Method of determining imaging quality of an optical system when illuminated by illumination light

Abstract

To determine the imaging quality of the optical system (13) when illuminated by the illumination light (1) within the entrance pupil or exit pupil (11) to be measured, the test structure (5) is initially arranged in the object plane (4) of the optical system (13) and an illumination angular distribution is specified for illuminating the test structure (5) with the illumination light (1). The test structure (5) is illuminated at different distance positions (z m ) of the test structure (5). The intensity I(x, y, z m ) of the illumination light (1) is measured in the image plane (15) of the optical system (13). The spatial image measured in this way is compared with the simulated spatial image, the fitting parameters of the function set used to describe the simulated spatial image are adjusted, and the wavefront of the optical system (13) is determined on the basis of the result of minimizing the difference. The specified illumination angular distribution corresponds to a sub-aperture (10 i ) within the entrance pupil (11) to be measured. For another specified sub-aperture, the steps from "specify" to "determine" are repeated. The wavefront of the optical system is determined by combining the results obtained for the measurement sub-apertures (10 i ) within the entrance pupil (11) to be measured.

Description

[0001] Cross-reference to related applications

[0002] The content of German patent application DE 10 2021 205 541.9 is incorporated herein by reference. TECHNICAL FIELD

[0003] The present invention relates to a method for determining an imaging quality of an optical system when being illuminated by an illumination light within an entrance pupil to be measured. BACKGROUND

[0004] From WO 2016 / 012 426 A1 a metrology system for measuring a three-dimensional aerial image of a photolithography mask is known. DE 10 2013 219 524 A1 describes an apparatus and a method for determining an imaging quality of an optical system and an optical system. DE 10 2013 219 524 A1 describes a phase retrieval method based on pinhole imaging for determining a wavefront. SUMMARY

[0005] It is an object of the present invention to design a method for determining an imaging quality of an optical system with respect to an entrance pupil to be measured as flexibly as possible.

[0006] According to the invention, this object is achieved by a determination method having the features specified hereinafter.

[0007] The present invention relates to a method for determining an imaging quality of an optical system when being illuminated by an illumination light within an entrance pupil to be measured and / or an exit pupil to be measured, comprising the following steps:

[0008] arranging a test structure in an object plane of the optical system,

[0009] specifying an illumination angle distribution with which the test structure is to be illuminated by the illumination light,

[0010] illuminating the test structure with the specified illumination angle distribution at different distance positions of the test structure relative to the object plane,

[0011] measuring an intensity of the illumination light in an image plane of the optical system using a spatially resolving detection device for determining a measurement aerial image of the test structure, the illumination light having been guided by the optical system when imaging the test structure at each distance position,

[0012] comparing the measurement aerial image with a simulated aerial image and adjusting fitting parameters of a set of functions used for describing the simulated aerial image until a difference between the measurement aerial image and the simulated aerial image has been minimized,

[0013] determining a wavefront of the optical system on the basis of the results of the minimization of the difference between the measured spatial image and the simulated spatial image,

[0014] the specified illumination angle distribution corresponds to a sub-aperture within the pupil to be measured,

[0015] repeating the steps from “specifying” to “determining” using another specified sub-aperture, which is offset with respect to the measured sub-aperture within the pupil to be measured,

[0016] determining the wavefront of the optical system by combining the results obtained for the measured sub-aperture over the entire pupil to be measured.

[0017] According to the application, it is recognized that determining the imaging quality on the basis of spatial image measurements does not require the complete illumination of the pupil to be measured during a single measurement. Rather, the measurement can be performed sequentially using sub-apertures within the pupil to be measured, and the measurement results obtained through the individual sub-apertures are then combined. In the case of a specified illumination angle distribution over a sub-aperture within the pupil to be measured, an appropriate sub-aperture diaphragm can be introduced into the entrance pupil of the projection optical unit of the optical system and can be positioned transversely to the illumination beam path, so that this produces the desired illumination direction in accordance with the specified pupil coordinates. It is also possible to record and measure a very irregular shape of the pupil to be measured by means of an appropriate coverage of the sub-apertures. The pupil to be measured can be an elliptical pupil, a circular pupil, or a pupil delimited by a free form. The pixel resolution of the spatially resolving detection device can be adapted to the numerical aperture of the pupil to be measured. For higher numerical apertures, a larger pixel resolution of the detection device is selected. In each sub-aperture measurement, the wavefront of the optical system in this sub-aperture can be derived by means of a phase retrieval method, which is known in principle from the literature, for example from DE 10 2013 219 524 A1. For the optimization of the determination of the difference, projection methods (error reduction algorithm, Gerchberg-Saxton method, IFTA method) and / or conventional iterative optimization methods (gradient descent, least squares method, damped least squares method, genetic search method, simplex method, Chambolle-Pock optimization method, backpropagation method) and / or direct inversion methods (extended Nijboer-Zernike decomposition method (S. Van Haver, “Extended Nijboer-Zernike diffraction theory and its applications”, http: / / resolver.tudelft.nl / uuid:8d96ba75-24da-4e31-a750-1bc348155061, 2010), database-based methods, machine learning methods) can be used.

[0018] Preferably, the pupil is scanned by the sub-apertures. Scanning the pupil by sub-apertures as described above facilitates an excellent comparative method process. The scanning of the pupil by sub-apertures can be realized by exactly one row of sub-apertures. Alternatively, a scanning over multiple rows of sub-apertures is also possible. The scanning can be such that the principal ray polar angle of the illumination light remains constant. In this case, the test structure is always illuminated with the same principal ray incidence angle. In a variant, there can even be a multi-row scanning with multiple rows, in each case the principal ray polar angle being constant within a row and the principal ray polar angle varying with different rows.

[0019] Preferably, in order to determine the imaging quality of the optical system independently of the test structure, a test structure contribution of the influence of the test structure on the wavefront is eliminated. The elimination of the test structure contribution as described above improves the results of the method by eliminating a systematic falsification of the imaging quality determination.

