Image preprocessing for overlay metrology using decomposition techniques

Abstract

A system may include a controller configured to: receive one or more images of a metrological target having periodic characteristics of one or more known pitches; preprocess the one or more images using a decomposition technique to generate one or more preprocessed images; and generate one or more metrological measurements of the metrological target based on the one or more preprocessed images. Preprocessing a specific image from the one or more images may include: constructing one or more trajectory matrices from the specific image; generating reconstructed components associated with the specific image from the one or more trajectory matrices using the decomposition technique; and generating the specific image from the one or more preprocessed images based on a subset of the reconstructed components containing signals having at least one of the one or more known pitches.

Description

[0001] Cross-reference of related applications

[0002] This application claims the right to U.S. Provisional Application No. 63 / 410,233, filed September 27, 2022, entitled “On Pre-processing Measurements and Signals for Accurate Overlay Extraction,” in accordance with 35 U.S. SC §119(e), the entire contents of which are incorporated herein by reference. Technical Field

[0003] This disclosure generally relates to overlay metrology, and more specifically, to image preprocessing for overlay metrology. Background Technology

[0004] Many metrological techniques rely on images of periodic structures on samples. However, the collected images may suffer from various sources of noise and inhomogeneity whose length scale differs from the periodicity of the structure of interest, which can negatively impact measurements, such as, but not limited to, detector-derived noise, target-derived noise, or illumination inhomogeneity. Therefore, there is a need to develop systems and methods to address these shortcomings. Summary of the Invention

[0005] According to one or more illustrative embodiments of this disclosure, a system is disclosed. In one illustrative embodiment, the system includes a controller. In another illustrative embodiment, the controller receives one or more images containing periodic characteristics of a metrological target having one or more known pitches. In another illustrative embodiment, the controller preprocesses the one or more images using a decomposition technique to generate one or more preprocessed images. In another illustrative embodiment, the controller generates one or more metrological measurements of the metrological target based on the one or more preprocessed images. In another illustrative embodiment, preprocessing a specific image from the one or more images includes: constructing one or more trajectory matrices from the specific image; generating reconstructed components associated with the specific image from the one or more trajectory matrices using the decomposition technique; and generating the specific image from the one or more preprocessed images based on a subset of the reconstructed components containing signals having at least one of the one or more known pitches.

[0006] According to one or more illustrative embodiments of this disclosure, a system is disclosed. In one illustrative embodiment, the system includes a metrology subsystem and a controller. In another illustrative embodiment, the controller receives from the metrology subsystem one or more images containing periodic characteristics of a metrology target having one or more known pitches. In another illustrative embodiment, the controller preprocesses the one or more images using a decomposition technique to generate one or more preprocessed images. In another illustrative embodiment, the controller generates one or more metrological measurements of the metrology target based on the one or more preprocessed images. In another illustrative embodiment, preprocessing a specific image from the one or more images includes: constructing one or more trajectory matrices from the specific image; generating reconstructed components associated with the specific image from the one or more trajectory matrices using the decomposition technique; and generating the specific image from the one or more preprocessed images based on a subset of the reconstructed components containing signals having at least one of the one or more known pitches.

[0007] According to one or more illustrative embodiments of this disclosure, a method is disclosed. In one illustrative embodiment, the method includes receiving one or more images of a metrological target that includes periodic characteristics having one or more known pitches. In another illustrative embodiment, the method includes preprocessing the one or more images using a decomposition technique to generate one or more preprocessed images. In another illustrative embodiment, preprocessing a specific image among the one or more images includes: constructing one or more trajectory matrices from the specific image; generating reconstructed components associated with the specific image from the one or more trajectory matrices using the decomposition technique; and generating the specific image among the one or more preprocessed images by means of a subset of the reconstructed components that includes signals having at least one of the one or more known pitches. In another illustrative embodiment, the method includes generating one or more metrological measurements of the metrological target based on the one or more preprocessed images.

[0008] It should be understood that the above general description and the following detailed description are for illustrative purposes only and do not necessarily limit the invention as claimed. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the general description, serve to explain the principles of the invention. Attached Figure Description

[0009] Those skilled in the art can better understand the many advantages of this disclosure by referring to the accompanying drawings.

[0010] Figure 1A This is a block diagram of a metrology system for generating and / or utilizing preprocessed images according to one or more embodiments of the present disclosure.

[0011] Figure 1BThis is a conceptual diagram of an optical metrology subsystem according to one or more embodiments of the present disclosure.

[0012] Figure 1C This is a conceptual diagram of a particle beam metrology subsystem according to one or more embodiments of the present disclosure.

[0013] Figure 2A This is a flowchart illustrating the steps performed in a method according to one or more embodiments of the present disclosure.

[0014] Figure 2B This is a flowchart illustrating additional steps performed in a method according to one or more embodiments of the present disclosure.

[0015] Figure 3 It is a simplified top view image of a target containing a periodic structure according to one or more embodiments of the present disclosure.

[0016] Figure 4A It is an image of a periodic structure according to one or more embodiments of the present disclosure.

[0017] Figure 4B It is a series of images corresponding to reconstructed components associated with images using decomposition techniques, according to one or more embodiments of this disclosure.

[0018] Figure 4C It is based on one or more embodiments of this disclosure and Figure 4A and 4B Plotting the spectrum of eigenvalues ​​of the associated large trajectory matrix. Detailed Implementation

[0019] The subject matter of the disclosure will now be described in detail with reference to the accompanying drawings. This disclosure has been particularly shown and described with respect to certain embodiments and their specific features. The embodiments set forth herein should be considered illustrative rather than restrictive. Those skilled in the art will readily understand that various changes and modifications in form and detail may be made without departing from the spirit and scope of this disclosure.

[0020] Embodiments of this disclosure relate to systems and methods for preprocessing images with periodic features using matrix factorization (e.g., factorization) techniques. The systems and methods disclosed herein are suitable for, but not limited to, images of periodic targets used in preprocessing metrology applications (e.g., but not limited to, overlay metrology).

