Measurement in the presence of CuA structures using an effective medium model based on the classification of CMOS underarray (CuA) structures.

Abstract

The system may include a controller configured to cause a processor to execute a measurement recipe by: receiving optical measurement data of a training sample after a first processing step for fabricating a complementary metal oxide semiconductor (CMOS) underarray (CuA) device, wherein the CuA device comprises a first structure having a non-uniform spatial distribution; classifying the first structure into spatially continuous regions based on unsupervised clustering; receiving optical measurement data of a training sample after a second processing step, wherein the CuA device after the second processing step comprises a periodic second structure on top of the first structure; constructing an effective medium model for the first structure; constructing a measurement model for determining measurements of the CuA device; receiving optical measurement data of a test sample after the second processing step; and generating measurement values ​​for the second structure based on the optical measurement data of the test sample and the measurement model.

Description

Technical Field

[0001] The present disclosure generally relates to optical measurement, and more specifically to optical measurement of a memory structure including a buried CMOS structure.

Background Art

[0002] As one approach to meet the requirement of improving performance while maintaining or reducing the physical size of a memory device (e.g., a 3D memory device), fabricating a CMOS circuit (e.g., a logic circuit) under a memory array structure can be mentioned. This approach is generally referred to as complementary metal-oxide semiconductor (CMOS) under array (CuA) technology. However, CuA technology presents specific issues for the measurement system used in process control, because the underlying CMOS circuit can affect the measurement of the memory array structure.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Patent Document 5

Patent Document 6

Patent Document 7

Patent Document 8

Patent Document 9

Patent Document 10

[0004] [Non-Patent Document 1] Germer, et al., “Intercomparison between optical and x-ray scatterometry measurements of FinFET structures” Proc.SPIE, v.8681, p.86810Q (2013) [Non-Patent Document 2] Kline,et al. “X-ray scattering critical dimensional metrology using a compact x-ray source for next generation semiconductor devices.”Journal of Micro / Nanolithography,MEMS,and MOEMS 16.1(2017) [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] Therefore, it is necessary to develop systems and methods to address this challenge. [Means for solving the problem]

[0006] A system is disclosed according to one or more exemplary embodiments of the present disclosure. In an embodiment, the system comprises a controller including one or more processors configured to execute program instructions, which cause one or more processors to execute a measurement recipe by: receiving optical measurement data of one or more training samples after a first processing step for fabricating a complementary metal oxide semiconductor (CMOS) underarray (CuA) device, wherein the CuA device includes a first structure having a non-uniform spatial distribution after the first processing step; classifying the first structure into spatially continuous regions based on unsupervised clustering of the optical measurement data of one or more training samples after the first processing step; and after a second processing step for fabricating the CuA device, one or more training samples The process involves receiving optical measurement data of a pull, wherein the CuA device after the second processing step includes a periodic second structure on top of the first structure; constructing an effective medium model for a spatially continuous region of the first structure; constructing a measurement model for determining one or more measurements of the CuA device based on the effective medium model for the spatially continuous region of the first structure and the optical measurement data of one or more training samples after the second processing step; receiving optical measurement data of one or more test samples after the second processing step for fabricating the CuA device; and generating one or more measurement values ​​of the second structure on one or more test samples based on the optical measurement data of one or more test samples and the measurement model.

[0007] A system is disclosed according to one or more exemplary embodiments of the present disclosure. In an embodiment, the system comprises an optical characterization system. In an embodiment, the system comprises a controller communicatively coupled to the optical characterization system, the controller comprising one or more processors configured to execute program instructions, the program instructions causing one or more processors to execute a measurement recipe by: receiving optical measurement data of one or more training samples from the optical characterization system after a first processing step for fabricating a complementary metal oxide semiconductor (CMOS) underarray (CuA) device, wherein the CuA device comprises a first structure having a non-uniform spatial distribution after the first processing step; classifying the first structure into spatially continuous regions based on unsupervised clustering of the optical measurement data of one or more training samples after the first processing step; and receiving from the optical characterization system a first for fabricating a CuA device 2. After processing steps, receive optical measurement data of one or more training samples, wherein the CuA device after the second processing step includes a periodic second structure on top of the first structure; construct an effective medium model for a spatially continuous region of the first structure; construct a measurement model for determining one or more measurements of the CuA device based on the effective medium model for the spatially continuous region of the first structure and the optical measurement data of one or more training samples after the second processing step; receive optical measurement data of one or more test samples from an optical characterization system after the second processing step for fabricating the CuA device; and generate one or more measurement values ​​of the second structure on one or more test samples based on the optical measurement data of one or more test samples and the measurement model.

[0008] Methods are disclosed according to one or more exemplary embodiments of the present disclosure. In embodiments, the method includes generating optical measurement data of one or more training samples after a first processing step for fabricating a complementary metal oxide semiconductor (CMOS) underarray (CuA) device, wherein the CuA device includes a first structure having a non-uniform spatial distribution after the first processing step. In embodiments, the method includes classifying the first structure into spatially continuous regions based on unsupervised clustering of the optical measurement data of one or more training samples after the first processing step. In embodiments, the method includes generating optical measurement data of one or more training samples after a second processing step for fabricating a CuA device, wherein the CuA device after the second processing step includes a periodic second structure on top of the first structure. In embodiments, the method includes constructing an effective medium model for the spatially continuous regions of the first structure. In embodiments, the method includes constructing a measurement model for determining one or more measurements of the CuA device based on the effective medium model for the spatially continuous regions of the first structure and the optical measurement data of one or more training samples after the second processing step. In an embodiment, the method includes generating optical measurement data of one or more test samples after a second processing step for fabricating a CuA device. In an embodiment, the method includes generating one or more measurement values ​​of a second structure on one or more test samples based on the optical measurement data of one or more test samples and a measurement model.

[0009] It should be understood that both the general description above and the detailed description below are for illustrative and illustrative purposes only and do not necessarily limit the claimed invention. The accompanying drawings incorporated herein and constituting part thereof illustrate embodiments of the invention and, together with the general description, contribute to illustrating the principles of the invention.

[0010] Those skilled in the art will better understand many advantages of the present disclosure by referring to the accompanying drawings.

Brief Description of the Drawings

[0011] [Figure 1A] It is a block diagram of a measurement system according to one or more embodiments of the present disclosure. [Figure 1B] It is a simplified schematic diagram of a characteristic evaluation subsystem configured as an optical characteristic evaluation subsystem according to one or more embodiments of the present disclosure. [Figure 1C] It is a simplified schematic diagram of a characteristic evaluation subsystem configured as an X-ray characteristic evaluation subsystem according to one or more embodiments of the present disclosure. [Figure 1D] It is a simplified schematic diagram of a characteristic evaluation subsystem configured as a particle beam characteristic evaluation subsystem according to one or more embodiments of the present disclosure. [Figure 2] It is a simplified schematic diagram of a CuA device according to one or more embodiments of the present disclosure. [Figure 3] It is a flowchart showing steps executed in a method for evaluating the characteristics of a CuA device according to one or more embodiments of the present disclosure.

