Metrology systems and methods

Abstract

A metrology system can configure metrological measurements of a plurality of metrological targets in a plurality of fields distributed across one or more samples into a signal vector, wherein the metrological measurements associated with the metrological targets in each of the plurality of fields are grouped within the signal vector. The system can further decompose the signal vector into reconstructed vectors associated with different spectral components of the signal vector. The system can further classify a subset of these reconstructed vectors into components of a metrology model, wherein the sum of these components corresponds to a metrology model describing the metrological measurements of the one or more samples. The system can further generate control signals based on the metrology model for controlling one or more processing tools.

Description

General Econometric Model The present invention generally relates to metrology measurements and, more particularly, to modeling metrology measurements across multiple metrology targets. Metrology measurements are commonly used in semiconductor processing to monitor and / or control various manufacturing processes. For example, a fabricated sample may include multiple instances of an exposure field, and measurements may be taken at various metrology targets within the field. It would then be desirable to generate a model of the metrology measurements that accounts for both intra-field and inter-field variations. However, existing modeling techniques suffer from various drawbacks, such as (but not limited to) inaccuracies or lack of robustness. Therefore, there is a need to develop systems and methods that address these drawbacks. According to one or more illustrative embodiments of the present invention, a metrology system is disclosed. In one illustrative embodiment, the system includes a controller. In another illustrative embodiment, the controller configures metrology measurements of metrology targets in various fields distributed over one or more samples into a signal vector, wherein the metrology measurements associated with the metrology targets in each of the fields are grouped within the signal vector. In another illustrative embodiment, the controller decomposes the signal vector into reconstruction vectors associated with different spectral components of the signal vector. In another illustrative embodiment, the controller classifies a subset of the reconstruction vectors into components of a metrology model, wherein a sum of the components corresponds to a metrology model describing the metrology measurements of the one or more samples. In another illustrative embodiment, the controller generates control signals for controlling one or more processing tools based on the metrology model. According to one or more illustrative embodiments of the present invention, a metrology system is disclosed. In one illustrative embodiment, the system includes a metrology subsystem for generating metrology measurements of metrology targets in various fields distributed over one or more samples according to a metrology recipe. In another illustrative embodiment, the system includes a controller. In another illustrative embodiment, the controller configures the metrology measurements into a signal vector, wherein the metrology measurements associated with the metrology targets in each of the fields are grouped within the signal vector. In another illustrative embodiment, the controller decomposes the signal vector into reconstruction vectors associated with different spectral components of the signal vector. In another illustrative embodiment, the controller classifies a subset of the reconstruction vectors into components of a metrology model, wherein a sum of the components corresponds to a metrology model describing the metrology measurements for the one or more samples. In another illustrative embodiment, the controller generates control signals for controlling one or more processing tools based on the metrology model. According to one or more illustrative embodiments of the present invention, a metrology method is disclosed. In one illustrative embodiment, the method includes generating metrology measurements of metrology targets in various fields distributed over one or more samples. In another illustrative embodiment, the method includes configuring the metrology measurements into a signal vector, wherein the metrology measurements associated with the metrology targets in each of the fields are grouped within the signal vector. In another illustrative embodiment, the method includes decomposing the signal vector into reconstruction vectors associated with different spectral components of the signal vector. In another illustrative embodiment, the method includes classifying a subset of the reconstruction vectors into components of a metrology model, wherein a sum of the components corresponds to a metrology model describing the metrology measurements for the one or more samples. In another illustrative embodiment, the method includes generating control signals for controlling one or more processing tools based on the metrology model. It should be understood that both the foregoing summary 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. Cross-reference to related applications This application claims the benefit of U.S. Provisional Application No. 63 / 347,133, filed May 31, 2022, entitled MODELLING OVERLAY ON WAFER WITHOUT POLYNOMIALS: A UNIVERSAL MODEL, under 35 U.S.C. § 119(e), the entirety of which is incorporated herein by reference. Reference will now be made in detail to the disclosed subject matter illustrated in the accompanying drawings. The present invention has been particularly shown and described with respect to certain embodiments and particular features thereof. The embodiments described herein are to be considered illustrative rather than restrictive. Those skilled in the art will readily appreciate that various changes and modifications in form and details may be made without departing from the spirit and scope of the present invention. Embodiments of the present invention relate to systems and methods for modeling metrology measurements taken by a metrology target across a field of one or more samples based on spectral decomposition of the metrology measurements. It is contemplated herein that this technique can provide a general modeling technique for generating metrology measurement models that can provide robust and accurate characterization of variations in metrology measurements across multiple length scales. Metrology measurements are widely used to monitor and / or control manufacturing processes. As an illustration in the context of semiconductor manufacturing, devices can be manufactured by continuously forming patterned layers. For example, a patterned layer can be formed by a series of steps, such as (but not limited to) depositing a sample layer and a photoresist, lithographically exposing the photoresist to a desired pattern, etching the photoresist and sample layer to produce the desired pattern in the sample layer, and removing the photoresist. Generally speaking, many devices are manufactured in parallel on a single sample, where the portions of the sample associated with different instances of the device (or portions thereof) are referred to as dies, which can be separated by sawing lines to facilitate subsequent singulation. In addition, lithographic tools (e.g., scanners, steppers, or the like) typically have an exposure field of view (e.g., field size) that is substantially smaller than the sample itself and therefore typically expose multiple fields across the sample, where each field can include patterns associated with multiple dies. It is often desirable to monitor and / or control the lithography exposure steps based on metrology measurements at various metrology targets across the sample. Such metrology targets may include dedicated metrology targets (e.g., overlay targets or the like) and / or device features. One or more metrology targets may then characterize the variation of metrology measurements across