Method for determining the imaging quality of an optical system when illuminated with illuminating light within an entrance pupil to be measured, and metrology system

Abstract

Method for determining an imaging quality of an optical system (13) when illuminated with illuminating light (1) within an entrance pupil (11; 25) to be measured and / or within an exit pupil to be measured, comprising the following steps: - arranging a test structure (5) in an object plane (4) of the optical system (13), - specifying an illumination angle distribution for illuminating the test structure (5) with the illumination light (1), - Illuminating the test structure (5) with the specified illumination angle distribution at different distance positions (e.g. m ) of the test structure (5) relative to the object plane (4), - Detecting an intensity I(x,y,z m ) of the optical system (13) when imaging the test structure (5) in each distance position (z m) guided illumination light (1) in an image plane (15) of the optical system (13) with a spatially resolving detection device (14) for determining a measured aerial image of the test structure (5), - Comparing the measured aerial image with a simulated aerial image and adjusting fit parameters of a set of functions to describe the simulated aerial image until a difference between the measured aerial image and the simulated aerial image is minimized, - determining a wavefront of the optical system (13) based on the result of the minimized difference between the measured and the simulated aerial image, - where the given illumination angle distribution of a sub-aperture (10 i ) within the pupil to be measured (11; 25), - Repeat the steps “Specify” to “Determine” with another specified sub-aperture (10 i+1 ), which is relative to the already measured sub-aperture (10i ) is shifted in the pupil (11; 25) to be measured, - Determine the wavefront of the optical system by combining the results obtained at the measured sub-apertures (10 i ) were obtained over the entire pupil to be measured (11; 25).

Description

[0001] The invention relates to a method for determining an imaging quality of an optical system when illuminated with illuminating light within an entrance pupil to be measured.

[0002] A metrology system for three-dimensionally measuring an aerial image of a lithography mask is known from WO 2016 / 012 426 A1. DE 10 2013 219 524 A1 describes a device and a method for determining the imaging quality of an optical system, as well as an optical system. DE 10 2013 219 524 A1 describes a phase retrieval method for determining a wavefront based on the image of a pinhole. DE 10 2014 210 641 A1 discloses a test object for measuring a point spread function of an optical system. DE 10 2017 216 703 A1 discloses a method for characterizing at least one optical component of a projection exposure system. DE 10 2015 213 163 A1 discloses a method for preparing a spatially resolved image data set for a subsequent intensity Fourier transform.

[0003] It is an object of the present invention to design a method for determining the image quality of an optical system with respect to the pupil to be measured as flexible as possible.

[0004] This object is achieved according to the invention by a determination method having the features specified in claim 1.

[0005] According to the invention, it was recognized that in order to determine image quality based on an aerial photographic survey, it is not necessary to illuminate the entire pupil to be measured during a single measurement. Rather, it is possible to carry out the measurement sequentially using subapertures within the pupil to be measured, with the measurement results obtained using the various subapertures then being combined. With the specified illumination angle distribution across a subaperture within the pupil to be measured, a corresponding subaperture diaphragm can be inserted into an entrance pupil of a projection optics of the optical system and positioned transversely to the illumination light beam path, resulting in a desired illumination direction corresponding to specified pupil coordinates. Even unconventional shapes of pupils to be measured can be detected and measured by appropriate coverage via subapertures.The pupil to be measured can be elliptical, round, or even a freeform pupil. The pixel resolution of the spatially resolving detection device can be adapted to the numerical aperture of the pupil to be measured. The higher this numerical aperture, the higher the pixel resolution of the detection device. For each subaperture measurement, the wavefront of the optical system in this subaperture can be determined using a phase retrieval method, which is known in principle from the literature, for example, from DE 10 2013 219 524 A1.To optimize the difference determination, a projection method (error reduction algorithm, Gerchberg-Saxton method, IFTA method) and / or a classic iterative optimization method (gradient descent, least square, damped least square, genetic search method, simplex, Chambolle-Pock optimization, back-propagation method) and / or a direct inversion method (extended Nijboer-Zernike decomposition (S. Van Haver, The Extended Nijboer-Zernike Diffraction Theory and its Applications, 2010, http: / / resolver.tudelft.nl / uuid:8d96ba75-24da-4e3 1-a750-1bc348155061), database-based method, machine learning method) can be used.

[0006] Scanning the pupil through the subapertures according to claim 2 enables a readily comparable process sequence. The pupil can be scanned through the subapertures using exactly one row of subapertures. Alternatively, scanning across multiple subaperture rows is also possible. The scanning can be configured such that a principal ray polar angle of the illumination light remains constant. In this case, the test structure is always illuminated with the same principal ray angle of incidence. In one variant, multi-row scanning can also be performed using multiple rows, each with a constant principal ray polar angle within a row, with the principal ray polar angle varying between rows.

[0007] An elimination of a test structure contribution according to claim 3 improves the method result by systematically eliminating test structure contributions that distort the image quality determination.

[0008] The method according to claim 4 reduces the effort required to determine the test structure contribution. The test structure contribution, once determined for exactly one given subaperture, can be post-processed or converted to eliminate the test structure contribution for the other subapertures, for example, by rotating the test structure contribution according to an illumination angle assigned to the respective subaperture, in particular a chief ray azimuth angle.

