Measurement solution for a complex structure of interest

Abstract

Complex structures such as gate-all-around (GAA) field-effect transistors or high-aspect ratio (HAR) channel hole etching in semiconductor devices are measured using a combination of physical modeling and machine learning modeling. Measurement signals collected in different manufacturing process steps, for example, pre-processing steps and post-processing steps of the structure of interest (SOI), can be used. The measurement signals obtained in the pre-processing steps are used, for example, to determine the first parameters of the SOI using physical modeling and machine learning, and this signal can be fed forward and used to generate a physical model of the SOI in the post-processing steps. The second parameters of the SOI in the post-processing steps are determined using physical modeling and machine learning, fed back, and used to generate a physical model of the SOI in the post-processing steps using the post-processing signals and can be used to determine other parameters.

Description

Technical Field

[0001] (Cross - Reference to Related Applications) This application claims the priority and benefit of U.S. Provisional Application No. 63 / 355,053, entitled "METROLOGY SOLUTIONS FOR GATE - ALL - AROUND TRANSISTORS", filed on June 23, 2022; U.S. Provisional Application No. 63 / 498,475, entitled "MULTIPLE SOURCES OF SIGNALS FOR HYBRID METROLOGY USING PHYSICAL MODELING AND MACHINE LEARNING", filed on April 26, 2023; and U.S. Non - Provisional Application No. 18 / 339,971, entitled "METROLOGY SOLUTIONS FOR COMPLEX STRUCTURES OF INTEREST", filed on June 22, 2023. All of these are assigned to the assignee of this application and are hereby incorporated by reference in their entirety.

[0002] (Field of the Invention) The subject matter described herein generally relates to metrology, and more specifically, to modeling and measurement of structures using multiple data sources and combinations of physical modeling and machine learning.

Background Art

[0003] In the semiconductor and other similar industries, measurement techniques such as optical metrology or X - ray metrology are often used to provide non - contact evaluation of samples during processing. In optical metrology, for example, a test sample is irradiated with light of, for example, a single wavelength or multiple wavelengths. After the light interacts with the sample, the resulting light is detected and analyzed to determine one or more characteristics of the sample.

[0004] Analysis typically involves modeling the test structure. The model can be generated based on the physical characteristics of the structure, such as the material of the structure and nominal parameters, such as film thickness, optical properties of the material, line, and pitch width, and thus may be referred to as a physical model. One or more parameters of the model can be varied, and the predicted data can be calculated for each parameter variation based on the model using, for example, Rigorous Coupled Wave Analysis (RCWA) or other similar techniques. The measured data can be compared with the predicted data for each parameter variation, for example, in a non-linear regression process, until a good fit is achieved between the predicted data and the measured data. At that point, the fitted parameters are considered to be an accurate representation of the parameters of the test structure. However, modeling can be time-consuming, computationally intensive, and expensive, especially for small and complex features. SUMMARY OF THE INVENTION

[0005] Complex structures, such as gate-all-around (GAA) field-effect transistors or high-aspect ratio (HAR) channel hole etching in semiconductor devices, are measured using a combination of physical modeling and machine learning modeling. Additionally, measurement signals are collected at different manufacturing process steps, for example, in the pre-processing and post-processing steps of the structure of interest (SOI). The measurement signals obtained in the pre-processing step are used, for example, using physical modeling and machine learning, to determine the first parameters of the SOI, and this signal can be fed forward and used to generate a physical model of the SOI in the post-processing step to improve accuracy. In the post-processing step, the second parameters of the SOI are determined using physical modeling and machine learning, fed back, and used to generate a physical model of the SOI in the post-processing step to improve sensitivity and eliminate parameter correlation.

[0006] In one implementation, a method for measuring a plurality of parameters of interest from a structure of interest (SOI) includes, in a post-processing step, obtaining a post-processing step measurement signal from a measurement device for the SOI on one or more samples. The method further includes extracting a post-processing measurement result based on the post-processing step measurement signal, the value of a first parameter of the SOI in a pre-processing step that is fed forward to the post-processing physical model, the value of a second parameter of the SOI in a post-processing step that is fed back to the post-processing physical model, and at least one of combinations thereof, from the post-processing physical model of the SOI. The method further includes predicting a final value of the second parameter of the SOI in the post-processing step from a trained post-processing machine learning model based on the post-processing measurement result extracted from the post-processing physical model, and providing at least the final value of the second parameter of the SOI.