[0021] This paper, after careful consideration, notes that many image-based metrology techniques are sensitive to noise and / or non-uniformity present in images. Typical approaches for providing accurate measurements focus on hardware-based techniques to avoid this noise and / or non-uniformity. However, completely removing this noise and / or non-uniformity from an image may be impractical or undesirable (e.g., due to cost or other constraints). In such cases, it is desirable to preprocess the image before generating the measurement, which allows the use of any suitable measurement and / or analysis techniques.

[0022] In an embodiment, one or more trajectory matrices are constructed for the image. Then, matrix factorization techniques (e.g., but not limited to singular value decomposition (SVD) or variations thereof) are used to generate reconstructed components associated with the image based on the trajectory matrices, wherein the reconstructed components may represent the decomposition of the image into different spectral components (e.g., different length scales). In this way, the reconstructed components may represent portions of the image corresponding to different length scales. Next, a preprocessed (e.g., filtered) image may be generated based on a subset of the reconstructed components corresponding to known intervals of superimposed targets in the image. This preprocessed image may contain a high-contrast representation of periodically superimposed targets, wherein noise and / or non-uniformity at other length scales are effectively removed or suppressed.

[0023] Upon careful consideration, this technique provides robust and universal filtering for images of periodic targets. Specifically, using decomposition techniques to generate reconstructed vectors allows for the identification of the dominant length scales (e.g., spectral components) in the image based on the image itself, facilitating efficient and accurate filtering of data at unwanted length scales. It should be recognized that a general metrology model incorporating the decomposition of a trajectory matrix containing metrological values ​​of targets across sample distributions is described in U.S. Patent Application No. 17 / 995,385, filed September 28, 2022, the entire contents of which are incorporated herein by reference. The systems and methods disclosed herein may utilize, but are not limited to, decomposition techniques similar to those described in U.S. Patent Application No. 17 / 995,385, but in which these mathematical decompositions are applied to different datasets at different stages of the metrology process. For example, the systems and methods disclosed herein apply decomposition techniques to identify and isolate the dominant length scales in images associated with the periodic features of interest as a preprocessing step prior to generating metrological measurements. Subsequently, any suitable technique (such as, but not limited to, that described in U.S. Patent Application No. 17 / 995,385) can be used to model or further process the metrological data generated from multiple targets across the sample.

[0024] The trajectory matrix can be generated in any suitable manner and can be customized based on the complexity of the imaged superimposed target (e.g., whether the target has periodicity along one or more dimensions) and / or computational considerations. Specifically, the number and / or embedding dimension of the constructed trajectory matrix can be customized for a particular application.

[0025] As an example, when the image of the target has a one-dimensional (1D) periodicity oriented along the rows of the image, one or more trajectory matrices can be generated based on one or more of the rows of the image. In some embodiments, trajectory matrices are generated for each row of the image (or a portion of the region of interest (ROI) therefore), and these are then combined into a larger trajectory matrix. In some embodiments, a single trajectory matrix is ​​generated for a single row of the image or a portion thereof. In some embodiments, a trajectory matrix is ​​generated based on the average of two or more rows of the image or a portion thereof. Reducing the number of trajectory matrices can increase computational processing (e.g., reduce computation time) but may potentially reduce the robustness of the analysis.

[0026] The embedding dimension can be selected based on the needs of a specific application. In some embodiments, the embedding dimension is selected as the length of a row or column in the image. This configuration may correspond to a direct SVD implementation of selected rows of the image and may generate reconstructed components based on the correlation between different rows. This configuration may also be relatively fast computationally. In some embodiments, the embedding dimension is selected as the known pitch of the target (e.g., in pixels). This configuration may generate reconstructed components based on the correlation between repeating patterns (e.g., different periods) within and between rows. Therefore, this configuration can provide a more statistically efficient image decomposition and thus provide reconstructed components that more accurately represent various length scales in the image, but may require relatively long computation times.

[0027] Additional embodiments of this disclosure relate to process control utilizing metrology data generated from preprocessed images as disclosed herein. In this manner, the metrology data can be used directly or indirectly for feedback and / or feedforward control of any number of process tools (e.g., but not limited to lithography tools (e.g., scanners and / or steppers), deposition tools, etching tools, or polishing tools). For example, metrology data for samples in a batch can be used to generate feedback correction values ​​to control the lithography exposure of subsequent samples in the same batch. As another example, metrology data for samples in a batch can be used to generate feedforward correction values ​​to control the lithography exposure of the same or similar samples in subsequent lithography steps to address any deviations in the current exposure.

[0028] For reference Figures 1A to 4C The present disclosure describes in more detail a system and method for preprocessing images with periodic features according to one or more embodiments.

[0029] Figure 1A This is a block diagram of a metrology system 100 for generating and / or utilizing preprocessed images according to one or more embodiments of the present disclosure.

[0030] In an embodiment, the metrology system 100 includes a metrology subsystem 102 adapted to generate metrological measurements of a target 104 (e.g., a metrology target) across one or more sample 106 distributions.

[0031] Sample 106 may contain any object that serves as a source of metrological measurement. For example, sample 106 may contain a substrate formed of a semiconductor or non-semiconductor material (e.g., a wafer or the like). Semiconductor or non-semiconductor materials may include, but are not limited to, single-crystal silicon, gallium arsenide, and indium phosphide. Sample 106 may contain one or more layers. For example, such layers may include, but are not limited to, photoresists, dielectric materials, conductive materials, and semiconducting materials. Many different types of such layers are known in the art, and the term "sample" as used herein is intended to cover all types of samples on which such layers may be formed. The one or more layers formed on sample 106 may be patterned or unpatterned. For example, sample 106 may contain multiple dies, each having repeatable patterned features. The formation and processing of such material layers can ultimately result in a completed device. Many different types of devices may be formed on sample 106, and the term "sample 106" as used herein is intended to cover sample 106 on which any type of device known in the art is manufactured. Furthermore, for the purposes of this disclosure, the terms Sample 106 and chip should be interpreted as interchangeable.

[0032] The metrological measurements of sample 106 generated by metrology subsystem 102 can provide any type of data and can be generated using any technique known in this art. In some embodiments, the metrological measurements generated by metrology subsystem 102 are superimposed measurements of registration (or registration errors) between different photolithographic exposures on one or more layers of sample 106. In some embodiments, the metrological measurements generated by metrology subsystem 102 characterize the conditions of the photolithographic exposure, such as, but not limited to, the focal position or illumination dose of sample 106. In some embodiments, the metrological measurements generated by metrology subsystem 102 characterize additional aspects of the manufacturing process, such as, but not limited to, etching or polishing steps.

