Method for producing an optical system for a lithography system, substrate for an optical component of a lithography system, and lithography system

Abstract

A method for producing an optical system (100) for a lithography system (1), wherein the optical system comprises an optical component (102) with a substrate (104) cut out of a raw block (200), comprising the steps: a) Providing (S2) a distribution function (g) of a zero crossing temperature (ZCT R ) a thermal expansion coefficient (a R ) of the ingot as a function of a location (p) of the ingot, wherein the distribution function with respect to an axis of symmetry (A) of the ingot corresponds to a rotationally symmetric pattern (218) of the zero-crossing temperature, b) computer-implemented determination (S3) of an imaging error (F i ) of the optical system, for the provided distribution function and each of several different positions (P i) of a cutting area (D) of the ingot, wherein the plurality of positions of the cutting area are located with respect to a radial position (r i ) and / or a height position (h i ) of the ingot differ from each other, and c) Determining (S4) at least one selection position (P a ) of the cutting area (D) than that of the plurality of positions (P i ), for which the determined aberration (F i ) is less than a predetermined threshold value (SW).

Description

The present invention relates to a method for producing an optical system for a lithography apparatus, to a substrate for an optical component of the optical system of the lithography apparatus and to a lithography apparatus having such a substrate.Microlithography is used for producing microstructured components, such as integrated circuits. The microlithography process is carried out with a lithography apparatus which has an illumination system and a projection system. The image of a mask (reticle) illuminated by means of the illumination system is projected by means of the projection system onto a substrate, for example a silicon wafer, coated with a photosensitive layer (photoresist) and arranged in the image plane of the projection system, in order to transfer the mask structure to the photosensitive coating of the substrate.Driven by the desire for smaller and smaller structures in the production of integrated circuits, EUV lithography apparatuses are currently being developed which use light with a wavelength in the range from 0.1 nm to 30 nm, in particular 13.5 nm. Since most materials absorb light of this wavelength, reflective optics, i.e. mirrors, must be used in such EUV lithography apparatuses instead of refractive optics, i.e. lenses, as before.A problem occurring in this case is that the mirrors heat up as a result of absorption of the radiation emitted by the EUV light source. This may result in thermal deformation of the mirrors. Furthermore, an optical coating of the mirrors can also degrade as a result of a temperature increase. Both thermal deformations of the mirrors and damage to their optical coatings can impair the imaging properties of the mirrors.The imaging quality of a projection system of an EUV lithography apparatus depends to a large extent on the quality of the mirror material. In order to reduce aberrations by heating the mirrors, a material having a very low coefficient of thermal expansion is used for mirror substrates. In particular, at the so-called zero crossing temperature of the thermal expansion coefficient of the mirror material, a deformation of the mirror material as a function of a temperature increase is minimal and / or zero. The average zero crossing temperature of the mirror material as well as variations in the zero crossing temperature within the mirror substrate volume have a direct influence on aberrations caused by mirror heating.Against this background, it is an object of the present invention to provide an improved method for producing an optical system for a lithography apparatus and an improved substrate for an optical component of an optical system of the lithography apparatus.According to a first aspect, a method for producing an optical system for a lithography apparatus is proposed. The optical system includes an optical component having a substrate cut from a ingot. Furthermore, the method comprises the steps: a) providing a distribution function of a zero crossing temperature of a coefficient of thermal expansion of the ingot as a function of a location of the ingot, wherein the distribution function is rotationally symmetrical with respect to an axis of symmetry of the ingot, b) computer-implemented ascertaining an imaging error of the optical system, for the provided distribution function and each of a plurality of mutually different positions of a cut-out region of the ingot, wherein the plurality of positions of the cut-out region differ from one another with respect to a radial position and / or a height position of the ingot, and c) ascertaining at least one selection position of the cut-out region as that of the plurality of positions for which the ascertained imaging error is less than a predetermined threshold value.The method makes it possible to cut out an area from the blank according to the determined cut-out area and to produce a substrate of an optical component therefrom. In particular, the method determines a cut-out region of the ingot which has an advantageous distribution of the zero crossing temperature. As a result, with the method, a distribution of the zero crossing temperature within the substrate-within the scope of the distribution of the zero crossing temperature specified by the ingot-can be adjusted in a targeted manner. As a result, aberrations of the optical system due to thermal expansion of the substrate can be reduced.A substrate material of an optical component usually has inhomogeneities which lead to an inhomogeneous distribution of the zero crossing temperature over the substrate volume. This is true even for a high performance substrate material. The inhomogeneous distribution of the zero crossing temperature has an influence on the imaging properties of the optical component and thus of the optical system with the optical component.The proposed method now makes it possible to determine a favorable and / or optimum cut-out region for the substrate of an optical component of a lithography apparatus for a predefined distribution of the zero crossing temperature over the volume of the ingot. Thermal deformations caused by heat inputs into the optical component (e.g. by irradiation with EUV light) and associated worsening of the imaging properties can thus be reduced or avoided.The lithography apparatus can be an EUV lithography apparatus. EUV stands for "extreme ultraviolet" and denotes a wavelength of the working light between 0.1 nm and 30 nm. The lithography apparatus can also be a DUV lithography apparatus. DUV stands for deep ultraviolet and denotes a wavelength of the working light between 30 nm and 250 nm.The optical system is, for example, a projection system of the lithography apparatus. However, in other examples, the optical system can also be an illumination system of the lithography apparatus (projection exposure apparatus).The optical component of the optical system has, in particular, an optically active surface and the substrate.The optical component is, for example, a mirror and the substrate is a mirror substrate. In particular, in this case the optically active surface is a reflecting surface.The substrate is cut out of the ingot in particular as one piece (in one piece).The coefficient of thermal expansion (coefficient of thermal expansion) indicates a change in the geometric shape and dimensions of a material upon a temperature change. The coefficient of thermal expansion is, for example, a linear coefficient of thermal expansion that indicates a change in length of a material as a function of a temperature change.The material of the ingot (and thus of the substrate to be produced from the ingot) is in particular a material with a very low coefficient of thermal expansion. For example, at a desired operating temperature, the coefficient of thermal expansion is within a range of + / -20 ppb / K (parts per billion per kelvin), + / -15 ppb / K, + / -10 ppb / K, and / or + / -5 ppb / K. However, the coefficient of thermal expansion may also be within another range. In such a material with very low thermal expansion, changes in the geometric shape and the dimensions due to temperature changes occur only to a very small extent.Examples of the material of the ingot (and thus of the substrate to be produced from the ingot) include quartz glass, titanium-doped quartz glass and a glass ceramic. For example, the ingot material is an ultra-low thermal expansion material (e.g., a substrate material sold under the designation "ULE" for "Ultra-Low Expansion" by Corning Inc.). For example, the material of the ingot comprises a glass material of TiO 2- SiO 2 in which the ultra low thermal expansion coefficient is realized by varying the concentration of TiO 2. Another example is a crystalline phase Li 2 O 2- Al 2 O 3- SiO 2- glass ceramic (marketed under the name "Zerodur" by Schott), in which the ultra-low coefficient of thermal expansion is realized by uniformly distributed nanocrystals in a residual glass phase.The coefficient of thermal expansion is itself temperature-dependent, i.e. a temperature-dependent function. The coefficient of thermal expansion may have a so-called zero crossing temperature (ZCT). At the zero crossing temperature, the thermal expansion coefficient of a material has a zero crossing in its temperature dependence, in the vicinity of which no or only negligible thermal expansion of the material takes place upon a temperature change.The ingot is produced, for example, in a direct separation process or in a soot process. The ingot is produced, for example, by depositing glass material from one or more burners onto a rotating ingot.The material builds up in layers, while the existing ingot rotates rapidly. As a result, inhomogeneities are smeared and as a result a rotationally symmetrical distribution of the inhomogeneities is formed.The distribution function of the zero-cross temperature of the ingot corresponds to, for example, a distribution function of a material composition of the ingot such as a titanium content or an OH content.The distribution function of the zero-crossing temperature of the ingot indicates, for example, a value of the zero-crossing temperature for each location of the ingot, i.e. for each volume element of the ingot.The distribution function of the zero crossing temperature is, in particular, a three-dimensional distribution function.The ingot has a rotationally symmetric distribution function of the zero crossing temperature. In particular, the ingot has the axis of symmetry, which is an axis of symmetry with respect to rotation. In particular, the distribution function of the zero crossing temperature of the ingot is mapped onto itself for rotations at any angles about the axis of symmetry. It can also be said that the distribution function with respect to the axis of symmetry of the ingot has a rotationally symmetric pattern of zero crossing temperature.For example, the ingot itself is also rotationally symmetrical, so that the ingot is mapped onto itself as a rotational body for rotations through any angles about the axis of symmetry.The ingot is in particular a material blank for producing the substrate.The cut-out region is in particular a three-dimensional cut-out region of the ingot. The cut-out region has, for example, a cuboid shape. However, the cut-out region can also have a different geometric shape. The same may apply in embodiments to the later mentioned one or more deviating cut-out areas.In order to determine the aberration of the optical system, different positions of a cut-out region are provided. It can also be said that different cut-out areas are provided therewith, wherein the different cut-out areas differ only in their position within the ingot. However, a shape (e.g., geometric shape) and a volume of the different cut-out areas do not differ from each other.A radial position of the ingot is in particular a radial position within the ingot. A height position of the ingot is in particular a height position within the ingot.A respective position of the cut-out region has, for example, a central position (e.g. a center point and / or geometric center point) of the cut-out region. A respective position of the cut-out region can alternatively or additionally also have positions of outer boundaries, outer edges and / or an outer shape of the cut-out region, for example. The same can apply in embodiments to the later mentioned one or more deviation positions and associated deviation cut-out area(s). In this respect, the respective or corresponding position and optionally deviation position of the cut-out region or deviation cut-out region can be defined as a point group or a vector or comprise such a point group or such a point group.The determination of the respective imaging error (and optionally deviating imaging