[0007] In one implementation, a computer system configured to measure a plurality of parameters of interest from a structure of interest (SOI) includes at least one processor, and the at least one processor is configured to obtain a post-processing step measurement signal from a measurement device for the SOI on one or more samples in a post-processing step. The at least one processor is further configured to extract a post-processing measurement result based on the post-processing step measurement signal, the value of a first parameter of the SOI in a pre-processing step that is fed forward to the post-processing physical model, the value of a second parameter of the SOI in a post-processing step that is fed back to the post-processing physical model, and at least one of combinations thereof, from the post-processing physical model of the SOI. The at least one processor is further configured to predict a final value of the second parameter of the SOI in the post-processing step from a trained post-processing machine learning model based on the post-processing measurement result extracted from the post-processing physical model, and provide at least the final value of the second parameter of the SOI.

[0008] In one implementation, a system for measuring a plurality of parameters of interest from a structure of interest (SOI) includes, in a post - processing step, means for obtaining a post - processing step measurement signal from a measurement device for the SOI on one or more samples. The system further includes means for extracting a post - processing measurement result based on at least one of the post - processing step measurement signal, the value of a first parameter of the SOI in a pre - processing step that is fed forward to the post - processing physical model, the value of a second parameter of the SOI in the post - processing step that is fed back to the post - processing physical model, and combinations thereof, from the post - processing physical model of the SOI. The system further includes means for predicting a final value of a second parameter of the SOI in the post - processing step from a trained post - processing machine learning model based on the post - processing measurement result extracted from the post - processing physical model, and means for providing at least the final value of the second parameter of the SOI.

Brief Description of the Drawings

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[0010] During the fabrication of semiconductors and similar devices, it is often necessary to monitor the fabrication process by non-destructively measuring the devices. One type of measurement that can be used for non-destructive measurement of samples during processing is optical measurement, which can use a single wavelength or multiple wavelengths and can include, for example, polarization analysis, reflectance measurement, Fourier Transform infrared spectroscopy (FTIR), etc. Other types of measurements, including X-ray measurement, photoacoustic measurement, electron beam (E-beam) measurement, etc., can also be used.

[0011] Optical measurements such as thin film measurements and Optical Critical Dimension (OCD) measurements, as well as other types of measurements, sometimes use physical modeling techniques to generate predicted data of a sample that is compared with measurement data from the sample. Using physical modeling techniques, a model of the sample including primary parameters and non-primary parameters is generated. The model can be based on the nominal parameters of the sample and can include, for example, one or more variable parameters such as layer thickness, line width, pitch, sidewall angle, material properties, etc. that can vary over a desired range depending on the process parameters used to fabricate the test sample. The model can further include parameters related to the toolset, such as the characteristics of the optical system used by the measurement device. The predicted data can be calculated based on the parameters of the physical model including variations of the variable parameters and the characteristics of the measurement device using analytical or semi-analytical methods, such as effective medium theory (EMT), finite-difference time-domain (FDTD), transfer matrix method (TMM), Fourier modal method (FMM) / rigorous coupled-wave analysis (RCWA), finite element method (FEM), etc. The measurement data obtained from the sample by the measurement device is compared with the predicted data for different parameter variations, for example, in a non-linear regression process, until the best fit is achieved. At the point when the best fit is achieved, the values of the fitting parameters are considered to be an accurate representation of the parameters of the sample.

[0012] Conventionally, modeling requires that preliminary structural and material information of a sample be known in order to generate an accurate representative model of the sample that includes one or more variable parameters. For example, the preliminary structural and material information about a sample can include the type of the sample's structure and a physical description having nominal values of various parameters, such as layer thickness, line width, pitch width, sidewall angle, material properties, etc., along with the ranges within which these parameters can vary. The model can further include one or parameters that are not variable, i.e., not expected to vary in significant amounts in the sample during manufacturing. The variable parameters of the model can be adjusted and prediction data can be generated in real time during a non-linear regression process, or a library can be pre-generated. Thus, modeling applies physical constraints in the analysis and provides a high level of fidelity for the measurement results accordingly. However, modeling has high computational costs due to the physical calculations required to generate prediction data. For example, modeling a complex 3D structure is plagued by a slow time to solution (TTS), and the modeling accuracy can be reduced due to the difficulty of fitting data for complex structures.

