.5163529969e-36 9.2677137770e-37 C146 x⁶ y¹⁰ -1.5536264664e-35 -6.9828235785e-37 4.9607214238e-37 C148 x⁴ y 6.5822674488e-36 -7.5580209226e-36 -3.8692334041e-36 C150 x 2 y 14 2.8100612126e-35 7.2453195773e-36 -1.1296814279e-35 C152 yl6 4.4527401733e-35 6.0816627360e-36 -1.3040432809e-37 C154 x¹⁶ y 4.5845784955e-39 7.8678295339e-40 -4.1298715825e-41 C156 x¹⁴ y³ -9.6216281465e-39 4.9032964252e-39 1.1915647395e-39 C158 x¹² y⁵ -2.5766040647e-38 9.5474175876e-39 9.4393443580e-39 C160 x¹⁰ y⁷ -2.1528043371e-38 1.2320183960e-38 3.1785792978e-38 C162 x⁸ y⁹ -4.2967285708e-38 3.9736935314e-38 6.6573769477e-38 C164 x⁶ y^{1 1} -3.0663443307e-38 8.9794102305e-39 5.9344429540e-38 C166 x⁴ y¹³ 1.4915677080e-38 -3.1038843607e-38 2.7007335777e-38 C168 x² y¹⁵ 4.0144415463e-38 4.6659668873e-38 -1.9353743447e-38 C170 17

y 6.3869698917e-38 -8.7863439251e-39 -1.5195405581e-39 C171 x¹⁸ 5.3227924067e-42 -8.8571317880e-43 1.2844976295e-43 C173 x¹⁶ y² -6.6920905695e-41 1.5138512613e-41 1.6192051689e-42 C175 x¹⁴ y⁴ 1.6977065413e-41 6.3276076569e-41 -4.3937068126e-42 C177 x¹² y⁶ 2.5142895832e-40 1.1338578508e-41 -1.3844151710e-41 C179 x¹⁰ y⁸ 6.7374436633e-41 2.062916863 le-40 -1.0417777204e-40 C181 x⁸ y¹⁰ 4.0998455199e-40 1.2777349567e-40 -1.6146806035e-40 C183 x⁶ y¹² 1.7945836941e-40 4.2215318266e-42 -1.1490032963e-40 C185 x⁴ y¹⁴ -2.4273690962e-40 1.8870904320e-40 5.0378540397e-41 C187 x² y¹⁶ -5.4768761100e-40 -2.3881253116e-40 1.8874642456e-40 C189 y¹⁸ -7.4874991060e-40 -2.8563901089e-41 9.8113278066e-42

Table 3b for Figure 44

Coefficient Formula M07 M08 M09

C7 x 2 y -6.3583234472e-08 3.3272103797e-07 1.4237168241e-06

C9 y 3 -1.3436287516e-07 -2.0503619379e-07 -9.1730133303e-07

CIO X⁴ 3.3773541262e-l 1 2.1398180325e-10 1.4805329663e-09

C12 x² y² -1.1979396872e-09 -5.0678217779e-10 5.0941310898e-09

C14 y⁴ 1.3221144719e-09 -5.7576545456e-10 2.2992982378e-09

C16 x 4 y -1.6004535620e-13 6.4177372943e-13 6.5523690651e-12

C18 x 2 3 2.2617432081e-13 -1.3529134286e-13 -3.7722746102e- 12

C20 y -2.7932771801e-12 -2.7714382119e-12 -1.0176093014e-l 1

C21 x⁶ 2.8696039371e-16 1.0800608910e-15 7.3088128194e-15

C23 x⁴ y² -7.4208115155e-16 -4.0933033327e-16 4.3565167433e-14

C25 x y⁴ 1.8355914124e-14 -5.9337614549e-15 7.5364695701e-14

C27 y⁶ 1.9567661604e-13 -1.5532390656e-14 3.9526641698e-14

C29 x⁶ y 1.3843295161e-17 1.5424314269e-17 5.7335815735e-17

C31 x⁴ y³ -3.470186442 le- 17 1.1245687570e-17 6.1826337856e-17

C33 x² y⁵ -2.3603681104e-16 -2.8971663434e-17 -2.4916733939e-16

C35 y⁷ 3.5928503623e-15 -9.7015402021e-17 -1.2621199843e-15

C36 x⁸ -1.7843685278e-20 -1.2572498663e-19 2.8541174392e-20

C38 x⁶ y² -2.7458686512e- 19 6.4347237925e-19 4.4159449609e-19

C40 x⁴ y⁴ -8.3270615176e-18 9.7992905840e-19 9.4185475345e-19

C42 x² y⁶ -9.0793555218e-17 3.8268881577e-19 -1.8457121764e-18

C44 y⁸ -2.1883514894e-16 -4.8138059418e-19 2.5145323292e-19

C46 x⁸ y -1.4185606740e-21 -4.1555217745e-21 6.1800875472e-22

C48 x⁶ y³ -1.3179685718e-21 -5.5693301477e-21 1.5976458118e-21

C50 x⁴ y⁵ 4.1633448906e-20 1.9675590020e-21 -4.832698591 le-21

C52 x² y⁷ -4.9583683533e-19 -7.794653793 le-21 3.2154557437e-20

C54 9

y -6.0485922748e-18 -2.5596355101e-21 -7.6032726225e-21

C55 X¹⁰ 8.9310190432e-25 3.5908817002e-23 6.7152258306e-25

C57 x⁸ y² 4.7386742665e-23 -1.1779474907e-22 5.8307625438e-24

C59 x⁶ y⁴ 1.0298289305e-21 -3.9645272152e-22 -5.5377828404e-24

C61 x⁴ y⁶ 1.6286015766e-20 -2.5051345423e-22 3.2905078383e-23

C63 x² y⁸ 8.8558809714e-20 -3.5792842077e-22 2.8051210073e-24

C65 yio 1.4307427914e-19 -5.2152717529e-23 2.0372051966e-21

C67 x¹⁰ y 1.2722902613e-25 7.2979657076e-25 -1.5025254790e-26

C69 x⁸ y³ 7.5552043258e-25 1.3287817208e-24 -6.1812364134e-26

C71 x⁶ y⁵ -6.3727310694e-24 -7.0990383613e-25 -8.1269069074e-26 C73 x 4 y 7 6.1156773788e-23 -1.3745308142e-24 -2.4048910081e-24

C75 x 2 y 9 8.0731106228e-22 -1.1455917368e-24 -1.1510194423e-23

C77 11

y 5.1698914881e-21 -8.7167096706e-25 1.3496310782e-23

C78 x¹² -2.1618556329e-29 -5.7624132159e-27 1.3618253092e-29

C80 x¹⁰ y² -4.6284102444e-27 1.0066014840e-26 -2.3778290566e-28

C82 x⁸ y⁴ -8.0315844181e-26 6.8858882546e-26 5.2798073718e-28

C84 x⁶ y⁶ -1.4398341808e-24 7.8163283118e-26 2.2550797440e-27

C86 x⁴ y⁸ -1.2119296826e-23 3.2340285046e-26 1.5706816049e-26

C88 x² y¹⁰ -4.4777327896e-23 6.1724292578e-26 1.8527637828e-25

C90 y¹² -3.8045082065e-23 -8.6453560847e-27 -4.2651467694e-25

C92 x¹² y -6.6476574355e-30 -7.0579029753e-29 1.4781880005e-30

C94 x¹⁰ y³ -7.2390185384e-29 -1.4431201077e-28 8.0671209777e-30

C96 x⁸ y⁵ 2.1283904399e-28 -4.9252080905e-29 2.7044595257e-29

C98 x⁶ y⁷ 2.2236132927e-27 6.1566688549e-28 1.6251870190e-28

CIOO x⁴ y⁹ -8.7943902625e-26 1.5717105924e-28 1.6101327466e-27

C102 x² y^{1 1} -5.4284632248e-25 5.8869843328e-28 2.1366322585e-27

C104 13

y -2.3113167814e-24 -6.3885104675e-29 -1.9400999068e-27

C105 x¹⁴ 2.5807091080e-34 5.1636008505e-31 -1.1034689067e-33

C107 x¹² y² 2.4804255706e-31 -2.8509796755e-31 2.3698389433e-32

C109 x¹⁰ y⁴ 4.3822851396e-30 -5.4580360547e-30 5.2357079302e-32 cm x⁸ y⁶ 6.4361075987e-29 -1.1440863060e-29 4.0986068735e-31

Cl 13 x⁶ y⁸ 8.3076340052e-28 -3.7819411006e-30 1.7850929836e-30 Cl 15 x⁴ y¹⁰ 3.9688258103e-27 -4.3063204989e-30 -9.1901086807e-30 Cl 17 x 2 y 12 1.1342341037e-26 -3.1825931628e-30 -4.1829752333e-29 Cl 19 y¹⁴ -3.9823834097e-27 -4.2967205236e-31 4.5098051844e-29 C121 x¹⁴ y 1.8256415238e-34 3.6634894622e-33 -4.7429361670e-35 C123 x¹² y³ 2.9442232100e-33 6.9661950504e-33 -3.5576327988e-34 C125 x¹⁰ y⁵ 1.5363127266e-33 1.5315755564e-32 -1.2762234539e-33 C127 x⁸ y⁷ -1.1746387012e-31 -5.1048433780e-32 -8.5446309103e-33 C129 x⁶ y⁹ 3.2092760952e-31 -6.7157168278e-32 -5.7403752538e-32 C131 x⁴ y^{1 1} 3.9652243593e-29 -2.9587392002e-32 -3.3182338514e-31 C133 x² y¹³ 1.8324576153e-28 -8.1160591537e-32 -2.2980276783e-31 C135 15

y 4.6797024112e-28 -2.4898315397e-33 1.1507640150e-31 C136 x¹⁶ -6.068704656 le-40 -2.4238955584e-35 4.4741025755e-38 C138 x¹⁴ y² -6.6994511277e-36 -7.4435850369e-36 -8.6885587567e-37 C140 x¹² y⁴ -1.4649616189e-34 1.8000840705e-34 -3.3541800894e-36 C142 x¹⁰ y⁶ -1.6184839421e-33 7.1946352166e-34 -2.3959764708e-35 C144 x⁸ y⁸ -2.2620469035e-32 3.7105356964e-34 -2.0671308059e-34 C146 x⁶ y¹⁰ -2.1295327527e-31 -1.4999946897e-34 -3.4444382350e-34 C148 x 4

4 y 12 -3.9450596971e-31 2.0977409621e-34 2.0939752407e-33

C150 x 2 y 14 -9.9160595099e-31 -5.2887552263e-34 4.2738844103e-33

C152 yl6 3.4075404529e-30 -1.0112948672e-35 -2.3216661623e-33

C154 x¹⁶ y -2.0040694046e-39 -7.8014848430e-38 6.5194208962e-40

C156 x¹⁴ y³ -4.5481110533e-38 -1.0926675454e-37 6.9308454977e-39

C158 x¹² y⁵ -4.9516885216e-38 -6.8131293825e-37 2.7629976772e-38

C160 x¹⁰ y⁷ -1.8296205639e-36 1.0271415550e-36 1.4965812557e-37

C162 x⁸ y⁹ 5.7571043280e-35 3.4977423384e-36 1.0639298782e-36

C164 x⁶ y^{1 1} -5.6638976793e-34 1.5594542108e-36 5.7294355153e-36

C166 x⁴ y¹³ -4.5531015365e-33 2.4653185108e-36 2.3103462668e-35

C168 x² y¹⁵ -2.9071403363e-32 -1.5332354300e-36 9.2866441153e-36

C170 17

y -2.2395127335e-32 -2.3874094192e-38 -2.9283754687e-36

C171 x¹⁸ 4.8790285277e-44 4.6495229099e-40 -6.2458941747e-43

C173 x¹⁶ y² 7.0084803013e-41 3.7287823615e-40 1.3494957785e-41

C175 x¹⁴ y⁴ 2.0477668260e-39 -1.4616311315e-39 8.2285041569e-41

C177 x¹² y⁶ 2.2227536047e-38 -1.6170756770e-38 3.6161253742e-40

C179 x¹⁰ y⁸ 1.7213771468e-37 -1.2641966168e-38 4.8599252655e-39

C181 x⁸ y¹⁰ 3.6844279683e-36 9.5207368070e-39 1.8824668719e-38

C183 x⁶ y¹² 1.2336308453e-35 6.7217625728e-39 9.1805220994e-39

C185 x⁴ y¹⁴ -3.2367537078e-38 6.1567620004e-39 -1.6420929832e-37

C187 x² y¹⁶ -1.3288655405e-34 -1.6911925308e-39 -1.6186418807e-37

C189 18

y -2.2375961986e-34 -2.4464748275e-41 4.8578001134e-38

Table 3c for Figure 44

Coefficient Formula M10

C7 x 2 y -9.3432520519e-09

C9 y 3 1.0160187971e-08

CIO X⁴ -2.2007053607e-l 1

C12 x² y² -5.8359502629e-l 1

C14 y⁴ - 1.248902249 le- 11

C16 x 4 y -2.3783386564e-14

C18 x 2 y 3^J 3.0663317332e-16

C20 y 1.3716223317e-14

C21 x⁶ -4.7810513619e-17

C23 x⁴ y² -1.7161749940e-16

C25 x y⁴ -1.4794853446e-16

C27 y⁶ -2.9565749394e-17

C29 x⁶ y -4.0669978522e-20

C31 x 4 3

4 y^J -3.9289350744e-20 C33 x² y⁵ 2.1419631679e-20

C35 7

y 3.2638197868e-20

C36 X -8.4072009280e-23

C38 x⁶ y² -4.0184045382e-22

C40 x⁴ y⁴ -5.9049609952e-22

C42 x² y⁶ -3.3409509633e-22

C44 y -4.5259998525e-23

C46 x⁸ y -6.2693620519e-26

C48 x⁶ y³ -1.4198685918e-25

C50 x⁴ y⁵ -6.0119058396e-26

C52 x² y⁷ 2.1317860398e-26

C54 9

y 5.7812082425e-26

C55 X¹⁰ -1.3968590850e-28

C57 x⁸ y² -8.5688301862e-28

C59 x⁶ y⁴ - 1.8389216215e-27

C61 x⁴ y⁶ -1.8720757908e-27

C63 x² y⁸ -8.3204769645e-28

C65 yio -2.0959765589e-28

C67 x¹⁰ y -1.3457392358e-31

C69 x⁸ y³ -3.3837482782e-31

C71 x⁶ y⁵ -3.8803304552e-31

C73 x 4 y 7 6.6208369542e-31

C75 x 2 y 9 1.4575660475e-30

C77 11

y -1.1765627032e-31

C78 x¹² -3.0366418802e-34

C80 x¹⁰ y² -1.8275696503e-33

C82 x⁸ y⁴ -4.2650422978e-33

C84 x⁶ y⁶ -3.1248197767e-33

C86 x⁴ y⁸ -1.0170281945e-33

C88 x² y¹⁰ -6.4333466089e-34

C90 y¹² 1.8049161521e-34

C92 x¹² y -1.6943363984e-37

C94 x¹⁰ y³ -1.5349803507e-36

C96 x⁸ y⁵ -3.1793608100e-37

C98 x⁶ y⁷ - 1.3768406140e-36

CIOO x⁴ y⁹ -9.9069175238e-36

C102 x² y^{1 1} -1.1101967630e-35

C104 13

y 1.0350161699e-36

C105 14

X -3.2280539622e-40 C107 x¹² y² -1.9003513299e-39

C109 x¹⁰ y⁴ -8.9719402177e-39 cm x⁸ y⁶ -4.5999914775e-38

Cl 13 x⁶ y⁸ -7.7242855449e-38 Cl 15 x⁴ y¹⁰ -5 2229592206e-38 Cl 17 x 2 y 12 -1.2512496842e-38 Cl 19 y¹⁴ -7.1769733072e-40 C121 x¹⁴ y -1.0393047452e-43 C123 x¹² y³ 4.6063463017e-42 C125 x¹⁰ y⁵ -2.3252010183e-42 C127 x⁸ y⁷ -1.5269987269e-41 C129 x⁶ y⁹ 1.9864043645e-41 C131 x⁴ y^{1 1} 7.5453795308e-41 C133 x² y¹³ 5.5975730665e-41 C135 15

