Image preprocessing for overlay measurement using decomposition method

Abstract

The system can include a controller for 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 method to generate one or more preprocessed images, and generating one or more metrology measurements for the metrology target based on the one or more preprocessed images. Preprocessing a particular image of the one or more images can include creating one or more trajectory matrices from the particular image, generating reconstruction components associated with the particular image from the one or more trajectory matrices using a decomposition method, and generating the particular image of the one or more preprocessed images based on a subset of the reconstruction components that include signals associated with at least one of the one or more known pitches.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Application No. 63 / 410,233, filed September 27, 2022, entitled "ON PRE-PROCESSING MEASURED IMAGES AND SIGNALS FOR ACCURATE OVERLAY EXTRACTION," inventors Nireekshan K. Reddy and Vladimir Levinski, which is incorporated herein by reference in its entirety.

[0002] FIELD OF THE DISCLOSURE This disclosure relates generally to overlay metrology, and more particularly to image pre-processing for overlay metrology. [Background technology]

[0003] Many metrology techniques utilize images of periodic structures on a sample. However, various sources can introduce noise and irregularities into the collected images that have length scales different from the period of the structures of interest. Such noise and irregularities can adversely affect measurements, and examples include, but are not limited to, detector-induced noise, target-induced noise, or illumination irregularities. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] U.S. Patent Application Publication No. 2022 / 0283514 [Patent Document 2] U.S. Patent Application Publication No. 2019 / 0252270 [Patent Document 3] International Publication No. 2021 / 107986 Summary of the Invention [Problem to be solved by the invention]

[0005] Therefore, there is a need to develop a system and method to address the above-mentioned shortcomings. [Means for solving the problem]

[0006] A system is disclosed in accordance with one or more exemplary embodiments of the present disclosure. In one exemplary embodiment, the system includes a controller. In another exemplary embodiment, the controller receives one or more images of a metrology target including periodic features having one or more known pitches. In another exemplary embodiment, the controller preprocesses the one or more images using a decomposition method to generate one or more preprocessed images. In another exemplary embodiment, the controller generates one or more metrology measurements for the metrology target based on the one or more preprocessed images. In another exemplary embodiment, preprocessing a particular image of the one or more images includes creating one or more trajectory matrices from the particular image, generating reconstruction components associated with the particular image from the one or more trajectory matrices using a decomposition method, and generating the particular image of the one or more preprocessed images based on a subset of the reconstruction components that include signals associated with at least one of the one or more known pitches.

[0007] A system is disclosed in accordance with one or more exemplary embodiments of the present disclosure. In one exemplary embodiment, the system includes a metrology subsystem and a controller. In another exemplary embodiment, the controller receives one or more images of a metrology target including periodic features having one or more known pitches from the metrology subsystem. In another exemplary embodiment, the controller preprocesses the one or more images using a decomposition method to generate one or more preprocessed images. In another exemplary embodiment, the controller generates one or more metrology measurements for the metrology target based on the one or more preprocessed images. In another exemplary embodiment, preprocessing a particular image of the one or more images includes creating one or more trajectory matrices from the particular image, generating reconstruction components associated with the particular image from the one or more trajectory matrices using a decomposition method, and generating the particular image of the one or more preprocessed images based on a subset of the reconstruction components that include signals associated with at least one of the one or more known pitches.

[0008] A method is disclosed in accordance with one or more exemplary embodiments of the present disclosure. In one exemplary embodiment, the method includes receiving one or more images of a metrology target including periodic features having one or more known pitches. In another exemplary embodiment, the method includes preprocessing the one or more images using a decomposition method to generate one or more preprocessed images. In another exemplary embodiment, preprocessing a particular image of the one or more images includes creating one or more trajectory matrices from the particular image, generating reconstruction components associated with the particular image from the one or more trajectory matrices using a decomposition method, and generating the particular image of the one or more preprocessed images based on a subset of the reconstruction components that includes signals associated with at least one of the one or more known pitches. In another exemplary embodiment, the method includes generating one or more metrology measurements for the metrology target based on the one or more preprocessed images.

[0009] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not necessarily restrictive of 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 summary, serve to explain the principles of the invention.

[0010] Those skilled in the art may better appreciate the many advantages of the present disclosure by reviewing the accompanying drawings. [Brief explanation of the drawings]

[0011] [Figure 1A] FIG. 1 is a block diagram of a metrology system for generating and / or utilizing preprocessed images in accordance with one or more embodiments of the present disclosure. [Figure 1B] FIG. 1 is a conceptual diagram of an optical metrology subsystem in accordance with one or more embodiments of the present disclosure. [Figure 1C] FIG. 1 is a conceptual diagram of a particle beam metrology subsystem in accordance with one or more embodiments of the present disclosure. [Figure 2A] FIG. 1 is a flow diagram illustrating steps performed in a method according to one or more embodiments of the present disclosure. [Figure 2B] FIG. 10 is a flow diagram illustrating additional steps performed in a method according to one or more embodiments of the present disclosure. [Figure 3] FIG. 1 is a schematic top view image of a target including periodic structures, according to one or more embodiments of the present disclosure. [Figure 4A] 1 is an image of a periodic structure according to one or more embodiments of the present disclosure. [Figure 4B] 1 is a series of images corresponding to image-related decomposition reconstruction components in accordance with one or more embodiments of the present disclosure. [Figure 4C] 4C is a graph of the spectrum of eigenvalues ​​of the grand orbital matrix associated with FIGS. 4A and 4B in accordance with one or more embodiments of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0012] Reference will now be made in detail to the subject matter of the present disclosure, which is illustrated in the accompanying drawings. This disclosure particularly shows and describes certain embodiments and their particular features. The embodiments described herein are to be construed as illustrative and not restrictive. It will be apparent to those skilled in the art that various changes and modifications in form and detail can be made therein without departing from the spirit and scope of the present disclosure.