[0013] Another technique that can be used to generate prediction data for a sample based on measurement data obtained from the sample by a measurement device is machine learning. Machine learning algorithms that can be used for measurement include, for example, linear regression, neural networks, deep learning, convolutional neural networks (CNNs), ensemble methods, support vector machines (SVMs), random forests, etc., or combinations of multiple models in sequential and / or parallel modes, but are not limited thereto. Machine learning does not require a physical model of the sample. Instead, reference data, for example, measurement data obtained from one or more reference samples by a measurement device, is acquired together with the values of the structural parameters of interest and used to generate and train a machine learning model. The machine learning model is automatically trained using the reference data and the known values of the structural parameters, finds relevant data features, and learns the inherent relationships and connections between the input features and the output features in order to make decisions and predictions on new data. The advantage of using machine learning is that the time to solution (TTS) is fast and the computing resource requirements are minimal. However, machine learning requires a large amount of reference data, which is costly and time-consuming to obtain. Without a large amount of reference data, the machine learning model may suffer from overfitting due to the lack of physical constraints.

[0014] As semiconductor devices continue to shrink, the measurement budget becomes more stringent. Additionally, complex 3D structures are being adopted more frequently to enable continuous device scaling. Advancements in semiconductor technology, such as the use of complex 3D structures, pose additional challenges to measurement due to increased modeling complexity and parameter correlation, as well as reduced sensitivity. For example, the signal from a single measurement tool or source may not have sufficient sensitivity to accurately measure the parameters of interest for semiconductor process quality control. Ultimately, there may not be a single measurement tool that can handle all measurement requirements for state-of-the-art semiconductor devices.

[0015] As contemplated herein, by using data collected from multiple data sources, such as from multiple tool sets and / or processing steps, and additional data such as sensor data related to samples collected from measurement and / or production equipment, a computationally efficient data analysis method can fuse multiple data sources and generate measurement results that are more accurate and consistent than those that can be provided by any individual data source. The analysis method can be flexible to adapt to various data of different natures, while at the same time maximizing the use of existing well-developed techniques such as physical modeling or machine learning for each type of data source and synergistically leveraging the strengths of individual measurement techniques.

[0016] As contemplated herein, physical modeling and machine learning are combined to analyze multiple data sources for a hybrid measurement and ecosystem. The methods described herein create predictive capabilities through data mining and data fusion from multiple data sources, such as from multiple measurement tool sets, sample data from multiple processing steps, measurement instrument parameters, and production equipment parameters. By way of example, a physical model can be used to analyze measurement signals from one or more measurement tools such as spectroscopic ellipsometers, spectroscopic reflectometers, X-ray measurements, photoacoustic measurements, Fourier transform infrared spectroscopy (FTIR), E-beam measurements, etc., to extract measurement results of primary and non-primary parameters of a sample in preprocessing steps and postprocessing steps. Additionally, a machine learning model can be constructed and trained to predict parameters of interest for a sample in preprocessing steps and postprocessing steps. A postprocessing physical model that extracts a postprocessing measurement signal can use, by feedforward, predicted parameters of interest from a preprocessing step predicted by a preprocessing physical model or a preprocessing machine learning model. Additionally or alternatively, predicted parameters of interest from a postprocessing step can be fed back to a postprocessing physical model or a postprocessing machine learning model to determine other parameters of interest.

[0017] The proposed technique can be used to combine and analyze multiple data sources in an efficient and flexible manner that synergistically combines physical modeling and machine learning with controllable computational cost and software and modeling complexity, thus providing a manageable time to solution (TTS) as well as the most feasible solution with improved final results and overall measurement performance. This approach is also versatile and applicable to measurements of any device, OCD, thin film, or other type of target.

[0018] FIG. 1A illustrates, by way of example, semiconductor devices 110, 120, and 130 having planar, fin, and gate-all-around (GAA) field effect transistor architectures, respectively. The planar transistor architecture used in device 110 uses a gate 112 positioned over channel 114 to control the flow of current through the channel between source and drain. The voltage applied to the gate creates an electric field (FET - field effect transistor) that excludes or allows carriers in the channel, thereby turning the current on or off. The source, channel, and drain are in the same plane, formed on the surface of the semiconductor wafer, and the gate is positioned over the channel. To address effects such as an increase in leakage current that degrades their performance due to the reduction in size, as illustrated in device 120, a finFET having a fin shape in which channel 124 is surrounded on three sides by gate 122 is employed. The use of gate 122 increases the effective area of gate 122 proximate to channel 124. However, finFETs have limitations and other more complex architectures have been adopted. For example, device 130 uses a gate-all-around (GAA) design in which gate 132 completely surrounds channel 134. The GAA transistor device 130 includes a plurality of vertically stacked nanosheet channels 134 passing through a single gate 132. The GAA device 130 promises continuous improvement in performance, but the three-dimensional features and small size significantly increase the complexity of the manufacturing process and require accurate monitoring using non-destructive measurements.

