Method for registering structures in an image of a photolithography mask to corresponding structures in a reference image and corresponding system

Abstract

The present invention relates to a method (26) for aligning a structure in an image (22) of a photolithography mask (14), comprising the steps of: providing an image (22) of a photolithography mask (14) obtained by an optical system (10, 10') - wherein the noise distribution of the image (22) varies according to at least one attribute of the image (22), the photolithography mask (14), or the optical system (10, 10'); and aligning a structure in a transformation of the image (22) to a corresponding structure of a reference image (64) of the photolithography mask (14) - wherein the variation in the noise distribution is reduced in the transformed image (28).

Description

Technology Field

[0001] Related applications

[0002] This application claims priority to German patent application No. 10 2025 102252.6 filed on January 22, 2025, the entirety of which is incorporated herein by reference.

[0003] Field of invention

[0004] The present invention relates to a method for aligning structures in an image of a photolithography mask obtained by an optical system, for example, an optical measurement system or an optical inspection system, and to a system said. The aligned structures can be used to evaluate the quality of the photolithography mask, for example, to measure the location of structures on the photolithography mask or to detect defects in the photolithography mask. Background Technology

[0005] Semiconductor manufacturing involves the precise manipulation of materials such as silicon or oxides on a very fine scale in the nanometer (nm) range (e.g., etching). Wafers, made from thin sheets of silicon, serve as substrates for microelectronic devices with semiconductor structures embedded within and on the surface of the wafer. Semiconductor structures are built layer by layer through a process that involves repeating chemical, mechanical, thermal, and optical processes. Photolithography is a process used to create patterns on a substrate. Patterns to be printed on the substrate surface are generated through computer-aided design (CAD). From this design, a photolithography mask is created for each layer, which contains an enlarged image of the computer-generated pattern to be etched onto the substrate. The photolithography mask can be further adjusted using methods such as optical proximity correction techniques. During the printing process, an illumination image projected from the photolithography mask is focused onto a thin film of photoresist formed on the substrate. For example, semiconductor chips that power mobile phones or tablets consist of approximately 80 to 120 patterned layers.

[0006] Due to the increasing integration density in the semiconductor industry, photolithography masks must image increasingly smaller structures onto wafers. The aspect ratio and number of layers in integrated circuits are continuously increasing, and structures are expanding in three dimensions (vertically). Currently, the height of memory stacks exceeds tens of microns. In contrast, feature sizes are becoming smaller. The minimum feature size, or critical dimension, is less than 10 nm—for example, 7 nm or 5 nm—and is expected to decrease to less than 3 nm in the near future. While the complexity and size of semiconductor structures expand in three dimensions, The horizontal dimensions of integrated semiconductor structures are shrinking. To realize small structure sizes imaged on a wafer, photolithography masks or templates for nanoimprint photolithography with increasingly smaller structure or pattern elements are required. Consequently, the production processes for photolithography masks and templates for nanoimprint photolithography are becoming more complex, resulting in time-consuming and ultimately higher costs. With the advent of EUV photolithography scanners, the characteristics of masks have shifted from transmission-based patterns to reflection-based patterns.

[0007] Because the structural size of pattern elements in photolithography masks is very small, errors cannot be completely eliminated during the mask fabrication process. As a result, defects may occur due to factors such as photolithography mask degradation or particle contamination. Therefore, in semiconductor process control, the inspection, review, and measurement of photolithography masks play a crucial role in systematically monitoring defects. Defects discovered during the quality assurance process are utilized for root cause analysis and can be used, for example, to modify, repair, or discard the photolithography mask.

[0008] Optical systems inspect structures on photolithography masks using images. Images are formed when light, such as EUV or DUV wavelengths, passes through the photolithography mask and is projected onto an imaging sensor, such as a CCD or CMOS array. Thus, an image represents the light distribution on the wafer surface. By aligning the structure in the image with the corresponding structure in a reference image, the location of the structure can be measured and defects on the photolithography mask can be detected. However, the accuracy of all these measurements is negatively affected by noise in the acquired image. Noise refers to random fluctuations in image brightness. Optical images are primarily affected by shot noise, which arises from the particle nature of light. Shot noise in an image depends on image intensity; the higher the image intensity, the higher the noise level. Other types of noise, such as Gaussian noise, can also occur in the image. Matching algorithms are generally based on the assumption that uniformly distributed noise exists within the image, particularly uniformly distributed Gaussian noise. Since images obtained by optical systems are dominated by shot noise, they do not adhere to this assumption, resulting in reduced accuracy in aligning the image with the reference image.

[0009] Therefore, the objective of the present invention is to improve the alignment accuracy between an image obtained by an optical system and a reference image. Furthermore, the objective of the present invention is to improve the accuracy of quality evaluation of a photolithography mask.

[0010] The present invention is achieved by the purpose specified in the independent claim. Advantageous embodiments and further developments of the present invention are specified in the dependent claims.

[0011] Embodiments of the present invention relate to a method and system for aligning the structure of an image of a photolithography mask obtained by an optical system with the corresponding structure of a reference image.

[0012] A first embodiment comprises a method for aligning a structure in an image of a photolithography mask, the method comprising the step of providing an image of a photolithography mask acquired by an optical system—wherein the noise distribution of the image depends on at least one property of the image, the photolithography mask, or the optical system—; and the step of aligning a structure in a transformation of the image to a corresponding structure of a reference image of the photolithography mask—wherein the variation in the noise distribution is reduced in the transformed image. The method may be implemented on a computer.

[0013] The noise distribution depends on the properties of the image, photolithography mask, or optical system, such as image intensity, image location, photolithography mask material, or the sensor of the optical system. This means that noise is not uniformly distributed across the entire image, and the type or parameters of the noise distribution depend on these properties. For example, in the case of shot noise, the noise follows a Poisson distribution, and its variance depends on the image intensity. Using image transformation reduces the variability of the noise distribution in the transformed image. Consequently, the noise distribution becomes more uniform and approaches an equal distribution. In the case of shot noise, the variance of the noise distribution becomes less dependent on image intensity. The variability of the noise distribution can be measured, for example, by calculating the variance of the variance or other statistical properties of the noise distribution across the entire image. Depending on a specific image transformation, the noise distribution of the transformed image can approximate a Gaussian distribution. In this way, the assumption of an equal-distribution noise distribution—specifically a Gaussian noise distribution—which is generally implicitly assumed in standard matching methods is better satisfied. Consequently, the accuracy of the matching is improved.

[0014] For example, the noise distribution in an image includes Poisson distribution components and / or Gaussian distribution components. Poisson-distributed shot noise is generally the primary source of noise in optical images and varies with image intensity. Therefore, this type of noise does not satisfy the assumptions of homogeneous or Gaussian noise distribution in standard matching methods.