y -1.2511392770e-42 C136 x¹⁶ -1.6301549686e-46 C138 x¹⁴ y² -1.2007484068e-44 C140 x¹² y⁴ -4.9787821738e-44 C142 x¹⁰ y⁶ 3.6511098676e-44 C144 x⁸ y⁸ 3.0243906666e-43 C146 x⁶ y¹⁰ 3.8579866168e-43 C148 x⁴ y 2.1321030034e-43 C150 x 2 y 14 4.2552857813e-44 C152 yl6 -3.0052816072e-45 C154 x¹⁶ y -1.9324534346e-48 C156 x¹⁴ y³ -2.4628612218e-47 C158 x¹² y⁵ -4.636805373 le-47 C160 x¹⁰ y⁷ -8.8083533623e-48 C162 x⁸ y⁹ 1.4648609993e-47 C164 x⁶ y^{1 1} -8.6006470466e-47 C166 x⁴ y¹³ - 1.7718892662e-46 C168 x² y¹⁵ -9.7242038084e-47 C170 17

y 1.1977125862e-48 C171 x¹⁸ -3.9511895348e-51 C173 x¹⁶ y² -1.5852831436e-50 C175 x¹⁴ y⁴ -3.6120605080e-50 C177 x¹² y⁶ -3.3897555701e-49 C179 x¹⁰ y⁸ -1.1689145102e-48 C181 x⁸ y¹⁰ -1.8734590016e-48 Table 3d for Figure 44

Coordinates of the stop edge

¾ [mm] yi [mm] ¾+N/2 [mm] yi+N/2 [mm]

109.791210 166.056094 -81.907728 -159.583142

91.368195 173.524883 -70.455584 -163.566497

73.941019 179.001996 -58.007601 -167.051932

53.526327 183.981189 -44.563779 -170.039448

34.605393 186.968705 -32.613716 -172.031126

10.207346 188.960382 -10.705265 -174.022803

-11.203185 188.960382 11.203185 -174.022803

-25.642845 187.964544 24.149087 -173.026964

-45.061699 185.474947 38.588747 -171.035287

-62.488875 181.989512 49.542972 -169.043610

-82.405648 176.512399 61.493036 -166.056094

-95.351550 172.031126 71.949342 -163.068578

-105.309936 168.047771 81.907728 -159.583142

-119.251677 161.574820 99.832824 -152.114353

-133.691338 153.608111 112.778726 -145.641401

-146.637240 145.143482 127.218387 -137.176773

-158.089385 136.678854 142.155966 -126.720467

-171.035287 125.226709 149.126837 -121.243355

-181.989512 113.774565 163.068578 -108.795372

-191.947898 101.326582 169.541529 -102.322421

-197.922930 92.364034 179.997835 -90.372357

-201.408365 86.389002 191.449979 -74.936858

-206.885478 75.932697 200.412527 -59.999278

-210.370913 67.965987 206.387559 -48.049215

-214.852187 54.522166 209.872994 -39.584586

-218.337622 40.082505 213.856349 -28.132442

-219.831380 28.630361 217.341784 -14.688620

-220.329300 21.161571 219.831380 2.240637

-220.329300 10.207346 220.329300 8.713588

-219.831380 1.742718 220.329300 21.161571

-218.835542 -6.223992 219.831380 28.630361 -216.843864 -16.680297 217.839703 42.572102

-213.856349 -28.132442 214.354268 56.513843

-207.881317 -44.563779 211.864671 63.982633

-199.416688 -61.990956 207.383397 74.936858

-190.454140 -76.430616 203.400043 82.903567

-179.997835 -90.372357 197.922930 92.364034

-169.541529 -102.322421 192.943737 99.832824

-161.574820 -110.289130 181.491593 114.272484

-151.616433 -119.251677 169.043610 127.218387

-138.172612 -129.707983 158.089385 136.678854

-128.712145 -136.180934 151.616433 141.658047

-117.260000 -143.151805 137.674692 151.118514

-99.832824 -152.114353 127.716306 157.093546

Table 4 for Figure 44

Wavelength 13.5 nm

NA 0.55

4.70

bg 8.00

Chief ray angle (CRA) 5.06°

Etendue 12.58 mm²

Mean wavefront aberration RMS 17.15 ihl

System transmission 7.20 %

Position of the entry pupil EP (x) -2383.43 mm

Position of the entry pupil EP (y) -2129.47 mm

Object-image offset 1860.60 mm

Working distance between M9 and

80 mm

image field

Reticle tilt 0 0

Installation length 2319.32 mm

Obscuration 18.4 %

Installation space cuboid (791 x 2203 x 1818) mm

Table 5 for Figure 44

Ml M2 M3 M4 M5

Maximum angle of 9.0 83.1 79.3 79.9 82.0

incidence [deg]

Minimum angle of incidence [deg] 5.6 72.2 72.6 74.5 75.7 Mirror extent (x) [mm] 614.4 370.4 303.5 260.0 288.9

Mirror extent (y) [mm] 278.0 313.1 211.0 246.5 276.4

Maximum mirror diameter 614.4 381.3 305.6 316.6 340.6

[mm]

Table 6a for Figure 44

M6 M7 M8 M9 M10

Maximum angle of incidence 79.5 82.1 78.6 20.2 8.3

[deg]

Minimum angle of incidence [deg] 73.7 73.1 71.0 0.0 5.0

Viirror extent (x) [mm] 332.4 299.1 233.2 291.1 790.6

Viirror extent (y) [mm] 261.4 113.5 231.7 155.7 768.2

Maximum mirror diameter 334.5 299.2 269.2 291.1 790.7

[mm]

Table 6b for Figure 44 Provided only the Pareto-optimal inscription of the structuring field 4i into the object

specification field 19 or only the auxiliary areas 25 to 28 is/are taken into account (cf. Figures 98 and 102), what was explained above in respect of the projection optical unit 7 applies in respect of the admissible scale ratio curves 24i. To the extent that the shadowing region D is additionally taken into account (Figure 108), the projection optical unit 39, in contrast to the projection optical unit 7, does not satisfy the scale ratio curve 24i, i.e., the combination of standard reticle and full field. In the projection optical unit 39, admissible scale ratio curves are the scale ratio curves 246 to 24i6.

Figures 58 to 71 show a further embodiment of a projection optical unit 40, which can be used instead of the projection optical unit 7 in the projection exposure apparatus 1. Components and functions corresponding to those which were already explained above with reference to Figures 1 to 15, in particular, are denoted by the same reference signs and are not discussed in detail again.

The projection optical unit 40 has a reduction scale b_c in the xz-plane of 4.10 and an integer reduction scale b_g in the yz-plane of -8.0.

In terms of its basic design, the projection optical unit 40 corresponds to the projection optical unit 7. The optical design data emerge from following Tables 1 to 6, which, in turn, correspond in terms of the basic structure to Tables 1 to 6 relating to the embodiment according to Figure 2. Radii of the surfaces

RadiuS_x [mm] Power_x [1/mm] RadiuS_y [mm] Power_y [1/mm]

M01 -2153.91318796 0.00090961 -1360.57297980 0.00144000

M02 3031.20790690 -0.00012341 2671.06678857 -0.00014004

M03 2141.17782565 -0.00021490 -13654.46162255 0.00003370

M04 3996.48790982 -0.00010146 -8247.94241382 0.00004916

M05 -2112.23763543 0.00015939 -5853.21581048 0.00005752

M06 -921.16774264 0.00050894 -1825.97789803 0.00025675

M07 -751.08754414 0.00062582 17986.50147715 -0.00002613

M08 -1072.92101512 0.00049812 -4970.77798515 0.00010752

M09 1137.97654265 -0.00175750 314.17776349 -0.00636582

M10 -784.36493151 0.00252999 -718.82637975 0.00276066

Table 1 for Figure 58

Decentring (location, angle) the surfaces

D_x [mm] D_y [mm] l)_z [mm]

Reticle 0.000000000 2161.963662900 2293.463985442

M01 0.000000000 2014.575340040 608.807746335

M02 0.000000000 1739.573953160 1446.205049270

M03 0.000000000 1518.196503845 1712.479693148

M04 0.000000000 1167.795380476 1865.986053005

M05 0.000000000 787.171013381 1867.738581450

M06 0.000000000 163.995268198 1651.723399936

M07 0.000000000 -63.653209854 1414.068794191

M08 0.000000000 -130.476167915 1189.657570934

M09 0.000000000 147.983152172 106.411634262

Stop 0.000000000 109.784896014 256.209890373

M10 0.000000000 0.000000000 686.742266049

Wafer 0.000000000 0.000000000 0.000000000

ax [°] ay [°] az [°]

Reticle -0.000000000 0.000000000 0.000000000

M01 6.590093567 180.000000000 0.000000000

M02 -61.040048024 0.000000000 0.000000000

M03 -36.958954635 0.000000000 180.000000000 M04 -11.960717071 0.000000000 0.000000000

MO 5 9.427176240 0.000000000 180.000000000

M06 32.675044953 0.000000000 0.000000000

M07 59.824985088 0.000000000 180.000000000

MO 8 88.917183425 0.000000000 0.000000000

M09 14.360885229 180.000000000 0.000000000

Stop 1.573800008 180.000000000 0.000000000

M10 7.152722206 0.000000000 0.000000000

Wafer 0.000000000 0.000000000 0.000000000

Table 2 for Figure 58

Free-form coefficients of the surfaces

Coefficient Formula M01 M02 M03

C7 x 2 y 1.7253489139e-08 -6.8489733052e-08 2.0843277494e-07

C9 3

y 7.9749363717e-10 -5.3748830899e-07 3.5731390147e-07

CIO x⁴ -6.9020346334e-12 2.6199710848e-10 7.870676563 le-10

C12 x² y² 3.3872176680e-l 1 -4.3485943610e-12 4.1376756966e-10

C14 y⁴ -1.1670716609e-10 2.0365190593e-09 -1.3628694979e-10

C16 x 4 y -2.2555301300e-17 -3.5480166953e-13 2.1965350784e-12

C18 x 2 y 3 8.4166488020e-14 1.3800654327e-12 4.2451927234e-13

C20 y -1.0923151873e-13 -9.3653209855e-12 3.1611513285e-12

C21 x⁶ -1.2315966648e-18 -9.7819269830e-18 5.9468167770e-16

C23 x⁴ y² -3.5330767899e-17 1.0734911913e- 15 3.7563002887e-15

C25 x y⁴ -1.0363692287e-16 -8.7081211286e-15 1.5480856576e-15

C27 y⁶ -5.1756577448e-16 4.617248381 le-14 2.5330310392e-16

C29 x⁶ y 5.3133484540e-21 2.5905369889e-19 6.5712831434e-18

C31 x⁴ y³ -1.0320914016e-19 -3.2915476605e-18 8.1606868614e-18

C33 x² y⁵ -1.3353723988e-19 4.9992664875e-17 8.9104237279e-18

C35 y⁷ 1.1728632898e-18 -2.1726372199e-16 4.4472966750e-17

C36 x⁸ 4.3188783854e-24 -1.7542955590e-21 8.4991706332e-21

C38 x⁶ y² -2.2429678588e-23 1.2788123028e-20 2.7286382522e-20

C40 x⁴ y⁴ 1.1219636587e-21 2.7577782317e-20 1.5531371668e-20

C42 x² y⁶ 6.0463237998e-21 -2.4963305442e-19 1.6428091804e-20

C44 y⁸ 2.8489929482e-21 9.0794992021e-19 7.9767501976e-20

C46 x⁸ y -3.869218446 le-26 -2.6815378591e-23 -1.6956075609e-22

C48 x⁶ y³ -2.8209892776e-25 -2.9361551554e-22 -2.3876515087e-22

C50 x⁴ y⁵ -2.5566384053e-24 -4.9767508993e-22 -3.0158737609e-22

C52 x² y⁷ 1.4857630004e-23 8.8278879453e-22 -7.2719134030e-22

C54 9

y -3.6947757520e-23 -4.2768759215e-21 2.5266922972e-22

C55 10

X -2.1831570659e-28 2.0226752891e-25 -7.5002685555e-25 C57 x⁸ y² 1.0644189736e-27 -1.2734591128e-25 -3.2203296534e-24

