Method for registering structures in at least one image of a photolithography mask obtained by an optical system with a resolution limit to corresponding structures in a reference image

Abstract

The invention relates to a method (30) for registering structures in at least one image (26, 26', 26'', 26''') of a photolithography mask (14) obtained by an optical system (10, 10') with a resolution limit, the optical system (10, 10') comprising an illumination optical unit (11) with an optical element (22) arranged in an illumination beam path (21) of the illumination optical unit (11), the illumination optical unit (11) being configured for illuminating the photolithography mask (14) with a spatially modulated illumination and an imaging beam path (19), the method (30) comprising: providing at least one image (26, 26', 26'', 26''') of a photolithography mask (14) acquired by the optical system (10, 10') with spatially modulated illumination; registering structures in the at least one provided image (26) to corresponding structures in a reference image (48) of the photolithography mask (14).

Description

[0001] 20.01.2026 h - se - 1 -

[0002] Method for registering structures in at least one image of a photolithography mask obtained by an optical system with a resolution limit to corresponding structures in a reference image

[0003] Related Applications

[0004] This application claims benefit of German patent application No. 10 2025 102245.3 filed on January 22nd, 2025, which is hereby incorporated by reference in its entirety.

[0005] Field of the Invention

[0006] The invention relates to methods and corresponding systems for registering structures in an image of a photolithography mask obtained by an optical system with a resolution limit, in particular in case the photolithography mask contains densely arranged structures with a characteristic length scale below the resolution limit or periodic structures below the resolution limit of the optical system. The invention also relates to computer implemented methods for training corresponding machine learning models, corresponding computer programs and computer-readable media.

[0007] Background of the Invention

[0008] Semiconductor manufacturing involves precise manipulation, e.g., etching, of materials such as silicon or oxide at very fine scales in the range of nm. A wafer made of a thin slice of silicon serves as the substrate for microelectronic devices containing semiconductor structures built in and upon the wafer. The semiconductor structures are constructed layer by layer using repeated processing steps that involve repeated chemical, mechanical, thermal and optical processes. Photolithography is a process used to produce patterns on the substrate. The patterns to be printed on the surface of the substrate are generated by computer-aided-design (CAD). From the design, for each layer a photolithography mask is generated, which contains a magnified image of the computer-generated pattern to be etched into the substrate. The photolithography mask can be further adapted, e.g., by means of optical proximity correction techniques. During the printing process an illuminated image projected from the photolithography mask is focused onto a photoresist thin film formed on the substrate. A semiconductor chip powering mobile phones or tablets comprises, for example, approximately between 80 and 120 patterned layers.Due to the growing integration density in the semiconductor industry, photolithography masks have to image increasingly smaller structures onto wafers. The aspect ratio and the number of layers of integrated circuits constantly increases and the structures are growing into 3rd(vertical) dimension. The current height of the memory stacks is exceeding a dozen of microns. In contrast, the feature size is becoming smaller. The minimum feature size or critical dimension is below 10nm, for example 7nm or 5nm, and is approaching feature sizes below 3nm in near future. While the complexity and dimensions of the semiconductor structures are growing into the 3rddimension, the lateral dimensions of integrated semiconductor structures are becoming smaller. Producing the small structure dimensions imaged onto the wafer requires photolithographic masks or templates for nanoimprint photolithography with ever smaller structures or pattern elements. The production process of photolithographic masks and templates for nanoimprint photolithography is, therefore, becoming increasingly more complex and, as a result, more time-consuming and ultimately also more expensive. With the advent of Ell V photolithography scanners, the nature of masks changed from transmission-based to reflection-based patterning.

[0009] On account of the tiny structure sizes of the pattern elements of photolithographic masks, it is not possible to exclude errors during mask production. The resulting defects can, for example, arise from degeneration of photolithography masks or particle contamination. Hence, in semiconductor process control, photolithography mask inspection, review, and metrology play a crucial role to monitor systematic defects. Defects detected during quality assurance processes can be used for root cause analysis, for example, to modify, repair or even discard the photolithography mask.

[0010] Optical systems examine positions of structures on photolithography masks using images. An image is formed by the projection of light, e.g. of EUV or DUV wavelength, through a photolithography mask onto an imaging sensor, e.g. CCD or CMOS arrays. The image, thus, represents the distribution of light on the surface of a wafer. Due to the small structure size on photolithography masks a high resolution of the image, e.g., with pixel sizes below 1nm, is required. However, let A indicate the wavelength of the illuminating light, NAmuthe numerical aperture of the illumination optical unit and NAimagthe numerical aperture of the imaging optics, then the resolution limit of the optical system is

[0011]

[0012] Thus, for dense structures with distances below the resolution limit of the optical system, in particular for densely arranged structures with a characteristic length scale below the resolution limit or for periodic structures with periodicity above the inverse resolution limit of the optical system, the images do not contain any information that could be examined.

[0013] Standard approaches to increase optical resolution target at improving the factors determining the resolution limit, e.g., using illumination of shorter wavelengths, e.g., extreme ultraviolet (EUV) wavelengths, increasing the illumination or imaging numerical aperture, or increasing the refractive index by using liquid or solid immersion with n > 1. However, these modifications require fundamental changes to the optical system and are, thus, expensive.

[0014] Therefore, it is an objective of the invention to examine positions of structures of photolithography masks below the resolution limit of the optical system.

[0015] The objectives are achieved by the invention specified in the independent claims. Advantageous embodiments and further developments of the invention are specified in the dependent claims.

[0016] Summary of the invention

[0017] Embodiments of the invention concern methods and corresponding systems for registering structures in at least one image of a photolithography mask obtained by an optical system with a resolution limit to corresponding structures in a reference image. The invention also refers to computer implemented methods for training corresponding machine learning models and defect detection methods.

[0018] A first embodiment involves a method for registering structures in at least one image of a photolithography mask obtained by an optical system with a resolution limit, the optical system comprising an illumination optical unit with an optical element arranged in an illumination beam path of the illumination optical unit, the illumination optical unit being configured for illuminating the photolithography mask with a spatially modulated illumination, and an imaging beam path for imaging the photolithography mask ontoan image sensor the method comprising: providing at least one image of a photolithography mask acquired by the optical system with spatially modulated illuminations; and registering structures in the at least one provided image to corresponding structures in a reference image of the photolithography mask.

[0019] By providing at least one image with spatially modulated illumination, high frequency information above the inverse resolution limit of the optical system becomes visible in the at least one image. This information can be used for registering the structures in the at least one image to corresponding structures in the reference image. In this way, densely arranged structures with sizes below the resolution limit and patterns with periodicity above the inverse resolution limit can be registered.

[0020] According to an example, the photolithography mask comprises multiple structures with a distance below the resolution limit of the optical system. In particular, the photolithography mask comprises a periodic mask pattern with a periodicity above the inverse resolution limit of the optical system. These kinds of structures cannot be distinguished in an image obtained by the optical system with the resolution limit.

[0021] According to an aspect of the invention, multiple images of the photolithography mask are provided with different spatially modulated illuminations. In this way, different high-frequency parts of the photolithography mask pattern are transformed to lower frequencies in the multiple images. Different high-frequency parts become visible in each of the multiple images and can be used for registration purposes. Thus, a registration of higher accuracy can be obtained using the multiple images.

[0022] Different spatially modulated illuminations can, for example, be generated by spatial transformations of a single spatially modulated illumination. Spatial transformations of a spatially modulated illumination can be obtained by relative spatial transformations between the photolithography mask and the optical element. Different spatially modulated illuminations can also be generated by introducing different optical elements in the illumination beam path.

[0023] According to an aspect of the invention, the method further comprises computing an image of an increased resolution from the provided multiple images. The image of an increased resolution can, for example, be used for registration with the reference im-age. Thus, structures in the image of an increased resolution are registered to corresponding structures in the reference image of the photolithography mask. In this way, the accuracy of the registration can be improved.

[0024] In an example, the image of an increased resolution is computed using a machine learning model that is trained to map multiple images of a photolithography mask acquired under different spatially modulated illuminations to an image with an increased resolution of the photolithography mask. In this way, the computation of the image of the increased resolution is learned automatically from training data, which is optimal with respect to the criteria formulated in the loss function and requires less user effort. In addition, this method can also be used for partially coherent or incoherent illumination.

[0025] In an example, the optical element is arranged, e.g., in a field plane close to the photolithography mask or close to illumination optics of the illumination optical unit or close to a light source of the illumination optical unit. In an example, the optical element comprises a pinhole aperture, an amplitude mask with a transmission coefficient between 0 and 1, a diffractive optical element, a phase mask, or a diffraction grating whose periodic structures have a minimum distance above the resolution limit of the optical system.

[0026] In an example, the spatially modulated illumination comprises a sinusoidal illumination pattern. Sinusoidal illumination patterns are well suitable to generate the Moireeffect which is used in super resolution techniques based on spatially modulated (structured) illumination. By using sinusoidal illumination patterns as spatially modulated illumination, phase shifts can be easily introduced into the sinusoidal illumination pattern. Each phase shift generates a different spatially modulated illumination that is used to derive different high frequency information of the photolithography mask. In this way, spatially modulated illumination can be generated in a particularly efficient way.

