Image preprocessing for overlay metrology using decomposition techniques

Abstract

A system may include a controller to: receive one or more images including metrology targets having periodic characteristics of one or more known pitches; pre-processing the one or more images using a decomposition technique to produce one or more pre-processed images; and generate one or more metrology measurements of the metrology target based on the one or more preprocessed images. Preprocessing a particular image of the one or more images may include: constructing one or more trajectory matrices from the particular image; generating a reconstruction component associated with the particular image from the one or more trajectory matrices using the decomposition technique; and generating a particular one of the one or more pre-processed images by based on a subset of the reconstructed components including a signal having at least one of the one or more known pitches.

Description

[0001] CROSS REFERENCE TO RELATED APPLICATIONS

[0002] This application claims the benefit of U.S. Provisional Application No. 63 / 410,233, filed on September 27, 2022, titled “ON PRE-PROCESSING MEASUREDIMAGES AND SIGNALS FOR ACCURATE OVERLAY EXTRACTION,” with Nireekshan K. Reddy and Vladimir Levinski as inventors, under 35 U.S.C. §119(e), the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present disclosure relates generally to overlay metrology, and more particularly, to image preprocessing for overlay metrology. Background Art

[0004] Many metrology techniques rely on images of periodic structures on a sample. However, the collected images may suffer from various sources of noise and inhomogeneity whose length scales differ from the periodicity of the structures of interest, which may negatively affect the measurement, 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 that address the above-mentioned deficiencies. Summary of the invention

[0005] According to one or more illustrative embodiments of the present 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 of a metrology target including periodic features 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 metrology measurements of the metrology target based on the one or more preprocessed images. In another illustrative embodiment, preprocessing a specific image of the one or more images includes: constructing one or more trajectory matrices from the specific image; generating a reconstruction component associated with the specific image from the one or more trajectory matrices using the decomposition technique; and generating a specific one of the one or more preprocessed images by based on a subset of the reconstruction components including a signal having at least one of the one or more known pitches.

[0006] According to one or more illustrative embodiments of the present 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 one or more images of a metrology target including periodic features having one or more known pitches from the metrology subsystem. 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 metrology measurements of the metrology target based on the one or more preprocessed images. In another illustrative embodiment, preprocessing a specific image of the one or more images includes: constructing one or more trajectory matrices from the specific image; generating a reconstruction component associated with the specific image from the one or more trajectory matrices using the decomposition technique; and generating a specific one of the one or more preprocessed images by based on a subset of the reconstruction components including a signal having at least one of the one or more known pitches.

[0007] According to one or more illustrative embodiments of the present disclosure, a method is disclosed. In one illustrative embodiment, the method includes receiving one or more images of a metrology target including periodic features 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 of the one or more images includes: constructing one or more trajectory matrices from the specific image; generating a reconstruction component associated with the specific image from the one or more trajectory matrices using the decomposition technique; and generating a specific one of the one or more preprocessed images by based on a subset of the reconstruction components including a signal having at least one of the one or more known pitches. In another illustrative embodiment, the method includes generating one or more metrology measurements of the metrology target based on the one or more preprocessed images.

[0008] It should be understood that both the foregoing general description and the following detailed description are exemplary and explanatory 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. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Those skilled in the art may better appreciate the numerous advantages of the present disclosure by referring to the accompanying drawings.

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

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

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

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

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

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

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

[0017] Figure 4B is a series of images corresponding to reconstructed components associated with an image using a decomposition technique in accordance with one or more embodiments of the present disclosure.

[0018] Figure 4C According to one or more embodiments of the present disclosure Figure 4A and 4B Plot of the spectrogram of the eigenvalues ​​of the associated large trajectory matrix. DETAILED DESCRIPTION

[0019] Reference will now be made in detail to the disclosed subject matter illustrated in the accompanying drawings. The present disclosure has been particularly shown and described with respect to certain embodiments and specific features thereof. The embodiments described herein should be regarded as illustrative rather than restrictive. It should be readily apparent to those skilled in the art that various changes and modifications in form and details may be made without departing from the spirit and scope of the present disclosure.