a single sample or multiple samples. For example, metrology measurements within a field typically follow a consistent pattern such that this pattern is periodic when considering multiple fields. Such patterns may be captured by a field model or a field contribution to a complete model. As another example, metrology measurements across a sample may exhibit relatively slow variations (e.g., on a length scale equal to or greater than the size of a field), which may be captured by a wafer model or a wafer contribution to a complete model. As another example, metrology measurements. Further variations may be considered noise and may be associated with residuals of the field and / or wafer contributions of a model. It is generally desirable to generate a field and / or wafer model that robustly and accurately distinguishes field and / or wafer components from noise. In other words, it is generally desirable that the residuals of a metrology model actually correspond to noise in the measurement rather than containing field and / or wafer components. In one embodiment, the metrology measurements of interest are hierarchically arranged into a signal vector. For example, metrology measurements associated with metrology targets in each field can be grouped within the signal vector based on spatial proximity. Furthermore, metrology measurements associated with different fields can be arranged within the signal vector based on spatial proximity. In one embodiment, this signal vector is decomposed (e.g., using a singular value decomposition (SVD) technique or the like) into reconstruction vectors associated with different spectral components (e.g., different length scales) of the signal vector. In this manner, the signal vector can be equal to the sum of the reconstruction vectors. In one embodiment, the reconstruction vector is then decomposed into various groups, such as (but not limited to) field components, wafer components, and residual components. For example, a sum of reconstruction vectors classified as field components can correspond to a field model describing the variation of metrology measurements between metrology targets within each field. Similarly, a sum of reconstruction vectors classified as wafer components can correspond to a wafer model describing the variation of metrology measurements between fields (e.g., relatively low-frequency variation). Upon careful consideration, this technique can provide a robust and general metrology model applicable to a wide range of applications and processes. Specifically, using spectral decomposition techniques to generate reconstruction vectors can effectively identify dominant length scales (e.g., spectral components) in the signal vector, which can correspond to field components, wafer components, and / or residuals. In other words, the techniques disclosed herein provide generality based on the analysis of metrology measurements in a given set, without the need for regression to an external basis (such as a polynomial). Specifically, regression-based techniques (e.g., polynomial-based regression techniques) can typically require a large number of fitting parameters to provide an adequate fit and can therefore suffer from relatively low robustness to variations. Furthermore, accurate modeling of different applications or processes can require different polynomial bases. In contrast, the spectral decomposition techniques disclosed herein can both identify a relevant basis (e.g., reconstruction vectors) based on the data itself and require relatively fewer basis elements for accurate characterization of field and / or wafer components. In this way, the techniques disclosed herein can be both general and robust. In addition, this technique may provide advantages over techniques based on principal component analysis. For example, an adaptive model based on principal component analysis is generally described in U.S. patent application Ser. No. 17 / 705,077, filed on March 25, 2022, entitled ADAPTIVE MODELING MISREGISTRATION MEASUREMENT SYSTEM AND METHOD, the entire text of which is incorporated herein by reference. These techniques may make unnecessary assumptions about the lack of correlation between various modeled terms (e.g., wafer and field terms). However, the systems and methods disclosed herein provide reconstruction vectors associated with different length scales, which can be classified into their different models or components (e.g., field and wafer models) without any such assumptions. Additional embodiments of the present invention relate to controlling one or more processing tools (eg, lithography tools) based on field and / or wafer components generated through spectral decomposition, as disclosed herein. 1A-7 , a system and method for metrology modeling will be described in more detail according to one or more embodiments of the present invention. FIG. 1A is a block diagram of a metrology system 100 according to one or more embodiments of the present invention. In an embodiment, the metrology system 100 includes a metrology subsystem 102 adapted to generate metrology measurements of a metrology target 104 distributed across one or more samples 106 . Sample 106 may include any object that is a source of a metrology measurement. For example, sample 106 may include a substrate (e.g., a wafer or the like) formed from a semiconductor or non-semiconductor material. A 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, a resist, a dielectric material, a conductive material, and a semiconductive material. Many different types of such layers are known in the art, and the term sample as used herein is intended to encompass a sample on which all types of such layers may be formed. One or more layers formed on a sample 106 may be patterned or unpatterned. For example, a sample 106 may include a plurality of grains, each having repeatable patterned features. The formation and processing of such material layers may ultimately result in a finished device. Many different types of devices can be formed on a sample 106, and the term sample 106 as used herein is intended to encompass a sample 106 on which any type of device known in the art is fabricated. Furthermore, for purposes of the present invention, the terms sample 106 and wafer should be interpreted as interchangeable. The metrology measurements of a sample 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 that characterize the registration (or registration error) between different lithographic exposures on one or more layers of a sample 106. In some embodiments, the metrology measurements generated by the metrology subsystem 102 characterize conditions of a lithographic exposure, such as, but not limited to, a focus position or an illumination dose of a sample 106. In some embodiments, the metrology measurements generated by the metrology subsystem 102 characterize additional aspects of a manufacturing process, such as, but not limited to, an etching step or a polishing step. A metrology target 104 can include any location on sample 106 suitable for performing a metrology measurement using a metrology subsystem 102. In some embodiments, a metrology target 104 includes features associated with a manufactured device, referred to herein as device features. In some embodiments, a metrology target 104 includes specialized features designed to facilitate metrology measurements. As an illustration in the context of overlay metrology, a specialized overlay metrology target 104 can include features associated with each lithographic exposure of interest in either overlapping or non-overlapping locations on sample 106, in a configuration that enables robust and accurate overlay metrology by the metrology subsystem 102. In one 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 a 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. The one or more processors 110 of a controller 108 may include any processor or processing element known in the art. For purposes of the present invention, the term "processor" or "processing element" is broadly defined to encompass any device having one or more processing or logic elements, such as 