[0019] FIG. 1B illustrates a more detailed view of a GAA transistor device 150 under fabrication, including a cross-sectional view 150A that extends longitudinally through a silicon (Si) channel 152 between a source and a drain (not shown). The GAA transistor device 150 is illustrated as showing an Si channel 152 that will be completely surrounded by a gate when a silicon germanium (SiGe) layer 154 and a dummy gate 156 are replaced. FIG. 1B illustrates three repeating SiGe regions having different critical dimensions (CDs), e.g., SiGe CD1, SiGe CD2, and SiGe CD3.

[0020] The GAA fabrication process flow is similar to, for example, the finFET process used to generate the device 120 shown in FIG. 1A. This process begins, for example, with the formation of a superlattice that is a stack of alternately epitaxially deposited silicon layers and silicon germanium (SiGe) layers. Trenches are etched through the lattice to form fin-like structures, and each fin includes three to four silicon nanosheet layers that become transistor Si channels 152 separated by SiGe layer 154. The silicon layers alternate with SiGe layers that are replaced by gate material. A dummy polysilicon gate 156 is deposited across the nanosheet fins, and a spacer material is conformally deposited over the dummy gate. The source and drain are etched on both sides of the gate to cut and expose the ends of the Si channel 152. In a series of important steps, the exposed SiGe layer between the ends of the Si channel 152 is selectively etched to form a cavity for an internal spacer 158, and then the internal spacer is deposited in the cavity. Although these features are very small, their dimensions are thought to be important in determining the performance of the device for several reasons. For example, the depth of the cavity and the internal spacer determines the gate length, the internal spacer protects the subsequently deposited source and drain during delamination when the dummy gate is etched away and replaced with gate material, and the spacer suppresses the parasitic capacitance between the source / drain and the gate.

[0021] Therefore, accurately monitoring these components within a GAA transistor device, or other similar components within a GAA transistor device or other complex 3D structure, is important during manufacturing but difficult using conventional metrology techniques.

[0022] FIG. 2 illustratively shows a schematic diagram of a measurement device 200 that can be used to characterize the structure on a sample, as described herein by way of example. The measurement device 200 can be configured to perform one or more types of measurements such as, for example, spectroscopic reflectance measurement, spectroscopic ellipsometry (including Mueller matrix ellipsometry), spectroscopic scattering measurement, overlay scattering measurement, interferometry, photoacoustic measurement, E-beam measurement, X-ray measurement, FTIR measurement, etc. of the sample 203. The measurement device 200 can include, for example, a first measurement tool 201 and a second measurement tool 270, but can include additional measurement tools or can be coupled to receive sample data measured by separate measurement tools. The measurement device 200 is illustrated as one exemplary configuration of a measurement device, and it should be understood that other configurations and other measurement devices can be used if desired.

[0023] The measurement device 200 includes an oblique incidence measurement tool 201 that includes a light source 210 that generates light 202. The light 202 can be, for example, UV-visible light having a wavelength such as 200 nm to 1000 nm. The light 202 generated by the light source 210 can include a range of wavelengths, i.e., a continuous range or a plurality of discrete wavelengths, or can be a single wavelength. The measurement device 200 includes condenser optical components 220 and 230 that collect and receive light and direct the light to obliquely impinge on the uppermost surface of the sample 203. The optical components 220, 230 can be refractive, reflective, or a combination thereof, and can be objective lenses.