[0020] Embodiments of the present disclosure relate to systems and methods for providing preprocessing of images having periodic features using matrix decomposition (e.g., factorization) techniques. The systems and methods disclosed herein may be suitable for, but not limited to, preprocessing images of periodic targets used in metrology applications (e.g., but not limited to, superposition metrology).

[0021] It is contemplated herein that many image-based metrology techniques may be sensitive to noise and / or non-uniformity present in an image. Typical approaches for providing accurate measurements focus on hardware-based techniques to avoid such noise and / or non-uniformity. However, completely removing such 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 may be desirable to pre-process the image prior to generating the image-based measurements, which may allow 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, a matrix decomposition technique (such as, but not limited to, singular value decomposition (SVD) or a variant thereof) may be used to generate reconstruction components associated with the image based on the trajectory matrix, wherein the reconstruction components may represent a decomposition of the image into different spectral components (e.g., different length scales). In this way, the reconstruction components may represent portions of the image corresponding to different length scales. Then, a pre-processed (e.g., filtered) image may be generated based on a subset of the reconstruction components corresponding to known pitches of superimposed objects in the image. This pre-processed image may include a high contrast representation of a periodic superimposed object, wherein noise and / or non-uniformity on other length scales are effectively removed or suppressed.

[0023] Upon careful consideration, this technique can provide robust and general filtering of images of periodic targets. In particular, the use of decomposition techniques to generate reconstruction vectors can identify the main length scales (e.g., spectral components) in the image based on the image itself to facilitate efficient and accurate filtering of data at unwanted length scales. It should be recognized that a general metrology model incorporating a decomposition of a trajectory matrix containing metrology values ​​from a target distributed across samples is described in U.S. Patent Application No. 17 / 995,385, filed on 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 wherein these mathematical decompositions are applied to different data sets at different stages of the metrology process. For example, the systems and methods disclosed herein apply decomposition techniques to identify and isolate the main length scales in an image associated with periodic features of interest as a preprocessing step prior to generating metrology measurements. The metrology data generated from multiple targets across the samples may then be modeled or further processed using any suitable technique, such as, but not limited to, the techniques described in US Patent Application No. 17 / 995,385.

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

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

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

[0027] Additional embodiments of the present disclosure relate to process control utilizing metrology data generated based on pre-processed images as disclosed herein. In this manner, metrology data may be used directly or indirectly for feedback and / or feed-forward control of any number of process tools, such as, but not limited to, lithography tools (e.g., scanners and / or steppers), deposition tools, etching tools, or polishing tools. As an illustration, metrology data of samples in a batch may be used to generate feedback correction values ​​to control lithography exposure of subsequent samples in the same batch. As another illustration, metrology data of samples in a batch may be used to generate feed-forward correction values ​​to control lithography exposure of the same or similar samples in subsequent lithography steps to account for any deviations in the current exposure.

[0028] Reference Figures 1A to 4C , describing in more detail a system and method for preprocessing an image of periodic features according to one or more embodiments of the present disclosure.

[0029] Figure 1A is a block diagram of a metrology system 100 for generating and / or utilizing pre-processed images in accordance with one or more embodiments of the present disclosure.

[0030] In an embodiment, the metrology system 100 includes a metrology subsystem 102 adapted to generate metrology measurements of a target 104 (eg, a metrology target) distributed across one or more samples 106 .

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

[0032] The metrology measurements of the sample 106 generated by the metrology subsystem 102 may provide any type of data and may be generated using any technique known in the art. In some embodiments, the metrology measurements generated by the metrology subsystem 102 are overlay measurements that characterize the registration (or registration error) between different photolithography exposures on one or more layers of the sample 106. In some embodiments, the metrology measurements generated by the metrology subsystem 102 characterize the conditions of the photolithography exposures, such as, but not limited to, the focus position or illumination dose of the sample 106. In some embodiments, the metrology measurements generated by the metrology subsystem 102 characterize additional aspects of the manufacturing process, such as, but not limited to, an etching step or a polishing step.