error) of the optical system based on the different positions of the cut-out region (and optionally deviating positions of the deviating cut-out region) is carried out, for example, with the aid of a computer-assisted simulation. Furthermore, the distribution function of the zero crossing temperature of the ingot provided in step a) and each of the plurality of provided positions of the cut-out region (and optionally deviation positions of the deviation cut-out region) of the ingot which are different from one another form input parameters of the simulation calculation. For each combination of the provided distribution function of the zero crossing temperature and the provided positions of the cut-out region (and optionally deviation positions of the deviation cut-out region), an aberration is determined. The determined aberrations (and, if appropriate, deviation aberrations) form, in particular, output parameters of the simulation calculation.Step a) and / or step c) is / are also carried out, for example, in a computer-implemented manner. For example, steps a), b) and / or c) are performed by a control device, e.g., a control device of one or more computers.In embodiments, in particular in or before step c), the predetermined threshold value is provided on a data memory of the control device or in a network (e.g. a cloud) in or to which the control device is connected or connectable in a data-communication manner. The predetermined threshold value may be determined or calculated before it is provided depending on one or more properties of the optical system, the lithography apparatus and / or the wafer to be produced with the lithography apparatus.In embodiments, in step c) a plurality of selection positions of the cut-out region (and optionally of the deviating cut-out region) are determined, for example more than 1, 2, 5 or 10 selection positions, wherein the imaging error determined for each selection position is less than the predetermined threshold value.If in step c) more than one selection position of the cut-out region is determined for which the determined aberration is less than the predetermined threshold value, then a substrate can be cut out from the ingot according to each of the plurality of determined selection positions.If in step c) no selection position of the cut-out region is determined for which the determined aberration is less than the predetermined threshold value, then it can be determined, for example, that the ingot is not suitable for producing a substrate.If the respective ascertained imaging error (and, if appropriate, deviation imaging error) has, for example, a focus error of the imaging (i.e. a deviation of an actual focus of the optical system from a setpoint focus), then the threshold value is, for example, 15 nm or less, 10 nm or less and / or 5 nm or less.If the respective ascertained imaging error (and, if appropriate, deviation imaging error) has, for example, an overlay error of the imaging (i.e. a deviation of an actual position of an object imaged with the aid of the optical system in an image in an image plane of the optical system from a setpoint position), then the threshold value is, for example, 3 nm or less, 1 nm or less and / or 0.5 nm or less.If the respective determined aberration (and optionally deviation aberration) has, for example, a spherical wavefront error of the imaging (i.e. a deviation of an actual wavefront of a beam guided by the optical system from an ideal spherical wave), the threshold value is, for example, 200 pm or less, 100 pm or less and / or 50 pm or less (RMS deviation).In embodiments of the first aspect, more than one distribution function of the zero crossing temperature of the ingot can also be applied as input parameters for determining the respective aberration, wherein the plurality of distribution functions of the zero crossing temperature of the ingot differ from one another by an offset of the mean zero crossing temperature of the distribution function. In other words, a distribution function of the zero crossing temperature of the ingot may be determined (e.g. measured) having a first average zero crossing temperature. Furthermore, one or more further distribution functions of the zero crossing temperature of the ingot can be determined in such a way that they emerge from the first distribution function of the zero crossing temperature by addition or subtraction of an offset of an average zero crossing temperature.According to one embodiment of the first aspect, in step c), an optimum position of the cut-out region is determined as that of the plurality of positions for which the determined aberration is minimal.The position of the cut-out region can thus be determined even better.For example, a plurality of selection positions of the cut-out region can first be determined. Then, the one of the plurality of selection positions for which the detected aberration is minimum can be determined as the optimum position.According to a further embodiment of the first aspect, the cut-out region is free of the axis of symmetry.That is, the cut-out region does not include the axis of symmetry. In other words, outer edges of the cut-out region do not intersect with the axis of symmetry of the ingot. In particular, none of the outer edges of the cut-out region coincides with the axis of symmetry of the ingot.As a result, a region of the axis of symmetry of the ingot in which inhomogeneities (i.e. fluctuations) of the zero crossing temperature are particularly large can be avoided for the cut-out region of the substrate of the optical component.Moreover, it can be achieved that the substrate cut out according to the determined cut-out area has a distribution function of the zero-crossing temperature of the coefficient of thermal expansion as a function of the location of the substrate with an advantageous pattern. In particular, the pattern of the zero crossing temperature of the substart has only concentric ring sections (which are respectively partial sections of a full ring) but not full rings. Furthermore, the concentric ring sections have exclusively concave or exclusively convex curvatures, as seen from an outer edge of the substrate.The deviation cut-out regions mentioned later herein can also be free of the axis of symmetry.According to a further embodiment of the first aspect, the ingot has a cylindrical shape with a cylinder axis corresponding to the axis of symmetry and a lateral surface. In addition, the radial position of the ingot is a position along a radial direction of the ingot, wherein the radial direction extends from a radius equal to zero at the axis of symmetry to an outer radius (greater than zero) at the lateral surface.The cylindrical shape has in particular two opposing end faces (base surfaces) which are connected to one another by the lateral surface. The two opposing end faces are arranged, for example, parallel to one another.The cylindrical shape is in particular the shape of a straight circular cylinder. The two opposing end faces are then in each case circular surfaces.According to a further embodiment of the first aspect, the plurality of positions of the cut-out region each have a radius greater than zero.That is, the cut-out region does not include the axis of symmetry at which the radius of the ingot is zero.For example, the entire cut-out region (i.e. also the positions of all its outer edges) has a radius greater than zero.The deviation positions of the deviation cut-out region mentioned later herein can also each have a radius greater than zero.According to a further embodiment of the first aspect:covering the plurality of positions of the cut-out region a radius region of the ingot from an inner radius adjacent to the axis of symmetry to an outer radius in the case of a lateral surface of the ingot, and / orThe plurality of positions of the cut-out region cover a height region of the ingot from a first end face to a second end face of the ingot.Consequently, for the determination of the aberrations of the optical system, positions of the cut-out region are taken into account which cover the entire radius of the blank with the exception of the axis of symmetry itself, at which the radius is equal to zero, and / or which cover the entire height of the blank.According to a further embodiment of the first aspect:the ingot has first, second and third directions,the third direction is arranged along the axis of symmetry of the ingot,the first and second directions are arranged perpendicular to one another and in each case perpendicular to the axis of symmetry, andThe plurality of positions of the cut-out region differ from one another with respect to the radial position and / or the height position of the ingot and with respect to a rotation about the first, second and / or third direction.As a result, one or more rotational degrees of freedom with respect to the first, second and / or third direction of the ingot can also be taken into account for determining the optimum cutting-out region (i.e. the optimum position of the cutting-out region).The applicant has found that imaging aberrations of the optical system with the substrate produced in this way can be reduced by up to 30 to 40% for specific cases of use.The first and second directions are each arranged parallel to a radial direction of the ingot, wherein an azimuth angle between the first and second directions is 90 degrees. The third direction corresponds in particular to the axis of symmetry.According to a further embodiment of the first aspect:determining, for each of the plurality of mutually different positions of the cut-out region, in addition to the aberration for the corresponding position of the corresponding cut-out region, also one or more deviating aberrations from one or more deviating positions of the cut-out region,the one or more deviation positions are selected such that one or more deviation cut-out areas defined thereby lie within a tolerance range around the corresponding cut-out area defined by the corresponding position, anddetermining the at least one selection position of the cut-out region as that of the plurality of positions for which the determined aberration and the one or more determined deviating aberrations are each less than the predetermined threshold value.By ascertaining and taking into account the imaging errors not only for a specific position of the cut-out region, but additionally for one or more deviating positions belonging to the specific position, inaccuracies during the later cutting out of the substrate (e.g. on account of tolerances of the cutting tool) can be taken into account in accordance with the ascertained selection position and / or the ascertained optimum position.The respective tolerance range comprises, for example, the corresponding cut-out region.The respective tolerance range is, for example, 0.01% or more, 0.1% or more, 1% or more and / or 3% or more greater than the corresponding associated cut-out region. The respective tolerance range can additionally or instead also be larger (e.g. in each spatial direction) by 1 mm or more, 5 mm or more and / or 10 mm or more than the corresponding associated cut-out region, for example.The respective tolerance range has, for example, the same geometric shape as the corresponding associated cut-out region and is only enlarged to scale in comparison with the corresponding associated cut-out region. The respective tolerance range and the corresponding associated cut-out range have in particular the same central position (e.g. the same centre point and / or the same geometric centre point).According to a further embodiment of the first aspect:the ingot has first, second and third directions,the third direction is arranged along the axis of symmetry of the ingot,the first and second directions are arranged perpendicular to one another and in each case perpendicular to the axis of symmetry, andThe one or more deviating positions differ from the corresponding position of the corresponding cut-out region in relation to:the radial position,the height position,a displacement in the first, second and / or third direction,a rotation about the first, second and / or third direction,non-parallel edges of the deviating cut-out region in the first, second and / or third direction, respectively, and / ora volume deviation of the one or more deviating cut-out areas from the corresponding cut-out area defined by the corresponding position.According to a further embodiment of the first aspect, in the computer-implemented determination of the respective aberration of the optical system, an error range of the determined aberration is additionally determined, and the at least one selection position of the cut-out range is determined as that of the plurality of positions for which the determined aberration including its error range is less than the predetermined threshold value.By considering the error range of the aberration, the selection position of the cut-out area can be determined even better. In particular, it can be ensured that the ascertained imaging error is also smaller than the