[0015] For example, the noise distribution of an image depends on at least one of the properties of the image, photolithography mask, or optical system from a group including image intensity, image location, image content, photolithography mask material, photolithography mask structure type, and detector properties of the optical system. This variable noise distribution causes non-uniformly distributed noise, resulting in inaccurate matching results.

[0016] For example, the variance of the noise distribution in an image depends on at least one attribute of the image, but in the transformed image, the variability of the noise distribution is reduced. As the variability of the noise distribution decreases, the noise distribution becomes more uniform and thus approaches noise that is evenly distributed in the image. Consequently, the assumption that noise is evenly distributed in the image is better satisfied, thereby improving matching accuracy.

[0017] According to one aspect of the present invention, the variance of the noise distribution of the transformed image is approximately constant. In particular, the noise distribution of the transformed image approximately follows a uniformly distributed Gaussian distribution. This noise distribution satisfies the assumptions of standard matching algorithms and improves matching accuracy.

[0018] According to a preferred embodiment, the image transformation includes a variance stabilizing transformation. The variance stabilizing transformation reduces the variation in the variance of the noise distribution within the image. The Anscombe transformation can be used to transform a Poisson noise distribution into a Gaussian distribution, in which case the noise variance is independent of the image intensity because the variance is independent of the mean. A generalized Anscombe transformation can also be used to transform a Poisson noise distribution with added Gaussian noise components into a Gaussian distribution. In this way, the matching accuracy is improved.

[0019] For example, the variance-stabilized transform is obtained by solving an optimization problem that minimizes the deviation between the estimated noise variance and the constant noise variance in an image. In this way, the variance-stabilized transform can be adjusted to match the accurate noise distribution of the image, thereby improving matching accuracy.

[0020] According to one aspect, an image is composed of at least two sub-images, each having a different noise distribution, and the variation in the noise distribution within each sub-image of the image is reduced. By transforming each sub-image individually, the image transformation for each sub-image is adjusted to match the noise distribution within that sub-image, thereby achieving higher matching accuracy.

[0021] For example, pixel-level confidence scores are estimated from the image's noise distribution and used as weighting factors when aligning the structure of the transformed image to the corresponding structure in the reference image. This ensures that areas of the image with less noise have a greater impact on the alignment result than areas with more noise. This improves alignment accuracy.

[0022] For example, parameters of the image noise distribution (and thus parameters of the image transformation) are estimated from one or more images obtained from the optical system and / or the optical system itself. In this way, the image transformation is specifically tuned to the image noise distribution and / or the optical system. The more images used for parameter estimation, the higher the accuracy of the match with the estimated parameters.

[0023] According to a preferred embodiment, the image transformation further includes the step of filtering the image using a filter that depends on the shape of the imaging pupil of the optical system. In this way, pure noise frequencies are filtered out of the image, thereby improving the matching accuracy.

[0024] For example, a transformation is applied to the reference image to reduce variations in its noise distribution. This reduces the variability in the reference image's noise distribution, further improving matching accuracy.

[0025] According to one example, the present method further includes the step of evaluating the quality of a photolithography mask using a matched structure of an image and a reference image. The matched structure can be used to measure the location of a structure on the photolithography mask (measurement system), or to detect defects in the photolithography mask (inspection system). Based on this information, a conclusion regarding the quality of the photolithography mask can be drawn.

[0026] For example, the optical system is an optical measurement system that measures the location of a structure within a photolithography mask from the aligned structure of an image and a reference image.

[0027] In one example, the optical system is an optical inspection system that detects defects in a photolithography mask by comparing the aligned structures of an image and a reference image.

[0028] In one example, the present method further includes the step of controlling at least one photolithography mask manufacturing process parameter based on a quality evaluation of the photolithography mask.

[0029] A system for aligning a structure in an image of a photolithography mask acquired by an optical system comprises: an optical system for acquiring an image of a photolithography mask; one or more processing devices; and one or more machine-readable hardware storage devices comprising instructions executable by one or more processing devices for performing an operation including a method for aligning a structure in an image of a photolithography mask according to any one of the embodiments, examples, or aspects of the present invention described above.

[0030] The invention described by the embodiments and examples is not limited to the embodiments and examples, and those skilled in the art may implement it through various combinations or modifications. Brief explanation of the drawing

[0031] Figure 1 illustrates an example of a transmission-based optical system, for example, a deep ultraviolet (DUV) optical system. Figure 2 illustrates an example of a reflection-based optical system, for example, an extreme ultraviolet (EUV) optical system. Figures 3a and 3b illustrate images including shot noise and an estimated noise distribution. FIG. 4 illustrates a flowchart of a method for aligning a structure in an image of a photolithography mask according to an embodiment of the present invention. Figures 5a-d illustrate the application of a transformation to an image that reduces variations in the noise distribution of the image. Figure 6 illustrates the estimation of noise distribution parameters of an image from one or more images acquired from an optical system. FIG. 7 illustrates a method for separating sub-images of images with different noise distributions using the method according to the present invention. Figure 8 shows the process of generating a confidence score from the noise distribution of an image, and this confidence score is used as a weighting factor in the matching process. Figures 9a and 9b illustrate the derivation process of an NA filter that filters noise frequencies from an image, depending on the shape of the imaging pupil of the optical system. Figures 10a-d illustrate the reproducibility results for image matching repeatedly acquired by an optical system for raw image data by comparing generalized Anscomb transformed image data. Figures 11a-f illustrate the error distribution of simulated matching results for different preprocessing methods. Figures 12a and 12b illustrate a reference image and the corresponding structure of the image that are aligned to measure the position of a structure on a photolithography mask in an optical measurement system. Figures 13a-c illustrate the structure of a reference image and the structure of the image that are matched to detect defects on a photolithography mask in an optical inspection system. FIG. 14 illustrates a system for aligning a structure in an image of a photolithography mask obtained by an optical system according to an embodiment of the present invention. Specific details for implementing the invention

[0032] Advantageous embodiments of the present invention are described below and schematically illustrated in the drawings. Throughout the drawings and description, the same reference numerals are used to describe the same features or components. Dotted lines indicate optional features.

[0033] The optical system described in this specification may use illumination light of different wavelengths, such as a transmission-based optical system (10) or a reflection-based optical system (10') (e.g., an EUV system).

[0034] FIG. 1 illustrates an example of a transmission-based optical system (10) for measuring a structure on a photolithography mask using DUV light. The main components are a light source (12) (which may be a deep ultraviolet (DUV) excimer laser light source), an imaging optical system that may include, for example, an optical system that defines partial coherence and forms radiation coming from the light source (12), a photolithography mask (14), an illumination optical system (16) that illuminates the photolithography mask (14), and a projection optical system (17) that projects an image of the photolithography mask onto a wafer plane (18). An adjustable filter or aperture in the pupil plane of the projection optical system (17) may limit the range of beam angles incident on the wafer plane (18), and the maximum possible angle is the numerical aperture of the projection optical system. Defines, where n is the refractive index of the medium between the substrate and the last element of the projection optical system (17), and is the maximum angle of the beam that can strike the wafer plane (18) coming from the projection optical system (17). The radiation distribution on the wafer plane (18) is imaged by the image sensor (20) of the camera (e.g., CCD or CMOS sensor) to produce an image used for measurement operations.