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

[0034] The metrology subsystem 102 may be configured to implement 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 associated with a number of regions of the sample 106 to be characterized (e.g., targets), the placement of targets, and / or the order of measurement of such targets. Additionally, in applications where targets are designed for measurement purposes (e.g., metrology targets, overlay 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. As an 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. As 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 metrology measurements based on the generated data.

[0035] In an embodiment, the metering system 100 includes a controller 108 communicatively coupled to any components therein. The controller 108 may include one or more processors 110. For example, the 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, the one or more processors 110 may include any microprocessor type device configured to execute algorithms and / or instructions.

[0036] The one or more processors 110 of the controller 108 may include any processor or processing element known in the art. For the purposes of this disclosure, the term "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, the one or more processors 110 may include any device configured to execute algorithms and / or instructions (e.g., program instructions stored in a 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 a program configured to operate the metering system 100 or operate in conjunction with the metering system 100, as described throughout this disclosure. In addition, different subsystems of the metering system 100 may include processors or logic elements suitable for implementing at least a portion of the steps described in this disclosure. Therefore, the above description should not be interpreted as limiting the embodiments of the present disclosure but is merely illustrative. Additionally, the steps described throughout this disclosure may be performed by a single controller or, alternatively, by multiple controllers. Additionally, the controller 108 may include one or more controllers housed in a common housing or multiple housings. In this manner, any controller or combination of controllers may be individually packaged as a module suitable for integration into the metering system 100.

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

[0038] The controller 108 may direct (e.g., via control signals) and / or receive data from any component or subsystem of the metrology system 100, such as, but not limited to, the metrology subsystem 102, as well as other systems such as one or more process tools (e.g., a lithography tool or the like) used to fabricate the sample 106. The controller 108 may be further configured to perform any of the various process steps described throughout the present disclosure, such as, but not limited to, implementing a metrology recipe, pre-processing one or more images, or generating metrology measurements based on pre-processed images.

[0039] In some embodiments, the metering 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 desktop computers, laptop computers, tablet computers, and the like. In some embodiments, the user interface 114 includes a display for displaying data of 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 implementation in the present 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] Reference Figures 2A to 4C , describes in more detail techniques for modeling metrology measurements according to one or more embodiments of the present disclosure.

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

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

[0043] The image in step 202 may be generated using any suitable means, such as but not limited to metrology subsystem 102. Additionally, the image may be generated using any suitable optical imaging technique, including but not limited to brightfield or darkfield imaging.

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

[0045] Figure 3 is a simplified top view image of a target 104 including a periodic structure 302 according to one or more embodiments of the present disclosure. In particular, Figure 3 The periodic structure 302 is shown as line / space features having a pitch p.

[0046] In some embodiments, target 104 or a unit thereof may include a single instance of periodic structure 302. In some embodiments, target 104 or a unit thereof may include multiple instances of periodic structure 302 in overlapping or non-overlapping configurations, where different instances 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, the target 104 may include different instances of such a periodic structure 302 on one or more sample layers associated with different lithographic exposures. In this way, an overlay measurement associated with a measurement of relative registration between features associated with different lithographic exposures may be provided based on the relative positions of the different instances of the periodic structure 302 (e.g., generated in step 206). As an illustration, the target 104 may include non-overlapping instances of the periodic structure 302 having the same or different pitches. For example, the target 104 may be characterized as an advanced imaging metrology (AIM) target 104. As another illustration, the target 104 may include one or more regions of overlapping instances of the periodic structure 302, which may be characterized as a grating-on-grating structure. In the case of different pitches, such regions may also be referred to as Moiré structures and may further exhibit 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 (eg, rAIM) target 104 .

