Method for determining the positioning of individual mirrors of a faceted mirror of a lighting optic of a projection exposure system

Abstract

To determine the positioning of individual mirrors of a faceted mirror (6) of an illumination optic (11) of a projection exposure system (1), a set of basic functions (fi) is specified, subsets of the individual mirrors are assigned to different basic functions, partial switching states of the individual mirrors of the individual mirror partitions are determined to generate multiples of the basic functions as partition contributions, and the partial switching states of the individual mirrors are stored in a storage device (28, 29).

Description

The invention relates to a method for determining the positioning of individual mirrors of a faceted mirror in an illumination optic of a projection exposure system. The invention further relates to an illumination system for a projection exposure system. It also relates to a method for positioning individual mirrors of a faceted mirror in a projection exposure system. Finally, the invention relates to a projection exposure system and a method for manufacturing a micro- or nanostructured component. A projection exposure system can include an illumination system that allows for a wide variety of illumination of a reticle positioned within the object field. The beams illuminating the reticle can be characterized by their angle of incidence, their point of impact within the object field, and optical parameters such as wavelength, polarization, and intensity. The choice of illumination can be tailored to the specific structures being imaged on the reticle. It is also possible to vary the illumination settings based on the location on the wafer, for example, to address process fingerprints in the feature width, which are generally dependent on the wafer's location. In illumination systems with multiple movable mirrors, the illumination characteristics at the reticulum can be adjusted by moving the individual mirrors. During the movement of the mirrors, the wafer illumination is typically interrupted. Therefore, there is a need to improve the relocation of the individual mirrors of a faceted mirror of a lighting optic of a projection exposure system, in particular to reduce the time required for relocation. This problem is solved by the methods according to the present invention. According to one aspect, partial switching states of the individual mirrors are determined and stored in a database. A partial switching state, in this context, refers to a specific positioning of a subset of all individual mirrors, particularly on the same mirror module, or the control signal required for this positioning. The partial switching states can be determined using an actual, installed lighting system. However, it is generally sufficient to provide a calibrated model of such a lighting system. This model can then be assigned to the corresponding hardware. The subset can comprise one or more individual mirrors. In particular, it can comprise at least 10, in particular at least 20, in particular at least 30, in particular at least 50, in particular at least 100 individual mirrors. Different partial switching states can include different subsets, in particular subsets with different numbers of individual mirrors. According to the invention, it has been recognized that by pre-calculating different partial switching states of the individual mirrors, in particular of individual mirror partitions, and storing these partial switching states in a database, the time required to relocate the individual mirrors can be significantly reduced. In particular, the time required to determine new positions of the individual mirrors can be significantly reduced. This method is used in particular to determine the positioning of individual mirrors of a first faceted mirror of an illumination optic in a projection exposure system. A first faceted mirror of an illumination optic is understood here to be, in particular, the first faceted mirror of the illumination optic in the direction of the beam path from the radiation source to the object field. The illumination optic may, in addition to the first faceted mirror, have a second faceted mirror downstream in the beam path of the illumination radiation. If the first faceted mirror is arranged in a field plane of the illumination optics, it is also referred to as a field faceted mirror. This is not mandatory. The faceted mirror modules can also be arranged at a distance from a field plane and / or at an angle to a pupil plane of the illumination optics. This can lead to greater flexibility in illuminating the object field. However, it can complicate determining the positions of the individual mirrors, especially their optimization. If the second faceted mirror is arranged in a pupil plane of the illumination optics, it is also referred to as a pupil faceted mirror. If the second faceted mirror is arranged at a distance from a pupil plane of the illumination optics, it is also referred to as a specular reflector when combined with the switchable faceted second mirror.For details of a specular reflector, refer to US 2006 / 0132747 A1. The individual mirrors may be, in particular, micromirrors. Micromirrors are defined, in particular, as mirrors with a reflective surface of a few square millimeters or less. The micromirrors have, in particular, an edge length and / or a diameter of at most 10 mm, in particular at most 5 mm, in particular at most 3 mm, in particular at most 2 mm, in particular at most 1 mm. The individual mirrors, as well as the faceted mirrors, may in particular constitute a microelectromechanical system (MEMS). For details of such a system, reference is made, by way of example, to EP 2 689 282 A2, which is hereby fully incorporated into the present application. By selectively choosing the illumination channels, particularly which individual mirrors of the first and second faceted mirrors guide the illumination radiation from the light source to the object field, the illumination of the reticle arranged in the object field, especially the angles of incidence of the illumination, can be adjusted depending on its location. Furthermore, the intensity distribution of the illumination can be influenced in this way. Generally, relocating an individual mirror of the first faceted mirror will lead to a change in the intensity angular distribution and the intensity spatial distribution. By relocating the individual mirrors of the first faceted mirror, the precise angular distribution of the illumination pupil and the intensity profile of the illumination, especially with regard to the cross-scan direction, can be adjusted, and in particular varied. This makes it possible to make wafer-by-wafer adjustments to the intensity distribution.It is also possible to make wafer-to-wafer-to-wafer adjustments to the intensity distribution. Adjusting the switching positions of the individual mirrors to achieve a desired mask illumination is also possible. This allows for responses to changes, especially fluctuations, in the radiation source and / or to degradation effects, for example, due to contamination. During operation of the projection exposure system, the reticulum arranged in the object field is typically illuminated using a scanning technique. It can be shifted, particularly moved, in a scan direction, especially during illumination. The direction perpendicular to the scan direction is then referred to as the cross-scan direction. To increase the throughput of the projection exposure system, the time required to adjust the switching states of the individual mirrors should be kept as short as possible. Particularly in the case of a specular reflector, where the field and pupil properties are inextricably linked, this can lead to a high-dimensional, non-local, discrete optimization problem that can only be solved approximately and with enormous computational effort. Especially with faceted mirrors containing many thousands of individual mirrors—the number of which can exceed 100,000, 200,000, or even 300,000—determining the positioning of the individual mirrors cannot be performed during the scanning process without causing delays or a loss of image quality. According to the invention, it was discovered that the time required to set new switching states of individual mirrors can be significantly reduced if the entire set of individual mirrors, or at least a subset thereof, is divided into partitions and partial switching states of the corresponding individual mirrors for the different partitions are pre-calculated and stored in a database. The difficult optimization problem is thereby shifted to the pre-calculation. This can be performed, for example, on a high-performance computer, typically with thousands of processors, while during machine operation only the stored partial switching states need to be accessed. This makes it possible to significantly reduce the time required to set a new lighting profile. The individual mirrors of a partition can be arranged in a geometrically simple, connected region. The smallest convex hulls of the different partitions can be non-overlapping or at least substantially non-overlapping. "Substantially non-overlapping" here means that they overlap within an overlap region of at most 1000 individual mirrors, and in particular at most 100 individual