[0027] According to an example, the spatially modulated illumination comprises a superposition of multiple periodic illumination patterns. A superposition of multiple periodicillumination patterns allows to simultaneously derive multiple different high frequency information from the photolithography mask. In this way, high frequency information can be derived from the photolithography mask very efficiently.

[0028] According to an aspect, the optical element is selected depending on the type of patterns on the photolithography mask. In this way, specific frequencies of the structures on the photolithography mask are made visible, allowing for a more accurate registration.

[0029] In an example, the spatially modulated illumination generated by the illumination optical unit is partially coherent. In this way, a higher resolution of small structures and a higher image intensity can be obtained, such that neighboring structures can be distinguished more easily and registrations of higher accuracy can be achieved.

[0030] In an example, the optical system comprises an additional aperture stop that is used for defining the distribution of incoming illumination angles on the photolithography mask. In this way, the contrast of the at least one image can be improved.

[0031] According to an aspect, the structures in the provided at least one image and the corresponding structures in the reference image of the photolithography mask are registered using a machine learning model that is trained to map at least one image obtained with spatially modulated illumination and a reference image to a displacement field. The machine learning model is learned from training data and, thus, automatically, which reduces the effort and required expert knowledge of a user and is optimal with respect to the criteria formulated in the loss function. Thus, the accuracy of the registration is improved.

[0032] In an example, the structures in the provided at least one image and the corresponding structures in the reference image of the photolithography mask are registered by interferometric reconstruction of relative phase information between the pattern on the photolithography mask and the spatially modulated illumination.

[0033] In an example, the reference image of the photolithography mask is obtained from a parametric model of the photolithography mask, whose parameters indicate transformations of the structures of the model of the photolithography mask, and wherein thestructures in the provided at least one image and the corresponding structures in the reference image are registered by solving an optimization problem for the transformation parameters that minimize the deviation of the provided at least one image and the reference image of the parametric model of the photolithography mask. In this way, the registration can be computed analytically and accurately.

[0034] In an example, the method further comprises evaluating the quality of the photolithography mask using the registered structures in the provided at least one image and the corresponding structures in the reference image, e.g., by detecting defects or measuring positional deviations of structures in the photolithography mask. In this way, qualified decisions can be taken to repair or discard a photolithography mask.

[0035] In an example, the optical system is an optical system that measures positions of structures in the photolithography mask from registered structures in the at least one image and the reference image.

[0036] In an example, the optical system is an optical inspection system that detects defects in the photolithography mask by comparing registered structures in the at least one image and the reference image.

[0037] In an example, the method further comprises controlling at least one photolithography mask manufacturing process parameter (e.g., a focus, exposure, etc.) based on the quality evaluation of the photolithography mask.

[0038] An embodiment of the invention refers to a computer implemented method for training a machine learning model according to any of the embodiments, examples or aspects described above.

[0039] An embodiment of the invention refers to a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the computer implemented method for training a machine learning model as described in the previous section.

[0040] An embodiment of the invention refers to a computer-readable medium, on which a computer program executable by a computing device is stored, the computer programcomprising code for executing the computer implemented method for training a machine learning model according to the previous section.

[0041] A system for registering structures in at least one image of a photolithography mask obtained by an optical system with corresponding structures in a reference image according to an embodiment of the invention comprises: an optical system comprising an illumination optical unit with an optical element arranged in an illumination beam path of the illumination optical unit of the optical system, the illumination optical unit being configured for illuminating a photolithography mask with spatially modulated illuminations, and an imaging beam path for imaging the photolithography mask onto an image sensor; one or more processing devices; and one or more machine-readable hardware storage devices comprising instructions that are executable by one or more processing devices to perform operations comprising a method for registering structures in at least one image of a photolithography mask with corresponding structures in a reference image according to any one of the embodiments, examples or aspects of the invention described above.

[0042] The invention described by examples and embodiments is not limited to the embodiments and examples but can be implemented by those skilled in the art by various combinations or modifications thereof.

[0043] Brief Description of the Drawings

[0044] Fig. 1 illustrates an exemplary transmission-based optical system, e.g., a deep ultraviolet (DUV) optical system;

[0045] Fig. 2 illustrates an exemplary reflection-based optical system, e.g., an extreme ultra-violet light (EUV) optical system;

[0046] Fig. 3a, b show a periodic photolithography mask pattern with structure sizes below the resolution limit of the optical system and a constant image without useful registration information;

[0047] Fig. 4a-e illustrates the use of spatially modulated illumination to make frequencies above the inverse resolution limit visible in the image;Fig. 5 shows a method for generating spatially modulated illumination by using a pinhole aperture;

[0048] Fig. 6 illustrates a flowchart of a method for registering structures in an image of a photolithography mask to corresponding structures in a reference image according to an embodiment of the invention;

[0049] Fig. 7a-e illustrates that registration information can be derived from images of photolithography mask patterns with structure distances below the resolution limit by using spatially modulated illumination;

[0050] Fig. 8 shows a machine learning model for mapping multiple images obtained with spatially modulated illumination to an image with an increased resolution;

[0051] Fig. 9 illustrates exemplary training data for training a machine learning model for mapping multiple images obtained with spatially modulated illumination to an image with an increased resolution;

[0052] Fig. 10a, b illustrates a registration method for registering structures in at least one image of a photolithography mask obtained with spatially modulated illumination to corresponding structures in a reference image;

[0053] Fig. 11 illustrated a machine learning based registration method for registering structures in at least one image of a photolithography mask obtained with spatially modulated illumination and corresponding structures in a reference image;

[0054] Fig. 12 illustrates exemplary training data for training a machine learning model for mapping at least one image obtained with spatially modulated illumination to a displacement field;

[0055] Fig. 13 illustrates a parametric model of a photolithography mask comprising transformation parameters;Fig. 14 illustrates the detection of defects in photolithography masks from registration information; and

[0056] Fig. 15 shows a system for registering structures in at least one image of a photolithography mask obtained by an optical system with corresponding structures in a reference image according to an embodiment of the invention.

[0057] Detailed Description

[0058] In the following, advantageous exemplary embodiments of the invention are described and schematically shown in the figures. Throughout the figures and the description, same reference numbers are used to describe same features or components. Dashed lines indicate optional features.

[0059] The optical systems herein can use illumination light of different wavelengths, e.g., transmission-based optical systems 10 or reflection-based optical systems 10’ such as EUV systems.

[0060] Fig. 1 illustrates an exemplary transmission-based optical system 10 for measuring structures on photolithography masks using DUV light. Major components are an illumination optical unit 11 that generates light that is directed onto the photolithography mask 14 via an illumination beam path 21. The illumination optical unit 11 comprises a light source 12, which may be a deep-ultraviolet (DUV) excimer laser source and illumination optics 16, imaging optics which, for example, define the partial coherence and which may include optics that shape radiation from the illumination optical unit 11. The optical system 10 further comprises a photolithography mask 14, and projection optics 17 that project an image of the photolithography mask onto a wafer plane 18 via an imaging beam path 19. An adjustable filter or aperture at the pupil plane of the projection optics 17 may restrict the range of beam angles that impinge on the wafer plane 18, where the largest possible angle defines the numerical aperture of the projection optics NA = nsin(Gmax), wherein n is the refractive index of the media between the substrate and the last element of the projection optics 17, and emaxis the largest angle of the beam exiting from the projection optics 17 that can still impinge on the wafer plane 18. The radiation distribution at the wafer plane 18 is imaged byan image sensor 20 of a camera, e.g., a CCD or CMOS sensor, to generate an image that is used for measuring tasks.

[0061] In the present document, the terms "illumination", “radiation” or “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g. with a wavelength of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultra-violet radiation, e.g. having a wavelength in the range of about 3-100 nm).

[0062] Illumination optics 16 may include optical components for shaping, adjusting and / or projecting radiation from the illumination optical unit 11 before the radiation passes the photolithography mask 14. Projection optics 17 may include optical components for shaping, adjusting and / or projecting the radiation after the radiation passes the photolithography mask 14. The illumination optics 16 exclude the light source 12, the projection optics 17 exclude the photolithography mask 14.

[0063] Illumination optics 16 and projection optics 17 may comprise various types of optics, including refractive optics, reflective optics, apertures and catadioptric optics, for example. Illumination optics 16 and projection optics 17 may also include components operating according to any of these design types for directing, shaping or controlling the projection beam of radiation, collectively or singularly.