[0048] In some embodiments, superposition measurements may be generated (e.g., in step 206) based on differences between centers of symmetry of different regions of target 104 (e.g., differences between centers of symmetry of different instances of periodic structure 302, different instances of moiré structures, or the like).

[0049] Figure 2B is a flow chart illustrating additional steps performed in method 200 according to one or more embodiments of the present disclosure. In particular, Figure 2B Depicts various sub-steps that may be performed in step 204 when preprocessing a particular one of the one or more images to produce a particular one of the one or more preprocessed images. In this manner, the preprocessing process may be repeated for each of the images (or portions of the images) captured in step 202. Figure 2B The steps described in .

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

[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. Orig , may correspond to an entire image (e.g., an image generated by metrology subsystem 102) or a ROI thereof. OrigThe ROI may correspond to a ROI that includes a central portion of the target 104 (or a cell thereof) that includes the periodic structure of interest. As an illustration, the ROI may be selected to avoid the edges of regions of the periodic structure that may be more likely to experience manufacturing defects.

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

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

[0056]

[0057] in It is satisfying The embedding dimension of this matrix can be characterized as a transfer matrix or a Hankel matrix and can have the property that the elements on the diagonal i+j=C are equal. In addition, the trajectory matrix τ k Arranged as a large trajectory matrix Decomposed, it can be written as:

[0058]

[0059] As will be described in more detail throughout this disclosure, the embedding dimensionality The choice of can affect the nature of the decomposition and the speed of computation. For example, the embedding dimension Set equal to image I Orig The number of pixels in a row of the image (or its ROI) can enable a simple decomposition (e.g., SVD) of the image. As another example, embedding dimension The pitch of target features set in pixels can be based on both the length within a row and between rows. The correlation between the fragments is used to provide the reconstruction component.

[0060] As another example, a single trajectory matrix may be generated for a single row of an image or in the case of a pure 1D image. In this case, the trajectory matrix is equivalent to a single trajectory matrix. As another example, a trajectory matrix may be generated for the average of two or more rows of an image. For example, a single trajectory matrix may represent data in the entire image (or a selected ROI). In another example, every x rows may be averaged to reduce the associated large trajectory matrix The overall size.

[0061] It should be noted that the description of the target 104 having periodic features oriented along the rows of the image is illustrative only and not limiting. In the case where the target 104 has periodic features oriented along the columns of the image, a trajectory matrix corresponding to any column or the average value of the columns of the image can be generated.

[0062] Additionally, the above equations (2)-(3) are generated with embedding dimensions along a single direction. In the case where the object 104 has periodicity along two directions (e.g., rows and columns of an image), one or more trajectory matrices may be generated using a two-dimensional window that provides embedding along both directions. This generalization may be used for two-dimensional objects that are not translationally invariant. For example, in this case, the large trajectory matrix It can be written as:

[0063]

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

[0065] In addition, it should be understood that the trajectory matrix τ and the large trajectory matrix in equations (2) to (4) are The specific description of is provided for illustrative purposes only and should not be construed as limiting. The trajectory matrix τ and / or the large trajectory matrix Any technique suitable for use with any decomposition (eg, factorization) technique may be used to construct. For example, the trajectory matrix τ and / or the large trajectory matrix It can be constructed in various ways while preserving the integrity of the vector space spanned.

[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 a decomposition technique.

[0067] Any suitable decomposition technique may 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 vectors describe different spectral components of the signal vector (e.g., different length scales of the signal vector). In this way, the large trajectory matrix (or a single trajectory matrix τ) may be represented as a sum of reconstruction vectors. Additionally, as will be described in more detail below, a pre-processed image may be generated based on a sum of a subset of reconstruction vectors.

[0068] The following equations (5) to (7) and Figures 4A to 4C A non-limiting illustration of using the SVD technique in the case of a 1D target (e.g., with a large trajectory matrix based on equations (2) to (3)) is provided. However, it should be understood that this is for illustrative purposes only, and the teachings can be extended to the case of a 2D target (e.g., with a large trajectory matrix based on equation (4)).