mirrors. A simply connected area is understood to mean, in particular, that within an area in which the individual mirrors of a particular partition are arranged, there are no individual mirrors that belong to a different partition. These limitations—an arrangement of the individual mirrors in a simple, continuous area and / or a lack of or only minimal overlap between the areas—are not mandatory. In particular, it is also possible to arrange the individual mirrors of the different partitions across the entire surface of the faceted mirror or at least across parts of it. This can offer advantages, especially with regard to a uniform, homogeneous adjustment of certain lighting parameters. In particular, it is possible to have a maximum of 10% of the individual mirrors of one partition adjacent to individual mirrors of another partition. In this case, the individual mirrors of a given partition will preferentially be adjacent to individual mirrors of other partitions. It is also possible to assign the individual mirrors to a partition in groups. For example, up to 4, in particular up to 16, in particular up to 64, in particular up to 256 individual mirrors of a partition can be arranged in a simply connected area and / or be adjacent to each other. When dividing the individual mirrors into partitions, the structure of the individual mirrors, in particular their geometric details and / or details of their mechanical arrangement on a support substrate and / or their switching range and / or their controllability, in particular via signal connections, can be taken into account. An illumination profile B(x) is understood to be the dependence of a quantity for characterizing the illumination radiation on the position in the object field, in particular on the position x in the cross-scan direction. The property in question can be, in particular, the intensity I of the illumination radiation, especially I(x) or I(x, y), the polarization of the illumination radiation, telecentricity, or ellipticity. In general, the illumination profile can depend not only on the position (x, y) in the object field, but also on the angle of incidence σx, σy. The illumination profile B(x) can be a scalar or a vector quantity. In particular, it can denote a multi-parameter illumination property. Different characteristics of the lighting profile have different units. The lighting profile to be set is also referred to as the target profile. The target profiles can, in particular, be the distribution of brightness across the field location x, especially scan-integrated, i.e., y-integrated. They can also be the brightness at a field location (x, y). They can also be the brightness within a specific illumination angle range l and / or illumination angle location, especially at the field center. They can also be the brightness within an illumination angle range at a field location x, especially scan-integrated. They can also be the brightness within an illumination angle range at a field location (x, y). In these cases, the deviation can be defined as the percentage deviation of the intensity from a desired intensity. Specific boundary conditions can be defined for the target profile. For example, a particular position of the pupil's center of gravity or telecentricity may be required. These values ​​are often specified in angles (millirads). According to the invention, it was discovered that a given lighting profile B(x) can be decomposed into partial contributions. In general, a given lighting profile can be represented as the sum of multiples of the basis functions, in particular in the form of suitably scaled basis functions fi, and a remainder R(x): The scaling factors of the respective basis function are also called coefficients. They depend on the given lighting profile. The coefficients can be real numbers. They are also called real multiples or simply multiples. The basis functions are real. They can be vectors. They typically have a compact support and are preferably, but not necessarily, continuous and differentiable. Subsets of individual mirrors, particularly the first faceted mirror, can be assigned to the basic functions from which one or more predefined lighting profiles can be composed. The subsets of individual mirrors assigned to the different basic functions form pairwise disjoint individual mirror partitions. Partial switching states can be determined for each individual mirror within its partition, such that the individual mirrors in each partition, in their respective partial switching states, serve to generate a multiple of the respective basic function. The individual mirrors within each partition, in their determined partial switching states, collectively contribute to the predefined lighting profiles. The determined partial switching states of the individual mirrors can be stored in a database, specifically in a storage device.According to the invention, it was recognized that they can then be retrieved very quickly. In particular, it is then possible to generate the partition contributions required to create a predefined lighting profile very quickly. The multiples of the basis functions are products of the basis functions fi with scaling factors, which are generally referred to as coefficients ai. The coefficients ai can be from a given range between a minimum and a maximum, in particular between zero and a maximum. The coefficients can be uniformly spaced, i.e., equidistant from each other. They can also be non-uniformly distributed, for example, logarithmically. It is also possible to assign a denser grid of coefficients to specific areas. The coefficient density can be higher in sub-areas that are expected to occur frequently than in sub-areas that are expected to be needed less often. According to one aspect, a subset of the individual mirrors, a residual set, cannot be assigned to any of the basis functions. The mirrors of this residual set can be used to approximate an expected residual R when representing a lighting profile from basis functions. The proportion of individual mirrors in the remaining quantity is, in particular, at most 50%, 30%, 20%, 10%, 5%, 3%, 2%, or 1% of the total number of individual mirrors. The proportion of individual mirrors in the remaining quantity may, in particular, be at least 1%, 3%, or 10%. A larger number of individual mirrors in the remaining set allows for a more flexible and precise representation of different lighting profiles. In particular, a larger number of individual mirrors in the remaining set allows for more flexible adjustment of the lighting profiles. A smaller number of individual mirrors in the remaining batch simplifies the optimization process for determining the positioning of the individual mirrors. In particular, a smaller number of individual mirrors in the remaining batch allows for faster positioning of individual mirrors, especially for setting a new lighting profile. According to another aspect, it may be possible to specify a plurality of different sets of basis functions f. It has been shown that the ability to represent different lighting profiles can depend significantly on the selection and properties of the basic functions f. It can be particularly advantageous to represent a lighting profile using a combination of different sets of basic functions. For example, different components of a lighting profile can preferably be represented by basic functions spanning the entire field or, more preferably, by local basic functions, i.e., basic functions with a small, compact carrier. The carrier of the local basic function can, in particular, be at most <10% of the object field width, in particular <5% of the object field width, in particular <1%, in particular <0.5% of the object field width. According to one aspect, all partition contributions have the same sign. The basic functions, in particular, cannot be strictly negative. According to the invention, it was recognized that this is advantageous for achieving the highest possible system transmission. According to another aspect, the positive polynomials, especially the positive polynomials on the interval [-1,1], can serve as basis functions. Virtual Unicom fingers, especially in the form of triangular functions, delta functions, one-dimensional Gaussian functions, rectangular functions or their approximations, can also serve as basic functions. Different partitioning of the individual mirrors into individual mirror partitions can be used for different sets of basis functions. In particular, it is possible to specify the subsets of the individual mirrors, especially the number of individual mirrors of the respective subsets that are assigned to different basis functions, depending on the respective set of basis functions and / or depending on a specific basis function of the selected set. In this context, at least two subsets, and in particular all subsets, can have the same number of individual mirrors. It is also possible for different subsets to have different numbers of individual mirrors. In particular, it is possible for different subsets to have numbers of individual mirrors that differ from each other by at least 10%, in particular at least 30%, in particular at least 50%, in particular at least 100%. The number of individual mirrors, at least some, in particular all of the subsets, is generally at least 100, at least 200, at least 300, at least 500, at