[0064] Fig. 2 illustrates an exemplary reflection-based optical system 10’ for measuring structures on photolithography masks using extreme ultraviolet (EUV) light. Major components are an illumination optical unit 11 that generates light that is directed onto the photolithography mask 14 via an illumination beam path 21. The illumination optical unit 11 comprises a light source 12 in the form of an EUV plasma source that is ignited by an IR-laser 13 and illumination optics 16 which, for example, define the partial coherence and which may include optics that shape radiation from the light source 12. The optical system 10’ further comprises a photolithography mask 14, and projection optics 17 that project an image of the photolithography mask onto a wafer plane 18 via an imaging beam path 19. An adjustable filter or aperture at the pupil plane of the projection optics 17 may restrict the range of beam angles that impinge on the wafer plane 18, where the largest possible angle defines the numerical aperture of the projection optics NA = nsin(0max), wherein n is the refractive index of the media between the substrate and the last element of the projection optics 17, and emaxis the largest angle of the beam exiting from the projection optics 17 that can still impingeon the wafer plane 18. The radiation distribution at the wafer plane 18 is imaged by an image sensor 20 of a camera to generate an image.

[0065] An optical system 10, 10’ such as the ones shown in Fig. 1 and 2 can be used to generate an image of the photolithography mask that is used for registering structures of the photolithography mask to corresponding structures in a reference image of the photolithography mask.

[0066] An optical system refers to a system that uses light to obtain an image of a photolithography mask. It illuminates the photolithography mask with light from an illumination source and projects the reflected or transmitted light from the photolithography mask surface to a camera sensor array. Optical systems comprise, for example, optical inspection systems, optical mask qualification systems, and optical metrology systems.

[0067] An optical inspection system refers to an optical system used to detect defects in a photolithography mask by acquiring and analyzing aerial images of the photolithography mask or one or more sections thereof. In particular, inspection systems comprise actinic photomask inspection systems

[0068] An optical mask qualification system refers to a system that is used to acquire an image of a portion of a photolithography mask, thereby emulating settings of a photolithography system, e.g. illumination and imaging parameters. The acquired image is of a higher quality than an image acquired by an optical inspection system, e.g., of a reduced noise level. The portions of the photolithography mask can comprise potential defect locations detected using an optical inspection system for further review. The acquired image can be used to examine the effect of a potential defect on a printed wafer, to verify that photolithography masks are defect-free, whether a repair attempt has been successful or for critical dimension estimation.

[0069] An optical metrology system refers to a system that is used to take measurements of structures in a photolithography mask by acquiring an image of the photolithography mask.

[0070] The photolithography mask may have an aspect ratio of between 1:1 and 1:4, preferably between 1:1 and 1:2, most preferably of 1:1 or 1:2. The photolithography maskmay have a nearly rectangular shape. The photolithography mask may be preferably 5 to 7 inch long and wide, most preferably 6 inch long and wide. Alternatively, the photolithography mask may be 5 to 7 inch long and 10 to 14 inch wide, preferably 6 inch long and 12 inch wide.

[0071] A structure in an image refers to the image of a component of the photolithography mask, e.g., absorber structures, channels, contact structures, word lines, deck transitions, bit lines, source lines, gates, etc.

[0072] An image of a photolithography mask can refer to different kinds of images of the photolithography mask, e.g., to a two-dimensional image, a three-dimensional image, a stack of images or a volumetric three-dimensional image that can, for example, be processed slice by slice. An image can be an image of a complete photolithography mask or of a section of the photolithography mask.

[0073] According to an example, an image refers to an aerial image. An aerial image indicates the radiation intensity distribution of an optical system in a wafer plane for a given photolithography mask. It refers to the image that is formed by the projection of light, e.g. of EUV or DUV wavelength, through a photolithography mask onto an imaging sensor, e.g. CCD or CMOS arrays. The aerial image, thus, simulates the structures on the surface of a wafer after printing. A wafer plane refers to a plane within the resist on top of the wafer. The imaging sensor can be part of a camera adapted for acquiring images at predetermined wavelengths. The camera can be an EUV camera, and / or a camera comprising a TDI sensor. In preferred embodiments, an image acquisition method comprises the use of an EUV camera comprising a TDI sensor. The camera's image sensor can accordingly be an EUV image sensor, i.e. , an image sensor that is sensitive to EUV light. EUV light is light in the extreme ultraviolet spectral range with wavelengths between 5 nm and 100 nm, in particular with wavelengths between 5 nm and 30 nm. Especially the EUV light can have a wavelength of 13.5 nm. In preferred embodiments, the image acquisition method comprises illuminating a photolithography mask with actinic radiation within the EUV wavelength range. EUV radiation reflected from the mask is then projected on an imaging sensor of an EUV camera via accordingly adapted projection optics.

[0074] A reference image refers to an image of a photolithography mask or of a section thereof, that represents (at least approximately) the same structures as the image ofthe photolithography mask. The reference image can be of the same type as the image or of a different type such as a SEM image or a design image. A reference image can comprise an acquired image of the same photolithography mask, e.g., at a different point in time, using a different optical system, using the same optical system with different settings, using a different section of the same photolithography mask that contains the same structures, etc. An image can also be used as a reference image for itself, e.g., a mirrored image can be used as a reference image in case the image contains structures that are self-symmetrical. A reference image can comprise an acquired image of a different photolithography mask comprising the same structures as the image of the photolithography mask using the same or a different optical system. A reference image can also comprise a simulated image. An image can be simulated from a model of a photolithography mask using image simulation methods. For example, rigorous simulation methods such as finite difference time domain (FDTD) or rigorous coupled wave analysis (RCWA) can be used that are known to a person skilled in the art. Since they require long computation times, fast but less accurate approximations such as the thin element approximation (TEA) that relies on a thin mask assumption can be used. To obtain fast and accurate results, simulation methods that are based on physical models but still do not rely on the thin mask assumption can be used, e.g., the not quite rigorous method disclosed in WO 2024 141484 A1 and in DE 2022 135019 A 1. Apart from physical simulations, trained machine learning models can be used to simulate images from designs. A reference image can also comprise a model of the photolithography mask.

[0075] A model (or design) of a photolithography mask refers to a representation of the photolithography mask or a section thereof. The model can, for example, comprise a computer readable file, such as a CAD file or a GDS file, or a technical drawing, a set of polygons representing the structures of the photolithography mask or a section thereof. A model of a photolithography mask can comprise parameters describing the location of structures in the photolithography mask, e.g., the location of absorber structures or layers in a multilayer. A model of a photolithography mask can comprise parameters describing the shape of structures in the photolithography mask, e.g., the shape of the absorber structures such as side wall angles or corner rounding, etc. A model of a photolithography mask can comprise descriptions of the structures within the photolithography mask, e.g., in the form of curves, contours, polygons, Splines, NURBS, Bezier curves, etc. A model of a photolithography mask can comprise mate-rial information, e.g., complex refractive indices of materials contained in the photolithography mask, electric permittivities, magnetic permeabilities, or derived representations. A model of a photolithography mask can comprise parameters describing dimensions of structures in the photolithography mask, e.g., the thicknesses of the layers in the multilayer of an EUV mask or the thickness of absorber layers, or the dimension of the absorber structures. A model of a photolithography mask can comprise an image, e.g., a 2D image or a 3D image (e.g., a volume of voxels or a number of 2D slices of a volume), that represents properties of the photolithography mask. The image can contain one, two or more channels. The image can comprise image elements, e.g., pixels or voxels. A model can refer to the model of a complete photolithography mask, or it can refer to the model of a section of the photolithography mask.

[0076] The image of the photolithography mask and the simulated image of the model of the photolithography mask can be registered using standard registration techniques, e.g., machine learning methods that map an image and a reference image to a displacement field, energy optimization methods that find a transformation of the image that minimizes the deviation between the transformed image and the reference image, optical flow techniques, Random Sample Consensus (RANSAC) techniques, feature matching methods, etc.

[0077] Such registration methods, however, fail for dense patterns with structure sizes below the resolution limit, in particular for periodic patterns with periodicity above the inverse resolution limit. As illustrated in Fig. 3a, b, the periodic pattern 24 with structure sizes below the resolution limit shown in Fig. 3a leads to the constant image 26 in Fig. 3b. From this image 26, no registration information can be derived such that the position of the structures on the photolithography mask cannot be examined.

[0078] In order to make frequencies above the inverse resolution limit visible in the image according to the invention, structured illumination is used. When two periodic patterns with frequencies fo and i are multiplied, a Moire fringe pattern with a frequency lower than either of the original patterns may be produced. If one of the patterns is known, the other can be solved algebraically from the Moire fringe pattern. The resolution of optical systems is limited by the wave diffraction nature, which functions as a low-pass filter during the imaging process. As a result, a sample’s fine structure (high-frequency component) cannot pass through the optical system. However, a Moire fringe with fine structure information shifted to low frequency can be obtained, whichcan be used to resolve the fine structure of the photolithography mask pattern. A series of different spatially modulated illuminations can be used to illuminate a photolithography mask. The resulting images contain information about the fine details of the unobservable pattern structure in a diffraction-limited image. Subsequently, a reconstruction procedure can be adopted to determine the fine details of the photolithography mask pattern.