[0009] A method according to claim 5 has proven itself in practice. Representatives of this method are known as the rotate-slide method. Examples of such a rotate-slide method can be found in the specialist article by D. Su et al., Absolute surface figure testing by shift-rotation method using Zernike polynomials, Optics Letters Vol. 37, No. 15, 3198-3200, 2012, https: / / doi.org / 10.1364 / OL.37.003198; Y. Liu, et al., Extended shift-rotation method for absolute interferometric testing of a spherical surface with pixel-level spatial resolution, Applied Optics Vol. 56, No. 16, 2017, https: / / doi.org / 10.1364 / AO.56.004886, DE 10 2013 226 668 A1 and from US5982490A.

[0010] A decomposition into basis functions according to claim 6 has proven successful in practice. The following basis functions can be used: Zernike polynomials, Bhatia-Wolf polynomials, Bessel functions, solutions of the Laplace equation, orthogonalized, locally distributed, narrow exponential functions and / or Gaussian functions (optionally distributed on a grid), orthogonalized, locally distributed spline polynomials (optionally distributed on a grid), and orthogonalized mixtures of basis functions. Such orthogonalization can be performed, for example, using the Gram-Schmidt orthogonalization method (Korn and Korn, "Mathematical Handbook for Scientists and Engineers", McGraw-Hill, 1968; D. Malacara, "Optical Shop Testing", Wiley-Interscience, 1992; http: / / de.wikipedia.org / wiki / Schmidtsches_Orthonormalisierungsverfahren).

[0011] A pinhole as a test structure according to claim 7 has proven itself in practice.

[0012] An elliptical pinhole according to claim 8 has proven particularly suitable for determining aberrations in anamorphic imaging systems, which therefore have different image scales in mutually perpendicular planes. An elliptical pinhole according to claim 8 has also proven particularly suitable for determining aberrations in isomophotic imaging systems with an elliptical entrance pupil.

[0013] Representations of a pupil function according to claims 9 and 10 have proven to be particularly suitable for implementation in the determination method.

[0014] The advantages of a measuring system according to claim 11 correspond to those already explained above in connection with the determination methods.

[0015] A further object of the present invention is to develop a metrology system of the type mentioned at the outset in such a way that a phase retrieval method, for example according to the prior art, is also accessible for an elliptical pupil to be measured.

[0016] This object is achieved according to the invention by a metrology system having the features specified in claim 12.

[0017] According to the invention, it was recognized that an elliptical pupil can be directly measured by using an elliptically edged aperture arranged in a pupil plane of the metrology system and can be used to determine a wavefront via a phase retrieval method. In this way, such a metrology system can be used, in particular, to determine the imaging quality of an optical system when illuminated with illuminating light within the entrance pupil to be measured and / or within an exit pupil to be measured. In the phase retrieval method, scaled parameterized basis functions, in particular compressed Zernike polynomials and / or scaled coordinate grids and uniformly scaled parameterized basis functions can be used in accordance with the determination method explained above.

[0018] The advantages of a metrology system according to claim 13 correspond to those already explained above in connection with the determination method.

[0019] Embodiments of the invention are explained in more detail below with reference to the drawings, in which: Fig. 1 shows a highly schematic plan view, viewed perpendicular to a plane of incidence, of a metrology system for determining the imaging quality of an optical system when illuminated with illuminating light within an entrance pupil to be measured, comprising an illuminating optic and an imaging optic, each of which is shown very schematically; Fig. 2 shows a perspective and enlarged view of a test structure in the form of an EUV pinhole, for use as a reflecting object to be imaged in the metrology system according to Fig. 1; Fig. 3 Results of an intensity measurement in an image plane of the imaging optics of the metrology system when imaging the test structure according to Fig. 2, for different positions of an arrangement plane of the test structure relative to an object plane (z-focus stack); Fig. 4 an entrance pupil to be measured of the optical system to be measured, designed as an elliptical entrance pupil, together with a set of subapertures, each designed as a circularly delimited subpupil, for single-line scanning of the entrance pupil to be measured, wherein each of the subapertures corresponds to a predetermined illumination angle distribution for illuminating the test structure with the illumination light, wherein the test structure is sequentially illuminated with an illumination angle distribution that corresponds to a superposition of all subapertures; Fig. 5 in one to Fig. 4 similar representation a variant of a scanning of the entrance pupil to be measured with subapertures, whereby the scanning is carried out in such a way that a main ray polar angle of the illumination of the test structure remains constant for all subapertures; Fig. 6 in one of the Fig. 4 and Fig. 5 similar representation, another variant of a multi-row Cartesian scanning of the entrance pupil to be measured with subapertures; Fig. 7 to 11 Wavefront measurement results, shown in a contour line diagram as phase contributions in a pupil plane of the imaging optics, for five selected subapertures of a scan according to Fig. 5; Fig. 12 to 16 separate test structure contributions to the wavefront measurement results according to the Fig. 7 to 11, again each shown in a contour line diagram; Fig. 17 to 21 Wavefront measurement results in the subapertures after the Fig. 7 to 11 corresponding sections of the entrance pupil to be measured, after deducting the test structure contributions according to the Fig. 12 to 16 from the original wavefront measurement results according to the Fig. 7 to 11, i.e. after elimination of the test structure contributions, again each shown in a contour line diagram; Fig. 22 a superposition of the subaperture contributions of the wavefront measurement results according to the Fig. 17 to 21; Fig. 23 a cut of the wavefront measurement results according to Fig. 22 on the entrance pupil to be measured, i.e. the phase of the wavefront of the optical system to be measured within the entrance pupil to be measured; Fig. 24 shows, less schematically with respect to the imaging optics, a representation of an imaging system with several lenses, which in a further embodiment of a metrology system instead of the metrology system according to Fig. 1 can be used, wherein the imaging system is shown between an object plane and image planes of a focus stack to be measured; Fig. 25 an example of a phase distribution in an exit pupil to be measured of an anamorphic optical system, represented on a square grid with an elliptic apodization, parameterized according to an ellipticity corresponding to compressed Zernike polynomials; Fig. 26 sections through pupil function after Fig. 25 along a long and a short semi-axis of the elliptical pupil mask; Fig. 27 in one to Fig. 25 similar representation of the pupil function after Fig. 25, shown on a non-square pupil grid, which is adapted to the principal axis ratio of the elliptical exit pupil, with circular apodization and parameterization of the pupil function via classical, non-compressed Zernike polynomials; and Fig. 28 in one to Fig. 26 similar representation two sections through the pupil function according Fig. 27 along the two perpendicular main axes.