[0069] For example, for the non-limiting example of a trajectory matrix containing n rows, SVD is applied to the large trajectory matrix of equation (2) Available:

[0070]

[0071] where Σ is the The singular values ​​σ 1 …σ p The diagonal matrix of (in decreasing order from largest to smallest), where is the covariance matrix In addition, The eigenvectors of form the columns of the matrix V, and The eigenvectors of form the columns of the matrix U. Decomposition supply Eigenvalues ​​and associated reconstruction of the trajectory matrix τ.

[0072] According to equation (5), the reconstruction component R can be generated to satisfy the following equation: 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) of .

[0075] For example, the matrix may each comprise a reconstructed version of the trajectory matrix. According to this, a reconstructed version of a row of the image (e.g., having length m) may be generated by a diagonal operation (e.g., a diagonal average or the like) of a corresponding reconstructed version of the trajectory matrix, wherein the reconstructed rows may be combined to form associated reconstructed components

[0076] Generally referring to steps 208 and 210, the embedding dimension The choice of can affect both the nature of the decomposition and the computational speed. Usually, it can have 1 and m (image in pixels I orig The length of the row).

[0077] In some embodiments, the embedding dimension is chosen to be equal to m (e.g., ). In this configuration, the large trajectory matrix The decomposition can be based on image I Orig The correlation between the rows of provides the reconstruction component. In addition, this choice of embedding dimension can achieve the original image I orig This implementation can be computationally faster, so that the decomposition can be produced quickly in many applications.

[0078] In some embodiments, the embedding dimension is chosen to be different from m (e.g., ) and can correspond to a generalized decomposition. In this configuration, the large trajectory matrix The decomposition can be based on the length of both the line and the length between lines. In some embodiments, the embedding dimension is selected to be equal to the pitch of the periodic features of target 104 (e.g., rounded up or down to an integer number of pixels), which may be known when implementing method 200. This configuration may be particularly advantageous because the resulting decomposition may be based on correlations between different periods in a given row and between rows. Additionally, this implementation may provide a relatively large trajectory matrix , where the reconstruction components are comparable The simpler SVD implementation of is statistically more efficient. Therefore, the reconstruction component Features having a length scale corresponding to a known pitch can be effectively distinguished from other features having a different length scale (eg, noise, non-uniformity, or the like). However, this implementation may be relatively computationally consuming.

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

[0080] Reference again Figure 2BIn some embodiments, step 204 includes step 212 of generating a particular one of the one or more pre-processed images based on a subset of reconstructed components including a signal having at least one of the one or more known pitches. For example, the pre-processed image I pp It can be written as

[0081]

[0082] in In some embodiments, Thus, step 212 may include identifying a subset l of reconstructed components that include a signal corresponding to the pitch of 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 In some cases, the preprocessed image I pp DC components (eg, constant signal components) or other signals with low spatial frequencies may be further removed.

[0083] Reference Figures 4A to 4C , providing a demonstration of method 200 according to one or more embodiments of the present disclosure.

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

[0085] Figure 4B 404 to 412 (respectively labeled) corresponding to reconstructed components associated with image 402 using a decomposition technique according to one or more embodiments of the present disclosure. arrive ). Figure 4C According to one or more embodiments of the present disclosure Figure 4A and 4B The associated large trajectory matrix Plot of the spectrum of the eigenvalues ​​of . Figure 4C As shown in , the strength of the eigenvalues ​​(and the associated reconstruction components) decreases rapidly. Therefore, the first few eigenvalues ​​(and the associated reconstruction components) may be significant, while the remainder corresponds to noise.