C59 x⁶ y⁴ -5.0932779608e-26 -4.8732347413e-25 -2.9834475445e-24

C61 x⁴ y⁶ -5.2267477328e-25 6.3225939822e-25 -3.0204583298e-26

C63 x² y⁸ - 1.0212767616e-24 -6.1880498041e-24 6.4068165352e-25

C65 yio 2.1951683182e-25 3.3612417264e-23 -3.4125046085e-24

C67 x¹⁰ y 5.5233286783e-31 1.4914735398e-27 8.1059300195e-27

C69 x⁸ y³ 3.1967089965e-30 1.6828560041e-26 2.8973420196e-26

C71 x⁶ y⁵ 4.0971014826e-29 4.3181303652e-26 2.9242339955e-26

C73 x 4 y 7 -3.4747403696e-28 5.0939817356e-26 6.3626657208e-26

C75 x 2 y 9 -3 0997269846e-27 9.3649856491e-26 1.7205323285e-25

C77 11

y 1.9799155467e-27 -2.4582494198e-25 9.9327003587e-26

C78 x¹² 4.7534866210e-33 -9.707379445 le-30 4.8166958861e-29

C80 x¹⁰ y² -3.2620706683e-32 -5.2802581426e-30 2.4968559467e-28

C82 x⁸ y⁴ 7.2418199372e-31 2.1917136949e-29 3.6132584562e-28

C84 x⁶ y⁶ 1.4607832428e-29 6.6171129077e-29 2.1867893642e-28

C86 x⁴ y⁸ 7.0003828236e-29 -1.8548652984e-28 1.2678327946e-28

C88 x² y¹⁰ 7.5287332695e-29 -5.9442209286e-28 6.0551744642e-28

C90 y¹² -6.8180369024e-29 6.1663240519e-28 7.5571763540e-28

C92 x¹² y 5.8135350004e-36 -5.9121523781e-32 5.0247637623e-32

C94 x¹⁰ y³ 3.6980718880e-35 -6.9555978292e-31 -1.6426956878e-30

C96 x⁸ y⁵ -2.1732644796e-35 -2.3403450773e-30 -2.8799498107e-30

C98 x⁶ y⁷ 5.983627091 le-33 -4.2541775699e-30 -3.7992944526e-31

CIOO x⁴ y⁹ 7.2845140649e-32 -2.5488573683e-30 -9.4964043959e-30

C102 x² y^{1 1} 2.1179261177e-31 3.3256618693e-31 -1.6373399048e-29

C104 13

y -2.5199979064e-31 4.5432350990e-30 -5.3307704621e-30

C105 x¹⁴ -5.7422589862e-38 2.4911174828e-34 -1.3376634501e-33

C107 x¹² y² 3.7256249464e-37 5.9720912710e-34 -9.6749923333e-33

C109 x¹⁰ y⁴ -3.9618629429e-36 1.2123247028e-33 -2.1118371641 e-32 cm x⁸ y⁶ -1.8436361781e-34 -1.0994880570e-33 -2.0786234049e-32

Cl 13 x⁶ y⁸ -1.5062837673e-33 5.5195940953e-33 -2.0124917876e-33 Cl 15 x⁴ y¹⁰ -4.6400029560e-33 1.6097310935e-32 -3.7250345082e-32 Cl 17 x 2 y 12 -3.1004874585e-33 4.1854957182e-33 -7.8902616124e-32 Cl 19 y¹⁴ 4.6547252057e-33 -1.9304773647e-32 -4.9753333709e-32 C121 x¹⁴ y -1.2268218319e-40 1.1244874804e-36 -1.0212350194e-35 C123 x¹² y³ -9.0701554967e-40 1.4956461788e-35 4.1399186534e-35 C125 x¹⁰ y⁵ -3.4014235302e-39 6.1311799847e-35 1.3916837427e-34 C127 x⁸ y⁷ -6.7465781696e-38 1.6218999393e-34 -2.9197822714e-35 C129 x⁶ y⁹ -7.8105532580e-37 1.4893502685e-34 4.1828454936e-35 C131 x⁴ y^{1 1} -3.8875752683e-36 4.3413035846e-37 6.9732981366e-34 C133 x 2 y 13 -5.7123473251e-36 7.5426824837e-35 8.1002947367e-34

C135 15

y 1.3664641192e-35 -2.2273282373e-34 1.8633086421e-34

C136 x¹⁶ 3.5382563057e-43 -3.1789288726e-39 1.0990626749e-38

C138 x¹⁴ y² -1.6020313895e-42 -1.6859209656e-38 1.8576932736e-37

C140 x¹² y⁴ -1.0127873883e-42 -7.1099677504e-38 6.2080994565e-37

C142 x¹⁰ y⁶ 1.0967611659e-39 -1.1729983864e-37 9.5218789081e-37

C144 x⁸ y⁸ 1.2840161244e-38 -3.0948769654e-37 -2.9790673669e-37

C146 x⁶ y¹⁰ 6.7114787655e-38 -3.3722622951e-37 3.2412128450e-37

C148 x⁴ y 1.4952208127e-37 -9.4218325183e-38 3.4470826745e-36

C150 x 2 y 14 6.1172323403e-38 -7.2447634373e-37 4.5689777639e-36

C152 yl6 -1.4991901405e-37 2.0657707990e-36 1.7520087692e-36

C154 x¹⁶ y 5.3369182902e-46 -8.2883102766e-42 1.6783721110e-40

C156 x¹⁴ y³ 4.6138127934e-45 -1.2716590616e-40 -3.6729130762e-40

C158 x¹² y⁵ 1.498886603 le-44 -6.1176139332e-40 -2.3043381810e-39

C160 x¹⁰ y⁷ 3.6754249732e-43 -2.2046628624e-39 9.2025446789e-41

C162 x⁸ y⁹ 2.8057693691e-42 -3.3751566064e-39 2.4194482093e-39

C164 x⁶ y^{1 1} 2.3161127198e-41 -2.0758041719e-39 -2.9791606548e-39

C166 x⁴ y¹³ 6.2185159478e-41 -3.5280071620e-40 -1.9548408949e-38

C168 x² y¹⁵ 4.6830746241e-41 2.2678920528e-39 -1.3947901977e-38

C170 17

y -2.5581720088e-40 -6.4781792315e-39 -1.2534633466e-39

C171 x¹⁸ -8.7106263137e-49 1.5909736637e-44 5.6412310058e-44

C173 x¹⁶ y² 1.3065808812e-48 1.5692316677e-43 -1.3730343423e-42

C175 x¹⁴ y⁴ 5.7724821550e-47 9.2463053236e-43 -7.1156444255e-42

C177 x¹² y⁶ -2.539932957 le-45 2.7573773750e-42 -1.7209828703e-41

C179 x¹⁰ y⁸ -3.8480556992e-44 7.8803423243e-42 7.4650261022e-42

C181 x⁸ y¹⁰ -2.8906423075e-43 1.0686884566e-41 1.3259734573e-41

C183 x⁶ y¹² -1.0710759915e-42 6.3005191864e-42 -2.0815143454e-41

C185 x⁴ y¹⁴ -1.9093028362e-42 1.3998881812e-42 -1.1081185271e-40

C187 x² y¹⁶ -3.6758206105e-43 -2.5085703463e-42 -8.6419940693e-41

C189 18

y 1.9226105852e-42 7.3627430941e-42 -1.8267900750e-41

Table 3a for Figure 58

Coefficient Formula M04 M05 M06

C7 x 2 y 5.9619652909e-08 -9.6306295638e-08 1.9227451807e-07

C9 y 3 -6.4627956566e-08 -1.0730315483e-07 -2.4556984659e-08

CIO X⁴ 1.1870458782e-10 -1.3108674026e-10 -3.6652240950e-10

C12 x² y² 4.2484517648e-l l -1.9074600914e-10 5.5260903506e-l 1

C14 y⁴ -1.7083044460e-10 -8.2387121265e-l 1 -3.0674996888e-10

C16 x 4 y 1.4473484670e-13 -3.9784398048e-13 -2.9162936785e-13 C18 x 2 3 5.0227880905e-13 -4.3076558139e-14 9.4168590585e-14

C20 y -3.2659709148e-13 -1.0065375895e-13 1.2672256858e-12

C21 x⁶ -6.1264573072e-16 -6.1713208598e-16 -4.1790113004e-16

C23 x⁴ y² -4.6722995064e- 16 -9.0367375806e-17 -3.7780225064e-16

C25 x y⁴ 7.1807994596e-16 -4.6021570894e-17 -2.3758008591e-15

C27 y⁶ -1.3897276106e-15 2.0760637622e-16 -9.0345913028e-16

C29 x⁶ y 3.5719085175e-18 -1.2768843454e-18 1.0173737480e-19

C31 x⁴ y³ 2.9798599285e-19 -1.3994444742e-18 2.1468282001e-18

C33 x² y⁵ 6.3089775664e-18 2.5977874654e-18 -2.6327449063e-18

C35 7

y -5.3367998807e-18 4.9671450998e-19 1.3314817802e-17

C36 X 6.9645120498e-20 6.1839204210e-21 -6.6532449871e-21

C38 x⁶ y² -1.5138637983e-20 5.6569155116e-21 -1.1111484151e-20

C40 x⁴ y⁴ -2.5563494603e-20 6.2582209919e-21 3.1940337834e-21

C42 x² y⁶ -9.6885980851e-21 1.7588567507e-21 -1.6348716182e-20

C44 y -4.7478149700e-20 -3.9561450530e-21 -9.0110415754e-20

C46 x⁸ y -4.9404416862e-23 3.8953242769e-22 1.9732570865e-23

C48 x⁶ y³ 2.9284412084e-22 2.2342683639e-22 1.5014823115e-23

C50 x⁴ y⁵ 3.2089532220e-22 8.8589786996e-23 4.7205530052e-23

C52 x² y⁷ 7.8477224013e-23 -2.0504385613e-22 6.3322704908e-22

C54 9

y 6.7281771634e-22 -4.0183954531e-23 -1.2080616869e-22

C55 X¹⁰ -4.5115823443e-24 -8.3395504092e-25 5.6849359909e-25

C57 x⁸ y² 1.1596778963e-24 - 1.1694694180e-24 5.3393565191e-25

C59 x⁶ y⁴ 3.1371621373e-25 2.2564100079e-25 5.0658246263e-25

C61 x⁴ y⁶ 4.0215331718e-24 -1.7725373853e-25 -6.065408441 le-24

C63 x² y⁸ 3.8228936375e-26 -3.7208091364e-25 -2.5528281427e-24

C65 yio 3.6686469783e-24 8.3369265250e-25 2.9620196237e-24

C67 x¹⁰ y 1.4823362161e-26 -3.1631210601e-26 -5.4222473970e-28

C69 x⁸ y³ -2.2670848692e-26 -2.261744947 le-26 3.7763151833e-27

C71 x⁶ y⁵ -5.6655763530e-26 -1.9333613343e-26 3.1912780542e-26

C73 x 4 y 7 -3.0351278199e-26 -1.2372637598e-26 3.5585551336e-27

C75 x 2 y 9 5.9678509430e-27 2.0792003000e-26 -2.2045048549e-26

C77 11

y -8.884866543 le-26 -8.2884124295e-28 3.2914028052e-26

C78 x¹² 5.405561563 le-29 3.7086259933e-29 -2.9034889293e-29

C80 x¹⁰ y² -1.0070011980e-28 1.0421821932e-28 -1.4111767821e-29

C82 x⁸ y⁴ 1.3952944970e-28 3.6176844261e-32 -6.3893054523e-29

C84 x⁶ y⁶ -1.9672629948e-28 -1.1949042112e-28 3.8213016342e-28

C86 x⁴ y⁸ -3.9016380745e-28 3.5923689503e-29 1.0487727615e-27

C88 x² y¹⁰ 1.0241742480e-28 3.7331109668e-30 1.4143687968e-28

C90 12

y -2.6184014766e-28 -6.3253778652e-29 -4.0071558454e-28 C92 x¹² y - 1.2635904019e-30 1.6104337521e-30 2.2399300728e-32

C94 x¹⁰ y³ 8.2197946604e-31 1.3550720653e-30 -2.7445272907e-31

C96 x⁸ y⁵ 3.8774777510e-30 8.7886313509e-31 -3.4871047178e-30

C98 x⁶ y⁷ 5.8338594201e-30 1.6980239554e-30 -7.3536423618e-30

CIOO x⁴ y⁹ 1.9245525482e-30 6.2198194417e-31 3.2025823509e-31

C102 x² y^{1 1} -3.6276058185e-31 -1.2201026444e-30 2.5469791839e-31

C104 13

y 6.7015966339e-30 2.0265864807e-31 -2.8342202196e-30

C105 x¹⁴ 7.0754461400e-33 -1.2461754197e-33 9.6892314589e-34

C107 x¹² y² 6.9483309172e-33 -4.9831878581e-33 -2.1754319445e-34

C109 x¹⁰ y⁴ -1.5898565106e-32 -2.0527081215e-33 4.1480454347e-33 cm x⁸ y⁶ -4.1261602263e-33 8.6813841887e-33 -6.8123372762e-34

Cl 13 x⁶ y⁸ 7.9018580389e-33 6.4964272060e-33 -5.3646066362e-32 Cl 15 x⁴ y¹⁰ 1.4730630079e-32 -2.1385527421e-33 -7.4438418697e-32 Cl 17 x 2 y 12 -9.3709053870e-33 1.3163947227e-33 1.6067709967e-33 Cl 19 y¹⁴ 3.1715227886e-33 2.6117410390e-33 2.6104858817e-32 C121 x¹⁴ y 4.861337371 le-35 -4.3151391979e-35 -3.5595430199e-37 C123 x¹² y³ -8.2786792099e-36 -4.2965290980e-35 5.6132269713e-36 C125 x¹⁰ y⁵ -1.1455279957e-34 -2.1459475775e-35 1.2496645767e-34 C127 x⁸ y⁷ -2.4535902330e-34 -4.5201912620e-35 5.4968822893e-34 C129 x⁶ y⁹ -3.0016552398e-34 -6.4684796477e-35 4.5990236264e-34 C131 x⁴ y^{1 1} -2.9500717929e-35 -1.8367959378e-35 -4.4852910240e-35 C133 x² y¹³ 2.328746381 le-35 4.4419693559e-35 3.5004526883e-35 C135 15

y -2.6937728465e-34 -1.0937409663e-35 1.3890479890e-34 C136 x¹⁶ -3.5416222941 e-37 3.2068197087e-38 -2.0407530149e-38 C138 x¹⁴ y² -2.9561837697e-37 1.2298273288e-37 1.5095827462e-38 C140 x¹² y⁴ 6.9823107816e-37 6.2115864707e-38 -9.8763903728e-38 C142 x¹⁰ y⁶ 2.9905367425e-37 -9.0190361713e-38 -7.0845111441e-37 C144 x⁸ y⁸ 6.7993674269e-37 -5.3235455708e-37 -5.4330376858e-37 C146 x⁶ y¹⁰ 1.3317380172e-37 -6.9963833007e-38 2.1142057404e-36 C148 x⁴ y -2.9602159509e-37 5.6138809191e-38 2.4381231790e-36 C150 x 2 y 14 2.4944798647e-37 -1.0522177669e-37 -5.8238584789e-37 C152 yl6 3.7010074817e-37 -4.1216639607e-38 -8.1739439859e-37 C154 x¹⁶ y -7.0030393159e-40 4.6655407513e-40 1.0293113341e-42 C156 x¹⁴ y³ -1.0107248761 e-40 5.3664597179e-40 -2.1802812095e-41 C158 x¹² y⁵ 1.343793871 le-39 3.5517226807e-40 -1.3268279979e-39 C160 x¹⁰ y⁷ 3.1379083042e-39 4.9264089524e-41 -1.0629457603e-38 C162 x⁸ y⁹ 6.4841206733e-39 1.4339689676e-39 -2.0116502619e-38 C164 x⁶ y^{1 1} 5.8950381744e-39 3.8000533331e-40 -8.2152472151e-39 C166 x⁴ y¹³ -4.9210179434e-40 5.1538948327e-40 9.9025471559e-40 C168 x² y¹⁵ -3.0663656656e-40 -7.7929492046e-40 -9.8625504558e-40

