Reflecting coating with optimized thickness

Abstract

An illumination system for an optical arrangement such as an EUV lithography apparatus, having: at least one optical element which has at least one optical surface, on which a coating which reflects illumination radiation is applied, and an actuator device aligning the optical surface in at least two angular positions in the radiation path. The coating either has a thickness (d.sub.OPT1) at which a mean value ((R.sub.1+R.sub.2)) formed from a thickness-dependent reflectivity (R.sub.1, R.sub.2) of the coating at the at least two angular positions is maximized or has a thickness (d.sub.OPT2) at which a maximum change (max(R.sub.1/R.sub.1, R.sub.2/R.sub.2)) in the reflectivity (R.sub.1, R.sub.2) caused by a thickness tolerance of the coating is minimized at the respective angular positions or else the reflecting coating has a thickness (d.sub.O2) at which the reflectivity (R.sub.1, R.sub.2) of the coating has the same magnitude in the at least two angular positions.

Claims

1. Illumination system for an optical arrangement, comprising: at least one optical element, which has at least one optical surface on which a reflecting coating which reflects the illumination radiation from a light source is applied, and an actuator device for aligning the at least one optical surface in at least two angular positions (.sub.1, .sub.2), a magnitude of an angle of incidence (.sub.1, .sub.2) of the incident illumination radiation in the at least two angular positions (.sub.1, .sub.2) being different, wherein either: the reflecting coating has a thickness (d.sub.OPT1) at which a mean value ((R.sub.1+R.sub.2)) formed from a thickness-dependent reflectivity (R.sub.1, R.sub.2) of the coating at the at least two angular positions (.sub.1, .sub.2) is maximized or the reflecting coating has a thickness (d.sub.OPT2) at which a maximum change (max(R.sub.1/R.sub.1, R.sub.2/R.sub.2)) in the reflectivity (R.sub.1, R.sub.2) caused by a thickness tolerance (d/d) of the coating is minimized at the respective angular positions (.sub.1, .sub.2).

2. The illumination system according to claim 1, wherein the mean value formed from the thickness-dependent reflectivity (R.sub.1, R.sub.2) is a mean value weighted over the at least two angular positions (.sub.1, .sub.2), with the weighting of the angular positions (.sub.1, .sub.2) being dependent on the position of the optical surface on the optical element.

3. The illumination system according to claim 1, wherein a difference angle (|.sub.1.sub.2|) between respectively two of the angular positions (.sub.1, .sub.2) is at least 1.

4. The illumination system according to claim 1, wherein the thickness (d.sub.OPT1, d.sub.OPT2) of the reflecting coating varies depending on the position on the optical surface.

5. The illumination system according to claim 1, further comprising: a light source that generates illumination radiation having a wavelength spectrum that has a maximum intensity at an operating wavelength of the illumination system.

6. Optical arrangement comprising: an illumination system according to claim 5.

7. The optical arrangement according to claim 6, wherein the thickness-dependent reflectivity (R.sub.1, R.sub.2) of the coating of the optical element at the at least two angular positions (.sub.1, .sub.2) is averaged over the wavelength spectrum which is generated by the light source and which is filtered by further optical elements of the optical arrangement.

8. The optical arrangement according to claim 6, wherein the arrangement is an extreme-ultraviolet lithography apparatus for exposing a substrate.

9. The illumination system according to claim 1, wherein the optical element is embodied as a facet mirror and the optical surfaces are formed on facet elements of the facet mirror.

10. The illumination system according to claim 1, wherein the optical arrangement is an extreme-ultraviolet lithography apparatus.