Modes for Carrying Out the Invention

[0012] Here, refer in detail to the subject matter of the disclosure shown in the accompanying drawings. The present disclosure is specifically illustrated and described in a particular embodiment and with respect to its particular features. The embodiments described herein are considered to be illustrative rather than restrictive. It should be readily apparent to those skilled in the art that various changes and modifications can be made in form and detail without departing from the spirit and scope of the present disclosure.

[0013] Embodiments of this disclosure relate to systems and methods for optical measurement of CMOS underarray (CuA) devices based on the identification of spatial variations in complementary metal oxide semiconductor (CMOS) structures (e.g., logic structures), effective medium modeling of different spatial regions of the CMOS structure, and modeling the effects of different CMOS structures on optical measurement data. The systems and methods disclosed herein can provide high-precision measurement of memory array structures, taking into account the presence of spatially varying underlying CMOS structures.

[0014] A CuA structure (e.g., a CuA memory structure) typically includes logic circuits (e.g., CMOS logic circuits) physically arranged beneath a memory array structure (e.g., a three-dimensional (3D) memory stack or a 3D NAND structure). As used herein, the term CuA structure may encompass a wide range of logic and memory array structure designs. Therefore, this disclosure is not limited to any particular CuA architecture.

[0015] Optical measurement is commonly used in semiconductor process control because it can offer relatively high measurement throughput and is generally non-destructive. In optical measurement, a sample is illuminated with light, and measurements are generated based on the corresponding light emitted from the sample. In optical measurement of subsurface features, the light typically needs to propagate through at least the top of the sample to reach the subsurface feature of interest. Therefore, optical measurement systems typically utilize wavelengths of light selected to propagate through the target structure with relatively low absorption.

[0016] On the other hand, in the case of CuA structures, incident light interacts with both the memory array structure and the embedded CMOS structure, which can impair the ability to generate independent measurements of the memory array structure. This specification argues that existing optical measurement techniques may become insufficient for accurately characterizing CuA structures, especially as devices become smaller and more complex. For example, some techniques may depend on the wavelength of light within the transparent window of the memory array structure in question, which may be absorbed at least partially by the underlying logic circuitry. For instance, some logic circuitry may utilize a polysilicon layer that absorbs light with wavelengths greater than approximately 450 nanometers (nm). In this case, optical measurements at wavelengths lower than approximately 450 nm may generate independent measurements of the memory array structure. However, such techniques may be limited to CuA designs selected to incorporate the aforementioned absorbing materials, may have limited sensitivity to deep structures, and may be limited in terms of broadband optical measurement methods where multi-wavelength data are advantageous. As another example, some techniques rely on supervised learning of artificial neural networks using optical measurement data with labels generated through additional measurement methods. However, these methods may have various limitations, including, but are not limited to, the requirement of high sampling of ground truth reference data, the considerable time required to generate enough labels for training, performance limitations for deeply embedded structures, insensitivity to process changes, and generally inapplicability to CuA structures outside the training dataset.

[0017] In some embodiments of this disclosure, optical measurements of CuA structures are performed using a physical-based model, such as exact coupled-wave analysis (RCWA), which may require periodic features in the sample being characterized. While such physical-based models are suitable for CuA structures because memory array structures are typically periodic, the underlying CMOS structures may not be. In some embodiments, a workaround for this limitation involves further modeling the CMOS structure as a periodic film stack providing an effective medium with properties corresponding to those of the CMOS structure.

[0018] However, in this specification, since the CMOS structure is considered to be spatially variable (for example, different between samples), modeling the CMOS structure as a uniform 1D effective medium may be insufficient.

[0019] In some embodiments, unsupervised classification is used to identify spatially varying regions of a CMOS structure so that different effective medium models can be constructed for different regions of the CMOS structure. For example, unsupervised clustering techniques (e.g., k-nearest neighbor techniques, support vector machine (SVM) techniques, or neural network techniques) can be applied to optical measurement data from training samples containing CMOS structures before the fabrication of the memory array structure. Such training samples may include CMOS structures alone or samples containing CMOS structures and molded structures (e.g., a series of unpatterned films that serve as precursors to fully fabricated memory array structures). Thus, unsupervised clustering techniques can identify different spatial regions (e.g., clusters) of the CMOS structure that have different effects on the optical measurement data. Subsequently, different effective medium models can be constructed for the different regions.

[0020] Subsequently, complete physical-based models can be constructed for various domains. In some embodiments, additional optical measurement data from training samples generated after the fabrication of the memory array structure (e.g., after the fabrication of a complete CuA structure) can be used to construct complete physical-based models for various domains. Once the physical-based models are constructed, they can be used in the production line for optical measurements of newly fabricated CuA structures (e.g., test CuA structures).

[0021] Furthermore, the systems and methods disclosed herein are considered to be suitable for a wide range of CuA designs. When a test CuA structure shares the same design as the underlying CMOS structure, the layout of spatially varying regions (e.g., clusters) of the CMOS structure is invariant, and appropriate physical-based models can be easily applied to various regions. However, the design of the underlying CMOS structure may not be the same for all applications. In this case, it may be necessary to determine which physical-based model to use for optical measurements at each location on the test sample. In some embodiments, a supervised machine learning algorithm is trained using complete CuA structure and label optical measurement data generated from an unsupervised clustering step. Such a supervised machine learning algorithm can then determine an appropriate measurement model to use for each region on the test CuA structure.

[0022] A system and method for characterizing CuA structures according to one or more embodiments of the present disclosure will now be described in more detail with reference to Figures 1A to 3.

[0023] Figure 1A is a block diagram of a measurement system 100 according to one or more embodiments of the present disclosure. In some embodiments, the measurement system 100 comprises a characterization subsystem 102 that generates measurement data of a sample 104 using optical techniques, and a controller 106 that generates one or more measurements based on the measurement data.

[0024] The characterization subsystem 102 may include any components or combinations of components suitable for generating measurement data for sample 104.

[0025] In some embodiments, the characterization subsystem 102 includes an optical characterization subsystem 102 that generates measurement data based on the interaction between the sample 104 and light. For example, the characterization subsystem 102 may include, but is not limited to, a spectroscopic ellipsometer (SE), an SE with illumination at multiple angles, an SE that measures Müller matrix elements (e.g., using a rotational compensator), a single-wavelength ellipsometer, a beam profile ellipsometer (angle-resolved ellipsometer), a beam profile reflectometer (angle-resolved reflectometer), a broadband reflectometer (spectrophotometer), a single-wavelength reflectometer, an angle-resolved reflectometer, an imaging system, a scattermeter (e.g., a speckle analyzer), or a combination thereof.

[0026] In some embodiments, the characterization subsystem 102 includes an X-ray characterization subsystem 102 for generating measurement data based on the interaction between the sample 104 and X-rays. For example, the characterization subsystem 102 may be, but is not limited to, a small-angle X-ray scattering (SAXS) system or an X-ray reflection scattering measurement (SXR) system.

[0027] In some embodiments, the characterization subsystem 102 includes a particle beam characterization subsystem 102 that generates measurement data based on the interaction between a particle beam, such as but not limited to an electron beam (e-beam), an ion beam, or a neutral particle beam, and a sample 104.