C170 17

y 4.4885903021e-39 2.1192228052e-40 -2.5833680929e-39

C171 x¹⁸ 5.1309968161e-42 -3.7893844990e-43 1.9301975877e-43

C173 x¹⁶ y² 5 2044049694e-42 -1.2285035840e-42 -1.7541043036e-43

C175 x¹⁴ y⁴ -1.1766543123e-41 -3.2203099193e-43 3.9816210665e-43

C177 x¹² y⁶ -2.3390651329e-42 -9.2026115855e-43 1.4637033818e-41

C179 x¹⁰ y⁸ -1.8863113098e-41 6.3836698688e-42 5.3346368013e-41

C181 x⁸ y¹⁰ -2.0670936737e-41 5.9100764857e-42 4.819594653 le-41

C183 x⁶ y¹² -1.4308481467e-41 1.3778084151e-42 -2.7248935524e-41

C185 x⁴ y¹⁴ 5.6094917591e-42 -2.0202666259e-42 -3.2644121585e-41

C187 x² y¹⁶ -2.5292311572e-42 2.8173014638e-42 1.7258691433e-41

C189 18

y -1.2590227357e-41 -8.8094576680e-44 8.8535445659e-42

Table 3b for Figure 58

Coefficient Formula M07 M08 M09

C7 x 2 y -1.3688636632e-07 2.7752316055e-07 1.5042562426e-06

C9 y 3 -3.6562839317e-07 -1.9124090722e-07 -7.9138018050e-07

CIO X⁴ 4.3668480726e-l 1 1.8921525902e-10 1.3302421312e-09

C12 x² y² - 1.2882387063e-09 -1.7753333696e-10 5.4922412133e-09

C14 y⁴ 2.2478456664e-09 -5.5891573060e-10 2.1170775267e-09

C16 x 4 y 3.9915359069e- 13 6.0252617982e- 13 7.9566805060e-12

C18 x 2 y 3^J -2.4915604645e-13 -2.1988915025e-14 -9.5752553040e-13

C20 y -2.6584746885e-12 -2.7033078478e-12 -1.0996575531e-l l

C21 x⁶ 1.0355358507e-16 8.1436100116e-16 7.1009981019e-15

C23 x⁴ y² 2.1047584927e- 15 2.4368217928e- 15 4.5501453876e-14

C25 x y⁴ -2.9936124637e-14 -1.9177412720e-15 8.9435770358e-14

C27 y⁶ 3.534364265 le- 14 -1.4538952930e-14 1.6820448385e-13

C29 x⁶ y 2.6124679416e-18 1.0895336117e-17 5.7466037470e-17

C31 x⁴ y³ 6.4049410027e- 17 1.9188958547e- 17 1.1289868631e-16

C33 x² y⁵ -3.9675196784e- 16 - 1.6059149618e- 17 3.0899856353e-16

C35 y⁷ -2.1261280702e-15 -8.2763028564e-17 -7.8202523094e- 16

C36 x⁸ 1.3918320834e-20 -5.7783778081e-20 3.4817617526e-20

C38 x⁶ y² -2.9374535762e-20 - 1.4837821532e- 19 4.7359948801e-19

C40 x⁴ y⁴ 2.8237799354e- 18 -7.6456622434e-20 1.9919875033e-18

C42 x² y⁶ 4.7202902322e- 18 -2.9848891376e- 19 1.2507447353e-18

C44 y⁸ -4.0308349054e-17 -5.4438237525e-19 -8.1704148477e-18

C46 x⁸ y 2.4441818089e-22 - 1.9762721950e-21 5.3354821362e-22

C48 x⁶ y³ -9.3939277976e-21 -6.5494127080e-21 3.6406378391e-21

C50 x⁴ y⁵ -3.8894701544e-20 -1.0751986352e-21 1.2083820635e-20 C52 x 2 y 7 8.6761679159e-19 -6.2935153381e-21 -4.0177768217e-20

C54 9

y 1.9054480444e-18 -4.8260290311 e-21 -2.9548201347e-20

C55 X¹⁰ -1.6763704485e-24 9.5776630875e-24 7.1633088969e-25

C57 x⁸ y² -2.3522355178e-24 5.3710306358e-23 4.7848731006e-24

C59 x⁶ y⁴ -3.8504521553e-22 1.7992304952e-23 2.5020167924e-23

C61 x⁴ y⁶ -3.5244874355e-21 1.7086866548e-23 -4.4998032486e-23

C63 x² y⁸ 2.2457033940e-21 -4.0440322204e-23 -7.5162676171e-23

C65 yio 5.0619587944e-20 -3.7229786491e-23 1.5977448485e-21

C67 x¹⁰ y -1.4918005519e-26 2.3996701840e-25 1.0140406083e-26

C69 x⁸ y³ 7.2827606192e-25 1.7501487158e-24 3.7053241962e-26

C71 x⁶ y⁵ 5.3841701529e-24 7.4457526928e-25 -1.1874473226e-24

C73 x 4 y 7 2.2248948699e-23 2.8589142707e-25 -7.1050908938e-24

C75 x 2 y 9 -1.0167293967e-21 4.9645130518e-25 -2.8310518027e-24

C77 11

y -6.3948673490e-22 -1.2335835759e-25 8.0553971154e-24

C78 x¹² 9.8023362020e-29 -9.0597950242e-28 -1.4301072740e-29

C80 x¹⁰ y² 9.5407546632e-28 -9.0012049803e-27 2.5474975517e-28

C82 x⁸ y⁴ 3.3795996453e-26 -8.1036569314e-27 8.3638629985e-28

C84 x⁶ y⁶ 3.6103028978e-25 4.0004718174e-27 -1.1905055581e-26

C86 x⁴ y⁸ 2.8855963881e-24 1.1963715502e-27 -2.2323752269e-26

C88 x² y¹⁰ -9.2775186112e-24 7.1173451189e-27 5.0215909185e-26

C90 y¹² -2.7377501722e-23 -1.7835859548e-29 -1.6688765299e-25

C92 x¹² y -4.4881863690e-32 -1.5502232139e-29 -2.8405056660e-31

C94 x¹⁰ y³ -3.2816859289e-29 -2.0807506072e-28 -2.7618250145e-30

C96 x⁸ y⁵ -1.284036877 le-28 -1.9828409258e-28 4.5634219065e-29

C98 x⁶ y⁷ -5.236891773 le-27 4.2591850131e-30 5.5064600993e-28

CIOO x⁴ y⁹ 1.1556865438e-26 -2.7573125896e-29 2.0957977789e-27

C102 x² y^{1 1} 5.6455694788e-25 -2.4874129517e-29 1.6113057471e-27

C104 13

y -1.0346370948e-25 -1.0655637181e-29 -1.3332366400e-27

C105 x¹⁴ -3.7234103202e-33 5.2039454247e-32 3.0225972532e-35

C107 x¹² y² -7.7423091829e-32 8.1293667676e-31 -1.3372785026e-32

C109 x¹⁰ y⁴ -2.0407345816e-30 1.8320993449e-30 - 1.185246020 le-31 cm x⁸ y⁶ -1.4350174259e-29 -4.0238627499e-31 3.9565424047e-31

Cl 13 x⁶ y⁸ -2.7522008894e-28 -6.6840274328e-31 6.2883276405e-30 Cl 15 x⁴ y¹⁰ -8.8286098090e-28 -3.3421321383e-31 9.280733893 le-30 Cl 17 x 2 y 12 6.6836310682e-27 -9.5586709447e-31 -7.6599969563e-30 Cl 19 y¹⁴ 5.7809272350e-27 -1.9539636427e-31 1.6641174179e-29 C121 x¹⁴ y 2.5468486327e-35 5.3956364343e-34 1.1302147627e-35 C123 x¹² y³ 8.1843079981e-34 1.1722775011e-32 2.0611996164e-34 C125 x¹⁰ y⁵ -3.1786202177e-33 1.8751250564e-32 -3.632876671 le-34 cm x⁸ y⁷ 1.6128905021e-31 4.8956636439e-33 -1.731 1 198679e-32

C129 x⁶ y⁹ 1.4856206327e-30 -9.4074941622e-33 -9.8121878044e-32

C131 x⁴ y¹¹ -1.0461890618e-29 1.9854960869e-33 -2.9138576812e-31

C133 x² y¹³ -1.4870774049e-28 -6.8868323549e-33 -2.3053321491e-31

C135 15

y 1.1048434256e-28 -1.4134066773e-33 9.8890261670e-32

C136 x¹⁶ 9.4024551059e-38 -1.6972328102e-36 2.1539194372e-38

C138 x¹⁴ y² 2.5971260384e-36 -3.6232126655e-35 4.9532187641e-37

C140 x¹² y⁴ 6.7990164328e-35 -1.5776675424e-34 6.8299244952e-36

C142 x¹⁰ y⁶ 3.3334098633e-34 -3.3025407321e-35 1.1263719992e-35

C144 x⁸ y⁸ 7.3984535304e-33 7.0159809934e-35 -1.8988518951e-34

C146 x⁶ y¹⁰ 8.3645430246e-32 -3.8690482208e-35 -1.06794471 10e-33

C148 x⁴ y 4.1339559386e-32 4.9865422491e-35 -8.1208067476e-34

C150 x 2 y 14 - 1.9638322655e-30 -2.0372670898e-35 1.0106034997e-33

C152 yl6 1.669608961 le-31 -5.1667769524e-36 -1.1 175822688e-33

C154 x¹⁶ y -5.5773939377e-40 -8.0080153729e-39 -1.0344734125e-40

C156 x¹⁴ y³ -8.5527847535e-39 -2.5407072091e-37 -3.4430160947e-39

C158 x¹² y⁵ 1.2994777601e-37 -5.9333201884e-37 -1.3421373869e-38

C160 x¹⁰ y⁷ -1.5028450332e-36 -4.0585245549e-37 2.2729668884e-37

C162 x⁸ y⁹ -2.5395921073e-35 4.5660813580e-37 1.6870445746e-36

C164 x⁶ y¹¹ -1.4169933882e-34 6.2254031361e-39 6.4229187941e-36

C166 x⁴ y¹³ 2.0030442912e-33 2.7841895073e-37 1.6097691047e-35

C168 x² y¹⁵ 1.4672106654e-32 -1.6325771950e-38 1.1623854035e-35

C170 17

y -1.7899306439e-32 -9.2771947433e-39 -3.1878097815e-36 cm x¹⁸ -1.1513361727e-42 2.4622996073e-41 -4.1203849009e-43

C173 x¹⁶ y² -3.2380065067e-41 6.0932687405e-40 -6.1216041895e-42

C175 x¹⁴ y⁴ -9.0269500168e-40 4.663365961 le-39 -1.2554925228e-40

cm x¹² y⁶ -4.3580940818e-39 2.8315772094e-39 -5.3772451628e-40

C179 x¹⁰ y⁸ -6.6198645363e-38 -1.0891088355e-39 1.4543997489e-39

C181 x⁸ y¹⁰ -1.2364920485e-36 1.0784338447e-39 1.9049482393e-38

C183 x⁶ y¹² -8.5360931507e-36 2.3563661099e-40 5.7000090045e-38

C185 x⁴ y¹⁴ 1.6729255587e-35 5.1554645133e-40 1.9740886141e-39

C187 x² y¹⁶ 2.052426996 le-34 2.0047489560e-41 -6.1674065396e-38

C189 18

y -1.5298757076e-34 -6.1493259847e-42 3.6309767029e-38

Table 3c for Figure 58

Coefficient Formula M10

C7 x² y -1.1963579370e-08

C9 y³ 8.7322952596e-09

CIO x⁴ -2.1296980535e-l l C12 x 2 y 2 -6.0081531496e-l l

C14 y⁴ -1.3100686441e-l l

C16 x 4 y -2.9453202317e-14

C18 x 2 3 -7.0711311368e-15

C20 y 1.2413476816e-14

C21 x⁶ -4.4751375902e- 17

C23 x⁴ y² -1.7381468208e-16

C25 x y⁴ -1.5538256681e-16

C27 y⁶ -3.6495586839e-17

C29 x⁶ y -5.1034460824e-20

C31 x⁴ y³ -5.8777424732e-20

C33 x² y⁵ 8.8723819629e-22

C35 7

y 1.7063977474e-20

C36 X -8.5217152131e-23

C38 x⁶ y² -3.9426334467e-22

C40 x⁴ y⁴ -6.0261397447e-22

C42 x² y⁶ -3.6936580816e-22

C44 y -5.4368523802e-23

C46 x⁸ y -7.4001974119e-26

C48 x⁶ y³ -2.0694915444e-25

C50 x⁴ y⁵ -1.6445257935e-25

C52 x² y⁷ -7.1379877112e-27

C54 9

y 6.5250253448e-26

C55 X¹⁰ -1.0368467343e-28

C57 x⁸ y² -9.9146699432e-28

C59 x⁶ y⁴ -2.2750636360e-27

C61 x⁴ y⁶ -2.2897755783e-27

C63 x² y⁸ -9.6658117555e-28

C65 yio -1.8069831798e-28

C67 x¹⁰ y -2.6447499153e-31

C69 x⁸ y³ -2.8737519246e-31

C71 x⁶ y⁵ -8.4741638906e-33

C73 x 4 y 7 8.9348304973e-31

C75 x 2 y 9 8.1135191352e-31

C77 11

y -4.9988190927e-32

C78 x¹² -3.7377373928e-34

C80 x¹⁰ y² -1.3859805746e-34

C82 x⁸ y⁴ 2.5011587910e-33

C84 x⁶ y⁶ 4.8799118600e-33 C86 x⁴ y⁸ 3.0429500103e-33

C88 x² y¹⁰ 5.7864904180e-34

C90 y¹² 2.7996785737e-36

C92 x¹² y 5.5993360240e-37

C94 x¹⁰ y³ -2.7299448452e-36

C96 x⁸ y⁵ -5.1780931527e-36

C98 x⁶ y⁷ -1.0420851865e-35

CIOO x⁴ y⁹ -1.1848327853e-35

C102 x² y^{1 1} -5.4107225260e-36

C104 13

y 1.4375366590e-38

C105 x¹⁴ -2.6630257208e-40

C107 x¹² y² -1.3505746627e-38

C109 x¹⁰ y⁴ -7.3804603968e-38 cm x⁸ y⁶ -1.5912474468e-37

Cl 13 x⁶ y⁸ -1.5669435176e-37 Cl 15 x⁴ y¹⁰ -8.1237037712e-38 Cl 17 x 2 y 12 -2.3319945230e-38 Cl 19 y¹⁴ -2.9277377350e-39 C121 x¹⁴ y -2.9283626370e-42 C123 x¹² y³ 6.9897787563e-42 C125 x¹⁰ y⁵ 7.3512149217e-42 C127 x⁸ y⁷ 2.5558690249e-41 C129 x⁶ y⁹ 6.5477665394e-41 C131 x⁴ y^{1 1} 6.1164214533e-41 C133 x² y¹³ 2.303760423 le-41 C135 15