11. The illumination system according to claim 1, wherein the optical element has a plurality of optical surfaces.

12. The illumination system according to claim 1, wherein R1 differs from R2.

13. Method for optimizing a thickness (d.sub.OPT1, d.sub.OPT2) of a reflecting coating of an optical surface of an optical element for an illumination system of an optical arrangement, comprising: determining a thickness-dependent reflectivity (R.sub.1, R.sub.2) of the reflecting coating in at least two angular positions (.sub.1, .sub.2), a magnitude of an angle of incidence (.sub.2, .sub.2) of the incident illumination radiation in the at least two angular positions (.sub.1, .sub.2) being different, in which the optical surface can be aligned in the illumination beam path of a light source and either: determining a thickness (d.sub.OPT1) for the reflecting coating at which a mean value ((R.sub.1+R.sub.2)) formed from the thickness-dependent reflectivity (R.sub.1, R.sub.2) at the at least two angular positions (.sub.1, .sub.2) is maximized or determining a thickness (d.sub.OPT2) for the reflecting coating at which a maximum change (max(R.sub.1/R.sub.1, R.sub.2/R.sub.2)) in the thickness-dependent reflectivity (R.sub.1, R.sub.2) caused by a thickness tolerance (d/d) stemming from a manufacturing process of the coating is minimized at the respective angular positions (.sub.1, .sub.2).

14. The method according to claim 13, wherein a weighting over the at least two angular positions (.sub.1, .sub.2) is made for forming the mean value, with the weighting of the angular positions (.sub.1, .sub.2) being dependent on the position of the optical surface on the optical element.

15. The method according to claim 13, wherein a difference angle (|.sub.1.sub.2|) between two respective angular positions (.sub.1, .sub.2) is at least 1.

16. The method according to claim 13, wherein the thickness (d.sub.OPT1, d.sub.OPT2) of the reflecting coating is determined depending on the position on the optical surface.

17. The method according to claim 13, wherein the thickness-dependent reflectivity (R.sub.1, R.sub.2) of the coating at the at least two angular positions (.sub.1, .sub.2) is averaged over the wavelength spectrum which is generated by a light source and which is filtered by further optical elements of the optical arrangement.

18. Method for generating a reflecting coating on an optical surface of an optical element for an illumination system, comprising: applying the coating on the optical surface with a thickness (d.sub.OPT1, d.sub.OPT2) determined in accordance with the method according to claim 13.

19. The method according to claim 13, wherein R1 differs from R2.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Exemplary embodiments are depicted in the schematic drawing and will be explained in the following description. In detail:

(2) FIG. 1 shows a schematic illustration of an EUV lithography apparatus with an illumination system in which two facet mirrors are arranged,

(3) FIGS. 2A, 2B show schematic illustrations of a facet element in two different angular positions,

(4) FIG. 3 shows a schematic illustration of a reflecting coating applied to the facet element from FIGS. 2A, 2B,

(5) FIG. 4A shows a schematic illustration of thickness-dependent reflectivity curves for the two angular positions in FIGS. 2A, 2B, and for a further angular position,

(6) FIG. 4B shows an illustration analogous to FIG. 4A with two reflectivity curves for the two angular positions,

(7) FIG. 4C shows an illustration analogous to FIG. 4B with a further reflectivity curve, which forms the mean value of the two reflectivity curves, and

(8) FIG. 4D shows an illustration of the relative change in the reflectivity depending on a predetermined manufacturing-dependent thickness tolerance.

DETAILED DESCRIPTION

(9) FIG. 1 schematically shows an EUV lithography apparatus 1. It has an EUV light source 2 that generates EUV radiation, which has a high energy density in an EUV wavelength range below 50 nm, in particular between approximately 5 nm and approximately 15 nm. By way of example, the EUV light source 2 can be embodied in the form of a plasma light source that generates a laser-induced plasma, or as a synchrotron radiation source. In particular in the former case, it is possible, as shown in FIG. 1, to use a collector mirror 3 in order to focus the EUV radiation from the EUV light source 2 to form an illumination beam 4 and thus further increase the energy density. The illumination beam 4 has a wavelength spectrum which is concentrated in a narrow-band wavelength range about an operating wavelength .sub.B, at which the EUV lithography apparatus 1 is operated. In order to select the operating wavelength .sub.B or in order to select the narrow-band wavelength range, use may optionally be made of a monochromator (not shown here).