[0020] Preferably, the test structure contribution is determined for exactly one specified sub-aperture and then this contribution is also used for determining the imaging quality of the optical system for another sub-aperture, independently of the test structure. In the method as described above, the effort associated with determining the test structure contribution is reduced. For example, the test structure contribution determined for exactly one specified sub-aperture can be post-processed or converted by rotating the test structure contribution in accordance with the illumination angle, in particular the principal ray azimuth angle, assigned to the respective sub-aperture, in order to eliminate the test structure contribution in the case of the other sub-aperture.

[0021] Preferably, in the method a system of linear equations is solved in order to determine the imaging quality and at the same time to eliminate the test structure contribution, in which system of linear equations the data of the wavefront determined before the elimination of the test structure contribution, the contribution of the test structure and a transformation matrix are included. The method as described above has proven its value in practice. A representative of this method is known as the shift-and-rotate method. Examples of this shift-and-rotate method can be found in the following specialist articles: D. Su et al., "Absolute surface figure testing by shift-and-rotate method using Zernike polynomials", Opt. Lett. 37, 3198-3200 (2012) (https: / / doi.org / 10.1364 / OL.37.003198); Y. Liu et al., "Extended shift-and-rotate method for spherical absolute interferometric testing with pixel-level spatial resolution", Appl. Opt. 56, 4886-4894 (2017) (https: / / doi.org / 10.1364 / AO.56.004886); DE 10 2013 226 668 A1 ; and US 5982490 A.

[0022] Preferably, in the method, the data of the wavefront determined before eliminating the contribution of the test structure, and / or the contribution of the test structure, and / or the correlation of the transformation matrix on the respective coordinates in the solution space to be determined, are described by a decomposition into basis functions. The "decomposition into basis functions" as described above has proven its value in practice. The following can be used as basis functions: Zernike polynomials, Bhatia-Wolf polynomials, Bessel functions, solutions of the Laplace equation, orthonormalized locally distributed narrow exponential functions and / or Gaussian functions (optionally distributed on a grid), orthonormalized locally distributed spline polynomials (optionally distributed on a grid), and orthonormalized mixtures of basis functions. Such orthonormalization can be achieved, for example, using the Gram-Schmidt orthonormalization method (1968, McGraw-Hill, Korn and Korn, "Mathematics Handbook for Scientists and Engineers"; 1992, D. Malacara, Wiley, "Optical Shop Testing", http: / / de.wikipedia.org / wiki / Schmidtsches_Orthonormalisierungsverfahren).

[0023] Preferably, in the method, a pinhole is used as the test structure. The pinhole as test structure as described above has proven its value in practice.

[0024] Preferably, in the method, the pinhole has an elliptical edge. The elliptical pinhole as described above was found to be particularly suitable for determining aberrations in the case of an anamorphic imaging system, i.e. an imaging system having different imaging scales in mutually perpendicular planes. The elliptical pinhole as described above was also found to be particularly suitable for determining aberrations in the case of an isomorphic imaging system having an elliptical entrance pupil.

[0025] Preferably, in the method, the pupil to be determined has an elliptical edge; in the determination of the wavefront, there is a representation of the pupil function for at least a cross-sectional description of the pupil to be determined on a coordinate grid equidistant in the mutually perpendicular pupil coordinates, and a parameterized basis function scaled in accordance with the ratio of the major axes of the elliptical edge of the pupil. Preferably, in the method, the pupil to be determined has an elliptical edge; in the determination of the wavefront, there is a representation of the pupil function for at least a cross-sectional description of the pupil to be determined on a coordinate grid scaled in the mutually perpendicular pupil coordinates in accordance with the ratio of the major axes of the elliptical edge of the pupil, and a uniformly scaled parameterized basis function. The representation of the pupil function as described above is found to be particularly suitable for implementation in the determination method.

[0026] The application also relates to a metrology system for carrying out a method as described above, having an illumination optical unit for illuminating the test structure and having an imaging optical unit, the imaging quality of which is intended to be determined, for imaging the test structure towards a spatially resolving detection device. The advantages of the measurement system as described above correspond to those already explained with reference to the determination method.

[0027] A further object of the application is to develop a metrology system of the type mentioned at the outset, such that a phase retrieval method, for example according to the prior art, can also be used for an elliptical pupil to be measured.

[0028] According to the application, this object is achieved by a metrology system having the features specified below.

[0029] The application relates to a metrology system, which

[0030] has a holder for a test structure,

[0031] has an illumination optical unit for illuminating the test structure in an object plane specified by the holder,

[0032] has a spatially resolving detection device,

[0033] has an imaging optical unit for imaging the test structure towards a detection device in an image plane,

[0034] has an aperture stop with an elliptical edge, which is arranged in an illumination pupil plane and / or in an entrance pupil of the imaging optical unit.

[0035] According to the application, it is recognized that an elliptical pupil can be measured directly by using an aperture with an elliptical edge arranged in the pupil plane of the metrology system and that this elliptical pupil can be used to determine the wavefront by a phase retrieval method. In this way, such a metrology system can be used in particular to determine the imaging quality of the optical system when illuminated with an illumination light within the entrance pupil to be measured and / or the exit pupil to be measured. In the phase retrieval method, according to the determination method explained above, basis functions parameterized in a scaled manner can be used, in particular compressed Zernike polynomials and / or a scaled coordinate grid and uniformly scaled parameterized basis functions.