[0013] Embodiments of the present disclosure are directed to systems and methods that provide pre-processing of images involving periodic features using matrix decomposition (e.g., factorization) techniques. The systems and methods disclosed herein may be suitable for, but are not limited to, pre-processing of images of periodic targets used in metrology applications, such as, but not limited to, overlay metrology.

[0014] It is contemplated herein that many image-based metrology techniques may be susceptible to noise and / or irregularities present in the images. Typical approaches to providing accurate measurements focus on hardware-based techniques to avoid such noise and / or irregularities. However, completely removing such noise and / or irregularities from the images may be impractical or undesirable (e.g., due to cost or other constraints). In such cases, it may be desirable to pre-process the images before generating the image-based measurements, which may enable the use of any suitable measurement and / or analysis techniques.

[0015] In some embodiments, one or more trajectory matrices are generated for an image. Based on the trajectory matrices, reconstruction components associated with the image can be generated using a matrix decomposition technique, such as, but not limited to, singular value decomposition (SVD) or its derivatives. The reconstruction components can represent the image's individual spectral components (e.g., individual length scales). In this manner, the reconstruction components can represent portions of the image corresponding to individual length scales. A preprocessed (e.g., filtered) image can then be generated based on a subset of the reconstruction components corresponding to the known pitch of the overlay targets in the image. Such a preprocessed image can include a high-contrast representation of the periodic overlay targets, effectively removing or suppressing noise and / or irregularities at other length scales.

[0016] It is envisioned that such techniques may enable robust and versatile filtering of periodic target images. Specifically, by using decomposition techniques to generate reconstruction vectors, dominant length scales (e.g., spectral components) within an image can be identified based on the image itself, thereby increasing the efficiency and accuracy of filtering data with unwanted length scales. It is recognized that a generalized metrology model incorporating decomposition of a trajectory matrix containing measurements from targets distributed throughout a sample is described in U.S. patent application Ser. No. 17 / 995,385, filed Sep. 28, 2022, and is incorporated herein by reference in its entirety. The systems and methods disclosed herein may utilize, but are not limited to, decomposition techniques similar to those described in U.S. patent application Ser. No. 17 / 995,385, but these mathematical decompositions are applied to different data sets from different stages of the metrology process. For example, in the systems and methods disclosed herein, decomposition techniques are applied to identify and isolate dominant length scales associated with periodic features of interest in an image as a preprocessing step before generating metrology measurements. Metrology data generated from multiple targets across the sample can then be modeled or further processed using any suitable technique, such as, but not limited to, the techniques described in U.S. Patent Application No. 17 / 995,385.

[0017] The trajectory matrices may be generated in any suitable manner and may be adjusted based on the complexity of the overlay targets being imaged (e.g., whether the targets are periodic along one dimension or multiple dimensions) and / or computational considerations. In particular, the number of trajectory matrices created and / or the embedding dimension may be adjusted to suit a particular application.

[0018] As an example, in the case of an image of a target having one-dimensional (1D) periodicity oriented along the rows of the image, one or more trajectory matrices can be generated based on one or more rows of the image. In some embodiments, a trajectory matrix is ​​generated for each row of the image (or a portion of the image corresponding to a region of interest (ROI)), and then combined into a grand trajectory matrix. In some embodiments, a single trajectory matrix is ​​generated for a single row of the image or a portion of the image. In some embodiments, one trajectory matrix is ​​generated based on the average of two or more rows of the image or portions of the image. Reducing the number of trajectory matrices may improve computational throughput (e.g., reduce computation time), but may result in a less robust analysis.

[0019] The embedding dimension can be selected based on the requirements of a particular application. In some embodiments, the embedding dimension is selected to be the length of a row or column in the image. This configuration can correspond to a simple SVD implementation on selected rows of the image and can generate reconstruction components based on correlations between individual rows. Such a configuration can also be relatively fast to compute. In some embodiments, the embedding dimension is selected to be the known pitch (e.g., in pixels) of the target. Such a configuration can generate reconstruction components based on correlations between repeating patterns (e.g., individual periods) within each row and between individual rows. Thus, such a configuration can provide a more statistically valid decomposition of the image, thereby providing reconstruction components that more accurately represent various length scales in the image, but can require a relatively long computation time.

[0020] Additional embodiments of the present disclosure are directed to process control that utilizes metrology data generated based on the preprocessed images disclosed herein. In this manner, metrology data may be used directly or indirectly for feedback and / or feedforward control of any number of processing tools, including, but not limited to, lithography tools (such as scanners and / or steppers), deposition tools, etching tools, or polishing tools. As one example, metrology data for a specimen within a lot may be used to generate feedback correctables that control the lithography exposure of subsequent specimens within the same lot. As another example, metrology data for a specimen within a lot may be used to generate feedforward correctables to compensate for any deviations in the current exposure, and the feedforward correctables may control the lithography exposure of subsequent lithography stages of the same or similar specimens.

[0021] 1A-4C, a system and method for pre-processing images of periodic features according to one or more embodiments of the present disclosure will now be described in detail.

[0022] FIG. 1A is a block diagram of a metrology system 100 for generating and / or utilizing preprocessed images in accordance with one or more embodiments of the present disclosure.

[0023] In some embodiments, the metrology system 100 includes a metrology subsystem 102 suitable for generating metrology measurements of targets 104 (e.g., metrology targets) distributed throughout one or more samples 106 .

[0024] The specimen 106 may include any object upon which metrology measurements are based. For example, the specimen 106 may include a substrate (e.g., a wafer) formed of a semiconductor or non-semiconductor material. The semiconductor or non-semiconductor material may include, but is not limited to, monocrystalline silicon, gallium arsenide, and indium phosphide. The specimen 106 may include one or more layers. For example, such layers may include, but are not limited to, resist, dielectric material, conductive material, and semiconductor material. Many different types of such layers are known in the art, and the term specimen, as used herein, is intended to encompass any type of such layer that may be formed on the specimen. The one or more layers formed on the specimen 106 may be patterned or unpatterned. For example, the specimen 106 may include multiple dies, each including features with a repeatable pattern. Such material layers may be formed and processed to ultimately result in a completed device. Many different types of devices may be formed on the specimen 106. The term specimen 106, as used herein, is intended to encompass a specimen 106 undergoing fabrication of any type of device known in the art. Furthermore, for purposes of this disclosure, the terms specimen 106 and wafer should be considered interchangeable.