[0028] In some embodiments, the characterization subsystem 102 provides multiple types of measurements. In some embodiments, the measurement system 100 includes multiple measurement subsystems 102, each providing one or more different combinations of measurements. Furthermore, the measurement system 100 may be provided as a single tool or as multiple tools. A single tool providing multiple measurement configurations is generally described in Patent Document 1, published April 26, 2011, which is incorporated herein by reference in its entirety. Multiple tools and structural analysis are generally described in Patent Document 2, published January 13, 2009, which is incorporated herein by reference in its entirety.

[0029] Furthermore, Patent Document 3, published on October 29, 2019, entitled "Model based optical measurements of semiconductor structures with anisotropic dielectric permittivity," Patent Document 4, published on February 7, 2023, entitled "Scatterometry based methods and systems for measurement of strain in semiconductor structures," Patent Document 5, published on June 15, 2021, entitled "Measurement models of nanowire semiconductor structures based on re-useable sub-structures," Patent Document 6, published on January 17, 2023, entitled "Measuring thin films on grating and bandgap on grating," Patent Document 7, published on October 26, 2021, entitled "Measurement methodology of advanced nanostructures," and Patent Document 8, published on October 6, 2020, entitled "Visualization of three-dimensional semiconductor structures," are all incorporated herein by reference in their entirety.

[0030] In some embodiments, the controller 106 comprises one or more processors 108 configured to execute a set of program instructions held in memory 110 or a memory device, the program instructions causing the processors 108 to perform various operations.

[0031] One or more processors 108 of the controller 106 may include any processor or processing element known in the art. For the purposes of this disclosure, the terms “processor” or “processing element” may be broadly defined to include any device having one or more processing or logic elements (e.g., one or more microprocessor devices, one or more application-specific integrated circuit (ASIC) devices, one or more field-programmable gate arrays (FPGAs), or one or more digital signal processors (DSPs)). In this sense, one or more processors 108 may include any device configured to execute algorithms and / or instructions (e.g., program instructions stored in memory). In some embodiments, one or more processors 108 may be embodied as a desktop computer, a mainframe computer system, a workstation, an image computer, a parallel processor, a network computer, or any other computer system configured to execute a program that operates or is configured to operate with the characterization subsystem 102, as described throughout this disclosure. Furthermore, different subsystems of the measurement system 100 may include processors or logic elements suitable for performing at least some of the steps described in this disclosure. Therefore, the above description should not be construed as an limitation to embodiments of the present disclosure, but rather as an example. Furthermore, the steps described throughout the present disclosure may be performed by a single controller, or alternatively, by multiple controllers. In addition, controller 106 may include one or more controllers housed in a common housing or multiple housings. In this way, any controller or combination of controllers can be separately packaged as modules suitable for integration into the measurement system 100.

[0032] The memory 110 may include any storage medium known in the art that is suitable for storing program instructions executable by one or more associated processors 108. For example, the memory 110 may include a non-temporary storage medium. Another example of the memory 110 may include, but is not limited to, read-only memory (ROM), random access memory (RAM), magnetic or optical memory devices (e.g., disks), magnetic tapes, and solid-state drives. It should be further noted that the memory 110 may be housed in a common controller housing together with one or more processors 108. In some embodiments, the memory 110 may be located remotely from the physical locations of one or more processors 108 and the controller 106. For example, one or more processors 108 of the controller 106 may access remote memory (e.g., a server) accessible via a network (e.g., the Internet, and an intranet).

[0033] The controller 106 may be communicatively coupled to any component or combination of components of the measurement system 100. In some embodiments, the controller 106 may receive data (e.g., measurement data) from one or more components of the measurement system 100. In some embodiments, the controller 106 may control one or more components of the measurement system 100 via drive signals. More generally, the controller 106 may perform any of the steps described herein.

[0034] In some embodiments, the controller 106 generates one or more measurements of sample 104 based at least in part on measurement data generated by the characterization subsystem 102. Measurement of the target parameter may involve numerous algorithms that can be performed by the controller 106. For example, the optical interaction between sample 104 and the incident beam can be modeled using an electromagnetic (EM) solver, and algorithms such as exact coupled-wave analysis (RCWA), finite element method (FEM), method of moments, surface integral, volume integral, or finite-difference time-domain (FDTD) methods may be used, but are not limited to these. Sample 104 may be modeled (e.g., parameterized) using a geometric engine, a process modeling engine, or a combination of both. The use of process modeling is generally described in Patent Document 9, published September 8, 2020, which is incorporated herein by reference in its entirety. Geometric engines are implemented, for example, in KLA Corporation's AcuShape software.

[0035] Controller 106 may analyze the collected measurement data using, but is not limited to, libraries, fast order reduction models, regression, statistical methods (see, for example, “Statistical model-based metrology” in Patent Document 10 by S. Pandev et al.), machine learning algorithms (e.g., more generally, neural networks, support vector machines (SVM), principal component analysis (PCA), independent component analysis (ICA), local linear embeddings (LLE), dimensionality reduction techniques), sparse representation techniques, Fourier transform techniques, wavelet transform techniques, or any appropriate combination of data fitting and / or optimization techniques such as Kalman filtering. Statistical model-based metrology is generally described in Patent Document 10, published on October 16, 2018, which is incorporated herein by reference in its entirety. Controller 106 may analyze the collected measurement data using algorithms that do not involve modeling, optimization, and / or fitting. The characterization of patterned wafers is generally described in Patent Document 11, published on December 10, 2019, which is incorporated herein by reference in its entirety. In some embodiments, the controller 106 utilizes one or more algorithms to facilitate matching from the same or different types of tools (e.g., different instances or configurations of the characterization subsystem 102).

[0036] The controller 106 may be designed to provide efficient performance through any appropriate technique such as parallelization, computational distribution, load balancing, multi-service support, or dynamic load optimization, but is not limited to these. Furthermore, the controller 106 may perform any step using any type or combination of configurations such as dedicated hardware (e.g., FPGA), software, or firmware, but is not limited to these.

[0037] Furthermore, the controller 106 may generate any type of measurement of sample 104 (or a portion thereof) based at least in part on measurement data from the characterization subsystem 102. In some embodiments, the controller 106 generates measurement measurements such as overlay measurements, limit dimension (CD) measurements, shape measurements (e.g., height measurements, inclination measurements, or sidewall angle measurements), stress measurements, composition measurements, bandgap measurements, electrical property measurements, or process condition measurements (e.g., focus and / or dose conditions, resist state, partial pressure, temperature, or focusing model). In some embodiments, the controller 106 generates inspection measurements in which one or more defects on sample 104 are identified or classified.

[0038] The measurement system 100 and any of its components (e.g., the characterization subsystem 102, or the controller 106) may be configured to implement a recipe (e.g., a measurement recipe) which can define various configuration parameters and / or steps performed in a measurement or a series of measurements.

[0039] For example, a recipe may include various embodiments of the design of sample 104 (e.g., the design of the CuA device 202 on sample 104). Such embodiments include, but are not limited to, the layout of features on one or more sample layers, the size of features, or the pitch of features. Another example of a recipe may include, but are not limited to, illumination parameters such as illumination wavelength, illumination pupil distribution (e.g., the distribution of illumination angles and the associated intensity of illumination at those angles), polarization of incident illumination, illumination spatial distribution, or sample height. Another example of a recipe may include, but are not limited to, collection parameters such as collection pupil distribution (e.g., the desired distribution of angular light from the sample used for measurement and the associated filtered intensity at those angles), collection field aperture settings for selecting the portion of the sample under consideration, polarization of collected light, or wavelength filters. Another example of a recipe may include various processing steps (e.g., those performed by controller 106 to generate measurements based on the measurement data generated according to the recipe).