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

[0087] In addition, if Figure 4B As shown in FIG. 3 , only some of the reconstructed components contain significant signal on the length scale associated with the pitch of the periodic structure 302. In this particular example, the reconstructed components and Contains substantial signal strength at the pitch of the periodic structure 302 and can be used to generate a high contrast pre-processed image of the periodic structure 302 (eg, in step 212) in which unwanted noise and / or inhomogeneities are at least partially removed. The DC component (eg, low spatial frequency component) of the target 104 and the associated DC non-uniformity, which may impair metrology measurements such as, but not limited to, superposition measurements. The remaining reconstructed components (eg, ) include noise and / or non-uniformities at higher spatial frequencies that can further impair metrological measurements.

[0088] In some cases, it may be possible to describe large trajectory matrices in a more efficient form than provided by the reconstruction component (or the original image I Orig ) . As an illustration, Figure 4C Indicates that the second and third eigenvalues ​​are degenerate or almost degenerate. Figure 4B This is also proven in , because the reconstruction component and Degenerate or nearly degenerate contain similar spatial frequencies. Any suitable decomposition and / or separation technique may be applied to generally obtain reconstruction components and / or for generating reconstruction components of the preprocessed image (e.g., in step 212). For example, a rotation technique (such as, but not limited to, varimax rotation, quarter-axis rotation, or equal-axis rotation) may be used to generate a reconstruction vector.

[0089] In addition, it should be noted that equations (3) to (5) and FIG. 4A to FIG. 4C Corresponding to non-parametric decomposition. In some embodiments, step 204 includes performing parameter decomposition and regression to provide a reconstruction vector for generating a pre-processed image. This technique can be used to generate a reconstructed vector of the original image I Orig The adaptive basis for the generation of the data in the Fourier decomposition can therefore provide a generalized or universal technique suitable for a variety of images with different noise and / or non-uniformity problems. In addition, this technique can be used from the original image I with frequencies different from those provided by the standard Fourier decomposition. Orig Extract the amplitude modulated sine wave component.

[0090] A subset of reconstruction vectors used to generate a pre-processed image may be selected at any point. Orig The subset of reconstructed components used to generate a particular pre-processed image may be selected based on individual analysis of the spectral plots of the reconstructed signals and / or eigenvalues ​​of the periodic structure 302. For example, the subset of reconstructed components may be selected based on the signal strength of the reconstructed components at a known pitch of the periodic structure 302 (e.g., the strength of the reconstructed components at spatial frequencies at or near the known pitch as determined by Fourier or other spectral analysis techniques) and / or the eigenvalue strength (e.g., at, e.g., Figure 4C The subset of reconstructed components can be selected by any combination of the frequency spectrum shown in FIG. 1 and FIG. 2 . In addition, this selection can be automated so that no user intervention is required. For example, the signal strength and / or eigenvalue strength of the reconstructed components at known pitches can be compared with preselected thresholds that can be generated based on previous experiments and / or simulations.

[0091] In some embodiments, the subset of reconstruction components used to generate a particular pre-processed image is based on prior selection or training. It may be the case that images of a target 104 having a common design across samples 106 or multiple samples 106 in a batch may exhibit similar noise and / or non-uniformity characteristics, such that a particular reconstruction component (e.g., Figures 4A to 4C In the example and ) may be consistent or at least adhere to a measurable pattern. Therefore, it is not sufficient to identify the desired reconstructed component in the training phase and use it for additional targets 104 in the test phase without further analysis. For example, the test phase may correspond to a first portion of the target 104 on a particular sample 106. As another example, the test phase may correspond to a set of one or more training samples 106 analyzed prior to run time in a production environment. It is contemplated herein that this training and testing technique may reduce the computational burden during run time so that pre-processed images may be generated efficiently (e.g., almost instantaneously). In this way, even computationally intensive methods such as, but not limited to, generalized decomposition (e.g., as previously described herein, ) can also be efficiently implemented during the testing phase.