y 1.9618549164e-42 C136 x¹⁶ 1.7117161010e-46 C138 x¹⁴ y² 3.0372117389e-44 C140 x¹² y⁴ 2.5156057362e-43 C142 x¹⁰ y⁶ 7.5608820786e-43 C144 x⁸ y⁸ 1.0196410225e-42 C146 x⁶ y¹⁰ 7.0059399446e-43 C148 x⁴ y 2.6948856854e-43 C150 x 2 y 14 6.9453820365e-44 C152 yl6 1.0740173035e-44 C154 x¹⁶ y 1.8455339326e-48 C156 x¹⁴ y³ -3.0358148708e-47 C158 x¹² y⁵ -5.5075196919e-47 C160 x¹⁰ y⁷ -7.8164171642e-47 C162 x⁸ y⁹ - 1.5626762420e-46

C164 x⁶ y^{1 1} -2.0595102987e-46

C166 x⁴ y¹³ -1.2440679310e-46

C168 x² y¹⁵ -3.3188164228e-47

C170 17

y -3.1229343880e-48

C171 x¹⁸ -4.3867520979e-51

C173 x¹⁶ y² -7.8207881113e-50

C175 x¹⁴ y⁴ -5.8730867189e-49

C177 x¹² y⁶ -2.0542952173e-48

C179 x¹⁰ y⁸ -3.5639631397e-48

C181 x⁸ y¹⁰ -3.4675250746e-48

C183 x⁶ y¹² -1.916438411 le-48

C185 x⁴ y¹⁴ -6.5130085142e-49

C187 x² y¹⁶ -1.6111568227e-49

C189 18

y -2.5128543295e-50

Table 3d for Figure 58

Coordinates of the stop edge

¾ [mm] yi [mm] ¾+N/₂ [mm] yi_+N/2 [mm]

-159.085223 112.280807 130.703822 156.097707

-143.649724 125.226709 116.762081 163.566497

-128.712145 135.683015 105.807856 168.545690

-113.774565 144.645563 84.397325 176.512399

-98.836985 152.114353 76.430616 179.001996

-84.895244 158.089385 60.497198 182.985351

-73.443100 162.072739 45.061699 185.972867

-61.493036 165.558174 30.622038 187.964544

-54.024246 167.549852 20.165733 188.960382

-42.074183 170.039448 8.713588 189.458302

-24.149087 172.529045 -9.709427 189.458302

-10.705265 173.524883 -25.642845 188.462463

10.705265 173.524883 -38.588747 186.968705

32.613716 171.533206 -62.986794 182.487431

49.542972 168.545690 -84.397325 176.512399

65.476391 164.562336 -91.866115 174.022803

80.413970 159.583142 -106.803694 168.047771

96.845308 -153.110191 -116.762081 163.566497

113.774565 -144.645563 -128.214225 157.591465

127.218387 -136.678854 -139.168450 151.118514 .180934 -130.703822 -146.637240 146.139321

.139321 -123.235032 -158.089385 137.674692

.587304 -112.778726 -164.064416 132.695499

.529045 -98.836985 -168.545690 128.712145

.989512 -87.882760 -180.495754 116.762081

.454140 -76.430616 -186.968705 109.293291

.931253 -67.965987 -191.947898 102.820340

.910446 -59.501359 -202.404204 86.886922

.885478 -47.551295 -209.872994 71.451423

.864671 -35.103312 -212.860510 63.982633

.848026 -22.655329 -216.843864 51.036730

.333461 -6.721911 -218.835542 42.074183

.827219 6.223992 -220.329300 32.115796

.827219 26.638684 -220.827219 26.638684

.835542 42.074183 -220.827219 5.726072

.350106 56.513843 -218.835542 -9.211507

.370913 70.455584 -215.848026 -22.655329

.400043 84.895244 -212.860510 -32.613716

.910446 89.376518 -206.885478 -47.551295

.952060 104.314098 -201.408365 -58.505520

.993673 116.264162 -196.927092 -66.472229

.549852 129.707983 -185.474947 -83.401486

.068578 133.691338 -173.026964 -98.339066

.130998 145.143482

Table 4 for Figure 58

Wavelength 13.5 nm

NA 0.55

bc 4.10

b_g -8.00

Chi ef ray angl e (CR A) 5.05°

Etendue 12.58 mm²

Mean wavefront aberration RMS 8.58 ihl

System transmission 7.62 %

Position of the entry pupil EP (x) -2379.88 mm

Position of the entry pupil EP (y) -2499.49 mm

Object-image offset 2161.96 mm Working distance between M9 and

81 mm

image field

Reticle tilt 0 0

Installation length 2293.46 mm

Obscuration 18.4 %

Installation space cuboid (790 x 2505 x 1811) mm

Table 5 for Figure 58

Ml M2 M3 M4 M5

Maximum angle of 13.3 84.3 79.8 80.7 83.5

incidence [deg]

Minimum angle of incidence [deg] 9.9 73.9 74.0 75.9 77.4

Mirror extent (x) [mm] 634.8 403.7 334.3 288.6 318.2

Mirror extent (y) [mm] 274.7 305.9 259.1 292.1 353.1

Maximum mirror diameter 635.2 403.9 346.3 370.0 412.2

[mm]

Table 6a for Figure 58

M6 M7 M8 M9 M10

Maximum angle of incidence 79.8 81.9 77.9 20.4 8.4

[deg]

Minimum angle of incidence [deg] 73.7 72.2 70.2 0.0 5.1

Viirror extent (x) [mm] 347.0 305.2 234.3 292.1 790.1

Viirror extent (y) [mm] 261.8 115.9 255.8 155.7 768.1

Maximum mirror diameter 348.6 305.3 285.2 292.3 790.3

[mm]

Table 6b for Figure 58

In respect of the admissible scale ratio curves 24i, what was explained above in respect of the projection optical unit 7 applies to the projection optical unit 40. Figures 72 to 85 show a further embodiment of a projection optical unit 41, which can be used instead of the projection optical unit 7 in the projection exposure apparatus 1. Components and functions corresponding to those which were already explained above with reference to Figures 1 to 15, in particular, are denoted by the same reference signs and are not discussed in detail again. The projection optical unit 41 has a reduction scale b_c in the xz-plane of 4.30 and a reduction scale p_y in the yz-plane of -8.40.

In terms of its basic design, the projection optical unit 41 corresponds to the projection optical unit 7.

The optical design data emerge from following Tables 1 to 6, which, in turn, correspond in terms of the basic structure to Tables 1 to 6 relating to the embodiment according to Figure 2. Radii of the surfaces

RadiuS_x [mm] Power_x [1/mm] RadiuS_y [mm] Power_y [1/mm]

M01 -2148.13972878 0.00091660 -1364.19829486 0.00144333

M02 2840.54829920 -0.00013866 2882.42778989 -0.00013665

M03 2074.90028844 -0.00022662 -16002.63929082 0.00002938

M04 3963.79277236 -0.00010423 -7793.24133377 0.00005301

M05 -2159.70388258 0.00016406 -5199.32226015 0.00006815

M06 -913.56415887 0.00051148 -1867.67731654 0.00025019

M07 -730.19600220 0.00064446 22740.84364639 -0.00002069

M08 -994.79418417 0.00053260 -5293.79178082 0.00010009

M09 1133.41067821 -0.00176459 314.74977190 -0.00635425

M10 -784.35890122 0.00252979 -718.85984473 0.00276029

Table 1 for Figure 72

Decentring (location, angle) the surfaces

D_x [mm] D_y [mm] l)_z [mm]

Reticle 0.000000000 2038.392305181 2297.219728265

M01 0.000000000 1890.314777047 604.685836832

M02 0.000000000 1660.860854555 1448.962676486

M03 0.000000000 1455.924014496 1712.021956375

M04 0.000000000 1132.191083826 1862.177739783

M05 0.000000000 772.997433895 1868.703783568

M06 0.000000000 161.405739311 1653.719091282

M07 0.000000000 -61.760657692 1419.453558142

M08 0.000000000 -128.587585821 1192.284497655

M09 0.000000000 148.800863970 106.530337423

Stop 0.000000000 110.392074085 256.292107008 M10 0.000000000 0.000000000 686.727755014

Wafer 0.000000000 0.000000000 0.000000000

ax [°] ay [°] az [°]

Reticle -0.000000000 0.000000000 0.000000000

M01 5.102179737 180.000000000 0.000000000

M02 -63.437599040 0.000000000 0.000000000

M03 -38.481329317 0.000000000 180.000000000

M04 -12.961985173 0.000000000 0.000000000

MO 5 9.163278542 0.000000000 180.000000000

M06 32.878689694 0.000000000 0.000000000

M07 59.998755692 0.000000000 180.000000000

MO 8 88.969464462 0.000000000 0.000000000

M09 14.357878811 180.000000000 0.000000000

Stop 1.652742640 180.000000000 0.000000000

M10 7.192193522 0.000000000 0.000000000

Wafer 0.000000000 0.000000000 0.000000000

Table 2 for Figure 72

Free-form coefficients of the surfaces

Coefficient Formula M01 M02 M03

C7 x 2 y 1.7365310846e-08 -6.0343356543e-08 2.0501077670e-07

C9 3

y 2.3566902634e-09 -4.9658495637e-07 3.6842969532e-07

CIO X⁴ -6.9237303387e- 12 2.2741322381e-10 8.8221004032e-10

C12 x² y² 4.0840339390e-l 1 -1.1726796694e-l l 4.8012549912e-10

C14 y⁴ -1.1483665592e-10 1.8216907480e-09 -1.3820038020e-10

C16 x 4 y -3 4248860004e- 15 - 1.779226942 le- 13 2.6898427019e-12

C18 x 2 y 3 8.2131350272e-14 1.6823351389e-12 4.1766372884e-13

C20 y -6.1749233084e-14 -8.3930319568e-12 3.4739747926e-12

C21 X .6 -1.1079000560e-18 7.8889098030e-17 5.0748219081e-16

C23 x 4

4 y 2 -3.3957619260e-17 3.6930968800e-16 4.1706763880e-15

C25 x 2 y 4

4 -1.0318830451e-16 -1.0573150338e-14 2.3580708684e-15

C27 .6

y -5.3902435498e-16 4.0355380796e-14 1.0553047104e-15

C29 x⁶ y 2.7418541785e-21 -7.7009175813e-19 7.9818128932e-18

C31 x⁴ y³ -1.6747153427e-19 -3.5966141424e-18 1.4097178664e-17

C33 x² y⁵ -1.7719360100e-19 5.8468665921e-17 6.8956747602e-18

C35 7

y 1.3364453401e-18 -1.7153486777e-16 6.8636030182e-17

C36 X 7.9030757794e-24 -1.4884540118e-21 1.2637108485e-20

C38 x⁶ y² -5.9420525635e-23 2.4943130960e-20 7.4316800507e-20

C40 x⁴ y⁴ 9.012717363 le-22 4.9302364129e-20 8.6160468162e-20 C42 x² y⁶ 1.0781262015e-20 -2.6164962588e-19 -1.4527691729e-20