[0040] Referring now to Figure 2, which is a simplified schematic diagram of a CuA device 202 according to one or more embodiments of the present disclosure. The CuA device 202 may comprise a memory array structure 204 and various CMOS structures 206 (e.g., logic structures) located beneath the memory array structure 204.

[0041] The memory array structure 204 may include any number or type of structures suitable for forming a memory array. For example, the memory array structure 204 may include, but is not limited to, a 3D NAND structure formed from patterned features 208 in a multilayer stack 210. Furthermore, such a memory array structure 204 is typically a periodic structure having periodicity along one or more dimensions.

[0042] The CMOS structure 206 may include any number or type of structures fabricated beneath the memory array structure 204. For example, the CMOS structure 206 may, but does not necessarily, be suitable for controlling and / or powering the memory array structure 204. In this way, a memory device can be formed by the combination of the CMOS structure 206 and the memory array structure 204 (e.g., a 3D memory device). Furthermore, the CMOS structure 206 may typically have a spatially variable distribution such that the number and / or design of its constituent features may not be periodic across the entire CuA device 202. Thus, the CMOS structure 206 can generally be described as aperiodic. However, it should be noted that the CMOS structure 206 may exhibit local periodicity in some regions.

[0043] Furthermore, the memory array structure 204 and / or CMOS structure 206 can generally have any design, and therefore the term CuA device 202 as used herein is not limited to any particular design. For example, the CuA device 202 may, but is not limited to, include an intervening layer between the memory array structure 204 and the CMOS structure 206, such as a source layer 212 (e.g., a polysilicon source layer). In another example not shown, the CuA device 202 may include an intervening layer between the CMOS structure 206 and the substrate 214.

[0044] Referring here to Figure 3, a technique for characterizing a CuA device 202 or a portion thereof, according to one or more embodiments of the present disclosure, will be described in more detail.

[0045] At various stages of the fabrication process, it may be desirable to generate measurements of the structural components of the CuA device 202 (e.g., CMOS structure 206 and / or memory array structure 204). Such measurements may include, but are not limited to, measurement or defect measurements (e.g., inspection measurements). Measurement may include, but are not limited to, overlay measurements, critical dimension (CD) measurements, shape measurements (e.g., height measurements, inclination measurements, or sidewall angle measurements), stress measurements, composition measurements, bandgap measurements, electrical property measurements, or process condition measurements (e.g., focus and / or dose conditions, resist state, partial pressure, temperature, or focusing model). Inspection measurements may include, but are not limited to, identification and / or characterization of defects in the fabrication process (e.g., unwanted features, missing features, or features with inappropriate shape or location). Furthermore, such measurements may be used for a wide range of purposes, including, but not limited to, process control, placement, or performance estimation of the fabricated CuA device 202.

[0046] Measurements may be generated after any processing step for fabricating the CuA device 202. For example, measurements may be generated after the fabrication of the CMOS structure 206 and / or after the fabrication of the memory array structure 204 for forming the complete CuA device 202. For convenience of explanation, measurements of the complete CuA device 202, including both the memory array structure 204 and the underlying CMOS structure 206, are referred to herein as “full-loop” measurements.

[0047] In general, this specification assumes that, depending on the interaction between the illumination beam 114 and the sample 104, a single processing step measurement may provide information about any features fabricated on the sample 104. Thus, performing independent measurements of newly fabricated features can be difficult. For example, full-loop measurements generally provide information about both the memory array structure 204 and the underlying CMOS structure 206, or may be influenced by both, which can limit or impair the ability to generate independent measurements of the memory array structure 204.

[0048] In some embodiments, measurements of various test structures may be generated to support the generation of independent measurements of specific features. For example, a measurement of a test structure including a memory array structure 204 without the corresponding embedded CMOS structure 206 is referred to herein as a “short-loop” measurement.

[0049] Furthermore, measurements at any processing step can generally be produced using any suitable technique, including but not limited to optical, X-ray, or particle-based techniques. However, different measurement techniques may have different trade-offs. For example, optical measurement techniques can generally provide non-destructive measurements with high measurement throughput, but may have limited resolution or be restricted to certain types of structures (e.g., periodic structures) based on the corresponding analysis or modeling step. Therefore, optical measurements are commonly used when throughput is particularly critical. As another example, X-ray and / or particle-based techniques may offer higher resolution than some optical techniques, but may have relatively lower throughput and / or may be destructive measurements. Consequently, such techniques are commonly used for reference measurements.

[0050] However, this specification does not consider it feasible or desirable in all applications to generate every possible type of measurement at every measurement step. In such cases, depending on the available data, various techniques may be used to generate measurements of a specific structure (e.g., independent measurements of the memory array structure 204).

[0051] Figure 3 is a flowchart illustrating the steps performed in a method 300 for characterizing a CuA device 202 according to one or more embodiments of the present disclosure. The applicant notes that embodiments and enabling techniques described herein with respect to the measurement system 100 should be construed to extend to method 300 as well. For example, any of the steps associated with method 300 may be implemented by the controller 106 and / or the characterization subsystem 102 of the measurement system 100. However, it should be further noted that method 300 is not limited to the architecture of the measurement system 100.

[0052] In this specification, Method 300 is considered suitable for applications where it is desirable to generate independent measurements of the memory array structure 204 without using short-loop measurements, but is not limited thereto. One goal of this approach is to construct effective markings of the CMOS structure 206 that can be used in physical-based models that generally depend on the presence of periodic structures, such as RCWA techniques, but are not limited thereto. One obstacle associated with this approach is that the CMOS structure 206 is not generally periodic, and therefore is not directly compatible with physical-based models that require periodic structures. In some embodiments, effective medium modeling techniques are used to model the CMOS structure 206 as an effective medium, and the properties of the effective medium vary spatially to capture the spatial variation of the CMOS structure 206.

[0053] In some embodiments, method 300 includes a step 302 to generate optical measurement data for one or more training samples after a first processing step for fabricating a CuA device, wherein the CuA device includes a first structure having a non-uniform spatial distribution after the first processing step. For example, the first structure may include a CMOS structure 206. As another example, the first structure may include a molded structure that, in addition to the CMOS structure 206, includes multiple layers of deposited material that are patterned into a memory array structure 204. Thus, the molded structure may correspond to a precursor of the memory array structure 204.

[0054] Optical measurement data may include, but are not limited to, any type of data generated by any type of optical system, such as the optical characterization subsystem 102 shown in Figure 1B. For example, optical measurement data may include, but are not limited to, spectral data from a polarization analyzer, reflectometer, or scattermeter (e.g., polarization analysis data, reflectance measurement data, or scattering measurement data, respectively).

[0055] Furthermore, in some embodiments, one or more training samples include known variations of the first structure (e.g., those related to expected process deviations). In this way, the effects of such variations can be identified and incorporated into the model of Method 300 described below. Such a procedure may be referred to as Design of Experiments (DOE) and may improve the strength of Method 300.