predetermined threshold value in the region of its error boundaries.According to a further embodiment of the first aspect, the respective aberration is determined with the aid of a computer-assisted simulation, and the error range of the determined aberration is determined on the basis of one or more error ranges of one or more input parameters of the simulation.It can thus be taken into account that input parameters of the simulation can be error-prone.According to a further embodiment of the first aspect, the error range of the ascertained aberration is ascertained on the basis of an error range of the provided distribution function of the zero crossing temperature.The error range of the provided zero crossing temperature distribution function comprises, for example, zero crossing temperature error limits for each ingot location. The error range of the provided distribution function of the zero crossing temperature can also comprise, for example, a deviation of the distribution function of the zero crossing temperature from a rotationally symmetrical distribution function.According to a further embodiment of the first aspect, the respective aberration is determined with the aid of a computer-assisted simulation, and the error range of the determined aberration is determined on the basis of the consideration of one or more systematic errors of the simulation.Systematic errors of the simulation include, for example, errors due to interpolation of data processed in the simulation calculation. Systematic errors of the simulation can also include, for example, deviations which arise through the selection of computing rules of the simulation.According to a further embodiment of the first aspect, the determination of the respective aberration of the optical system comprises:determining a plurality of mutually different individual errors with respect to mutually different types of errors of the optical system, anddetermining the respective imaging error of the optical system based on the plurality of determined individual errors.The embodiments and features described herein of determining the respective imaging error based on the plurality of determined individual errors may optionally also apply to determining respective deviating imaging errors.For example, a plurality of mutually different relative individual errors are determined with respect to the mutually different types of errors of the optical system. Furthermore, for example, the respective aberration (and, if appropriate, deviation aberration) of the optical system is determined as a maximum, an average value, a median and / or a quantile of the plurality of determined relative individual errors.For example, the at least one selection position of the cut-out region in step c) can also be determined as that of the plurality of positions for which each of the plurality of determined individual errors is less than a corresponding predetermined individual threshold value for the corresponding type of error.The plurality of individual errors that are different from one another have, in particular, error values for different types of individual errors.By taking into account different types of individual errors of the imaging of the optical system, the final error of the imaging of the optical system for the provided distribution function and each provided position of the cut-out region can be determined even better.In addition, for the provided distribution function and each position of the cut-out region taken into account, for example, the maximum, the mean value, the median and / or the quantile of the plurality of individual errors determined is calculated and then the final error of the mapping of the optical system is taken as this maximum, this mean value, this median and / or this quantile. As a result, large contributions of errors can be taken into account better.In embodiments, the plurality of determined individual errors are weighted according to predetermined weights. As a result, the individual errors can be weighted with this component depending on a planned use of the optical component to be produced and of the optical system. Thus, error contributions of performance parameters that are particularly important for a specific application of the optical component / of the optical system can be kept selectively small.According to a further embodiment of the first aspect, the plurality of individual errors that are different from one another are determined with respect to the different types of errors and with respect to different setting parameters of an illumination of the optical component of the optical system to be produced.Thus, different setting parameters of the planned illumination of the optical component to be produced are taken into account in the computer-implemented determination of the individual errors. Consequently, the different types of single errors can be determined for different simulated illumination scenarios of the optical component to be produced.The various setting parameters of the planned illumination of the optical component to be produced have, for example, a radiation intensity of a working light (e.g. EUV light) which is radiated onto the optical component.The various illumination setting parameters may also include, for example, a pattern in which the working light is irradiated to the optical component (e.g., X dipole, Y dipole, ring shape, circular shape, DRAM profile, stripe pattern, irregular pattern, etc.). In other words, the illumination adjustment parameters may have a heat flux distribution with heat flux poles caused by working light irradiated on the optical component to be manufactured in a specific pattern.The various illumination setting parameters may also have, for example, a structure of a mask (e.g. lithography mask), which is imaged onto a wafer in the image plane of the optical system with the aid of the optical component to be produced.According to a further embodiment of the first aspect, the plurality of determined individual errors with respect to the different types of errors have:a deviation of an actual focus of the optical system from a setpoint focus,a deviation of an actual position of an object imaged in an image plane of the optical system with the aid of the optical system from a setpoint position of the imaged object,an image shift of an image imaged in an image plane of the optical system with the aid of the optical system, and / ora deviation of an actual wavefront, which images an image in an image plane of the optical system, from a setpoint wavefront.The individual errors are determined in particular in a computer-implemented manner, e.g. based on a simulation of an imaging with the optical system to be produced.The image displacement is, for example, a displacement of the image relative to a desired position of the image. The image shift is, for example, a shift of the image in a direction parallel to the image plane of the optical system.The image imaged in an image plane of the optical system is, for example, an image imaged on a wafer of the lithography apparatus.The actual wavefront is in particular the wavefront of a beam guided by the optical system. The actual wavefront is, for example, the wavefront of the beam at the location of the image plane.The desired wavefront is, for example, a spherical wave. The deviation of the actual wavefront from the desired wavefront is, for example, a deviation from an ideal spherical wave.According to a further embodiment of the first aspect:the deviation of the actual wavefront from the setpoint wavefront has a tilt of the wavefront, a displacement of the wavefront, an astigmatism of the wavefront, a coma of the wavefront, a multiple ripple of the wavefront and / or a spherical aberration of the wavefront, and / orThe deviation of the actual wavefront from the desired wavefront is quantified in the form of Zernike polynomials.The tilt of the wavefront is, for example, a tilt about an axis (e.g. x- and / or y-axis) which is arranged parallel to the image plane of the optical system.The displacement of the wavefront is, for example, a displacement parallel to the image plane of the optical system (e.g. in the x- and / or y-direction).The multi-ripple is, for example, a three-ripple, four-ripple, five-ripple, six-ripple, etc. of the wavefront.With the aid of Zernike polynomials, a deviation of a real wavefront from an ideal wavefront can be mathematically represented by a sum of polynomials. Zernike polynomials are represented using polar coordinates in a normalized unit circle. Mathematically, the individual Zernike polynomials of a circular surface are characterized by polar coordinates with a power series in the radial direction ρ and a Fourier-like series in the direction of the angle θ. In the general form Z n,±m, n indicates the atomic number of the polynomial in the radial direction, and m corresponds to the frequency of the angle θ per revolution. Polynomials with even-numbered n and m=0 are rotationally symmetrical, all remaining angle-dependent.For example, the Zernike polynomial Z 1 ±1 describes a tilt (+1 in the x direction, -1 in the y direction), the Zernike polynomial Z 2.0 describes a focus error (spherical error), the Zernike polynomial Z 2 ± 2 describes an astigmatism, the Zernike polynomial Z 3 ±1 describes a coma, the Zernike polynomial Z 3 ± 3 describes a three ripple, the Zernike polynomial Z 4.0 describes a spherical aberration and the Zernike polynomial Z 4 ± 2 describes an astigmatism of 4th order.According to a further embodiment of the first aspect, the method comprises the steps of:providing the ingot, andmeasuring the distribution function of the zero crossing temperature of the ingot.The distribution function of the zero crossing temperature is measured in particular for the entire volume, i.e. all positions, of the ingot.When measuring the distribution function of the zero crossing temperature of the ingot, an error range of the distribution function of the zero crossing temperature can also be determined.According to a further embodiment of the first aspect, the method comprises the steps of:providing the ingot, andcutting the substrate out of the ingot according to the at least one determined selection position of the cutting region and / or the determined optimum position of the cutting region.In particular, the ingot is physically provided. In addition, the ingot is provided in particular before step a).The substrate is cut out of the ingot in particular as one piece (i.e. in one piece).According to a second aspect, a substrate for an optical component of an optical system of a lithography apparatus is proposed. The substrate has a distribution function of a zero-cross temperature of a coefficient of thermal expansion as a function of a location of the substrate. In addition, the distribution function has a zero crossing temperature pattern which has a plurality of concentric ring portions, each of which is partial portions of a full ring.The respective full rings are in particular circular rings.According to an embodiment of the second aspect:an auxiliary line of the substrate is defined such that it is arranged perpendicular to mutually parallel tangents to the ring sections and runs through an imaginary center point of the imaginary full rings corresponding to the ring sections, andthe auxiliary line is arranged parallel to a longitudinal direction of the substrate, orthe auxiliary line is arranged inclined to the longitudinal direction of the substrate.According to a third aspect, a lithography apparatus is proposed. The lithography apparatus has a substrate as described above, and / or an optical system having an optical component having a substrate as described above.According to a further aspect, a computer program product is proposed, which comprises instructions which, when the program is executed by at least one computer, cause the latter to execute the method described above (e.g. one or more embodiments of the method described above).A computer program product, such as a computer program means, can be provided or supplied, for example, as a storage medium, such as a memory card, USB stick, CD-ROM, DVD, or else in the form of a downloadable file from a server in a network. This can be effected, for example, in a wireless communication network by the transmission of a corresponding file with the computer program product or the computer program means.According to a further aspect, a control device for producing an optical system for a lithography apparatus is proposed. The control device comprises:providing means for executing step a) of the method described above,first determining means for executing step b) of the method described above, andsecond determination means for executing step c) of the above-described method.The respective unit, for example the control device, the provision device, the first and second determination devices, can be implemented by hardware and / or also by software. In a hardware implementation, the respective unit can be designed as a device or as part of a device, for example as a computer or