[0036] Preferably, the metrology system is used to carry out the method as described above. The advantages of the metrology system as described above correspond to those already explained with reference to the determination method. BRIEF DESCRIPTION OF DRAWINGS

[0037] Exemplary embodiments of the application are explained in greater detail below with reference to the drawings, in which:

[0038] Figure 1 A plan view of a metrology system for determining the imaging quality of an optical system when illuminated with an illumination light within an entrance pupil to be measured is shown very schematically, wherein the viewing direction is perpendicular to the entrance plane, the metrology system comprising an illumination optical unit and an imaging optical unit, both units being represented very schematically;

[0039] Figure 2 A test structure in the form of an EUV pinhole is shown in perspective and enlarged, serving as a reflecting object imaged in a metrology system according to Figure 1 ;

[0040] Figure 3 Intensity measurements in the image plane of the imaging optical unit of the metrology system are shown for different positions of the arrangement plane of the test structure relative to the object plane (Z-focal stack) when imaging a test structure according to Figure 2 ;

[0041] Figure 4 An entrance pupil to be measured of an optical system to be measured, embodied as an elliptical entrance pupil, and a set of sub-apertures for a single row scan of the entrance pupil to be measured, each sub-aperture embodied as a sub-pupil with a circular edge, each sub-aperture corresponding to a specified illumination angular distribution with which a test structure is illuminated, and the test structure illuminated in a sequence with an illumination angular distribution corresponding to the superposition of all sub-apertures, are shown;

[0042] Figure 5 A test structure in the form of an EUV pinhole is shown in perspective and enlarged, serving as a reflecting object imaged in a metrology system according to Figure 4The representation shows a variation that uses sub-apertures to scan the entrance pupil to be measured, which is implemented such that the polar angle of the principal ray of the illumination of the test structure remains constant for all sub-apertures;

[0043] Figure 6 With similar Figure 4 and 5 The representation shows another variation of using a sub-aperture to perform a multi-line Cartesian scan of the incident pupil to be measured;

[0044] Figures 7 to 11 The contour map shows the results based on... Figure 5 The wavefront measurements of the five selected sub-apers of the scan are expressed in each case as the phase contribution in the pupil plane of the imaging optics unit;

[0045] Figures 12 to 16 The test structures are shown respectively according to Figures 7 to 11 The contribution of wavefront measurements was again represented using contour plots in each case;

[0046] Figures 17 to 21 It is shown that from the basis Figures 7 to 11 Subtract from the original wavefront measurement results Figures 12 to 16 After the test structure contribution, that is: after eliminating the test structure contribution, corresponding to according to Figures 7 to 11 The wavefront measurement results in the cross section of the incident pupil to be measured in the sub-aperture are again represented using contour plots in each case;

[0047] Figure 22 It shows that according to Figures 17 to 21 The superposition of sub-aperture contributions from wavefront measurements;

[0048] Figure 23 It shows that according to Figure 22 The wavefront measurement results are a limitation of the entrance pupil to be measured, that is, the wavefront phase of the optical system to be measured within the entrance pupil to be measured;

[0049] Figure 24 A schematic diagram of an imaging system with multiple lenses is shown, which is less illustrative than an imaging optics unit. This imaging system could be used to replace [the previous one]. Figure 1 In another embodiment of the metrology system, the imaging system is shown between the image plane and the object plane of the focused stack to be measured;

[0050] Figure 25 An example of the phase distribution in the exit pupil of a deformable optical system to be measured is shown, which is represented on a square grid with elliptic apods and has been parameterized according to the ellipticity corresponding to the compressed Zernike polynomial.

[0051] Figure 26 The semi-major and semi-minor axes along the elliptical pupil mask are shown, by means of... Figure 25 The cross section of the pupil function;

[0052] Figure 27 With similar Figure 25 The representation shows the representation on a non-square pupil grid, according to Figure 25 The pupil function is matched to the principal axis ratio of the elliptical exit pupil, and is circularly apodized and parameterized using conventional uncompressed Zernike polynomials; and

[0053] Figure 28 With similar Figure 26 The representation shows the path along two orthogonal principal axes, through... Figure 27 Two sections of the pupil function. Detailed Implementation

[0054] To facilitate the representation of positional relationships, the Cartesian xyz coordinate system will be used in the following text. Figure 1 In the diagram, the x-axis is perpendicular to the drawing plane and extends away from the drawing. The y-axis is... Figure 1 Extending to the right from the center. The z-axis is at... Figure 1 Extending upwards from the middle.

[0055] In the view corresponding to the meridional section, Figure 1 The optical path of the EUV illumination or imaging light in metrology system 2 is shown. This metrology system 2 is used to determine the imaging quality of the optical system when illuminated by illumination light 1 within the entrance pupil 11 to be measured. In this case, EUV illumination light 1 is used to test structure 5 in the form of a mask master or photolithographic mask arranged in the object field 3 in the object plane 4 (see...). Figure 2 Imaging is performed. In the following text, test structure 5 is also referred to as an object or sample. Metrology system 2 is used to analyze three-dimensional (3-D) spatial images (spatial image metrology system). Applications include the reproduction of spatial images of lithographic masks, as spatial images are also produced in projection exposure equipment, such as in a scanner. For this purpose, it is particularly necessary to measure and optionally adjust the imaging quality of metrology system 2 itself. Therefore, the analysis of spatial images can be used to determine the imaging quality of the projection optics unit of metrology system 2, or more specifically, to determine the imaging quality of the projection optics unit within the projection exposure equipment. (See WO2016 / 012 426A1, US 2013 / 0063716A1). Figure 3 DE 102 20 815A1 (see within) Figure 9 DE 102 20 816A1 (see within)Figure 2 ) and US 2013 / 0083321 Al.

[0056] The illumination light 1 is reflected at the object. In the case of central illumination, the plane of incidence of the illumination light 1 is parallel to the yz plane (kx = 0; see below, for example, with regard to the description of Figure 4

[0057] The EUV illumination light 1 is generated by an EUV light source 6. The light source 6 can be a laser plasma source (LPP; laser produced plasma) or a discharge source (DPP; discharge produced plasma). In principle, also a synchrotron-based light source, for example a free electron laser (FEL), can be used. The EUV light source can use wavelengths in the range between 5 nm and 30 nm. In principle, in the case of variants of the metrology system 2, also other light sources using light wavelengths can be used instead of the light source 6, for example a light source using wavelengths of 193 nm.

[0058] Based on the embodiment of the metrology system 2, the metrology system 2 can be used for reflective or transmissive objects. One example of a transmissive object is a pinhole aperture.