[0056] In some embodiments, Method 300 includes step 304 of classifying the first structures into spatially contiguous regions based on unsupervised clustering of optical measurement data for one or more training samples. Herein, it is assumed that structural variations in the number and / or design of the first structures may have different effects on the optical measurement data of the first structures (e.g., those generated in step 302). Therefore, the unsupervised clustering technique may divide the samples into different spatially contiguous regions with similar optical measurement data, so that different regions can be modeled independently. It should be noted that classifying the first structures into regions based on optical measurement data rather than the design of the first structures may result in beneficial grouping based on the actual impact on the optical measurement data in question.

[0057] Step 304 may utilize, but is not limited to, any unsupervised clustering technique known in the art, such as k-nearest neighbor technique, SVM technique, or neural networks adapted for unsupervised clustering.

[0058] In some embodiments, method 300 includes a step 306 to generate optical measurement data of one or more training samples after a second processing step for fabricating a CuA device 202, wherein the CuA device 202 after the second processing step includes a periodic second structure on top of the first structure. For example, the second structure may include a periodic memory array structure 204. Thus, the optical measurement data generated in step 306 may correspond to full-loop data.

[0059] In some embodiments, method 300 includes step 308 of constructing an effective medium model for a region of the first structure. In some embodiments, after the second processing step, method 300 includes step 310 of constructing a measurement model for determining one or more measurements of the CuA device 202 based on the effective medium model for the group of the first structure and optical measurement data of one or more learning samples. The measurements may characterize any part of the CuA device 202, including but not limited to a memory array structure 204 or a CMOS structure 206.

[0060] For example, various properties of the CuA device 202 (or a particular part thereof) may be provided as floating parameters in a model, with values ​​that can be obtained by fitting optical data to a measurement model. One or more measurements of the CuA device 202 or its constituent features (e.g., memory array structure 204 and / or CMOS structure 206) may be generated, either directly or in combination, based on these values ​​of the floating parameters determined by the fit. Non-limiting examples of such measurements include, but are not limited to, overlay, CD, height, tilt, defect identification, or defect classification.

[0061] In some embodiments, the measurement model requires various assumptions or constraints regarding the relevant features on the sample, including, but not limited to, the periodicity of the features. In these cases, a first structure (e.g., CMOS structure 206 alone and / or with molded structure) which may generally be aperiodic (but may exhibit some local periodicity) is used as a valid material having valid properties that provide optical measurement data consistent with the measured optical measurement data from step 302. This process may be repeated in step 308 for each region identified by the unsupervised clustering in step 304.

[0062] For example, an effective medium model may treat the first structure as an effective medium formed as either a single material or a stack of different materials, and provide a representation of the effective dispersion of this effective medium. In this way, various parameters related to the effective medium, such as, but not limited to, the thickness or dispersion of any layer, may be provided as floating parameters that can be determined either directly to the optical measurement data provided in step 302, or by fitting to values ​​derived from this data. Examples of effective medium models include, but are not limited to, the harmonic oscillator model, the Tauc-Lorentz model, the Cauchy model, the Bruggeman effective medium approximation (BEMA) model, or the nk-offset model, and any other technique and / or dispersion model may be used.

[0063] Furthermore, in step 310, a measurement model may be generated for each of these regions using the effective medium model for each region. As a result, any number of measurements of the memory array structure 204 and / or CMOS structure 206 may be generated based on fitting the optical measurement data to the measurement model of step 310 in a manner that takes into account the spatial variations of the CMOS structure 206 that affect the optical measurement data.

[0064] The measurement model constructed in step 310 may include any type of model or combination of models that incorporate different effective medium models for the regions of the first structure.

[0065] In some embodiments, the measurement model constructed in step 310 may include a physical-based model in which the properties of the CuA device 202 relate to the measurement under consideration through a model of the interaction between one or more illumination beams 114 and the properties of the constituent features. Examples include, but are not limited to, RCWA models, FEM models, method of moments models, surface integral models, volume integral models, or FDTD models, and any suitable physical-based measurement model may be used.

[0066] In some embodiments, the measurement model constructed in step 310 includes a machine learning model that is at least partially trained on data generated from a physical-based model as described above. For example, Method 300 may include the step of generating synthetic measurement data using a physical-based measurement model having a set of parameters describing a synthetic CuA device 202. Method 300 may then include the step of training a machine learning model to generate one or more measurements based on the training data, where the training data includes at least one of optical measurement data for one or more training samples, or synthetic data describing a synthetic CuA device 202. Thus, the physical-based model may be used to provide supplementary training data beyond the experimental data (e.g., optical measurement data and / or reference data) associated with the training and / or test samples described above.

[0067] For example, the synthetic measurement data may include a synthesized equivalent of optical measurement data (which may be generated, for example, by the optical characterization subsystem 102) based on various combinations of geometric and dispersion parameters of the CuA device 202. For instance, different combinations of geometric and dispersion parameters of the memory array structure 204, as well as different effective medium models of the CMOS structure 206, may be provided to a physical-based measurement model as input to generate the synthetic measurement data as output. Thus, this synthetic measurement data can be characterized as a synthetic DOE suitable for providing training data for machine learning models.

[0068] The measurement model constructed in step 310 can then be used during the fabrication process to generate measurements of additional samples (e.g., test samples) with unknown properties.

[0069] In some embodiments, the method 300 includes a step 312 after the second processing step for fabricating the CuA device 202, which generates optical measurement data for one or more test samples. Thus, step 312 may include generating full-loop data of the CuA device 202 on the test samples.

[0070] In some embodiments, Method 300 includes step 314, which generates one or more measurement values ​​of the CuA device 202 for one or more test samples based on optical measurement data of one or more test samples and a measurement model. For example, the optical measurement data from step 312 may be fitted to the measurement model from step 310 to determine the values ​​of various parameters of the CuA device 202. The measurements can characterize any aspect of the CuA device 202 on a test sample, including but not limited to a memory array structure 204 or a CMOS structure 206. In particular, it should be noted that step 314 can provide accurate measurements of the memory array structure 204 in the presence of a spatially heterogeneous CMOS structure 206, based on corresponding modeling of different regions as described above.

[0071] This specification further considers that step 314 may be used to generate measurements of a wide range of CuA devices 202 on a test sample. Generally, it may be necessary to determine which measurement model of step 314 (e.g., associated with a specific region identified in step 304) to utilize at any particular location on the test sample.

[0072] In some embodiments, the CuA device 202 on the training and test samples has substantially the same design. In these cases, the location of each region within the CuA device 202 may be known and fixed so that a corresponding measurement model for each region can be applied when generating measurements of the CuA device 202 on the test sample.

[0073] In some embodiments, the CuA device 202 on the training and test samples differ either by design or as a result of process variations. In these cases, it may be necessary to select an appropriate measurement model to use at each location on the test sample. In some embodiments, method 300 includes the step of training a supervised machine learning model based on measured optical measurement data from step 306 (e.g., full-loop data from the CuA device 202 on the training sample) with labels associated with relevant regions identified in step 304. Thus, the trained supervised machine learning model may classify each location on the test sample as similar to one of the regions identified in step 304 so that an appropriate effective medium model (e.g., from step 308) and measurement model (e.g., from step 310) can be applied. For example, step 314 may include, for each location on one or more test samples, selecting one of the measurement models that uses a machine learning model having relevant optical measurement data from the location of one or more test samples, and further, for each location on one or more test samples, generating one or more measurement values ​​based on the optical measurement data of one or more test samples and the selected measurement model.