least 1000, at least 2000, at least 3000, at least 5000, at least 10,000, at least 30,000. The number of individual mirrors of at least some, in particular all, of the subsets can in each case be at most 100,000, in particular at most 50,000, in particular at most 30,000. A smaller number of individual mirrors per subset, combined with a large number of basic functions, can lead to greater flexibility. A larger number of individual mirrors per subset, combined with a large number of basic functions, can lead to a reduction in computational effort. It could be shown that with such a number of individual mirrors, deviations from the desired target profile of less than 3%, in particular less than 2%, in particular less than 1%, in particular less than 0.5%, in particular less than 0.3%, in particular less than 0.2%, in particular less than 0.1% are possible in at least some, in particular all, of the subsets. The number of individual mirrors per subset can be selected depending on the frequency spectrum and / or support of the basic function. Preferably, only the individual reflections of a basis function are assigned, which contribute where the function is not equal to zero. The number of mirrors can be chosen proportionally to the amplitude of the basis function at that field location. Another aspect is that different partitioning of individual mirrors into individual mirror partitions can be selected for one or more sets of basic functions. Each of these different partitioning arrangements can form a partition group. This can be advantageous if a particular basic function is not needed, or only needed to a small extent, when displaying a specific lighting profile. In this case, it can be beneficial to reduce the number of individual mirrors assigned to that basic function. The remaining individual mirrors can then be assigned to the other, more frequently used basic functions or to the remaining set. A partition is defined as a subset of all individual mirrors. The pairwise disjoint division of all individual mirrors into partitions is called a partition group. In different partition groups, a given single mirror can be assigned to different basis functions of the same set. The partition groups can differ in particular by the number of individual mirrors that are assigned to the different basis functions of a given set of basis functions. According to another aspect, a high-frequency residue may remain when the lighting profiles are decomposed into sub-contributions. This refers in particular to the distribution of the desired lighting parameter with a spatial frequency of at least 1 × 10³ / m, especially at least 2 × 10³ / m, especially at least 3 × 10³ / m, especially at least 5 × 10³ / m. To generate or approximate the high-frequency remainder, the remaining set of individual mirrors that are not assigned to one of the basis functions can be used. The switching states of the individual mirrors in the remaining quantity can be determined using an optimization method. Since the number of individual mirrors in the remaining quantity is smaller than the total number of individual mirrors, the computational effort and thus the time required to determine the switching states of the individual mirrors in the remaining quantity is considerably less than that required to determine the switching states of all individual mirrors. In the limiting case where the number of individual mirrors of the remaining quantity, in particular the contribution of the individual mirrors of the remaining quantity to the illumination profile, is only insignificantly large, in particular smaller than a specified limit value, it is also possible to dispense with an optimization of the switching states of the individual mirrors. According to another aspect, the allocation of individual mirrors to individual mirror partitions is preferably carried out under the constraint that the overall transmission should be as large as possible, in particular maximized. It can be particularly advantageous to select the allocation of individual mirrors to individual mirror partitions such that, especially under given constraints, for example, when selecting lighting profiles to be displayed, the number of individual mirrors used to transmit the illumination radiation is greater than a certain limit. The number of individual mirrors used to transmit illumination radiation can thus be maximized. This can improve the throughput of the projection exposure system. It has been shown that when solving the optimization problem, finding a switching state that offers both the desired relative profile and maximum transmission is significantly more difficult and time-consuming. Pre-calculating the solutions not only allows for faster access to the solution but also generally provides higher-quality solutions (e.g., regarding transmission). According to another aspect, the number of basis functions in a given set of basis functions can range from 2 to 200. In particular, the number of basis functions in a given set can be at least 3, at least 5, at least 8, and at least 16. The number of basis functions in a given set can be, in particular, at most 200, in particular at most 150, in particular at most 120, in particular at most 100, in particular at most 80, in particular at most 50, in particular at most 30. A larger number of basic functions can lead to better representation of the lighting profiles, particularly to a lower residual error. A smaller number of basic functions can lead to a reduction in the computational effort required to display the lighting profiles and / or to a significantly smaller database of solutions, as well as faster decomposition of the lighting profile. Different sets of basis functions can have different numbers of basis functions. The number of basis functions in the different sets of basis functions can differ, in particular, by a factor of at least 2, in particular by a factor of at least 3, in particular by a factor of at least 5, in particular by a factor of at least 10. In principle, it is also possible for all sets of basic functions to have the same number of basic functions. This can be advantageous when allocating memory space. According to another aspect, the lighting optics can include a second faceted mirror with a multitude of individual mirrors. For each of the partial switching states of the individual mirrors in the subsets of the first faceted mirror module, corresponding partial switching states of the individual mirrors in the second faceted mirror can be determined. These partial switching states of the individual mirrors in the second faceted mirror can also be stored in a database. This can be the same database that also stores the detailed switching states of the individual mirrors in the first faceted mirror. This can lead to advantages when retrieving the partial switching states from the database. Alternatively, the partial switching states of the individual mirrors of the second faceted mirror can be stored in a separate database. This can be particularly advantageous with a parallel structure of the control unit for positioning the individual mirrors. The second faceted mirror can, in particular, be a specular reflector. It can, in particular, be arranged at a distance from a pupil plane of the illumination optics. According to one aspect, the specified illumination profile can describe one or more of the following parameters: the intensity of the illumination radiation, in particular as a function of one field coordinate, or as a function of both field coordinates, or as a function of one or both field coordinates and the angles of incidence of the illumination radiation at that location. The polarization, depending on the field location and illumination direction, can also be required. Another aspect is that a sequence of different switching states of the individual mirrors can be determined and saved to set a sequence of different lighting profiles. This further reduces the time required to switch from one switching state to another. According to another aspect, boundary conditions are taken into account when determining the partial switching states of the individual mirrors within the individual mirror partitions. These boundary conditions can include, in particular, specifications for minimum transmission. Boundary conditions relating to the displacement of adjacent individual mirrors or groups of individual mirrors can also be considered. Another object of the invention is to improve a lighting system for a projection exposure system. This task is solved by a lighting system in which a control device for controlling the positioning of the individual mirrors of a faceted mirror is connected in a signal-transmitting manner to a storage device for storing partial switching states of subsets of the individual mirrors for generating partition contributions of lighting profiles. The faceted mirror may in particular be the first faceted mirror in the beam path of the lighting optics. A corresponding control unit, which is connected to a corresponding storage device via signal transmission, can also be provided for the second faceted mirror in the beam path of the illumination optics. This can be a pupil faceted mirror or a specular reflector. The two control units can be designed as separate units. They can also be integrated into a single component. The storage