(10) The illumination beam 4 serves to illuminate a structured object M with an illumination system 10, which has five reflecting optical elements 12 to 16 in the present example. By way of example, the structured object M can be a reflective mask, which has reflecting and non-reflecting, or at least less strongly reflecting, regions for generating at least one structure on the object M. Alternatively, the structured object M can be a plurality of micromirrors, which are arranged in a one- or multi-dimensional arrangement and which can optionally be moved about at least one axis in order to set the angle of incidence of the EUV radiation 4 on the respective mirror.

(11) The structured object M reflects part of the illumination beam 4 and forms a projection beam 5, which carries the information about the structure of the structured object M and which is radiated into a projection lens 20, which has four further optical mirror elements 21 to 24 in order to produce an image of the structured object M, or of a respective portion thereof, on a substrate W. The substrate W, for example a wafer, has a semiconductor material, e.g. silicon, and is arranged on a mount, which is also referred to as wafer stage WS.

(12) In the present case, the second and the third reflecting element 13, 14 in the illumination system 10 are embodied as facet mirrors and have a plurality of facet elements in the form of micromirrors, which are arranged in a grid arrangement. In FIG. 1, four facet elements with the corresponding first and second optical surfaces 13a-d, 14a-d thereof are shown in an exemplary manner for each optical element 13, 14, at which surfaces the illumination beam 4 or a respective partial beam is reflected. The first optical element 13 is also denoted as a field raster element and serves for generating secondary light sources in the illumination system 10. The second optical element 14 is arranged at the position of the secondary light sources produced by the first optical element 13 and is also referred to as pupil raster element 14.

(13) A partial beam of the illumination beam 4 incident on a respective optical surface 13a-d of the first optical element 13 is deflected on said optical surface onto an optical surface 14a-d of the second optical element 14. The optical surfaces 13a-d of the first optical element 13 may be rectangular and have an aspect ratio (x:y) of e.g. 20:1, wherein the X-direction extends perpendicular to the plane of the drawing of FIG. 1.

(14) Each of the first optical surfaces 13a-d of the first optical element 13 can be tilted about an axis direction extending parallel to the X-direction in the present example. Additionally, a respective optical surface 13a-d may optionally also be tiltable about a further axis lying in the XZ-plane (plane of the drawing). This is how the direction in which the illumination beam 4 is incident on the optical surface 13a-d can be set. In particular, as a result of the tilt, it is also possible to modify the assignment between the optical surfaces 13a-d of the first optical element 13 and the optical surfaces 14a-d of the second optical element 14 in order to produce a desired illumination distribution (illumination pupil or angular distribution) at the position of the illuminated object M.

(15) For selecting a respective illumination mode (setting), which corresponds to a desired illumination pupil, a different assignment between the optical surfaces 13a-d of the first optical element 13 and the optical surfaces 14a-d of the second optical element 14 may be selected, as is described, for example, in U.S. Pat. No. 6,658,084B2, by the applicant, to which reference is made in its entirety. Depending on which switch positions are selected for the optical surfaces 13a-d of the first optical element 13, the respective partial beams of the illumination beam 4 are directed to different optical surfaces 14a-d of the second optical element 14 in order to realize the respectively desired illumination setting, e.g. annular illumination or dipole illumination. In general, a 1:1 assignment between the optical surfaces 13a-d of the first optical element 13 and the optical surfaces 14a-d of the second optical element 14 is selected in a respective illumination mode or at a given time. However, an assignment can optionally also be brought about in such a way that two or more of the optical surfaces 13a-d of the first optical element 13 are assigned to a single optical surface 14a-d of the second optical element 14 in order to set different illumination modes. Details in this respect are found in U.S. 2009/0041182 A1, by the applicant, to which reference is made in its entirety.

(16) FIGS. 2A and 2B show, as a representative for all facet elements of the first optical element 13, an individual facet element 19 with an associated optical surface 13a and with an assigned actuator device 17, which serves for aligning the facet element 19 in the illumination beam path 4. The actuator device 17 can be embodied for tilting the facet element 19 or the optical surface 13a, but optionally it may also serve to rotate said facet element about an axis of rotation, as illustrated e.g. in DE 10 2009 054 888 A1, by the applicant, to which reference is made in its entirety. The actuator device 17 has a signaling connection to a central control device (not shown) via a signal line (not shown) in order to actuate the actuator devices 17 assigned to the respective optical surfaces 13a-d, 14a-d independently of one another. Here, several or all actuator devices 17 can be actuated at the same time or in succession in order to switch between different illumination settings.