[0024] The reflected light can be focused by the lens 214 and received by the detector 250. The detector 250 can be a conventional charge coupled device (CCD), a photodiode array, a CMOS, or a detector of a similar type. The detector 250 can be, for example, a spectrometer when broadband light is used, and the detector 250 can generate a spectral signal, for example, according to the wavelength. The spectrometer can be used to disperse the entire spectrum of the received light into spectral components across an array of detector pixels. One or more polarization elements can be present in the beam path of the measurement device 200. For example, the measurement device 200 can include one or both (or may not include any) of one or more polarization elements 204 in the beam path before the sample 203 and a polarization element (analyzer) 212 in the beam path after the sample 203, and can include one or more additional elements 205a and 205b such as a compensator or a photoelastic modulator, which can be before, after, or both before and after the sample 203. By using a spectroscopic ellipsometer that uses a dual-rotation compensator between the polarization elements 204 and 212 and the sample, a complete Mueller matrix can be measured.

[0025] The measurement device 200 can include an additional measurement device or can be coupled to an additional measurement device. For example, as illustrated, the measurement device 200 can include a second normal incidence measurement tool 270. The second measurement tool 270 can be configured, for example, for spectroscopic reflectometry, spectroscopic scatterometry, overlay scatterometry, interferometry, e-beam measurement, x-ray measurement, FTIR measurement, and the like. In some implementations, the measurement device 200 can include an additional tool, for example, a third (or more) measurement tool. In some implementations, the additional measurement tool can be separate from the measurement device 200.

[0026] The measurement device 200 further includes one or more computing systems 260 configured to characterize one or more parameters of the sample 203 using the methods described herein. The one or more computing systems 260 are coupled to a first measurement tool 201, such as a detector 250, and a second measurement tool 270, and any additional measurement tools, if present, to receive measurement data obtained during measurement of the structure of the sample 203. Obtaining the data can be performed during pre-processing fabrication steps and post-processing fabrication steps. The one or more computing systems 260 can be, for example, a workstation, a personal computer, a central processing unit or other suitable computer system, or a plurality of systems.

[0027] The one or more computing systems 260 can be a single computer system or a plurality of separate or linked computer systems, and it should be understood that herein the computing system 260, at least one computing system 260, one or more computing systems 260 can be referred to interchangeably. The computing system 260 can be included in, or connected to, or otherwise associated with the measurement device 200 and any additional measurement tools. Different subsystems of the measurement device 200 can each include a computing system configured to perform steps associated with the relevant subsystem. For example, the computing system 260 can control the positioning of the sample 203, for example, by controlling the movement of stage 209 coupled to the chuck. For example, stage 209 can be capable of horizontal movement in either Cartesian (i.e., X and Y) coordinates, or polar (i.e., R and θ) coordinates, or some combination of the two. The stage can also be capable of vertical movement along the Z coordinate. The computing system 260 can further control the operation of the chuck 208 to hold or release the sample 203. The computing system 260 can further control or monitor the rotation of one or more polarizing elements 204, 212, or additional elements 205a, 205b, etc.

[0028] The computing system 260 can be communicatively coupled to the detector 250 within the first measurement tool 201 and the detector (if present) within the second measurement tool 270 in any manner known in the art. For example, one or more computing systems 260 can be coupled to a separate computing system associated with the detector 250. The computing system 260 is configured to receive and / or obtain measurement data from, for example, the detector 250, as well as from the controller polarizing elements 204, 212, and additional elements 205a, 205b, etc., and from the components of the second measurement tool 270 via a transmission medium that can include a wired portion and / or a wireless portion. Thus, the transmission medium can function as a data link between the computing system 260 and other subsystems of the measurement device 200. The computing system 260 can be further configured to receive and / or obtain additional information regarding the sample and one or more subsystems of the first measurement tool 201 and the production equipment from, for example, a user interface (UI) 268 or via a transmission medium that can include a wired portion and / or a wireless portion.

[0029] Computing system 260 includes at least one processor 262, along with memory 264, and UI 268, which are communicatively coupled via bus 261. Memory 264 or other non-transitory computer-usable storage media includes its embodied computer-readable program code 266, which can be used by computing system 260 to cause at least one computing system 260 to control measurement device 200 and perform functions including the techniques and analysis described herein. For example, as illustrated, memory 264 can include instructions for causing processor 262 to perform both modeling and machine learning, and in some implementations, can employ feedforward and / or feedback as discussed herein. Data structures and software code for automatically implementing one or more of the acts described in this detailed description can be implemented by one of ordinary skill in the art in light of this disclosure and can be a computer-usable storage media, such as, for example, memory 264, that can store code and / or data for use by a computer system, such as computing system 260. Computer-usable storage media can include, but is not limited to, magnetic and optical storage devices such as read only memory, random access memory, disk drives, magnetic tape, and the like. Additionally, the functions described herein can be wholly or partially embodied within the circuitry of an application specific integrated circuit (ASIC) or a programmable logic device (PLD), and the functions can be embodied in a computer understandable descriptor language that can be used to create an ASIC or PLD that operates as described herein.