device for storing partial switching states of the individual mirrors of the first faceted mirror can be separate, in particular physically separate, from the storage device for storing partial switching states of the individual mirrors of the second faceted mirror. Alternatively, a common storage device for storing partial switching states of the individual mirrors of the first and the second faceted mirror can be provided. A further object of the invention is to improve a method for positioning individual mirrors of a faceted mirror of a projection exposure system. This can involve a field faceted mirror and / or a pupil faceted mirror or a specular reflector. This task is solved by a procedure with the following steps: - Providing a lighting system according to the preceding description, - Specifying a target lighting profile, - Decomposing the lighting profile into sub-contributions, each of which is a multiple of a specified set of basic functions, - Generating the sub-contributions of the lighting profile by positioning predetermined subsets of the individual mirrors, - whereby partial switching states of the individual mirrors are retrieved from a database to position the subsets of the individual mirrors. For details on determining the positioning of individual mirrors and, in particular, on determining and saving the partial switching states of the individual mirrors in a database, please refer to the preceding description. Retrieving the partial switching states of the individual mirrors from the database requires, in particular, a time of at most 100 ms, in particular at most 50 ms, in particular at most 30 ms, in particular 20 ms, in particular at most 10 ms. This allows the positioning of the individual mirrors to be done very quickly. The lighting profile is typically represented as the sum of multiples of the basic functions. A remainder may remain. When determining the partial switching states, the coefficients aiz for representing a predefined target profile as a floating-point number can first be calculated. The calculated floating-point number can then be rounded to the appropriate increment of the coefficient values ​​stored in the database. In the case of an uneven distribution of the stored coefficient values, the value closest to the floating-point number can be determined. Reading the solutions from the database is usually much faster than calculating a solution for a given lighting profile. To generate the remaining components, a designated residual quantity of individual faceted mirrors can be used. An optimization procedure can be employed to determine the positioning of these individual mirrors. Since the number of individual mirrors in the residual quantity is considerably smaller than the total number of individual mirrors in the faceted mirror, the time required to determine the positioning of the individual mirrors in the residual quantity is significantly shorter than the time that would be necessary to determine the positioning of all individual mirrors using a corresponding optimization procedure. If the subsequent illumination profile is already known during the illumination of the reticle, particularly during its imaging onto the wafer, the selection of the next intended positioning of the individual mirrors, and in particular the retrieval of the partial switching states of the individual mirrors within the individual mirror partitions, can be performed during the illumination of the reticle, especially during its imaging onto the wafer. The retrieved partial switching states can be stored in a buffer. This reduces the time required to set the subsequent illumination profile. This is particularly advantageous if all desired profiles are already available a priori, i.e., at the beginning of the wafer exposure process. The decomposition and the retrieval of the solution from the database can be performed in parallel during wafer processing. The buffer ensures that the solution is available almost instantly at the start of a new exposure phase. The desired profile can be set in significantly less than 10 ms. According to another aspect, different sets of basic functions, for which partial switching states are stored in the memory device, can be used in parallel to represent the lighting profile. In this case, the control device can be configured to select a specific set of basic functions for positioning the individual mirrors after comparing the quality of the lighting profile representation provided by the different basic functions. This can increase the transmission of the projection exposure system. Further details and advantages of the invention will become apparent from the description of exemplary embodiments with reference to the figures. The figures show: Fig. 1 schematically the components of a projection exposure system and the beam path in such a system; Fig. 2 schematically and also in meridional section a beam path of selected individual beams of illumination beams within the illumination optics according to Fig. 1, starting from an intermediate focus to a reticle or object arranged in the object plane of the projection optics in the area of ​​the illumination or object field; Fig. 3 schematically the representation of an intensity profile in partial contributions and a high-frequency residue and a partitioning of the field facet mirror into subsets for generating the partial contributions and a residue for generating the residual component; Fig. 4A and Fig.Figure 4B shows, by way of example, the decomposition of an intensity distribution b into a low-frequency component t, which is decomposed into positive basis functions ak, mfk, m(x), where Figure 4B represents the same decomposition as Figure 4A, but in piecewise summed form; Figures 5A to 5C schematically and by way of example show a partitioning of the individual mirrors of the field facet mirror into different partition groups; Figure 5D schematically represents concrete switching states as an integer list for different coefficient values ​​of a partition Pi; Figure 6 schematically shows the sequence of procedure steps for reading out a previously calculated solution; Figure 7 shows slightly overlapping, locally limited basis functions, here triangles or "virtual Unicom fingers"; Figure 8, analogous to Figure 7, shows locally limited basis functions which result from a superposition of micromirror images. The following section describes, by way of example, a possible setup and components of a projection exposure system 1. The details of the projection exposure system 1 shown in the figures are purely exemplary and not to be understood as limiting. A projection exposure system 1 for microlithography, shown schematically in meridional section in Fig. 1, has a radiation source 2 for illumination radiation 3. The radiation source 2 is an EUV radiation source that generates radiation in a wavelength range between 5 nm and 30 nm. This can be an LPP (laser-produced plasma) radiation source, a DPP (discharge-produced plasma) radiation source, or a synchrotron radiation-based radiation source, for example, a free-electron laser (FEL). A transmission optic 4 guides the illumination radiation 3 emanating from the radiation source 2. This optic has a collector 5, shown in Fig. 1 only with respect to its reflective effect, and a transmission facet mirror 6, also referred to as the first facet mirror or field facet mirror, which will be described in more detail below. An intermediate focus 5a for the illumination radiation 3 is arranged between the collector 5 and the transmission facet mirror 6. The numerical aperture of the illumination radiation 3 in the region of the intermediate focus 5a is, for example, NA = 0.182. Downstream of the transmission facet mirror 6, and thus of the transmission optic 4, is an illumination preset facet mirror 7, also referred to as the second or further facet mirror, which will also be explained in more detail below. The optical components 5 to 7 are parts of an illumination optic 11 of the projection exposure system 1. The transmission facet mirror 6 is arranged in a field plane of the illumination optics 11. The illumination-setting facet mirror 7 of the illumination optics 11 is arranged at a distance from the pupil planes of the illumination optics 11. Such an arrangement is also referred to as a specular reflector. Alternatively, the illumination-setting facet mirror 7 can also be arranged in the region of a pupil plane of the illumination optics 11 and is then referred to as a pupil facet mirror. Downstream of the illumination-preserving faceted reflector 7 in the beam path of the illumination radiation 3 is a reticle 12, which is arranged in an object plane 9 of a downstream projection optic 10 of the projection exposure system 1. The projection optic 10 is a projection lens. The illumination optic 11 illuminates an object field 8 on the reticle 12 in the object plane 9 in a defined manner. The object field 8 simultaneously constitutes an illumination field of the illumination optic 11. In general, the illumination field is designed such that the object field 8 can be positioned within it. The illumination preset facet mirror 7, like the transmission facet mirror 6, is part of a pupil illumination unit of the illumination optics and serves to illuminate an entrance pupil 12a in a pupil plane 12b of the projection optics 10 with the illumination