(17) In FIG. 2A, the facet element 19 of the first facet mirror 13 is shown in a first tilt angle position .sub.1=73, set by the actuator device 17, in which position the surface normal of the optical surface 13a is arranged at an angle of incidence .sub.1=17 relative to the incident partial beam of the illumination beam 4. By contrast, in FIG. 2B, the facet element 19 is shown in a second tilt angle position .sub.2=77, in which the surface normal of the optical surface 13a is aligned at an angle of incidence .sub.2=13 with respect to the incident partial beam of the illumination beam 4. It is understood that the optical surface 13a can also be operated in several further tilt angle positions through the actuator device 17, which tilt angle positions lie between the two angular positions .sub.1, .sub.2 shown in FIGS. 2A, 2B, which are measured in a plane perpendicular to a rotation or tilt axis of the facet element 19, which is aligned perpendicular to the plane of the drawing in FIGS. 2A, 2B and forms the central axis of the optical surface 13a in the present example. In the rest position, in which the actuator device 17 exerts no force on the facet element 19, the angle at which the facet element 19 is aligned may for example lie at .sub.0=90 (not shown in FIGS. 2A, 2B).

(18) Since a partial beam of the illumination beam 4 incident on a respective optical surface 13a-d of the first optical element 13 is intended to be deflected onto an optical surface 14a-d of the second optical element 14 (and not in part between the optical surfaces 14a-d), only a few (discrete) angular positions .sub.1, .sub.2, . . . , .sub.N of the first optical surfaces 13a-d are typically expedient and are set by the control unit during the operation of the illumination system 10. In FIGS. 2A, 2B, the direction of the incident illumination radiation 4 is identical in both angular positions .sub.1, .sub.2. However, it is understood that, in the case of the optical surfaces 14a-d of the second optical element 14 in a respective switch position, the direction of the incident illumination radiation 4, and hence of the angle of incidence, is dependent on the respective angular position .sub.1, .sub.2 of the optical surface 13a-d, assigned in a specific illumination mode to the respective optical surface 14a-d, of the first optical element 13, which naturally needs to be taken into account during the optimization.

(19) In order to reflect the illumination radiation 4 on a respective optical surface 13a-d, 14a-d of the optical elements 13, 14, a reflecting coating 18 is applied thereon, which is depicted in an exemplary manner in FIG. 3 for the facet element 19 of FIGS. 2A, 2B. The reflecting coating 18 is a multilayer coating and has a plurality of subunits 25, which each have two individual layers 26, 27, which consist of materials with different refractive indices. If EUV radiation with a wavelength .sub.B in the region of 13.5 nm is used, the individual layers 26, 27 usually consist of molybdenum and silicon. Depending on the operating wavelength .sub.B, other material combinations, such as e.g. molybdenum and beryllium, ruthenium and beryllium or lanthanum and B.sub.4C are likewise possible.

(20) In addition to the individual layers 26, 27, a reflective coating can also contain intermediate layers for preventing diffusion and a capping layer for preventing oxidation or corrosion; however, these are not shown in FIG. 3 and not taken into account in the optimization of the thickness d. The top side of the facet element 19 is referred to as optical surface 13a in the following text, even if, in a strict sense, the reflecting coating 18 as a whole brings about the reflection of the EUV radiation. The material of the facet element 19, on which the multilayer coating 18 is applied, may be a metallic material, e.g. ruthenium, but use can optionally also be made of a so-called zero-expansion material, e.g. ULE, Zerodur, etc.