[0020] To facilitate the representation of positional relationships, a Cartesian xyz coordinate system is used below. The x-axis runs in the Fig. 1 perpendicular to the plane of the drawing. The y-axis runs in the Fig. 1 to the right. The z-axis runs in the Fig. 1 up.

[0021] Fig. 1 shows, in a view corresponding to a meridional section, a beam path of EUV illumination light or imaging light 1 in a metrology system 2 for determining an imaging quality of an optical system when illuminated with the illumination light 1 within an entrance pupil 11 to be measured. A test structure 5 arranged in an object field 3 in an object plane 4 is imaged here (cf. Fig. 2) in the form of a reticle or a lithography mask with the EUV illumination light 1. The test structure 5 is also referred to below as an object or a sample. The metrology system 2 is used to analyze a three-dimensional (3D) aerial image (Aerial Image Metrology System). Applications include the reproduction of an aerial image of a lithography mask as the aerial image would appear in a production projection exposure system, for example, in a scanner. For this purpose, in particular, the imaging quality of the metrology system 2 itself must be measured and adjusted if necessary. The analysis of the aerial image can thus be used to determine the imaging quality of a projection optics of the metrology system 2 or also to determine the imaging quality, in particular, of projection optics within a projection exposure system. Such systems are known from WO 2016 / 012 426 A1, from US 2013 / 0063716 A1 (cf. there Fig. 3), from DE 102 20 815 A1 (see there Fig. 9), from DE 102 20 816 A1 (see there Fig. 2) and known from US 2013 / 0083321 A1.

[0022] The illumination light 1 is reflected at the object 5. The plane of incidence of the illumination light 1 is at central illumination (kx = 0, see the following description, for example for Fig. 4) parallel to the yz-plane.

[0023] 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, a synchrotron-based light source can also be used, e.g., a free-electron laser (FEL). The useful wavelength of the EUV light source can be in the range between 5 nm and 30 nm. In principle, a variant of the metrology system 2 can also use a light source for a different useful light wavelength instead of the light source 6, for example, a light source for a useful wavelength of 193 nm.

[0024] Depending on the design of the metrology system 2, it can be used for a reflective or a transmissive object 5. An example of a transmissive object is a pinhole.

[0025] An illumination optics 7 of the metrology system 2 is arranged between the light source 6 and the object 5. The illumination optics 7 serves to illuminate the object 5 to be examined with a defined illumination intensity distribution across the object field 3 and, simultaneously, with a defined illumination angle distribution with which the field points of the object field 3 are illuminated. This illumination angle distribution is also referred to below as the illumination sub-aperture.

[0026] The illumination sub-aperture is limited by a sigma sub-aperture diaphragm 8 of the illumination optics 7, which is arranged in an illumination optics pupil plane 9. Alternatively or additionally, a corresponding sub-aperture diaphragm can also be present in the imaging optics of the metrology system 2, which will be described below. The sigma sub-aperture diaphragm 8 limits the edge of a beam of illumination light 1 incident thereon. Alternatively or additionally, the sigma sub-aperture diaphragm 8 and / or the diaphragm in the imaging optics can also shade the illumination light beam from the inside, thus acting as an obscuration diaphragm. A corresponding diaphragm can have an inner diaphragm body that correspondingly shades the beam from the inside and is connected to an outer diaphragm support body via a plurality of webs, for example, via four webs.The sigma sub-aperture diaphragm 8 can be moved in a defined manner in the illumination optics pupil plane 9, i.e. parallel to the xy plane, via a displacement drive 8a.

[0027] Fig. 4 shows several such subapertures 10 i (i = 1 to 5) that scan an elliptical entrance pupil 11 of the optical system to be measured. The elliptical entrance pupil 11 has a ratio between the major semi-axis parallel to the x-axis and the minor semi-axis parallel to the y-axis of 2:1. Other axis ratios of the elliptical edge contour 10 in the range of 10:1 and 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.