as a microprocessor or as a control computer. In a software implementation, the respective unit can be designed as a computer program product, as a function, as a routine, as part of a program code or as an executable object.According to a further aspect, a method for producing an optical system for a lithography apparatus is proposed. The optical system includes an optical component having a substrate cut from a ingot. Furthermore, the method comprises the steps: a) providing a distribution function of a zero crossing temperature of a coefficient of thermal expansion of the ingot as a function of a location of the ingot, wherein the distribution function is rotationally symmetrical with respect to an axis of symmetry of the ingot, b) computer-implemented ascertaining, for the provided distribution function and each of a plurality of mutually different positions of a cut-out region of the ingot, a measure of an non-uniformity of the zero crossing temperature of the cut-out region, wherein the plurality of positions of the cut-out region differ from one another with respect to a radial position and / or a height position of the ingot, and c) ascertaining an optimum position of the cut-out region as that of the plurality of positions for which the ascertained measure of non-uniformity is minimum.The measure of the non-uniformity of the zero crossing temperature of the cut-out region has, for example, a parameter of a distribution function of the zero crossing temperature of the cut-out region. The distribution function of the zero crossing temperature of the cut-out region is in particular a function of the location of the cut-out region. Furthermore, the distribution function of the zero crossing temperature of the slicing region is in particular a subset of the distribution function of the zero crossing temperature of the ingot for the respective slicing region.The parameter for the extent of non-uniformity of the zero-crossing temperature of the cut-out region has, for example, a deviation from a pre-averaged nominal value, a determined mean value and / or a determined median value of the distribution function of the cut-out region and / or a deviation from a pre-averaged nominal distribution function of the zero-crossing temperature.For example, based on the zero-cross temperature distribution function of the cut-out region, which is a function of the location of the cut-out region, a statistical zero-cross temperature distribution function of the cut-out region may be determined. For example, based on the statistical distribution function of the zero crossing temperature of the cut-out region, an average value of the zero crossing temperature, a median value of the zero crossing temperature and / or a (statistical) standard deviation is determined. The parameter for the extent of non-uniformity of the zero crossing temperature of the cut-out region then has, for example, a deviation from the determined mean value, the determined median value and / or the standard deviation."An" is not necessarily to be understood as limiting to exactly one element. Rather, a plurality of elements, such as two, three or more, can also be provided. Any other counting word used here is also not to be understood as being limited to exactly the number of elements mentioned. Instead, numerical deviations upwards and downwards are possible, unless indicated to the contrary.The embodiments and features described for the method according to the first aspect apply correspondingly and vice versa to the further proposed aspects.Further possible implementations of the invention also include combinations, not explicitly mentioned, of features or embodiments described above or below with respect to the exemplary embodiments. In this case, the person skilled in the art will also add individual aspects as improvements or additions to the respective basic form of the invention.Further advantageous embodiments and aspects of the invention are the subject matter of the dependent claims and of the exemplary embodiments of the invention described below. The invention is explained in more detail below on the basis of preferred embodiments with reference to the enclosed figures. FIG. 1 shows a schematic meridional section of a projection exposure apparatus for EUV projection lithography according to one embodiment; FIG. 2 shows an optical system of the projection exposure apparatus of FIG. 1 according to an embodiment, wherein the optical system comprises an optical component; FIG. 3 shows a flow diagram of a method for producing an optical system of the projection exposure apparatus from FIG. 1 according to one embodiment; FIG. 4 shows a perspective view of a ingot for manufacturing a substrate of the optical component of FIG. 2 according to an embodiment; FIG. 5 shows a top view of the ingot of FIG. 4 according to an embodiment; FIG. 6 shows a further top view of the ingot of FIG. 4 according to an embodiment; FIG. 7 shows a further top view of the ingot of FIG. 4 according to an embodiment; FIG. 7A shows a detail from FIG. 7 ; FIG. 8 shows a cross-sectional view of the ingot of FIG. 4 according to an embodiment; FIG. 8A shows a detail from FIG. 8 ; FIGS. 8B to 8E each show a cut-out area and a tolerance range from FIG. 8A together with one or more deviating cut-out areas of the corresponding cut-out area; FIG. 9 shows another cross-sectional view of the ingot of FIG. 4 according to an embodiment; FIG. 9A illustrates an aberration of the optical system of FIG. 2 compared to a threshold value; FIG. 10 illustrates a computer-implemented determined single error of the mapping of the optical system from FIG. 2 according to one embodiment; FIG. 11 illustrates a further computer-implemented determined single error of the mapping of the optical system from FIG. 2 according to one embodiment; FIG. 12 illustrates an adjustment of illumination of the optical component of FIG. 2, according to an embodiment; FIG. 13 shows a substrate manufactured using the method of FIG. 3, according to an embodiment; and FIG. 14 shows a further substrate produced using the method from FIG. 3 according to a further embodiment.In the figures, identical or functionally identical elements have been provided with the same reference symbols, unless indicated to the contrary. It should also be noted that the representations in the figures are not necessarily to scale.FIG. 1 shows an embodiment of a projection exposure apparatus 1 (lithography apparatus), in particular an EUV lithography apparatus. An embodiment of an illumination system 2 of the projection exposure apparatus 1 has, in addition to a light or radiation source 3, an illumination optical unit 4 for illuminating an object field 5 in an object plane 6. In this case, the illumination system 2 does not include the light source 3.A reticle 7 arranged in the object field 5 is exposed, and the reticle 7 is held by a reticle holder 8. The reticle holder 8 can be displaced via a reticle displacement drive 9, in particular in a scanning direction.For the purpose of explanation, FIG. 1 shows a Cartesian coordinate system with an x-direction x, a y-direction y and a z-direction z. The x-direction x extends perpendicularly into the plane of the drawing. The y-direction y runs horizontally and the z-direction z runs vertically. In FIG. 1, the scanning direction extends along the y-direction y. The z-direction z extends perpendicular to the object plane 6.The projection exposure apparatus 1 comprises a projection optical unit 10. the projection optical unit 10 serves for imaging the object field 5 into an image field 11 in an image plane 12. the image plane 12 runs parallel to the object plane 6.A structure on the reticle 7 is imaged onto a light-sensitive layer of a wafer 13 arranged in the region of the image field 11 in the image plane 12, the wafer 13 being held by a wafer holder 14. The wafer holder 14 is displaceable via a wafer displacement drive 15, in particular along the y-direction y. The displacement of the reticle 7 via the reticle displacement drive 9 on the one hand and of the wafer 13 via the wafer displacement drive 15 on the other hand can take place in synchronization with one another.The light source 3 is an EUV radiation source. The light source 3 emits in particular EUV radiation 16, which is also referred to below as useful radiation, illumination radiation or illumination light. The useful radiation 16 has in particular a wavelength in the range between 5 nm and 30 nm. The light source 3 can be a plasma source, for example a LPP (laser produced plasma) source or a DPP (gas discharged produced plasma) source. It can also be a synchrotron-based radiation source. The light source 3 can be a free-electron laser (FEL).The illumination radiation 16 emanating from the light source 3 is focused by a collector 17. The collector 17 can be a collector with one or more ellipsoidal and / or hyperbolic reflection surfaces. The illumination radiation 16 can be applied to the at least one reflection surface of the collector 17 in the case of a scattering incidence (GI), that is to say with angles of incidence greater than 45°, or in the case of a normal incidence (NI), that is to say with angles of incidence less than 45°. The collector 17 can be structured and / or coated on the one hand for optimizing its reflectivity for the useful radiation and on the other hand for suppressing false light.After the collector 17, the illumination radiation 16 propagates through an intermediate focus in an intermediate focus plane 18. the intermediate focus plane 18 can represent a separation between a radiation source module, comprising the light source 3 and the collector 17, and the illumination optical unit 4.The illumination optical unit 4 comprises a deflection mirror 19 and, downstream thereof, a first facet mirror 20 in the beam path. The deflection mirror 19 can be a planar deflection mirror or alternatively a mirror having an effect influencing the beam beyond the pure deflection effect. Alternatively or additionally, the deflecting mirror 19 can be designed as a spectral filter which separates a used light wavelength of the illumination radiation 16 from false light of a wavelength deviating therefrom. If the first facet mirror 20 is arranged in a plane of the illumination optical unit 4 which is optically conjugate to the object plane 6 as a field plane, this is also referred to as a field facet mirror. The first facet mirror 20 comprises a multiplicity of individual first facets 21, which can also be referred to as field facets. Of these first facets 21, only some are illustrated by way of example in FIG. 1.The first facets 21 can be designed as macroscopic facets, in particular as rectangular facets or as facets with an arcuate or part-circular edge contour. The first facets 21 can be embodied as planar facets or alternatively as convexly or concavely curved facets.As is known, for example, from DE 10 2008 009 600 A1, the first facets 21 themselves can also each be composed of a multiplicity of individual mirrors, in particular a multiplicity of micromirrors. The first facet mirror 20 can be designed, in particular, as a microelectromechanical system (MEMS system). For details, reference is made to DE 10 2008 009 600 A1.Between the collector 17 and the deflecting mirror 19, the illumination radiation 16 extends horizontally, that is to say along the y-direction y.Arranged downstream of the first facet mirror 20 in the beam path of the illumination optical unit 4 is a second facet mirror 22. The second facet mirror 22 can also be arranged at a distance from a pupil plane of the illumination optical unit 4. In this case, the combination of the first facet mirror 20 and the second facet mirror 22 is also referred to as a specular reflector. Specular reflectors are known from US 2006 / 0132747 A1, EP 1 614 008 B1 and U.S. Pat. No. 6,573,978.The second facet mirror 22 comprises a plurality of second facets 23. the second facets 23 are also referred to as pupil facets in the case of a pupil facet mirror.The second facets 23 can likewise be macroscopic facets, which can be round, rectangular or else hexagonally bordered, for example, or alternatively facets composed of micromirrors. In this respect, reference is likewise made to DE 10 2008 009 600 A1.The second facets 23 can have planar or alternatively convexly or concavely curved reflection surfaces.The illumination optics 4 thus form a double faceted system. This basic principle is also referred to as a honeycomb capacitor (Fly's Eye Integrator).It may be advantageous not to arrange the second facet mirror 22 exactly in a plane which is optically conjugate to a pupil plane of the projection optical unit 10. In particular, the second facet mirror 22 can be arranged tilted with respect to a pupil plane of the projection optical unit 10, as is described, for example, in DE 10 2017 220 586 A1.With the aid of the second facet mirror 22, the individual first facets 21 are imaged into the object field 5. The second facet mirror 22 is the last beam-forming mirror or indeed the last mirror for the illumination