Methods for the design, manufacture and use of sector heaters

Abstract

The invention relates to a method for designing a sector heater (100) for the on-demand area-specific heat input into an optical element (25) of a projection system (20) of a projection exposure system (1) for photolithography, as well as a method for manufacturing such a sector heater (100) and its subsequent use. The procedure for designing a sector heater (100) comprises the following steps: a) Creation of a state-space model for the area (101) of the optical element (25) to be irradiated by the sector heater (100), wherein this area (101) is subdivided into a plurality of separate heating zones (102) for the state-space model; b) Optimization of the heating output for individual heating zones (102) for a plurality of predefined lighting scenarios, each with regard to a predefined objective; c) Grouping of heating zones (102) into a specified number of sectors (103) for individual irradiation by the sector heater (100) to be designed; d) Adaptation of the design of the sector heater (100) so that individual irradiation of the combined sectors (103) is possible.

Description

[0001] The invention relates to a method for designing a sector heater for the on-demand, area-by-area heat input into an optical element of a projection system of a projection exposure apparatus for photolithography, as well as a method for producing a sector heater designed in this way and its subsequent use.

[0002] Photolithography is used in the production of microstructured components, such as integrated circuits. The photolithography process is carried out in a so-called projection exposure system, which has an illumination device and a projection device. The image of a mask (also called a "reticle") illuminated by the illumination device is projected by the projection device onto a substrate coated with a light-sensitive layer (so-called "photoresist") and arranged in the image plane of the projection device, e.g., a silicon wafer, in order to transfer the mask structure to the light-sensitive coating of the substrate. In subsequent production steps, the transferred structure is implemented in the substrate, e.g., by etching.

[0003] Due to the increasing miniaturization in the semiconductor sector and the transition in wavelength during exposure from DUV (e.g., 193 nm) to EUV (e.g., 13.5 nm), the projection devices of projection exposure systems must exhibit high imaging quality. Projection devices in the EUV range (5-20 nm) exclusively use reflective optical elements to image a mask in the object plane onto a substrate in the image plane, e.g., with a reduction factor of 8:1.

[0004] Depending on the structure to be imaged on the light-sensitive layer of the substrate, a suitable illumination setting is used to illuminate the mask. This illumination setting determines the intensity and / or angle of incidence distribution of the illumination radiation on the mask and thus in the object field of the projection device. The illumination setting is generally selected so that effects that could impair image quality, such as diffraction at the mask structure, are minimized or eliminated. Typical illumination settings are dipole or quadrupole illumination settings.

[0005] At least if the intensity and angle of incidence distribution on a mask is not absolutely homogeneous, the optical elements of the projection device are not used evenly across their entire surface, i.e., are not evenly exposed to projection radiation. However, since a portion of the projection radiation incident on the optical elements is absorbed by them, only local heat inputs into the optical elements usually occur. Due to such only local heat inputs and the resulting local thermal expansion in the optical elements, the optical element can deform to such an extent that the image quality deteriorates.

[0006] To counteract this, so-called sector heaters are known. These allow heating radiation, particularly infrared radiation, to be directed specifically at those areas of an optical element where, at least temporarily, no projection radiation is incident, in order to introduce heat into precisely these areas. By appropriately selecting the intensity and radiation pattern of the sector heater, a significantly more uniform temperature distribution can be achieved in an optical element, which reduces deformation of the optically active surface(s) of the optical element and benefits the imaging quality.

[0007] The design of the individual sectors that can be individually irradiated by a sector heater - in particular their respective limitation on the optical element and, if applicable, also the radiation density within the respective sectors - must be determined within the framework of the design of sector heaters and are directly implemented in the optical configuration of a sector heater.

[0008] The design of sector heaters is usually selected by a specialist based on their experience and knowledge of the expected lighting settings, and is verified experimentally or by simulation. This verification is very complex and computationally intensive and usually only allows for an evaluation of a given sector heater design, but does not provide direct indications for possible optimization of the sector heater design.

[0009] The object of the present invention is to provide an improved method for designing sector heaters and to manufacture and use a sector heater designed in this way.