[0028] After reflection at the object 5, the illumination or imaging light 1 enters an imaging optics or projection optics 13 of the metrology system 2. Analogous to the illumination sub-aperture, there is a projection optics sub-aperture, which is defined by an NA sub-aperture diaphragm 11a in the entrance pupil 11 of the projection optics 13 in Fig. 1 is specified. The NA subaperture diaphragm 11a can be displaced in a defined manner in the projection optics pupil plane 11, i.e., parallel to the xy plane, via a displacement drive 11b. Typically, the sigma subaperture diaphragm and the NA subaperture diaphragm are aligned with each other such that both diaphragms are centrally struck by a central light beam of the illumination light 1 and the reflection from the test structure 5. The sigma subaperture diaphragm and the NA subaperture diaphragm can be centered relative to each other. The area of ​​the entrance pupil 11 of the projection optics 13 defined by the NA subaperture diaphragm is referred to as the subaperture.

[0029] The imaging optics 13 to be measured serves to project the object 5 onto 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 an image plane 15 of the projection optics 13.

[0030] The detection device 14 is in signal connection with a digital image processing device 17.

[0031] A pixel spatial resolution of the detection device 14 in the xy plane can be specified such that it is inversely proportional to the numerical aperture of the entrance pupil 11 to be measured in the coordinate directions x and y (NA x , N / A y ). This pixel spatial resolution is regularly smaller than λ / 2NA in the x-coordinate direction x and in the direction of the y-coordinate less than λ / 2NA y. λ is the wavelength of the illumination light 1. The pixel spatial resolution of the detection device 14 can also be implemented with square pixel sizes, independent of NA x , N / A y .

[0032] 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.

[0033] The object 5 is supported by an object holder or mount 18. The mount 18 can be displaced via a displacement drive 19, either parallel to the xy plane or perpendicular to this plane, i.e., in the z direction. The displacement drive 19, as well as the entire operation of the metrology system 2, is controlled by a central control device 20, which is in signal communication with the components to be controlled in a manner not shown in detail.

[0034] The optical structure of the metrology system 2 serves to emulate as accurately as possible an illumination and an image within the framework of a projection exposure of the object 5 during the projection lithographic production of semiconductor components.

[0035] Fig. 1 shows various possible arrangement levels of the test structure 5 in the area of ​​the object plane 4, each dashed. During operation of the metrology system 2, the test structure 5 is aligned with the plane of the object 4 via the subaperture 10 i each given illumination angle distribution at different distance positions z m the test structure 5 is illuminated relative to the object plane 4 and it is in the respective distance position z m an intensity I(x,y,z m ) is recorded spatially resolved in the image plane 15. This measurement result I(x,y,z m ) is also called an aerial photograph.

[0036] The number of focal planes z mcan be between two and twenty, for example between ten and fifteen. In the z-direction, a total of several Rayleigh units (NA / λ 2 ) shifted.

[0037] Shown in the Fig. 1 as inserts an xy-view of the test structure 5, which can be designed as a round or as an elliptical test structure.

[0038] In addition to the entrance pupil 11, the Fig. 1 also schematically shows an exit pupil 21 of the projection optics 13.

[0039] The Fig. 1 shows three measurement results of the detection device 14 below, again in an xy view, with the middle measurement result showing the image of the test structure 5 when arranged in the object plane 4, and the other two measurement results showing the images in which the test structure 5 is displaced once in the positive z-direction and once in the negative z-direction relative to the z-coordinate of the object plane 4. The totality of the measurement results assigned to the respective z-coordinates results in an aerial image of the test structure 5.

[0040] Fig. Figure 2 shows details of the test structure 5, which is designed as a reflective pinhole. The path of a main ray of the illumination light 1 upon reflection at the test structure 5 is shown schematically. The angle of incidence of the main ray of the illumination light 1 on the pinhole of the test structure 5 is in the range between 3° and 8°, for example 5° or 6°. The pinhole of the test structure 5 has a diameter in the range between 100 nm and 150 nm. The pinhole is formed in an absorber layer 22, which in turn is applied to a highly reflective multilayer coating 23. The absorber layer has a thickness in the range between 50 nm and 70 nm. The multilayer coating has a thickness in the range between 250 nm and 300 nm.

[0041] The pinhole of the test structure 5 can be elliptical. The principal axes of the pinhole can be approximately the same size as the Airy disk of the projection optics 13, i.e. 2.44 λ / NA x in the direction of the x-coordinate and 2.44 λ / NAy in the direction of the y-coordinate.

[0042] The test structure 5 can have a single pinhole or a plurality of pinholes, in particular a periodic array of pinholes. Other test structures are possible, as described, for example, in US 2015 / 0355052 A1.

[0043] Fig. 3 shows a result I(x,y,z m ) as a sequence of five measurements with different z-coordinates of the test structure 5, whereby the middle of the five measurements was taken with the test structure arranged in the object plane 4. Thus, again measurement results of the detection device 14 are shown. A comparison of the Fig. 3 measurement shown on the far left with the one shown in the Fig. The measurement shown on the far right in Figure 3 shows an asymmetry of the imaging measurement results when imaging the round pinhole of test structure 5, which is due to the oblique illumination of test structure 5 with illumination light 1. This results in an illumination angle-dependent test structure contribution of a wavefront influence by test structure 5.

[0044] Fig. 4 shows an embodiment of a single-line scanning of the entrance pupil 11 of the projection optics 13 to be measured with the subapertures 101 to 105, which are specified via the subaperture diaphragms 8 and 11a of the illumination optics 7 and the projection optics 13.