[0092] Now generally refer to Figure 2A to 2B It is contemplated herein that the systems and methods disclosed herein may be suitable for images exhibiting more than one harmonic component (e.g., different pitches p and / or non-trivial harmonics of any pitch of the periodic structure 302 in the spatial frequency space). In particular, the decomposition techniques as disclosed herein may naturally identify the dominant spatial frequencies in the image based on data in the image itself and further provide reconstructed components that include these spatial frequencies. In other words, the decomposition techniques may automatically provide reconstructed components having an adaptive basis based on data in the image itself.

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

[0094] Additionally, in some embodiments, one or more pre-processed images may be generated that isolate desired spatial frequencies and / or exclude undesired spatial frequencies. For example, a pre-processed image may be generated in which certain harmonics are intentionally excluded (e.g., to isolate a fundamental spatial frequency). As another example, in a case where the target includes different instances of periodic structures 302 having different pitches (e.g., in a non-overlapping configuration or in an overlapping moiré configuration), a pre-processed image may be generated that isolates structures having a particular pitch. Additionally, different pre-processed images may be generated that isolate structures having different pitches. In this manner, features having different pitches may be considered separately. Such multiple pre-processed images may then be used together to generate one or more metrology measurements (e.g., in step 206).

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

[0096] For example, based on a reconstructed signal containing data associated with a length scale of known pitch The decomposition and selected pre-processing techniques can provide high contrast images of periodic features and effectively filter out unwanted signals (eg, associated with noise, inhomogeneity, or the like) that can negatively impact image-based metrology measurements.

[0097] By way of illustration, the systems and methods disclosed herein may be particularly well suited 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 constant term non-uniformities (e.g., in the Fourier series decomposition) may contribute to significant errors in the superposition measurement. The second approach is based on comparing the phases of different instances of the periodic structure 302 in one or more images. Such phase-based techniques may be more naturally robust to the types of non-uniformities that impair cross-correlation techniques (e.g., which may be up to quadratic in local extension), but may largely require only a single primary harmonic in the core (e.g., image). Therefore, the presence of any additional harmonics may result in substantial superposition errors. In general, typical image-based superposition measurement techniques are unable to simultaneously accept more than one harmonic in a signal (e.g., image) while also being robust to non-uniformities and target noise.

[0098] However, the systems and methods disclosed herein are suitable for filtering out noise and / or image non-uniformities even in the presence of harmonics in the signal, e.g., harmonics in the spatial frequency space due to the edges of the periodic structure 302. In this way, 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.

[0099] The method 200 may further include controlling one or more process tools based on the metrology measurements generated in step 206. For example, metrology data associated with any number of targets 104 distributed across one or more samples 106 may be used to generate correctable values ​​for controlling the process tools as additional samples 106 are fabricated. As an illustration, metrology data for samples 106 in a batch may be used to generate feedback correctable values ​​for controlling lithographic exposure of subsequent samples 106 in the same batch. As another illustration, metrology data for samples 106 in a batch may be used to generate feed-forward correctable values ​​for controlling lithographic exposure of the same or similar samples 106 in subsequent lithographic steps to account for any deviations.

[0100] Reference again Figures 1A to 1C , various aspects of the metering system 100 according to one or more embodiments of the present disclosure are described in more detail.

[0101] In some embodiments, metrology subsystem 102 is an optical subsystem that generates metrology measurements by illuminating target 104 with light and collecting light from target 104 as a basis for the measurement. Figure 1B 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 generally include an illumination source 116 to generate an illumination beam 118 having any spectral or temporal profile, an illumination path 120 to direct the illumination beam 118 to the target 104, an objective lens 122 or other suitable component to collect light from the target 104 (also referred to herein as sample light 124), a detector 126, and a collection path 128 to direct 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 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., a field plane image in which the detector 126 is located 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., as measured by the detector 126 in a pupil plane). Additionally, the sample 106 may be static or in motion during the measurement.