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, a video computer, a parallel processor, a network-connected computer, or any other computer system configured to execute a program configured to operate or operate in conjunction with the metrology system 100, as described throughout the present invention. Furthermore, the various subsystems of metering system 100 may include a processor or logic element suitable for performing at least a portion of the steps described herein. Therefore, the above description should not be construed as limiting the embodiments of the present invention, but rather as merely illustrative. Furthermore, the steps described throughout the present invention may be performed by a single controller or, alternatively, multiple controllers. Furthermore, 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 metering system 100. Memory device 112 may comprise any storage medium known in the art suitable for storing program instructions executable by the associated processor(s) 110. For example, memory device 112 may comprise a non-transitory memory medium. By way of another example, memory device 112 may include, but is not limited to, a read-only memory (ROM), a random access memory (RAM), a magnetic or optical memory device (e.g., a disk), a tape, a solid-state drive, and the like. It should be further noted that memory device 112 may be housed in a common controller housing with one or more processors 110. In some embodiments, memory device 112 may be remotely located relative to the physical location of one or more processors 110 and controller 108. For example, one or more processors 110 of controller 108 may access a remote memory (e.g., a server) that is accessible via a network (e.g., the Internet, an intranet, and the like). 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 further be configured to perform any of the various process steps described throughout the present disclosure. In one embodiment, the metering system 100 includes a user interface 114 communicatively coupled to the controller 108. In one embodiment, the user interface 114 may include, but is not limited to, one or more desktop computers, laptop computers, tablet computers, and the like. In another embodiment, the user interface 114 includes a display for displaying information from the metering system 100 to a user. The display of the user interface 114 may include any display known in the art. For example, the display may include, but is not limited to, a liquid crystal display (LCD), an organic light-emitting diode (OLED)-based display, or a CRT display. Those skilled in the art will recognize that any display device capable of integration with a user interface 114 is suitable for implementation within the present invention. In another embodiment, a user may input selections and / or commands via a user input device of the user interface 114 in response to information displayed to the user. 2-7 , techniques for modeling metrology measurements are described in more detail according to one or more embodiments of the present invention. FIG2 is a flow chart illustrating the steps performed in a method 200 according to one or more embodiments of the present invention. Applicants should note that the embodiments and implementation techniques previously described herein in the context of the metrology system 100 should be interpreted as extending to the method 200. However, it should be further noted that the method 200 is not limited to the architecture of the metrology system 100. In one embodiment, the method 200 includes a step 202 of generating metrology measurements of the metrology target 104 distributed across a field 306 on one or more samples 106 (eg, according to a metrology recipe). FIG. 3 is a conceptual top view of a sample 106 depicting a distribution of metrology targets 104 , in accordance with one or more embodiments of the present invention. As shown in FIG3 , various die 302 comprising fabricated features can be distributed across a sample 106, with the die 302 separated by scribe lines 304. Furthermore, the various die 302 across the sample 106 can be identical. Furthermore, the die 302 can be associated with different fields 306 (e.g., exposure fields) associated with a lithography tool (e.g., a scanner, stepper, or the like). For example, features on the die 302 can be fabricated by sequential processing steps including, but not limited to, depositing a sample layer (e.g., a dielectric layer, a conductive layer, or the like); depositing a photoresist; lithographically exposing a pattern into the photoresist (e.g., through sequential exposure of the various fields 306); and etching the photoresist and sample layer. 3 further depicts various metrology targets 104 distributed within each field 306. Metrology targets 104 may generally be positioned in any suitable location within a field 306, such as within a scribe line 304 and / or within any die 302. In one embodiment, each field 306 has a common number and distribution of metrology targets 104. The metrology measurements measured in step 202 may include any type of data, including, but not limited to, overlay measurements of the sample 106 during a lithography exposure step, illumination dose measurements, or focus position measurements. Furthermore, the metrology measurements may be generated using any technique known in the art. For example, the metrology measurements may (but need not) be generated using the metrology subsystem 102. Metrology measurements of a metrology target 104 distributed across one or more samples 106 can be captured in any order (e.g., using any sampling plan). In some embodiments, metrology measurements of a metrology target 104 in one field 306 can be captured before metrology measurements of a metrology target 104 in another field 306. In some embodiments, measurements of a metrology target 104 across a sample 106 are captured regardless of the field 306. For example, a sampling plan can be selected to provide for efficient generation of measurements of a metrology target 104 across a sample 106. Furthermore, metrology measurements of a metrology target 104 can be captured in series or through parallel measurements of two or more metrology targets 104. It should be noted that FIG3 and the associated description are provided for illustrative purposes only and should not be construed as limiting. For example, FIG3 is not drawn to scale and the number, type, size, and / or configuration of features (e.g., die 302, metrology target 104, field 306, and the like) are illustrative only. In one embodiment, method 200 includes a step 204 of arranging metrology measurements into a signal vector, wherein metrology measurements associated with the metrology targets 104 in each field 306 are grouped within the signal vector. The signal vector may generally have any number of dimensions (e.g., one, two, or the like). Furthermore, the order of metrology measurements associated with the metrology targets 104 in each field 306 within the signal vector may be constant. In this manner, any systematic variations between metrology measurements of the metrology targets 104 in each field 306 may result in periodicity in the signal vector. As will be shown below with respect to step 208, such systematic variations between metrology measurements of the metrology targets 104 in each field 306 may correspond to a field model of the process. As a graphic representation of a one-dimensional signal vector, the signal vector Can be written as: in Corresponding to a specific measurement, The number of one of the 306 fields, superscript Corresponding to field 306, The number of measurement targets 104 in each field 306, and the subscript Corresponding to the measurement target 104 in each field 306. In this way, A metrology measurement corresponding to a first metrology target 104 in a first field 306, corresponding to a metrology measurement of a second metrology target 104 in the first field 306, corresponding to a metrology measurement of a first metrology target 104 in a second field 306, and so on. Signal vector A number in a measurement. The metrology measurements associated with the