[0074] Measurements of the CuA device 202 on a test sample can then be used for various purposes. In some embodiments, the measurements are used to estimate the process control, placement, and / or performance of the CuA device 202 on the test sample. For example, the measurements may be used to generate modifiable values ​​for one or more process tools (e.g., scanners or steppers) in a feedback and / or feedforward process.

[0075] With reference to Figures 1B to 1D, various non-limiting configurations of the characterization subsystem 102 according to one or more embodiments of the present disclosure will be described in more detail.

[0076] In some embodiments, the characterization subsystem 102 is an optical measurement subsystem that generates measurement data based on the interaction between the sample 104 and light. Figure 1B is a simplified schematic diagram of the characterization subsystem 102 configured as an optical characterization subsystem 102 according to one or more embodiments of the present disclosure. For example, the characterization subsystem 102 may include, but is not limited to, a spectroscopic ellipsometer (SE), a multi-angle illumination SE, an SE that measures Müller matrix elements (e.g., using a rotational compensator), a single-wavelength ellipsometer, a beam profile ellipsometer (e.g., an angle-resolved ellipsometer), a beam profile reflectometer (e.g., an angle-resolved reflectometer), a broadband reflectance spectrometer (e.g., a spectrophotometer), a single-wavelength reflectometer, an angle-resolved reflectometer, an imaging system, a scattermeter (e.g., a speckle analyzer), or a combination thereof.

[0077] In some embodiments, the characterization subsystem 102 includes an illumination source 112 configured to produce at least one illumination beam 114. The illumination from the illumination source 112 may include, but not limited to, ultraviolet (UV), visible, or infrared (IR) radiation, one or more selected wavelengths of light. For example, the characterization subsystem 102 may include one or more apertures in the illumination pupil plane to split the illumination from the illumination source 112 into one or more illumination beams 114 or illumination lobes. In this regard, the characterization subsystem 102 may provide dipole illumination, or orthogonal illumination, etc. Furthermore, the spatial profiles of one or more illumination beams 114 on the sample 104 may be controlled by a field plane aperture to have any selected spatial profile.

[0078] The illumination source 112 may include any type of illumination source suitable for providing at least one illumination beam 114. In some embodiments, the illumination source 112 is a laser source. For example, the illumination source 112 may include, but is not limited to, one or more narrowband laser sources, broadband laser sources, supercontinuum laser sources, or white light laser sources. In some embodiments, the illumination source 112 includes a laser sustained plasma (LSP) source. For example, the illumination source 112 may include, but is not limited to, an LSP lamp, LSP bulb, or LSP chamber, which preferably includes one or more elements capable of emitting broadband illumination when excited to a plasma state by a laser source. In some embodiments, the illumination source 112 includes a lamp source. In some embodiments, the illumination source 112 may include, but is not limited to, an arc lamp, a discharge lamp, or an electrodeless lamp.

[0079] The illumination source 112 may provide one or more illumination beams 114 using free-space technology and / or optical fibers.

[0080] In some embodiments, the characterization subsystem 102 directs the illumination beam 114 to the sample 104 via an illumination path 118 through at least one illumination lens 116 (e.g., an objective lens). The illumination path 118 directs the illumination beam 114 to the sample 104 and may include one or more optical components suitable for modifying and / or adjusting the illumination beam 114. In some embodiments, the illumination path 118 includes one or more illumination path optics 120 for shaping or otherwise controlling the illumination beam 114. For example, the illumination path optics 120 may include, but are not limited to, one or more field diaphragms, one or more pupil diaphragms, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, one or more beam shapers, or one or more mirrors (e.g., static mirrors, translationally movable mirrors, or scanning mirrors).

[0081] The characterization subsystem 102 may position the sample 104 for measurement using any suitable technique. In some embodiments, as shown in Figure 1B, the characterization subsystem 102 includes a sample stage 122 which includes one or more actuators (e.g., linear actuators, tip / tilt actuators, or rotary actuators) for positioning the sample 104 relative to the illumination beam 114. In some embodiments, although not explicitly shown, the characterization subsystem 102 includes a beam scanning optical system (e.g., galvanometer mirrors, or scanning prisms) for adjusting the position and / or scanning one or more illumination beams 114.

[0082] In some embodiments, the characterization subsystem 102 includes at least one collecting lens 124 for capturing light or other radiation emitted from the sample 104, referred to in this detail as collected light 126, and directing this collected light 126 to one or more detectors 128 via a collecting path 130. The collecting path 130 may include one or more optical elements suitable for modifying and / or adjusting the collected light 126 from the sample 104. In some embodiments, the collecting path 130 includes one or more collecting path optics 132 for shaping or otherwise controlling the collected light 126. For example, the collecting path optics 132 may include, but are not limited to, one or more field diaphragms, one or more pupil diaphragms, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, one or more beam shapers, or one or more mirrors (e.g., static mirrors, translationally movable mirrors, or scanning mirrors).

[0083] The characterization subsystem 102 may generally include any number or type of detectors 128. For example, the characterization subsystem 102 may include, but is not limited to, a photodiode, avalanche photodiode, or single-photon detector, at least one single-pixel detector 128. Another example is the characterization subsystem 102, which may include, but is not limited to, a charge-coupled device (CCD) or complementary metal-oxide-semiconductor (CMOS) device, a line detector, or a time-delay integral (TDI) detector, at least one multi-pixel detector 128.

[0084] The detector 128 can be positioned at any selected location within the collection path 130. In some embodiments, the characterization subsystem 102 includes the detector 128 on the field of view (e.g., the plane conjugate to the sample 104) to generate an image of the sample 104. In some embodiments, the characterization subsystem 102 includes the detector 128 on the pupil plane (e.g., the diffraction plane) to generate a pupil image. In this regard, the pupil image may correspond to the angular distribution of light from the sample 104 captured by the detector 128. For example, the diffraction order related to the diffraction of the illumination beam 114 from the sample 104 may be imaged on the pupil plane or otherwise observed. Generally, the detector 128 can capture any combination of reflected (or transmitted), scattered, or diffracted light from the sample 104.

[0085] The illumination path 118 and collection path 130 of the characterization subsystem 102 can be oriented in a wide range of configurations. For example, as shown in Figure 1B, the illumination path 118 and collection path 130 can include non-overlapping optical paths. In some embodiments, though not explicitly shown, the characterization subsystem 102 may include an oriented beam splitter such that a common objective lens directs the illumination beam 114 towards the sample 104 while simultaneously capturing the collected light 126.