[0033] Target 104 may include any location on sample 106 suitable for metrological measurement using metrology subsystem 102. In some embodiments, target 104 includes features associated with a device being manufactured, referred to herein as device features. In some embodiments, target 104 includes dedicated features designed to facilitate metrological measurement. As an illustration in the context of overlay metrology, dedicated overlay target 104 may include features associated with each of the lithographic exposures of interest at overlapping or non-overlapping locations on sample 106 in an arrangement where robust and accurate overlay measurements are achieved by metrology subsystem 102.

[0034] The metrology subsystem 102 can be configured to implement a metrology recipe. The recipe may include various parameters and / or conditions controlling the acquisition of measurements across at least one sample 106. For example, the recipe may include parameters associated with certain regions (e.g., targets) to be characterized in the sample 106, the placement of the targets, and / or the measurement sequence of such targets. Additionally, in applications where targets are designed for measurement purposes (e.g., metrology targets, superimposed targets, or the like), the recipe may include aspects of the design of such targets, including, but not limited to, the layout of features on one or more layers. As another example, the recipe may include parameters associated with the configuration of the metrology subsystem 102 during measurement. For illustration, the recipe may include parameters associated with the illumination of the target 104, such as, but not limited to, wavelength, polarization, power, angle of incidence, spot size, or number of illumination beams. For another illustration, the recipe may include parameters associated with the collection of light from the target 104, such as, but not limited to, wavelength, polarization, or collection angle. As another example, the recipe may include various processing and / or analysis steps associated with generating metrological measurements based on the generated data.

[0035] In an embodiment, the metering system 100 includes a controller 108 communicatively coupled to any components thereto. The controller 108 may include one or more processors 110. For example, one or more processors 110 may be configured to execute a set of program instructions maintained in a memory device 112 or memory. The one or more processors 110 of the controller 108 may include any processing element known in the art. In this sense, one or more processors 110 may include any microprocessor-type device configured to execute algorithms and / or instructions.

[0036] One or more processors 110 of controller 108 may include any processor or processing element known in the art. For the purposes of this disclosure, the terms “processor” or “processing element” may be broadly defined to encompass any device having one or more processing or logic elements (e.g., one or more microprocessor devices, one or more application-specific integrated circuit (ASIC) devices, one or more field-programmable gate arrays (FPGAs), or one or more digital signal processors (DSPs)). In this sense, one or more processors 110 may include any device configured to execute algorithms and / or instructions (e.g., program instructions stored in memory). In some embodiments, one or more processors 110 may embody a desktop computer, host computer system, workstation, graphics computer, parallel processor, networked computer, or any other computer system configured to execute a program configured to operate or in conjunction with the operation of metering system 100, as described throughout this disclosure. Furthermore, different subsystems of metering system 100 may include processors or logic elements suitable for carrying out at least a portion of the steps described in this disclosure. Therefore, the above description should not be construed as limiting the embodiments of this disclosure but is merely illustrative. Furthermore, the steps described throughout this disclosure can be performed by a single controller or alternatively by multiple controllers. Additionally, controller 108 may comprise one or more controllers housed within a common housing or multiple housings. In this manner, any controller or combination of controllers can be individually packaged as a module suitable for integration into the metering system 100.

[0037] Memory device 112 may include any storage medium known in the art suitable for storing program instructions executable by one or more associated processors 110. For example, memory device 112 may include non-transitory memory media. As another example, memory device 112 may include, but is not limited to, read-only memory (ROM), random access memory (RAM), magnetic or optical storage devices (e.g., magnetic disks), magnetic tape, solid-state drives, and the like. It should be further noted that memory device 112 may be housed together with one or more processors 110 in a common controller housing. In some embodiments, memory device 112 may be remotely located relative to the physical location of one or more processors 110 and controller 108. For example, one or more processors 110 of controller 108 may access remote storage (e.g., a server) accessible via a network (e.g., the Internet, intranet, and the like).

[0038] The controller 108 may be directed (e.g., via control signals) and / or receive data from any component or subsystem of the metrology system 100 (e.g., but not limited to metrology subsystem 102 and other systems, such as one or more process tools (e.g., lithography tools or the like) used to manufacture sample 106). The controller 108 may be further configured to perform any of the various process steps described in this disclosure, such as, but not limited to, implementing metrological formulations, preprocessing one or more images, or generating metrological measurements based on preprocessed images.

[0039] In some embodiments, the metering system 100 includes a user interface 114 communicatively coupled to a controller 108. In some embodiments, the user interface 114 may include, but is not limited to, one or more desktop computers, laptop computers, tablet computers, and the like. In some embodiments, the user interface 114 includes a display for displaying data from the metering system 100 to a user. The display of the user interface 114 may include any display known in the art. For example, the display may include, but is not limited to, a liquid crystal display (LCD), an organic light-emitting diode (OLED) based display, or a CRT display. Those skilled in the art will recognize that any display device capable of being integrated with the user interface 114 is suitable for embodiments of this disclosure. In some embodiments, a user may input selections and / or instructions in response to data displayed to the user via a user input device of the user interface 114.

[0040] For reference Figures 2A to 4C The present disclosure describes in more detail a technique for modeling metrological measurements according to one or more embodiments.

[0041] Figure 2A This is a flowchart illustrating the steps performed in method 200 according to one or more embodiments of the present disclosure. The applicant clarifies that the embodiments and enabling technologies previously described herein in the context of metering system 100 should be interpreted as extending to method 200. For example, the processor 110 of controller 108 may execute program instructions that cause processor 110 to perform any of the steps of method 200. In some embodiments, at least some steps of method 200 may be implemented as part of a metering recipe by any combination of components of metering system 100. However, it should be further noted that method 200 is not limited to the architecture of metering system 100.