[0025] The metrology measurements of the specimen 106 generated by the metrology subsystem 102 can provide any type of data and can be generated using any technique known in the art. In some embodiments, the metrology measurements generated by the metrology subsystem 102 are overlay measurements, which characterize the alignment (or alignment error) between different lithography exposure surfaces on one or more layers of the specimen 106. In some embodiments, the metrology measurements generated by the metrology subsystem 102 characterize the condition of the lithography exposure surface, such as, but not limited to, the focus position or illumination amount of the specimen 106. In some embodiments, the metrology measurements generated by the metrology subsystem 102 characterize additional characteristics of the manufacturing process, such as, but not limited to, an etching stage or a polishing stage.

[0026] The target 104 may include any location on the specimen 106 suitable for metrology measurements by the metrology subsystem 102. In some embodiments, the target 104 includes features associated with the device being fabricated (referred to herein as device features). In some embodiments, the target 104 includes dedicated features designed to facilitate metrology measurements. As an example in the context of overlay metrology, the dedicated overlay target 104 may include features associated with each lithography exposure plane of interest, which may be in overlapping or non-overlapping positions on the specimen 106, in an arrangement that enables robust and accurate overlay measurements by the metrology subsystem 102.

[0027] The metrology subsystem 102 may be configured to execute a metrology recipe. The recipe may include various parameters and / or conditions that control the acquisition of measurements across at least one sample 106. For example, the recipe may include parameters related to the number of regions (e.g., targets) of the sample 106 to be characterized, the placement of the targets, and / or the order in which such targets are measured. Additionally, in applications where targets are designed for measurement purposes (e.g., metrology targets or overlay targets), the recipe may include design aspects of such targets, including, but not limited to, the layout of features in one or more layers. As another example, the recipe may include parameters related to the configuration of the metrology subsystem 102 during measurement. As an example, the recipe may include parameters related to the illumination of the target 104, including, but not limited to, the wavelength, polarization, power, angle of incidence, spot size, or number of rays of the illumination beam. As another example, the recipe may include parameters related to the collection of light from the target 104, including, but not limited to, the wavelength, polarization, or collection angle. As another example, a recipe may include various processing and / or analysis steps related to generating metrology measurements based on the generated data.

[0028] In some embodiments, measurement system 100 includes a controller 108 communicatively coupled to any of the components therein. 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 memory device 112, i.e., memory. One or more processors 110 of 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.

[0029] The one or more processors 110 of the controller 108 may include any processor or processing element known in the art. For purposes of this disclosure, the term “processor” or “processing element” may be broadly defined to encompass any device having one or more processing elements 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, the 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, the one or more processors 110 may be embodied as a desktop computer, a mainframe computer system, a workstation, an image computer, a parallel processor, a networked computer, or any other computer system configured to execute programs configured to operate the measurement system 100 or to operate in conjunction with the measurement system 100 described throughout this disclosure. Additionally, various subsystems of the measurement system 100 may include processors or logic elements suitable for performing at least a portion of the steps described in this disclosure. Therefore, the above description should not be construed as limiting the embodiments of the present disclosure, but merely as illustrative. Furthermore, the steps described throughout this disclosure may be performed by a single controller or, alternatively, by multiple controllers. Additionally, controller 108 may include one or more controllers housed in a common housing or within multiple housings. In this manner, any controller or combination of controllers may be individually packaged as a module suitable for incorporation into measurement system 100.

[0030] The memory device 112 may include any storage medium known in the art suitable for storing program instructions executable by the one or more processors 110 associated therewith. For example, the memory device 112 may include a non-transitory memory medium. As other examples, the memory device 112 may include, but is not limited to, read-only memory (ROM), random access memory (RAM), magnetic or optical memory devices (e.g., disks), magnetic tape, and solid-state drives. It should be noted that the memory device 112 may be housed together with one or more processors 110 in a common controller housing. In some embodiments, the memory device 112 may be located remotely relative to the physical locations of the one or more processors 110 and the controller 108. For example, the one or more processors 110 of the controller 108 may access a remote memory (e.g., a server) accessible via a network (e.g., the Internet, an intranet, etc.).

[0031] The controller 108 may issue instructions (e.g., via control signals) and / or receive data to any components or subsystems of the metrology system 100, such as, but not limited to, the metrology subsystem 102, as well as to other systems (e.g., one or more processing tools for producing the specimen 106, such as a lithography tool). The controller 108 may be further configured to perform any of the various process steps described throughout this disclosure, such as, but not limited to, executing a metrology recipe, pre-processing one or more images, or generating metrology measurements based on pre-processed images.

[0032] In some embodiments, the measurement system 100 includes a user interface 114 communicatively coupled to the controller 108. In some embodiments, the user interface 114 may include, but is not limited to, one or more desktops, laptops, tablets, and the like. In some embodiments, the user interface 114 includes a display used to display data from the measurement 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 that can be integrated with the user interface 114 is suitable for implementation in the present disclosure. In some embodiments, a user can input selections and / or instructions responsive to data displayed to the user via a user input device of the user interface 114.

[0033] 2A-4C, techniques for modeling metrology measurements in accordance with one or more embodiments of the present disclosure will now be described in detail.

[0034] 2A is a flow diagram illustrating steps performed in method 200 in accordance with one or more embodiments of the present disclosure. It should be understood that embodiments and enabling techniques previously described herein in the context of metrology system 100 also apply to method 200. For example, processor 110 of controller 108 executes program instructions that may implement any of the steps of method 200. In some embodiments, at least some of the steps of method 200 may be implemented by any combination of components of metrology system 100 as part of a metrology recipe. It should be further noted, however, that method 200 is not limited to the configuration of metrology system 100.