[0045] These pupils are shown in angular space, i.e., in the pupil coordinates kx (corresponding to the x-coordinate) and ky (corresponding to the y-coordinate). Due to the oblique illumination, the center of the entrance pupil 11 is at kx = 0 and ky ≠ 0. The centers of the various subapertures 10 i , i.e. the position of the respective main rays, are shown in the Fig. 4 are marked with triangles. These centers of neighboring subapertures 10 i , 10 i+1 are shifted from each other by a constant increment in the kx direction. The centers of the subapertures 10 i each have the same ky coordinate. An envelope of all subapertures 10 i completely covers the entrance pupil 11 to be measured. The center of the elliptical entrance pupil 11 is located at (kx = 0, ky = 0.1). The center of the subaperture 103 coincides with the center of the elliptical entrance pupil 11 to be measured.

[0046] Fig. 5 shows a variant of a scanning of the entrance pupil 11 to be measured with the subapertures 10 i . Shown is again a scanning with five subapertures 101 to 105. The scanning according to Fig. 5 is such that a chief ray polar angle θ between the origin (kx = 0, ky = 0) of the pupil plane 9 and the centers of the subapertures 10 i remains constant. In the kx, ky space, the principal ray polar angle θ has a value that is slightly larger than 0.1. This principal 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 . When scanning for Fig. 5 are the subapertures 10 i i.e. shifted against each other so that the main ray polar angle θ of the respective sub-aperture remains constant.

[0047] When scanning the entrance pupil 11, the subapertures 101 to 105 cover a main beam azimuth angle φ, which in the embodiment according to Fig. 5 is about 75°.

[0048] Fig. 6 shows another variant of scanning the elliptical entrance pupil 11 to be measured with subapertures 10 i,j . i indicates the row number and j the column number of the respective subaperture 10 i,j The scanning according to Fig. 6 is carried out with a total of twenty-one subapertures 10 i,j in three rows (i = 3) and seven columns (j = 7).

[0049] As an alternative to a single-line scanning with a constant main ray polar angle θ as in the variant according to Fig. 5, multi-line scanning is also possible, in which the respective main ray polar angle θ i remains constant, with the main ray polar angles θ i , θ i+1of the different rows i, i+1 are different from each other.

[0050] The Fig. 7 to 11 show, in the form of contour line diagrams, the results of a wavefront measurement based on the use of the subapertures 105 ( Fig. 7), 104 ( Fig. 8), 103 ( Fig. 9), 102 ( Fig. 10) and 101 ( Fig. 11). The measurements were taken using the scanning method according to Fig. 5 with the constant main ray polar angle. To the right of each wavefront representation is a legend for the relative phase values ​​corresponding to the respective contour line.

[0051] Shown in the Fig. 7 a phase of a wavefront resulting from the measurement results of the focus stack at the respective set subaperture 10 i This phase contribution determination according to the Fig. 7 to 11 is carried out using a phase retrieval method, which is known from DE 10 2013 219 524 B4.

[0052] Fig. 12 to 16 show in to the Fig. 7 to 11 similar representations again the phases of a test structure contribution of a wavefront influence of the illumination light 1 by the test structure 5. This test structure contribution can be determined from the measurement result according to the Fig. 7 to 11 are separated and eliminated. This takes advantage of the fact that the test structure contribution when illuminated with the respective subaperture 105 ( Fig. 12) to 101 ( Fig. 16), the phase distribution remains constant, with only one orientation of this phase distribution changing according to the rotation of the main beam azimuth angle φ. A “pole” of 24 smallest phase values ​​of the test structure contribution has Fig. 12 approximately to the right and in the Fig. 16 approximately upwards, corresponding to the main beam azimuth angle φ changed by about 75°.

[0053] The test structure contribution according to the Fig. 12 to 16 can be measured by wavefront measurement according to the Fig. 7 to 11 can be determined independently.

[0054] Fig. 17 to 21 show again in a Fig. 7 to 11 similar representation the result of the wavefront measurement at the respective subaperture 105 ( Fig. 17) to 101 ( Fig. 21) after elimination of the test structure contribution according to the Fig. 12 to 16. The area measured over the respective sub-aperture 105 to 101 is limited by a circular, dotted border when measuring according to the Fig. 17 to 21 measured or determined wavefront phase contribution and in addition the wavefront phase of the optical system to be measured within the pupil plane of the respective subaperture 10 i shown.

[0055] Fig. 22 shows in a Fig. 17 to 21 similar representation the superposition of the subaperture determination results according to the Fig. 17 to 21, i.e. the total determined wavefront component in the pupil plane of the optical system to be measured.

[0056] Fig. 23 shows the trimming of the determination result after Fig. 22 to the elliptical entrance pupil 11 to be measured.

[0057] When determining the wavefront measurement data according to Fig. 23 from the original measurement data according to the Fig. 7 to 11 and the test structure contributions according to the Fig. 12 to 16 a turn-slide process is used.

[0058] Examples of such a shift-rotation method can be found, for example, in the article by D. Su et al. Absolute surface figure testing by shift-rotation method using Zernike polynomials. Optics Letters Vol. 37, No. 15, 3198-3200, 2012. https: / / doi.org / 10.1364 / OL.37.003198 as well as in DE 10 2013 226 668 A1.