radiation 3 with a predefined pupil intensity distribution. The entrance pupil 12a of the projection optics 10 can be arranged in the illumination beam path in front of the object field 8 or after the object field 8. Fig. 1 shows the case in which the entrance pupil 12a is arranged in the illumination beam path after the object field 8. In this case, the pupil distance PA of the second facet mirror 7 from the pupil plane 12b is the sum of the z-distance PA1 of the second facet mirror 7 to the object plane 9 and the z-distance PA2 of the object plane 9 to the pupil plane 12b. Therefore: PA = PA1 + PA2. The pupillary distance PA can alternatively also be measured in the direction of the beam. To facilitate the representation of spatial relationships, a Cartesian xyz coordinate system is used below. In Fig. 1, the x-direction runs perpendicular to the plane of the drawing and into it. The y-direction runs to the right in Fig. 1. The z-direction runs downwards in Fig. 1. The coordinate systems used in the drawing each have x-axes that run parallel to each other. The course of a z-axis in these coordinate systems follows a respective principal direction of the illumination radiation 3 within the figure under consideration. The object field 8 has an arc-shaped or semicircular form and is bounded by two arcs, in particular two parallel arcs, especially elliptical arcs, and two straight side edges that extend with a length y0 in the y-direction and are spaced x0 apart in the x-direction. The aspect ratio x0 / y0 is 13 to 1. An inset in Fig. 1 shows a top view of the object field 8, not to scale. One boundary shape 8a is arc-shaped. In an alternative and equally possible object field 8, its boundary shape is rectangular, also with an aspect ratio x0 / y0. During a projection exposure, the reticulum 12 is displaced along an object displacement direction y through the object field 8. The projection optics 10 are only partially and highly schematically indicated in Fig. 1. A numerical aperture 13 on the object field side and a numerical aperture 14 on the image field side of the projection optics 10 are shown. The image field-side numerical aperture 14 can be in the range between 0.2 and 0.8 and can be, for example, 0.3, 0.33, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, or even 0.75. Between the indicated optical components 15, 16 of the projection optics 10, which can, for example, be designed as mirrors reflecting the EUV illumination radiation 3, there are further optical components of the projection optics 10, not shown in Fig. 1, for guiding the illumination radiation 3 between these optical components 15, 16. The projection optics 10 image the object field 8 onto an image field 17 in an image plane 18 on a wafer 19, which, like the reticulum 12, is supported by a holder (not shown in detail). Both the reticulum holder and the wafer holder can be moved in the x- and y-directions via corresponding displacement drives. The wafer holder's footprint is shown in Fig. 1 at 20 as a rectangular box. The footprint 20 is cuboid with dimensions in the x-, y-, and z-directions that depend on the components to be housed within it. For example, the footprint 20 has a length of 1 m in both the x- and y-directions, starting from the center of the image field 17. The footprint 20 also has a length of, for example, 1 m in the z-direction, starting from the image plane 18.The illumination radiation 3 must be guided in the illumination optics 11 and the projection optics 10 in such a way that it is guided past the space requirement 20 in each case. The transmission facet mirror 6 has a plurality of transmission facets 21, which are also referred to as first facets. The transmission facet mirror 6 can be designed as a microelectromechanical system (MEMS), in particular as a MEMS mirror. The transmission facets 21 are individual mirrors switchable between at least two tilting positions and are designed as micromirrors. The transmission facets 21 can be designed as micromirrors that are driven to tilt about two mutually perpendicular tilting axes. Of these individual mirrors or transmission facets 21, a row with a total of nine transmission facets 21 is schematically shown in the yz section of Fig. 2, which are indexed from left to right in Fig. 2 by 211 to 219. In reality, the transmission facet mirror 6 has a considerably larger number of transmission facets 21. The transmission facets 21 are grouped into a plurality of transmission facet groups, which are not shown in detail in Fig. 2. These transmission facet groups are also referred to as individual mirror groups, virtual field facets, or virtual facet groups. Each of the transmission facet groups guides a portion of the illumination radiation 3, also referred to as an illumination radiation partial beam, via an illumination channel to partially or completely illuminate the object field 8. Via this illumination channel and the illumination radiation partial beam 3 guided through it, exactly one illumination specification facet 25 of the illumination specification facet mirror 7 is assigned to each of the individual mirror groups or transmission facet groups. In principle, each of the illumination specification facets 25 can itself be composed of a plurality of individual mirrors. The illumination specification facets 25 are subsequently also referred to as second facets. If the second facet mirror 7 is arranged in the region of a pupil plane of the illumination optics 11, the illumination specification facets 25 are also referred to as pupil facets. A single-mirror group is a group of the single mirrors 21 of the first faceted mirror 6, which are mapped into the object field 8 by the same second facet 25. For further details of possible designs of the transmission faceted mirror 6 and the projection optics 10, reference is made to WO 2010 / 099 807 A . At least some of the illumination control facets 25 can be configured to illuminate only a sub-area or sub-field of the object field 8. These sub-fields can be shaped very individually and also depend on the desired illumination direction distribution (pupil shape) in the object field 8, i.e., the lighting setting. The illumination control facets 25 are therefore illuminated by very differently shaped virtual field facets, whose shape corresponds precisely to the shape of the respective sub-field to be illuminated. Each illumination control facet 25 also contributes to different areas of the pupil depending on its location in the object field 8. The illumination control facet mirror 7 can be designed as a MEMS mirror, particularly if each of the illumination control facets 25 is composed of a plurality of individual mirrors. The illumination control facets 25 are micromirrors that can be switched between at least two tilting positions. The illumination control facets 25 are designed as micromirrors that can be tilted in two dimensions and, in particular, continuously and independently about two mutually perpendicular tilting axes, thus enabling them to be set into a multitude of different tilting positions. An example of a predefined assignment of individual transmission facets 21 to the illumination specification facets 25 is shown in Fig. 2. The illumination specification facets 25 assigned to the transmission facets 211 to 219 are indexed according to this assignment. Based on this assignment, the illumination specification facets 25 are illuminated from left to right in the sequence 256, 258, 253, 254, 251, 257, 255, 252, and 259. The indices 6, 8, and 3 of facets 21 and 25 correspond to three illumination channels 36, 38, and 33, which illuminate the three object field points OF1, OF2, and OF3 (numbered from left to right in Fig. 2) from a first illumination direction. The indices 4, 1, and 7 of facets 21 and 25 correspond to three further illumination channels 34, 31, and 37, which illuminate the three object field points OF1 to OF3 from a second illumination direction. The indices 5, 2, and 9 of facets 21 and 25 correspond to three further illumination channels 35, 32, and 39, which illuminate the three object field points OF1 to OF3 from a third illumination direction. Corresponding illumination beam sub-bundles 31 to 39 are assigned to the illumination channels 31 to 39. The lighting directions assigned to illumination channels 36, 38, 33, 34, 31, 37, and 35, 32, 39 are identical. The assignment of the transmission facets 21 to the illumination specification facets 25 is therefore such that, in the figuratively depicted lighting example, a telecentric illumination of the object field 8 results. The illumination of the object field 8 via the transmission faceted mirror 6 and the illumination setting faceted mirror 7 can be carried out in the manner of a specular reflector. The principle of the specular reflector is known from US 2006 / 0132747 A1. A control device 26, 27 is provided for each of the individual mirrors of the first faceted mirror 6 and the second faceted mirror 7, in particular for controlling the positioning, especially the tilting positions. The control devices 26, 27 can be designed as separate components. They can also be designed as a single component. The control unit 26 includes a storage unit 28 in which partial switching states of the individual mirrors of the first faceted mirror 6 can be stored. The control unit 27 includes a storage unit 29 in