C44 y 1.2754067715e-20 6.9221861253e-19 9.9322710473e-20

C46 x⁸ y 1.6567217047e-25 -2.3692410287e-23 -4.0742247073e-22

C48 x⁶ y³ 1.9161852480e-24 -2.2305708459e-22 -1.4181143598e-21

C50 x⁴ y⁵ 1.8951826736e-24 -5.5806434083e-22 -1.3339991364e-21

C52 x² y⁷ 9.7708995176e-24 5.3027053656e-22 1.5159207757e-21

C54 9

y 3.6204022982e-23 -3.9285485751e-21 -1.6697748235e-22

C55 X¹⁰ -3.8004043444e-28 2.3607485281e-25 -1.1119702066e-24

C57 x⁸ y² 1.2408050817e-27 -5.3255210788e-25 -1.0845598855e-23

C59 x⁶ y⁴ -2.8347832247e-26 -2.1017890336e-24 -2.174602444 le-23

C61 x⁴ y⁶ -7.1309480226e-25 -7.6311156472e-25 -1.6004755492e-23

C63 x² y⁸ -2.4113951478e-24 -5.8399872025e-24 1.763283691 le-23

C65 yio - 1.3941884290e-24 3.2197155780e-23 2.6192920205e-24

C67 x¹⁰ y -3.7417725609e-30 1.1711775069e-27 3.1285750479e-26

C69 x⁸ y³ -5.5176013803e-29 7.4650570563e-27 1.5403810547e-25

C71 x⁶ y⁵ -2.8047564124e-28 3.2650962330e-26 2.7206812573e-25

C73 x 4 y 7 -5.7736685569e-28 7.6416550637e-26 7.6829099900e-26

C75 x 2 y 9 -3.1085248480e-27 1.4167353722e-25 -2.5551500034e-25

C77 11

y -2.6633585239e-27 -2.2718730140e-25 2.7043398312e-25

C78 x¹² 8.0048263301e-33 -1.2538487186e-29 7.1761816244e-29

C80 x¹⁰ y² -5.6118794530e-33 1.3167192512e-29 8.6685067282e-28

C82 x⁸ y⁴ 1.4298861506e-31 1.7422143645e-28 2.0985152849e-27

C84 x⁶ y⁶ 1.6640474118e-29 2.8265219972e-28 3.3832850056e-27

C86 x⁴ y⁸ 1.2493638058e-28 -1.3488520149e-28 7.5092146108e-28

C88 x² y¹⁰ 2.4625545297e-28 -7.1327077137e-28 -2.4415888920e-27

C90 y¹² 1.1257695043e-28 6.2001497466e-28 9.7990149333e-28

C92 x¹² y 5.8810044071e-35 -4.7244429694e-32 -1.0995287350e-30

C94 x¹⁰ y³ 9.211002433 le-34 -3.4182739957e-31 -8.6230496939e-30

C96 x⁸ y⁵ 7.2666617452e-33 -1.5788212501e-30 -2.3221557242e-29

C98 x⁶ y⁷ 2.6567793698e-32 -5.6336083442e-30 -1.9078406747e-29

CIOO x⁴ y⁹ 9.2581969118e-32 -5.7591491878e-30 3.7829006747e-30

C102 x² y^{1 1} 1.9847704727e-31 -3.8662623382e-30 2.6726747355e-29

C104 13

y -1.4962747560e-31 4.0747194506e-30 -2.3263971315e-29

C105 x¹⁴ -9.4872264230e-38 3.5260147174e-34 -2.2050351838e-33

C107 x¹² y² -3.4173568058e-37 2.4503815485e-34 -3.9323005565e-32

C109 x¹⁰ y⁴ 2.1670548824e-36 -5.4206493377e-33 -1.0725248401e-31 cm x⁸ y⁶ -1.7526844602e-34 -1.2909251687e-32 -2.5066932016e-31

Cl 13 x⁶ y⁸ -2.2966260973e-33 -2.2635788914e-33 -2.2407852170e-31 Cl 15 x⁴ y¹⁰ -1.0117353340e-32 2.5481969732e-32 6.1870830904e-32 Cl 17 x 2 y 12 -1.4390438477e-32 3.1832631483e-32 2.2699760254e-31 Cl 19 y¹⁴ -6.8415725204e-33 -2.0635911170e-32 -1.2674630669e-31

C121 x¹⁴ y -4.7603889878e-40 9.4149983704e-37 1.6437661228e-35

C123 x¹² y³ -8.1742112648e-39 9.2786821968e-36 2.2847135076e-34

C125 x¹⁰ y⁵ -7.5924887834e-38 4.1350502851e-35 9.0732765342e-34

C127 x⁸ y⁷ -4.2923605365e-37 1.9760015677e-34 1.0283579276e-33

C129 x⁶ y⁹ -1.3823817624e-36 3.1387777065e-34 5.4183912915e-34

C131 x⁴ y^{1 1} -5.5332166204e-36 1.0133966523e-34 -6.9740971360e-34

C133 x² y¹³ -3.7883902297e-36 1.4781918533e-34 -1.1852596092e-33

C135 15

y 1.7537884070e-35 -2.1107297141e-34 1.1384880678e-33 C136 x¹⁶ 5.8134479570e-43 -4.8718047953e-39 2.2997139768e-38

C138 x¹⁴ y² 5.4931191530e-42 -1.6883278427e-38 9.3840759757e-37

C140 x¹² y⁴ -1.8913693040e-41 5.7143234826e-38 2.8864958205e-36

C142 x¹⁰ y⁶ 9.0203399482e-40 1.8537900018e-37 8.6904244018e-36

C144 x⁸ y⁸ 1.7071493529e-38 -1.4022881409e-37 1.1037447383e-35

C146 x⁶ y¹⁰ 1.2537108072e-37 -6.4609289024e-37 6.1312390846e-36

C148 x⁴ y 3.9029767670e-37 -5.9512154809e-37 -8.3499243145e-36

C150 x 2 y 14 4.4095102186e-37 -2.0601666540e-36 -9.5680443063e-36

C152 yl6 2.3084471775e-37 2.1462904301e-36 6.9879429188e-36

C154 x¹⁶ y 1.4993507744e-45 -7.4209413139e-42 -6.7499739728e-41

C156 x¹⁴ y³ 2.9080194316e-44 -9.4866972882e-41 -2.2976093219e-39

C158 x¹² y⁵ 2.8766571252e-43 -4.2545234385e-40 -1.3340026248e-38

C160 x¹⁰ y⁷ 2.3414866026e-42 -2.5324688129e-39 -1.8683264155e-38

C162 x⁸ y⁹ 7.7051789933e-42 -6.3389515645e-39 -1.5467684724e-38

C164 x⁶ y^{1 1} 3.4670262144e-41 -5.5352748606e-39 4.5402834304e-40

C166 x⁴ y¹³ 1.0281975847e-40 -5.0538416708e-40 1.8267074328e-38

C168 x² y¹⁵ -9.8860625908e-42 7.3516789717e-39 2.4968581747e-38

C170 17

y -4.2446276147e-40 -7.1097305336e-39 -1.8712018602e-38 C171 x¹⁸ -1.4316718267e-48 2.6097665500e-44 4.0248945504e-44

C173 x¹⁶ y² -2.3486538205e-47 2.0378904977e-43 -9.1099411645e-42

C175 x¹⁴ y⁴ 8.2477460993e-48 5.3128957556e-44 -3.2148597851e-41

C177 x¹² y⁶ -2.1587439138e-45 -2.7950902967e-43 -1.2220342037e-40

C179 x¹⁰ y⁸ -4.5767223304e-44 7.6555464629e-42 -1.7249473173 e-40

C181 x⁸ y¹⁰ -4.7358957323e-43 2.0385911166e-41 -1.7910389147e-40

C183 x⁶ y¹² -2.3679233139e-42 1.7738118143e-41 -8.9081151170e-43

C185 x⁴ y¹⁴ -5.9181076796e-42 3.9699993657e-42 2.1440088748e-40

C187 x² y¹⁶ -5.3961047672e-42 -9.1528380558e-42 1.8536561975e-40

C189 18

y -3.1683786825e-42 8.4639493637e-42 -1.2577358535e-40

Table 3a for Figure 72 Coefficient Formula M04 M05 M06

C7 x 2 y 5.3438811424e-08 -1.0496184531e-07 1.7644778636e-07

C9 3

y -6.7980032749e-08 -1.2083968815e-07 -2.3665582746e-08

CIO X⁴ 1.7460610681e-10 -1.0156577960e-10 -3.9943321227e-10

C12 x² y² 5.7691545827e-l 1 -2.0628942502e-10 6.8413895782e-l 1

C14 y⁴ -2.0053907196e- 10 -8.3671106840e-l 1 -3.1324679932e-10

C16 x 4 y 1.5841794528e-13 -4.6459707293e-13 -2.9578109121e-13

C18 x 2 y 3 5.7020816823e-13 1.6916351121e-15 1.1538444727e-13

C20 y -3.9261020325e-13 -1.0360135395e-13 1.1167065554e-12

C21 .6

X -2.2177435908e-16 -5.5002671440e-16 -5.0296248719e-16

C23 x 4

4 y 2 -5.6829442353e- 16 6.3844614459e-17 -2.1210078501e-16

C25 x 2 y 4

4 7.7757581226e-16 6.9813021254e-17 -2.0359656263e-15

C27 .6

y -2.1754945916e-15 3.9362470391e-16 -2.2513813538e- 15

C29 x⁶ y 6.0464628247e- 18 -1.8418494940e-18 2.7805696416e-19

C31 x⁴ y³ 3.3526890566e-18 -1.7296391059e-18 3.3796207461e-18

C33 x² y⁵ 1.1578666515e-17 5.3220554636e-18 7.3474535697e-18

C35 7

y -9.3274690108e- 18 -8.2082087105e-19 2.6072208784e-17

C36 X 8.6859260732e-20 7.3589683615e-21 -8.6757474685e-21

C38 x⁶ y² - 1.2955242238e-20 1.0085025322e-20 -3.3179800628e-20

C40 x⁴ y⁴ -1.2534597171e-20 -2.2581005265e-20 -8.6213191000e-20

C42 x² y⁶ 4.6701690210e-20 -1.4529234314e-20 -1.8439340355e-19

C44 y⁸ -9.3674731938e-21 -1.1325123068e-20 -3.6052056902e-20

C46 x⁸ y -2.0131505981e-22 6.6710910162e-22 2.1717804229e-23

C48 x⁶ y³ -2.8002362260e-22 4.9100316790e-22 -1.2057698365e-22

C50 x⁴ y⁵ -2.0163603577e-22 2.5468976354e-23 -3.7282073790e-22

C52 x² y⁷ -4.5408213677e-22 -5.9292111170e-22 -8.9961667928e-22

C54 9

y 1.6128692652e-21 1.9764333871e-22 -6.9152293082e-22

C55 X¹⁰ -8.2471639467e-24 -1.8678786692e-24 8.9420492317e-25

C57 x⁸ y² 1.7631153366e-24 -2.9299397440e-24 2.3395751195e-24

C59 x⁶ y⁴ 2.1814446542e-25 4.0828814313e-24 1.0130493302e-23

C61 x⁴ y⁶ 3.8179846196e-24 2.8645392645e-24 1.3917583268e-23

C63 x² y⁸ -1.0151752082e-23 -6.8211075693e-25 2.3692156037e-23

C65 yio -1.7209547172e-24 1.6813567055e-24 2.7403002308e-25

C67 x¹⁰ y 2.7514575547e-26 -5.7156817930e-26 -1.2658809439e-27

C69 x⁸ y³ 4.8804045169e-26 -6.0410195657e-26 8.6608927159e-27

C71 x⁶ y⁵ 6.1278818630e-27 -5.4167264716e-26 8.4859132591e-26

C73 x 4 y 7 2.0155194148e-26 -4.3302166872e-27 6.4977089146e-26

C75 x 2 y 9 6.6843584914e-26 6.0198198690e-26 2.0288001310e-25 C77 11

y -2.5404778524e-25 -2.8740488140e-26 4.3445094615e-26

C78 x¹² 2.982767796 le-28 1.1537955322e-28 -5.2351734690e-29

C80 x¹⁰ y² -1.8448502322e-28 2.7225948422e-28 -7.2100488852e-29

C82 x⁸ y⁴ 1.2368166754e-30 -1.8226721392e-28 -6.8724074790e-28

C84 x⁶ y⁶ -3.0372837677e-28 -7.452293853 le-28 -1.044492991 le-27

C86 x⁴ y⁸ -4.1572908134e-28 8.5111338471e-29 -1.6264319562e-27

C88 x² y¹⁰ 1.2189273127e-27 6.3922176674e-29 -2.8651634902e-27

C90 y¹² 1.7341371957e-28 - 1.1695102217e-28 -4.3321193942e-28

C92 x¹² y -2.0397151353e-30 3.0834937086e-30 7.0354123356e-32

C94 x¹⁰ y³ -4.2371093554e-30 3.8654556606e-30 7.5906198859e-33

C96 x⁸ y⁵ -1.7466483865e-30 3.7857542592e-30 -8.5589328797e-30

C98 x⁶ y⁷ 4.8283192281e-30 4.7361839502e-30 -1.0600049615e-29

CIOO x⁴ y⁹ -9.6270215822e-31 -4.5496643435e-31 -5.6605656581e-30

C102 x² y^{1 1} -3.8907791157e-30 -3.4183383810e-30 -1.8235912513e-29

C104 13

y 2.2537247167e-29 1.9042145660e-30 -2.1348828960e-30

C105 x¹⁴ 3.1640286760e-33 -4.3225996592e-33 1.8625029669e-33

C107 x¹² y² 1.3473857640e-32 -1.2318532238e-32 -6.1412199298e-34

C109 x¹⁰ y⁴ -3.4796169342e-33 -2.7236689556e-33 2.4839642815e-32 cm x⁸ y⁶ 1.4265856842e-32 5.1687119258e-32 7.2925558733e-32

Cl 13 x⁶ y⁸ 1.0337084513e-32 3.0210447115e-32 4.0453804454e-32 Cl 15 x⁴ y¹⁰ 1.2861928313e-32 -1.5929623371e-32 1.4254705036e-31 Cl 17 x 2 y 12 -7.3974614854e-32 1.6775464990e-34 2.1840791768e-31 Cl 19 y¹⁴ -3.8268610243 e-32 4.6987072990e-33 3.5021579641e-32 C121 x¹⁴ y 7.6475372798e-35 -8.8269284637e-35 -1.4803996130e-36 C123 x¹² y³ 1.8259943521e-34 -1.2499018389e-34 -1.9610547099e-35 C125 x¹⁰ y⁵ 1.260211471 le-34 -1.2634414851e-34 3.2358855872e-34 C127 x⁸ y⁷ -1.2578462944e-34 -1.8865278088e-34 1.0144040846e-33 C129 x⁶ y⁹ -5.0005870709e-34 -1.8330394547e-34 3.6475572026e-34 C131 x⁴ y^{1 1} 1.3280389898e-34 3.1488561311 e-35 4.1817917628e-34 C133 x² y¹³ 1.2949954463e-34 1.2465926967e-34 8.2462357019e-34 C135 15

y -1.0612573329e-33 -6.8281849396e-35 9.2380336220e-35 C136 x¹⁶ -5.2263702504e-37 9.9831981940e-38 -3.9386070623e-38 C138 x¹⁴ y² -5.7423499737e-37 2.6120032919e-37 7.6284468689e-38 C140 x¹² y⁴ 3.5418657777e-37 2.5278862198e-37 -3.4444180776e-37 C142 x¹⁰ y⁶ -1.1793645802e-36 -1.0660180917e-36 -3.4027129082e-36 C144 x⁸ y⁸ 1.1383174845e-36 -2.5141641976e-36 -3.5740679012e-36 C146 x⁶ y¹⁰ 7.1341837925e-38 4.3225287749e-38 -1.3336143283e-36 C148 x⁴ y 2.0141582612e-37 4.9399400072e-37 -7.4390884232e-36 C150 x 2 y 14 1.9140110847e-36 -2.1800208956e-37 -9.3595354532e-36 C152 yl6 3.0285280687e-36 -5.2866229869e-38 -1.1423899096e-36