[0104] In some embodiments, metrology subsystem 102 is a particle beam subsystem that generates metrology measurements by illuminating 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 target 104 as the basis for the measurement. Figure 1C 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 includes 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 to be 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, unipotential, bipotential 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 stigmators 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. As an illustration, Figure 1C A detector 126 arranged to capture secondary electrons emitted from the target 104 is depicted.

[0106] The subject matter described herein sometimes illustrates different components contained in or connected to other components. It should be understood that such depicted architectures are for demonstration only, and in fact many other architectures that realize the same functionality can be implemented. In a conceptual sense, any arrangement of components that realize the same functionality is effectively "associated" so that the desired functionality is realized. Therefore, any two components combined to realize a specific functionality herein can be considered to be "associated" with each other so that the desired functionality is realized, regardless of the architecture or intermediate components. Similarly, any two components so associated can also be considered to be "connected" or "coupled" to each other to realize the desired functionality, and any two components that can be so associated can also be considered to be "coupleable" to each other to realize the desired functionality. Specific examples that can be coupled include, but are not limited to, physically interactable and / or physically interacting components and / or wirelessly interactable and / or wirelessly interacting components and / or logically interactable and / or logically interacting components.

[0107] It is believed that the present disclosure and its many attendant advantages will be understood from the above description, and it should be understood that various changes may be made in the form, construction and arrangement of components without departing from the disclosed subject matter or sacrificing all of its material advantages. The forms described are for illustration only, and the appended claims are intended to cover and include such changes. In addition, it should be understood that the invention is defined by the appended claims.

Claims

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

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

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

4. The system according to claim 1, wherein the specific image is defined as: wherein n represents a row of the particular image, wherein m 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 in 5. The system according to claim 4, wherein .

6. The system of claim 4, wherein 7. The system according to 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 k = 1, 2, ... n, where the large trajectory matrix Formed as Wherein generating the reconstructed components associated with the particular image from the one or more trajectory matrices using the decomposition technique comprises: The reconstructed components associated with the particular image are generated from the large trajectory using the decomposition technique.

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

11. The system according to claim 1, wherein the specific image is defined as: Where n represents the row of the specific image, where m represents the column of the specific image, where the large trajectory matrix is formed from the one or more trajectory matrices: Each matrix τ has the embedding dimensions along the row and column of the specific image, respectively. and One of the one or more trajectory matrices of and 12. The system according to claim 11, wherein corresponds to a value of one of the one or more known pitches rounded to an integer in pixels along the row, where 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 comprising the signal 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 signal 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 metrological measurements include: Overlay measurement.

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 comprising: Metering subsystem; and A controller communicatively coupled to the metering subsystem, the controller comprising one or more processors configured to execute program instructions that cause the one or more processors to implement a metering recipe by: receiving from the metrology subsystem 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 comprises: constructing one or more trajectory matrices from the particular image; generating, from the one or more trajectory matrices, a reconstructed component associated with the particular image using the decomposition technique; and generating a particular one of the one or more pre-processed images based on a subset of the reconstructed components including a signal having at least one of the one or more known pitches; and One or more metrology measurements of the metrology target are generated based on the one or more pre-processed 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 subsystem comprises: Optical metrology imaging subsystem.

20. The system of claim 17, wherein the metrology subsystem comprises: Particle beam imaging subsystem.

21. A method comprising: receiving one or more images of a metrology target including one or more 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 comprises: constructing one or more trajectory matrices from the particular image; generating, from the one or more trajectory matrices, a reconstructed component associated with the particular image using the decomposition technique; and generating a particular one of the one or more pre-processed images based on a subset of the reconstructed components including a signal having at least one of the one or more known pitches; and One or more metrology measurements of the metrology target are generated based on the one or more pre-processed images.

22. 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: The reconstructed components associated with the particular image are generated from the one or more trajectory matrices using a singular value decomposition (SVD) technique.

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: The reconstructed components associated with the particular image are generated from the one or more trajectory matrices using at least one of a principal component analysis technique or an independent component analysis technique.

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