[0035] In this document, the terms “illumination,” “radiation,” or “beam” are used to encompass all types of electromagnetic radiation, including ultraviolet rays (e.g., wavelengths of 365, 248, 193, 157, or 126 nm) and extreme ultraviolet rays (e.g., wavelengths of about 3 to 100 nm).

[0036] The illumination optical system (16) may include an optical component that shapes, adjusts, and projects the radiation emitted from the light source (12) before it passes through the photolithography mask (14). The projection optical system (17) may include an optical component that shapes, adjusts, and projects the radiation after it passes through the photolithography mask (14). The illumination optical system (16) does not include the light source (12), and the projection optical system does not include the photolithography mask (14).

[0037] The illumination optical system (16) and the projection optical system (17) may include various types of optical systems, including refractive optical systems, reflective optical systems, aperture and reflective refractive optical systems (catadioptric optics). Additionally, the illumination optical system (16) and the projection optical system (17) may include components that operate according to any one of these design types to direct, shape, or control the projected beam of radiation individually or collectively.

[0038] FIG. 2 illustrates an example of a reflection-based optical system (10') for measuring the structure of a photolithography mask using extreme ultraviolet (EUV) light. The main components are a light source (12) in the form of an EUV plasma source ignited by an IR laser (13), an illumination optical system (16) which may include, for example, an optical system that defines partial coherence and shapes the radiation coming from the light source (12), a photolithography mask (14), and a projection optical system (17) that projects an image of the photolithography mask onto a wafer plane (18). An adjustable filter or aperture in the pupil plane of the projection optical system (17) may limit the range of the beam angle incident on the wafer plane (18), wherein the maximum possible angle is the numerical aperture of the projection optical system. Defines, where n is the refractive index of the medium between the substrate and the last element of the projection optical system (17), and is the maximum angle of the beam coming from the projection optical system (17) that can collide with the wafer plane (18). The radiation distribution on the wafer plane (18) is imaged by the image sensor (20) of the camera to generate an image.

[0039] An optical system (10, 10') as shown in FIGS. 1 and 2 can be used to generate an image of a photolithography mask, and this image is used to align a structure in the image of the photolithography mask with a corresponding structure in a reference image of the photolithography mask.

[0040] An optical system refers to a system that uses light to obtain an image of a photolithography mask. This system illuminates the photolithography mask with light from a light source and projects the light reflected or transmitted from the mask surface onto a camera sensor array. Examples of optical systems include optical inspection systems, optical mask verification systems, and optical measurement systems.

[0041] An optical inspection system refers to an optical system used to detect defects in a photolithography mask by acquiring and analyzing aerial images of a photolithography mask or one or more parts thereof. In particular, the inspection system includes an actinic photomask inspection system.

[0042] An optical mask verification system is a system that acquires partial images of a photolithography mask to emulate the settings of a photolithography system (e.g., illumination and imaging parameters). The acquired images are of superior quality, such as having lower noise levels than images acquired by an optical inspection system. A portion of the photolithography mask may contain potential defect locations detected by the optical inspection system, which are utilized for further review. The acquired images can be used to inspect the impact of potential defects on printed wafers, verify that the photolithography mask is free of defects, determine the success of repair attempts, or estimate critical dimensions.

[0043] An optical measurement system refers to a system used to acquire an image of a photolithography mask and measure the size of structures within the photolithography mask.

[0044] The photolithography mask may have an aspect ratio of 1:1 to 1:4, preferably between 1:1 and 1:2, most preferably 1:1 or 1:2. The photolithography mask may have a nearly rectangular shape. The photolithography mask is preferably 5 to 7 inches in length and 6 inches in width. Alternatively, the photolithography mask may be 5 to 7 inches in length and 10 to 14 inches in width, preferably 6 inches in length and 12 inches in width.

[0045] The structure within the image refers to the image of photolithography mask components such as absorber structures, channels, contact structures, word lines, deck transitions, bit lines, source lines, gates, etc.

[0046] The image of the photolithography mask may refer to various types of images, such as two-dimensional images, three-dimensional images, stacks of images, or three-dimensional images that can be processed by slice. The image may be an image of the entire photolithography mask or an image of a part of the photolithography mask.

[0047] For example, an image refers to an aerial image. An aerial image represents the distribution of radiant intensity of an optical system on a wafer plane relative to a given photolithography mask. This refers to an image formed by projecting light, such as EUV or DUV wavelengths, through a photolithography mask onto an imaging sensor (e.g., a CCD or CMOS array). Thus, the aerial image simulates the structure of the wafer surface after printing. A wafer plane refers to a plane within the resist on the top of the wafer. An imaging sensor may be part of a camera configured to acquire an image at a predetermined wavelength. The camera may be a camera comprising an EUV camera and / or a TDI sensor. In a preferred embodiment, the image acquisition method involves using an EUV camera comprising a TDI sensor. Thus, the image sensor of the camera may be an EUV image sensor, that is, an image sensor sensitive to EUV light. EUV light is light in the extreme ultraviolet spectral region with wavelengths between 5 nm and 100 nm, particularly between 5 nm and 30 nm. In particular, EUV light may have a wavelength of 13.5 nm. In a preferred embodiment, the image acquisition method includes the step of irradiating a photolithography mask with actinic radiation within the EUV wavelength range. The EUV radiation reflected from the mask is projected onto an imaging sensor of an EUV camera through a suitably adjusted projection optical system.

[0048] A reference image refers to an image of a photolithography mask or a part thereof that exhibits a structure identical (at least approximately) to the image of the photolithography mask. The reference image may be of the same type as the present image, or it may be of a different type, such as an SEM image or a design image. The reference image may include images obtained using the same photolithography mask at different times, using a different optical system, using the same optical system but with different settings, or using a different part of the same photolithography mask containing the same structure. Additionally, the image itself may be used as the reference image. For example, if the image contains a self-symmetric structure, a mirror image may be used as the reference image. The reference image may also include images of other photolithography masks containing the same structure as the image of the photolithography mask, obtained using the same or different optical systems. The reference image may be a simulated image. The image may be simulated from a model of the photolithography mask using an image simulation method. For example, rigorous simulation methods known to those skilled in the art, such as the Finite Difference Time Domain (FDTD) or Roughly Coupled Wave Analysis (RCWA), may be used. Because these methods are computationally intensive, faster but less accurate approximations, such as the Thin Element Approximation (TEA) based on the thin mask assumption, may be used. To obtain fast and accurate results, simulation methods based on physical models but without the thin mask assumption may be used. For example, there are the less rigorous methods disclosed in WO 2024 141484 A1 and DE 2022 135 019 A1. In addition to physical simulation, images from the design can be simulated using trained machine learning models.The reference image may include a model of the photolithography mask, for example, a design file or other representations indicating the structure on the photolithography mask. The shape of the photolithography mask model can be adjusted to resemble the image of the photolithography mask obtained using simulation software or shape-modifying machine learning models, such as generative adversarial models or conditional generative adversarial models.