[0010] This object is achieved by a method according to the main claim, a manufacturing method according to claim 10 and a use according to claim 11. Advantageous further developments are the subject of the dependent claims.

[0011] Accordingly, the invention relates to a method for designing a sector heater for the on-demand, area-by-area heat input into an optical element of a projection system of a projection exposure apparatus for photolithography by thermal radiation, comprising the steps: a) creating a state-space model for the area of ​​the optical element to be irradiated with the sector heater, this area being divided into a plurality of separate heating zones for the state-space model; b) Optimisation of the heating output for individual heating zones for a number of predefined lighting scenarios, each with regard to a predefined objective; c) grouping of heating zones into a predetermined number of sectors for individual irradiation by the sector heater to be designed; d) Adaptation of the design of the sector heater so that individual irradiation of the combined sectors is possible.

[0012] The invention further relates to the production of a sector heater designed according to the invention and to the use of a sector heater according to the invention in a projection system of a projection exposure apparatus for the area-by-area heat input into an optical element of the projection system as required.

[0013] The invention recognizes that by creating a state-space model for the area of ​​the optical element to be irradiated with the sector heater, in which the area is divided into a plurality of theoretical heating zones, a computationally efficient optimization of the design of a sector heater can be achieved. The design of the sector heater can be optimized with regard to a given objective.

[0014] For example, the optimization objective can be to achieve the most homogeneous temperature distribution possible across the modeled surface of the optical element. Particularly for an optical element positioned close to the illumination system along the radiation path within a projection system, the illumination radiation can cause a significant heat input into the optical element, which, depending on the selected illumination setting, only occurs in parts of the optical element. In this case, the sector heater can be used to provide heat to the areas of the optical element not exposed to the illumination radiation, thus achieving the most homogeneous temperature distribution possible in the mirror.

[0015] In the case of optical elements that are arranged away from the illumination system along the radiation path within a projection system, the heat input from the illumination radiation is lower, for example due to reflection or transmission losses in the optical elements arranged in front of it, and requires little or no compensation. In particular with such optical elements, the objective for the design of sector heaters can be to achieve one or more desired wavefront effects caused by the optical element, for example to reduce one or more predetermined wavefront errors caused by the optical element. By specifically introducing heat using a sector heater, the optical properties, in particular the surface, of an optical element can often be changed sufficiently to reduce possible wavefront errors in the projection lens. Wavefront errors can, for example,caused by imperfections of mirror surfaces, but also by deformations due to inhomogeneous heat input into mirrors.

[0016] In the method according to the invention, the total area of ​​the optical element to be irradiated by a sector heater is first divided into a plurality of separate heating zones, each of which is individually considered in the state-space model. For the optical elements of a projection system of a projection exposure system, such an area can be divided, for example, into 50 or more, preferably 100 or more, heating zones.

[0017] The state space model can be designed to enable minimization of the deviation of the stationary wavefront from a given wavefront and subsequent grouping of heating zones into sectors.

[0018] Based on mathematical representations of the stationary wavefront Z=S⋅KωT⋅α(TSS) the thermomechanical coupling based on the inverse stiffness matrix KωT=KinvKut the non-linear material strain α(T)=a0+a1T+a2T2 and the stationary temperature field TSS=CTA−1(Bd,j+BuWuN0u) In a state space model, an optimization problem for the design of sector heaters can be formulated as argminu J(u, j) where J(u,j) is a deviation from a desired stationary wavefront Z des can describe J(u, j)=(Z−Zdes)TQ(Z−Zdes) or the deviation from a desired stationary temperature field T SS,des J(u, j)=(T−TSS,des)TQ(TSS−TSS,des) is.

[0019] Where B d,j the intensity profile of the load j, B u the intensity profile of the individual heating zones, WuN0 an assignment matrix of heating zones to sectors, u the amplitude of the sectors, Z the wavefront effect of the sector heater, S the sensitivity matrix of mirror deformations to the wavefront effect, K -1 the inverse mechanical stiffness matrix, K T the thermal stiffness matrix, C T is the mapping matrix of the thermal state to the stationary temperature field T SS and Q is a weighting matrix.

[0020] For a plurality of given loads j, which ultimately correspond to different lighting settings, the stationary wavefront Z desired for the given optimization objective can then be determined. des determine the optimal heating output for each individual heating zone.