metrology targets 104 in each field 306 may generally be in any order (e.g., The order may correspond to any order of specific metrology targets 104 within a field 306), as long as the order is constant for all fields 306 in the signal vector. However, in some embodiments, the order is based on the physical layout of the metrology targets 104 within the field. For example, the order The associated metrology targets 104 may be selected so that they are physically close (e.g., adjacent, nearest neighbors, or similar). It is contemplated herein that arranging the order of metrology measurements within each field 306 of the signal vector based on the physical layout of the metrology targets 104 can facilitate physically meaningful relationships between data points in the signal vector. For example, systematic variations in metrology measurements within each field (e.g., a pattern captured by a field model) can be correlated with spatial variations in a manufacturing process across samples that can be easily captured through such an ordering. In some embodiments, the signal vector may include metrology measurements from two or more samples 106. In this case, the metrology measurements in the signal vector may be further grouped by sample 106. For example, the pattern in equation (1) may be repeated for each sample 106. As described in more detail below, such a configuration may enable modeling of sample-to-sample variations in the metrology measurements. In an embodiment, method 200 includes a step 206 of decomposing the signal vector into reconstruction vectors associated with different spectral components of the signal vector. Any suitable spectral decomposition technique may be utilized, such as (but not limited to) SVD, principal component analysis techniques, or any eigenvalue-based decomposition technique. In some embodiments, the reconstruction vectors describe different spectral components of the signal vector (e.g., different length scales of the signal vector). In this way, the signal vector It can be expressed as the sum of one of the reconstruction vectors. For example, the signal vector Can be expressed as reconstruction vector One of the sum. It is contemplated herein that the reconstructed vectors generated using spectral decomposition techniques as disclosed herein can be based on an analysis of the metrological data itself (e.g., using eigenvalue-based techniques or the like). Thus, the techniques disclosed herein can provide a general model (e.g., a general metrological model) applicable to a wide variety of applications and data sets. Consequently, the techniques disclosed herein can outperform regression-based techniques, such as (but not limited to) polynomial regression techniques in which polynomials are used as basis vectors for representing metrological data. Specifically, the accuracy of regression-based techniques can be limited by the ability of the selected basis to accurately represent the variations in the metrological data. In an embodiment, the method 200 includes a step 208 of classifying a subset of the reconstructed vectors into components of a metrology model, wherein a sum of the components corresponds to a metrology model describing metrology measurements for one or more samples. Step 208 may generally include classifying the reconstruction vectors into any number of subsets that may correspond to different aspects of the metrology model. In one embodiment, step 208 includes classifying a subset of the reconstruction vectors into wafer components, wherein a sum of the reconstruction vectors classified as wafer components corresponds to a wafer pattern that describes the variation in metrology measurements between fields 306. These patterns can be characterized as variations between metrology measurements between adjacent metrology targets 104 for the wafer. to ) may not be noticeable low-frequency (LF) patterns or large length scales. In one embodiment, step 208 includes classifying a subset of the reconstruction vectors into field components, wherein a sum of the reconstruction vectors classified as field components corresponds to a field model that describes the variation of the metrology measurement between the metrology targets 104 within each field 306. For example, the field model may describe a field having a number ( ) of the order of magnitude of the periodic signal vector These patterns can be characterized as medium frequency (MF) patterns or medium length scales whose metrology measurements can vary between the various metrology targets 104 in a field 306, but a pattern associated with the metrology can be constant between fields 306. More generally, method 200 may include classifying the reconstruction vectors into any number of meaningfully distinct groups (e.g., categories). In the case of multi-sample measurements, a subset of the reconstruction vectors may be classified into inter-sample components that may correspond to drift of the process over the plurality of samples 106. For example, a metrology model can include both a field model and a wafer model, which can describe the variation of metrology measurements at different length scales (e.g., within-field length scale, between-field length scale, sample-wide length scale, or the like). Furthermore, identifying the field and / or wafer models and associated components does not require a priori information or assumptions. In one embodiment, method 200 includes a step 210 of classifying a subset of the reconstructed vectors as residuals. For example, the remaining portion of the reconstructed vectors that were not classified as part of the metrology model (e.g., in step 208) can be considered residuals. These patterns can be characterized as high-frequency (HF) patterns or small length scales that may not fit into the above categories. The resulting classified reconstruction vectors and / or associated models (eg, part of a metrology model) may be used for any suitable purpose. In one embodiment, method 200 includes a step 212 of generating control signals for controlling one or more processing tools based on the metrology model. For example, the field model (and / or wafer model) can be used as control data for controlling any type of processing tool, such as, but not limited to, a lithography tool (e.g., a scanner, stepper, or the like). In this manner, step 212 can include generating corrective terms for the one or more processing tools to compensate for any undesirable deviations in metrology measurements. Furthermore, the corrective terms can be associated with feedback control associated with the formation of similar structures on subsequent samples 106 and / or feedforward control associated with the formation of additional structures on additional layers of the same sample 106 (e.g., one or more samples associated with the signal vector). Referring now to equations (3) and (4), the decomposition of a signal vector into reconstruction vectors is described in more detail according to one or more embodiments of the present invention. Specifically, equations (3) and (4) illustrate a non-limiting example of a singular spectrum analysis (SSA) technique utilizing SVD. As shown herein, this technique can facilitate the decomposition of a signal vector into both field components and wafer components (e.g., more generally, the number of metrology targets 104 relative to each field 306 ( ) of low-frequency, mid-frequency and high-frequency patterns). In some embodiments, the signal vector is mapped to a vector having an embedding size One matrix .For example, Can be written as: For example, the matrix Each column (or row) can contain the signal vector This matrix can be characterized as a transfer matrix or a Hankel matrix and can have a diagonal Elements of the Upper The nature of equality. Embedded size Usually can have a signal vector Any value between the length ( ). In some embodiments, the embedding size is selected to be equal to the number of metrology targets 104 measured in each field 306 ( ). This choice facilitates decomposing the signal vector in a way that the field components are well characterized so that an accurate field model can be constructed. However, in this paper, it is prudent to use the embedding size Any suitable value. In some embodiments, the matrix Perform SVD so that Can be written as: In this formula, the matrix Contains Singular values A diagonal matrix (in descending order from largest to smallest) where Covariance matrix In addition, The eigenvalue matrix The trip, and The eigenvalue matrix trip. Each has a signal vector Same length ( ) of the reconstruction vector (See equation (2) above) can then be obtained by the matrix A diagonal operation (eg, a diagonal mean or the like) results. 