(21) The thicknesses of the individual layers of the coating 18 are in this case matched to the operating wavelength .sub.B of the illumination radiation (and the respective angle of incidence) in such a way that the coating 18 has the greatest possible reflectivity for the illumination radiation 4. For simplification purposes, the assumption is made below that the reflecting coating 18 has a number N of subunits 25 with in each case two individual layers 26, 27, i.e. d=N*d.sub.U applies, where d.sub.U denotes the thickness of the respective subunit 25 (i.e. the sum of the thicknesses of the individual layers 26, 27 with high and low refractive indices). The maximum reflectivity is typically obtained if the thickness d.sub.U of the subunits 25 satisfies the Bragg condition with respect to the angle of incidence and the employed wavelength .sub.B (or the employed wavelength spectrum). Here, the angle of incidence has an influence on the optical path length which the illumination radiation 4 traverses in the coating 18 or in the individual layers 26, 27 thereof such that the reflectivity is also dependent on the angle of incidence.

(22) FIG. 4A shows the dependence of the reflectivity R on the thickness d of the coating 18 for the first angular position .sub.1 (first reflectivity curve R.sub.1) and for the second angular position .sub.2 (second reflectivity curve R.sub.2) of FIGS. 2A, 2B. It can clearly be seen that the two reflectivity curves R.sub.1, R.sub.2, in the thickness range between approximately 7.05 nm and approximately 7.2 nm observed here, have an opposing dependence on the thickness d, i.e. the first reflectivity curve R.sub.1 has a reflectivity maximum at the lower edge of the depicted thickness interval (at approximately 7.05 nm), while the second reflectivity curve R.sub.2 has a reflectivity maximum at the upper edge of the depicted thickness interval (at approximately 7.2 nm). Therefore, the reflectivity R of the coating 18 cannot be maximized simultaneously for both angular positions .sub.1, .sub.2 at a given thickness d.

(23) One option for setting a thickness for the coating 18, at which an acceptable reflectivity R is still achieved in both angular positions .sub.1, .sub.2, consists of initially determining the thickness-dependent reflectivity curve R.sub.M for the mean value of the two angles .sub.1, .sub.2, i.e. for .sub.M=(.sub.1+.sub.2)=15 in the present case, and selecting that thickness d.sub.O1 for the coating at which the reflectivity curve R.sub.M has a maximum. In the present example, this maximum lies at a thickness d.sub.O1 of 7.1242 nm.

(24) However, a problem arising in the case of such setting is that manufacturing-dependent thickness tolerances occur in a coating process for applying the reflecting coating 18 on the optical surface 13a, such that the actual thickness of the coating 18 generally deviates from the intended thickness d.sub.O1 of 7.1242 nm. If the intended layer thickness d.sub.O1 is not achieved exactly during the coating process, this may possibly lead to a significant reduction in the reflectivity R. For the example shown in FIG. 4A, the relative change in the reflectivity R/R lies at 4% in the case of a relative thickness tolerance d/d.sub.O1 of 0.1%, i.e. a comparatively small deviation in the thickness from the intended thickness d.sub.O1 already leads to significant reduction in the reflectivity R.

(25) As was illustrated further above, the reflectivity R of the coating 18 cannot be maximized simultaneously for both angular positions .sub.1, .sub.2. However, a thickness should be selected for the coating 18 at which deviations from the intended thickness or relative thickness tolerances, which are generated due to the manufacturing process when applying the coating 18, have the smallest possible influence on the reflectivity or on the relative change in the reflectivity.

(26) Such an option for selecting an optimized thickness is depicted in FIG. 4B. There, a thickness d.sub.O2 for the coating 18 is selected, at which the reflectivities R.sub.1, R.sub.2 for the two angular positions .sub.1, .sub.2 have the same magnitude, wherein the thickness d.sub.O2 lies at 7.1444 nm in the present case, at which thickness R.sub.1=R.sub.2 applies. The selection of the point of intersection of the reflectivity curves R.sub.1, R.sub.2 for setting the thickness already leads to a significant reduction in the sensitivity of the reflectivity in relation to the thickness tolerance. In the case of a relative thickness tolerance d/d.sub.O2 of 0.1%, the relative change R/R in the reflectivity only lies at approximately 2.12%.