[0059] If the measurement data (m pixel values) of all n (n= 5 in the example shown) subapertures are summarized as a vector, the following system of equations can be set up: M=T⋅(WP) M=(M11⋮Mm1⋮M1n⋮Mmn) : Measurement data of the wavefront measurement (see above, Fig. 7 to 11), n ​​subapertures with m wavefront points each, i.e. m pixels within the pupil plane as the result of the wavefront measurement evaluated on a pixel grid; W=(W1⋮Wq) : wavefront points of the projection optics 13 to be determined (see above, Fig. 17 to 21), typically q > m (superposition of the results according to the Fig. 7 to 11, cf. Fig. 22 and Fig. 23), the index q runs over all points which are surrounded by at least one subaperture 10 i (i = 1 to n) are covered; P=(P1⋮Pm) : Pinhole contribution (cf. Fig. 12 to 16), m wavefront points; T=(Tw1TP1⋮⋮TwnTPn) : combined transformation matrix; T wi : m × q transformation matrix optics, subaperture i T Pi : m × m transformation matrix pinhole, subaperture i

[0060] For sub-aperture scanning according to the above Fig. 4 are {T Pi} by the mxm identity matrices I m given if the pinhole contribution is independent of kx. If the pinhole amount depends on kx, this dependence is taken into account by a suitable choice of the transformation matrices {T Pi} is shown.

[0061] In the case of sub-aperture scanning according to the above Fig. 5, the matrices correspond to a rotation of the wavefront points. If the wavefronts are described on a Cartesian grid, the rotation usually requires an interpolation of the pixel values. Both nearest-neighbor interpolation and linear (or higher-order) interpolation are possible and are described in {TPi} mapped accordingly.

[0062] The system of equations M=T⋅(WP) can be solved using conventional methods for solving systems of linear equations and thus the wavefront error W of the projection optics to be measured as well as the proportion of the wavefront error P caused by the pinhole can be determined.

[0063] Zernike polynomials can be fitted to the determined wavefront errors W of the projection optics in the area of ​​the elliptical pupil to be measured and the pinhole P, thus determining the Zemike spectrum.

[0064] The method from the application example can also be used to improve the wavefront measurement on a round, circular entrance pupil of an optic to be measured instead of the elliptical entrance pupil 11, since the contributions of the pinhole and the projection optics can be separated.

[0065] During phase retrieval, the measured aerial image I(x,y,zm ) with a simulated aerial photograph I sim compared and fit parameters of a set of functions describing the simulated aerial image are adjusted until a difference between the measured aerial image and the simulated aerial image is minimized.

[0066] Based on the minimized difference between the measured and the simulated aerial image, the wavefront of the optical system is determined during phase retrieval.

[0067] Difference minimization during phase retrieval can be optimized using various methods. These include projection methods, also known as error reduction algorithms, Gerchberg-Saxton methods, or IFTA methods. Classic iterative optimization methods can also be used. Examples of such methods include gradient descent, least square, damped least square, genetic search, simplex, Chambolle-Pock optimization, and backpropagation. Direct inversion methods can also be used. Examples include extended Nijbour-Zernike decomposition or a machine learning-based method based on preliminary results stored in a database, for example. If aberrations of the optical system within the entrance pupil to be measured are generally to be expected, a sufficiently densely sampled database can be generated using simulation.Retrieval can then be performed by searching this database. In machine learning, a network can be trained using a pre-calculated aberration database.

[0068] For the parametric detection and determination of the imaging errors of the optical system, a description of these imaging errors, for example a description of the phase distribution according to Fig. 23, into basis functions. Such optimization using basis functions avoids unwanted result noise.

[0069] For accurate image quality determination, it is important that the basis functions accurately describe the expected aberrations. It should be noted that an elliptical pupil to be measured is scanned with circular subapertures. In this case, areas of the wavefronts determined by phase retrieval overlap. In order to calculate the entire elliptical entrance pupil to be measured, it is advantageous to choose the basis of a function decomposition for the individual wavefronts so that it can be described by a translation / rotation.

[0070] Zernike polynomials are generally suitable as basis functions. Bhatia-Wolf polynomials, Bessel functions, solutions of the Laplace equation, orthogonalized, locally distributed, narrow exponential functions and / or Gaussian functions (optionally distributed on a grid), orthogonalized, locally distributed spline polynomials (optionally distributed on a grid), and orthogonalized mixtures of basis functions have proven advantageous in describing a translation / rotation.

[0071] Orthogonalizing the functions improves the robustness of the optimization and comparability of the results. Partial orthogonalization of the basis functions is also possible.

[0072] A mixture of the possible basis functions listed above can also be particularly suitable, for example, a combination of Zemike polynomials and orthogonalized, locally distributed, narrow exponential functions. For this purpose, a small number of Zernike polynomials, for example, nine to sixteen Zernike polynomials, are used to describe the classic aberrations. In addition, localized Pilk functions, for example in the form of an exponential function or a Gaussian function, are used to describe local deviations. The exponential functions are partially orthogonalized with respect to the Zernike functions. By partial orthogonalization of a function set F with respect to another function set G, we mean that each element of F is transformed using a method so that it is subsequently orthogonal to all elements of G. This can, for example,with the orthogonalization step of the Gram-Schmidt orthogonalization method. The difference to complete orthogonalization is that the elements in F and G do not necessarily have to be orthogonal to each other.

[0073] Such orthogonalization can be carried out, for example, using the Gram-Schmidt orthogonalization method (D. Malacara, “Optical Shop Testing”, Wiley-Interscience, 1992; http: / / de.wikipedia.org / wiki / Schmidtsches_Orthonormalisierungsverfahren).