[0086] Figure 1C is a simplified schematic diagram of a characterization subsystem 102 configured as an X-ray characterization subsystem 102 according to one or more embodiments of the present disclosure. Such a characterization subsystem 102 may, but is not limited to, a small-angle X-ray scattermeter (SAXR) or a soft X-ray reflectometer (SXR). X-ray characterization systems and related measurement techniques are generally described in Patent Document 12, published April 19, 2011; Patent Document 13, published February 6, 2018; Patent Document 14, published July 3, 2018; Patent Document 15, published June 18, 2019; Patent Document 16, published July 16, 2019; Patent Document 17, published September 15, 2020; Non-Patent Document 1; Non-Patent Document 2; Patent Document 18, published May 17, 2022; and Patent Document 19, published July 8, 2021, which are incorporated herein by reference in their entirety.

[0087] In some embodiments, the illumination source 112 is an X-ray source configured to produce an X-ray illumination beam 114 having any particle energy (e.g., soft X-rays or hard X-rays). The characterization subsystem 102 may include any combination of components suitable for capturing the associated acquired signal 134, which may include, but are not limited to, X-ray emission, optical emission, or particle emission.

[0088] For example, the characterization subsystem 102 may include an X-ray illumination lens 116 suitable for collimating or focusing the X-ray illumination beam 114, and a collection path lens (not shown) suitable for collecting, collimating, and / or focusing the collected signal 134 from the sample 104. Furthermore, the characterization subsystem 102 may include, but is not limited to, various illumination path optics (not shown) and / or collection path optics (not shown), such as a specular X-ray optical system including an X-ray collimating mirror, an oblique incidence ellipsoidal mirror, a polycapillary optical system including a hollow capillary X-ray waveguide, a multilayer optical system, or a system, or any combination thereof. In embodiments, the characterization subsystem 102 may include, but is not limited to, an X-ray detector 128, such as an X-ray monochromator (e.g., a crystalline monochromator such as a Loxley-Tanner-Bowen monochromator), an X-ray aperture, an X-ray beam diaphragm, or a diffraction optical system (e.g., a zone plate).

[0089] Figure 1D is a simplified schematic diagram of a characterization subsystem 102 configured as a particle beam characterization subsystem 102 according to one or more embodiments of the present disclosure.

[0090] In one embodiment, the illumination source 112 includes a particle source (e.g., an electron beam source or an ion beam source), thereby the illumination beam 114 includes a particle beam (e.g., an electron beam or a particle beam). The illumination source 112 may include any particle source known in the art that is suitable for generating the particle illumination beam 114. For example, the illumination source 112 may include, but is not limited to, an electron gun or an ion gun. In another embodiment, the illumination source 112 is configured to provide a particle beam with adjustable energy. For example, the illumination source 112 including an electron source may provide, but is not limited to, an acceleration voltage in the range of 0.1 kilovolts (kV) to 30 kV. As another example, the illumination source 112 including an ion source may provide, but is not necessarily limited to, an ion beam with energy in the range of 1 kiloelectron volt (keV) to 50 keV.

[0091] In another embodiment, the illumination path 118 includes one or more particle focusing elements (e.g., an illumination lens 116 or a collecting lens 124). For example, one or more particle focusing elements may include, but are not limited to, a single particle focusing element or one or more particle focusing elements forming a composite system. In another embodiment, one or more particle focusing elements include an illumination lens 116 configured to guide the particle illumination beam 114 to the sample 104. Furthermore, one or more particle focusing elements may include, but are not limited to, electrostatic lenses, magnetic lenses, single-potential lenses, or double-potential lenses, or any type of electron lens known in the art.

[0092] In another embodiment, the characterization subsystem 102 includes one or more particle detectors 128 for imaging or otherwise detecting particles emitted from the sample 104. For example, the detector 128 may include an electron collector (e.g., a secondary electron collector, or a backscatter electron detector). In another example, the detector 128 may include a photon detector (e.g., a photodetector, an X-ray detector, or a scintillation element coupled to a photomultiplier tube (PMT) detector) for detecting electrons and / or photons from the sample surface.

[0093] The subject matter described herein may also refer to different components that are contained within or connected to other components. It should be understood that such illustrated architectures are merely illustrative, and that numerous other architectures achieving the same functionality are, in fact, possible. Conceptually, any arrangement of components to achieve the same functionality is effectively “related” to achieve the desired functionality. Therefore, any two components combined herein to achieve a particular functionality, regardless of the architecture or components in between, can be considered “related” to achieve the desired functionality. Similarly, any two such related components can also be considered “connected” or “linked” to each other to achieve the desired functionality, and any two such related components can also be considered “linkable” to each other to achieve the desired functionality. Specific examples of linkable components include, but are not limited to, physically interactable and / or physically interacting components, as well as / or wirelessly interactable and / or wirelessly interacting components, and / or logically interactable and / or logically interacting components.

[0094] Many of the present disclosure and its associated advantages are to be understood from the foregoing description, and it will be clear that various modifications can be made to the shape, structure, and arrangement of the components without departing from the disclosed subject matter or without impairing any of its important advantages. The shapes described are for illustrative purposes only, and the claims below are intended to encompass and include such modifications. Furthermore, it should be understood that the present invention is defined by the appended claims.

Claims

1. It is a system, A controller including one or more processors configured to execute program instructions, wherein the program instructions are to be executed by the one or more processors The process involves receiving optical measurement data of one or more training samples after a first processing step for fabricating a complementary metal oxide semiconductor (CMOS) underarray (CuA) device, wherein the CuA device includes a first structure having a non-uniform spatial distribution after the first processing step. Based on unsupervised clustering of the optical measurement data of one or more learning samples after the first processing step, the first structure is classified into spatially continuous regions. The process involves receiving optical measurement data of one or more learning samples after a second processing step for fabricating the CuA device, wherein the CuA device after the second processing step includes a periodic second structure on top of the first structure. To construct an effective medium model for the spatially continuous region of the first structure, Based on the effective medium model of the spatially continuous region of the first structure and the optical measurement data of the one or more learning samples after the second processing step, a measurement model is constructed for determining one or more measurements of the CuA device. After the second processing step for fabricating the CuA device, optical measurement data of one or more test samples is received. Based on the optical measurement data of the one or more test samples and the measurement model, one or more measurement values ​​of the second structure on the one or more test samples are generated. The controller executes the measurement recipe. A system that includes these features.

2. The system according to claim 1, wherein the first structure comprises a CMOS structure.

3. The system according to claim 1, wherein the first structure comprises a CMOS structure and a molded structure, and the molded structure includes a precursor of the second structure.

4. The one or more measurements described above are Measurement The system according to claim 1, including the following:

5. The aforementioned measurement is, At least one of the following: overlay measurement, limit dimension (CD) measurement, shape measurement, stress measurement, composition measurement, band gap measurement, electrical property measurement, or process condition measurement. The system according to claim 4, including the system described in claim 4.

6. The one or more measurements described above are Inspection and Measurement The system according to claim 1, including the following:

7. The aforementioned inspection and measurement is At least one of the identification or classification of defects in the second structure The system according to claim 6, including the system described in claim 6.

8. The system according to claim 1, wherein the first structure on one or more test samples has a common spatial distribution with the first structure on one or more training samples.

9. The system according to claim 1, wherein the first structure on one or more test samples has a different spatial distribution from the first structure on one or more training samples.