[0035] In some embodiments, method 200 includes step 202, in which one or more images of one or more targets 104 including periodic features having one or more known pitches are generated. In some embodiments, method 200 includes step 204, in which one or more images are preprocessed using a decomposition technique to generate one or more preprocessed images. In some embodiments, method 200 includes step 206, in which one or more metrology measurements of the targets 104 are generated based on the one or more preprocessed images. More generally, step 206 can include generating any type or number of metrology measurements based on any number of targets 104. For example, the imaged targets 104 can be, but are not limited to, overlay targets 104 suitable for overlay metrology measurements.

[0036] The images of step 202 may be generated using any suitable tool, such as, but not limited to, metrology subsystem 102. Furthermore, the images may be generated using any suitable optical imaging technique, including, but not limited to, bright-field or dark-field imaging.

[0037] The target 104 may have any design suitable for any type of metrology, for example, the target 104 may have periodic features in one or more layers (e.g., sample layers) of the sample 106.

[0038] 3 is a schematic top view image of a target 104 including periodic structures 302, in accordance with one or more embodiments of the present disclosure. Specifically, the periodic structures 302 in FIG. 3 are shown as line / space features having a pitch p.

[0039] In some embodiments, the target 104 or a cell thereof may include a single instance of the periodic structure 302. In some embodiments, the target 104 or a cell thereof may include multiple instances of the periodic structure 302 in an overlapping or non-overlapping configuration, in which case the individual instances of the periodic structure 302 may have the same or different pitches (e.g., values ​​p).

[0040] For example, in a non-limiting overlay metrology application, the target 104 may include different instances of such periodic structures 302 associated with different lithographically exposed planes on one or more sample layers. In this manner, overlay measurements (e.g., generated in step 206) can be provided that relate to relative alignment measurements between features associated with different lithographically exposed planes based on the relative positions of the different instances of periodic structures 302. As one example, the target 104 may include non-overlapping instances of periodic structures 302 with the same or different pitches. For example, the target 104 may be characterized as an advanced image metrology (AIM) target 104. As another example, the target 104 may include one or more regions of overlapping instances of periodic structures 302, which may be characterized as grating-over-grating structures. In instances where the pitches are different, such regions may also be referred to as Moiré structures. Such regions may also experience a moiré pitch that is different from the pitch of the constituent periodic structures 302 (e.g., related to the difference between the pitches of the constituent periodic structures 302). For example, a target 104 that includes one or more moiré structures may be characterized as a robust AIM (e.g., rAIM) target 104.

[0041] In some embodiments, generating the overlay measurements (e.g., in step 206) may be based on the difference between the centers of symmetry of different regions of the target 104 (e.g., the difference between the centers of symmetry of different entities of the periodic structure 302, or the difference between the centers of symmetry of different entities of a moiré structure, etc.).

[0042] 2B is a flow diagram illustrating additional steps performed in method 200, according to one or more embodiments of the present disclosure. Specifically, FIG. 2B illustrates various substeps that may be performed in step 204, in which a particular image of the one or more images is preprocessed to generate a particular image of the one or more preprocessed images. In this manner, the steps illustrated in FIG. 2B may be repeated for each image (or portion of an image) captured in step 202.

[0043] In some embodiments, step 204 includes step 208, in which one or more trajectory matrices are created (eg, from a particular image or ROI thereof).

[0044] An image can be represented as follows:

number

[0045] Step 208 may include generating a trajectory matrix, which is associated with any direction in the image that corresponds to the periodic orientation of features of the target 104 .

[0046] As an example, in the case where the target 104 contains periodic features oriented along the rows of the image, for any kth row, the trajectory matrix τ k can be generated as follows:

number

Equation

[0047] As described in detail throughout this disclosure, the selection of the embedding dimension M can affect both the nature of the decomposition and the calculation speed. For example, if the embedding dimension M is made equal to the number of pixels in a row of the image I Orig (or its ROI), a simple decomposition of the image (e.g., SVD) can be obtained. As another example, if the embedding dimension M is made equal to the pitch (in pixel units) of the target feature, reconstruction components can be provided based on the correlation between segments of length M both within and between rows.

[0048] As another example, for one row of an image or in the case of a pure 1D image, a single orbit matrix can be generated. In this case, the grand orbit matrix G is equivalent to a single orbit matrix. As another example, an orbit matrix can be generated for the average of two or more rows of an image. For example, a single orbit matrix can represent the data of the entire image (or a selected ROI). In another example, averaging every x rows can reduce the overall size of the associated large orbit matrix G.

[0049] Note that the description of the target 104 having periodic features oriented along the rows of the image is merely illustrative and not limiting. In the case where the target 104 has periodic features oriented along the columns of the image, an orbit matrix corresponding to any column or the average of columns of the image can be generated.

[0050] Also, the above equations (2)-(3) are generated using the embedding dimension along a single direction. In the case where the target 104 has periodicity along two directions (e.g., rows and columns of an image), one or more orbital matrices can be generated using a two-dimensional window that provides embedding along two directions. Such a generalization can be used for two-dimensional targets without translational invariance. For example, in this case, the large orbital matrix G can be given by the following equation. [Number] Here, each matrix τ i is given as an orbital matrix of window size (x×y) by the embedding dimensions M and N along the row and column directions respectively, where (1 < M < m) and (1 < N < n). Similar to the explanation for the 1D case, the embedding dimension of each matrix τ i can be defined based on the pitch (in pixel units) of the structure of the target in the relevant direction. In this form, the large orbital matrix G can have the characteristics of a Hankel block-Hankel matrix.

[0051] Additionally, of course, the specific descriptions of the orbital matrix τ and the large orbital matrix G in equations (2)-(4) are provided for illustrative purposes only and should not be construed as limiting. The orbital matrix τ and / or the large orbital matrix G can be created using any technique suitable for use in any decomposition (such as factorization) method. For example, the orbital matrix τ and / or the large orbital matrix G can be created in various ways while maintaining the completeness of the generated vector space.