[0074] Fig. 24 shows an embodiment of the metrology system 2 between the object plane 4 and the image plane 15 to illustrate the phase retrieval method. Components and functions that correspond to those explained with reference to the figures explained above, in particular with reference to Fig. 1, already described, bear the same reference numerals and will not be discussed in detail again. The situation is shown when using illumination light 1 with a wavelength λ = 193 nm and a pinhole as the test structure 5 in the object plane 4. The projection optics 13 is illustrated as a lens system with a total of ten lenses L1 to L10. Also shown is a pupil plane 25 of the projection optics 13 to be measured, which is optically conjugated to the illumination optics pupil plane 9.

[0075] Fig. 24 also illustrates a wave surface 26 of a wavefront of the optical system to be measured, which is used to describe the imaging quality of the optical system. For example, the Fig. 23 shows a phase curve of such a wave surface 26 of the pupil plane.

[0076] In addition to the image plane 15, in which the detection device 14 is arranged, the Fig. 24, in parallel, further reflective image planes are created, which result from the displacement of the test object 5 in the z-direction. Alternatively, the detection device 14 can also be displaced in the z-direction, which is shown in the Fig. 24 is illustrated.

[0077] The following relationship can be established for the intensity I(x,y,z) measured by the detection device 14: I=abs(Hpupil_image(Hobject_pupil(Eobject)⋅Epupil))2+N

[0078] Ho bject_pupil is an optical transfer function between the object plane 4 and the pupil 11 in the pupil plane 25; H pupil_image an optical transfer function between the pupil 11 and the image plane 15; E object a complex amplitude (amplitude and phase) of the test object 5; E pupila system transfer function in the form of a complex pupil amplitude, i.e. the desired wave function of the optical system; and N a contribution which describes, among other things, the noise of the detection device 14.

[0079] During phase retrieval, the measured intensity value I is mapped to the wave function E pupil recalculated.

[0080] Here, a forward simulation of the image of the test object 5 through the projection optics 3 is implemented and a difference between a simulation parameterized in the aberrations, i.e. the imaging errors, and the measurement results I is minimized.

[0081] If anamorphic projection optics 13 are used, the simulation must be adapted to the anamorphic setup. To achieve a fast and accurate simulation, a simulation formulation based on Fourier transforms is recommended.

[0082] The elliptically shaped pupil 11 of the projection optics to be parameterized for this purpose can be parameterized using the following variants: On the one hand, the pupil function can be represented on a square grid together with an elliptic apodization and a parameterization of the pupil function via compressed Zernike polynomials, i.e., differently scaled in the x- and y-direction. This is exemplified in the Fig. 25 and Fig. 26, which shows an example of such a parameterization of the elliptical pupil 11 in an equidistant kx and ky grid (square grid). Within the elliptical boundary of the pupil 11, a description is given as a linear combination of correspondingly compressed Zernike polynomials. Outside the elliptical boundary, the pupil function is set to zero within a circle with the radius of the longer ellipse major axis (zero padding).

[0083] The Fig. 26 shows a section through the Fig. 25 Pupil function shown in a kx, ky view on the one hand in the kx direction (section line 27) and on the other hand in the ky direction (section line 28).

[0084] A variant of the representation of the pupil function is based on a non-square pupil grid, where the scaling in the kx and ky directions is different. The scaling of the grids, i.e., the grid widths in kx and ky, are coupled to the sizes of the corresponding numerical apertures NAx, NAy of the elliptical pupil 11. This representation then has a circular apodization with respect to the pixels and a parameterization of the pupil function via classical, i.e., non-compressed, Zernike polynomials. During the simulation, the different grid widths in kx and ky must then be taken into account in the scaling of the Fourier transform. This can be achieved by using either adapted zero padding or a chirp-z transformation, for which various adapted scaling parameters must be selected.The pupil grid widths in kx and ky can be selected so that the pupil function is maximally gridded and has the highest numerical information density.

[0085] The Fig. 27 and Fig. 28 show the representation of an exemplary pupil function, which corresponds to that according to the Fig. 25 and Fig. 26, according to this variant with the non-square pupil grid and the circular apodization. Note that the pupil coordinates kx, ky in the Fig. 27 and Fig. 28 are scaled differently.

[0086] The scaling factor scal x / y the chirp-z transformation between a given pixel grid of the detection device 14 and the x- or y-rasterization according to the pupil representation according to the Fig. 27 and Fig. 28 with maximum rasterization of the pupil function is calculated as: scalx / y=λ2⋅dx / dy⋅NAx / y

[0087] Here, λ is the wavelength of the illuminating light 1; dx (dy) is the pixel size and N / A x / y the numerical aperture of pupil 11 in x and y directions.

[0088] Depending on the different numerical apertures NA x , N / A y the pupil 11 then results in different scaling in the x- and y-direction.

[0089] As a rule, dx = dy applies. However, the pixel sizes of the detection device 14 in the x and y directions can also be selected differently.

[0090] Another variant of the calculation is the use of a so-called error reduction algorithm, either with a classic FFT and an elliptic apodization matrix or with the chirp-z transform, adjusted scaling parameters, and a circular apodization matrix. This allows one to alternate between pupil space and image space, applying the appropriate constraints in each space (as in the classic IFTA algorithm, also known as the Gerchberg-Saxton algorithm).

[0091] With the above-described display variants for the pupil function, the entire entrance pupil 11 to be measured can be displayed or the subapertures 10 i .