[0059] An illumination optical unit 7 of the metrology system 2 is arranged between the light source 6 and the object. The illumination optical unit 7 serves to illuminate the object to be inspected with a defined illumination intensity distribution on the object field 3 and at the same time with a defined illumination angle distribution of the field points of the illumination object field 3. This illumination angle distribution is also referred to in the following as an illumination sub-aperture.

[0060] The illumination sub-aperture is delimited by a sigma sub-aperture stop 8 of the illumination optical unit 7, which is arranged in an illumination optical unit pupil plane 9. Alternatively or additionally, a respective sub-aperture stop can also be present in the imaging optical unit of the metrology system 2, which will be described below. The sigma sub-aperture stop 8 limits the light beam of the illumination light 1 incident to its edge. Alternatively or additionally, the sigma sub-aperture stop 8 and / or the stop in the imaging optical unit can also mask the illumination light beam from the inside, that is to say act as a shadow stop. The respective stop can have an inner stop body which masks the light beam accordingly from the inside, which is connected to an outer stop support body by a plurality of webs, for example by four webs. The sigma sub-aperture stop 8 can be moved in a defined manner in the illumination optical unit pupil plane 9, that is to say parallel to the xy plane, by a displacement drive 8a.

[0061] Figure 4 A plurality of such sub-apertures 10 i ​(i = 1 to 5) which scan the elliptical entrance pupil 11 to be measured in the optical system to be measured. The ratio of the long semi-axis parallel to the x-axis to the short semi-axis parallel to the y-axis of the elliptical entrance pupil 11 is 2:1. Other ratios of the axes of the elliptical edge profile 10 in the range of 10:1 to 1.1:1 are also possible, for example 1.5:1, 1.6:1, 2.5:1, 3:1, 4:1, 5:1 or 8:1.

[0062] After reflection at the object, the illumination and imaging light enters the imaging optical unit or the projection optical unit 13 of the metrology system 2. In a similar manner to the illumination sub-aperture, there is a projection optical unit sub-aperture designated by a NA sub-aperture stop 11a in the entrance pupil 11 of the projection optical unit 13. The NA sub-aperture stop 11a can be displaced in a defined manner in the projection optical unit pupil plane, that is to say parallel to the xy plane, by means of a displacement drive 11b. Typically, the sigma sub-aperture stop and the NA sub-aperture stop are aligned relative to one another in such a way that the centre of both stops is hit by the central ray of the illumination light 1 and the reflection at the test structure 5. The sigma sub-aperture stop and the NA sub-aperture stop can be centred relative to one another. The region of the entrance pupil 11 of the projection optical unit 13 which is defined by the NA sub-aperture stop is referred to as the sub-aperture. Figure 1

[0063] The imaging optical unit to be measured serves to image the object towards a spatially resolving detection device 14 of the metrology system 2. The detection device 14 is designed, for example, as a CCD detector. A CMOS detector can also be used. The detection device 14 is arranged in the image plane 15 of the projection optical unit 13.

[0064] The detection device 14 is signal-connected to a digital image processing device 17.

[0065] The pixel spatial resolution of the detection device 14 in the xy plane can be specified in such a way that it is inversely proportional to the numerical aperture (NA x , NA y ) of the entrance pupil 11 to be measured in the coordinate directions x and y. In the x coordinate direction, this pixel spatial resolution is typically smaller than λ / 2NA x , and in the y coordinate direction typically smaller than λ / 2NA y . In this case, λ is the wavelength of the illumination light 1. The pixel spatial resolution of the detection device 14 can also be implemented independently of NA x , NA y in square pixel sizes.

[0066] The spatial resolution of the detection device 14 can be increased or decreased by resampling. A detection device with pixels of different sizes in the x and y directions is also possible.

[0067] ​The object is carried by an object holder or holder 18. The holder 18 can be moved by displacement drives 19, on the one hand parallel to the xy plane and on the other hand perpendicular to the xy plane, i.e. in the z direction. The displacement drives 19 as well as the entire operation of the metrology system 2 are controlled by a central control device 20, which is in signal connection with the components to be controlled in a manner not shown in detail.

[0068] The optical setup of the metrology system 2 is used to simulate the illumination and imaging in the projection exposure of the object during the projection lithography production of the semiconductor component as precisely as possible.

[0069] Figure 1 Various possible arrangement planes of the test structure 5 in the object plane 4 are shown, in each case using dashed lines. During the operation of the metrology system 2, the test structure 5 is illuminated at different distance positions z i of the specified illumination angle distribution, and the intensity I(x, y, z m ) is recorded in the image plane 15 in a spatially resolved manner for the respective distance position z m .This measurement result I(x, y, z m ) is also referred to as spatial image. m

[0070] The number z m of focal planes can be between 2 and 20, for example between 10 and 15. In this case, the total displacement in the z direction exceeds several Rayleigh units (NA / λ 2 ).

[0071] Depicted as an inset in Figure 1 is an xy plane view of the test structure 5, which can be in the form of a circular or elliptical test structure.

[0072] In addition to the entrance pupil 11, Figure 1 the exit pupil 21 of the projection optical unit 13 is also shown schematically.

[0073] Figure 1 (bottom) the three measurement results of the detection device 14 are again shown in an xy plane view, wherein the middle measurement result shows an image representation of the test structure 5 arranged in the object plane 4, while the other two measurement results show image representations of the test structure 5 which have been displaced relative to the z coordinate of the object plane 4, once in the positive z direction and once in the negative z direction. The spatial image of the test structure 5 results from the sum of the measurement results assigned to the respective z coordinate.