[0030] Computing system 260 can be configured to obtain data for a reference sample that includes, for example, but is not limited to, structures of interest such as 3D composite structures including GAA transistors, from one or both of measurement tools 201 and 270 and a plurality of data sources including any desired additional measurement tools, as well as data related to the sample such as reference data and / or design of experiment (DOE) data, and data related to measurement tools and / or processing equipment such as process parameters, Advanced Parameter Control (APC) parameters, context data, and sensor data from production equipment. The DOE data can be, for example, data measured from a set of reference samples processed under intentionally introduced skew conditions, such that the structural parameters of interest vary with process conditions skewed in a known pattern. Computing system 260 can be configured to generate and use one or more physical models (model 264pm) for the sample based on measurement data from one or more reference samples and optionally additional information related to the sample and / or processing equipment, and, as discussed herein, to generate, train, and use one or more machine learning models (ML 264ml) for the sample based on one or more physical models and measurement results extracted from the data. In some implementations, different computing systems and / or different measurement devices can be used to obtain measurement data and additional information from training samples, generate one or more physical models (model 264pm), and / or generate and train one or more machine learning models (ML 264ml), and the resulting physical model and / or trained machine learning model (or portions thereof) can be provided to computing system 260 via computer-readable program code 266 on a non-transitory computer-usable storage medium such as memory 264.

[0031] Computing system 260 can additionally or alternatively be used to obtain data from test samples from multiple data sources. The data can be of the same type as that used to generate physical models and to generate and train the machine learning models discussed above, and the test samples can have the same structure as the reference samples, e.g., SOI. Computing system 260 can be configured to determine one or more parameters of interest of SOI using data from multiple sources, one or more physical models (model 264pm), and one or more trained machine learning models (ML264ml), as discussed herein.

[0032] The results of the data analysis can be reported and, for example, stored in memory 264 associated with sample 203 and / or presented to the user via UI 268, an alarm, or other output device. Further, the results from the analysis can be reported to the process equipment and fed forward or feedback to adjust appropriate fabrication steps to correct any variations detected in the fabrication process. Computing system 260 can include a communication port 269 that can be any type of communication connection, such as to the Internet or any other computer network. Communication port 269 can be used to receive instructions for programming computing system 260 to perform any one or more of the functions described herein and / or, for example, to export signals with measurement results and / or instructions to another system, such as an external process tool, in a feed forward or feedback process to adjust process parameters associated with the fabrication process steps of the sample based on the measurement results.

[0033] As considered herein, to characterize a measured SOI, e.g., a complex 3D structure including, but not limited to, GAA transistors, at least one physics-based model is constructed to analyze measurement signals from one or more tools such as spectroscopic ellipsometry (SE), spectroscopic reflectometry (SR), X-rays, E-beams, photoacoustic data, Fourier transform infrared spectroscopy (FTIR), etc., and from one or more sources, to extract measurement results of primary and non-primary parameters. Additionally, (2) at least one machine learning model is constructed and trained to predict parameters of interest. The machine learning model can take as input more than one of the following data. a) Measurement results (primary and non-primary parameters) from the physics model in (1); b) raw signals of the physics model in (1), and optionally misfits; data sources from different tool sets, or data sources from the same tool in (1) but not included in the physics modeling; process parameters, APC parameters, context data, and sensor data from production equipment. Additionally, (3) in-line measurements of the SOI can be performed using physics models and machine learning models created and trained offline to predict parameters of interest based on data from multiple data sources.

[0034] FIG. 3 illustrates, by way of example, a workflow 300 for offline recipe creation, e.g., generation of one or more physics models and one or more machine learning models, according to a first exemplary scenario using data collected from multiple data sources, e.g., different tools and / or sources. In FIG. 3, solid black arrows indicate processes used in the workflow 300, dashed black arrows indicate processes that are optional but at least one exists, and gray dotted arrows indicate optional processes.

[0035] As illustrated, measurement signals 302 from one or more reference samples are collected from a first data source or tool (source 1). The measurement signals 302 from the SOI can be collected from any desired measurement device, such as the measurement tool 201 shown in FIG. 2, or from any other desired type of measurement device.