[0092] The above measurement was carried out with round subapertures 10 iIn principle, the measurement can also be performed with elliptically edged subapertures. This can also be used to determine apertures via an elliptical entrance pupil. Measurements can be made directly with an elliptical aperture at the location of apertures 8 and 11a.

Claims

[1] Method for determining an imaging quality of an optical system (13) when illuminated with illuminating light (1) within an entrance pupil (11; 25) to be measured and / or within an exit pupil to be measured, comprising the following steps: - arranging a test structure (5) in an object plane (4) of the optical system (13), - specifying an illumination angle distribution for illuminating the test structure (5) with the illumination light (1), - Illuminating the test structure (5) with the specified illumination angle distribution at different distance positions (e.g. m ) of the test structure (5) relative to the object plane (4), - Detecting an intensity I(x,y,z m ) of the optical system (13) when imaging the test structure (5) in each distance position (z m) guided illumination light (1) in an image plane (15) of the optical system (13) with a spatially resolving detection device (14) for determining a measured aerial image of the test structure (5), - Comparing the measured aerial image with a simulated aerial image and adjusting fit parameters of a set of functions to describe the simulated aerial image until a difference between the measured aerial image and the simulated aerial image is minimized, - determining a wavefront of the optical system (13) based on the result of the minimized difference between the measured and the simulated aerial image, - where the given illumination angle distribution of a sub-aperture (10 i ) within the pupil to be measured (11; 25), - Repeat the steps “Specify” to “Determine” with another specified sub-aperture (10 i+1 ), which is relative to the already measured sub-aperture (10i ) is shifted in the pupil (11; 25) to be measured, - Determine the wavefront of the optical system by combining the results obtained at the measured sub-apertures (10 i ) were obtained over the entire pupil to be measured (11; 25). [2] Method according to claim 1, characterized by that the pupil (11; 25) is divided by the subapertures (10 i ) is scanned. [3] Method according to claim 1 or 2, characterized by an elimination of a test structure contribution of a wavefront influence by the test structure (5) for the test structure-independent determination of the imaging quality of the optical system (13). [4] Method according to claim 3, characterized by that the test structure contribution at exactly one given subaperture (10 i ) is determined and this contribution is then also used for the test structure-independent determination of the imaging quality of the optical system (13) for the further sub-apertures (10i+1 , 10 i+2 ...) is used. [5] Method according to claim 3 or 4, characterized by that to determine the imaging quality, eliminating the test structure contribution, a linear system of equations is solved, in which - Data (M) of the wavefront determination before elimination of the test structure contribution, - Contributions of the test structure and - a transformation matrix (T). [6] Method according to claim 5, characterized by that a dependency - the data (M) of the wavefront determination before the elimination of the test structure contribution and / or - the contributions of the test structure and / or - the transformation matrix (T) is described by a respective coordinate (kx, ky) in the solution space to be determined via a decomposition into basis functions. [7] Method according to one of claims 1 to 6, characterized bythat a pinhole is used as the test structure (5). [8] Method according to claim 7, characterized by that the pinhole has an elliptical border. [9] Method according to one of claims 1 to 8, characterized by that the pupil (11; 25) to be determined has an elliptical border, wherein, when determining the wavefront, a representation of a pupil function for at least a section-wise description of the pupil (11; 25) to be determined is carried out on a coordinate grid equidistant in mutually perpendicular pupil coordinates (kx, ky) and parameterized basis functions scaled in accordance with a principal axis ratio of an elliptical border of the pupil (11; 25). [10] Method according to one of claims 1 to 8, characterized bythat the pupil (11; 25) to be determined has an elliptical border, wherein, when determining the wavefront, a representation of a pupil function for at least a section-wise description of the pupil (11; 25) to be determined is carried out on a coordinate grid scaled in mutually perpendicular pupil coordinates (kx, ky) according to a principal axis ratio of an elliptical border of the pupil (11; 25) and uniformly scaled parameterized basis functions. [11] Metrology system (2) for carrying out a method according to one of claims 1 to 10, with an illumination optical system (7) for illuminating the test structure (5) and with the imaging optical system (13), the imaging quality of which is to be determined, for imaging the test structure (5) towards a spatially resolving detection device (14), having a sub-aperture diaphragm (8) of the illumination optical system (7), arranged in an illumination optical system pupil plane (9), for delimiting a sub-aperture within a pupil (11; 25) to be measured, wherein the sub-aperture diaphragm (8) is displaceable in the illumination optical system pupil plane (9) via a displacement drive (8a). [12] Metrology system (2) - with a holder (18) for a test structure (5), - with an illumination optics (7) for illuminating the test structure (5) in an object plane (4) predetermined by the holder (18), - with a spatially resolving detection device (14), - with an imaging optics (13) for imaging the test structure (5) towards the detection device (14) in an image plane (15), characterized by an aperture (8; 10 i ; 11a) with an elliptically edged diaphragm opening, arranged in an illumination optics pupil plane (9) and / or in an entrance pupil (11) of the imaging optics (13), having a sub-aperture diaphragm (8) of the illumination optics (7), arranged in an illumination optics pupil plane (9), for delimiting a sub-aperture within a pupil (11; 25) to be measured, wherein the sub-aperture diaphragm (8) is displaceable in the illumination optics pupil plane (9) via a displacement drive (8a). [13] Metrology system according to claim 12 for carrying out a method according to one of claims 1 to 10.

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