[0074] Figure 2Details of the test structure 5 are shown, which is implemented as a reflective pinhole. The optical path of the chief ray of the illumination light 1 is schematically depicted when being reflected at the test structure 5. The range of the angle of incidence of the chief ray of the illumination light 1 on the pinhole of the test structure 5 is between 3° and 8°, for example 5° or 6°. The diameter of the pinhole of the test structure 5 ranges between 100 nanometers and 150 nanometers. The pinhole is formed in an absorbing layer 22, which in turn is applied onto a highly reflective multilayer 23. The thickness of the absorbing layer ranges between 50 nanometers and 70 nanometers. The thickness of the multilayer ranges between 250 nanometers and 300 nanometers.

[0075] The pinhole of the test structure 5 can be elliptical. The major axis of the pinhole can have approximately the same size as the Airy disk of the projection optical unit 13, that is to say 2.44 λ / NA x in the x coordinate direction and 2.44 λ / NA y .

[0076] The test structure 5 can have a single pinhole or a plurality of pinholes, in particular a periodic pinhole array. Other test structures are possible, for example described in US 2015 / 0355052 Al.

[0077] Figure 3 The result I(x, y, z m ) is shown as a sequence of five measurement values of different z coordinates of the test structure 5, and the middle measurement value of the five measurement values occurs with the arrangement of the test structure in the object plane 4. Thus, the measurement result of the detection device 14 is described again. Figure 3 The comparison of the leftmost shown measurement value with Figure 3 the rightmost shown measurement value in Fig. 6 shows the asymmetry of the imaging measurement result when imaging the circular pinhole of the test structure 5, which can be traced back to the oblique illumination of the test structure 5 by the illumination light 1. This results in a test structure contribution related to the illumination angle in the influence of the wavefront by the test structure 5.

[0078] Figure 4 An embodiment is shown in which a single row scan of the entrance pupil 11 of the projection optical unit 13 to be measured is carried out using the sub-pins 101 to 105, which are specified by the sub-pinhole diaphragms 8 and 11a of the illumination optical unit 7 and the projection optical unit 13.

[0079] These pupils are represented in angle space, that is to say in the pupil coordinates kx (corresponding to the x spatial coordinate) and ky (corresponding to the y spatial coordinate). Due to the oblique illumination, the center of the entrance pupil 11 is located at kx = 0 and ky ≠ 0. The center of the respective sub-pinhole 10 i , that is to say the relative position of the respective chief ray, is at Figure 4are marked with triangles. Adjacent sub-apertures 10 i i+1 These centers of the sub-apertures 10 i each have the same ky coordinate. The envelope of all sub-apertures 10 i completely covers the entrance pupil 11 to be measured. The center of the elliptical entrance pupil 11 to be measured is located at (kx = 0, ky = 0.1). The center of the sub-aperture 103 coincides with the center of the elliptical entrance pupil 11 to be measured.

[0080] Figure 5 A variant is shown in which the entrance pupil 11 to be measured is scanned using sub-apertures 10 i Again, a scan using five sub-apertures 101 to 105 is described. According to the scan, the centers of the sub-apertures 10 i are offset relative to each other by a constant increment in the kx direction. Each center of the sub-apertures 10 i has the same ky coordinate. The envelope of all sub-apertures 10 i completely covers the entrance pupil 11 to be measured. The center of the elliptical entrance pupil 11 to be measured is located at (kx = 0, ky = 0.1). The center of the sub-aperture 103 coincides with the center of the elliptical entrance pupil 11 to be measured. Figure 5 Figure 5 The main ray polar angle θ between the origin (kx = 0, ky = 0) of the pupil plane 9 and the center of the sub-aperture 10 i remains constant in each case. In the (kx, ky) space, the main ray polar angle θ has an absolute value of slightly more than 0.1°. This main ray polar angle θ is measured between the origin 0, 0 of the pupil plane 9 and the respective center of the sub-aperture 10 i . In the scan according to Figure 5 , the sub-apertures 10 i are thus moved relative to each other such that the main ray polar angle θ of the respective sub-aperture remains unchanged.

[0081] When scanning the entrance pupil 11, the sub-apertures 101 to 105 sweep through a main ray azimuth angle In the embodiment according to Figure 5 , this main ray azimuth angle is approximately 75°.

[0082] Figure 6 Another variant is shown in which the elliptical entrance pupil 11 to be measured is scanned using sub-apertures 10 i，j . In this case, i specifies the row number and j specifies the column number of the respective sub-aperture 10 i，j . The scan according to Figure 6 is implemented using a total of 21 sub-apertures 10 i，j in 3 rows (i = 3) and 7 columns (j = 7).

[0083] As an alternative to the single-row scan with constant main ray polar angle θ in the variant according to Figure 5 , a multi-row scan can also be carried out in which the respective main ray polar angle θi remains constant in each row and, in each case, the main ray polar angles θ i , θ i+1 of the different rows i, i + 1 differ from each other.

[0084] Figures 7 to 11 The results of the wavefront measurement based on the use of the sub-apertures 105( Figure 7 ), 104( Figure 8 ), 103( Figure 9 ), 102( Figure 10 ) and 101( Figure 11 ) are shown in the form of contour plots. In this case, the measurement was performed with constant chief ray polar angle by means of a scan according to Figure 5 On the right of the respective wavefront representation, there is a specification of the relative phase values corresponding to the respective contour lines.

[0085] Figure 7 The phase of the wavefront is depicted, which is determined from the measurement results of the focusing stack of the sub-apertures 10 i According to the determination of this phase contribution according to Figures 7 to 11 The determination of this phase contribution according to

[0086] In a representation similar to Figures 7 to 11 , Figures 12 to 16 the contributions of the test structure to the influence of the test structure 5 on the wavefront of the illumination light 1 are shown in succession. In each case, the test structure contribution can be separated and eliminated from the measurement results according to Figures 7 to 11 What is exploited here is that the test structure contribution remains unchanged in terms of the phase distribution during illumination with the respective sub-aperture 105( Figure 12 ) to 101( Figure 16 ), and only the orientation of this phase distribution changes with the rotation of the chief ray azimuth The "pole" 24 of the minimum phase values of the test structure contribution points approximately to the right in Figure 12 and approximately to the top in Figure 16 corresponding to a change in the chief ray azimuth of approximately 75°.