[0021] For different lighting settings 1 to n AnzahlSettings then results in a matrix Uopt=[uopt,1, …, uopt,NNumberSettings] with dimensions NAnzahlHeizzonen × N AnzahlSettings .

[0022] If individual row vectors of this matrix point at least approximately in the same direction, which can be achieved, for example, by specifying a maximum angle γ max and the formula cos−1(uPi⋅uPk|uPi|⋅|uPk|)<γmax can be determined, whereby they differ significantly only in the intensity of the required heat input, the row vectors can be summarized.

[0023] The (remaining) row vectors can then be used to group heating zones into a specified number of sectors. The aim is to group heating zones that exhibit comparable heat flow for the different underlying lighting scenarios, or at least comparable changes in heat flow between the individual lighting scenarios. Since the number of sectors is usually significantly lower than the number of heating zones, namely between 5 and 28, preferably between 10 and 14, deviations in the heat input resulting from belonging to a sector from the optimal heat input determined for a heating zone in one or more lighting scenarios must regularly be accepted when grouping. These deviations can be minimized by optimizing the layout of the individual sectors using well-known mathematical optimization methods.

[0024] Furthermore, additional boundary conditions can be specified when combining heating zones into sectors. For example, it can be specified that only adjacent heating zones are combined into a sector, creating exclusively contiguous sectors. Alternatively, it is also possible to specify a minimum number of adjacent heating zones to be combined. In this case, non-contiguous sectors can also be created, but it is ensured that the individual areas of such a sector have a certain minimum size.

[0025] Based on the heating zones created for the state model by combining them into a manageable number of sectors, the design of a sector heater can then be appropriately adapted. "Design adaptation" here means adapting at least the optical configuration of a sector heater such that it is designed for on-demand, area-by-area heat radiation onto an optical element according to the sectors determined according to the invention.

[0026] The optical properties of the optical elements of a projection system are generally optimized for a specified operating temperature, which is usually higher than the ambient temperature or standard conditions (e.g., 20°C or 21°C) due to the inevitable heat input during exposure. To ensure that the optical elements are at the specified operating temperature before the actual exposure begins, and thus exhibit the desired optical properties immediately at the beginning of an exposure process, it is common practice to preheat the optical mirrors to the specified operating temperature.

[0027] In a preferred embodiment of the method according to the invention, the intensity distribution within the combined sectors is optimized with regard to the specified or an alternative objective and is taken into account when adapting the design of the sector heater. This allows differences in heat input in the individual heating zones within a sector to be achieved.

[0028] An alternative objective, in particular, is the uniform heating of the optical element by simultaneously irradiating several, preferably all, sectors with the sector heater. If the intensity distribution within the individual sectors is suitably adjusted so that, for example, by simultaneously irradiating all sectors, the optical element is heated sufficiently uniformly to the operating temperature, a separate heating element for preheating optical elements, which is sometimes provided in the prior art, can be dispensed with.

[0029] The optical element for which a state-space model is created is preferably a reflective element or a mirror. Further preferably, the optical element is designed to reflect EUV radiation, in particular with a wavelength of 13.5 nm.

[0030] For an explanation of the manufacture and use of a sector heater designed according to the invention, reference is made to the above explanations.

[0031] The invention will now be described by way of example using an advantageous embodiment with reference to the accompanying drawings. In the drawings: Fig. 1: a schematic representation of a projection exposure apparatus for photolithography comprising sector heaters designed according to the invention; Fig. 2a, b: schematic representation for the creation of a state space model for an optical element of the projection exposure system according to Fig. 1; Fig. 3a, b: schematic representation of the state space model according to Fig. 2 determined heating power for two exemplary selected lighting settings of the projection exposure system from Fig. 1; Fig. 4: schematic representation of results comparable Fig. 3 sectors determined for the optical element according to Fig. 2 provided sector heaters; and Fig. 5: an exemplary schematic representation of sectors of a sector heater determined according to the invention for another optical element of the projection exposure apparatus according to Fig. 1.