4 to 7, an exemplary spectral decomposition based on the non-limiting technique illustrated by equations (1) to (4) is described. In this example, a sample 106 includes 27 fields 306 ( ), where each field contains 10 measurement targets 104 ( ). Furthermore, in this example, the specific metrology measurement is overlay (OVL) measurement. FIG. 4 is a diagram illustrating a signal vector as formulated by equation (1) according to one or more embodiments of the present invention. Specifically, FIG4 depicts the value of the metrology measurement OVL for each point (e.g., metrology target 104) configured according to equation (1). Box 402 in FIG4 depicts a first field 306 (e.g., ). FIG. 5 is a diagram illustrating a method of embedding a plurality of embedded devices according to one or more embodiments of the present invention. The covariance matrix of equations (3) to (4) is The eigenvalue of In this way, Figure 5 corresponds to the covariance matrix A curve diagram of the spectrum. FIG. 6 depicts a matrix according to one or more embodiments of the present invention. The diagonal mean of Reconstruction vector A series of curve graphs. As shown in Figure 6, different reconstruction vectors Contains the signal vector It should be noted that according to equation (4) and Figure 5, the reconstruction vector The relative contribution of Increase and decrease. Referring back to FIG. 2 (eg, steps 208 and 210), the reconstruction vector The classification into different groups is used to quantify different behaviors of the measurement measures across the sample 106 . For example, you can As another example, 、 、 and The classification into field components allows the sum of these components to correspond to a field model. As another example, Reconstruction vector The classification into residual components allows the sum of these components to be the residual of a model. FIG7 is a series of graphs 702, 704, 706, which respectively describe the wafer model, the field model, and the residuals compared to the original signal vector based on these classifications, according to one or more embodiments of the present invention. As shown in graph 704, the field model captures the periodic systematic variations of the metrology data within each field well, the wafer model captures the scale variations of relatively large lengths (e.g., field-to-field variations), and the residuals capture the measurement noise. Moreover, this analysis is possible without requiring any a priori knowledge or assumptions about the field model, and further without imposing any particular polynomial basis for regression. Instead, the classification is based on an eigenvalue-based decomposition of the metrology data itself after being configured in a meaningful way into a signal vector as depicted in Equation (1) (e.g., step 204). In this way, the techniques disclosed herein can provide a general model for characterizing metrology measurements. It should be noted that the definition of the residuals in the techniques disclosed herein is different from that in regression-based methods. In this case, the residuals are only associated with pure noise associated with insignificant eigenvalues, and the mean of the residuals is not guaranteed to be absolutely zero. As previously described herein, the embedding length The value of may be any suitable value. However, in at least some cases as illustrated in Figures 4 to 7, the embedding length Setting the number of metrology targets 104 equal to each field 306 may provide for accurate and versatile determination of field models (eg, a field signature). Furthermore, it is contemplated herein that any suitable technique (e.g., based on steps 208 and / or 210) may be used to classify the reconstruction vectors. In some embodiments, the reconstruction vectors are classified based on a relationship between the length scales captured by the reconstruction vectors and the length scales within an operating range (e.g., scan range) and / or the resolution of a processing tool (e.g., a lithography tool or the like). For example, a lithography tool may control the placement of a field 306 on a sample 106 within a specific operating range and at a specific resolution. Thus, if a reconstruction vector contains length scales with an operating range and / or resolution, it may be classified as a field component. As an illustration, reconstruction vectors containing length scales less than the resolution of the lithography tool (e.g., high-frequency signals) may be considered residuals because any control signals required to correct for these signals may exceed the capabilities of the lithography tool. In some embodiments, the reconstruction vectors may be classified at least in part by user input. For example, the reconstruction vectors may be displayed to a user via the user interface 114 (eg, in the form of a graph similar to the graph depicted in FIG. 6 ) for evaluation and input. 5 to 7, it is contemplated herein to describe the signal vector in a more efficient form than that provided directly by reconstructing the vector As an illustration, FIG5 indicates several pairs of degenerate or nearly degenerate eigenvalues. (E.g., k=1 and k=2, k=4 and k=5, k=6 and k=7, k=8 and k=9.) This is also demonstrated in FIG6 , where the reconstructed vectors in each of these pairs contain similar frequencies and have non-uniform envelopes indicating additional structure. In some embodiments, method 200 includes applying a rotation to the set of reconstruction vectors (or a portion thereof), which may provide the signal vector spectral components of the reconstructed vectors. Any suitable rotation technique may be utilized, such as, but not limited to, varimax rotation, quartimax rotation, or equimax rotation. This step may, but need not, be performed before or as part of the following step: classifying the reconstructed vectors into field components, wafer components, residuals, or the like (e.g., as depicted in steps 208 and / or 210 of FIG. 2 ). Referring generally to FIG2, it is contemplated herein that the spectral decomposition techniques for metrology modeling disclosed herein can inform metrology sampling plans (e.g., step 202). As depicted in equation (4) and FIG5, the matrix (e.g., the covariance matrix) has rank one However, in many applications, the matrix Quite redundant and targetable Rapidly decreasing eigenvalues. Therefore, the covariance matrix can be used The redundancy can be achieved by appropriately selecting or adjusting the sampling plan (e.g., in generating the signal vector For example, the number of sampled metrology targets 104 can be selected or adjusted (e.g., reduced) to reconstruct the particular selection of metrology targets 104 and / or the number of metrology targets 104 sampled at the time. ) to effectively capture field and / or wafer models. A sampling plan describing which metrology targets 104 are sampled (e.g., by the metrology subsystem 102) to generate metrology data can be reduced by skipping a randomly selected metrology measurement for the metrology target 104 (e.g., in step 202). A matrix reconstruction technique (e.g., a gap filling technique or the like) can then be used to fill in the values ​​of these skipped metrology measurements. In other words, a complete sampling plan can include the signal vector All metrology targets 104 associated with the signal vector 306 (e.g., a repeating pattern of metrology targets 104 in each field 306) are generated based on metrology data generated by sampling the corresponding metrology targets (e.g., by the metrology