[0042] In some embodiments, method 200 includes a step 202 of generating one or more images of one or more targets 104 having periodic characteristics with one or more known pitches. In some embodiments, method 200 includes a step 204 of preprocessing one or more images using a decomposition technique to generate one or more preprocessed images. In some embodiments, method 206 includes a step 206 of generating one or more metrological measurements of targets 104 based on one or more preprocessed images. More generally, step 206 may include generating any type or number of metrological measurements based on any number of targets 104. For example, the imaging targets 104 may be, but need not be, superimposed targets 104 suitable for superimposing metrological measurements.

[0043] The image in step 202 can be generated using any suitable tool (e.g., but not limited to metrology subsystem 102). Alternatively, any suitable optical imaging technique (including, but not limited to, bright-field or dark-field imaging) can be used to generate the image.

[0044] Target 104 can have any design suitable for any type of metrological measurement. For example, target 104 can have periodic features on one or more layers (e.g., sample layers) of sample 106.

[0045] Figure 3 This is a simplified top view of a target 104 including a periodic structure 302 according to one or more embodiments of this disclosure. Specifically, Figure 3 The periodic structure 302 is presented as a linear / spatial feature with a pitch p.

[0046] In some embodiments, target 104 or its units may comprise a single example of periodic structure 302. In some embodiments, target 104 or its units may comprise multiple examples of periodic structure 302 in overlapping or non-overlapping configurations, wherein different examples of periodic structure 302 may have the same or different pitches (e.g., value p).

[0047] For example, in a non-limiting application of overlay metrology, target 104 may comprise different examples of such periodic structures 302 on one or more sample layers associated with different lithographic exposures. In this way, overlay measurements associated with relative registration between features associated with different lithographic exposures can be provided based on the relative positions of the different examples of periodic structures 302 (e.g., generated in step 206). As an illustration, target 104 may comprise non-overlapping examples of periodic structures 302 having the same or different pitches. For example, target 104 may be characterized as an advanced imaging metrology (AIM) target 104. As another illustration, target 104 may comprise one or more regions of overlapping examples of periodic structures 302, which may be characterized as a grating-overlaid grating structure. In the case of different pitches, such regions may also be referred to as moiré structures and may further exhibit moiré pitches different from the pitches constituting the periodic structures 302 (e.g., related to differences between the pitches constituting the periodic structures 302). For example, a target 104 containing one or more moiré patterns can be characterized as a robust AIM (e.g., rAIM) target 104.

[0048] In some embodiments, superposition measurements may be generated based on the differences between the centers of symmetry of different regions of target 104 (e.g., differences between the centers of symmetry of different examples of periodic structure 302, different examples of moiré structure, or similar).

[0049] Figure 2B This is a flowchart illustrating additional steps performed in method 200 according to one or more embodiments of this disclosure. Specifically, Figure 2B This describes the various sub-steps that can be performed in step 204 when preprocessing a specific individual in one or more images to produce one or more preprocessed individuals in a specific image. In this way, it can be repeated for each individual (or a portion of an image) captured in step 202. Figure 2B The steps described in the document.

[0050] In some embodiments, step 204 includes step 208 of constructing one or more trajectory matrices (e.g., from a particular image or its ROI).

[0051] The image can be represented as:

[0052]

[0053] Where 'a' represents the pixel value and 'n' and 'm' represent the row and column, respectively. It should be understood that I... Orig This can correspond to the entire image (e.g., the image generated by the metrology subsystem 102) or its ROI. For example, I OrigThis can correspond to a region of interest (ROI) that includes the central portion of target 104 (or its units) containing the periodic structure of interest. For illustration, an ROI can be selected to avoid the edges of regions of periodic structures that are more likely to experience manufacturing defects.

[0054] Step 208 may include generating a trajectory matrix associated with any direction in the image corresponding to the periodic orientation of the feature of target 104.

[0055] As an example, in the case of target 104 containing periodic features oriented along the rows of the image, it can be any k th The row generates the trajectory matrix τ k as follows:

[0056]

[0057] in It is satisfactory The embedding dimension. This matrix can be characterized as a transition matrix or a Hankel matrix and can have the property that the elements on the diagonal i+j=C are equal. Additionally, the trajectory matrix τ can be... k Arranged as a large trajectory matrix Decomposing it, it can be written as:

[0058]

[0059] As will be described in more detail throughout this disclosure, the embedding dimension The choice of embedding dimension can affect the properties of the decomposition and the computational speed. For example, the embedding dimension... Set to equal image I Orig The number of pixels in a row (or its ROI) allows for simple image decomposition (e.g., SVD). As another example, embedding dimension... The pitch of a target feature, set in pixels, can be based on both the length of the inline and interline elements. The correlation between fragments is used to provide reconstructed components.

[0060] As another example, a single trajectory matrix can be generated for a single row of an image or in the case of a purely 1D image. In this case, the trajectory matrix is ​​assigned... This is equivalent to a single trajectory matrix. As another example, a trajectory matrix can be generated by averaging two or more rows of an image. For instance, a single trajectory matrix can represent data from the entire image (or a selected ROI). In another example, averaging over each x rows can reduce the associated large trajectory matrix. The overall size.

[0061] It should be noted that the description of target 104 having periodic characteristics oriented along the rows of the image is illustrative rather than limiting. In the case where target 104 has periodic characteristics oriented along the columns of the image, a trajectory matrix corresponding to any column or the average value of any column of the image can be generated.

[0062] Furthermore, equations (2) to (3) above are generated with an embedding dimension along a single direction. In cases where the target 104 has periodicity along two directions (e.g., rows and columns of an image), a two-dimensional window providing embedding along both directions can be used to generate one or more trajectory matrices. This generalization can be applied to two-dimensional targets that do not have translation invariance. For example, in this case, a large trajectory matrix... It can be written as:

[0063]

[0064] Each matrix τ i As an embedding dimension having directions along rows and columns respectively. and The trajectory matrix with a window size of (x×y) is given, where and As described relative to the 1D case, each matrix τ can be defined based on the pixel-level pitch of the target structure in the associated directions. i The embedding dimension. In this form, the large trajectory matrix... It can be characterized as a Hankel-block-Hankel matrix.

[0065] In addition, it should be understood that equations (2) to (4) relate to the trajectory matrix τ and the large trajectory matrix. The specific descriptions are provided for illustrative purposes only and should not be interpreted as limiting. Trajectory matrix τ and / or large trajectory matrix It can be constructed using any technique suitable for use with any decomposition technique (e.g., factorization). For example, the trajectory matrix τ and / or a large trajectory matrix... It can be constructed in various ways while preserving the integrity of the vector space it spans.