[0036] Additionally, data is obtained from one or more additional data sources. For example, in some implementations, measurement signals 304 and 306 from one or more reference samples can be collected from one or more additional sources or tools, illustrated as, for example, a second source or tool (Source 2) and a third source or tool (Source 3). The additional measurement signal 304 can be collected from a measurement device different from Source 1, such as the measurement tool 270 shown in FIG. 2, or from any other desired type of measurement device, and the measurement signal 306 can be collected from a measurement device different from Sources 1 and 2, such as a different type of measurement from either measurement tool 201 or 270, or from any other desired type of measurement device. As illustrated by the block arrows, additional data 308 related to the SOI is collected and can be used as training data for one or more machine learning models 322. The additional data 308 can include, for example, reference data for the sample and DOE data. The reference data can be measurement data obtained from one or more reference samples by a measurement device, along with the values of the structural parameters of interest typically provided by, for example, CD-AFM (atomic force microscopy), CD-SEM (scanning electron microscopy), or TEM (transmission electron microscopy). The reference data and / or DOE data can be used as a training data set to train a machine learning model to find relevant data features and learn the inherent relationships and connections between input features and output features for making decisions and predictions on new data. In some implementations, the additional data 308 related to the reference sample can further include wafer state, accuracy, tool matching data, etc. The accuracy data is, for example, a parameter based on data repeatedly measured from the same target multiple times from the same instance of the tool. Accuracy is another key performance indicator (KPI) of measurement that indicates the consistency of measurement results from multiple runs on the same sample. The tool matching data is, for example, a parameter based on data measured from the same sample from multiple instances of tools of the same tool type.Tool matching is another measurement KPI that indicates the consistency of results measured from different tools of the same type for the same sample. Measurement accuracy (evaluated by matching to reference values provided by CD-AFM, CD-SEM, TEM, etc. and / or consistency to DOE conditions), precision, and tool matching are typical measurement KPIs. When accuracy and tool matching data are provided, physical modeling or machine learning models can be optimized not only to match reference values exactly but also to predict consistent results for the same sample using measurement signals from multiple runs from the same tool or different tools of the same type.

[0037] Furthermore, in some implementations, the additional data signal 309 can be used as an input for a physical model or as input features for a machine learning model. The additional data signal 309 can be related to sources (e.g., source 1, source 2, and source 3) from which it can be obtained, such as, for example, process parameters, Advanced Process Control (APC) parameters, context data, and sensor data from production equipment. As an example, some process control parameters, such as substrate temperature and chemical concentration for wet etching, can affect the etching rate (how fast material is removed from the surface of the wafer), and the etching rate is one of the important factors for determining the etching depth and CD profile. Some of these parameters, such as temperature, are measured by sensors from production equipment. Other parameters, such as etching time, the name of the etching chamber, are user control parameters. The name of the etching chamber is an example of context data. Since each etching chamber has its own characteristic distribution of the etching profile across the wafer, knowing this information can help machine learning to predict the correct wafer map. An example of an APC parameter is atomic force microscope (AFM) results measured from the same sample in different process steps that include related information, such as non-critical parameters of the structure of interest. Adding non-critical parameters as machine learning input features can help improve the machine learning robustness in predicting critical parameters. Adding all these related parameters as machine learning input features can provide additional information useful for determining the structure parameters of interest controlled by these process parameters and conditions.

[0038] Measurement signals and data from multiple data sources can be used to generate one or more physical models of the SOI. For example, as illustrated by the solid black arrow, the measurement signal 302 from the first source (Source 1) can be used to generate the first physical model 312 of the sample. The physical model of the sample is created, for example, based on the known geometry, nominal values, and materials of the structure. The measurement signal 302 can be used to generate the first physical model 312 by providing the data from which the measurement results are extracted, and the first physical model 312 can be adjusted and optimized such that the calculated signal fits well with the measurement signal and a good matching is achieved between the extracted measurement results and the known parameters of the reference sample. In some implementations, additional data can be used to assist in the generation of the first physical model 312. For example, as illustrated by the gray dotted arrow, additional data 308 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool matching data can be used to assist in the generation of the first physical model 312. Additionally, as illustrated by the gray dotted arrow, a data signal 309 can be used to assist in the generation of the first physical model 312. In another example, as illustrated by the gray dotted arrow, the measurement signal 304 from the second source (Source 2) can be used to assist in the generation of the first physical model 312 of the sample. In some implementations, both the additional data 308 and the measurement signal 304 can be used to assist in the generation of the first physical model 312.