(27) In the following text, two further options for selecting the thickness of the coating 18 are described on the basis of FIG. 4C and FIG. 4D, by which the influence of manufacturing variations can be reduced further. In the criterion for setting the thickness of the coating 18 depicted in FIG. 4C, a mean value R.sub.M=(R.sub.1+R.sub.2) is initially formed from the two reflectivity curves R.sub.1, R.sub.2, which is depicted by a dashed curve in FIG. 4C. This thickness-dependent mean value R.sub.M is optimized, i.e. that thickness d.sub.OPT1 is determined at which the reflectivity curve R.sub.M has a maximum. In the present example, this is the case at d.sub.OPT1=7.1504 nm. In the case of a predetermined thickness tolerance d/d of 0.1%, the relative change in the reflectivity R/R only lies at approximately 1.74% for this selection for the thickness of the coating.

(28) In the criterion for setting the thickness of the coating 18 depicted in FIG. 4D, a relative thickness tolerance d/d is initially predetermined for a given thickness d, which is 0.1% in the present example. Using the known reflectivity curves R.sub.1, R.sub.2, the relative change in the reflectivity R.sub.1/R.sub.1, R.sub.2/R.sub.2 associated with this thickness tolerance d/d is determined at the two angular positions .sub.1, .sub.2. Subsequently, the minimum of that curve which constitutes the maximum in the change in the reflectivity R.sub.1/R.sub.1, R.sub.2/R.sub.2 at the two angular positions .sub.1, .sub.2 is sought after, i.e. that value is determined for the thickness d.sub.OPT2 at which the value max R.sub.1/R.sub.1, R.sub.2/R.sub.2) is minimized. In the present example, d.sub.OPT2=7.1512 nm results for the thickness determined according to this criterion. At this thickness, the relative change in the reflectivity R/R only lies at 1.70% and is therefore even lower than in the case of the thickness d.sub.OPT1 determined in accordance with FIG. 4c.

(29) For setting the thickness d.sub.OPT2 of the coating 18 as described in conjunction with FIG. 4D, it is necessary to know the (relative) manufacturing tolerances, or to determine these. The manufacturing tolerances depend, inter alia, on the type of the coating process employed for applying the coating 18 and on the employed coating parameters. If the manufacturing tolerances are unknown, it is possible to estimate these. It is understood that the deviation d in the thickness d from the intended thickness is depicted in an exaggerated manner in FIG. 3 for clarification purposes. In general, the measured change in reflectivity is assigned to a deviation d, constant over the surface 13a, of the intended thickness d. However, it is understood that the optimization of the thickness of the coating 18 described here may optionally also take place in a position-dependent manner, i.e., for each point of the surface 13a, the respective angle of incidence spectrum incident there is taken into account, as a result of which a coating 18 typically emerges with a thickness varying over the surface 13a.

(30) Both the method depicted in conjunction with FIG. 4C and the method depicted in conjunction with FIG. 4D can be generalized to more than two angular positions .sub.1, .sub.2, . . . .sub.N (N>2) in a manner that will be apparent to a person skilled in the art upon reviewing the present disclosure; however, this is not readily possible in the case of the method described in conjunction with FIG. 4B since no common point of intersection of the reflectivity curves is generally obtained in the case of more than two angular positions. In order to enable illumination that is as flexible as possible of the downstream optical system, it is advantageous if the difference between the individual tilt angles .sub.1, .sub.2, . . . is not too small. This is typically the case if the difference angle |.sub.a.sub.b| between two of the angular positions .sub.a, .sub.b lies at at least 1, preferably at at least 2, in particular at at least 3. However, the respective angles of incidence should not differ too much from one another in the different angular positions. The larger the angle of incidence is or the larger the difference between the angles of incidence on the respective optical surface 13a-d, 14a-d in the different angular positions .sub.1, .sub.2, . . . is, the more important the above-described optimization of the thickness d of the coating 18 becomes.