[0087] The test structure contribution according to Figures 12 to 16 can be determined independently of the wavefront measurement according to Figures 7 to 11

[0088] Figures 17 to 21 The wavefront measurement results of the individual sub-apertures 105( Figure 17 ) to 101( Figure 21 ) are shown again in a representation similar to Figures 7 to 11 after the elimination of the test structure contribution according to Figures 12 to 16 Figures 17 to 21 ​​The wavefront phase contributions determined or measured by the respective sub-aperture 105 to 101 during the measurement process are delimited by using a circular edge drawn by the point and, in addition, the wavefront phase of the optical system to be measured is drawn in the pupil plane of the respective sub-aperture 101.

[0089] In a similar manner to Figures 17 to 21 , Figure 22 the superposition of the sub-aperture determinations according to Figures 17 to 21 is shown, that is to say the entire determined wavefront component in the pupil plane of the optical system to be measured.

[0090] Figure 23 The restriction of the determined result according to Figure 22 to the elliptical entrance pupil 11 to be measured is shown.

[0091] When determining the wavefront measurement data according to Figures 7 to 11 from the raw measurement data according to Figures 12 to 16 and the test structure contribution according to Figure 23 , a shift-rotation method is used.

[0092] An example of this shift-rotation method can be found in the professional article "Absolute surface profile testing by shift-rotation method using Zernike polynomials" by D. Su et al., published in 2012 in Optics Letters, Vol. 37, No. 15, pages 3198-3200 (https: / / doi.org / 10.1364 / OL.37.003198) and in German patent 102013 226 668 A1.

[0093] If the measurement data (m pixel values) of all n (in the described example n = 5) sub-apertures are combined into one vector, the following system of equations can be constructed:

[0094]

[0095] measurement data of the wavefront measurement (see above Figures 7 to 11 ); n sub-apertures, each with m wavefront points, that is to say m pixels in the pupil plane as a result of the wavefront measurement evaluated on a pixel grid;

[0096] wavefront points to be determined of the projection optical unit 13 (see above Figures 17 to 21 ), usually q > m (superposition of the results according to Figures 7 to 11 ; see Figure 22 and 23 ), the index q runs over the at least one sub-aperture 10i all points covered by (i = 1 to n);

[0097] pinhole contribution (see Figures 12 to 16 ), m wavefront points;

[0098] combined transformation matrix;

[0099] m x q optical transformation matrix, sub-aperture i;

[0100] m x m pinhole transformation matrix, sub-aperture i.

[0101] For a sub-aperture scan according to the above Figure 4 , if the pinhole contribution is independent of kx, then the m x m identity matrix I m is given If the pinhole contribution depends on kx, then this dependency is modeled by a proper choice of the transformation matrix .

[0102] In case of a sub-aperture scan according to the above Figure 5 , the matrix corresponds to a rotation of the wavefront points. If the wavefront is described on a Cartesian grid, then the rotation usually requires an interpolation of the pixel values. In this case, both a “nearest neighbor” interpolation and a linear (or higher order) interpolation are possible and are therefore modeled in

[0103] The system of equations can be solved using conventional methods for solving linear systems of equations and the wavefront aberration W of the projection optical unit to be measured and in this way the component of the wavefront aberration P caused by the pinhole is determined.

[0104] Zernike polynomials can be fitted to the determined wavefront aberration W of the projection optical unit in the elliptical pupil area to be measured and the wavefront aberration W in the pinhole P area and thus the Zernike spectrum can be determined.

[0105] Since the contributions of the pinhole and the projection optical unit can be separated, the method from the application example can also be used for improving a wavefront measurement on a circular entrance pupil of an optical unit to be measured instead of a wavefront measurement on an elliptical entrance pupil 11.

[0106] In phase retrieval, the measured spatial image I(x, y, z m ) is compared with the simulated spatial image I sim and the fitting parameters of the set of functions used to describe the simulated spatial image are adjusted until the difference between the measured spatial image and the simulated spatial image is minimized. ​

[0107] Based on the minimized difference between the measured and the simulated spatial image, the wavefront of the optical system is determined in the phase retrieval.

[0108] The phase retrieval difference minimization can be optimized by means of various methods. These methods include the projection method, also known as error reduction algorithm, the Gerchberg-Saxton method or the IFTA method. Conventional iterative optimization methods can also be used. By way of example, these methods include the gradient descent method, the least squares method, the damped least squares method, the genetic search method, the simplex method, the Chambolle-Pock optimization method, the backpropagation method. Direct inversion methods can also be used. Examples thereof include the extended Nijboer Zernike decomposition method or a machine learning-based method based on, for example, previous results stored in a database. If the aberrations of the optical system are expected to be a matter of principle within the entrance pupil to be measured, a sufficiently densely sampled database can be generated by simulation. The retrieval can then be achieved by a search in this database. Within the scope of machine learning, a network can be trained by means of a previously calculated aberration dataset.

[0109] For the parameter capture and determination of the imaging aberrations of an optical system, the description of these imaging aberrations, that is to say, for example, the description of the phase distribution according to Figure 23 , can be decomposed into basis functions. This optimization by means of basis functions avoids undesirable result noise.

[0110] For the precise determination of the imaging quality, it is important that the basis functions are able to well describe the expected imaging aberrations. It is to be considered here that a circular sub-aperture is used to scan the elliptical pupil to be measured. In this case, the regions of the wavefront determined by the phase retrieval overlap. In order to be able to use this for the calculation of the entire elliptical entrance pupil to be measured, it is advantageous if the basis of the functional decomposition of the individual wavefronts is chosen in such a way that the individual wavefronts can be described by means of shifts / rotations.

[0111] In principle, Zernike polynomials are suitable as basis functions. Bhatia-Wolf polynomials, Bessel functions, solutions of the Laplace equation, narrow exponential functions of a localized distribution which are orthogonalized and / or Gaussian functions, optionally distributed on a grid, spline polynomials of a localized distribution which are orthogonalized and optionally distributed on a grid, and orthogonalized mixtures of basis functions are found to be advantageous in terms of the describability by means of shifts / rotations.