[0079] Fig. 4a to e illustrate this process. Fig. 4a shows a periodic pattern 24 of a photolithography mask that is illuminated by a spatially modulated illumination 28. The circle in Fig. 4b indicates the frequencies that the optical system can transmit, i.e. , all frequencies below the inverse resolution limit

[0080]

[0081] Here, A indicates the average observed emission wavelength of the illuminating light, NAmuthe numerical aperture of the illumination optical unit and NAimagthe numerical aperture of the imaging optics. Thus, k0is the magnitude of the maximum observable spatial frequency in the optical system. High-frequency information residing outside of the circular area cannot be observed in the image. The optical system acts as a low pass filter, only allowing the observation of frequencies with a magnitude less than or equal to that of k0as illustrated in Fig. 4b. Structured illumination of frequency k results in a sum frequency k + k and a difference frequency k - k at each sample frequency of k and is visible in the form of moire fringes as illustrated in Fig. 4c. Moire fringes are a physical phenomenon resulting from the superposition of two fine patterns in a multiplicative fashion, in this case they are visible at the difference frequency k - k for each value k. This interaction is illustrated in Figure 4a, which shows the overlay of two fine sinusoidal patterns, with the resulting near-vertical bars being the moire fringes. Due to frequency mixing, the observable regions also contain, in addition to the normal image of spatial frequencies (center circle), two new offset frequency images (Fig. 4d) that are centered on the edge of the original field. These offset images contain higher spatial frequencies that are not observed using standard optical systems. Finally, in Fig. 4e, a set of images is shown that were prepared from three phases at 120 degree orientations, which ultimately after processing, yield an image that contains twice the spatial resolution.

[0082] As illustrated in Fig. 1 and 2, spatially modulated illumination can be generated by introducing an optical element 22 into an illumination beam path 21 of the illuminationoptical unit 11 between the light source 12 and the photolithography mask 14. The optical element 22 can be introduced, for example in a field plane or in an aperture plane, in different locations, e.g., in a first location 23 close to the photolithography mask 14, in a second location 23’ close to the illumination optics 16 of the illumination optical unit 11 or in a third location 23” close to the light source 12 of the illumination optical unit 11. The first location 23 close to the photolithography mask 14 has the advantage that it does not require imaging of the optical element 22. It is a type of nearfield position. The second location 23‘ close to the illumination optics 16 has the advantage that a larger optical element can be used, since its structures can be imaged with a reduced size on the photolithography mask 14 using the illumination optics 16. In this way, the production of the optical element is simplified, the positioning of the optical element is simplified and manufacturing and positioning tolerances are improved. The third location 23” close to the light source 12 has the advantage that the optical element is arranged in an aperture respectively pupil plane allowing the insertion of spatially modulated illumination in the pupil of the optical system 10, 10’.

[0083] There are various optical elements that can be used to generate spatially modulated illumination. In an example, an amplitude mask with a transmission coefficient between 0 and 1 is used. The transmission coefficient determines the light amplitudes that are filtered by the optical element. In this way, illumination of high diffraction orders is reduced in the illumination beam path, such that less ghost light reaches the photolithography mask.

[0084] In an example, the optical element comprises a diffractive optical element. In this way absorption is prevented and a higher efficiency is achieved. In addition, heat generation is reduced.

[0085] In an example, the optical element comprises a phase mask. A phase mask is used to filter light of specific phases from the illumination. Phase masks allow a higher transmission of light, and they allow for a fine gradation of a spatially modulated illumination.

[0086] In an example, the optical element comprises a diffraction grating whose periodic structures have a minimum distance above the resolution limit of the optical system. This is particularly interesting for optical elements 22 arranged in a field plane in the illumination optical unit (second location 23’) or in the aperture plane in the illuminationoptical unit (third location 23”), since the light afterwards passes through the illumination optics 16.

[0087] In an example, the optical element comprises a switchable optical element, for example a micro-mirror array. The micro-mirror array can be used to program different spatially modulated illuminations. This allows for a simple and highly flexible configuration of the optical element.

[0088] The optical element is preferably configured such that the greatest isolated illumination structures above the resolution limit of the optical system are smaller than the field of view of the imaging beam path. This ensures that the spatially modulated illumination generated by the optical element is imaged in the at least one image of the photolithography mask obtained by the optical system.

[0089] In an example illustrated in Fig. 5, the optical element comprises a pinhole aperture 27. The mask design 32 contains structures below the resolution limit of the optical system. To make these structures visible in an image, the photolithography mask is only locally illuminated by a pinhole aperture 27. In the image 26 of the photolithography mask acquired using the pinhole aperture 27 a local structure is visible. The difference image 29 shows the difference between two images with different spatially modulated illumination obtained by slightly shifting the mask design 32. To obtain a complete image, the position of the pinhole aperture with respect to the mask design is moved, e.g., be moving the pinhole aperture 27 or by moving the mask design 32. As illustrated by the difference image 29, the resulting image contains structures that can be registered to corresponding structures in a reference image.

[0090] Each of the at least one image 26 obtained using a different pinhole aperture 27 position or a different photolithography mask 14 position can be further enhanced by deconvolution with the point spread function (PSF) of the imaging beam path 19 of the optical system 10, 10’. From the at least one deconvolved image 26 an image of an increased resolution can be computed, which is composed of a set of deconvolved respectively reconstructed images 26. Subsequently, the image of an increased resolution can be used for subpixel accurate registration of structures in the at least one image and corresponding structures in the reference image. Instead of the deconvolution of the at least one (pinhole) image 26 with the PSF of the imaging beam path 19, an edge sharping or image acuity enhancement filter can be applied to the at leastone (pinhole) image 26. Instead of a single pinhole that is moved relative to the photolithography mask, the pinhole aperture 27 can contain multiple pinholes with sufficient spatial distance in between. The spatial distance is sufficient, if the PSFs of each two illumination pinholes imaged onto the surface of the photolithography mask do not or only minimally overlap on the image sensor 20. The pinholes may, for example, be arranged in a periodic manner on the pinhole aperture 27.

[0091] In an example, the spatially modulated illumination comprises a sinusoidal illumination pattern. In a preferred example, sinusoidal illumination patterns with three different phase shifts are generated for each spatial direction. More robust reconstructions of the high frequency information on the photolithography mask can be achieved by using additional sinusoidal patterns with further phase shifts or for additional spatial directions. In two-dimensional space, for example, sinusoidal illumination patterns along two perpendicular lateral axes of the optical system and an additional axis in the same lateral plane with a different angle could be used as spatially modulated illumination.

[0092] According to an example, the spatially modulated illumination comprises a superposition of multiple periodic illumination patterns. This approach usually aims at a more robust method in terms of noise suppression and artifact removal.

[0093] According to an example, the optical element is selected depending on the type of patterns on the photolithography mask. For example, the optical element can comprise the same or similar structures as the photolithography mask but with minimum size above the resolution limit, for example a scaled version of the structures on the photolithography mask. Preferably, the optical element comprises structures that show the same symmetries as the structures on the photolithography mask. In this way, cancellation effects can be maximized and post-processing of the at least one image is simplified. The optical element can, for example, comprise a grating, holes, contact holes, etc.

[0094] According to an example, the optical system comprises an additional aperture stop that is used for defining the distribution of incoming illumination angles on the photolithography mask. In this way, the contrast of the image can be improved.Two or more images with different spatially modulated illuminations can be generated in various ways.

[0095] In an example, different spatially modulated illuminations are generated by spatial transformations of a single spatially modulated illumination. Thus, an illumination pattern is generated, and this pattern is subsequently transformed, e.g., by translation or rotation.

[0096] Spatial transformations of a spatially modulated illumination can, for example, be obtained by relative spatial transformations between the photolithography mask and the optical element, e.g., by moving the photolithography mask and / or by moving the optical element.

[0097] In another example, different spatially modulated illuminations are generated by introducing different optical elements in the illumination beam path of the illumination optical unit. For example, gratings with different structures or with different magnifications of the same structures.

[0098] According to an example, the spatially modulated illumination generated by the illumination optical unit is partially coherent. In this way, a higher resolution of small structures and a higher image intensity can be obtained, such that neighboring structures can be distinguished more easily.

[0099] Fig. 6 illustrates a flowchart of a method for registering structures in at least one image of a photolithography mask obtained by an optical system with a resolution limit to corresponding structures in a reference image of the photolithography mask according to an embodiment of the invention. The optical system comprises an illumination optical unit with an optical element arranged in an illumination beam path of the illumination optical unit, the illumination optical unit being configured for illuminating the photolithography mask with spatially modulated illuminations, and an imaging beam path for imaging the photolithography mask onto an image sensor. The method comprises: providing at least one image of a photolithography mask acquired by the optical system with spatially modulated illuminations in a step M1; and registering structures in the at least one provided image to corresponding structures in a reference image of the photolithography mask in a step M2.According to an example, the photolithography mask comprises multiple structures with a distance below the resolution limit of the optical system. Due to their distance below the resolution limit, these structures interfere in the image obtained by the optical system and make an accurate registration impossible. The same holds true for the case that the photolithography mask comprises a periodic mask pattern with a periodicity above the inverse resolution limit of the optical system.