[0052] In some embodiments, step 204 includes step 210, in which reconstruction components related to a specific image are generated from one or more orbital matrices using a decomposition method.

[0053] Any suitable decomposition method may be utilized, such as, but not limited to, SVD, principal component analysis, independent component analysis, or some eigenvalue-based decomposition method. In some embodiments, the reconstruction vectors represent different spectral components of the signal vector (e.g., different length scales of the signal vector). In this manner, the grand trajectory matrix G (or a single trajectory matrix τ) may be expressed as a sum of the reconstruction vectors. Furthermore, as described in more detail below, a preprocessed image may be generated based on the sum of a subset of the reconstruction vectors.

[0054] Equations (5)-(7) below and Figures 4A-4C provide a non-limiting example of the use of the SVD method in the case of a 1D target (e.g., using a grand orbit matrix based on Equations (2)-(3)), although of course this is for illustrative purposes only, and the teachings can also be applied to the case of a 2D target (e.g., using a grand orbit matrix based on Equation (4)).

[0055] For example, in a non-limiting example involving an orbital matrix with n rows, by applying SVD to the grand orbital matrix G in equation (2), we obtain:

number

number

[0056] From equation (5), the reconstruction component R satisfies the following p can be generated.

number

[0057] For example, the matrix G p may each contain a reconstruction of the trajectory matrix, such that a reconstruction of the image rows (e.g., having length m) can be generated by operating on the diagonal (e.g., averaging the diagonal) of the corresponding trajectory matrix reconstruction, and the reconstructed rows can be combined to form the associated reconstruction component R p can be formed.

[0058] Referring generally to steps 208 and 210, the choice of embedding dimension M can affect both the nature of the decomposition and the speed of computation. The embedding dimension M is typically 1 ~ m (the size of the image I in pixels). Orig can take any value of

[0059] In some embodiments, the embedding dimension M is chosen to be equal to m (e.g., M=m). In this configuration, the image I is obtained by decomposing the large trajectory matrix G. Orig Furthermore, by selecting the embedding dimension, we can obtain the reconstruction components based on the correlation between the rows of the original image I Orig can be simply decomposed (e.g., by SVD). Such an implementation can be computed quickly and therefore can generate decompositions immediately for many applications.

[0060] In some embodiments, the embedding dimension M may be chosen to be different from m (e.g., M ≠ m), corresponding to a generalized decomposition. In this configuration, the large orbit matrix G may be decomposed to obtain reconstruction components based on correlations between M-length segments both within and between rows. In some embodiments, the embedding dimension M is chosen to be equal to the pitch of the periodic features of the target 104 (e.g., rounded up or down to an integer number of pixels). This pitch may be known when performing method 200. Such a configuration may be particularly advantageous because the resulting decomposition may be based on correlations between individual periods within a given row, not just between rows. Furthermore, in such an implementation, a relatively large large orbit matrix G may be formed, in which case the reconstruction components may be more statistically effective than a simple SVD implementation where M = m. As a result, the reconstruction components R p can effectively distinguish between features with length scales corresponding to a known pitch and other features with various length scales (such as noise or mura), although such implementations can be relatively computationally expensive.

[0061] In some embodiments, a generalized decomposition is applied to a limited data set to balance resolution performance and computational speed. For example, a generalized decomposition with M≠m (e.g., M is selected to be equal to the pitch of the periodic structure) may be applied to a single row of an image (or 1D measurement signal) or to an average of multiple rows. Such an implementation is computationally fast while still providing accurate reconstruction based on correlation along the measurement direction of the analyzed rows.

[0062] 2B, in some embodiments, step 204 includes step 212, in which a particular one of the one or more preprocessed images is generated based on a subset of reconstruction components that includes signals related to at least one of the one or more known pitches. For example, preprocessed image I pp can be given by the following formula:

Number

[0063] Next, referring to FIGS. 4A-4C, an illustration of method 200 according to one or more embodiments of the present disclosure is provided.

[0064] FIG. 4A is an image 402 of a periodic structure 302 according to one or more embodiments of the present disclosure. For example, image 402 may correspond to the original image I Orig generated by measurement subsystem 102. Further, there are significant non-uniformities in image 402, such that the contrast of periodic structure 302 is non-uniform across the entire image.

[0065] FIG. 4B is a series of images 404-412 (labeled R1-R5, respectively) corresponding to each reconstruction component by a decomposition method, related to image 402, according to one or more embodiments of the present disclosure. FIG. 4C is a graph of the spectrum of the eigenvalues of the large orbit matrix G related to FIGS. 4A and 4B according to one or more embodiments of the present disclosure. As shown in FIG. 4C, the intensity of the eigenvalues (and related reconstruction components) decreases rapidly. Thus, the first few eigenvalues (and related reconstruction components) may be significant, while the remaining ones correspond to noise.

[0066] Images 404-412 in Figure 4B correspond to the first five reconstructed components of image 402. These reconstructed components are associated with the first five eigenvalues ​​generated using SVD of the grand trajectory matrix G. The grand trajectory matrix G contains the trajectory matrix of the rows of image 402, and its embedding dimension M is chosen to be equal to the period (in pixels) of the periodic structure 302 (e.g., the generalized decomposition described above).

[0067] 4B, only a few of the reconstructed components contain significant signal with a length scale related to the pitch of the periodic structure 302. In this particular example, reconstructed components R2 and R3 contain high signal intensity at the pitch of the periodic structure 302 and can be used to generate a preprocessed, high-contrast image of the periodic structure 302 (e.g., in step 212) from which unwanted noise and / or irregularities have been at least partially removed. Reconstructed component R1 represents DC components (e.g., low spatial frequency components) of the target 104 and associated DC irregularities, which can adversely affect metrology measurements (e.g., but not limited to, overlay measurements). The remaining reconstructed components (here, R i>3 ) contain noise and / or irregularities with higher spatial frequencies that can further adversely affect metrology measurements.