[0112] In this case, the orthogonalization of the functions increases the robustness of the optimization and the comparability of the results. A partial orthogonalization of the basis functions is also possible.

[0113] A mixture of the possible basis functions listed above can also be particularly suitable, for example a combination of Zernike polynomials and narrow exponential functions of a local distribution which are orthogonalized. For this purpose, a small number of Zernike polynomials, for example 9 to 16 Zernike polynomials, are used to describe the conventional imaging aberrations in this way. In addition, a local Pilk function in the form of, for example, an exponential function or a Gaussian function is used to describe the local deviations. In this case, the exponential function is partially orthogonal with respect to the Zernike functions. Partial orthogonalization of a function set F with respect to another function set G is understood to mean that each element of F is converted by means of a method such that the element is then orthogonal to all elements of G. As an example, this can be achieved using the orthogonalization step of the Gram-Schmidt orthogonalization method. The difference to complete orthogonalization is that the elements in F and G do not have to be orthogonal to each other.

[0114] This orthogonalization can be achieved, for example, using the Gram-Schmidt orthogonalization method (D. Malacara, 1992, Wiley-VCH, "Optical Shop Testing", http: / / de.wikipedia.org / wiki / Schmidtsches_Orthonormalisierungsverfahren).

[0115] To illustrate the phase retrieval method, Figure 24 An embodiment of the metrology system 2 between the object plane 4 and the image plane 15 is shown. Correspondence to the components and functions described above with reference to the above figures, in particular to the Figure 1 The components and functions corresponding to those described above with reference to the above figures, in particular to the

[0116] In addition, Figure 24 A wavefront 26 of the wavefront of the optical system to be measured is illustrated, on the basis of which the imaging quality of the optical system is described. By way of example, Figure 23 The phase profile of such a wavefront 26 in the pupil plane is shown.

[0117] In addition to the image plane 15 in which the detection device 14 is arranged, Figure 24 A further parallel reflection image plane at a distance therefrom is also shown, which arises as a result of a displacement of the test object in the z direction. As an alternative, the detection device 14 can also be moved in the z direction; this is not shown in the figures.Figure 24 The above is illustrated in more detail in the following.

[0118] For the intensity I(x, y, z) measured by the detection device 14, the following relationship can be constructed:

[0119] I = abs(H pupil_image (H object_pupil (E object ) · E pupil )) 2 + N. (2)

[0120] In this case, H object_pupil is the optical transfer function between the object plane 4 and the pupil 11 in the pupil plane 25;

[0121] H pupil_image is the optical transfer function between the pupil 11 and the image plane 15;

[0122] E object is the complex amplitude (amplitude and phase) of the test object;

[0123] E pupil is the system transfer function in the form of a complex pupil amplitude, that is to say, the desired wave function of the optical system; and

[0124] N is the contribution that specifically describes the noise in the detection device 14.

[0125] In the context of phase retrieval, the wave function E pupil is back-calculated from the measured intensity values I.

[0126] In this case, a forward simulation of the imaging of the test object by the projection optical unit 13 is implemented, and the difference between the simulated values parameterized in the aberrations, that is to say, the imaging aberrations, and the measurement results I is minimized.

[0127] If a deformation projection optical unit 13 is used, the simulation needs to be adapted to the deformation setting. Formulas for the simulation based on the Fourier transform facilitate a fast and precise simulation.

[0128] For this purpose, the elliptical pupil 11 of the projection optical unit to be parameterized can be parameterized by the following variants:

[0129] Firstly, the pupil function can be represented on a square grid by compressed Zernike polynomials together with an elliptical apodization and a parameterization of the pupil function, that is to say, the Zernike polynomials are scaled differently in the x and y directions. This is visualized in an exemplary manner in Figure 25 and 26 , Figure 25 and 26An example of the parameterization of the elliptical pupil 11 is shown, which is therefore represented in an equidistant kx and ky grid (square grid). Within the elliptical edge of the pupil 11, there exists a description as a linear combination of appropriately compressed Zernike polynomials. Outside the elliptical boundary, within a circle with a radius equal to the semi-major axis of the ellipse, the pupil function is set to zero (zero-fill).

[0130] Figure 26 The (kx, ky) plane diagram is shown Figure 25 The cross section of the pupil function depicted is first in the kx direction (cutting line 27), and secondly in the ky direction (cutting line 28).

[0131] The variation in the pupil function representation is implemented on a non-square pupil grid, meaning that the scaling in the kx and ky directions differs in a non-square pupil grid. The grid scaling, i.e., the grid width in kx and ky, is related to the numerical aperture NA of the elliptical pupil 11. x NA y The absolute values ​​are correlated. Then, in terms of pixels, this representation has a circular apodization and parameterization of the pupil function via conventional Zernike polynomials instead of compressed Zernike polynomials. Within the scope of the simulation, the different grid widths in kx and ky must be taken into account in the scaling of the Fourier transform. In this case, either adaptive zero-padding or linear frequency-modulated Z-transform can be used, where different adaptive scaling parameters should be chosen. The pupil grid widths in kx and ky can be chosen in such a way that the pupil function is scanned to the maximum extent and has the highest information density numerically.

[0132] Figure 27 and 28 An exemplary representation of the pupil function according to this variant with a non-square pupil grid and a circular apod is shown, which corresponds to the representation according to Figure 25 and 26 The way it is represented. It should be noted that in Figure 27 and 28 In this context, the scaling of the pupil coordinates kx and ky is different.

[0133] The given pixel grid of the detection device 14 and according to Figure 27 and 28 The scaling factor scal of the linear frequency modulated Z-transform between the x and y grids of the pupil representation (where the pupil function has a maximum scan) x / y Calculated as:

[0134]

[0135] Here:

[0136] λ is the wavelength of the illumination light 1 ;

[0137] dx(dy) is the pixel size, and

[0138] NA x / y is the numerical aperture of the pupil 11 in the x and y direction.