[0049] A model (or design) of a photolithography mask represents a photolithography mask or a part thereof. For example, the model may include computer-readable files such as CAD files or GDS files, technical drawings, or a set of polygons representing the structure of the photolithography mask or a part thereof. The model of the photolithography mask may include parameters describing the location of structures within the photolithography mask, for example, the location of absorber structures or layers in a multilayer structure. The model of the photolithography mask may include parameters describing the shape of structures within the photolithography mask. Examples include sidewall angles or corner roundings of absorber structures. Additionally, the photolithography mask model may include descriptions of structures within the mask expressed in forms such as curves, contours, polygons, splines, NURBS, Bézier curves, etc. Furthermore, the photolithography mask model may include material information, for example, the complex refractive index, electric permittivity, magnetic permeability of the material contained in the photolithography mask, or derived representations thereof. Finally, the photolithography mask model may include parameters describing the dimensions of the structures within the photolithography mask. For example, in the multilayer structure of an EUV mask, these include the thickness of each layer, the thickness of the absorber layer, or the dimensions of the absorber structure. The model of the photolithography mask may include an image representing the properties of the photolithography mask, for example, a 2D image or a 3D image (e.g., a voxel volume or multiple 2D slices of a volume). This image may include one, two, or more channels. Additionally, the image may include image elements such as pixels or voxels. The model may refer to a model of the entire photolithography mask or a model of a part of the photolithography mask.

[0050] For example, variations in the noise distribution of a reference image can be reduced by applying a transformation to the reference image. For instance, if the reference image is the photolithography mask (die-in-die) image itself or another section of the mask image, it is advantageous to apply the same transformation to the reference image to stabilize its noise distribution. Even if the reference image was acquired using a different optical system or under different imaging conditions, it is advantageous to stabilize the noise distribution by applying a transformation that reduces variations in the noise distribution to the reference image. As such, since the registration is performed based on an image and a reference image with a more uniform noise distribution, the accuracy of the registration results is improved.

[0051] The structure of the image of the photolithography mask and the corresponding structure of the reference image of the photolithography mask can be aligned using standard alignment techniques, for example, machine learning techniques that map the image and the reference image to a displacement field, energy optimization techniques that find an image transformation that minimizes the deviation between the transformed image and the reference image, optionally normalization terms, optical flow techniques, RANSAC (Random Sample Consensus) techniques, feature matching techniques (e.g., SIFT features, Garbor features, features derived from a learned neural network layer, etc.), and the high-speed image alignment technique disclosed in German patent application 10 2024 139 922.8, which is incorporated herein by reference in its entirety.

[0052] However, these matching methods are generally implicitly based on the assumption that image noise is uniformly distributed, specifically uniformly distributed Gaussian noise. This is because matching methods do not consider the diverse noise distributions in images. Most matching methods assume that the noise in the image is uniformly distributed Gaussian noise. This is the difference between matched images This is because minimizing the -norm or maximizing the cross-correlation of the difference between the matched images corresponds to the maximum likelihood estimator in the case of uniformly distributed Gaussian noise. However, in the case of optical images, shot noise is the main cause of noise in the image. Shot noise is illustrated in FIGS. 3a and 3b. FIG. 3a illustrates an image (22) acquired by an optical system containing shot noise. FIG. 3b illustrates a difference image (24) between two images acquired by an optical system, which is an estimate of the noise in the acquired image (22). The lower the intensity, the lower the noise variance, and the higher the intensity, the higher the noise variance. Therefore, shot noise varies depending on the image intensity. Since shot noise is the main cause of noise in the image (22), the assumption that it is uniformly distributed noise, as well as the assumption that it is uniformly distributed Gaussian noise, does not hold, and this reduces the accuracy of the match.

[0053] Therefore, according to an embodiment of the present invention illustrated in FIG. 4, a method (26) for aligning a structure to an image of a photolithography mask comprises: providing an image of a photolithography mask obtained by an optical system in step M1, wherein the noise distribution of the image varies according to the properties of the image, the photolithography mask, or the optical system; and aligning a structure in the transformation of the image to a corresponding structure of a reference image of the photolithography mask in step M2, wherein the variation in the noise distribution is reduced in the transformed image.

[0054] As can be seen in FIGS. 5a-d, by reducing the variation in the noise distribution in the transformed image, the noise in the image approaches uniformly distributed noise, and thus the dependence on at least one property of the image, photolithography mask, or optical system is reduced. The noise distribution becomes more uniform across the entire image. The variance of the noise distribution becomes independent of the mean of the noise distribution. FIG. 5a illustrates an image (22) containing shot noise that varies with image intensity. FIG. 5b illustrates a difference image (24) between two different images, thus estimating the noise distribution of the image (22). FIG. 5c illustrates a transformed image (28) in which the variation in the noise distribution, particularly the variation in the variance of the noise distribution, is reduced. FIG. 5d illustrates a difference image between two transformed images (28), thus estimating the noise distribution of the transformed image (28). Here, it can be seen that the variation in the noise distribution is significantly reduced. In fact, as shown in FIG. 5d, the variance of the noise distribution in the converted image (28) is approximately constant and is therefore almost independent of at least one property of the image, photolithography mask, or optical system. Therefore, the assumption of the matching method is better satisfied in the converted image (28) than in the acquired image (22). In this way, the matching accuracy is improved.

[0055] In the case of shot noise, the noise distribution in an image depends on the image intensity. Therefore, noise can be modeled as a Poisson distribution in which the variance of the distribution follows the mean. As the image intensity decreases, the variance of the noise decreases, and as the image intensity increases, the variance of the noise increases. By converting the image into a transformed image having a modified noise distribution in which its variance depends less on image intensity, a more stable noise distribution that better satisfies the assumptions of the matching method can be obtained in the transformed image.

[0056] The noise distribution of an image may include a Poisson distribution component. Additionally, the noise distribution of an image may include a Gaussian distribution component. The noise distribution of an image may also include other noise components. In a preferred example, the noise distribution includes two or more components that follow different distributions (e.g., a Poisson distribution component and a Gaussian distribution component).