C154 x¹⁶ y -1.1075529633e-39 1.0209535062e-39 8.6492075053e-42

C156 x¹⁴ y³ -3.0844236729e-39 1.5801110360e-39 4.6137330446e-40

C158 x¹² y⁵ -2.3829473642e-39 1.9796638212e-39 -3.6165233166e-39

C160 x¹⁰ y⁷ -8.9231385723e-40 1.5179460559e-39 -2.3878351950e-38

C162 x⁸ y⁹ 9.9616254148e-39 5.4230800433e-39 -2.8584562982e-38

C164 x⁶ y^{1 1} 1.2917692175e-38 6.8314981925e-40 -2.4433247953e-39

C166 x⁴ y¹³ -5.0041923192e-39 5.3334936174e-40 -1.3054168958e-38

C168 x² y¹⁵ -1.2861767635e-39 -2.4955164539e-39 -1.4389314364e-38

C170 17

y 2.0587416459e-38 1.1043048552e-39 -1.6853398245e-39

C171 x¹⁸ 1.0172805571e-41 -1.0318939994e-42 3.6581588748e-43

C173 x¹⁶ y² 1.0284984367e-41 -1.9484420800e-42 -1.1208279748e-42

C175 x¹⁴ y⁴ -9.2215764168e-42 -2.9505316426e-42 -8.2681788795e-43

C177 x¹² y⁶ 2.6845328509e-41 4.9711258306e-42 5.4314390467e-41

C179 x¹⁰ y⁸ -6.497762494 le-42 3.8330304073e-41 1.4262801822e-40

C181 x⁸ y¹⁰ -5.8711093928e-41 2.4524006646e-41 9.0849198955e-41

C183 x⁶ y¹² -1.8376648577e-41 -3.8245735303e-42 2.9044303574e-41

C185 x⁴ y¹⁴ -5.3573846118e-42 -1.0313295608e-41 1.6251830010e-40

C187 x² y¹⁶ -1.6730875460e-41 8.7088488916e-42 1.6553570937e-40

C189 18

y -8.0612771879e-41 -1.3667857149e-42 1.1948621320e-41

Table 3b for Figure 72

Coefficient Formula M07 M08 M09

C7 x 2 y -9.9163854003e-08 3.3327495630e-07 1.4942746122e-06

C9 y 3 -2.7955639978e-07 -1.9831651423e-07 -8.6661468433e-07

CIO X⁴ 3.9034117708e-l l 2.1290051696e-10 1.3697659959e-09

C12 x² y² -1.3799390195e-09 -3.0095276882e-10 5.2330849021e-09

C14 y⁴ 2.0694821863e-09 -5.8587906163e-10 1.9958742343e-09

C16 x 4 y 1.4574708934e-13 6.8209252757e-13 7.1845363047e-12

C18 x 2 y 3^J 2.9683471463e-13 -1.1879948138e-13 -2.5965549872e-12

C20 y -6.0539627206e-14 -2.8478090468e-12 -1.2852139008e-l 1

C21 x⁶ 9.1877835666e-17 9.7881654725e-16 6.9424338805e-15

C23 x⁴ y² -2.5538607242e-16 1.3371399094e-15 4.4241134799e-14

C25 x y⁴ -2.1584971240e-14 -3.3096093431e-15 8.4353079879e-14

C27 y⁶ 6.2796934068e-14 -1.5115022579e-14 1.5336550469e-13

C29 x⁶ y 8.6473613202e-18 2.6089811326e-17 5.6636394083e-17

C31 x⁴ y³ -1.0092321064e-17 3.0255111493e-17 9.2968065933e-17

C33 x² y⁵ -8.3571092798e-16 -1.4236299061e-17 2.2906100134e-16

C35 7

y -4.3390705060e-15 -8.2207712686e-17 -5.1921114908e-16 C36 x 1.7343902984e-20 -7.9071230709e-20 3.1776988834e-20

C38 x⁶ y² 3.2288560760e-19 4.1999217337e-20 4.2655309513e-19

C40 x⁴ y⁴ 8.0553168453e-19 1.2689838657e-19 1.7446959404e-18

C42 x² y⁶ -1.5644721903e-17 -2.5428337346e-19 2.1847356802e-18

C44 y -8.6369427875e-17 -4.9827914502e-19 -3.4138338575e-18

C46 x⁸ y -5.7516102037e-22 -6.8163388904e-21 5.4815557875e-22

C48 x⁶ y³ 1.7222528808e-21 -1.3456420091e-20 3.1244442984e-21

C50 x⁴ y⁵ -6.1792808728e-21 -3.5823712183e-21 1.1018210543e-20

C52 x² y⁷ 1.6375799033e-18 -8.7613822280e-21 -1.3368603127e-20

C54 9

y 4.1103859789e-18 -4.8748535697e-21 -7.6685932312e-20

C55 X¹⁰ -2.2996520737e-24 1.6192306026e-23 1.0563678914e-24

C57 x⁸ y² -5.5034366086e-23 3.2256712971e-23 6.8784222705e-24

C59 x⁶ y⁴ -1.116549603 le-22 -8.5133794687e-23 4.2649304250e-23

C61 x⁴ y⁶ -1.1868737784e-21 -2.3212368916e-23 2.9190678903e-23

C63 x² y⁸ 2.6697263938e-20 -7.0290941087e-23 -3.3565645824e-22

C65 yio 1.0017746029e-19 -4.6333634034e-23 7.8550416403e-22

C67 x¹⁰ y 5.9591383667e-26 1.0494669826e-24 1.9421287088e-27

C69 x⁸ y³ -3.773868266 le-25 3.4722869826e-24 3.5329103894e-26

C71 x⁶ y⁵ 3.1860840880e-24 1.4301964733e-24 -8.5189587423e-25

C73 x 4 y 7 1.6241025890e-23 5.6447330337e-25 -6.5048280888e-24

C75 x 2 y 9 -1.8533661732e-21 5.8721919245e-25 -1.0995953393e-23

C77 11

y -1.7562490793e-21 -2.1135505685e-25 1.0360801263e-23

C78 x¹² 1.5211127747e-28 -2.0172606727e-27 -3.3778010319e-29

C80 x¹⁰ y² 5.6123680217e-27 -1.1103382964e-26 2.1504473684e-29

C82 x⁸ y⁴ 1.0211210144e-26 1.0030346583e-26 -1.0303141894e-27

C84 x⁶ y⁶ 1.8318497948e-25 1.7197485007e-26 -1.8589777820e-26

C86 x⁴ y⁸ 1.6073313896e-24 5.7553825425e-27 -3.3046076821e-26

C88 x² y¹⁰ -2.8297794145e-23 8.1451490043e-27 9.7731691521e-26

C90 y¹² -5.5774261760e-23 -2.6064491969e-28 -8.5416017167e-26

C92 x¹² y -3.9776856560e-30 -8.8212903202e-29 2.9374810419e-31

C94 x¹⁰ y³ 2.8333500279e-29 -4.2951867129e-28 -2.4461510023e-30

C96 x⁸ y⁵ 1.2317199907e-28 -3.2299624952e-28 3.6672514884e-29

C98 x⁶ y⁷ -7.7811151561e-27 -8.2588979398e-29 3.9232294859e-28

CIOO x⁴ y⁹ 1.7986896056e-26 7.3335057300e-30 1.9868950069e-27

C102 x² y^{1 1} 1.0514850944e-24 -6.2059556439e-29 3.0136082578e-27

C104 13

y 6.5879005859e-26 -1.0669738806e-29 -8.5181047792e-28

C105 x¹⁴ -5.9955235351e-33 1.4738665184e-31 6.5891369546e-34

C107 x¹² y² -3.1833468848e-31 1.4529010181e-30 -2.9130325399e-34

C109 x¹⁰ y⁴ -1.0575735583e-30 3.7569938768e-31 -7.0501257509e-33 cm x⁸ y⁶ 1.5488903745e-30 -1.8021914232e-30 1.1318479620e-30

Cl 13 x⁶ y⁸ -3.0795949505e-28 -2.9112549149e-30 6.8462217335e-30 Cl 15 x⁴ y¹⁰ -2.6729861247e-28 6.9921502429e-31 8.012845171 le-30 Cl 17 x² y¹² 1.5578007195e-26 -1.5529624457e-30 -1.5582947536e-29 Cl 19 y¹⁴ 1.3416673563e-26 -2.0545997259e-31 1.2239949021e-29 C121 x¹⁴ y 1.3542805415e-34 3.8902314806e-33 -9.2502046050e-36 C123 x¹² y³ -8.4835816735e-34 2.5691451601e-32 1.8848789689e-34 C125 x¹⁰ y⁵ -1.9269506856e-32 2.8280410786e-32 -5.3702954064e-34 C127 x⁸ y⁷ 3.0046945413e-31 2.0534434970e-32 -1.3795033545e-32 C129 x⁶ y⁹ 2.2775173298e-30 -2.3678032444e-32 -7.4526696812e-32 C131 x⁴ y^{1 1} -1.2705670385e-29 1.3648369723e-32 -3.0414481484e-31 C133 x² y¹³ -2.9355915375e-28 -1.1244621065e-32 -3.5544744604e-31 C135 15

y 1.6224684514e-28 -1.4936482118e-33 -1.3192133427e-32 C136 x¹⁶ 1.4065909932e-37 -5.7342616952e-36 1.1692301359e-38 C138 x¹⁴ y² 9.2574791135e-36 -8.5006497021e-35 7.2129065303e-38 C140 x¹² y⁴ 5.5468482917e-35 -1.1211175423e-34 3.4675674221e-36 C142 x¹⁰ y⁶ -4.326194956 le-34 1.7244765351e-35 -2.6322561090e-35 C144 x⁸ y⁸ 8.9251804922e-33 2.8783258114e-34 -3.0582452569e-34 C146 x⁶ y¹⁰ 1.0615321336e-31 -1.0673232927e-34 -1.0076930550e-33 C148 x⁴ y -1.1907584609e-31 8.0692822109e-35 -2.8445237575e-34 C150 x 2 y 14 -4.2965902834e-30 -4.1309441461e-35 1.8619360433e-33 C152 yl6 -2.5085316780e-31 -5.0736763495e-36 -6.6782448024e-34 C154 x¹⁶ y -1.7949962354e-39 -6.9537312746e-38 1.8156340976e-40 C156 x¹⁴ y³ 8.0327554897e-39 -5.9885968469e-37 -3.2398646224e-39 C158 x¹² y⁵ 4.8883707662e-37 -8.4279738727e-37 -7.2267956723e-39 C160 x¹⁰ y⁷ -3.9452777494e-36 -1.1784839822e-36 2.2129749716e-37 C162 x⁸ y⁹ -4.1320644552e-35 1.1116803366e-36 1.3247789548e-36 C164 x⁶ y^{1 1} -2.9141937934e-34 -3.9207359852e-37 5.4935237760e-36 C166 x⁴ y¹³ 2.4640988284e-33 1.2919583376e-37 1.8762573713e-35 C168 x² y¹⁵ 3.1597759333e-32 -8.2573605867e-38 1.5711613601e-35 C170 17

y -3.2959853415e-32 -7.0033043308e-39 4.0057107527e-36 C171 x¹⁸ - 1.4997419975e-42 9.0513220649e-41 -3.5595206643e-43 C173 x¹⁶ y² -1.0802568735e-40 1.8461077168e-39 -3.2113165098e-43 C175 x¹⁴ y⁴ -1.0166580789e-39 4.5636512564e-39 -8.6702631133e-41 C177 x¹² y⁶ 8.4188152202e-39 2.3031597322e-39 1.0031549113e-40 C179 x¹⁰ y⁸ -5.9960761375e-38 -6.2778003312e-39 4.8743149422e-39 C181 x⁸ y¹⁰ -1.8227731841e-36 1.1287028017e-39 2.5577957989e-38 C183 x⁶ y¹² -1.2376013000e-35 -9.0390315541e-40 4.7260701283e-38 C185 x⁴ y¹⁴ 3.6074268664e-35 -1.3967121303e-40 -4.2712054826e-38 C187 x² y¹⁶ 4.6249227368e-34 -7.8192796629e-41 -9.4817542658e-38