[0139] Then, depending on the different numerical apertures NA x , NA y , different scaling occurs in the x and y direction.

[0140] In general, the following applies: dx = dy. However, the pixel size of the detection device 14 in the x and y direction can also be chosen to be different in principle.

[0141] A further variant of this calculation consists in using a so-called error reduction algorithm: either a conventional FFT is used and an elliptical apodization matrix is used, or a chirp Z transform is used, an adaptive scaling parameter is used and a circular apodization matrix is used. As a result, it is possible to alternate between pupil space and image space in turn, in which the respective restriction is implemented in the respective space (similar to the case of the conventional IFTA algorithm, also known as the Gerchberg-Saxton algorithm).

[0142] By using variants of the representation of the pupil function described above, on the one hand, the entire entrance pupil 11 to be measured can be represented, or sub-apertures 10 i .

[0143] The measurement described above is carried out with a circular sub-aperture 10 i . In principle, it is also possible to carry out the measurement using an elliptical boundary of the sub-aperture. This can also be used to determine the aberrations on an elliptical entrance pupil. In this case, it is possible to carry out the measurement directly using an elliptical diaphragm in the place of the diaphragms 8 and 11a, respectively.

Claims

1. A method for determining the imaging quality of an imaging optical unit when illuminated by an illumination light (1) in an entrance pupil (11; 25) to be measured and / or an exit pupil to be measured, comprising the following steps: arranging a test structure (5) in an object plane (4) of the imaging optical unit, specifying an illumination angle distribution with which the test structure (5) is to be illuminated by the illumination light (1), recording a measurement spatial image of the test structure (5) illuminated by the illumination light (1), comparing the measurement spatial image with a simulated spatial image, and adjusting fitting parameters of a set of functions used to describe the simulated spatial image until the difference between the measurement spatial image and the simulated spatial image has been minimized, determining a wavefront of the imaging optical unit on the basis of the result of the minimized difference between the measurement spatial image and the simulated spatial image, scanning the pupil (11; 25) by the sub-aperture (10i). In order to determine the imaging quality of the imaging optical unit independently of the test structure, a test structure contribution (P) of the test structure (5) to the wavefront is eliminated. Solving a system of linear equations in order to determine the imaging quality and at the same time eliminating the test structure contribution of the test structure (5) to the wavefront, at different distance positions (z m ) of the test structure (5) relative to the object plane (4), illuminating the test structure (5) with a specified illumination angle distribution, measuring an intensity I(x, y, z) of the illumination light (1) in an image plane (15) of the imaging optical unit using a spatially resolving detection device (14) for determining a measurement spatial image of the test structure (5), when the test structure (5) is imaged at each distance position (z m ), m ) the illumination light has been guided by the imaging optical unit, including in the system of linear equations: data (M) of the wavefront determined before the elimination of the test structure contribution, The specified illumination angular distribution corresponds to a sub-aperture (10 i ), using another designated sub-aperture (10 i+1 ) repeating the steps from "designating" to "determining" for another designated sub-aperture (10 i+1 ) offset with respect to the measured sub-aperture (10 i ) within the pupil (11; 25) to be measured, The wavefront of the imaging optical unit is determined by combining the results of the minimised differences obtained for the measured sub-apertures (10 i ) over the entire pupil (11; 25) to be measured.

2. The method of claim 1, wherein, a contribution (P) of the test structure, and 3. The method of claim 1, wherein, a transformation matrix (T).

4. The method of claim 3, wherein, for exactly one specified sub-aperture (10 i ) and then this contribution is also used for determining the imaging quality of the imaging optical unit independent of the test structure for another sub-aperture (10 i+1 , 10 i+2 ,...).

5. The method of claim 3 or 4, wherein, describing: the data (M) of the wavefront determined before the elimination of the test structure contribution, and / or the contribution (P) of the test structure, and / or the transformation matrix (T) a correlation on respective coordinates (kx, ky) in a solution space to be determined.

6. The method of claim 5, wherein, using a pinhole as the test structure (5). The pinhole has an elliptical edge. The pupil (11; 25) to be determined has an elliptical edge; in the determination of the wavefront there is: a representation of a pupil function for at least a cross-sectional description of the pupil (11; 25) to be determined on a coordinate grid equidistant in mutually perpendicular pupil coordinates (kx, ky), and a parameterized basis function scaled according to a ratio of the major axes of the elliptical edge of the pupil (11; 25). The pupil (11; 25) to be determined has an elliptical edge; in the determination of the wavefront there is: a representation of a pupil function for at least a cross-sectional description of the pupil (11; 25) to be determined on a coordinate grid scaled in mutually perpendicular pupil coordinates (kx, ky) according to a ratio of the major axes of the elliptical edge of the pupil (11; 25), and a uniformly scaled parameterized basis function.

11. A metrology system (2) for carrying out the method according to any one of claims 1 to 10, having an illumination optical unit (7) for illuminating the test structure (5) and having an imaging optical unit whose imaging quality is intended to be determined, the imaging optical unit serving to image the test structure (5) towards a spatially resolving detection device (14).

7. The method of any one of claims 1 to 4, wherein, 12. A metrology system (2), 8. The method of claim 7, wherein, having a holder (18) for a test structure (5), 9. The method of any one of claims 1 to 4, wherein, ​ 10. The method of any one of claims 1 to 4, wherein, ​ ​ ​ ​ having an illumination optical unit (7) for illuminating the test structure (5) in an object plane (4) specified by the holder (18), having a spatially resolving detection device (14), having an imaging optical unit for imaging the test structure (5) toward a detection device (14) in an image plane (15), characterized in that Aperture (8; 10 i ; 11a) having holes with elliptical edges, which is arranged in an illumination pupil plane (9) and / or in an entrance pupil of the imaging optical unit, and the metrology system is configured to perform the method of any one of claims 1 to 10.

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