which partial switching states of the individual mirrors of the second faceted mirror 7 can be stored. The partial switching states of the individual mirrors can be retrieved from the storage devices 28, 29. This enables a particularly rapid repositioning of the individual mirrors into predefined positions, especially tilt positions. By tilting the individual mirrors of the first faceted mirror 6 and the second faceted mirror 7, the desired illumination characteristics at the reticle 12 can be flexibly adjusted. Each individual micromirror of the first faceted mirror 6 can contribute a portion of the intensity. The sum of all these contributions results in a predetermined illumination at the reticle 12. By appropriately tilting an individual mirror, it is also possible to prevent illumination radiation from that mirror from reaching the reticle 12. This is also referred to simply as switching off the individual mirror. By assigning a specific individual mirror of the first faceted mirror 6 to different individual mirrors of the second faceted mirror 7, the angle of incidence of the illumination radiation at the reticulum 12 of the illumination radiation 3 guided from the individual mirror of the first faceted mirror 6 to the reticulum 12 can be changed. For a fixed arrangement of the second facets, each individual facet on the first mirror module can be assigned a number N of switching states, where N typically lies between 0 and 10. A value of 0 means that this individual mirror has no possibility of illuminating the reticle for the given facet angles of the second mirror module. Most mirrors of the first facet module have only two switching positions: 0 ("off" / beam dump) or 1 (into the reticle). However, for some (K) of these, there are also other tilt positions [2, 3, 4, ... N], so that their image appears further into the reticle's usable field via one of the facets of the second mirror module. The larger the pupillary fill ratio of the reticle illumination pupil, the larger N and, generally, also K. By tilting the individual mirrors of the first faceted mirror 6 and the second faceted mirror 7, the intensity spatial distribution and the intensity angle distribution of the illumination radiation 3 at the reticle 12 can generally be changed. To achieve the required illumination of reticulum 12, an adjustment of the illumination profile may be necessary or desirable from wafer to wafer, and also from wafer location to wafer location. Such an adjustment may be desirable to compensate for fluctuations in the radiation source 2 or other changes. In this case, the individual mirrors of the second faceted mirror 7 do not necessarily need to be repositioned. Since the first faceted mirror 6 has a very large number of individual mirrors, determining an optimized positioning of the individual mirrors of the first faceted mirror 6 requires a high computational effort. This generally leads to a delay and / or a reduction in quality when providing a desired lighting profile. This problem is particularly relevant in the case of a specular reflector, where the field and pupil properties are inextricably linked. The following describes how this problem can be solved. According to the invention, it has been recognized that the time required to set a desired lighting profile can be significantly reduced if the switching positions of the individual mirrors are pre-calculated and stored in the storage device 28 and / or the storage device 29. However, since it is not known in advance which lighting profile is to be set, it is necessary to pre-calculate and store partial switching states of the individual mirrors in such a way that different lighting profiles can be represented as flexibly as possible with the help of these pre-calculated partial contributions. Furthermore, it was recognized that the lighting profiles for this purpose can be decomposed into sub-contributions, in particular additive sub-contributions. This means that it may suffice to pre-calculate the switching states of the individual mirrors in such a way that they are suitable for generating these sub-contributions. For the actual positioning of the individual mirrors, it is sufficient to combine the appropriately scaled basic contributions or basic functions into an overall lighting profile. Since reading and assembling several hundred thousand numerical values ​​from a storage device is still orders of magnitude faster than the time required to solve the optimization problem, this can lead to significant time savings. It has been shown that high-quality pre-computed solutions can be retrieved within microseconds, but at most within milliseconds. It should be noted in general that a partitioning, that is, the subset of individual mirrors assigned to a basis function, does not need to be arranged in a geometrically connected area on the faceted mirror 6 or 7. However, a connected, and in particular a simply connected, arrangement of the individual mirrors of the different partitionings is also not excluded. Preferably, the individual mirrors of different partitions are non-interacting with each other. For example, it is advantageous if the individual mirrors of a certain subset do not cast a shadow on individual mirrors of another subset. Furthermore, it should be noted that lighting profiles do not necessarily have to be decomposed exclusively into additive sub-contributions. Multiplicative decomposition is also possible, especially when different optical elements are processed sequentially. A combination of additive and multiplicative decomposition is also possible. The general idea of ​​the invention, in particular the partitioning approach, will be explained below using an example. In this specific example, an intensity or dose profile is generated or set. However, the idea according to the invention can be applied to essentially any lighting profile. First, it was demonstrated that a desired lighting profile can be set using only a subset of individual mirrors. In a specific case, it was shown that approximately 10,000 individual mirrors could be used to achieve a desired lighting profile with a deviation of less than 0.25%. This corresponded to about 3% of the total number of individual mirrors. The individual mirrors of the first faceted mirror 6 could thus be divided into approximately 30 different subsets or partitions. A possible division of the individual mirrors 21 of the first faceted mirror 6 into four partitions P1, P2, P3 and P6s, as well as a residual set R, is shown by way of example in Fig. 3. As already mentioned, the simple, interconnected arrangement of the individual mirrors 21 is solely for the sake of clarity. It does not need to correspond to the actual distribution of the individual mirrors 21 on the first faceted mirror 6. In schematic Fig. 3, an exemplary lighting profile 30 is shown, here as intensity I across the field coordinate x, i.e., the location in the object field 8 in the cross-scan direction. The decomposition of the lighting profile 30 into four low-frequency components 31, 32, 33, and 34 and a high-frequency remainder 35 is also shown as an example. The ideal decomposition and partitioning naturally depends on the specific system properties. It's important to note that there are significantly more ways to make a field location (x, y) darker than lighter. However, it is advantageous to maintain a minimum system transmission value as a boundary condition for setting a specific lighting profile. This transmission is a valuable performance metric because it directly correlates with the machine's throughput. Ideally, the system transmission should be maximized. At least, the use of partitioning should ideally not lead to a reduction in system transmission that exceeds a predefined limit. Whether this is possible may depend on the specific choice of the system of basic functions. With the worst choice of basic functions, it may be necessary to turn off a large number of mirrors in order to set a specific target profile at a particular field location. Advantageously, the basic functions are chosen in such a way that the target profile at each field point (x, y) can be represented as a sum of partial contributions, in particular non-negative partial contributions. One possible choice of basis functions are the so-called positive polynomials on the interval [-1, 1]: Here, R(x) denotes a remaining residue. An exemplary decomposition of a profile I(x) into this basis up to order 2 and a high-frequency residue 35 is shown in Figures 4A and 4B. Figure 4B illustrates that no negative contributions occur, since the next summed curve never intersects the previous one. For example, c0,1 + c0,2 never intersects c0,1. Once a suitable set of basic functions has been selected, the next step is to determine the subsets of the individual mirrors 21i with which the differently scaled variants, i.e. the multiples of these basic functions, can be set. Under the simplifying assumption that radiation can only be filtered out, i.e., removed, it becomes clear that a larger number of individual mirrors are necessary at the field locations (x, y) where more radiation is to be removed. One way to ensure this is to choose the number of individual mirrors inversely to the basis function fi as a function of the field location x, particularly with a smaller offset. As an offset, a certain excess of mirrors can