[0066] In some embodiments, step 204 includes step 210 of generating reconstructed components associated with a particular image from one or more trajectory matrices using decomposition techniques.

[0067] Any suitable decomposition technique can be used, such as, but not limited to, SVD, principal component analysis, independent component analysis, or any eigenvalue-based decomposition technique. In some embodiments, the reconstructed vector describes different spectral components of the signal vector (e.g., different length scales of the signal vector). In this way, large trajectory matrices... (Or a single trajectory matrix τ) can be represented as the sum of the reconstructed vectors. Furthermore, as will be described in more detail below, a preprocessed image can be generated based on the sum of a subset of the reconstructed vectors.

[0068] The following equations (5) to (7) and Figures 4A to 4C Non-limiting illustrations of the use of SVD techniques are provided for 1D targets (e.g., having a large trajectory matrix based on equations (2) to (3). However, it should be understood that this is for illustrative purposes only, and the teachings can be extended to 2D targets (e.g., having a large trajectory matrix based on equation (4)).

[0069] For example, for an unrestricted instance of a trajectory matrix containing n rows, applying SVD to a large trajectory matrix in equation (2) Available:

[0070]

[0071] Where Σ is a subset of The singular values ​​σ1…σ p A diagonal matrix (in descending order from largest to smallest), where It is the covariance matrix The eigenvalues. Additionally... The eigenvectors form the columns of matrix V, while The eigenvectors form the columns of matrix U. Decomposition supply Correlation reconstruction of eigenvalues ​​and trajectory matrix τ.

[0072] According to equation (5), the reconstructed component R that satisfies the following expression can be generated. p :

[0073]

[0074] In this way, the reconstructed components generated in step 210 It can correspond to image I Orig Different spectral components (e.g., different length scales).

[0075] For example, matrix Each row of an image may contain a reconstructed version of the trajectory matrix. Based on this, a reconstructed version of a row (e.g., having a length m) can be generated by a diagonal operation (e.g., diagonal average or similar) on the corresponding reconstructed version of the trajectory matrix, where the reconstructed rows can be combined to form associated reconstructed components.

[0076] Generally referring to steps 208 and 210, the embedding dimension The choice of embedding dimension can affect both the properties of the decomposition and the computational speed. Typically, an image can have 1 and m (in pixels). orig Any value between the length of the line and the given value.

[0077] In some embodiments, the embedded dimension Selected as equal to m (e.g., In this configuration, the large trajectory matrix The decomposition can be based on image I Orig The correlation between rows is used to provide reconstructed components. Additionally, this choice of embedding dimension allows for the reconstruction of the original image I. orig A simple decomposition (e.g., SVD). This implementation is computationally fast, allowing decompositions to be generated quickly in many applications.

[0078] In some embodiments, the embedded dimension Selected as different from m (e.g., And it can correspond to a generalized decomposition. In this configuration, the large trajectory matrix The decomposition can be based on both the length of the inline and interline elements. The correlation between fragments is used to provide reconstructed components. In some embodiments, the embedding dimension... The pitch (e.g., pixels rounded up or down to an integer) of the periodic feature chosen to be equal to the target 104 can be known when implementing method 200. This configuration can be particularly advantageous because the resulting decomposition can be based on the correlation between different periods within and between a given row. Additionally, this implementation can provide a relatively large trajectory matrix. The reconstructed components are comparable A simpler SVD implementation is statistically more efficient. Therefore, reconstructing components... It can effectively distinguish features with a length scale corresponding to a known pitch from other features with different length scales (e.g., noise, non-uniformity, or the like). However, this implementation may be relatively computationally time-consuming.

[0079] In some embodiments, a generalized decomposition is applied to a finite dataset to balance decomposition performance and computational speed. For example, a generalized decomposition, where... (For example, The pitch selected (equal to the periodic structure) can be applied to a single line of the image (or a 1D measurement signal) or to the average of multiple lines. This implementation may be computationally faster, but it preserves accurate reconstruction based on the correlation along the measurement direction in the analysis line.

[0080] Refer again Figure 2BIn some embodiments, step 204 includes step 212 of generating one or more specific elements in a preprocessed image based on a subset of reconstructed components containing signals having at least one of one or more known pitches. For example, preprocessed image I pp Can be written as

[0081]

[0082] in In some embodiments, Therefore, step 212 may include identifying a subset l of reconstructed components of a signal containing a pitch corresponding to target 104 and generating a preprocessed image based on the identified subset l of reconstructed components. In some cases, the preprocessed image I pp It can correspond to the original image I Orig The low-rank approximation. In some cases, the preprocessed image I... pp The DC component (e.g., a constant signal component) or other signals with low spatial frequencies can be further removed.

[0083] For reference Figures 4A to 4C This provides a demonstration of a method 200 according to one or more embodiments of the present disclosure.

[0084] Figure 4A Image 402 is an image of a periodic structure 302 according to one or more embodiments of this disclosure. For example, image 402 may correspond to the original image I generated by the metering subsystem 102. Orig Additionally, image 402 exhibits fundamental non-uniformity, which results in non-uniform contrast across the periodic structure 302 of the image.

[0085] Figure 4B A series of images 404 to 412 (each labeled) according to one or more embodiments of the present disclosure, corresponding to the reconstructed components associated with image 402 using a decomposition technique. arrive ). Figure 4C It is based on one or more embodiments of this disclosure and Figure 4A and 4B Associated large trajectory matrix Plotting the spectrum of the eigenvalues. For example... Figure 4C As shown, the intensity of the eigenvalues ​​(and associated reconstructed components) decreases rapidly. Therefore, the first few eigenvalues ​​(and associated reconstructed components) can be significant, while the remainder corresponds to noise.

[0086] Figure 4B Images 404 to 412 in the diagram correspond to the first five reconstructed components of image 402, which are associated with a large trajectory matrix using the trajectory matrix containing the rows of image 402. The first five eigenvalues ​​generated by SVD are correlated, where the embedding dimension is... It is selected to be equal to the period of the periodic structure 302 in pixels (e.g., the generalized decomposition as described above).