subsystem 102). However, in some embodiments, the sampling plan only includes the signal vector 306. A portion of the associated metrology target 104. In this configuration, a first portion of the measurement is generated based on metrology data generated by sampling the corresponding metrology target 104, while a second portion of the metrology measurement is generated by matrix reconstruction based on the first portion of the metrology measurement. It is considered that the matrix for a given application can be based on various factors (including but not limited to A specific number of skipped metrology measurements may be tailored for a given application (e.g., a sparsity of the measurement, a tolerance for artifacts or inaccuracies introduced by replacing skipped measurements with reconstructed values, or the like). As an illustration, spectral decomposition of metrology measurements based on a first sampling scheme may be performed (e.g., based on method 200 or any subset of the steps therein). An analysis reveals that one or more eigenvalues If the characteristic is zero or has a negligible value (e.g., below a selected threshold), this may be an indication of oversampling. Therefore, the sampling plan may be selected and / or adjusted to reduce the number of zero or negligible characteristic values. In other words, the sampling plan can be selected and / or adjusted to provide a selected number of feature values ​​having values ​​above a selected threshold value. This selection and / or any adjustments may be made prior to a high volume manufacturing (HVM) phase (eg, during a testing or evaluation phase) or during an HVM phase (eg, where the adjustments affect the sampling plan for future measurements). 1A-1C , various aspects of the metering system 100 are described in more detail according to one or more embodiments of the present invention. In some embodiments, metrology subsystem 102 is an optical subsystem that generates a metrology measurement by illuminating metrology target 104 with light and collecting light from metrology target 104 as the 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 invention. An optical metrology subsystem 102 may generally include an illumination source 116 for generating an illumination beam 118 having any spectral or temporal profile, an illumination path 120 for directing the illumination beam 118 toward a metrology target 104, an objective lens 122 or other suitable component for collecting light from the metrology 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, 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. An optical metrology subsystem 102 can generate a metrology measurement using any suitable technique. In some embodiments, an optical metrology subsystem 102 generates a metrology measurement based on an image of the metrology target 104 (e.g., a field plane image where the detector 126 is in a field plane conjugate to the sample 106). In some embodiments, an optical metrology subsystem 102 generates a metrology measurement based on collected diffraction orders (e.g., as measured by a detector 126 in a pupil plane) using a scatterometry technique. Furthermore, during a measurement, the sample 106 can be static or in motion. In some embodiments, metrology subsystem 102 is a particle beam subsystem that generates a metrology measurement by illuminating metrology 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 metrology target 104 as the basis for the measurement. FIG1C is a conceptual diagram of a particle beam metrology subsystem 102 according to one or more embodiments of the present invention. A particle beam metrology subsystem 102 may include a particle source 136 (e.g., an electron beam source, a particle beam source, or the like) such that an illumination beam 118 comprises a particle beam (e.g., an electron beam, a particle beam, or the like). The illumination source 116 may include any particle source known in the art suitable for generating an 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) for controlling one or more aspects 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 light 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 (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 photodetector, 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, FIG1C depicts a detector 126 configured to capture secondary electrons emitted from metrology target 104. The subject matter described herein sometimes depicts different components contained within or connected to other components. It should be understood that the architectures depicted are merely exemplary, and in fact many other architectures that achieve the same functionality can be implemented. In a conceptual sense, any configuration of components used to achieve the same functionality is effectively "associated" so that the desired functionality is achieved. Therefore, any two components combined herein to achieve a specific functionality can be considered to be "associated" with each other so that the desired functionality is achieved without regard to the architecture or intermediate components. Similarly, any two components so associated can also be considered to be "connected" or "coupled" to each other to achieve the desired functionality, and any two components that can be so associated can also be considered to be "coupleable" to each other to achieve the desired functionality. Specific examples of coupleability include (but are not limited to) physically interactive and / or physically interactive components and / or wirelessly interactive and / or wirelessly interactive components and / or logically interactive and / or logically interactive components. It is believed that the present invention and many of its attendant advantages will be understood from the foregoing description, and it will be appreciated that various changes may be made to 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 merely illustrative, and the following claims are intended to encompass and include such changes. Furthermore, it should be understood that the invention is defined by the appended claims. 100: Metrology System 102: Metrology Subsystem 104: Metrology Target 106: Sample 108: Controller 110: Processor 112: Memory Device 114: User Interface 116: Illumination Source 118: Illumination Beam 120: Illumination Path 122: Objective Lens 124: Sample Light 126: Detector 128: Collection Light Path 130: Lens 132: Optical Element 134: Beam Splitter 136: Particle Source 138: Particle Beam Lens 200: Method 202: Step 204: Step 206: Step 208: Step 210: Step 212: Step 302: Die 304: Slice Street 306: Field 402: Frame 702: Graph 704: Graph 706: Graph Those skilled in the art may better understand several advantages of the present invention by referring to the accompanying drawings. FIG. 1A is a block diagram of a metrology system according to one or more embodiments of the present invention. 1B is a conceptual diagram of an optical metrology subsystem according to one or more embodiments of the present invention. 1C is a conceptual diagram of a particle beam metrology subsystem according to one or more embodiments of the present invention. FIG. 2 is a flow chart illustrating steps performed in a method according to one or more embodiments of the present invention. 3 is a conceptual top view of a sample depicting a distribution of metrology targets in accordance with one or more embodiments of the present invention. FIG. 4 is a graph of a signal vector according to one or more embodiments of the present invention. FIG. 5 is a graph illustrating eigenvalues ​​of a covariance matrix according to one or more embodiments of the present invention. FIG. 6 is a series of graphs depicting reconstruction vectors in accordance with one or more embodiments of the present invention. 7 is a series of graphs depicting a wafer model, field model, and residuals compared to the original signal vectors of FIG. 6 , in accordance with one or more embodiments of the present invention. 100:Metering system 102:Metering subsystem 104: Measurement Target 106: Sample 108: Controller 110: Processor 112: Memory device 114: User Interface