[0100] Fig. 7a-e illustrates that registration information can be derived from images of photolithography mask patterns with structure distances below the resolution limit by using spatially modulated illumination. Fig. 7a shows a periodic mask design 32 with a critical dimension of 45 nm, which is below the resolution limit of the optical system. The image 26 obtained by the optical system in Fig. 7d is constant, since it cannot resolve the different structures of the mask design 32. Thus, no registerable information can be derived from this image 26. To alleviate this problem, a spatially modulated illumination is used, which is generated by a diffraction grating of the diffraction grating design 34 shown in Fig. 7b. The periodic structures of the diffraction grating 34 have a minimum distance of 75nm, which is above the resolution limit of the optical system. Fig. 7c shows the resulting pattern 36 generated by the mask design 32 in Fig. 7a and the diffraction grating design 34 in Fig. 7b. The resulting image 26’ is obtained by illuminating a photolithography mask of the mask design 32 in Fig. 7a with spatially modulated illumination generated by a diffraction grating of the diffraction grating design 34 in Fig. 7b. Due to the use of structured illumination, frequencies above the inverse resolution limit of the optical system are visible in the image 26. Thus, the image contains registrable information that can be used for registering structures of the photolithography mask to corresponding structures in the reference image.

[0101] According to an example, multiple images of the photolithography mask are provided, and each of the multiple images is obtained with a different spatially modulated illumination. Since each of the multiple images of the photolithography mask contains different frequencies above the inverse of the resolution limit, each of the multiple images can be registered to the reference image, and the multiple registrations can be combined to obtain a more reliable registration, e.g., by averaging or median filtering. Alternatively, the multiple images can be used to compute an image of increased resolution, which is then registered to the reference image. Both ways lead to an increased accuracy of the generated registration information.There are various methods for computing high resolution images from multiple images with spatially modulated illumination, as described, for example, in “Superresolution structured illumination microscopy reconstruction algorithms: a review” by Xin Chen, Suyi Zhong, Yiwei Hou, Ruijie Cao, Wenyi Wang, Dong Li, Qionghai Dai, Donghyun Kim, and Peng Xi, in Light: Science & Applications, July 2023. Alternatively, machine learning methods can be used.

[0102] In order to analyze large amounts of data requiring large amounts of measurements to be taken, machine learning methods can be used. Machine learning is a field of artificial intelligence. Machine learning methods generally build a parametric machine learning model based on training data consisting of a large number of samples. After training, the method is able to generalize the knowledge gained from the training data to new previously unencountered samples, thereby making predictions for new data. There are many machine learning methods, e.g., linear regression, k-means, support vector machines, decision trees, random forests, diffusion models, neural networks, transformers or deep learning approaches. Machine learning models are parametric models whose parameters are optimized during training. The machine learning model and the learned parameters can be applied to make predictions for new input data. Machine learning models comprise, for example, neural networks, support vector machines, decision trees, random forests, subspaces, cluster sets, etc.

[0103] Deep learning is a class of machine learning that uses artificial neural networks with numerous hidden layers between the input layer and the output layer. Due to this complex internal structure the networks are able to progressively extract higher-level features from the raw input data. Each level learns to transform its input data into a slightly more abstract and composite representation, thus deriving low and high level knowledge from the training data. The hidden layers can have differing sizes and tasks such as convolutional or pooling layers.

[0104] Machine learning models are trained using training data, i.e., examples, and, thus, independently derive their knowledge from the training data instead of requiring a user to define rules to obtain the desired results. In this way, optimal results with respect to the minimized loss function can be obtained automatically in a data-driven way. Thus, the use of machine learning methods increases the recall and precision of the method and reduces the required user effort.According to an example illustrated in Fig. 8, the image of an increased resolution is computed using a machine learning model 38 that is trained to map multiple images 26, 26’, 26”, 26”’, 26”” of a photolithography mask acquired under different spatially modulated illuminations to an image 42 with an increased resolution of the photolithography mask. Throughout this application, the term “multiple images” refers to at least two images. Optionally, a design 32 of the photolithography mask can be used as additional input to the machine learning model.

[0105] The machine learning model 38 maps multiple images 26, 26’, 26”, 26’”, 26”” to an image 42 with an increased resolution. Neural networks, in particular, deep neural networks, can be used for this task, but also other machine learning models such as diffusion models. Among the neural networks, in particular convolutional neural networks (e.g., ll-Nets), generative adversarial neural networks, conditional adversarial neural networks or neural networks comprising at least one attention mechanism such as Transformers can be used.

[0106] The machine learning model 38 is trained by optimizing a loss function using training data illustrated in Fig. 9. The training data comprises multiple training datasets 44, 44’, 44” that are iteratively or in a batchwise manner presented to the machine learning model 38. Each of the training datasets 44, 44’, 44” comprises multiple images 26, 26’, 26”, 26’”, 26”” of a photolithography mask comprising mask patterns below the resolution limit of the optical system used to acquire the multiple images 26, 26’, 26”, 26’”, 26””. Each image 26, 26’, 26”, 26’”, 26”” is obtained with a different spatially modulated illumination. In addition, each training dataset 44, 44’, 44” comprises a target image 40 of an increased resolution. The training datasets 44, 44’, 44” can be obtained by the same optical system or by different metrology systems, or they can be simulated. The machine learning model 38 can be trained, for example, using a loss function that contains a distance measure. The loss function can, for example, measure the deviation of predicted images 42 of increased resolution for multiple images of varying spatially modulated illumination from target images 40 of increased resolution. Let T=

[0107]

[0108] .,{ / „, / ?„}} indicate training data comprising n training datasets 44, 44’, 44”, each with a set of images Ikand a corresponding image of increased resolution Rk. Let indicate the prediction of the machine learning model with model parameters 6 for a set of image with varying spatially modulated illumination. The machine learning model is then trained by finding a set of parameters 6that minimize the loss function. Such a loss function can take, for example, the following form:

[0109]

[0110] where, m > 0 indicates a norm, e.g., an L1 or L2 norm. The optimization can be carried out using, e.g., a variant of the backpropagation algorithm or the adaptive moment estimation (ADAM) optimization algorithm. ADAM is an optimization algorithm that builds upon the strengths of two other popular techniques: adaptive gradient algorithm (AdaGrad) and root mean square propagation (RMSProp). It is an adaptive learning rate algorithm that dynamically reduces the learning rate for each individual parameter within a machine learning model, rather than using a single global learning rate. One of the advantages of this machine learning model is that it can reconstruct images of increased resolution from images obtained with incoherent or partially coherent illumination.

[0111] The registration of the structures of the photolithography mask in the at least one image and the reference image can be carried out in different ways. According to an example illustrated in Fig. 10a, an image 26 is registered to a reference image 48. To this end, the design 46 of the photolithography mask is shifted (for simplicity shifts are only shown in x-direction) by different lengths. The shifted design 46’ is obtained by shifting the design 46 by 5nm in horizontal direction, the shifted design 46” is obtained by shifting the design 46 by 10nm in horizontal direction, the shifted design 46”’ is obtained by shifting the design 46 by 15nm in horizontal direction, and the shifted design 46”” is obtained by shifting the design 46 by 20nm in horizontal direction. The corresponding shifted reference images 48’, 48”, 48’”, 48”” are obtained by simulation, e.g., using FDTD, RCWA, TEA or the not quite rigorous method as described above. By computing a difference image 50, 50’, 50”, 50’”, 50”” between the image 26 and the shifted reference images 48, 48’, 48”, 48’”, 48””, registration information can be obtained, e.g., by minimizing a norm of the difference images 50, 50’, 50”, 50’”, 50”” as illustrated in Fig. 10b. The shift of 10nm leads to the minimum deviation of the structures of the photolithography mask in the image 26 and the shifted reference image 48”. In this way, pattern transformations can be determined.

[0112] A machine learning based method for registering structures in at least one image of a photolithography mask obtained with spatially modulated illumination and corresponding structures in a reference image is illustrated in Fig. 11. The machine learningmodel 54 maps at least one image 26 of a photolithography mask acquired under spatially modulated illumination and a reference image 48 to a displacement field 52. Optionally, a design 32 of the photolithography mask can be used as additional input to the machine learning model 54.

[0113] Neural networks, in particular, deep neural networks, can be used for this task, but also other machine learning models such as diffusion models. Among the neural networks, in particular convolutional neural networks (e.g., ll-Nets), generative adversarial neural networks, conditional adversarial neural networks or neural networks comprising at least one attention mechanism such as Transformers can be used.