radiation 16 in the beam path in front of the object field 5.In a further embodiment of the illumination optics 4, not shown, a transmission optics can be arranged in the beam path between the second facet mirror 22 and the object field 5, which in particular contributes to the imaging of the first facets 21 into the object field 5. The transmission optics can have exactly one mirror, but alternatively also two or more mirrors, which are arranged one behind the other in the beam path of the illumination optics 4. The transmission optics can comprise in particular one or two mirrors for perpendicular incidence (NI mirror, Normal Incidence mirror) and / or one or two mirrors for fringe incidence (GI mirror, Growing Incidence mirror).In the embodiment shown in FIG. 1, the illumination optical unit 4 has exactly three mirrors downstream of the collector 17, namely the deflecting mirror 19, the first facet mirror 20 and the second facet mirror 22.In a further embodiment of the illumination optical unit 4, the deflecting mirror 19 can also be omitted, so that the illumination optical unit 4 can then have exactly two mirrors downstream of the collector 17, namely the first facet mirror 20 and the second facet mirror 22.The imaging of the first facets 21 by means of the second facets 23 or with the second facets 23 and a transmission optical unit into the object plane 6 is regularly only an approximate imaging.The projection optical unit 10 comprises a plurality of mirrors Mi, which are numbered according to their arrangement in the beam path of the projection exposure apparatus 1.In the example illustrated in FIG. 1, the projection optical unit 10 includes six mirrors M 1 to M 6. Alternatives with four, eight, ten, twelve or another number of mirrors Mi are also possible. The projection optical unit 10 is a double-obscured optical unit. The next-to-last mirror M 5 and the last mirror M 6 each have a passage opening for the illumination radiation 16. The projection optical unit 10 has an image-side numerical aperture which is greater than 0.5 and which can also be greater than 0.6 and which can be, for example, 0.7 or 0.75.Reflection surfaces of the mirrors Mi can be designed as free-form surfaces without a rotational symmetry axis. Alternatively, the reflection surfaces of the mirrors Mi can be designed as aspherical surfaces with exactly one axis of rotational symmetry of the reflection surface shape. The mirrors Mi, like the mirrors of the illumination optical unit 4, can have highly reflective coatings for the illumination radiation 16. These coatings can be designed as multilayer coatings, in particular with alternating layers of molybdenum and silicon.The projection optical unit 10 has a large object image offset in the y direction y between a y coordinate of a center of the object field 5 and a y coordinate of the center of the image field 11.The projection optical unit 10 can be designed in particular anamorphically. It has in particular different imaging scales βx, βyin the x- and y-directions x, y. The two imaging scales βx, βyof the projection optical unit 10 are preferably (βx, βy)=(+ / - 0.25, + / - 0.125). A positive imaging scale β means imaging without image reversal. A negative sign for the imaging scale β means image reversal imaging.The projection optical unit 10 thus leads in the x-direction x, i.e. in the direction perpendicular to the scanning direction, to a reduction in the ratio 4:1.The projection optical unit 10 leads to a reduction of 8:1 in the y-direction y, i.e. in the scanning direction.Other imaging scales are also possible. Identical-sign and absolutely identical imaging scales in the x- and y-directions x, y, for example with absolute values of 0.125 or of 0.25, are also possible.The number of intermediate image planes in the x- and y-directions x, y in the beam path between the object field 5 and the image field 11 can be the same or can be different depending on the embodiment of the projection optical unit 10. Examples of projection optics with different numbers of such intermediate images in the x and y directions x, y are known from US 2018 / 0074303 A1.In each case one of the second facets 23 is assigned exactly to one of the first facets 21 for forming in each case an illumination channel for illuminating the object field 5. This can result in particular in illumination according to the Kohler principle. The far field is broken down into a plurality of object fields 5 with the aid of the first facets 21. The first facets 21 generate a plurality of images of the intermediate focus on the second facets 23 assigned to them in each case.The first facets 21 are imaged onto the reticle 7 in each case by an associated second facet 23 in a manner overlapping one another in order to illuminate the object field 5. The illumination of the object field 5 is in particular as homogeneous as possible. It preferably has a uniformity error of less than 2%. The field uniformity can be achieved by superimposing different illumination channels.By arranging the second facets 23, the illumination of the entry pupil of the projection optical unit 10 can be geometrically defined. By selecting the illumination channels, in particular the subset of the second facets 23, which guide light, the intensity distribution in the entrance pupil of the projection optical unit 10 can be adjusted. This intensity distribution is also referred to as illumination setting or illumination pupil filling.A likewise preferred pupil uniformity in the region of sections of an illumination pupil of the illumination optical unit 4 that are illuminated in a defined manner can be achieved by redistribution of the illumination channels.Further aspects and details of the illumination of the object field 5 and in particular of the entry pupil of the projection optical unit 10 are described below.The projection optical unit 10 can have, in particular, a homocentric entry pupil. This can be accessible. It may also be inaccessible.The entrance pupil of the projection optical unit 10 cannot be illuminated exactly with the second facet mirror 22 as a rule. In an imaging of the projection optical unit 10, which images the center of the second facet mirror 22 telecentrically onto the wafer 13, the aperture beams often do not intersect at a single point. However, an area can be found in which the paired distance of the aperture beams becomes minimum. This surface represents the entry pupil or a surface in the spatial domain which is conjugated to it. In particular, this surface exhibits a finite curvature.It can be that the projection optical unit 10 has different positions of the entry pupil for the tangential and for the sagittal beam path. In this case, an imaging element, in particular an optical component of the transmission optics, should be provided between the second facet mirror 22 and the reticle 7. With the aid of this optical element, the different position of the tangential entry pupil and of the sagittal entry pupil can be taken into account.In the arrangement of the components of the illumination optical unit 4 illustrated in FIG. 1, the second facet mirror 22 is arranged in a surface conjugate to the entry pupil of the projection optical unit 10. The first facet mirror 20 is arranged tilted with respect to the object plane 6. The first facet mirror 20 is arranged tilted with respect to an arrangement plane which is defined by the deflecting mirror 19. The first facet mirror 20 is arranged tilted with respect to an arrangement plane which is defined by the second facet mirror 22.FIG. 2 shows an optical system 100 (e.g. a part of an optical system 100) having an optical component 102 according to an embodiment. The optical component 102 comprises a substrate 104 and an optically active surface 106. The optical component 102 is, for example, a mirror having a mirror substrate 104 and a reflective surface 106.The optical system 100 is, for example, a projection optical unit 10 of the EUV lithography apparatus 1 (FIG. 1 ). However, the optical system 100 can also be, for example, an illumination optical unit 4 of the lithography apparatus 1.The optical component 102 is, for example, one of the mirrors M 1 to M 6 of the projection optical unit 10 (FIG. 1 ). The optical component 102 can also be, for example, one of the mirrors 19, 20, 22 of the illumination optical unit 4 (FIG. 1 ).Although not shown in the figures, the optical component 102 may also be a mirror or a lens of a DUV lithography apparatus.The optical component 102 can heat up by irradiation with working light 16 (e.g. EUV light 16 of the lithography apparatus 1, FIG. 1 ) and absorption of the working light 16. As a result, the optical component 102 can be thermally deformed. As a result of this thermal deformation, aberrations F of the optical component 102 or of the optical system 100 comprising the optical component 102 can occur.To reduce thermal distortion and associated aberrations F, high-quality substrate material 108 is used for the substrate 104. In particular, the material 108 of the substrate 104 has a very small coefficient of thermal expansion α. The material 108 has, in particular, a zero crossing temperature ZCTof the thermal expansion coefficient α, at which a thermal deformation of the mirror material 108 as a function of a temperature increase is minimal and / or zero.Due to inhomogeneities of the material 108 of the substrate 104, the zero crossing temperature ZCTof the substrate 104 is not distributed homogeneously over a substrate body 110 of the substrate 104, but rather has fluctuations ΔZCTas a function of a location of the substrate body 110. A value of an average zero crossing temperature M of the substrate material 108 and variations ΔZCT of the zero crossing temperature ZCT as a function of the location have a direct influence on imaging errors F of the optical component 102 and thus of the optical system 100 with the optical components 102.In the following, with reference to FIGS. 3 to 12, a method for producing an optical system 100 for a lithography apparatus 1 is described. The optical system 100 comprises the optical component 102 with the optically active surface 106 and the substrate 104 (FIG. 2 ).In a first optional step S 1 of the method, a ingot 200 (FIG. 4 ) is provided. The substrate 104 (FIG. 2 ) may be cut out of the ingot 200 during the process.The ingot 200 is made of a material 202 having very small thermal expansion coefficients a R. The material 202 has, in particular, a zero crossing temperature ZCT R of the coefficient of thermal expansion a R at which a thermal deformation of the material 202 as a function of a temperature increase is minimal and / or zero.Due to inhomogeneities of the material 202 of the ingot 200, the zero crossing temperature ZCT R of the ingot 2002 is not distributed homogeneously over a body 204 of the ingot 200, but rather has fluctuations ΔZCT R about an average zero crossing temperature M R as a function of a location p of the ingot body 204.The ingot 200 is produced, for example, in a direct deposition process or in a soot process.In a second step S 2 of the method, a distribution function g(p) of the zero crossing temperature ZCT R of the ingot 200 is provided.The distribution function g(p) of the zero-cross temperature ZCT R of the ingot 200 is measured in step S 2, for example. However, the distribution function g(p) of the zero crossing temperature ZCT R of the ingot 200 can also be determined based on parameters of the ingot 200, for example with computer assistance.A provided distribution function g(p) of the zero-crossing temperature ZCT R of the ingot 200 indicates, for example, a value ZCT j of the zero-crossing temperature ZCT R for each location p j of the ingot 200. By way of example, FIG. 4 shows an enlarged detail of the ingot 200, which illustrates a plurality of volume elements V j of the ingot 200. The enlarged section of the ingot 200 shows, as example, 27 (3x3x3) volume elements V j, three of which are provided with a reference sign. Furthermore, in FIG. 4, for each volume element V j a location p j of the corresponding volume element V j is marked in the coordinates x j, y j, z j of the shown Cartesian coordinate system x', y', z'. For example, in step S 2, a zero crossing temperature ZCT j of this location p j is provided and / or measured assigned to each location p j of the ingot 200.In the present case, the distribution function g(p) of the ingot 200 is in particular rotationally symmetrical with respect to an axis of symmetry A of the ingot 200. That is, the distribution function g(p) of the zero-crossing temperature ZCT R of the ingot 200 is mapped to itself for rotations by arbitrary angles (azimuth angle φ, FIG. 5 ) about the axis of symmetry A.In step S 2, an error range Δg of the distribution function g(p) of the zero crossing temperature ZCT R of the ingot 200 can optionally also be provided.As shown in FIG. 4, the ingot 200 has, for example, a cylindrical shape 206, e.g., the shape 206 of a right circular cylinder. The ingot 200, i.e. the cylinder shape 206 of the ingot 200, has a