[0032] In Fig. Figure 1 shows a schematic meridional section of a projection exposure system 1 for photolithography. The projection exposure system 1 comprises an illumination system 10 and a projection system 20.

[0033] With the aid of the illumination system 10, an object field 11 is illuminated in an object plane or reticle plane 12. The illumination system 10 comprises an exposure radiation source 13, which, in the illustrated embodiment, emits illumination radiation at least comprising useful light in the EUV range, i.e., in particular, with a wavelength between 5 nm and 30 nm. The exposure radiation source 13 can be a plasma source, for example an LPP source (laser produced plasma) or a DPP source (gas discharge produced plasma). It can also be a synchrotron-based radiation source. The exposure radiation source 13 can also be a free-electron laser (FEL).

[0034] The illumination radiation emanating from the exposure radiation source 13 is first focused in a collector 14. The collector 14 can be a collector with one or more ellipsoidal and / or hyperboloidal reflection surfaces. The at least one reflection surface of the collector 14 can be exposed to the illumination radiation at grazing incidence (GI), i.e., at angles of incidence greater than 45°, or at normal incidence (NI), i.e., at angles of incidence less than 45°. The collector 14 can be structured and / or coated, on the one hand, to optimize its reflectivity for the useful radiation and, on the other hand, to suppress stray light.

[0035] After the collector 14, the illumination radiation propagates through an intermediate focus in an intermediate focal plane 15. If the illumination system 10 is constructed in a modular design, the intermediate focal plane 15 can generally be used for the - also structural - separation of the illumination system 10 into a radiation source module, comprising the exposure radiation source 13 and the collector 14, and the illumination optics 16 described below. With such a separation, the radiation source module and illumination optics 16 then together form a modular illumination system 10.

[0036] The illumination optics 16 comprises a deflecting mirror 17. The deflecting mirror 17 can be a flat deflecting mirror or, alternatively, a mirror with a beam-influencing effect beyond the pure deflection effect. Alternatively or additionally, the deflecting mirror 17 can be designed as a spectral filter that separates a useful light wavelength of the illumination radiation from stray light of a different wavelength.

[0037] The deflecting mirror 17 deflects the radiation originating from the exposure radiation source 13 onto a first facet mirror 18. If the first facet mirror 18 is arranged—as in the present case—in a plane of the illumination optics 16 that is optically conjugated to the reticle plane 12 as the field plane, it is also referred to as a field facet mirror.

[0038] The first facet mirror 18 comprises a plurality of micromirrors 18', each of which can be individually pivoted about two mutually perpendicular axes, for the controllable formation of facets. Each micromirror 18' is preferably equipped with an orientation sensor (not shown) for determining the orientation of the micromirror 18'. The first facet mirror 18 is thus a microelectromechanical system (MEMS system), as described, for example, in DE 10 2008 009 600 A1.

[0039] In the beam path of the illumination optics 16, a second facet mirror 19 is arranged downstream of the first facet mirror 18, resulting in a double-faceted system whose basic principle is also referred to as a honeycomb condenser (fly's eye integrator). If the second facet mirror 19—as in the illustrated embodiment—is arranged in a pupil plane of the illumination optics 16, it is also referred to as a pupil facet mirror. However, the second facet mirror 19 can also be arranged at a distance from a pupil plane of the illumination optics 16, whereby the combination of the first and second facet mirrors 18, 19 results in a specular reflector, as described, for example, in US 2006 / 0132747 A1, EP 1 614 008 B1, and US 6,573,978.

[0040] The second facet mirror 19 does not necessarily have to be constructed from pivotable micromirrors, but can instead comprise individual facets formed from one or a manageable number of mirrors that are significantly larger than micromirrors, which are either fixed or can only be tilted between two defined end positions. However, as shown, it is also possible to provide the second facet mirror 19 with a microelectromechanical system comprising a plurality of micromirrors 19' that can each be individually pivoted about two mutually perpendicular axes, each preferably comprising an orientation sensor.

[0041] With the help of the second facet mirror 19, the individual facets of the first facet mirror 18 are imaged into the object field 11, which is usually only an approximate image. The second facet mirror 19 can be the last beam-forming mirror or actually the last mirror for the illumination radiation in the beam path before the object field 11.