[0114] The machine learning model 54 is trained by optimizing a loss function using training data illustrated in Fig. 12. The training data comprises multiple training datasets 56, 56’, 56” that are iteratively or in a batchwise manner presented to the machine learning model 54. Each of the training datasets 56, 56’, 56” comprises at least one image 26 of a photolithography mask comprising mask patterns below the resolution limit of the optical system used to acquire the at least one image 26 and a reference image 48. Each image 26 is obtained with a spatially modulated illumination. In addition, each training dataset 56, 56’, 56” comprises a ground truth displacement field 58. The training datasets 56, 56’, 56” can be obtained by the same optical system or by different metrology systems, or they can be simulated. The machine learning model 54 can be trained, for example, using a loss function that contains a distance measure. The loss function can, for example, measure the deviation of predicted displacement fields 52 from ground truth displacement fields 58. Let T=

[0115]

[0116] . ,{ln,Dn}} indicate training data comprising n training datasets 56, 56’, 56”, each with a set of images Ikand a corresponding ground truth displacement field 58 Dk. Let

[0117]

[0118] indicate the prediction of the machine learning model 54 with model parameters 6 for a set of images with varying spatially modulated illumination. The machine learning model 54 is then trained by finding a set of parameters 6 that minimize the loss function. Such a loss function can take, for example, the following form:

[0119]

[0120] where, m > 0 indicates a norm, e.g., an L1 or L2 norm. The optimization can be carried out using, e.g., a variant of the backpropagation algorithm or the adaptive moment estimation (ADAM) optimization algorithm. ADAM is an optimization algorithm thatbuilds upon the strengths of two other popular techniques: adaptive gradient algorithm (AdaGrad) and root mean square propagation (RMSProp). It is an adaptive learning rate algorithm that dynamically reduces the learning rate for each individual parameter within a machine learning model, rather than using a single global learning rate.

[0121] Structures in the image of the photolithography mask can also be registered to corresponding structures in a reference image by solving an optimization problem as illustrated in Fig. 13. According to an example, the reference image of the photolithography mask is obtained from a parametric model 64 of the photolithography mask, whose parameters indicate transformations 60 of the structures 62 of the model 64 of the photolithography mask, and the structures in the provided at least one image and the corresponding structures 62 in the reference image are registered by solving an optimization problem for the transformation parameters 60 that minimize the deviation of the provided at least one image and the reference image of the parametric model of the photolithography mask. Such a parametric model 64 of the photolithography mask can, for example, comprise a number of polygon structures 62 that undergo transformations 60 such as translation with a parametric translation vector or rotation with an angle parameter. Alternatively, the parametric model can comprise transformations in the form of a displacement field comprising displacement vectors 61 that each indicate a translation of a location in the image to a corresponding location in the reference image, and the optimization problem is optimized for one or more displacement fields, e.g., using energy optimization methods. Optionally, a parametric reference image can be analytically simulated from this parametric model 64. Alternatively, the parametric model itself can be used as reference image for the registration. The provided at least one image is then registered to the parametric reference image by minimizing a difference, e.g., a norm, between the provided at least one image and the parametric reference image for the transformation parameters. The resulting transformation parameters in the minimum then indicate the transformations or displacement field, respectively. Optionally, the optimization problem can contain regularization terms, e.g., for enforcing smoothness between neighboring displacement field vectors, or for limiting a transformation parameter to a meaningful interval.

[0122] Another registration method relies on interferometric reconstruction of relative phase information. In this case, the structures in the provided at least one image and the corresponding structures in the reference image of the photolithography mask are registered by interferometric reconstruction of relative phase information between thepattern on the photolithography mask and the spatially modulated illumination. In a first step, an image of increased resolution is reconstructed from the at least one image with known phase variations. Subsequently, the high-resolution image is used for high-precision subpixel-accurate registration. For example, a correlation with a reference image can be used for this purpose.

[0123] According to an example illustrated in Fig. 14, the method further comprises evaluating the quality of the photolithography mask using the registered structures in the at least one image 26 and the corresponding structures in the reference image 48.

[0124] The quality of the photolithography mask can be evaluated by detecting defects in the photolithography mask, e.g., by detecting structures in the image that deviate from corresponding structures in the reference image. Therefore, in an example, the optical system is an optical inspection system that detects defects in the photolithography mask by comparing registered structures in the at least one image and the reference image. In this way, quality statements can be made about the photolithography mask, e.g., about the number of defects per area, the total number of defects, the type of defects, the severity of defects, measurements of defects, etc. Thresholds can be defined, and in case a threshold is exceeded, the photolithography mask can be repaired or discarded.

[0125] To detect defects, a registration error, i.e., the deviation of the structures in the image and the reference image after registration or the remaining local energy, an objective function value or a loss function value after optimization, can be used. Local structures that lead to a high registration error indicate a defect 63 in the structures of the photolithography mask, since, usually, there are no corresponding structures in the reference image. Alternatively, displacement vectors 65 that deviate from their neighbors can indicate a defect 63 as shown, for example, in Fig. 14. In orderto locate the outline of a defect 63, a segmentation of the registration error can, for example, be computed using image processing methods. The segmented defects 63 can be measured. In addition, the defects can be classified, e.g., by using a trained machine learning model. Depending on properties of the defects (e.g., their size, location, type, relevance, etc.) a defect can be reduced, repaired or ignored, or the whole photolithography mask can be discarded.The quality of the photolithography mask can also be evaluated by determining positional deviations of structures on the photolithography mask. Therefore, in an example, the optical system is an optical system that measures positions of structures in the photolithography mask from registered structures in the at least one image and the reference image. Provided the positions of structures in the reference image are known, their positions on the photolithography mask can be derived from the registration information, i.e., from the relative displacement 65 of the structures in the image from the corresponding structures in the reference image as illustrated in Fig. 14. In this way, quality statements can be made about the photolithography mask, e.g., about an average or a maximum deviation of a position of a structure from a reference position, or about a statistic of position deviations. In addition, accurate overlays between consecutive layers of the photolithography mask can be verified, e.g., for structures that traverse consecutive layers. Thresholds can be defined, and in case a threshold is exceeded, the photolithography mask can be repaired or discarded.

[0126] In an example called mask overlay, positional deviations of corresponding structures in subsequent layers of a stack of photolithography masks are analyzed relative to each other or relative to a different reference image using any of the methods described above. In this way, the correct vertical arrangement of structures that connect subsequent layers of a semiconductor object can be verified. If the mask overlay does not fulfill the predefined semiconductor manufacturing process related requirements, the photolithography mask must be repaired or discarded.

[0127] In an example, the method further comprises controlling at least one photolithography mask manufacturing process parameter (e.g., a focus, exposure, etc.) based on the quality evaluation of the photolithography mask (e.g., based on the measured positions of the structures in the photolithography mask in case of an optical metrology system or based on the detected defects in the photolithography mask in case of an optical inspection system).

[0128] In some implementations, after defects are detected, the photolithography mask can be modified to repair or eliminate the defects. Repairing the defects can include, e.g., depositing materials on the mask using a deposition process, removing materials from the mask using an etching process, or locally modifying a property of the object. This can, for example, comprise locally modifying at least one of a density, a refractive index, a transparency, or a reflectivity of the photolithography mask.In some implementations, the information about the defects serve as feedback to improve the process parameters of the manufacturing process, e.g., exposure time, focus, etc., For example, after the defects are identified from a first photolithography mask or first batch of photolithography masks, the process parameters of the manufacturing process are adjusted to reduce defects in a second mask or a second batch of masks.

[0129] A system 66 for registering structures in at least one image of a photolithography mask 14 obtained by an optical system 10 with corresponding structures in a reference image according to an embodiment of the invention illustrated in Fig. 15 comprises: an optical system 10 comprising an illumination optical unit with an optical element arranged in an illumination beam path of the illumination optical unit of the optical system, the illumination optical unit being configured for illuminating a photolithography mask with spatially modulated illuminations as illustrated in Fig. 1 and 2, and an imaging beam path for imaging the photolithography mask onto an image sensor; one or more processing devices 68; one or more machine-readable hardware storage devices 70 comprising instructions that are executable by one or more processing devices 68 to perform operations comprising a method for registering structures in at least one image of a photolithography mask 14 with corresponding structures in a reference image as described in any of the embodiments, examples or aspects above.

[0130] The system 66 optionally comprises a database for loading and / or saving data, e.g., machine learning models, defect detection method control parameters, reference images, training data, defect properties, optical element configurations, etc. The optical system 10, 10’ is used for obtaining at least one image of the photolithography mask 14 with spatially modulated illumination. It can provide at least one image 26 to the data analysis device 72. The data analysis device 72 includes one or more processors 68, e.g., implemented as a CPU or GPU. The one or more processors 68 can receive the at least one image via an interface 74. The one or more processors 68 can load program code from a hardware-storage device 70, e.g., program code for executing a computer implemented method 30 for registering structures in at least one image of a photolithography mask to corresponding structures in a reference image as described above, or for training a machine learning model, etc. The one or more processors 68 can execute the program code. The system 66 optionally comprises a userinterface, e.g., for monitoring the training progress of a machine learning model, for selecting training parameters, for selecting optical element configurations to generate spatially modulated illuminations, etc.