be provided where the function first becomes 0 or in this vicinity (image size of the micromirror). Next, the solution, that is, the partial switching states of the individual mirrors for setting the basis functions fi(x) scaled with different coefficients, can be determined and stored in a database, in particular in the storage device 28 and / or 29. It is particularly possible to store the data outside the micromirror modules. This is shown schematically in Fig. 1. It was demonstrated that by combining the individual switching states of the disjoint partitions, the required lighting profiles, in particular the required intensity profiles, could indeed be generated. According to a particularly advantageous alternative, the individual mirrors can be divided into partition groups 361, 362, 363. This is illustrated by way of example in Figs. 5A, 5B, 5C and 5D. Theoretically, a separate, individual partitioning could be chosen for each ensemble of basis functions. However, it has been recognized that it is advantageous to solve similar tasks with the same subsets of individual mirrors. Using the same subset of individual mirrors for similar tasks (same coefficient with approximately the same amplitude) allows for iterative correction based on differences. - Derive the desired difference - Set the desired difference - Remeasure → a smaller difference remains - Set this smaller difference as the desired value - ... This is because the errors in the partition used, which are responsible for the small difference between prediction and reality, remain constant. This approach has been shown to converge. In particular, it is very fault-tolerant. Figures 5A to 5D illustrate the possibility of hierarchical grouping. For example, for the basis functions f0,1(x), the values ​​of the coefficient a0,1 in the interval from 0% to 0.5% can be realized with the same subset of micromirrors. This means that the subset of micromirrors remains the same, but multiple solutions for different values ​​of the coefficient a0,1 from the interval 0% to 0.5% are stored. For the partitions Pi, solutions for the basis function fi(x) with coefficients ai equal to 0,1, 0,2, 0,3,... 0,5 are available. Here, the switching state of the individual mirrors is schematically shown by an integer sequence 371, 372, 373 within a partition. If, for example, not all second-order basis functions are needed to represent a desired intensity profile—for instance, if the basis functions f0,2(x) are not required while f1,2(x) is scaled with a large coefficient a1,2—it would be useful to choose a partitioning that takes precisely this into account. Figures 5A, 5B, 5C, and 5D illustrate this idea by showing different partitionings, each with partitions P1, P2, P3, and P4, respectively. A procedure for retrieving a previously calculated solution is shown schematically and by way of example in Fig. 6. In a first procedure step 38, the target profile is decomposed into basis functions, or represented by a given set of basis functions. A set of coefficients 39 is provided for this purpose. In selection step 40, the group of basis functions (partition group) is selected. The distribution of the magnitudes of the coefficients is taken into account here. In a further selection step 41, the switching states within each subset are then selected by comparison with the value of the coefficient. Then, in a further step 42, the partial switching states are combined to form an overall switching state, in particular an overall switching state vector. This overall switching state vector can be provided by the control device 26 and / or 27. It is also possible that verification steps, such as follow-up measurements, may take place after step 42 to check whether the desired lighting profile was satisfactorily achieved in step 42. As an alternative to positive polynomials, locally limited functions, such as triangular functions (Fig. 6) or Gaussian / delta-like distributions (Fig. 7), can also be chosen as basis functions. Such locally limited basis functions are also referred to as virtual Unicom fingers. "Unicom" refers to a finger-wiper system for reducing light at the upper and / or lower edge of scan profiles (y-dependent intensity distribution). For details, see US 7,362,413 B2. Further such uniformity correction modules are described in DE 10 2008 001 553 A1 and US 9,310,692 B2. When selecting the basic functions, the geometric specifications of the lighting system, in particular the arrangement and / or dimensions of the individual mirrors, especially the first faceted mirror 6, can also be taken into account. This can lead, for example, to basic functions such as those shown in Fig. 8. Such "native" basic functions can be generated as follows: 1. Select a typical length scale in the object field (natural correction limit, e.g., 0.8 mm, on the order of a single mirror image). 2. Rasterize the object field using this length scale. 3. Assign micromirrors to these intervals in pairs, disjointly spaced around their (energetic) image intensity center. 4. This yields the maximum correction capability, the greatest amplitude of the virtual Unicom finger. 5. Generate weaker versions (lower amplitudes) of each of these Unicom fingers by switching off some of the assigned mirrors. Further aspects of the invention are explained in point form below. New solutions, especially new partial switching states, can be predefined whenever a new lighting setting is applied. This might be the case when a completely new lighting setting is to be implemented, or when changes have been made to the lighting system. When assigning individual mirrors to the different basic functions, it can be advantageous to leave a residual set of individual mirrors, meaning those not assigned to any basic function. This residual set of individual mirrors can be used to approximate the remaining frequency, particularly a high-frequency residue, when a lighting profile is represented by the basic functions. An optimization procedure can be used to determine the positioning of the individual mirrors in this residual set. Since the number of individual mirrors in the residual set is significantly smaller than the total number of individual mirrors, the time required to perform the optimization procedure is considerably less than that needed to optimize a larger number, especially the total number of individual mirrors. The expectedly lower amplitude of the residual set also aids in optimization, particularly because it results in a smaller number of degrees of freedom. In determining the partial switching states for each individual partition, an optimization of the transmission can preferably be taken into account under the boundary condition of a maximum deviation of 1%, in particular a maximum of 0.5%, in particular a maximum of 0.3%, in particular a maximum of 0.2%, in particular a maximum of 0.1% from the target profile. Alternatively, optimization can also be performed for a small deviation from the target profile under the boundary condition of a transmission loss of a maximum of 10%, in particular a maximum of 5%, in particular a maximum of 3%, in particular a maximum of 2%, in particular a maximum of 1%. Advantageously, especially with regard to the stability of the solution, partial switching states that are as similar as possible are used, particularly for different adjacent and / or similar coefficient values. The coefficient values ​​ai can be rasterized into uniform or non-uniform steps. To represent the lighting profile using basic functions from a selected set of basic functions, the coefficients can first be determined as floating-point numbers. The determined floating-point values ​​can then be rounded to the nearest coefficient values. These can then be read from a database, in particular from storage device 28 and / or 29. The partial solutions can then be combined to form the overall switching state. This can be sent to the control unit 26 and / or 27. Using the control unit 26 and / or 27, the lighting profile can then actually be adjusted, meaning that the individual mirrors 21i can be moved to the predetermined positions. This is possible within a time period of at most 50 ms, in particular at most 30 ms, in particular 26 ms, in particular at most 10 ms. To fabricate a microstructured component, in particular a highly integrated semiconductor device, for example a memory chip, using the projection exposure system 1, the reticle 12 and the wafer 19 are first prepared. Subsequently, a structure on the reticle 12 is illuminated with the illumination optics 11 using the illumination light 3 and projected onto a photosensitive layer on the wafer 19 using the projection optics of the projection exposure system 1. Development of the photosensitive layer then creates a microstructure on the wafer 19, resulting in the micro- or nanostructured component. The component produced can be a microchip, in particular a memory chip. In this process, when projecting the structures of the reticle 12 onto the wafer 19, the positioning of the individual mirrors 21 can be switched in a simple way, and in particular very quickly, by specifying predetermined partial switching states which are read from the storage device 28 and / or 29. QUOTES INCLUDED IN THE DESCRIPTION This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature US 2006 / 0132747 A1 [0012, 0122]EP 2 689 282 A2