[0057] In addition to image intensity, the noise distribution of an image can vary depending on the image, the photolithography mask, or other properties of the optical system. For example, the noise distribution can vary depending on the location within the image. For instance, the noise distribution at the center of an image may differ from that at the edges, as differences in contrast or focus can result in lower noise dispersion at the center compared to the edges. The noise distribution can also vary depending on the image content, such as the type of structures within the image. Furthermore, the noise distribution can depend on the structural material of the photolithography mask, such as its reflection coefficient. The noise distribution depends on optical system components, such as various detectors or their properties, camera sensors, or pixels; in particular, it can vary depending on defective or degraded optical system components, such as faulty detectors, camera sensors, or pixels. For instance, damage or defects in one or more detectors, camera sensors, or pixels can generate sub-images or image signals with different noise distributions. These issues can be mitigated by reducing variations in the image's noise distribution through transformation.

[0058] Various transformation techniques can be used to reduce variations in the noise distribution of an image.

[0059] In a preferred example, the image transformation includes a variance stabilization transformation. The variance stabilization transformation reduces the variability of the noise distribution variance of the image. After applying the variance stabilization transformation to the image, the noise distribution variance of the image becomes closer to a constant variance. The variability of the noise distribution variance can be measured, for example, by the variance of the noise distribution variance of the image. In a specific case, the variance stabilization transformation converts an image having a Poisson noise distribution, whose variance varies depending on at least one property of the image, photolithography mask, or optical system, into a transformed image having a Gaussian noise distribution that has approximately the same distribution.

[0060] The purpose of selecting a variance-stabilizing transform is to apply a function to the image such that the variance of the transformed image's values ​​depends less on the properties of the image, photolithography mask, or optical system (e.g., image intensity). For example, assume that a value x is drawn from different Poisson distributions (e.g., low image intensity and high image intensity). Then, each distribution has a different mean. In the case of a Poisson distribution, since the variance is equal to the mean, the variance varies according to the mean of the noise distribution, i.e., the image intensity. However, the variance-stabilizing transform When applied, the variance of the noise distribution of the transformed image becomes nearly constant, thus better satisfying the assumptions of the matching method.

[0061] For example, variance-stabilizing transformations include the Anscomb transformation. The Anscomb transformation is a variance-stabilizing transformation that converts a random variable following a Poisson distribution into a random variable that follows approximately a standard Gaussian distribution. Random variable The Anscombe transformation for is as follows.

[0062]

[0063] For example, variance-stabilizing transformations include the generalized Anscomb transformation. The generalized Anscomb transformation is a variance-stabilizing transformation that converts a random variable with Poisson and countable Gaussian components into a random variable with approximately a standard Gaussian distribution. of the image Assume that noise pixel intensity is explained using a random variable.

[0064]

[0065] Here is a scaling factor, is an independent Poisson random variable, is the average and variance It represents independent Gaussian noise components having . Then the generalized Anscomb transform for the random variable is It is as follows:

[0066]

[0067] Image noise distribution parameters, specifically the parameters of the generalized Anscomb transform, are often unknown in advance or change over time due to factors such as performance degradation of the optical system sensor or differences in software normalization steps. Therefore, it is useful to estimate these parameters from one or more images acquired from an optical system.

[0068] When estimating the noise distribution parameters of an image from a single image of an optical system, specific assumptions about the measured structure and / or optical system are required to distinguish between the effects of the signal and the noise. For example, the parameters can be estimated from a uniform region of the image. To improve accuracy, the parameters can be estimated from two or more images, preferably multiple images, of the same photolithography mask acquired by the optical system as shown in FIG. 6. Multiple images (30) of the same die of the photolithography mask are acquired. From these images (30), the parameters of the generalized Anscomb transform, in particular the pixel mean (32) and standard deviation (34) of the Gaussian noise distribution component, are estimated.

[0069] Instead of or in addition to estimating image noise distribution parameters from one or more images acquired from an optical system, image noise distribution parameters may also be estimated from the optical system itself. In a particular example, the estimation of the expected number of photons and the associated shot noise model may also include measurement information from an energy monitor in a system that acquires images using pulsed illumination.

[0070] The transformed image in Fig. 5c was obtained by applying the Anscomb transform, generalized to the variance-stabilizing transform, to the image in Fig. 5a, and exhibits a noise distribution that follows a nearly Gaussian distribution as shown in Fig. 5d. These parameters were estimated from multiple acquired images.

[0071] For example, a variance-stabilizing transform is obtained by solving an optimization problem that minimizes the deviation between the estimated noise variance and the constant noise variance in an image. The parameter vector of a variance-stabilizing transform (e.g., Anscum transform or generalized Anscum transform) It is said that. Then these parameters It can be estimated by minimizing the following objective function from one or more images.

[0072]

[0073] Here represents a pixel-level variance estimator (a standard Monte Carlo variance estimator for multiple acquired images of a photolithography mask containing well-defined mask features such as alignment markers, voids, or large absorber structures), and is a parameter Represents a parameterized variance-stabilizing transformation having, is a constant (e.g., It represents ). By solving the optimization problem, the variance of the noise distribution of the transformed image is constant. It gets closer to.

[0074] In the example illustrated in FIG. 7, the image (22) comprises at least two sub-images (36, 38) each having a different noise distribution (40, 42), and the variation in the noise distribution within each sub-image (36, 38) of the image (22) is reduced. The noise in the first sub-image (36) is distributed according to the first noise distribution (40), and the noise in the second sub-image (38) is distributed according to the second noise distribution (42). First transformation By applying this to the first sub-image (36), a noise distribution with lower variation can be obtained, and the second transformation By applying this to the second sub-image (36), a noise distribution with lower variation can be obtained. These transformations and Since they may differ from each other, they can be adjusted to match the noise distribution of each sub-image (36, 38). The resulting transformed image has a mean (44) and a standard deviation (46), and the standard deviation is independent of the mean. The noise distribution becomes more uniform, and dependence on the properties of the image, photolithography mask, or optical system is reduced. By reducing the variation in the noise distribution within each sub-image, the transformation can be individually and accurately fitted to each sub-image. For example, this procedure may be useful when one sensor is degraded or when image portions obtained from different sensors are assigned to different sub-images. This allows for more accurate matching results.

[0075] According to the example shown in FIG. 8, a pixel-level confidence score is estimated from the noise distribution of the image, and this confidence score is used as a weighting factor when matching the structure of the transformed image to the corresponding structure of the reference image. The image (22) is displayed along with the corresponding noise distribution estimate in the form of a difference image (24) of two images acquired from an optical system. The reciprocal of the variance of the noise distribution is used as the confidence score (48). The greater the variance of the noise distribution, the lower the confidence score (48), and conversely, the smaller the variance, the higher the confidence score (48). Since the part of the image (22) with low noise variance is more reliable than the part with high noise variance, it is given a higher weight in the matching method. This weighting factor can be used, for example, to weight each pixel in the difference between the image and the shifted reference image. This difference is optimized in many matching methods, such as the energy optimization method. In this way, the accuracy of the matching is improved.