[0131] Embodiments, examples and aspects of the invention can be described by the following clauses:

[0132] 1. A method 30 for registering structures in at least one image 26, 26’, 26”, 26”’ of a photolithography mask 14 obtained by an optical system 10, 10’ with a resolution limit, the optical system 10, 10’ comprising an illumination optical unit 11 with an optical element 22 arranged in an illumination beam path 21 of the illumination optical unit 11, the illumination optical unit 11 being configured for illuminating the photolithography mask 14 with a spatially modulated illumination, and an imaging beam path 19 for imaging the photolithography mask 14 onto an image sensor 20, the method 30 comprising:

[0133] Providing at least one image 26, 26’, 26”, 26’” of a photolithography mask 14 acquired by the optical system 10, 10’ with spatially modulated illumination;

[0134] Registering structures in the at least one provided image 26 to corresponding structures in a reference image 48 of the photolithography mask 14.

[0135] 2. The method of any one of the preceding clauses, wherein the photolithography mask 14 comprises multiple structures with a distance below the resolution limit of the optical system 10, 10’.

[0136] 3. The method of any one of the preceding clauses, wherein the photolithography mask 14 comprises a periodic mask pattern with a periodicity above the inverse resolution limit of the optical system 10, 10’.

[0137] 4. The method of any one of the preceding clauses, wherein multiple images 26, 26’, 26”, 26’” of the photolithography mask 14 are provided with different spatially modulated illuminations.

[0138] 5. The method of clause 4, wherein different spatially modulated illuminations are generated by spatial transformations of a single spatially modulated illumination.6. The method of clause 5, wherein spatial transformations of a spatially modulated illumination are obtained by relative spatial transformations between the photolithography mask 14 and the optical element 22.

[0139] 7. The method of clause 4 or 5, wherein different spatially modulated illuminations are generated by introducing different optical elements 22 in the illumination beam path 21 of the illumination optical unit 11.

[0140] 8. The method of any one of clauses 4 to 7, further comprising computing an image 42 of an increased resolution from the provided multiple images 26, 26’, 26”, 26’”.

[0141] 9. The method of clause 8, wherein structures in the image 42 of an increased resolution are registered to corresponding structures in the reference image 48 of the photolithography mask 14.

[0142] 10. The method of clause 8 or 9, wherein the image 42 of an increased resolution is computed using a machine learning model 38 that is trained to map multiple images 26, 26’, 26”, 26’” of a photolithography mask 14 acquired under different spatially modulated illuminations to an image 42 with an increased resolution of the photolithography mask 14.

[0143] 11. The method of any one of clauses 1 to 10, wherein the optical element 22 is arranged in the illumination beam path 21 close to the photolithography mask 14.

[0144] 12. The method of any one of clauses 1 to 10, wherein the optical element 22 is arranged in the illumination beam path 21 close to illumination optics 16 of the illumination optical unit 11.

[0145] 13. The method of any one of clauses 1 to 10, wherein the optical element 22 is arranged in the illumination beam path 21 close to a light source 12 of the illumination optical unit 11.

[0146] 14. The method of any one of the preceding clauses, wherein the optical element 22 comprises a pinhole aperture 27.15. The method of any one of the preceding clauses, wherein the optical element 22 comprises an amplitude mask with a transmission coefficient between 0 and 1.

[0147] 16. The method of any one of the preceding clauses, wherein the optical element 22 comprises a diffractive optical element.

[0148] 17. The method of any one of the preceding clauses, wherein the optical element 22 comprises a phase mask.

[0149] 18. The method of any one of the preceding clauses, wherein the optical element 22 comprises a diffraction grating whose periodic structures have a minimum distance above the resolution limit of the optical system 10, 10’.

[0150] 19. The method of any one of the preceding clauses, wherein the spatially modulated illumination comprises a superposition of multiple periodic illumination patterns.

[0151] 20. The method of any one of the preceding clauses, wherein the spatially modulated illumination comprises a sinusoidal illumination pattern.

[0152] 21. The method of any one of the preceding clauses, wherein the optical element 22 is selected depending on the type of patterns on the photolithography mask 14.

[0153] 22. The method of any one of the preceding clauses, wherein the spatially modulated illumination generated by the illumination optical unit is partially coherent.

[0154] 23. The method of any one of the preceding clauses, wherein the optical system 10, 10’ comprises an additional aperture stop, and wherein the aperture stop is used for defining the distribution of incoming illumination angles on the photolithography mask 14.

[0155] 24. The method of any one of the preceding clauses, wherein the structures in the provided at least one image 26, 26’, 26”, 26’” and the corresponding structures in the reference image 48 of the photolithography mask are registered using a machine learning model 54 that is trained to map at least one image 26, 26’, 26”, 26’” obtained with spatially modulated illumination and a reference image 48 to a displacement field 52.The method of any one of the preceding clauses, wherein the structures in the provided at least one image 26, 26’, 26”, 26”’ and the corresponding structures in the reference image 48 of the photolithography mask 14 are registered by interferometric reconstruction of relative phase information between the pattern on the photolithography mask and the spatially modulated illumination.

[0156] The method of any one of the preceding clauses, wherein the reference image 48 of the photolithography mask 14 is obtained from a parametric model 64 of the photolithography mask 14, whose parameters indicate transformations 60 of the structures of the model 64 of the photolithography mask 14, and wherein the structures in the provided at least one image 26, 26’, 26”, 26’” and the corresponding structures in the reference image 48 are registered by solving an optimization problem for the transformation parameters that minimize the deviation of the provided at least one image 26, 26’, 26”, 26’” and the reference image 48 of the parametric model 64 of the photolithography mask 14.

[0157] The method of any one of the preceding clauses, further comprising evaluating the quality of the photolithography mask 14 using the registered structures in the provided at least one image 26, 26’, 26”, 26’” and the corresponding structures in the reference image 48.

[0158] The method of any one of the preceding clauses, wherein the optical system 10, 10’ is an optical system that measures positions of structures in the photolithography mask 14 from registered structures in the at least one image 26, 26’, 26”, 26’” and the reference image 48.

[0159] The method of any one of the preceding clauses, wherein the optical system 10, 10’ is an optical inspection system that detects defects 63 in the photolithography mask 14 by comparing registered structures in the at least one image 26, 26’, 26”, 26’” and the reference image 48.

[0160] A computer implemented method for training a machine learning model 38, 54 according to clause 10 or 24.

[0161] A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the computer implemented method for training a machine learning model 38, 54 according to clause 30.32. A computer-readable medium, on which a computer program executable by a computing device is stored, the computer program comprising code for executing the computer implemented method for training a machine learning model 38, 54 according to clause 30.

[0162] 33. A system 66 for registering structures in at least one image 26, 26’, 26”, 26”’ of a photolithography mask 14 obtained by an optical system 10, 10’ with corresponding structures in a reference image 48, the system 66 comprising:

[0163] - An optical system 10, 10’ comprising an illumination optical unit 11 with an optical element 22 arranged in an illumination beam path 21 of the illumination optical unit 11 of the optical system 10, 10’, the illumination optical unit 11 being configured for illuminating a photolithography mask 14 with spatially modulated illuminations, and an imaging beam path 19 for imaging the photolithography mask 14 onto an image sensor 20;

[0164] one or more processing devices 68;

[0165] one or more machine-readable hardware storage devices 70 comprising instructions that are executable by one or more processing devices 68 to perform operations comprising a method 30 for registering structures in at least one image 26, 26’, 26”, 26’” of a photolithography mask 14 with corresponding structures in a reference image 48 according to any one of clauses 1 to 29.

[0166] Reference throughout this specification to “an embodiment” or “an example” or “an aspect” means that a particular feature, structure or characteristic described in connection with the embodiment, example or aspect is included in at least one embodiment, example or aspect. Thus, appearances of the phrases “according to an embodiment”, “according to an example” or “according to an aspect” in various places throughout this specification are not necessarily all referring to the same embodiment, example or aspect, but may. Furthermore, the particular features or characteristics may be combined in any suitable manner, as would be apparent to one of ordinary skill in the art from this disclosure, in one or more embodiments.Furthermore, while some embodiments, examples or aspects described herein include some but not other features included in other embodiments, examples or aspects combinations of features of different embodiments, examples or aspects are meant to be within the scope of the claims, and form different embodiments, as would be understood by those skilled in the art.