cylinder axis B corresponding to the axis of symmetry A. Furthermore, the ingot 200 or its cylindrical shape 206 has two opposing end faces 208, 210 (e.g. circular faces 208, 210) and a lateral surface 212.In FIG. 4, a location p of the ingot 200 (e.g. p j= x j, y j z j) is described by way of example by means of a Cartesian coordinate system 214 on the basis of Cartesian coordinates x', y', z'.FIG. 5 shows a top view of the ingot 200 from FIG. 4 together with the Cartesian coordinate system 214 and a cylinder coordinate system 216.As illustrated in FIG. 5, a location p of the ingot 200 can also be described with a cylinder coordinate system 216 (cylinder coordinates ρ, φ, z') instead of with the Cartesian coordinate system 214. In the example shown in FIG. 5, the z' axes of the cartesian coordinate system 214 and the cylindrical coordinate system 216 coincide with each other. In addition, in FIG. 5, the x' axis of the Cartesian coordinate system 214 is oriented toward φ equal to zero (φ=0) and the angle φ increases from the x' axis to the y' axis.A radial direction r (FIG. 5 ) of the ingot 200 is arranged in particular along the cylinder coordinate ρ and all directions generated from the cylinder coordinate ρ by rotation by the angle φ. In addition, a height direction h (FIG. 5 ) of the ingot 200 is arranged along the cartesian and the cylinder axis z'.The fact that the distribution function g(p) of the zero-crossing temperature ZCT R of the ingot 200 is rotationally symmetrical with respect to the axis of symmetry A of the ingot 200 means that the zero-crossing temperature ZCT R of the ingot 200 shows a pattern 218 as illustrated in FIG. 6. The pattern 218 has in particular concentric rings 220 (in particular circular rings 220) which are arranged concentrically about the axis of symmetry A. In FIG. 6, three of the rings 220 are exemplarily denoted by a reference sign. Additionally, rings 220 in FIG. 6 are shown excessively large with respect to a ring width 222 for purposes of illustration.Along a respective ring 220, the zero crossing temperature ZCT R does not change. In other words, the distribution function g(p) of the zero crossing temperature ZCT R of the ingot 200 has azimuthal symmetry with respect to the azimuth angle φ.In the radial direction r, on the other hand, the zero-crossing temperature ZCT R of the ingot 200 changes. Furthermore, the zero-cross temperature ZCT R of the ingot 200 also changes in the height direction h.In a third step S 3 of the method, different cut-out regions D i of the ingot 200 are examined in a computer-implemented manner in order to cut the substrate 104 of the optical component 102 (FIG. 2 ) from the ingot 200.In particular, in step S 3, a computer-implemented simulation is carried out for the provided distribution function ZCT R of the ingot 200 and each of a plurality of mutually different positions P i of a cut-out region D i of the ingot 200. In particular, a number n of mutually different positions P i of the cut-out region D i is provided. Herein, n is a natural number larger than 1, and i denotes an index running from 1 to n. In the simulation, an aberration F i of an optical component 102 produced on the basis of the respective cut-out region D i and / or of the optical system 100 with the corresponding optical component 102 is determined. That is, F i is an aberration obtained by simulation for the ithof the n provided positions P i of the cut-out area D i. In other words, a number n of different aberrations F i is determined during the simulation.That is, the distribution function g(p) of the zero-cross temperature ZCT R of the ingot 200 provided in step S 2 and each of the plurality (number n) of positions P i of the cut-out area D i of the ingot 200 different from each other are input parameters of the simulation calculation of step S 3. In addition, the mapping errors F determined i( number n) are output parameters of the simulation calculation.FIGS. 7 and 8 illustrate different positions P i of the cut-out region D i which are used as input variables in the simulation. In particular, the imaging error F i is determined for a plurality of positions P i of the cut-out region D which differ from one another with respect to a radial position r i and / or a height position h i of the ingot 200.FIG. 7 shows a plan view of the ingot 200 from FIG. 4. Also illustrated as an example are two different positions P i of a cut-out region D i which differ from one another with respect to a radial position r i. The radial position r i is, in particular, a position along the radial direction r of the ingot 200. In addition, the radial direction r extends from a radius r 0 equal to zero (r 0= 0) at the axis of symmetry A of the ingot 200 to an outer radius r A at the lateral surface 212 (FIG. 4 ) of the ingot 200.A first example position P 1 of a first cut-out region D 1 is at a radial position r 1. In addition, a second example position P 2 of a second cut-out region D 2 is at a radial position r 2. In FIG. 7, a position of a (e.g. geometric) center point m 1, m 2 of the respective cut-out region D 1, D 2 is identified as an example as position P 1, P 2 of a respective cut-out region D 1, D 2. However, a position P i of a cut-out region D i can also have positions r 1A, r 1E of outer edges 224, 226 of the respective cut-out region D i as illustrated by way of example for the cut-out region D 1 in FIG. 7.Each of the n cut-out areas D i( e.g., D 1, D 2) may be selected (i.e., disposed within ingot 200) to be free of axis of symmetry A. In other words, the respective cut-out region D i does not contain the axis of symmetry A, for example. That is, the different positions P i of the cut-out areas D i( for example also the positions of outer edges 224, 226 of the cut-out areas D i) are each located at a radius r 1, r 2, which is greater than zero, as shown in FIG. 7.The plurality of positions P i of the plurality of cut-out areas D i may include different height positions h 1, h 2 instead of or in addition to different radial positions (FIG. 7 ), as shown in FIG. 8.In the example of FIG. 8, a third example position P 3 of a third cut-out region D 3 is at a radial position r 3 and a height position h 3. Further, a fourth example position P 4 of a fourth cut-out region D 4 is located at a radial position r 4 and a height position h 4. In addition, a fifth example position P 5 of a fifth cut-out region D 5 is located at a radial position r 5 and a height position h 5. That is, in the example of FIG. 8, the cut-out areas D 3 and D 4 have the same radial position r 3, r 4 (r 3= r 4), but different height positions h 3, h 4. Furthermore, the cut-out regions D 4 and D 5 have the same height position h 4, h 5 (h 4= h 3), but different radial positions r 4, r 5.The positions P i of the cut-out regions D i, which are shown in FIGS. 7 and 8 and which are used as input parameters for the simulation in step S 3, are to be regarded merely as examples of different positions P i with respect to the radial position r i and the height position h i. Various other positions P i of the cut-out areas D i within the ingot 200 are possible with respect to the radial position r i and the height position h i.The positions P i of the cut-out regions D i can, for example, cover a radius region Δr (FIG. 7 ) of the ingot 200 from an inner radius rt adjacent to the axis of symmetry A to an outer radius r A in the lateral surface 212 of the ingot 200. In other words, the radial positions r i of the cut-out areas D i may cover the entire radius area Δr of the ingot 200 except for the axis of symmetry A.Additionally or instead, the positions P i of the cut-out areas D i may cover, for example, a height range Δh of the ingot 200 from the first end face 208 (h 0= 0, FIG. 8 ) to the second end face 210 of the ingot 200 (h A, FIG. 8 ). In other words, the height positions h i of the cut-out areas D i may cover the entire height Δh of the ingot 200.In FIGS. 7 and 8, different positions P i of the cut-out areas D i are shown with respect to the radial position r i and the height position h i.In addition, the plurality of positions P i of the cut-out areas D i may also be different from each other with respect to rotation with respect to one or more rotational degrees of freedom, e.g., rotation about the x' direction x' (first direction), the y' direction y' (second direction), and / or the z' direction z' (third direction). The third direction z' of the ingot 200 is arranged in particular along (i.e. in accordance with) the axis of symmetry A of the ingot 200. The first and second directions x', y' are arranged in particular perpendicular to one another and in each case perpendicular to the axis of symmetry A.As an example, positions P 6, P 7 of two cut-out areas D 6, D 7 which differ from each other with respect to rotation about the x' direction x' (first direction) are shown in FIG. 9. In particular, in FIG. 9, the position P 6 is rotated by the angle β relative to the position P 7.Although not shown in the figures, the plurality of positions P i of the cut-out area D may also be different from each other with respect to rotation about the y' direction y' (second direction) and / or the z' direction z' (second direction).As illustrated in FIGS. 7A and 8A-8E, for each of the plurality of different positions P i of the respective cut-out areas D i in addition to the aberration F i for the respective position P i one or more deviating aberrations E q of one or more deviating positions Q q of the cut-out area D may also be taken into account. As a result, an imprecision in the later cutting out (step S 5) of the substrate 104 from the ingot 200 can be taken into account.In FIG. 7A, a tolerance range T i= T 1 and T i= T 2 is shown for the exemplary cut-out areas D 1 and D 2 respectively. In addition, in FIG. 8A, for the exemplary cut-out areas D 3 to D 5 a tolerance range T 3( for D 4 and D 5 without reference sign) is shown in each case. Although not shown in FIG. 9, a corresponding tolerance range can also be provided for each of the cut-out areas D 6 and D 7 respectively.As shown by way of example in FIGS. 8B to 8E for the cut-out region D 3 with the tolerance range T 3 one or more deviating positions Q q of the corresponding cut-out region D 3 can now be taken into account. The deviation positions Q q of the corresponding cut-out region D 3 are selected in particular such that the deviation cut-out regions C q defined thereby lie within the tolerance range T 3. Herein, q denotes an index ranging from 1 to the total number of deviation positions Q q.FIG. 8B illustrates two deviating positions Q 1 and Q 2 of the cut-out area D 3. The deviation positions Q 1 and Q 2 are different from the position P 3 of the cut-out area D 3 in terms of a displacement in the first direction x' (Q 1) and a displacement in the third direction z' (Q 2). Although not shown, a deviation position from the position P 3 of the cut-out area D 3 may also be different in terms of displacement in the second direction y'.FIG. 8C illustrates another deviating position Q 3 of the cut-out area D 3. The deviation position Q 3 is different from the position P 3 of the cut-out area D 3 with respect to rotation about the second direction y'. Although not shown, a deviation position from the position P 3 of the cut-out area D 3 may also differ with respect to a rotation about the first and / or third direction x', z'.FIG. 8D illustrates another deviating position Q 4 of the cut-out region D 3. The deviation position Q 4 is different from the position P 3 of the cut-out region D 3 with respect to non-parallel edges 230, 232 (i.e., outer edges) of the deviation cut-out region C 4 in the first direction x'. Although not shown, edges of a deviation-cut region in the second and / or third direction y', z' may also be non-parallel.FIG. 8D illustrates another deviating position Q 5 of the cut-out region D 3. The deviating position Q 5 is different from the position P 3 of the cut-out region D 3 with respect to a volume deviation ΔW (e.g., ΔW=W2-W1) of the deviating cut-out region C 5 from the cut-out region D 3. Volume deviations other than those shown (e.g. in other directions x', y', z') can also be taken into account.All types of deviation positions Q i( e.g., Q 1 to Q 5) and deviation cut areas C i( e.g., C 1 to C 5) shown (FIGS. 8B to 8E ) and / or described herein may be combined with one another as desired to generate further deviation positions Q i and deviation cut areas C i.Next, for each considered deviation position Q i( e.g., Q 1 to Q 5) of each cut-out region D i( i.e., for each deviation cut-out region C i) a corresponding deviation aberration E i may be determined.Then, the at least one selection position P a of the cropping area D may be determined as that of the plurality of positions P i for which the determined aberration F i and the one or more determined deviating aberrations E q( e.g. E 1 to E 5) are each less than a predetermined threshold value SW (FIG. 9A ).Optionally, in step S 3, each error F i( and optionally each error Eq) can be determined based on a