[0042] Each facet of the second facet mirror 19 is assigned to exactly one of the facets of the first facet mirror 18 to form an illumination channel for illuminating the object field 11. This can, in particular, result in illumination according to the Köhler principle.

[0043] The facets of the first facet mirror 18 are each imaged by an associated facet of the second facet mirror 19, superimposed on one another, to illuminate the object field 11. The illumination of the object field 11 is as homogeneous as possible. It preferably has a uniformity error of less than 2%. Field uniformity can be achieved by superimposing different illumination channels.

[0044] By selecting the illumination channels ultimately used, which is easily possible by appropriately adjusting the micromirrors 18' of the first facet mirror 18, the intensity distribution in the entrance pupil of the projection system 20 described below can also be adjusted. This intensity distribution is also referred to as the illumination setting. It may also be advantageous not to arrange the second facet mirror 19 exactly in a plane that is optically conjugated to a pupil plane of the projection system 20. In particular, the pupil facet mirror 19 can be arranged tilted relative to a pupil plane of the projection system 20, as described, for example, in DE 10 2017 220 586 A1.

[0045] At the Fig. However, in the arrangement of the components of the illumination optics 16 shown in Figure 1, the second facet mirror 19 is arranged in a surface conjugated to the entrance pupil of the projection system 20. Deflecting mirror 17 and the two facet mirrors 18, 19 are arranged tilted both relative to the object plane 12 and relative to each other.

[0046] In an alternative, not shown embodiment of the illumination optics 16, a transmission optics comprising one or more mirrors can be provided in the beam path between the second facet mirror 19 and the object field 11. The transmission optics can, in particular, comprise one or two mirrors for normal incidence (NI mirrors, normal incidence mirrors) and / or one or two mirrors for grazing incidence (GI mirrors, gracing incidence mirrors). With an additional transmission optics, in particular, different positions of the entrance pupil for the tangential and for the sagittal beam path of the projection system 20 described below can be taken into account.

[0047] Alternatively, it is possible that the Fig. 1 is dispensed with, for which purpose the facet mirrors 18, 19 are then to be suitably arranged opposite the radiation source 13 and the collector 14.

[0048] With the help of the projection system 20, the object field 11 in the reticle plane 12 is transferred to the image field 21 in the image plane 22.

[0049] The projection system 20 comprises a plurality of mirrors M i , which are numbered according to their arrangement in the beam path of the projection exposure system 1.

[0050] In the Fig. In the example shown in Figure 1, the projection system 20 comprises six mirrors M 1 to M 6 as optical elements 25. Alternatives with four, eight, ten, twelve or any other number of mirrors M i are also possible. The penultimate mirror M 5 and the last mirror M 6Each has a passage opening for the illumination radiation, which means that the projection system 20 shown is a double-obscured optic. The projection system 20 has an image-side numerical aperture that is greater than 0.3 and can also be greater than 0.6, for example, 0.7 or 0.75.

[0051] The reflection surfaces of the mirrors M i or the optical elements 25 can be designed as free-form surfaces without a rotational symmetry axis. Alternatively, the reflection surfaces of the mirrors M i but can also be designed as aspherical surfaces with exactly one axis of rotational symmetry of the reflection surface shape. The mirrors M iJust like the mirrors of the illumination optics 16, they can have highly reflective coatings for the illumination radiation. These reflective coatings can be designed as multilayer coatings, in particular with alternating layers of molybdenum and silicon.

[0052] The projection system 20 has a large object-image offset in the y-direction between a y-coordinate of a center of the object field 11 and a y-coordinate of the center of the image field 21. This object-image offset in the y-direction can be approximately as large as a z-distance between the object plane 12 and the image plane 22.

[0053] The projection system 20 can in particular be anamorphic, ie it has in particular different image scales β x , β y in the x- and y-direction. The two magnifications β x , β y of the projection system 20 are preferably at (β x , βy ) = (+ / - 0.25, / +- 0.125). A magnification ratio β of 0.25 corresponds to a reduction in the ratio 4:1, while a magnification ratio β of 0.125 results in a reduction in the ratio 8:1. A positive sign for the magnification ratio β means an image without image inversion, a negative sign means an image with image inversion.