[0087] In addition, such as Figure 4B As shown, only some of the reconstructed components contain significant signals on the length scale associated with the pitch of the periodic structure 302. In this particular instance, the reconstructed components... and The periodic structure 302 contains a fundamental signal intensity at its pitch and can be used to generate a high-contrast preprocessed image of the periodic structure 302 (e.g., in step 212), wherein at least some unwanted noise and / or non-uniformity is removed. Reconstructed components This represents the DC components of target 104 (e.g., low spatial frequency components) and associated DC non-uniformity, which can impair metrological measurements, such as, but not limited to, superposition measurements. The remaining reconstructed components (e.g., here) This includes noise and / or non-uniformity at higher spatial frequencies that can further impair metrology measurements.

[0088] In some cases, it may be possible to describe large trajectory matrices in a more efficient form than that provided by the reconstructed components. (or original image I) Orig The spectral components of ). For illustration, Figure 4C This indicates that the second and third eigenvalues ​​are degenerate or nearly degenerate. Figure 4B This is also proven because of the reconstructed components. and Degraded or nearly degraded images contain similar spatial frequencies. Any suitable decomposition and / or separation techniques can be applied to typically obtain reconstructed components and / or to generate reconstructed components of the preprocessed image (e.g., in step 212). For example, rotation techniques (e.g., but not limited to maximum variance rotation, quadrature limit rotation, or equal limit rotation) can be used to generate reconstructed vectors.

[0089] Additionally, it should be noted that equations (3) to (5) and Figures 4A to 4C This corresponds to nonparametric decomposition. In some embodiments, step 204 includes performing parametric decomposition and regression to provide a reconstructed vector for generating the preprocessed image. This technique can use the original image I... Orig The data generated in this process forms an adaptive basis and can therefore provide a generalized or universal technique suitable for a variety of images with different noise and / or non-uniformity problems. Furthermore, this technique can extract data from the original image I with frequencies different from those provided by standard Fourier decomposition. Orig Extract the amplitude-modulated sine wave component.

[0090] A subset of vectors for generating the preprocessed image can be selected at any point. In some embodiments, this is based on a subset of vectors from a specific original image I. Orig A subset of reconstructed components for generating a specific preprocessed image can be selected based on individual analysis of the spectrograms of the reconstructed signal and / or eigenvalues. For example, the reconstructed components at known pitches of the periodic structure 302 can be selected based on the signal strength of the reconstructed components (e.g., the strength of the reconstructed components at or near spatial frequencies at a known pitch, as determined by Fourier or other spectral analysis techniques) and / or the eigenvalue strength (e.g., in...). Figure 4C The subset of reconstructed components can be selected from any combination of the spectrograms shown in the diagram. Furthermore, this selection can be automated, eliminating the need for user intervention. For example, the signal strength and / or eigenvalue strength of the reconstructed components at a known pitch can be compared with a pre-selected threshold generated based on previous experiments and / or simulations.

[0091] In some embodiments, the subset used to generate reconstructed components for a particular preprocessed image is based on prior selection or training. The situation may be that images of a target 104 with a common design across samples 106 or more samples 106 in a batch may exhibit similar noise and / or non-uniformity characteristics, such that a particular reconstructed component provides a strong signal at a known pitch of the periodic structure 302 on the target 104 (e.g., Figures 4A to 4C In the example and The components can be consistent or at least maintain a measurable pattern. Therefore, it is insufficient to identify the components to be reconstructed during the training phase and use them for additional targets 104 during the testing phase without further analysis. For example, the testing phase may correspond to the first part of the target 104 on a specific sample 106. As another example, the testing phase may correspond to a set of one or more training samples 106 analyzed prior to runtime in a production environment. This training and testing technique, carefully considered, reduces the computational burden during runtime, enabling efficient (e.g., almost instantaneous) generation of preprocessed images. In this way, even computationally intensive methods (e.g., but not limited to generalized decomposition, e.g., as previously described herein) can be used. It can also be implemented efficiently during the testing phase.

[0092] For general reference Figures 2A to 2B After careful consideration, the systems and methods disclosed herein are suitable for representing images with more than one harmonic component (e.g., different pitches p of any pitch of the periodic structure 302 in the spatial frequency space and / or nontrivial harmonics). Specifically, the decomposition techniques disclosed herein can naturally identify the main spatial frequencies in an image based on data within the image itself and further provide reconstructed components containing these spatial frequencies. In other words, the decomposition techniques can automatically provide reconstructed components with an adaptive basis based on data within the image itself.

[0093] Therefore, the systems and methods disclosed herein can provide filtering of noise and non-uniformity even when non-trivial harmonics are present. For example, a preprocessed image (e.g., in step 212) can be generated based on any combination of reconstructed components that more generally contain the desired harmonic or spatial frequency and exclude sources of noise or non-uniformity as described herein.

[0094] Additionally, in some embodiments, one or more preprocessed images may be generated that isolate desired spatial frequencies and / or exclude non-desired spatial frequencies. For example, preprocessed images may be generated in which certain harmonics are intentionally excluded (e.g., to isolate fundamental spatial frequencies). As another example, in cases where the target comprises different examples of periodic structures 302 with different pitches (e.g., in a non-overlapping configuration or in an overlapping moiré configuration), preprocessed images that isolate structures with specific pitches may be generated. Furthermore, different preprocessed images that isolate structures with different pitches may be generated. In this way, features with different pitches can be considered individually. These multiple preprocessed images can then be used together to generate one or more metrological measurements (e.g., in step 206).

[0095] Refer again Figure 2A Step 206 may include generating a metrological measurement based on the preprocessed image using any suitable technique. For example, any technique or algorithm suitable for generating image-based metrological measurements (e.g., on the original image) may be applied to the preprocessed image generated in step 204. In this way, step 204 may improve the quality of the metrological measurement based on any number of metrics (e.g., but not limited to accuracy, sensitivity, or robustness).

[0096] For example, a reconstructed signal based on data that is associated with a length scale of known pitch. The decomposition and selection of preprocessing techniques can provide high-contrast images of periodic features and effectively filter out unwanted signals (e.g., those associated with noise, non-uniformity, or the like) that can negatively impact image-based metrology measurements.