[0167] In summary, the invention relates to a method 30 for registering structures in at least one image 26, 26’, 26”, 26”’ of a photolithography mask 14 obtained by an optical system 10, 10’ with a resolution limit, the optical system 10, 10’ comprising an illumi-nation optical unit 11 with an optical element 22 arranged in an illumination beam path 21 of the illumination optical unit 11, the illumination optical unit 11 being configured for illuminating the photolithography mask 14 with a spatially modulated illumination, and an imaging beam path 19 for imaging the photolithography mask 14 onto an image sensor 20, the method 30 comprising: providing at least one image 26, 26’, 26”, 26’” of a photolithography mask 14 acquired by the optical system 10, 10’ with spatially modulated illumination; registering structures in the at least one provided image 26 to corresponding structures in a reference image 48 of the photolithography mask 14.Reference number list

[0168] 10, 10’ Optical system

[0169] 11 Illumination optical unit

[0170] 12 Light source

[0171] 14 Photolithography mask

[0172] 16 Illumination optics

[0173] 17 Projection optics

[0174] 18 Wafer plane

[0175] 19 Imaging beam path

[0176] 20 Image sensor

[0177] 21 Illumination beam path

[0178] 22 Optical element

[0179] 23 First location

[0180] 23’ Second location

[0181] 23” Third location

[0182] 24 Pattern

[0183] 26, 26’, 26”, 26’”, 26”” Image

[0184] 27 Pinhole aperture

[0185] 28 Spatially modulated illumination

[0186] 29 Difference image

[0187] 30 Method

[0188] 32 Mask design

[0189] 34 Diffraction grating design

[0190] 36 Pattern

[0191] 37 Input dataset

[0192] 38 Machine learning model

[0193] 40 Target image of an increased resolution 42 Predicted image of an increased resolution 44 Training dataset

[0194] 46 Design

[0195] 46’, 46”, 46’”, 46”” Shifted design

[0196] 48 Reference image

[0197] 48’, 48”, 48’”, 48”” Shifted reference image

[0198] 50, 50’, 50”, 50’”, 50”” Difference image

[0199] 52 Predicted displacement fieldMachine learning model

[0200] Training dataset

[0201] Ground truth displacement field Transformation

[0202] Displacement vector

[0203] Structure

[0204] Defect

[0205] Model

[0206] Displacement vector

[0207] System

[0208] Processing device

[0209] Machine-readable hardware storage device Data analysis device

[0210] Interface

Claims

- 38 -Claims1. A method (30) for registering structures in at least one image (26, 26’, 26”, 26”’) of a photolithography mask (14) obtained by an optical system (10, 10’) with a resolution limit, the optical system (10, 10’) comprising an illumination optical unit (11) with an optical element (22) arranged in an illumination beam path (21) of the illumination optical unit (11), the illumination optical unit (11) being configured for illuminating the photolithography mask (14) with a spatially modulated illumination, and an imaging beam path (19) for imaging the photolithography mask (14) onto an image sensor (20), the method (30) comprising:Providing at least one image (26, 26’, 26”, 26’”) of a photolithography mask (14) acquired by the optical system (10, 10’) with spatially modulated illumination;Registering structures in the at least one provided image (26) to corresponding structures in a reference image (48) of the photolithography mask (14).

2. The method of any one of the preceding claims, wherein the photolithography mask (14) comprises multiple structures with a distance below the resolution limit of the optical system (10, 10’).

3. The method of any one of the preceding claims, wherein the photolithography mask (14) comprises a periodic mask pattern with a periodicity above the inverse resolution limit of the optical system (10, 10’).

4. The method of any one of the preceding claims, wherein multiple images (26, 26’, 26”, 26’”) of the photolithography mask (14) are provided with different spatially modulated illuminations.

5. The method of claim 4, wherein different spatially modulated illuminations are generated by spatial transformations of a single spatially modulated illumination.

6. The method of claim 5, wherein spatial transformations of a spatially modulated illumination are obtained by relative spatial transformations between the photolithography mask (14) and the optical element (22).- 39 -7. The method of claim 4 or 5, wherein different spatially modulated illuminations are generated by introducing different optical elements (22) in the illumination beam path (21) of the illumination optical unit (11).

8. The method of any one of claims 4 to 7, further comprising computing an image (42) of an increased resolution from the provided multiple images (26, 26’, 26”, 26’”).

9. The method of claim 8, wherein structures in the image (42) of an increased resolution are registered to corresponding structures in the reference image (48) of the photolithography mask (14).

10. The method of claim 8 or 9, wherein the image (42) of an increased resolution is computed using a machine learning model (38) that is trained to map multiple images (26, 26’, 26”, 26’”) of a photolithography mask (14) acquired under different spatially modulated illuminations to an image (42) with an increased resolution of the photolithography mask (14).

11. The method of any one of claims 1 to 10, wherein the optical element (22) is arranged in the illumination beam path (21) close to the photolithography mask (14).

12. The method of any one of claims 1 to 10, wherein the optical element (22) is arranged in the illumination beam path (21) close to illumination optics (16) of the illumination optical unit (11).

13. The method of any one of claims 1 to 10, wherein the optical element (22) is arranged in the illumination beam path (21) close to a light source (12) of the illumination optical unit (11).

14. The method of any one of the preceding claims, wherein the optical element (22) comprises a pinhole aperture (27).

15. The method of any one of the preceding claims, wherein the optical element (22) comprises an amplitude mask with a transmission coefficient between 0-40 -16. The method of any one of the preceding claims, wherein the optical element (22) comprises a diffractive optical element.

17. The method of any one of the preceding claims, wherein the optical element (22) comprises a phase mask.

18. The method of any one of the preceding claims, wherein the optical element (22) comprises a diffraction grating whose periodic structures have a minimum distance above the resolution limit of the optical system (10, 10’).

19. The method of any one of the preceding claims, wherein the spatially modulated illumination comprises a superposition of multiple periodic illumination patterns.

20. The method of any one of the preceding claims, wherein the spatially modulated illumination comprises a sinusoidal illumination pattern.

21. The method of any one of the preceding claims, wherein the optical element (22) is selected depending on the type of patterns on the photolithography mask (14).

22. The method of any one of the preceding claims, wherein the spatially modulated illumination generated by the illumination optical unit is partially coherent.

23. The method of any one of the preceding claims, wherein the optical system (10, 10’) comprises an additional aperture stop, and wherein the aperture stop is used for defining the distribution of incoming illumination angles on the photolithography mask (14).

24. The method of any one of the preceding claims, wherein the structures in the provided at least one image (26, 26’, 26”, 26’”) and the corresponding structures in the reference image (48) of the photolithography mask are registered using a machine learning model (54) that is trained to map at least one image (26, 26’, 26”, 26’”) obtained with spatially modulated illumination and a reference image (48) to a displacement field (52).

25. The method of any one of the preceding claims, wherein the structures in the provided at least one image (26, 26’, 26”, 26’”) and the corresponding struc-tures in the reference image (48) of the photolithography mask (14) are registered by interferometric reconstruction of relative phase information between the pattern on the photolithography mask and the spatially modulated illumination.

26. The method of any one of the preceding claims, wherein the reference image (48) of the photolithography mask (14) is obtained from a parametric model (64) of the photolithography mask (14), whose parameters indicate transformations (60) of the structures of the model (64) of the photolithography mask (14), and wherein the structures in the provided at least one image (26, 26’, 26”, 26”’) and the corresponding structures in the reference image (48) are registered by solving an optimization problem for the transformation parameters that minimize the deviation of the provided at least one image (26, 26’, 26”, 26’”) and the reference image (48) of the parametric model (64) of the photolithography mask (14).

27. The method of any one of the preceding claims, further comprising evaluating the quality of the photolithography mask (14) using the registered structures in the provided at least one image (26, 26’, 26”, 26’”) and the corresponding structures in the reference image (48).

28. The method of any one of the preceding claims, wherein the optical system (10, 10’) is an optical system that measures positions of structures in the photolithography mask (14) from registered structures in the at least one image (26, 26’, 26”, 26’”) and the reference image (48).

29. The method of any one of the preceding claims, wherein the optical system (10, 10’) is an optical inspection system that detects defects (63) in the photolithography mask (14) by comparing registered structures in the at least one image (26, 26’, 26”, 26’”) and the reference image (48).

30. A computer implemented method for training a machine learning model (38, 54) according to claim 10 or 24.

31. A computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the computer implemented method for training a machine learning model (38, 54) according to claim 30.

32. A computer-readable medium, on which a computer program executable by a computing device is stored, the computer program comprising code for executing the computer implemented method fortraining a machine learning model (38, 54) according to claim 30.

33. A system (66) for registering structures in at least one image (26, 26’, 26”, 26”’) of a photolithography mask (14) obtained by an optical system (10, 10’) with corresponding structures in a reference image (48), the system (66) comprising:- An optical system (10, 10’) comprising an illumination optical unit (11) with an optical element (22) arranged in an illumination beam path (21) of the illumination optical unit (11) of the optical system (10, 10’), the illumination optical unit (11) being configured for illuminating a photolithography mask (14) with spatially modulated illuminations, and an imaging beam path (19) for imaging the photolithography mask (14) onto an image sensor (20); one or more processing devices (68);one or more machine-readable hardware storage devices (70) comprising instructions that are executable by one or more processing devices (68) to perform operations comprising a method (30) for registering structures in at least one image (26, 26’, 26”, 26’”) of a photolithography mask (14) with corresponding structures in a reference image (48) according to any one of claims 1 to 29.

Images