[0054] Other magnifications are also possible, including identical and absolutely identical magnifications β x , β y in x and y directions are possible.

[0055] The number of intermediate image planes in the x- and y-directions in the beam path between the object field 11 and the image field 21 can be the same or different, depending on the design of the projection system 20. Examples of projection systems 20 with different numbers of such intermediate images in the x- and y-directions are known from US 2018 / 0074303 A1.

[0056] The projection system 20 may, in particular, have a homocentric entrance pupil. This may be accessible. However, it may also be inaccessible.

[0057] A reticle 30 (also called a mask) arranged in the object field 11 is illuminated by the illumination system 10 and transferred to the image plane 21 by the projection system 20. The reticle 30 is held by a reticle holder 31. The reticle holder 31 can be displaced, in particular in a scanning direction, via a reticle displacement drive 32. In the illustrated embodiment, the scanning direction runs in the y-direction.

[0058] A structure on the reticle 30 is imaged onto a light-sensitive layer of a wafer 35 arranged in the region of the image field 21 in the image plane 22. The wafer 35 is held by a wafer holder 36. The wafer holder 36 can be displaced, in particular along the y-direction, via a wafer displacement drive 37. The displacement of the reticle 30, on the one hand, via the reticle displacement drive 32, and the wafer 35, on the other hand, via the wafer displacement drive 37, can be synchronized with each other.

[0059] The Fig. The projection exposure apparatus 1 shown in Figure 1 or its projection system 10, the above description of which essentially reflects known prior art, comprises for two of the optical elements 25, namely the mirrors M 2 and M 4 , each have a sector heater 100, with which, if required, the mirror M 2 and M 4Heat can be introduced individually in the form of infrared radiation. The sector heaters 100 are designed according to the invention, wherein the sector heater 100 for the mirror M 2 is designed to compensate for different heat inputs from the EUV radiation in order to avoid deformation of the mirror surface as far as possible, while the sector heater 100 for the mirror M 4 If necessary, targeted deformations of the mirror surface should be created in order to compensate for wavefront errors.

[0060] In Fig. 2a is an example of the reflecting surface of the mirror M 2 the projection exposure system 1 Fig. 1 as an optical element 25, as seen from the viewing direction of the sector heater 100 provided for this optical element 25 (cf. Fig. 1). In the Fig. The surface shown in Figure 2a is therefore the area 101 to be irradiated by the sector heater 100.

[0061] For the optical element 25, a state space model is created, as explained, for example, in the general part of the description, for which purpose the surface 101 to be irradiated is divided into a plurality of - namely more than 100 - separate heating zones 102 (cf. Fig. 2b). The heating zones 102 are hexagonal in this embodiment.

[0062] Using this state space model, a number of different illumination settings of the projection exposure system 1 (cf. Fig. 1) determines the optimal heating power for each of the individual heating zones 102. The objective of the optimization is to achieve the most homogeneous temperature possible across the entire surface 101 to be irradiated, with the heat input of the EUV radiation intended for exposure and the individual heating zones 102 complementing each other.

[0063] In Fig. 3a, b show exemplary required heating powers for only two different lighting settings, namely for the lighting settings “Y-Dipole” ( Fig. 3a) and “X-dipole” ( Fig. 3b). Typically, a number of additional lighting settings are taken into account, and optimized heating outputs for the individual heating zones 102 are determined for these as well.

[0064] The representation in Fig. 3a, b are further simplified with regard to heating power in such a way that only two different levels of heating power are shown for the individual heating zones 101 (recognizable by the different densities of the hatched lines). Of course, it is possible to determine the optimal heating power for the individual heating zones 102 in the different lighting settings much more precisely.

[0065] Is the optimization of the heating output in the individual heating zones 101 for all (and not only for the two in Fig. 3a, b) lighting settings, the heating zones are then combined into sectors 103, whereby the sectors 103 are designed in such a way as to reflect the optimized heating output for the individual heating zones 101 for the individual lighting settings as best as possible. Even if the presently envisaged reduction to 10 sectors 103, as shown in Fig. 4, some generalizations have to be made, it is nevertheless possible to combine only adjacent heating zones 101 into subsequently connected sectors 103 and still achieve good temperature homogenization of the area 101 to be irradiated in the different lighting settings.