[0076] According to the example shown in FIGS. 9a and 9b, the transformation of the image further includes the step of filtering the image using a filter (52) that varies according to the shape of the imaging pupil (50) of the optical system. The imaging pupil (50) of FIG. 9a represents the spatial frequency range of the electric field passing through the projection optical system of the optical system. These spatial frequencies form a circle (left). The image sensor measures the strength of the electric field, which may include spatial frequencies up to twice the maximum frequency of the electric field (the right circle with twice the radius of the left circle). Thus, the optical system acts as a corresponding low-pass filter. High-frequency components above the maximum frequency of the filter (52) are due to noise in the image and can be filtered by the filter (52) of FIG. 9b. This filter is hereinafter referred to as an NA filter. By filtering these noise frequencies from the image, the noise in the image is reduced and the matching quality is improved. The shape of the imaging pupil is not limited to a circle and can take other shapes, and a corresponding NA filter can be derived.

[0077] FIGS. 10a-d show results regarding the reproducibility of the method according to the present invention. FIG. 10a shows an image acquired by an optical system, and FIG. 10b shows a partial region (54) including a 500 nm insulating contact structure of a photolithography mask. The alignment of this image with a reference image is affected by noise in the image. FIGS. 10c and 10d show the results of a reproducibility test for alignment measurements, FIG. 10c for horizontal displacement and FIG. 10d for vertical displacement. Alignment is performed for different laser intensities on the horizontal axis, and for each laser intensity, alignment is repeated 20 times on images repeatedly acquired by the optical system. The horizontal axis (56) represents the increase in laser intensity, and the vertical axis (58) represents the standard deviation of the horizontal ( FIG. 10c) and vertical ( FIG. 10d) displacement measurements. The first graph (60) shows the reproducibility results for the original image, and the second graph (62) shows the reproducibility results for the generalized Anscom transformed image. As the laser intensity increases, the number of photons incident on the photolithography mask increases, and thus, as can be seen in graphs (60, 62), image noise decreases. As can be seen in graphs (60, 62), transforming the image to reduce the variability of the noise distribution of the image before alignment improves measurement reproducibility by about 20% for a fixed laser intensity. At the same time, it can be concluded that transforming the image to reduce the variability of the noise distribution of the image before alignment allows the same alignment reproducibility to be obtained even if the laser intensity is reduced by about 50%. By reducing the laser intensity, damage to the photolithography mask can be reduced or prevented.

[0078] FIGS. 11a-f illustrate the alignment error distribution for various image preprocessing methods. FIGS. 11a and 11b represent a simulation image (22) and a simulation reference image (24), respectively, consisting of 100 x 100 pixels, with each pixel corresponding to a size of 25 nm x 25 nm on a photolithography mask. Both images are simulated for a photolithography mask with a square absorber of 300 nm in the center of the field of view, and the shift of the absorber has different shifts extracted from a uniform distribution over the [-50 nm, 50 nm] interval. Monochromatic light with a wavelength of 100 nm was used for the simulation, and partial coherent imaging simulations were performed for a conventional illumination setup using circular illumination and an imaging pupil with a numerical aperture of 0.7, as shown in FIG. 9a. Both images consist of random shot noise realizations assuming an average of 2000 photons in bright pixels. Image alignment is the difference image's This is performed by minimizing the -norm. The matching error is measured by the Euclidean norm of the difference between the shift estimated through matching and the known actual shift. Figures 11c-f illustrate the matching error distributions for various preprocessing methods: for no preprocessing (Fig. 11c), the RMSE is 0.86 nm; for the application of an NA filter after anscomb transform (Fig. 11d), the RMSE is 0.34 nm; for the application of only anscomb transform (Fig. 11e), the RMSE is 0.47 nm; and for the application of only an NA filter (Fig. 11f), the RMSE is 0.44 nm. This demonstrates that using an image transformation such as the anscomb transform to reduce the variability of the image noise distribution and using an NA filter, which depends on the shape of the imaging pupil of the optical system, significantly improves matching accuracy. In particular, the matching accuracy is most significantly improved when the anscomb transform and the NA filter are used together.

[0079] Regarding the application order of the Anscomb transform and the NA filter, as shown in Fig. 11d, the Anscomb transform can be applied before the NA filter. However, this is not theoretically the optimal order because the Anscomb transform is a non-linear transformation that affects the image spectrum, and applying the NA filter afterward removes not only noise frequencies but also frequencies constituting the image signal. Nevertheless, this combination of the Anscomb transform and the NA filter exhibits the lowest match error. Applying the Anscomb transform after the NA filter is also not theoretically the optimal order because the noise in the low-pass filtered image no longer follows a Poisson distribution. To mitigate this problem, the parameters of a general image transformation About

[0080]

[0081] It can be derived, and this image transformation can be induced to be particularly suitable for NA-filtered images.

[0082] According to one example, the method further includes the step of evaluating the quality of a photolithography mask from a structure aligned with an image and a reference image.

[0083] The quality of a photolithography mask can be evaluated by measuring the positional deviation of a structure on the photolithography mask, as shown in FIGS. 12a and 12b. FIG. 12a shows a reference image (64) (e.g., a design file) containing a structure (66), and FIG. 12b shows a measurement image (22) of a photolithography mask containing shot noise. If the position of the structure (66) in the reference image (64) is known, the absolute position on the photolithography mask can be obtained from alignment information, that is, the relative displacement between the structure in the image (22) and the corresponding structure in the reference image. If the absolute position on the photolithography mask is unknown, the relative displacement between the aligned structures can be calculated. Through this, quality statements for the photolithography mask can be performed, and, for example, an evaluation regarding the average or maximum deviation of the structure position relative to the reference position, or statistics regarding the positional deviation, is possible. In addition, accurate overlays between successive layers of a photolithography mask can be verified, for example, for structures crossing successive layers. A threshold can be defined, and if the threshold is exceeded, the photolithography mask can be modified or discarded.

[0084] The quality of the photolithography mask may be evaluated by detecting defects (68) in the photolithography mask, as shown in FIG. 13a-c. For example, it may be evaluated by detecting structures within the image (22) (Fig. 13b) that deviate from the corresponding structures of the reference image (64) (Fig. 13a). After reducing the noise distribution variation of the image (and potentially the reference image), the transformed image and the reference image are more accurately aligned. Then, defects are detected in the aligned transformed image and the reference image, or in the unaligned aligned image and the reference image. To do this, the alignment error, i.e., the structural deviation between the image and the reference image after alignment, may be used. For example, it is possible to calculate a difference image and apply a threshold to the difference, or to apply a learned machine learning model that takes the aligned image and the reference image as input and maps them to a defect indicator (e.g., an image indicating the likelihood of defect occurrence). Alternatively, the local energy remaining after alignment, the objective function value, or the loss function value may be used as the alignment error. Local structures causing high alignment errors generally represent defects in the photolithography mask structure because there is no structure corresponding to the reference image. To find the contours of the defects (68), the segmentation of the alignment error can be calculated, for example, using an image processing method. The segmented defects (68) can be measured. Additionally, the defects can be classified using a learned machine learning model. Depending on the attributes of the defects (e.g., size, location, type, importance, etc.), the defects can be reduced, corrected, ignored, or the entire photolithography mask can be discarded. In this way, a quality evaluation of the photolithography mask can be performed, such as the number of defects per area, total number of defects, defect type, defect severity, and defect measurements. A threshold can be defined, and if the threshold is exceeded, the photolithography mask can be repaired or discarded.