Claims

1. A measurement system comprising: A controller includes one or more processors configured to execute program instructions stored in memory, the program instructions being configured to cause the one or more processors to: configure metrological measurements of a plurality of metrological targets in a plurality of fields distributed across one or more samples into a signal vector, wherein the metrological measurements associated with the metrological targets in each of the plurality of fields are grouped within the signal vector; decompose the signal vector into reconstruction vectors associated with different spectral components of the signal vector by mapping the signal vector to a matrix having an embedding size, decompose the matrix to generate multiple matrices, and generate the reconstruction vectors from the matrices; A subset of the reconstructed vectors is classified as a component of a metrology model, wherein the sum of one of the components corresponds to the metrology model describing the metrology measurements of the one or more samples; and correctables for one or more processing tools are generated based on the metrology model; and the correctables are provided to the one or more processing tools to provide feedback or feedforward control to the one or more processing tools.

2. The metrology system of claim 1, wherein the metrology model corresponds to a field model that describes the variation of the metrological measurements among the metrological targets within each of the plurality of fields.

3. The metrology system of claim 1, wherein the one or more processing tools include a lithography tool, wherein the lithography tool is controllable based on the control signals, wherein classifying a subset of the reconstructed vectors as components of the metrology model includes: The subset of the reconstructed vectors with spectral components is classified as the components of the econometric model.

4. The metrology system of claim 1, wherein the metrology model corresponds to a wafer model describing the variations of the metrological measurements of the plurality of fields.

5. As in Request 1, the reconstructed vectors of components not classified as components of the econometric model correspond to residuals.

6. The metrology system of claim 1, wherein the metrology model comprises a field model and a wafer model, wherein classifying a subset of the reconstructed vectors as components of the metrology model includes: The first subset of the reconstructed vectors is classified as field components, where the field model corresponds to the sum of the field components; and the second subset of the reconstructed vectors is classified as wafer components, where the wafer model corresponds to the sum of the wafer components.

7. The metrology system of claim 6, wherein the reconstructed vectors of components not classified as the field model or the wafer model correspond to the residuals.

8. The metering system of claim 6, wherein the control signals for controlling the one or more processing tools are based on at least one of the field model or the wafer model.

9. The metrology system of claim 1, wherein all such metrological measurements are generated based on metrological data produced by sampling corresponding metrological targets of the plurality of metrological targets.

10. The metrology system of claim 1, wherein a first portion of the metrology measurements is generated based on metrology data generated by sampling the corresponding metrology targets of the plurality of metrology targets, wherein a second portion of the metrology measurements is generated by matrix reconstruction based on the first portion of the metrology measurements.

11. The metrology system of claim 1, wherein the order of the metrological measurements associated with the metrological targets in each of the plurality of fields within the signal vector is constant.

12. The metrology system of claim 1, wherein the one or more samples comprise two or more samples, wherein the metrological measurements associated with each of the two or more samples are grouped within the signal vector, wherein the order of one of the metrological measurements associated with each of the metrological targets in the two or more samples is constant.

13. The metrology system of claim 1, wherein decomposing the signal vector into reconstructed vectors associated with different spectral components of the signal vector includes: Perform singular spectral analysis on one of the signal vectors to generate the reconstructed vectors.