[0068] In some cases, the grand orbit matrix G (or the original image I Orig) in a more efficient manner than that provided by the reconstruction components. As an example, FIG. 4C shows that the second and third eigenvalues ​​are degenerate or nearly degenerate. This is also evident in FIG. 4B, where reconstruction components R2 and R3 contain similar spatial frequencies. Any suitable decomposition and / or separation method can be applied to obtain the reconstruction components overall and / or to obtain the reconstruction components used to generate the preprocessed image (e.g., step 212). Rotation methods that can be used to generate the reconstruction vectors include, but are not limited to, varimax rotation, quartimax rotation, or equimax rotation.

[0069] Further, it should be noted that equations (3)-(5) and Figures 4A-4C correspond to non-parametric decompositions. In some embodiments, step 204 includes performing a parametric decomposition and regression to provide a reconstruction vector and generate a pre-processed image. Such techniques are used to generate a pre-processed image from the original image I Orig , thus providing a generalized or generic technique suitable for a variety of images with various noise and / or unevenness problems. Furthermore, such a technique can be used to generate adaptive bases for the original image I. Orig From this, amplitude modulated sinusoidal components can be extracted that have frequencies different from those provided by standard Fourier decomposition.

[0070] The subset of reconstruction vectors used to generate the preprocessed image can be selected based on any criteria. In some embodiments, the selection of the subset of reconstruction components used to generate a particular preprocessed image is based on the OrigThe selection of the subset of reconstructed components may be based on individual analysis of the reconstructed signals and / or a spectral map of eigenvalues ​​obtained from the periodic structure 302. For example, the selection of the subset of reconstructed components may be based on any combination of signal intensities of reconstructed components having a known pitch of the periodic structure 302 (e.g., intensities of reconstructed components having spatial frequencies at or near the known pitch as determined by Fourier or other spectral analysis methods) and / or eigenvalue intensities (e.g., in a spectral map such as that shown in FIG. 4C). Furthermore, such selection may be automated so that user intervention is not required. For example, the signal intensities and / or eigenvalue intensities of reconstructed components having a known pitch may be compared to a preselected threshold, which may be generated based on preliminary experiments and / or simulations.

[0071] In some embodiments, the subset of reconstruction components used to generate a particular preprocessed image is determined based on prior selection or training. This may be the case if images of each target 104 of a common design across an entire sample 106, or across multiple samples 106 in a single lot, may exhibit similar noise and / or mura characteristics, and therefore, particular reconstruction components (such as R2 and R3 in the example of FIGS. 4A-4C ) that provide a strong signal at the known pitch of the periodic structures 302 on these targets 104 may be consistent, or at least retain a measurable pattern. Therefore, it may be insufficient to identify desired reconstruction components during the training phase and then utilize them for additional targets 104 without further analysis during the testing phase. For example, the testing phase may correspond to the first portion of targets 104 on a particular sample 106. As another example, the testing phase may correspond to a set of one or more training samples 106 that are analyzed prior to deployment in a production environment. It is contemplated herein that such training and testing techniques reduce computational load during deployment, thereby enabling efficient (e.g., near-instant) generation of preprocessed images. In this way, even computationally intensive techniques (such as, but not limited to, generalized decompositions such as M≠m described herein above) can be implemented in an efficient manner during the testing phase.

[0072] 2A-2B, it is contemplated herein that the systems and methods disclosed herein may be suitable for images exhibiting multiple harmonic components (e.g., various pitches p of the periodic structure 302 in spatial frequency space and / or non-trivial harmonics of any pitch). Specifically, the decomposition techniques disclosed herein can naturally identify dominant spatial frequencies in an image based on the image data itself and then provide reconstructed components that include these spatial frequencies. That is, the decomposition techniques can naturally provide reconstructed components with an adaptive basis based on the image data itself.

[0073] As a result, the systems and methods disclosed herein may enable filtering of noise and unevenness even in the presence of non-trivial harmonics. For example, a preprocessed image may be generated (e.g., step 212) based on any combination of reconstruction components that includes desired harmonics, or more generally, spatial frequencies, and that excludes sources of noise or unevenness as described herein.

[0074] Additionally, in some embodiments, one or more preprocessed images may be generated that capture desired spatial frequencies and / or filter out undesired spatial frequencies. For example, a preprocessed image may be generated that purposely filters out certain harmonics (e.g., to capture fundamental spatial frequencies). As another example, in cases where the target includes various instances of periodic structures 302 with different pitches (e.g., non-overlapping or overlapping Moiré configurations), a preprocessed image may be generated that captures structures with specific pitches. Additionally, various preprocessed images may be generated that capture structures with various pitches. In this manner, features with various pitches may be considered separately. Accordingly, such multiple preprocessed images may be used in combination to generate one or more metrology measurements (e.g., step 206).

[0075] 2A, step 206 may include generating metrology measurements based on the preprocessed image using any suitable technique. For example, any technique or algorithm suitable for generating image-based metrology measurements (such as for the original image) may be applied to the preprocessed image generated in step 204. In this manner, step 204 may improve the quality of the metrology measurements based on any number of metrics, such as, but not limited to, accuracy, sensitivity, and robustness.

[0076] For example, a reconstructed signal R containing data related to the length scale of a known pitch pPreprocessing techniques based on decomposition and selection provide high contrast images of periodic features and can effectively filter out unwanted signals (e.g., related to noise or irregularities) that can adversely affect image-based metrology measurements.