plurality of individual errors f k( FIG. 10 ) different from one another. In particular, for the determination of each error F i( and optionally each error Eq), a plurality of individual errors f k can be used, which belong to different types of errors of the imaging of the optical system 100.For example, the individual errors f k different from one another are taken into account as relative error values. In this variant of step S 3, the error F i( and optionally the error Eq) of the imaging of the optical system 100 can be determined, for example, as a maximum of the plurality of individual errors f k determined, e.g. based on the following equation:Here, f k denotes the (e.g. relative) individual errors for the provided distribution function g(p) and a specific position P i of the cut-out region D. Here, k is an index which runs from 1 to m, where m is a natural number greater than 1 and the number of individual errors f k which differ from one another denotes.In other examples, in step S 3, the error F i of the imaging of the optical system 100 can also be determined as an average value, a median and / or a quantile of the plurality of individual errors f k determined.The plurality of individual errors f k different from one another may be, for example, a deviation of an actual focus F Ist of the optical system 100 from a target focus F Soll (focus error, spherical aberration, Zernike polynomial ZP of Z 2), as illustrated in FIG. 10. In FIG. 10, radiation 300 (e.g., working light 16 in FIG. 1 ) is shown arriving at an image plane 302 of optical system 100 (FIG. 2 ). The setpoint focus F Soll is situated in particular in the image plane 302. The actual focus F Ist is deviated from the target focus F Soll so that blurring occurs in imaging. A deviation of the actual focus F Ist from the target focus F Soll represents an example of a single error f k e.g. a first (k=1) single error f 1.In FIG. 10, an error range ΔF fokus is also drawn as an example of a threshold value SW (FIG. 9A ) and / or an individual threshold value. For example, an actual focus that is in the range F Soll ± ΔF fokus is an aberration F i which is smaller than the threshold value SW. The actual focus F Ist shown in FIG. 10, however, is no longer in the range F Soll ±ΔF fokus and the associated position P i of a corresponding cut-out region D i thus no longer satisfies the condition for a selection position P a. Example values for an error range ΔF fokus, which corresponds to a threshold value SW and / or a single threshold value for the focus, include, for example, 15 nm or less, 10 nm or less and / or 5 nm or less.The plurality of individual errors f k that differ from one another can also be, for example, a displacement of a wavefront (e.g. 304 in FIG. 10 ) relative to a setpoint wavefront 306, such that an actual position P Ist of an object 402 imaged in an image plane 302 (FIG. 10 ) of the optical system 100 with the aid of the optical system 100 deviates from a setpoint position P Soll of the imaged object 404, as illustrated in FIG. 11. A deviation of the actual position P Ist from the desired position P Soll( overlay error) represents a further example of an individual error f k e.g. a second (k=2) individual error f 2.The plurality of mutually different individual errors f k can additionally or instead be individual errors f k with respect to the mutually different types of errors also be individual errors f k with respect to mutually different setting parameters of an illumination of the optical component 102 of the optical system 100 to be produced.The various setting parameters of the planned illumination of the optical component 102 to be produced have, for example, a radiation intensity of a working light (e.g. EUV light 16, FIG. 1 ) which is radiated onto the optical component 102.The various illumination setting parameters can also have, for example, a pattern 500 or a heat flux distribution 500 in which the working light 16 is radiated onto the optical component 102. FIG. 12 illustrates, by way of example, two heat flux poles 502, 504 (dipole patterns) of a heat flux distribution 500 of an optically active surface 506 of an optical component (e.g. of the optical component 102 in FIG. 2 ).Although not shown in the figures, the plurality of individual errors f k determined may be weighted according to predetermined weights. As a result, the individual errors f k can be weighted with this component 102 depending on a planned use of the optical component 102 to be produced and of the optical system 100.For determining the aberrations F i( and optionally the deviating aberrations Eq) in step S 3, the following adaptation function can be applied, for example:Therein, W ref denotes a reference wavefront. The reference wavefront has, for example, a vector of a Zernike coefficient that includes all illumination settings (thermal load cases) of the optical system 100 for the case that the cut-out region D is determined based only on a radial displacement (FIG. 7 ) and height displacement (FIG. 8 ) of the position P i of the cut-out region D i (i.e. without rotation, FIG. 9 ). The reference wavefront has, for example, a vector of a Zernike coefficient which also takes into account time series of use cases of the optical component 102 of the optical system 100.Moreover, sensitivities are defined as follows:W (p 1) here denotes a wavefront which is obtained if, in the selection of the cut-out regions D i a rotation 228 about the first, second and / or third axis x', y', z' of the ingot 200 is also taken into account (FIG. 9 ). The index 1 identifies the different optimization cases, such as a rotation 228 about the first, second and / or third axis x', y', z' of the ingot 200 (FIG. 9 ), a radial displacement (FIG. 7 ) and a height displacement (FIG. 8 ).However, in other examples, in step S 3, a different adjustment function than that described above may be applied.In a fourth step S 4 of the method, at least one selection position P a of the cut-out region D i is determined as that of the plurality of positions P i for which the determined aberration F i is less than a predetermined threshold value SW.In FIG. 9A, an aberration F i= F 6 of the cut-out region D 6( for i=6) of FIG. 9 is exemplarily illustrated. As seen in FIG. 9A, the aberration F 6 of the cut-out area D 6 is smaller than the predetermined threshold value SW. In this example, the position P 6 of the cut-out region D 6 is thus determined in step S 4 as the at least one selection position P a.As illustrated in FIG. 9A, optionally, when the respective imaging error F i( and optionally the respective deviating imaging error E q) are determined in a computer-implemented manner, an error range ΔF i of the determined imaging error F i can additionally be determined. In this case, the at least one selection position P a of the cropping area D may be determined as that of the plurality of positions P i for which the determined aberration F i including its error range ΔF i is less than the predetermined threshold value SW. In the example of FIG. 9A, the aberration F 6 of the cut-out area D 6 including its error range ΔF 6 is smaller than the predetermined threshold value SW. Specifically, F 6 ± ΔF 6 is less than the predetermined threshold value SW.If in step S 4 no selection position P a of the cut-out region D is determined, because none of the determined aberrations F i is less than the predetermined threshold value SW, then it can be determined, for example, that the ingot 200 is not suitable for producing a substrate 104. In this case, step S 5 is not executed.Optionally, instead of or in addition to being based on the threshold value SW, the at least one selection position P a of the cut-out region D i- can also be an optimum position P opt of the cut-out region D i for a minimum imaging error F i. In other words, in step S 4, an optimum position P opt of the cut-out region D i can also be determined as that of the plurality of positions P i for which the determined aberration F i is minimal.For example, a minimum of the plurality of error values F i of the imaging of the optical system 102 ascertained in step S 3 is ascertained as final error F EHerein, n is a natural number greater than 1, and denotes the number of aberrations Fi obtained in step S 3. In addition, i is an index running from 1 to n.Subsequently, the position P i of the cut-out region D i belonging to this minimum F E is determined as the optimum position P opt of the cut-out region D i for the production of the substrate 104 of the optical component 102.Merely by way of example, the position P i= P 6 shown in FIG. 9 is identified as a position whose associated ascertained individual error F i= F 6 has been ascertained as a minimum error F E of all ascertained individual errors F i for all provided positions P i. Thus, in this example, the position P 6 associated with this single error F 6 is determined as the optimum position P opt of the cut-out area D i.In a fifth step S 5 of the method, the substrate 104 (FIG. 2 ) is cut out of the ingot 200 (FIG. 4 ) according to the at least one determined selection position P a of the cut-out region D i and / or the optimum position P opt of the cut-out region D i.The method makes it possible, for the production of a substrate 104 of an optical component 102, to cut out a region from the blank 200 in accordance with a favourable and / or optimum determined cut-out region D (i.e. the at least one selection position P a and / or the optimum position P opt of the cut-out region D). In particular, a cut-out region D can be selected which has an advantageous distribution of the zero crossing temperature ZCT. As a result, aberrations F of the optical system 100 due to thermal expansion of the substrate 104 can be reduced.In FIG. 13, an example of a substrate 104' of an optical component 102 of an optical system 100 of a lithography apparatus 1 is shown, which was produced based on the method described above. The substrate 104' has a distribution function g'(p') of a zero crossing temperature ZCT' of a coefficient of thermal expansion a' as a function of a location p' of the substrate 102'. In addition, the distribution function g'(p') has a pattern 112 of the zero crossing temperature ZCT' which has a plurality of concentric ring sections 114, which are each partial sections of a full ring 116.In FIG. 13, tangents T to the ring sections 114 are shown, wherein the tangents T are arranged parallel to one another. Furthermore, one of the imaginary full rings 116 of one of the ring sections 114 is indicated with dashed lines. In addition, reference numeral 118 denotes an imaginary center point of the full ring 116. Also drawn in FIG. 13 is an auxiliary line 120 (or auxiliary direction 120) of the substrate 104'. The auxiliary line 120 of the substrate 104' is defined to be perpendicular to the tangents T and to pass through the imaginary center 118 of the concentric full rings 116 corresponding to the ring portions 114. In the example of FIG. 13, the auxiliary line 120 is arranged parallel to a longitudinal direction L of the substrate 104'.The substrate 104' shown in FIG. 13 was produced (i.e., cut out from the ingot 200) based on the above-described method, and the optimum position P opt of the cut-out region D was selected by shifting positions P i of the cut-out region D in the radial direction r (FIG. 7 ) and in the height direction h (FIG. 8 ).In FIG. 14, a further example of a substrate 104" of an optical component 102 of an optical system 100 of a lithography apparatus 1 is shown, which was produced based on the method described above. In the example of FIG. 14, the substrate 104" was carried out on the basis of a selection of the optimum position P opt of the cut-out region D by-in addition to displacing positions P i of the cut-out region D in the radial direction r and in the height direction h-also by rotation 228 about the first, second and / or third direction x', y', z' of the blank 200S (FIG. 9 ).For FIG. 14, analogously to FIG. 13, the reference symbol T" identifies tangents on ring sections 114", wherein the tangents T" are arranged parallel to one another. Furthermore, one of the imaginary solid rings 116'' of one of the ring sections 114'', an imaginary center point 118'' of the solid ring 116'' and an auxiliary line 120'' (or auxiliary direction 120'') of the substrate 104'' is also drawn in FIG. 14. The auxiliary line 120" of the substrate 104" in FIG. 14 is defined exactly as the auxiliary line 120 in FIG. 13, namely that the auxiliary line 120" is arranged perpendicular to the tangents T" and runs through the imaginary center point 118" of the concentric full rings 116" corresponding to the ring sections 114". Unlike the example of Fig. 13, the auxiliary line 120" of the substrate 104" is arranged inclined to the longitudinal direction L" of the substrate 104".Although the present invention has been described on the basis of exemplary embodiments, it can be modified in various ways.LIST OF REFERENCE CHARACTERS1 Projection exposure apparatus 2 Illumination system 3 Light source 