(31) It should be understood that the respective reflectivity R.sub.1, R.sub.2 of the coating 18 at the two angular positions .sub.1, .sub.2 is dependent on the wavelength of the illumination radiation 4 which is incident on the optical surface 13a-d, 14a-d. In the simplest case, the reflectivity of the individual angular positions .sub.1, .sub.2 can be determined for the operating wavelength .sub.B, at which the intensity of the illumination radiation is at a maximum. In order to improve the accuracy when setting the intended value for the thickness of the coating 18, an average can also be formed over the angles of incidence AOI, and also over the wavelength spectrum of the illumination radiation 4, i.e. the reflectivity emerges as <<f(AOI)*g()*R(d, AOI, )>.sub.AOI>.sub..

(32) The weighting factor g() in the functional to be optimized in this case relates to the wavelength spectrum which arrives in the target area on the wafer W after the effect of all optical elements 12 to 16, M, 21 to 24 of the EUV lithography apparatus 1. Therefore, for the weighting g(), the wavelength spectrum of the light source 2 and the spectral filtering of the illumination radiation 4, provided thereby, on all optical elements 12 to 16, M, 21 to 24 of the EUV lithography apparatus 1, which undertake spectral filtering, are taken into account.

(33) The weighting over the angle of incidence spectrum f(AOI) can take place to take account of the fact that, in the case of a predetermined tilt angle, the angle of incidence spectrum is not discrete. It is understood that, under the assumption of a single (discrete) angle of incidence at a given angular position .sub.1, .sub.2, the functional when averaging over the angles of incidence AOI corresponds to a sum of the reflectivities at the respective tilt angle positions .sub.1, .sub.2, wherein a different weighting factor is optionally to be taken into account for each angular position .sub.1, .sub.2.

(34) The weighting function f(AOI) typically differs for the respective optical surfaces 13a-d, 14a-d and, both in the discrete and in the continuous case, can take into account the fact that an angle of incidence or angle of incidence range which is assigned to a first tilt angle .sub.1 is employed less frequently during the operation of the illumination system 10 than an angle of incidence or angle of incidence range which is assigned to a second tilt angle .sub.2. The weighting function f(AOI) can also take account of the fact that a change in the reflectivity of the coating 18 has a differently pronounced effect on errors in the exposure process of the EUV lithography apparatus 1, depending on the angle of incidence (and the respective optical surface 13a-d, 14a-d).

(35) Since the angular positions or the angles of incidence of the illumination radiation 4 generally depend on the position of the respective optical surface 13a-d, 14a-d in the illumination beam path, a coating 18 with an individually optimized thickness d.sub.OPT1, d.sub.OPT2, d.sub.O2 can be applied to the respective optical surfaces 13a-d, 14a-d of the individual facet elements 19 during the production of a respective optical element 13, 14. If the individual angular positions are the same for a plurality of facet elements 19, or optionally for all of these, a coating 18 with an identical thickness d.sub.OPT1, d.sub.OPT2, d.sub.O2 can be applied to the associated optical surfaces 13a-d, 14a-d. In this case, the coating process can occur in parallel or at the same time for the corresponding number of facet elements 19.

(36) It is understood that, unlike as depicted further above, it is not mandatory for a coating 18 with a homogeneous thickness d.sub.OPT1, d.sub.OPT2, d.sub.O2 over the optical surface 13a-d, 14a-d to be applied, but there may optionally also be a position-dependent optimization of the thickness of the coating 18 at a respective optical surface 13a-d, 14a-d. Such a position-dependent optimization takes account of the fact that the angle of incidence spectrum at a respective optical surface 13a-d, 14a-d may vary depending on position.

(37) Although the layer thickness optimization was described in the context of an EUV lithography apparatus, it is understood that the above-described criteria can also be employed in an advantageous manner in illumination systems in other optical apparatuses, for example in illumination systems for UV lithography, provided that these are equipped with reflecting optical elements which are operated in several different (in particular discrete) angular positions. Also, only tilt angle positions .sub.1, .sub.2 with respect to a single tilt axis were taken into account in the illustration above. However, it is understood that, in the case where the optical surfaces 13a-d, 14a-d can also be tilted by a further tilt axis, which is e.g. perpendicular to the first tilt axis, by an appropriate actuator unit 17, the corresponding angular positions about the further tilt axis can likewise be taken into account when optimizing the thickness.