[0085] For example, the present method further includes the step of controlling at least one photolithography mask manufacturing process parameter (e.g., focus, exposure, etc.) based on a quality evaluation of the photolithography mask (e.g., measured location of a structure within the photolithography mask in the case of an optical metrology system or defect detected in the photolithography mask in the case of an optical inspection system).

[0086] In some embodiments, the photolithography mask may be modified after the defect is detected to repair or remove the defect. Defect repair may include, for example, depositing material onto the mask using a deposition process, removing material from the mask using an etching process, or locally changing the properties of the target. For example, this may include locally changing at least one of the density, refractive index, transparency, or reflectance of the photolithography mask.

[0087] In some implementations, information about defects is used as feedback to improve process parameters of the manufacturing process (e.g., exposure time, focus, etc.). For example, if a defect is detected in a first photolithography mask or a first batch of photolithography masks, process parameters of the manufacturing process are adjusted to reduce defects in a second mask or a second batch of masks.

[0088] A system (70) for aligning a structure to an image of a photolithography mask (14) obtained by an optical system (10, 10') according to an embodiment of the present invention illustrated in FIG. 14 comprises: an optical system (10, 10') for obtaining an image of a photolithography mask as illustrated in FIG. 1 and 2; one or more processing units (72); and one or more machine-readable hardware storage devices (74) comprising instructions executable by one or more processing units (72) for performing operations including a method of aligning a structure to an image of a photolithography mask as described in the embodiment, example, or aspect.

[0089] The system (70) may optionally include a database for loading and / or storing data such as noise distribution, image transformation, defect detection method control parameters, reference image, defect attributes, etc. An optical system (10, 10') is used to obtain an image (22) of a photolithography mask (14). This optical system may provide the image (22) to a data analysis device (76). The data analysis device (76) includes one or more processors (72) implemented with a CPU or GPU, etc. One or more processors (72) may receive at least one image through an interface (78). One or more processors (72) may load program code from a hardware storage device (74), for example, program code that executes a computer implementation method (26) for matching the structure of the image of the photolithography mask described above. One or more processors (72) may execute the program code. The system (70) may optionally include a user interface for inputting a noise distribution or its parameters, an image transformation or its parameters, etc.

[0090] Throughout this specification, the terms “Example,” “Example,” or “Aspect” mean that a specific feature, structure, or characteristic described in relation to such Example, Example, or Aspect is included in one or more Examples, Examples, or Aspects. Accordingly, the phrases “according to an Example,” “according to an Example,” or “according to an Aspect” in various places in this specification do not all refer to the same Example, Example, or Aspect, but they may. Furthermore, as will be apparent to those skilled in the art from the disclosures in this specification, such specific features or characteristics may be combined in any suitable manner in one or more Examples.

[0091] Furthermore, some embodiments, examples, or aspects described herein include only some features included in other embodiments, examples, or aspects and do not include other features, whereas combinations of features of different embodiments, examples, or aspects are deemed to be included within the scope of the claims and constitute different embodiments as understood by those skilled in the art.

[0092] Embodiments, examples, and aspects of the present invention may be described by the following provisions.

[0093] 1. A method (26) for aligning a structure to an image (22) of a photolithography mask (14), wherein the method comprises the following:

[0094] A step of providing an image (22) of a photolithography mask (14) obtained by an optical system (10, 10') - the noise distribution of the image (22) depends on at least one property of the image (22), the photolithography mask (14), or the optical system (10, 10') - ;

[0095] A step of matching the structure in the transformation of the image (22) to the corresponding structure of the reference image (64) of the photolithography mask (14) - the variation in the noise distribution is reduced in the transformed image (28) -.

[0096] 2. In Clause 1, the noise distribution of the image (22) includes a Poisson distribution component.

[0097] 3. In any one of the above provisions, the noise distribution of the image (22) includes a Gaussian distribution component.

[0098] 4. In any one of the above provisions, the noise distribution of the image (22) depends on at least one attribute from the group including image intensity, image location, image content, photolithography mask material, photolithography mask structure type, and detector attribute of the optical system of the image (22), photolithography mask (14), or optical system (10, 10').

[0099] 5. In any one of the above provisions, the variance of the noise distribution of the image (22) varies according to at least one attribute of the image, and the variation of the noise distribution variance in the converted image (28) is reduced.

[0100] 6. In any one of the above provisions, a method in which the variance of the noise distribution of the converted image (28) is approximately constant.

[0101] 7. In any one of the above provisions, the noise distribution of the converted image (28) follows a uniformly distributed Gaussian distribution.

[0102] 8. In any one of the above provisions, the transformation of the image (22) includes a variance-stabilizing transformation.

[0103] 9. In Clause 8, the variance-stabilizing transformation includes an Anscombe transformation.

[0104] 10. In Clause 8 or Clause 9, the variance stabilization transformation comprises a generalized Anscomb transformation.

[0105] 11. In any one of Clauses 8 to 10, the variance-stabilized transform is obtained by solving an optimization problem that minimizes the deviation between the estimated noise variance of an image and the constant noise variance.

[0106] 12. In any one of the above provisions, the image (22) comprises at least two sub-images (36, 38) each having a different noise distribution (40, 42), wherein the variation in the noise distribution is reduced within each sub-image (36, 38) of the image (22).

[0107] 13. A method in which, in any one of the above provisions, a pixel-unit confidence score (48) is estimated from the noise distribution of an image (22), and the confidence score (48) is used as a weighting factor when matching the structure of the converted image (28) to the corresponding structure of a reference image (64).

[0108] 14. A method for estimating parameters of the noise distribution of an image (22) from one or more images (30, 30') obtained by an optical system (10, 10') in any one of the above provisions.

[0109] 15. In any one of the above provisions, the parameters of the noise distribution of the image (22) are estimated from the optical system (10, 10').

[0110] 16. In any one of the above provisions, the method further comprises the step of filtering the image (22) using a filter (52) that depends on the shape of the imaging pupil (50) of the optical system (10, 10').

[0111] 17. A method of applying a transformation to a reference image that reduces the variation in the noise distribution of the reference image in any one of the above provisions.

[0112] 18. A method further comprising the step of evaluating the quality of a photolithography mask (14) from a structure (66) aligned with an image (22) and a reference image (64) in any one of the above provisions.