14. The metering system as described in claim 1, wherein the signal vector system is one-dimensional.

15. The metering system of claim 1, wherein the signal vector system is two-dimensional.

16. The metrology system of claim 1, wherein decomposing the signal vector into reconstructed vectors associated with different spectral components of the signal vector includes: Map the signal vector to a matrix with one of the embedding dimensions; Decomposition to produce a matrix, where; And from these matrices, these reconstructed vectors are generated.

17. A measurement system as described in claim 16, wherein the elements on the diagonal are equal.

18. The metrology system of claim 16, wherein the decomposition to produce such matrices includes: One of the singular value decompositions is performed to produce such matrices.

19. The metrology system of claim 16, wherein the decomposition to produce such matrices includes: Perform one principal component analysis to produce such matrices.

20. The metrology system of claim 16, wherein the reconstructed vectors are associated with their respective feature values, wherein configuring the metrological measurements for the plurality of metrological targets in the plurality of fields distributed across the one or more samples into the signal vectors includes: The measurement quantities from a sampling plan are configured into the signal vector, wherein the sampling plan is selected to provide a selected number of the characteristic values ​​having values ​​higher than a selected threshold.

21. The metering system of claim 16, wherein the embedding size is equal to the number of metering targets in each of the plurality of fields.

22. The metering system of claim 21, wherein the signal vector is formed as: , where corresponding to a particular of the metering measurements is a number of the plurality of fields, the superscript corresponding to the plurality of fields is a number of the metering targets in each of the plurality of fields, and the subscript corresponding to the metering targets in each of the plurality of fields.

23. The metering system as requested in item 22, wherein.

24. The metrology system of claim 16, wherein generating the reconstructed vectors from the matrices includes: These reconstructed vectors are generated from the diagonal mean of these matrices.

25. The metering system of claim 1, wherein the metering measurements include: Overlapping measurement, wherein the plurality of measurement targets includes overlapping measurement targets.

26. A measurement system comprising: A metrology subsystem comprising an illumination source and a detector, wherein the metrology subsystem is configured to generate metrological measurements of a plurality of metrological targets distributed across a plurality of fields on one or more samples, according to a metrological formula; a controller comprising one or more processors configured to execute program instructions stored in memory, the program instructions being configured to cause the one or more processors to: configure the metrological measurements into a signal vector, wherein the metrological measurements associated with the metrological targets in each of the plurality of fields are grouped within the signal vector; decompose the signal vector into reconstructed vectors associated with different spectral components of the signal vector by mapping the signal vector to a matrix having an embedding size, decompose the matrix to generate a plurality of matrices, and generate the reconstructed vectors from the matrices; A subset of the reconstructed vectors is classified as a component of a metrology model, wherein the sum of one of the components corresponds to the metrology model describing the metrology measurements of the one or more samples; and based on the metrology model, correctable terms are generated for one or more processing tools; and the correctable terms are provided to the one or more processing tools to provide feedback or feedforward control to the one or more processing tools.

27. The metrology system of claim 26, wherein the metrology subsystem includes an optical metrology subsystem.

28. The metrology system of claim 26, wherein the metrology subsystem includes a particle beam metrology subsystem.

29. The metrology system of claim 26, wherein all such metrological measurements are generated based on metrological data produced by sampling corresponding metrological targets of the plurality of metrological targets using the metrology subsystem.

30. The metrology system of claim 26, wherein a first portion of the metrology measurements is generated based on metrology data generated by sampling corresponding metrology targets of the plurality of metrology targets using the metrology subsystem, wherein a second portion of the metrology measurements is generated by matrix reconstruction based on the first portion of the metrology measurements.

31. The metrology system of claim 26, wherein the metrology model corresponds to a field model describing the variation of the metrological measurements among the metrological targets within each of the plurality of fields.

32. The metrology system of claim 26, wherein the metrology model corresponds to a wafer model describing the variations of the metrological measurements of the plurality of fields.

33. The econometric system as requested in claim 26, wherein the reconstructed vectors of components not classified as components of the econometric model correspond to residuals.

34. The metrology system of claim 26, wherein the metrology model comprises a field model and a wafer model, wherein classifying a subset of the reconstructed vectors as components of the metrology model includes: The first subset of the reconstructed vectors is classified as field components, where the field model corresponds to the sum of the field components; and the second subset of the reconstructed vectors is classified as wafer components, where the wafer model corresponds to the sum of the wafer components.

35. A measurement method, comprising: The method generates metrological measurements of a plurality of metrological targets in a plurality of fields distributed across one or more samples; configures these metrological measurements into a signal vector, wherein the metrological measurements associated with the metrological targets in each of the plurality of fields are grouped within the signal vector; decomposes the signal vector into reconstructed vectors associated with different spectral components of the signal vector by mapping the signal vector to a matrix having an embedding size, decomposes the matrix to generate a plurality of matrices, and generates the reconstructed vectors from the matrices; classifies a subset of the reconstructed vectors as components of a metrological model, wherein the sum of the components corresponds to the metrological model describing the metrological measurements of the one or more samples; generates correctable terms for one or more processing tools based on the metrological model; and provides the correctable terms to the one or more processing tools to provide feedback or feedforward control to the one or more processing tools.

36. The measurement method of claim 35, wherein the measurement model corresponds to a field model describing the variation of the measurement targets among the measurement targets within each of the plurality of fields.

37. The metrology method of claim 35, wherein the metrology model corresponds to a wafer model describing the variation of the metrological measurements of the plurality of fields.

38. The econometric method of claim 35, wherein the reconstructed vectors of components not classified as components of the econometric model correspond to residuals.

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