C189 y¹⁸ -2.6793715300e-34 -8.5522697680e-43 -4.0086243176e-39

Table 3c for Figure 72

Coefficient Formula M10

C7 x 2 y -1.1135925881e-08

C9 y 3 9.4489474997e-09

CIO X⁴ -2.1648054275e-l l

C12 x² y² -5.9621091352e-l 1

C14 y⁴ -1.2663811344e-l 1

C16 x 4 y -2.7176472556e-14

C18 x 2 y 3^J -4.0009778226e-15

C20 y 1.4141511737e-14

C21 x⁶ -4.5880482545e-17

C23 x⁴ y² -1.7392393674e-16

C25 x y⁴ -1.5369695774e-16

C27 y⁶ -3.4244784588e-17

C29 x⁶ y -4.6184111376e-20

C31 x⁴ y³ -4.9710892138e-20

C33 x² y⁵ 9.9588944303e-21

C35 7

y 1.8390633337e-20

C36 X -8.5853232786e-23

C38 x⁶ y² -3.9929038177e-22

C40 x⁴ y⁴ -6.0247845405e-22

C42 x² y⁶ -3.6291038858e-22

C44 y -6.5259311158e-23

C46 x⁸ y -6.9598342785e-26

C48 x⁶ y³ - 1.9694698871 e-25

C50 x⁴ y⁵ - 1.5366496782e-25

C52 x² y⁷ -1.3481080044e-26

C54 9

y 6.4525194182e-26

C55 X¹⁰ -9.9184590239e-29

C57 x⁸ y² -9.410768984 le-28

C59 x⁶ y⁴ -2.1218619138e-27

C61 x⁴ y⁶ -2.2000785725e-27

C63 x² y⁸ -9.7595243866e-28

C65 yio -1.0121292730e-28

C67 x¹⁰ y -2.4208704823e-31

C69 x⁸ y³ -5.3668659158e-32 C71 x⁶ y⁵ 4.8860557274e-31

C73 x 4 y 7 1.3512155626e-30

C75 x 2 y 9 1.1566716304e-30

C77 11

y 6.0919566890e-32

C78 x¹² -5.2169877879e-34

C80 x¹⁰ y² -8.9079149109e-34

C82 x⁸ y⁴ -3.9369126360e-34

C84 x⁶ y⁶ 1.2013242523e-33

C86 x⁴ y⁸ 2.6080180505e-33

C88 x² y¹⁰ 7.0083888101e-34

C90 y¹² -2.926329971 le-34

C92 x¹² y 6.6404057867e-37

C94 x¹⁰ y³ -4.1870528170e-36

C96 x⁸ y⁵ -1.0283900608e-35

C98 x⁶ y⁷ -1.6300053824e-35

CIOO x⁴ y⁹ - 1.5892262825e-35

C102 x² y^{1 1} -7.1860406460e-36

C104 13

y -2.6312672352e-37

C105 x¹⁴ 5.953389041 le-40

C107 x¹² y² -7.9071848175e-39

C109 x¹⁰ y⁴ -4.7254806588e-38 cm x⁸ y⁶ -1.0173634653e-37

Cl 13 x⁶ y⁸ -1.2292476274e-37 Cl 15 x⁴ y¹⁰ -8.4972375049e-38 Cl 17 x 2 y 12 -2.1554756540e-38 Cl 19 y¹⁴ -1.5251829282e-39 C121 x¹⁴ y -3.7334662648e-42 C123 x¹² y³ 1.3852955180e-41 C125 x¹⁰ y⁵ 4.0060655442e-41 C127 x⁸ y⁷ 7.8273915649e-41 C129 x⁶ y⁹ 1.0909902290e-40 C131 x⁴ y^{1 1} 8.6264792829e-41 C133 x² y¹³ 2.9282855343e-41 C135 15

y 1.3311609400e-42 C136 x¹⁶ -2.0525221154e-45 C138 x¹⁴ y² 7.1994464354e-45 C140 x¹² y⁴ 1.3022102958e-43 C142 x¹⁰ y⁶ 3.9938141782e-43 C144 x⁸ y⁸ 6.0660879120e-43 C146 x⁶ y¹⁰ 6.0465487080e-43

C148 x⁴ y¹² 3.266924870 le-43

C150 x 2 y 14 5.2430792755e-44

C152 yl6 3.3990271908e-45

C154 x¹⁶ y 3.822810290 le-48

C156 x¹⁴ y³ -4.1011846530e-47

C158 x¹² y⁵ -1.2390697768e-46

C160 x¹⁰ y⁷ -2.2932781098e-46

C162 x⁸ y⁹ -3.1144747690e-46

C164 x⁶ y^{1 1} -3.0757424604e-46

C166 x⁴ y¹³ -1.7431168639e-46

C168 x² y¹⁵ -4.0194271308e-47

C170 17

y 1.9477460832e-49

C171 x¹⁸ -2.6364435798e-51

C173 x¹⁶ y² -3.9046752420e-50

C175 x¹⁴ y⁴ -3.6463571037e-49

C177 x¹² y⁶ -1.2618972590e-48

C179 x¹⁰ y⁸ -2.1743524254e-48

C181 x⁸ y¹⁰ -2.5364506860e-48

C183 x⁶ y¹² -1.9388279237e-48

C185 x⁴ y¹⁴ -8.2307322204e-49

C187 x² y¹⁶ -1.1858465375e-49

C189 18

y -8.6176846395e-51

Table 3d for Figure 72

Coordinates of the stop edge

¾ [mm] yi [mm] ¾+N/₂ [mm] yi_+N/2 [mm]

-9.717937 189.126008 -27.160388 -172.680268

-30.150523 187.630941 -6.229447 -174.175335

-50.583109 184.640806 6.727803 -174.175335

-65.035426 181.650672 16.196562 -173.676980

-75.999252 178.660537 37.625859 -171.185201

-95.933482 172.181912 48.589686 -169.191778

-111.382511 165.703287 57.061734 -167.198355

-126.333183 158.227951 74.504185 -162.214797

-133.310164 154.241105 92.943348 -155.237817

-148.759192 144.273990 114.372645 -144.772346

-158.726307 136.798654 125.336472 -138.293721

-168.693422 128.326606 144.772346 -124.838116 - I l l -

-179.158893 117.861135 153.244394 -117.861135

-183.145739 113.375934 163.211509 -108.890732

-188.129296 107.395665 177.663826 -93.441703

-195.106277 97.926905 182.647383 -87.461434

-203.079969 84.969656 189.624364 -77.992675

-210.555305 69.520627 194.607921 -70.517339

-213.545440 61.546935 201.584902 -58.556801

-217.033930 49.586397 209.060238 -42.609417

-218.528997 43.107773 213.545440 -30.648879

-220.024064 33.639013 217.532286 -16.196562

-221.020776 21.678475 219.027353 -8.222870

-221.020776 11.213004 220.522420 3.239312

-220.522420 2.740957 221.020776 10.714649

-218.030641 -13.704783 221.020776 21.180119

-216.037218 -22.176831 220.522420 28.655456

-213.047084 -32.143946 219.027353 40.117638

-206.568459 -48.589686 217.532286 47.592974

-199.093123 -63.042003 215.538863 55.068311

-193.611210 -72.012406 212.050372 65.533781

-188.627652 -79.487742 206.070103 79.487742

-182.149027 -87.959790 198.096411 93.441703

-167.696710 -104.405530 188.129296 107.395665

-162.713153 -109.389088 179.657249 117.362780

-150.254259 -120.352914 170.686845 126.333183

-137.297010 -130.320029 158.726307 136.798654

-125.336472 -138.293721 145.270702 146.765769

-117.861135 -142.778923 127.329895 157.729595

-98.425261 -152.746038 111.382511 165.703287

-89.454857 -156.732884 90.451569 174.175335

-79.986098 -160.221374 74.504185 179.158893

-64.537070 -165.204932 56.065022 183.644095

-53.074888 -168.195066 34.635725 187.132585

-43.606128 -170.188489 10.216293 189.126008

Table 4 for Figure 72

Wavelength 13.5 nm

NA 0.55

P x 4.30 bg -8.40

Chief ray angle (CRA) 5.16°

Etendue 12.58 mm²

Mean wavefront aberration RMS 12.81 ihl

System transmission 7.47 %

Position of the entry pupil EP (x) -2380.79 mm

Position of the entry pupil EP (y) -2367.68 mm

Object-image offset 2038.39 mm

Working distance between M9 and

81 mm

image field

Reticle tilt 0.0°

Installation length 2297.22 mm

Obscuration 18.4 %

Installation space cuboid (790 x 2376 x 1807) mm

Table 5 for Figure 72

Ml M2 M3 M4 M5

Maximum angle of incidence 11.8 83.7 79.6 80.6 83.0

[deg]

Minimum angle of incidence [deg] 8.5 73.4 73.5 75.5 76.9

Mirror extent (x) [mm] 625.3 389.3 323.1 276.3 303.5

Mirror extent (y) [mm] 265.0 294.8 240.4 266.9 331.0

Maximum mirror diameter 625.5 331.0 347.8 390.2

[mm] 390.0

Table 6a for Figure 72

M6 M7 M8 M9 M10

Maximum angle of incidence 79.8 81.7 78.0 20.3 8.4

[deg]

Minimum angle of incidence [deg] 73.8 72.4 70.4 0.0 5.2

Mirror extent (x) [mm] 338.2 301.0 233.0 292.0 790.1

Mirror extent (y) [mm] 263.3 112.0 247.5 155.7 768.1

Maximum mirror diameter 340.1 301.1 278.5 292.1 790.3

[mm]

Table 6b for Figure 72 In the projection optical unit 41, the mirror M7 has the largest x/y-aspect ratio of approximately 2.69. None of the mirrors Ml to M10 of the projection optical unit 41 has an x/y-aspect ratio that is greater than 2.7. If only the Pareto-optimal inscription of structuring fields 4i into the field specification field 19 is considered, what was already explained above in respect of the projection optical unit 7 applies to the admissible scale ratio curves 24i in the case of the projection optical unit 41. This also applies when additionally considering the auxiliary areas 25 to 28. If the shadowing region D is additionally taken into account, the scale ratio curves 24s, 24₉ and 24ii to 24i₆ remain admissible for the projection optical unit 41.

In principle, the respective projection optical unit for the projection exposure apparatus 1 can be embodied in such a way that the first reduction scale b_c and/or the second reduction scale b_n has an integer configuration.

In order to produce a microstructured or nanostructured component, the projection exposure apparatus 1 is used as follows: first, the reflection mask 10 or the reticle and the substrate or the wafer 11 are provided. Subsequently, a structure on the reticle 10 is projected onto a light- sensitive layer of the wafer 11 with the aid of the projection exposure apparatus 1. Then, a microstructure or nanostructure on the wafer 11, and hence the microstructured component, is produced by developing the light-sensitive layer.

Claims

Patent Claims

1. Imaging optical unit (7; 37; 38; 39; 40; 41) for a projection exposure apparatus (1), for imaging an object field (4) into an image field (8),

wherein the projection exposure apparatus (1) is embodied in such a way that a rectangular structuring field (4i) on an object (10) to be imaged, which carries structures to be imaged, is imaged in the entirety thereof into an imaging field (21) by displacing the structuring field (4i) relative to the object field (4), said imaging field being displaced relative to the image field (8) in a manner synchronized with the object displacement,

wherein the structuring field (4i) is situated within a larger object specification field (19) that is defined by the object (10) and delimited by a rectangular specification field basic shape and convexly curved specification field comer regions (20),

wherein the object field (4) is spanned by a first field direction (x) and a second field direction (y) perpendicular thereto,

wherein the imaging optical unit (7; 37; 38; 39; 40; 41) has a first reduction scale b_c in the first field direction (x), given by a ratio of the extent in the first field direction (x) of, firstly, the structuring field (4i) and, secondly, the imaging field (21),

wherein the imaging optical unit (7; 37; 38; 39; 40; 41) has a second reduction scale b_g in the second field direction (y), given by a ratio of the extent in the second field direction (y) of, firstly, the structuring field (4i) and, secondly, the imaging field (21), wherein the reduction scales b_c and b_n are chosen in such a way that an area of the structuring field (4i) is no more than 10% smaller than the area of the largest, rectangular Pareto structuring field which can be fitted into the object specification field (19).

2. Imaging optical unit according to Claim 1, characterized in that the reduction scale b_c in the first field direction (x) is integer and/or in that the second reduction scale b_n in the second field direction (y) is integer.

3. Imaging optical unit according to Claim 1 or 2, characterized by a ratio (b_c/b_g) of

a first reduction scale (b_c) in the first field direction (x) and a second reduction scale (b_n) in the second field direction (y),

which leads to the x/y-aspect ratio of the structuring field (4i) which can be inscribed in the object specification field (19) when the rounded specification field corner regions (20) are taken into account, wherein an area of the structuring field (4i) deviates by less than 10% from the area of the Pareto structuring field with a Pareto-optimal x/y-aspect ratio.

4. Imaging optical unit according to any one of Claims 1 to 3, characterized in that the

imaging field (21) has dimensions of 26 mm x 16.5 mm in the two field directions (x, y).

5. Imaging optical unit according to any one of Claims 1 to 3, characterized in that the object specification field (19) has an extent of 1514 mm in both field directions (x, y).

6. Imaging optical unit according to any one of Claims 1 to 5, characterized in that the

specification field corner regions (20) are rounded with a radius of curvature of 19 mm.

7. Method for designing an imaging optical unit (7; 37; 38; 39; 40; 41) according to any one of Claims 1 to 6, including the following steps:

specifying

— a first reduction scale (b_c) of the imaging optical unit (7; 37; 38; 39; 40; 41) in a first field direction (x) and

— a second reduction scale (b_g) of the imaging optical unit (7; 37; 38; 39; 40; 41) in a second field direction (y),

wherein the following is included when ascertaining the reduction scales (b /b_n) to be specified:

— a shape of the object specification field (19), which is delimited by the rectangular specification field basic shape and the convexly rounded specification field comer regions (20),

— dimensions of the image field (8) in both field directions (x, y),

specifying an arrangement of optical components (Ml to M8, AS) of the imaging optical unit (7; 37; 38; 39; 40; 41), by means of which the reduction scales (b /b_n) are produced between the object field (4) and the image field (8).

8. Method according to Claim 7, characterized in that the ascertainment of the reduction scales (b /b_n) to be specified incorporates a need for at least one auxiliary area (25 to 28) on the object specification field (19), wherein no structures to be imaged are present on the auxiliary area (25 to 28), and so the structuring field (4i) does not overlap with the auxiliary area (25 to 28).

9. Method according to Claim 3 or 4, characterized in that the ascertainment of the reduction scale ratio (b /b_n) to be specified incorporates a need for at least one stop-shadowed area (D) on the specification field (19), wherein no structures to be imaged are present on the stop- shadowed area (D), and so the structuring field (4i) does not overlap with the stop-shadowed area (D).

10. Optical system

comprising an imaging optical unit according to any one of Claims 1 to 6,

comprising a reticle holder (10a) for holding the object (10), said reticle holder being displaceable along a field direction (y), which represents an object displacement direction, with the aid of a reticle displacement drive (10b),

comprising a substrate holder (12) for holding a wafer (11), on which the structures to be imaged are imaged, wherein the substrate holder (12) is displaceable by means of a substrate displacement drive (12a) in a manner synchronized with the reticle displacement drive (10b).

11. Optical system comprising an imaging optical unit according to one of Claims 1 to 6 and comprising an illumination optical unit (6) for illuminating the object field (4) with illumination and imaging light (3).

12. Optical system according to Claim 11, characterized by an EUV light source (2).

13. Projection exposure apparatus for projection lithography, comprising an optical system

according to Claims 10 to 12.

14. Projection exposure apparatus according to Claim 13, characterized in that a reduction factor of the projection optical unit in the object displacement direction is greater than in the direction perpendicular thereto.

15. Method for producing a structured component, including the following method steps:

providing a reticle (10) and a wafer (11),

projecting a structure on the reticle (10) onto a light-sensitive layer of the wafer (11) with the aid of the projection exposure apparatus according to Claim 13 or 14, producing a microstructure or nanostructure on the wafer (11).