[0113] 19. In any one of the above provisions, the optical system (10, 10') is an optical measurement system for measuring the position of the structure (66) of the photolithography mask (14) from the structure aligned with the image (22) and the reference image (64).

[0114] 20. In any one of the above provisions, the optical system (10, 10') is an optical inspection system that detects defects (68) in a photolithography mask (14) by comparing the aligned structure (66) of an image (22) and a reference image (64).

[0115] 21. A method comprising, in any one of Articles 18 to 20, further comprising the step of controlling at least one photolithography mask manufacturing process parameter based on a quality evaluation of the photolithography mask.

[0116] 22. A system (70) for aligning a structure in an image (22) of a photolithography mask (14) obtained by an optical system (20, 10'), wherein the system comprises the following:

[0117] An optical system (10, 10') for acquiring an image (22) of a photolithography mask (14);

[0118] One or more processing units (72);

[0119] One or more machine-readable hardware storage devices (74) containing instructions executable by one or more processing devices (72) for performing a task including a method (26) of aligning a structure to an image (22) of a photolithography mask (14) according to any one of the above provisions.

[0120] In summary, a method (26) for aligning a structure to an image (22) of a photolithography mask (14) comprises the following steps: providing an image (22) of a photolithography mask (14) obtained by an optical system (10, 10') - wherein the noise distribution of the image (22) depends on at least one property of the image (22), the photolithography mask (14), or the optical system (10, 10'); and aligning the structure to a corresponding structure of a reference image (64) of the photolithography mask (14) in a transformation of the image (22) - wherein the variation in the noise distribution is reduced in the transformed image (28). Explanation of the symbols

[0121] 10, 10' Optical measurement system 12 light source 14 photolithography mask 16 Illumination optical system 17 Projection optical system 18 wafer plane 19 Projection section 20 Image sensor 22 image 24 Difference image 26 method 28 Converted image 30, 30' video 32 average 34 standard deviation 36 1st sub-image 38 2nd sub-image 40 First noise distribution 42 Second noise distribution 44 average 46 standard deviation 48 Reliability score 50 Imaging pupil 52 filter 54 partial area 56 horizontal axis 58 vertical axis 60 Graph 1 62 Graph 2 64 Reference Image 66 structure 68 defect 70 System 72 Processing unit 74 Machine-readable hardware storage devices 76 Data analysis device 78 interface

Claims

Claim 1 A method (26) for aligning a structure in an image (22) of a photolithography mask (14), the method comprising: providing an image (22) of a photolithography mask (14) obtained by an optical system (10, 10') - wherein the noise distribution of the image (22) depends on at least one property of the image (22), the photolithography mask (14), or the optical system (10, 10'); and aligning a structure in a transformation of the image (22) to a corresponding structure of a reference image (64) of the photolithography mask (14) - wherein the variation in the noise distribution is reduced in the transformed image (28). Claim 2 A method according to claim 1, wherein the noise distribution of the image (22) includes a Poisson distribution component. Claim 3 A method according to claim 2, wherein the noise distribution of the image (22) includes a Gaussian distribution component. Claim 4 A method according to claim 1, wherein the noise distribution of the image (22) depends on at least one attribute from the group comprising the image intensity, image position, image content, photolithography mask material, photolithography mask structure type, and detector attribute of the optical system of the image (22), photolithography mask (14), or optical system (10, 10'). Claim 5 A method according to claim 1, wherein the variance of the noise distribution of the image (22) varies according to at least one attribute of the image, and the variation of the variance of the noise distribution is reduced in the transformed image (28). Claim 6 A method according to claim 1, wherein the variance of the noise distribution of the converted image (28) is approximately constant. Claim 7 A method according to claim 1, wherein the noise distribution of the converted image (28) approximately follows a uniformly distributed Gaussian distribution. Claim 8 The method of claim 1, wherein the transformation of the image (22) includes a variance-stabilizing transformation. Claim 9 A method according to claim 8, wherein the dispersion stabilization transformation comprises an Anscombe transformation. Claim 10 A method according to claim 8, wherein the variance stabilization transform comprises a generalized Anscomb transform. Claim 11 A method according to any one of claims 8 to 10, wherein the variance stabilization transform is obtained by solving an optimization problem that minimizes the deviation between the estimated noise variance and the constant noise variance in an image. Claim 12 A method according to claim 1, wherein the image (22) comprises at least two sub-images (36, 38) each having a different noise distribution (40, 42), and the variation in the noise distribution is reduced within each sub-image (36, 38) of the image (22). Claim 13 A method according to claim 1, wherein a pixel-unit confidence score (48) is estimated from the noise distribution of an image (22), and the confidence score (48) is used as a weighting factor when matching the structure of the converted image (28) to the corresponding structure of the reference image (64). Claim 14 A method according to claim 1, wherein the parameters of the noise distribution of the image (22) are estimated from one or more images (30, 30') obtained by an optical system (10, 10'). Claim 15 A method according to claim 1, wherein the parameters of the noise distribution of the image (22) are estimated from two or more images (30, 30') obtained by an optical system (10, 10'). Claim 16 A method according to claim 1, wherein the parameters of the noise distribution of the image (22) are estimated from the optical system (10, 10'). Claim 17 The method of claim 1, wherein the transformation of the image (22) further comprises the step of filtering the image using a filter (52) that depends on the shape of the imaging pupil (50) of the optical system (10, 10'). Claim 18 The method of claim 17, wherein the transformation is a variance-stabilizing transformation specifically optimized to take into account the modified noise distribution of the filtered image. Claim 19 In claim 18, the parameterized nonlinear transformation is Method having a form. Claim 20 A method according to claim 1, wherein a transformation that reduces variation in the noise distribution of a reference image is applied to a reference image. Claim 21 A method according to claim 1, further comprising the step of evaluating the quality of a photolithography mask (14) from a matched structure (66) of an image (22) and a reference image (64). Claim 22 The method according to claim 1, wherein the optical system (10, 10') is an optical measurement system for measuring the position of the structure (66) of the photolithography mask (14) from the aligned structure of the image (22) and the reference image (64). Claim 23 The method according to claim 1, wherein the optical system (10, 10') is an optical inspection system that detects defects (68) of a photolithography mask (14) by comparing the aligned structure (66) of an image (22) and a reference image (64). Claim 24 A method according to any one of claims 21 to 23, further comprising the step of controlling at least one photolithography mask manufacturing process parameter based on a quality evaluation of the photolithography mask. Claim 25 A system (70) for aligning a structure in an image (22) of a photolithography mask (14) obtained by an optical system (20, 10'), wherein the system comprises: an optical system (10, 10') for acquiring an image (22) of a photolithography mask (14); one or more processing units (72); and one or more machine-readable hardware storage units (74) comprising instructions executable by one or more processing units (72) for performing an operation including a method (26) for aligning a structure of an image (22) of a photolithography mask (14) as described in claim 1.

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