4 Illumination optical unit 5 Object field 6 Object plane 7 Reticle 8 Reticle holder 9 Reticle displacement drive 10 Projection optical unit 11 Image field 12 Image plane 13 Wafer 14 Wafer holder 15 Wafer displacement drive 16 Illumination radiation 17 Collector 18 Intermediate focal plane 19 Deflection mirror 20 First facet mirror 21 First facet 22 Second facet mirror 23 Second facet 100 Optical system 102 Optical component 104, 104', 104" Substrate 106 Optically active surface 108 Material 110 Body 112 Pattern 114, 114" Ring section 116, 116" Full ring 118, 118" Center point 120, 120" auxiliary line 200 blank 202 material 204 body 206 cylinder shape 208 surface 210 surface 212 surface 214 coordinate system 216 coordinate system 218 pattern 220 ring 222 width 224 edge 226 edge 228 rotation 230 edge 232 edge 300 radiation 302 image plane 304 actual wavefront 306 desired wavefront 400 image 402 object 404 object 500 heat flux distribution 502 heat flux pole 504 heat flux pole 506 optically active surface α, α', α" Thermal expansion coefficient α R Thermal expansion coefficient A Axis β Angle B Axis C q Deviating cutting region C 1- C 5 Deviating cutting region D Cutting region D i Cutting region D 1- D 7 Cutting region ΔF i, δf_ner 370_error range ΔF Fokus error range Δg error range Δh height range Δr radius range ΔW volume deviation ΔZCT temperature difference ΔZCT R temperature difference E q deviation aberration E 1- E 5 deviation aberration F error F i error F 1- F 6 error f k error F Ist actual focus FSolldesired focus g, g', g" function h height h 1- h 5 height h 0, h A height L, L" direction m number m 1, m 2 center point M mean value M R mean value M1-M6 mirror n number p, p', p" location p j location P 1- P 7 position P a selection position P i position P 1- P 7 position Q q deviation position Q 1- Q 5 deviation position r direction r0, ri, rt radius r1-r5 radius r1A, r 1E radius p cylinder coordinate φ cylinder coordinate (angle) S1-S5 method steps SW threshold value T, T" tangent T i tolerance range T 1- T 3 tolerance range V j volume element W1, W2 volume x j, y j, z j location (coordinates) x, y, z directions x', y', z' directions x", y", z" directions ZCT zero crossing temperature ZCT', zct' zero crossing temperature ZCT j zero crossing temperature ZCT R zero crossing temperatureReferences included in the specificationThis list of documents cited by the applicant has been produced in an automated manner and is only included for the better information of the reader. The list is not part of the German patent application or utility model application. The DPMA does not take any adhesion for any faults or omissions.Patent Literature citedDE 10 2008 009 600 A1 [0135, 0139]US 2006 / 0132747 A1

[0137] EP 1 614 008 B1

[0137] U.S. Pat. No. 6,573,978

[0137] DE 10 2017 220 586 A1

[0142] US 2018 / 0074303 A1

[0156]

Claims

Method for producing an optical system (100) for a lithography apparatus (1), wherein the optical system (100) has an optical component (102) with a substrate (104) cut out from a ingot (200), having the steps: a) providing (S2) a distribution function (g) of a zero crossing temperature (ZCT R) of a thermal expansion coefficient (a R) of the ingot (200) as a function of a location (p) of the ingot (200), wherein the distribution function (g) is rotationally symmetrical with respect to an axis of symmetry (A) of the ingot (200), b) computer-implemented ascertaining (S3) an imaging error (F i) of the optical system (100), for the provided distribution function (g) and each of a plurality of mutually different positions (P i) of a cut-out region (D) of the ingot (200), wherein the plurality of positions (P i) of the cut-out region (D) differ from one another with respect to a radial position (r i) and / or a height position (h i) of the ingot (200), and c) determining (S4) at least one selection position (P a) of the cut-out region (D) as that of the plurality of positions (P i), for which the determined aberration (F i) is less than a predetermined threshold value (SW).The method according to claim 1, wherein in step c) an optimal position (P opt) of the cut-out area (D) is determined as that of the plurality of positions (P i) for which the determined aberration (F i) is minimal.Method according to claim 1 or 2, wherein the cut-out area (D) is free from the axis of symmetry (A).Method according to one of Claims 1 to 3, wherein the ingot (200) has a cylindrical shape (206) with a cylinder axis (B) corresponding to the axis of symmetry (A) and a lateral surface (212), and the radial position (r i) of the ingot (200) is a position along a radial direction (r) of the ingot (200), wherein the radial direction (r) extends from a radius (r 0) equal to zero at the axis of symmetry (A) to an outer radius (r A) at the lateral surface (212).Method according to one of claims 1 to 4, wherein the plurality of positions (P i) of the cut-out region (D) cover a radius region (Δr) of the ingot (200) from an inner radius (rt) adjacent to the axis of symmetry (A) to an outer radius (r A) in a lateral surface (212) of the ingot (200), and / or the plurality of positions (P i) of the cut-out region (D) cover a height region (Δh) of the ingot (200) from a first end face (208) to a second end face (210) of the ingot (200).Method according to any one of claims 1 to 5, wherein the ingot (200) has a first, second and third direction (x', y', z'), the third direction (z') is arranged along the axis of symmetry (A) of the ingot (200), the first and second direction (x', y') are arranged perpendicular to each other and respectively perpendicular to the axis of symmetry (A), and the plurality of positions (P i) of the cut-out region (D) differ from each other with respect to the radial position (r i) and / or the height position (h i) of the ingot (200) and with respect to a rotation (228) about the first, second and / or third direction (x', y', z').Method according to any one of claims 1 to 6, wherein for each of the plurality of mutually different positions (P i) of the cut-out area (D), in addition to the aberration (F i) for the corresponding position (P i) of the corresponding cut-out area (D i) one or more deviating aberrations (E q) of one or more deviating positions (Q q) of the cut-out area (D) are also determined, the one or more deviating positions (Q q) being selected in such a way, wherein one or more deviation-cropping areas (C q) defined thereby lie within a tolerance range (T i) around the corresponding cropping area (D i) defined by the corresponding position (P i) and the at least one selection position (P a) of the cropping area (D) is determined as that of the plurality of positions (P i) for which the determined aberration (F i) and the one or more determined deviation aberrations (E q) are each smaller than the predetermined threshold value (SW).The method according to claim 7, wherein the ingot (200) has a first, second and third direction (x', y', z'), the third direction (z') is arranged along the axis of symmetry (A) of the ingot (200), the first and second direction (x', y') are arranged perpendicular to each other and respectively perpendicular to the axis of symmetry (A), and the one or more deviation positions (Q q) differ from the corresponding position (P i) of the corresponding cut-out area (D i) with respect to: the radial position (r i), the height position (h i), a displacement in the first, second and / or third direction (x', y', z'), a rotation about the first, second and / or third direction (x', y', z'), non-parallel edges (230, 232) of the deviating cut-out region (C 4) in the first, second and / or third direction (x', y', z'), respectively, and / or a volume deviation (ΔW) of the one or more deviating cut-out regions (C 5) from the corresponding cut-out region (D i). defined by the corresponding position (P i).Method according to one of Claims 1 to 8, wherein, in the computer-implemented determination of the respective aberration (F i) of the optical system (100), an error range (ΔF i) of the determined aberration (F i) is additionally determined, and the at least one selection position (P a) of the cut-out region (D) is determined as that of the plurality of positions (P i) for which the determined aberration (F i) including its error range (ΔF i) is less than the predetermined threshold value (SW).Method according to claim 9, wherein the respective aberration (F i) is determined with the aid of a computer-aided simulation, and the error range (ΔF i) of the determined aberration (F i) is determined based on one or more error ranges (Δg) of one or more input parameters (g) of the simulation.Method according to Claim 9 or 10, wherein the error range (ΔF i) of the determined imaging error (F i) is determined on the basis of an error range (Δg) of the provided distribution function (g) of the zero crossing temperature (ZCT R).Method according to one of Claims 9 to 11, wherein the respective aberration (F i) is determined with the aid of a computer-assisted simulation, and the error range (ΔF i) of the determined aberration (F i) is determined on the basis of the consideration of one or more systematic errors of the simulation.The method according to any one of claims 1 to 12, wherein the determination of the respective imaging error (F i) of the optical system (100) comprises: determining a plurality of mutually different individual errors (f k) with respect to mutually different types of errors of the optical system (100), and determining the respective imaging error (F i) of the optical system (100) based on the plurality of determined individual errors (f k).Method according to claim 13, wherein the plurality of mutually different individual errors (f k) are determined with respect to the mutually different types of errors and with respect to mutually different setting parameters (500) of an illumination of the optical component (102) of the optical system (100) to be produced.Method according to Claim 13 or 14, wherein the plurality of determined individual errors (f k) with respect to the different types of errors comprise: a deviation (f 1) of an actual focus (F Ist) of the optical system (100) (100) from a desired focus (F Soll), a deviation of an actual position (P Ist) of an object (402) imaged in an image plane (302) of the optical system (100) by means of the optical system (100) from a desired position (P Soll of the imaged object (404), an image displacement of an image (400) imaged in an image plane (302) of the optical system (100) by means of the optical system (100), and / or a deviation of an actual wavefront (304), which images an image (400) in an image plane (302) of the optical system (100), from a target wavefront (306).Method according to Claim 15, wherein the deviation of the actual wavefront (304) from the desired wavefront (306) comprises a tilt of the wavefront (304), a displacement of the wavefront (304), an astigmatism of the wavefront (304), a coma of the wavefront (304), a multiple ripple of the wavefront (304) and / or a spherical aberration of the wavefront (304), and / or the deviation of the actual wavefront (304) from the desired wavefront (306) is quantified in the form of Zernike polynomials (ZP).Method according to one of Claims 1 to 16, comprising: providing (S1) the ingot (200), and measuring (S2) the distribution function (g) of the zero crossing temperature (ZCT R) of the ingot (200).Method according to one of Claims 1 to 17, comprising: providing (S1) the ingot (200), and cutting (S5) the substrate (104) out of the ingot (200) in accordance with the at least one determined selection position (P a) of the cutting region (D) and / or the optimum position (P opt) of the cutting region (D).Substrate (104, 104', 104") for an optical component (102) of an optical system (100) of a lithography apparatus (1), having a distribution function (g', g") of a zero crossing temperature (ZCT', ZCT") of a coefficient of thermal expansion (α', α") as a function of a location (p', p") of the substrate (104', 104"), wherein the distribution function (g', g") has a pattern (112, 112") of the zero crossing temperature (ZCT', ZCT") which has a plurality of concentric ring sections (114, 114"), which are respectively partial sections of a full ring (116, 116").The substrate according to claim 19, wherein an auxiliary line (120, 120") of the substrate (104', 104") is defined such that it is arranged perpendicular to mutually parallel tangents (T, T") to the ring portions (114, 114") and runs through an imaginary center point (118, 118") of the imaginary full rings (116, 116") corresponding to the ring portions (114, 114"), and the auxiliary line (120) is arranged parallel to a longitudinal direction (L) of the substrate (104'), or the auxiliary direction (120") is arranged inclined to the longitudinal direction (L") of the substrate (104").Lithography apparatus (1) comprising a substrate (104, 104', 104") according to claim 19 or 20, and / or an optical system (100) comprising an optical component (102) comprising a substrate (104, 104', 104") according to claim 19 or 20.

Images