10. At least one of the effective dispersion models is, At least one of the following: harmonic oscillator model, Tauc-Lorentz model, Cauchy model, Bruggeman effective medium approximation (BEMA) model, or nk-offset model The system according to claim 1, including the following:

11. The system according to claim 1, wherein one particular effective medium model describes a portion of the plurality of first structures in one particular spatially continuous region as one or more films.

12. Constructing the effective medium model for at least one of the spatially continuous regions is, The dispersion or thickness of the one or more films is determined by fitting the one or more learning samples after the first processing step to match the corresponding optical measurement data. The system according to claim 11, including the following:

13. The measurement model is based on the interaction of light and matter with the CuA device, according to claim 1.

14. The system according to claim 1, wherein the measurement model includes a machine learning model that has at least partially learned synthesized data from a model based on the interaction of light and matter with the CuA device.

15. The system according to claim 1, wherein, after the first processing step, unsupervised clustering of the optical measurement data of one or more training samples is performed using at least one of the k-nearest neighbor algorithm, support vector machine, or neural network to identify the spatially continuous regions.

16. The machine learning model is trained based on the optical measurement data of one or more training samples after the second processing step and labels associated with the spatially continuous regions based on unsupervised clustering of the optical measurement data of one or more training samples after the first processing step. It further includes, To generate the values ​​of the one or more measurement of the second structure on the one or more test samples based on the optical measurement data of the one or more test samples and the measurement model, For each location on the one or more test samples, one of the measurement models is selected that uses the machine learning model having the relevant optical measurement data from the location on the one or more test samples. For each location on the one or more test samples, one or more measurement values ​​are generated based on the one or more test samples and the selected optical measurement data of the measurement model. including, The system according to claim 1.

17. The optical measurement data of the learning sample and at least one of the one or more test samples after the first processing step or after the second processing step is At least one of the following: polarization analysis data, reflectance measurement data, or scattering measurement data. The system according to claim 1, including the following:

18. It is a system, Optical characterization system, A controller communicatively coupled to the optical characterization system, the controller includes one or more processors configured to execute program instructions, the program instructions are transmitted to the one or more processors, The optical characterization system receives optical measurement data of one or more training samples after a first processing step for fabricating a complementary metal oxide semiconductor (CMOS) underarray (CuA) device, wherein the CuA device includes a first structure having a non-uniform spatial distribution after the first processing step. Based on unsupervised clustering of the optical measurement data of one or more learning samples after the first processing step, the first structure is classified into spatially continuous regions. The optical characterization system receives optical measurement data of one or more learning samples after a second processing step for fabricating the CuA device, wherein the CuA device after the second processing step includes a periodic second structure on top of the first structure. To construct an effective medium model for the spatially continuous region of the first structure, Based on the effective medium model of the spatially continuous region of the first structure and the optical measurement data of the one or more learning samples after the second processing step, a measurement model is constructed for determining one or more measurements of the CuA device. The optical characterization system receives optical measurement data of one or more test samples after the second processing step for fabricating the CuA device. Based on the optical measurement data of the one or more test samples and the measurement model, one or more measurement values ​​of the second structure on the one or more test samples are generated. The controller and A system that includes these features.

19. The aforementioned optical characterization system is At least one of the following: a polarization analyzer, a reflectometer, or a scattermeter. The system according to claim 18, comprising:

20. It is a method, The method involves generating optical measurement data of one or more training samples after a first processing step for fabricating a complementary metal oxide semiconductor (CMOS) underarray (CuA) device, wherein the CuA device is generated having a first structure with a non-uniform spatial distribution after the first processing step. Based on unsupervised clustering of the optical measurement data of one or more learning samples after the first processing step, the first structure is classified into spatially continuous regions. The process involves generating optical measurement data of one or more learning samples after a second processing step for fabricating the CuA device, wherein the CuA device after the second processing step includes a periodic second structure on top of the first structure. To construct an effective medium model for the spatially continuous region of the first structure, Based on the effective medium model of the spatially continuous region of the first structure and the optical measurement data of the one or more learning samples after the second processing step, a measurement model is constructed for determining one or more measurements of the CuA device. After the second processing step for fabricating the CuA device, optical measurement data of one or more test samples is generated. Based on the optical measurement data of the one or more test samples and the measurement model, one or more measurement values ​​of the second structure on the one or more test samples are generated. Methods that include...

21. The method according to claim 20, wherein the first structure comprises a complementary metal oxide semiconductor (CMOS) structure.

22. The method according to claim 20, wherein the first structure comprises a CMOS structure and a molded structure, and the molded structure comprises a precursor of the periodic second structure.

23. The one or more measurements described above are Measurement The method according to claim 20, including the method described in claim 20.

24. The aforementioned measurement is, At least one of the following: overlay measurement, limit dimension (CD) measurement, shape measurement, stress measurement, composition measurement, band gap measurement, electrical property measurement, or process condition measurement. The method according to claim 23, including the method described in claim 23.

25. The one or more measurements described above are Inspection and Measurement The method according to claim 20, including the method described in claim 20.

26. The aforementioned inspection and measurement is At least one of the identification or classification of defects in the second structure The method according to claim 25, including the method described in claim 25.

27. The method according to claim 20, wherein the first structure on one or more test samples has a common spatial distribution with the first structure on one or more training samples.

28. The method according to claim 20, wherein the first structure on one or more test samples has a different spatial distribution from the first structure on one or more training samples.

29. At least one of the effective dispersion models is, At least one of the following: harmonic oscillator model, Tauc-Lorentz model, Cauchy model, Bruggeman effective medium approximation (BEMA) model, or nk-offset model The method according to claim 20, including the method described in claim 20.

30. The method according to claim 20, wherein one particular model of the effective medium describes a portion of the plurality of first structures in one particular spatially continuous region as one or more films.

31. Constructing the effective medium model for at least one of the spatially continuous regions is, The dispersion or thickness of the one or more films is determined by fitting the one or more learning samples after the first processing step to match the corresponding optical measurement data. The method according to claim 30, including the method described in claim 30.

32. The method according to claim 20, wherein the measurement model is based on the interaction of light and matter with the CuA device.

33. The method according to claim 20, wherein the measurement model includes a machine learning model that has at least partially learned synthetic data from a model based on the interaction of light and matter with the CuA device.

34. The method according to claim 20, wherein, after the first processing step, unsupervised clustering of the optical measurement data of one or more training samples is performed using at least one of the k-nearest neighbor algorithm, support vector machine, or neural network to identify the spatially continuous regions.

35. The machine learning model is trained based on the optical measurement data of one or more training samples after the second processing step and the labels associated with the spatially continuous regions based on the unsupervised clustering of the optical measurement data of one or more training samples after the first processing step. It further includes, To generate the values ​​of the one or more measurement of the second structure on the one or more test samples based on the optical measurement data of the one or more test samples and the measurement model, For each location on the one or more test samples, one of the measurement models is selected that uses the machine learning model having the relevant optical measurement data from the location on the one or more test samples. For each location on the one or more test samples, one or more measurement values ​​are generated based on the one or more test samples and the selected optical measurement data of the measurement model. including, The method according to claim 20.

36. The optical measurement data of the learning sample and at least one of the one or more test samples after the first processing step or after the second processing step is At least one of the following: polarization analysis data, reflectance measurement data, or scattering measurement data. The method according to claim 20, including the method described in claim 20.

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