[0077] As an example, the systems and methods disclosed herein may be particularly well-suited for non-limiting applications in overlay metrology. For example, image-based overlay metrology techniques typically employ one of two approaches. The first approach is based on a Fourier series decomposition regression (e.g., targeting harmonics generated by the periodic structure 302) and a cross-correlation filter. However, even simple linear trends and / or constant term variations (such as in the case of a Fourier series decomposition) can contribute significant errors to the overlay measurement. The second approach is based on comparing the phases of different instances of the periodic structure 302 in one or more images. While such phase-based techniques may be relatively robust in nature to the types of variations that are detrimental to cross-correlation techniques (e.g., up to second order in local expansions), they may critically require that only one harmonic be dominant in the kernel (e.g., image). Therefore, the presence of any other harmonics can result in significant errors in the overlay measurement. Generally speaking, typical image-based overlay measurement techniques are also robust to mura and target noise, but cannot accommodate multiple simultaneous harmonics in the signal (e.g., image).

[0078] However, the systems and methods disclosed herein are suitable for filtering out noise and / or image irregularities even in the presence of harmonics in the signal (e.g., harmonics in the spatial frequency space due to edges of the periodic structure 302). As such, the systems and methods disclosed herein may be suitable for improving overlay measurements generated using any image-based technique, including, but not limited to, cross-correlation or phase-based techniques.

[0079] Method 200 may further include controlling one or more processing tools based on the metrology measurements generated in step 206. For example, metrology data associated with any number of targets 104 distributed throughout one or more specimens 106 may be used to generate correctable amounts for controlling processing tools during the fabrication of additional specimens 106. As one example, metrology data for specimens 106 within a lot may be used to generate feedback correctable amounts to control the lithography exposure of subsequent specimens 106 within the same lot. As another example, metrology data for specimens 106 within a lot may be used to generate feedforward correctable amounts to compensate for any deviations and control the lithography exposure of subsequent lithography stages of the same or similar specimens 106.

[0080] 1A-1C, various aspects of the metrology system 100 according to one or more embodiments of the present disclosure will now be described in detail.

[0081] In some embodiments, the metrology subsystem 102 is an optical subsystem that generates metrology measurements by illuminating a target 104 with light and collecting light from the target 104 as the basis for the measurements. Figure 1B is a conceptual diagram of the optical metrology subsystem 102, in accordance with one or more embodiments of the present disclosure.

[0082] The optical metrology subsystem 102 may generally include an illumination source 116 for generating an illumination beam 118 having a desired spectral or temporal profile, an illumination path 120 for directing the illumination beam 118 toward the target 104, an objective lens 122 or other suitable components for collecting light from the target 104 (referred to herein as sample light 124), a detector 126, and a collection path 128 for directing the sample light 124 toward 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. The optical elements 132 may include, for example, but are not limited to, one or more polarizers, one or more beam splitters 134, one or more homogenizers, or one or more apodizers.

[0083] The optical metrology subsystem 102 can generate metrology measurements using any suitable technique. In some embodiments, the optical metrology subsystem 102 generates metrology measurements based on an image of the target 104 (e.g., an image of a field plane, where the detector 126 is in a field plane conjugate to the sample 106). In some embodiments, the optical metrology subsystem 102 generates metrology measurements using a scatterometry technique based on collected diffraction orders (e.g., measured with the detector 126 in a pupil plane). Furthermore, the sample 106 may be stationary or moving during the measurements.

[0084] In some embodiments, the metrology subsystem 102 is a particle beam subsystem that generates metrology measurements by irradiating the target 104 with a particle beam (such as an electron beam, an ion beam, or a neutral particle beam) and collecting any combination of particles or light from the target 104 as the basis for the measurements. Figure 1C is a conceptual diagram of the particle beam metrology subsystem 102 in accordance with one or more embodiments of the present disclosure.

[0085] The particle beam metrology subsystem 102 may include a particle source 136 (e.g., an electron beam source or an ion beam source), such that the illumination beam 118 comprises a particle beam (e.g., an electron beam or a particle beam). 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. The illumination path 120 may include one or more particle beam lenses 138 (e.g., electrostatic lenses, magnetic lenses, monopotential lenses, or bipotential lenses) or other beam manipulation elements (not shown) for controlling one or more characteristics of the illumination beam 118, such as, but not limited to, one or more astigmatism correctors or aberration control elements. The particle beam metrology subsystem 102 may further include a collection path 128 for directing any combination of particles or light to at least one detector 126. For example, detector 126 may include an electron collector (such as a secondary electron collector or a backscattered electron detector). As another example, detector 126 may include a photon detector (such as a light detector, an x-ray detector, or a scintillation element coupled to a photomultiplier tube (PMT) detector) for detecting electrons and / or photons from the sample surface. As an example, FIG. 1C shows detector 126 positioned to capture secondary electrons emitted from target 104.

[0086] The subject matter described herein sometimes illustrates various components contained within or connected to other components. It should be understood that such configurations described herein are merely exemplary, and that in fact many other configurations that achieve the same functionality may be implemented. In a conceptual sense, any arrangement of components to achieve the same functionality is effectively “associated” such that the desired functionality is achieved. Thus, any two components herein that combine to achieve a particular function may be considered to be “associated” with each other such that the desired functionality is achieved, regardless of configuration or intermediate components. Similarly, any two components so associated may also be considered to be “connected” or “coupled” to each other to achieve the desired functionality, and any two components so associated may also be considered to be “couplable” to each other to achieve the desired functionality. Examples of combinable include, but are not limited to, physically interactable and / or physically interacting components, wirelessly interactable and / or wirelessly interacting components, and / or logically interactable and / or logically interacting components.

[0087] The present disclosure and many of its attendant advantages will be understood from the foregoing description, and it will be apparent that various changes in form, construction, and arrangement of elements may be made without departing from the disclosed subject matter or sacrificing all of its important advantages. The described forms are illustrative only, and it is the intent of the following claims to embrace and include all such modifications. It will further be understood that the invention is defined by the appended claims.