[0013] WO 2010 / 099 807 A

[0116] US 7,362,413 B2

[0172] DE 10 2008 001 553 A1

[0172] US 9,310,692 B2

[0172]

Claims

Method for determining the positioning of individual mirrors of a faceted mirror (6) of an illumination optic (11) of a projection exposure system (1) comprising the following steps: 1.

1. Providing at least one calibrated model of an illumination system for a projection exposure system (1) with 1.1.

1. an illumination optic (11) with a faceted mirror (6) with a plurality of individual mirrors and 1.1.

2. a radiation source (2) for generating illumination radiation (3), 1.

2. Specifying a set of basis functions (fi), 1.

3. Assigning subsets of the individual mirrors to different basis functions, 1.3.

1. wherein the subsets of the individual mirrors assigned to the different basis functions form pairwise disjoint individual mirror partitions, 1.

4. Determining partial switching states of the individual mirrors of the individual mirror partitions to generate real multiples of the basis functions as partition contributions, 1.5.Storing the partial switching states of the individual mirrors in a database (28, 29). Method according to claim 1, characterized in that a subset of the individual mirrors are not assigned to any of the basis functions (fi). Method according to one of the preceding claims, characterized in that a plurality of different sets of basis functions (fi) are specified. Method according to claim 3, characterized in that all partition contributions have the same sign. Method according to one of the preceding claims, characterized in that positive polynomials, triangular functions, Gaussian functions or δ-functions, or their approximations, serve as basis functions (fi). Method according to one of claims 1 to 5, characterized in that at least one of the basic functions (fi) is assigned different subsets of the individual mirrors. Method according to one of the preceding claims, characterized in that the partitioning of the individual mirrors into subsets is carried out in such a way that different subsets are assigned to different basis functions (fi), but the same subset is used to generate the partial contribution (aifi(x)) of a specific basis function (fi(x)). Method according to one of the preceding claims, characterized in that lighting profiles (30) are decomposed into partial amounts belonging to basic functions (fi), wherein a high-frequency residue (35) remains after decomposition of the lighting profiles (30) into partial contributions (31 to 34). Method according to one of the preceding claims, characterized in that at least some of the subsets have between 1000 and 100000 individual mirrors. Method according to one of the preceding claims, characterized in that the lighting profiles (30) are each divided into two to 20 sub-contributions. Method according to one of the preceding claims, characterized in that the illumination optics (11) has a second faceted mirror (7) with a plurality of individual mirrors and partial switching states of the individual mirrors of the second faceted mirror (7) are determined for the partial switching states of the individual mirrors of the subsets of the first faceted mirror (6). Method according to one of the preceding claims, characterized in that the illumination profiles (30) describe the course of one of the following parameters: intensity of the illumination radiation (I(x)) or I(x,y), polarization(x), telecentrias Tx(x), Ty(x), structure-dependent quantities as a function of the x,y-field coordinate, and / or, for example, the critical dimension) of the smallest structure (CD(x), CD(y), CD(x,y).] Method according to one of the preceding claims, characterized in that a sequence of different switching states of the individual mirrors is determined and stored. Lighting system for a projection exposure system (1) comprising 14.

1. a lighting optic (11) with a faceted mirror (6) with a plurality of individual mirrors, 14.

2. a radiation source (2) for generating illumination radiation (3) and 14.

3. a control device (26) for controlling the positioning of the individual mirrors for setting different illumination profiles (30), 14.

4. wherein the control device (26) has a storage device (28) for storing partial switching states of subsets of the individual mirrors for generating partial contributions of illumination profiles (30). A method for positioning individual mirrors of a faceted mirror (6) of a projection exposure system (1) comprising the following steps: 15.

1. Providing a lighting system according to claim 14, 15.

2. Specifying a lighting profile (30), 15.

3. Decomposing the lighting profile (30) into sub-contributions (31 to 34), 15.

4. Generating the sub-contributions (31 to 34) of the lighting profile by positioning predetermined subsets of the individual mirrors, 15.

5. wherein partial switching states of the individual mirrors are retrieved from a memory (28) for positioning the subsets of the individual mirrors. Projection exposure system (1) with 16.

1. a lighting system according to claim 14 and 16.

2. a projection optic (10) for transferring illumination radiation (3) from an object field (8) of the lighting optic (11) to an image field (7).

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