[0066] Once the sectors 103 have been defined, the intensity distribution within a sector 103 can still be adjusted. In this case, it can be provided that the intensity distribution within the individual sectors 103 is adjusted such that, with simultaneous heat input in all sectors 103, a uniform heating of the surface 101 to be irradiated is achieved. The heat input into the sectors 103 or a sector heater 100 designed for this purpose can then also be used to preheat the irradiated optical element 25, whereby a corresponding preheater can possibly be completely omitted.

[0067] In Fig. 5 shall be determined by a procedure corresponding to that established by the Fig. 2 to 4 Explained found sectors 103 for another optical element 25 - namely the mirror M 4 of the projection exposure systems 1 according to Fig. 1. The sectors 103 are not arranged contiguously and partially overlap, which is why a second group of sectors 103' is shown only in dashed lines.

[0068] The sectors 103 or the underlying optimization of the heating power of individual heating zones 101 created for a state-space model were not carried out with a view to achieving the most homogeneous temperature distribution possible, but with the objective of specifically reducing certain wavefront errors in different lighting settings or wavefront errors due to manufacturing tolerances.

[0069] The manufacture of sector heaters 100 according to the design explained above, as well as their use as described in Fig. 1 is within the skill of the specialist and does not require any further explanation. QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] DE 10 2008 009 600 A1

[0038] US 2006 / 0132747 A1

[0039] EP 1 614 008 B1

[0039] US 6,573,978

[0039] DE 10 2017 220 586 A1

[0044] US 2018 / 0074303 A1

[0055]

Claims

[1] Method for designing a sector heater for the on-demand, area-by-area heat input into an optical element (25) of a projection system (20) of a projection exposure apparatus (1) for photolithography by thermal radiation, comprising the steps: a) creating a state space model for the area (101) of the optical element (25) to be irradiated with the sector heater (100), said area (101) being divided into a plurality of separate heating zones (102) for the state space model; b) optimising the heating output for individual heating zones (102) for a plurality of predefined lighting scenarios, each with regard to a predefined objective; c) combining heating zones (102) into a predetermined number of sectors (103) for individual irradiation by the sector heater (100) to be designed; d) Adapting the design of the sector heater (100) so that individual irradiation of the combined sectors (103) is possible. [2] Method according to claim 1, characterized by that, with regard to the given or an alternative objective, the intensity distribution within the combined sectors (103) is optimised and taken into account when adapting the design of the sector heater (100). [3] Method according to claim 2, characterized by that the alternative objective is the uniform heating of the optical element (25) with simultaneous irradiation of several, preferably all, sectors (103) by the sector heater (100). [4] Method according to one of claims 1 to 3, characterized by that the predetermined objective for the optimization is a temperature distribution that is as homogeneous as possible over the surface (101) of the optical element (25) to be irradiated. [5] Method according to one of claims 1 to 3, characterized by that the given objective for optimization is the reduction of one or more given wavefront errors. [6] Method according to one of the preceding claims, characterized by that 50 or more, preferably 100 or more heating zones (101) are provided. [7] Method according to one of the preceding claims, characterized by that the predetermined number of sectors (103) is between 5 and 28, preferably between 10 and 14. [8] Method according to one of the preceding claims, characterized by that only adjacent heating zones (102) are combined to form sectors (103). [9] Method according to one of the preceding claims, characterized by that the optimization of the heating output for individual heating zones is based on the optimization problem argminu J(u, j) where J(u,j) is a deviation from a desired stationary wavefront Z des J(u, j)=(Z−Zdes)TQ(Z−Zdes) or the deviation from a desired stationary temperature field T SS,des J(u, j)=(T−TSS,des)TQ(TSS−TSS,des) describes. [10] Method for manufacturing a sector heater, characterized by that the sector heater (100) is designed with a method according to one of the preceding claims. [11] Use of a sector heater (100) according to claim 9 in a projection system (20) of a projection exposure apparatus (1) for the area-wise introduction of heat into an optical element of the projection system (20) as required.

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