Claims

1. It is a system, A controller comprising one or more processors configured to execute program instructions, wherein the one or more processors execute a measurement recipe by the program instructions, and the execution of the measurement recipe is Receiving one or more images of a measurement target containing one or more periodic features with one or more known pitches, The process involves preprocessing one or more images using a decomposition method to generate one or more preprocessed images, wherein preprocessing a specific image among the one or more images is performed. Creating one or more orbital matrices from the aforementioned specific images, Using the aforementioned decomposition method, a reconstructed component related to the specific image is generated from the one or more orbital matrices. From the generated reconstructed components, select a reconstructed component that includes a signal relating to at least one of the one or more known pitches, wherein the selected reconstructed component forms a subset of the reconstructed components. A specific image from the one or more preprocessed images is generated based on the subset of the reconstructed component which includes a signal relating to at least one of the one or more known pitches, This includes, To generate one or more measurement values ​​for the measurement target based on the one or more pre-processed images, The controller A system that includes this.

2. Using the aforementioned decomposition method to generate the reconstructed components related to the specific image from one or more orbital matrices is, Using the singular value decomposition (SVD) method, generate the reconstructed components related to the specific image from one or more orbital matrices. The system according to claim 1, including the following:

3. Using the aforementioned decomposition method to generate the reconstructed components related to the specific image from one or more orbital matrices is, To generate the reconstructed components related to the specific image from one or more orbital matrices using at least one of principal component analysis or independent component analysis, The system according to claim 1, including the following:

4. The aforementioned specific image [Math 1] Defined as follows, Here, n represents a row of the specific image, m represents a column of the specific image, one or more orbital matrices are associated with one or more rows of the specific image, and one or more orbital matrices have an embedding dimension M such that (1 < M ≤ m), The system according to claim 1.

5. The system according to claim 4, wherein M = m.

6. The system according to claim 4, wherein M ≠ m.

7. The system according to claim 6, wherein M corresponds to a value obtained by rounding one of the one or more known pitches (in pixels) to an integer.

8. The one or more orbital matrices mentioned above [Math 2] This includes k = 1, 2, ..., n, and the large orbit matrix G is [Math 3] Formed in such a way, generating the reconstructed components related to the specific image from the one or more orbital matrices using the decomposition method is, Using the aforementioned decomposition method, generate the reconstructed components related to the specific image from the large orbit matrix. The system according to claim 4, including the system described in claim 4.

9. The system according to claim 4, wherein the orbit matrix includes a single orbit matrix associated with one of the rows of the particular image.

10. The system according to claim 4, wherein the trajectory matrix includes a single trajectory matrix associated with the mean of at least two rows of the particular image.

11. The aforementioned specific image, [Math 4] It is defined as follows, where n represents a row of the particular image, m represents a column of the particular image, and the large orbit matrix G is derived from one or more orbit matrices. [Math 5] The system according to claim 1, wherein each matrix τ is one of the one or more trajectory matrices with embedding dimensions M and N along the row and column directions of the particular image, respectively, (1 < M ≤ m) and (1 < N ≤ n).

12. The system according to claim 11, wherein M corresponds to a value (in pixels) obtained by rounding one of the one or more known pitches along the row to an integer, and N corresponds to a value (in pixels) obtained by rounding one of the one or more known pitches along the column to an integer.

13. The system according to claim 1, wherein a subset of the reconstruction components, which includes a signal relating to at least one of the one or more known pitches, is determined for each of the one or more images.

14. The system according to claim 1, wherein a subset of the reconstructed components, which includes a signal relating to at least one of the one or more known pitches, is determined based on one or more training images.

15. The measured value is, Overlay measurement The system according to claim 1, including the following:

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

17. It is a system, Measurement subsystem and A controller communicatively coupled to the measurement subsystem, the controller comprising one or more processors configured to execute program instructions, the one or more processors executing a measurement recipe by the program instructions, and the execution of the measurement recipe is Receiving one or more images of a measurement target containing one or more periodic features with one or more known pitches from the measurement subsystem, The process involves preprocessing one or more images using a decomposition method to generate one or more preprocessed images, wherein preprocessing a specific image among the one or more images is performed. Creating one or more orbital matrices from the aforementioned specific images, Using the aforementioned decomposition method, a reconstructed component related to the specific image is generated from the one or more orbital matrices. From the generated reconstructed components, select a reconstructed component that includes a signal relating to at least one of the one or more known pitches, wherein the selected reconstructed component forms a subset of the reconstructed components. A specific image from the one or more preprocessed images is generated based on the subset of the reconstructed component which includes a signal relating to at least one of the one or more known pitches, This includes, To generate one or more measurement values ​​for the measurement target based on the one or more pre-processed images, The controller A system that includes this.

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

19. The measurement subsystem, Optical measurement and imaging subsystem, The system according to claim 17, including the system described in claim 17.

20. The measurement subsystem, Particle beam imaging subsystem The system according to claim 17, including the system described in claim 17.

21. It is a method, Receiving one or more images of a measurement target containing one or more periodic features with one or more known pitches, The process involves preprocessing one or more images using a decomposition method to generate one or more preprocessed images, wherein preprocessing a specific image among the one or more images is performed. Creating one or more orbital matrices from the aforementioned specific images, Using the aforementioned decomposition method, a reconstructed component related to the specific image is generated from the one or more orbital matrices. From the generated reconstructed components, select a reconstructed component that includes a signal relating to at least one of the one or more known pitches, wherein the selected reconstructed component forms a subset of the reconstructed components. A specific image from the one or more preprocessed images is generated based on the subset of the reconstructed component which includes a signal relating to at least one of the one or more known pitches, This includes, To generate one or more measurement values ​​for the measurement target based on the one or more pre-processed images, Methods that include...

22. Using the aforementioned decomposition method to generate the reconstructed components related to the specific image from one or more orbital matrices is, Using the singular value decomposition (SVD) method, generate the reconstructed components related to the specific image from one or more orbital matrices. The method according to claim 21, including the method described in claim 21.

23. Using the aforementioned decomposition method to generate the reconstructed components related to the specific image from one or more orbital matrices is, To generate the reconstructed components related to the specific image from one or more orbital matrices using at least one of principal component analysis or independent component analysis, The method according to claim 21, including the method described in claim 21.

Images