[0097] As an illustration, the systems and methods disclosed herein are particularly suitable for non-limiting applications of superposition metrology. For example, image-based superposition metrology techniques typically involve one of two approaches. The first approach is based on Fourier series decomposition regression (e.g., for harmonics generated by the periodic structure 302) and cross-correlation filters. However, even simple linear trends and / or non-uniformity of the constant term (e.g., in Fourier series decomposition) can contribute to significant errors in superposition measurements. The second approach is based on comparing the phases of different examples of the periodic structure 302 in one or more images. Such phase-based techniques may be more naturally robust to the types of non-uniformity that compromise cross-correlation techniques (e.g., it can be up to quadratic in local expansion), but may largely require only a single principal harmonic in the core (e.g., the image). Therefore, the presence of any additional harmonics can lead to fundamental superposition errors. In general, typical image-based superposition metrology techniques cannot simultaneously accept more than one harmonic in the signal (e.g., the image) while also being robust to non-uniformity and target noise.

[0098] However, even when harmonics are present in the signal (e.g., harmonics in the spatial frequency space at the edges of the periodic structure 302), the systems and methods disclosed herein are suitable for filtering out noise and / or image non-uniformity. In this way, the systems and methods disclosed herein are suitable for improving superposition measurements produced using any image-based technique (including, but not limited to, cross-correlation or phase-based techniques).

[0099] Method 200 may further include controlling one or more process tools based on the metrological measurements generated in step 206. For example, metrological data associated with any number of targets 104 across one or more sample 106 distributions can be used to generate correctable values ​​for controlling the process tools when manufacturing additional samples 106. As an illustration, metrological data of samples 106 in a batch can be used to generate feedback correctable values ​​for controlling the lithographic exposure of subsequent samples 106 in the same batch. As another illustration, metrological data of samples 106 in a batch can be used to generate feedforward correctable values ​​for controlling the lithographic exposure of the same or similar samples 106 in subsequent lithography steps to address any deviations.

[0100] Refer again Figures 1A to 1C The following describes in more detail various aspects of the metering system 100 according to one or more embodiments of the present disclosure.

[0101] In some embodiments, the metrology subsystem 102 is an optical subsystem that generates metrological measurements by using light to illuminate the target 104 and collecting the light from the target 104 as the basis for measurement. Figure 1B This is a conceptual diagram of an optical metrology subsystem 102 according to one or more embodiments of the present disclosure.

[0102] The optical metrology subsystem 102 may typically include an illumination source 116 for generating an illumination beam 118 having any spectral or temporal profile, an illumination path 120 for guiding the illumination beam 118 to a target 104, an objective lens 122 or other suitable component for collecting light from the target 104 (also referred to herein as sample light 124), a detector 126, and a collection path 128 for guiding the sample light 124 to the detector 126. The illumination path 120 and / or the collection path 128 may include any number or type of lenses 130 or other optical elements 132 suitable for manipulating the illumination beam 118 and / or the sample light 124, such as, but not limited to, one or more polarizers, one or more beam splitters 134, one or more homogenizers, or one or more apodizers.

[0103] The optical metrology subsystem 102 may use any suitable technique to generate metrological measurements. In some embodiments, the optical metrology subsystem 102 generates metrological measurements based on an image of the target 104 (e.g., a field plane image in which the detector 126 is located in a field plane conjugate with the sample 106). In some embodiments, the optical metrology subsystem 102 uses a scattering measurement technique based on (e.g., as measured by the detector 126 in the pupil plane) a collected diffraction order to generate metrological measurements. Additionally, the sample 106 may be static or in motion during the measurement.

[0104] In some embodiments, the metrology subsystem 102 is a particle beam subsystem that generates metrological measurements by illuminating the target 104 with a particle beam (e.g., an electron beam, an ion beam, a neutral particle beam, or the like) and collecting any combination of particles or light from the target 104 as the basis for the measurement. Figure 1C This is a conceptual diagram of a particle beam metrology subsystem 102 according to one or more embodiments of the present disclosure.

[0105] The particle beam metrology subsystem 102 may include a particle source 136 (e.g., an electron beam source, an ion beam source, or the like) such that the illumination beam 118 comprises a particle beam (e.g., an electron beam, a particle beam, or the like). The illumination source 116 may include any particle source known in the art suitable for generating the illumination beam 118. For example, the illumination source 116 may include, but is not limited to, an electron gun or an ion gun. The particle beam metrology subsystem 102 may further include an illumination path 120 having one or more particle beam lenses 138 (e.g., electrostatic, magnetic, single-potential, dual-potential lenses, or the like) or other beam manipulation elements (not shown) to control one or more aspects of the illumination beam 118, such as, but not limited to, one or more astigmatism reducers or aberration control elements. The particle beam metrology subsystem 102 may further include a collection path 128 to direct any combination of particles or light to at least one detector 126. For example, the detector 126 may include an electron collector (e.g., a secondary electron collector, a backscattered electron detector, or the like). As another example, detector 126 may include a photon detector (e.g., a light detector, an X-ray detector, a scintillation element coupled to a photomultiplier tube (PMT) detector, or the like) for detecting electrons and / or photons from the sample surface. For illustration, Figure 1C A detector 126 is depicted, arranged to capture secondary electrons emitted from target 104.

[0106] The objects described herein sometimes refer to different components contained within or connected to other components. It should be understood that such depicted architectures are for illustrative purposes only, and many other architectures that achieve the same functionality can in fact be implemented. Conceptually, any arrangement of components that achieve the same functionality is effectively “associated” to achieve the desired functionality. Therefore, any two components combined herein to achieve a particular functionality can be considered “associated” with each other to achieve the desired functionality, regardless of the architecture or intermediate components. Similarly, any two such associated components can also be considered “connected” or “coupled” with each other to achieve the desired functionality, and any two components that can be suchly associated can also be considered “coupleable” with each other to achieve the desired functionality. Specific examples of coupleability include, but are not limited to, physically interacting and / or physically interacting components and / or wirelessly interacting and / or logically interacting components.

[0107] It is believed that this disclosure and its many accompanying advantages will be understood from the above description, and it should be understood that various changes can be made to the form, construction, and arrangement of the components without departing from the disclosed subject matter or sacrificing all its material advantages. The forms described are for illustrative purposes only, and the appended claims are intended to cover and encompass such changes. Furthermore, it should be understood that the invention is defined by the appended claims.

Claims

1. A system for pre-processing images, comprising: a controller including one or more processors configured to execute program instructions that cause the one or more processors to implement a metrology recipe by: receiving one or more images of a metrology target including periodic features having one or more known pitches; pre-processing the one or more images using a decomposition technique to generate one or more pre-processed images, wherein pre-processing a particular image of the one or more images comprises: constructing one or more trajectory matrices from the particular image; generating, using the decomposition technique, reconstructed components associated with the particular image from the one or more trajectory matrices; selecting, from the generated reconstructed components, reconstructed components including signals having at least one of the one or more known pitches, the selected reconstructed components forming a subset of the reconstructed components; and generating a particular one of the one or more pre-processed images based on the subset of the reconstructed components including signals having at least one of the one or more known pitches; and generating one or more metrology measurements of the metrology target based on the one or more pre-processed images.

2. The system of claim 1, wherein generating, using the decomposition technique, the reconstructed components associated with the particular image from the one or more trajectory matrices comprises: generating, using a singular value decomposition (SVD) technique, the reconstructed components associated with the particular image from the one or more trajectory matrices.

3. The system of claim 1, wherein generating, using the decomposition technique, the reconstructed components associated with the particular image from the one or more trajectory matrices comprises: generating, using at least one of a principal component analysis technique or an independent component analysis technique, the reconstructed components associated with the particular image from the one or more trajectory matrices.

4. The system of claim 1, wherein the particular image is defined as: wherein represents a pixel value, wherein represents a row of the particular image, wherein represents a column of the particular image, wherein the one or more trajectory matrices are associated with one or more rows of the particular image, wherein the one or more trajectory matrices have an embedding dimension wherein .

5. The system of claim 4, wherein .

6. The system of claim 4, wherein .

7. The system of claim 6, wherein a value corresponding to one of the one or more known pitches rounded to an integer in pixels.

8. The system of claim 4, wherein the one or more trajectory matrices include ， For where the large trajectory matrix is formed as where generating the reconstruction component associated with the particular image from the one or more trajectory matrices using the decomposition technique comprises: generating, using the decomposition technique, the reconstructed components associated with the particular image from a large trajectory.

9. The system of claim 4, wherein the trajectory matrices include a single trajectory matrix associated with a single one of the rows of the particular image.

10. The system of claim 4, wherein the trajectory matrices include a single trajectory matrix associated with an average of at least two of the rows of the particular image.

11. The system of claim 1, wherein the particular image is defined as: wherein represents a pixel value, wherein represents a row of the particular image, wherein represents a column of the particular image, wherein the large trajectory matrix is formed from the one or more trajectory matrices as: ， Each matrix These are embedding dimensions, respectively, along the directions of the rows and columns of the specific image. and , with window size One of the one or more trajectory matrices, wherein and .

12. The system of claim 11, wherein a value corresponding to one of the one or more known pitches rounded to an integer in pixels along the row, wherein a value corresponding to one of the one or more known pitches rounded to an integer in pixels along the column.

13. The system of claim 1, wherein the subset of the reconstructed components including the signals having at least one of the one or more known pitches is determined for each of the one or more images.

14. The system of claim 1, wherein the subset of the reconstructed components including the signals having at least one of the one or more known pitches is determined based on one or more training images.

15. The system of claim 1, wherein the metrology measurements include: overlay measurements.

16. The system of claim 1, wherein the program instructions are further configured to cause the one or more processors to control a lithography tool based on the one or more metrology measurements.

17. A system for preprocessing images, comprising: a metrology sub-system; and a controller communicatively coupled with the metrology sub-system, the controller including one or more processors configured to execute program instructions that cause the one or more processors to implement a metrology recipe by: receiving, from the metrology sub-system, one or more images of a metrology target including periodic features having one or more known pitches; preprocessing the one or more images using a decomposition technique to generate one or more preprocessed images, wherein preprocessing a particular image of the one or more images includes: constructing one or more track matrices from the particular image; generating, using the decomposition technique, reconstructed components associated with the particular image from the one or more track matrices; selecting, from the generated reconstructed components, reconstructed components including signals having at least one of the one or more known pitches, the selected reconstructed components forming a subset of the reconstructed components; and generating a particular one of the one or more preprocessed images based on the subset of the reconstructed components including signals having at least one of the one or more known pitches; and generating one or more metrology measurements of the metrology target based on the one or more preprocessed images.

18. The system of claim 17, wherein the program instructions are further configured to cause the one or more processors to control a lithography tool based on the one or more metrology measurements.

19. The system of claim 17, wherein the metrology sub-system comprises: an optical metrology imaging sub-system.

20. The system of claim 17, wherein the metrology sub-system comprises: a particle beam imaging sub-system.

21. A method for preprocessing images, comprising: receiving one or more images of a metrology target including periodic features having one or more known pitches; preprocessing the one or more images using a decomposition technique to generate one or more preprocessed images, wherein preprocessing a particular image of the one or more images includes: constructing one or more track matrices from the particular image; generating, using the decomposition technique, reconstructed components associated with the particular image from the one or more track matrices; selecting, from the generated reconstructed components, reconstructed components including signals having at least one of the one or more known pitches, the selected reconstructed components forming a subset of the reconstructed components; and generating a particular one of the one or more preprocessed images based on the subset of the reconstructed components including signals having at least one of the one or more known pitches; and generating one or more metrology measurements of the metrology target based on the one or more preprocessed images.

22. The method of claim 21, wherein generating, using the decomposition technique, the reconstructed components associated with the particular image from the one or more track matrices includes: generating the reconstructed components associated with the particular image from the one or more trajectory matrices using singular value decomposition (SVD) techniques.

23. The method of claim 21, wherein generating the reconstructed components associated with the particular image from the one or more trajectory matrices using the decomposition technique comprises: generating the reconstructed components associated with the particular image from the one or more trajectory matrices using at least one of principal component analysis techniques or independent component analysis techniques. generating the reconstructed components associated with the particular image from the one or more trajectory matrices using at least one of principal component analysis techniques or independent component analysis techniques.

Images