[0039] In some implementations, multiple physical models can be generated. For example, as illustrated by the gray dotted - arrow and the gray dotted - box, a second physical model 314 can be generated based on a measurement signal 304 from a second source (source 2). In some implementations, additional data can be used to generate the second physical model 314. For example, as illustrated by the gray dotted - arrow, additional data 308 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool - matching data can be used to assist in the generation of the second physical model 314. In another example, as illustrated by the gray dotted - arrow, a measurement signal 306 from a third source (source 3) can be used to assist in the generation of the second physical model 314 of a sample. In some implementations, both additional data 308 and the measurement signal 306 can be used to assist in the generation of the second physical model 314. Additionally, as illustrated by the gray dotted - arrow, a data signal 309 can be used to assist in the generation of the second physical model 314. Further, the multiple physical models can be optimized independently or co - optimized. For example, in some implementations, as illustrated by the gray dotted line, the first physical model 312 and the second physical model 314 can be linked such that at least some parameters can be coupled across the physical models 312 and 314, and the combined parameter space can be searched to conform to measurement signals from one or more data sources. The first physical model 312, and optionally the second physical model 314, can be configured to provide a goodness - of - fit 323 of the physical modeling.

[0040] Using multiple data sources, one or more machine learning models 322 are constructed and trained to predict parameters 325 of interest. Machine learning metrics 327 are developed and reported along with the goodness-of-fit from physical modeling to demonstrate the measurement quality of the synergistically derived recipe from physical modeling and machine learning. As illustrated by the solid black arrows, the machine learning model 322 is constructed using measurement results extracted by a first physical model 312 as input features. As indicated by the dashed black arrows, the input features of the machine learning model 322 may additionally include at least one of measurement signals 304 from one or more reference samples collected from a second source (Source 2), measurement signals 306 from one or more reference samples collected from a third source (Source 3), additional data signals 309, measurement results extracted by a second physical model 314, or any combination thereof. In some implementations, as illustrated by the dotted gray arrows, the input features of the machine learning model 322 may optionally include measurement signals 302 from one or more reference samples collected from a first source (Source 1). In some implementations, the input features from the measurement signals 302 may include data channels or data chunks not used in generating the first physical model 312. For example, generally, a data channel may be a measurement subsystem defined by at least one of an energy source such as a light source, an optical path directed by optical components, a detector, or any combination thereof, and a data chunk may be a wavelength (e.g., used in spectroscopic measurement), frequency (e.g., used in frequency-resolved measurement), angle (e.g., used in angle-resolved measurement), time interval (e.g., used in time-resolved measurement), or a subset of any combination thereof from the complete data set provided by the data channel. For example, a first measurement device may collect normal incidence signals and oblique incidence spectroscopic ellipsometry (SE) signals. The SE signals may be used to generate the first physical model 312, but the normal incidence signals may not be used because they may be difficult to fit.Thus, the vertically incident signal can be a data channel used as data for the input features of the machine learning model 322, in addition to the physical modeling results generated from different data channels, e.g., SE signals. In another example, the same data channel can be split into multiple data chunks, e.g., signals from different wavelength ranges, and some data chunks may be difficult to fit using physical modeling but can be used as data for the input features of the machine learning model 322.

[0041] The machine learning model 322 is trained using at least a portion of the data 308 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool matching data. The data 308 is training data and is used for offline training. For example, the reference data can be a set of signals having labels (e.g., values of key parameters provided by other measurement systems such as CD-SEM, TEM, CD-AFM, etc.), including any of the measurement results from the first physical model 312, measurement signal 304, measurement signal 306, additional data signal 309, and measurement signal 302. During the training of the machine learning model 322, the set of signals from the reference data is used as machine learning input features, and based on these input features, the machine learning model 322 makes predictions of the key parameters. The machine learning model 322 is trained to learn and predict key parameters that match the labels of the reference data. The DOE from the data 308 is a set of signals measured from reference samples processed under intentionally introduced skew conditions (e.g., including any of the measurement results from the first physical model 312, measurement signal 304, measurement signal 306, additional data signal 309, and measurement signal 302). During machine learning training, the machine learning model 322 takes the signals from the DOE data as input features and makes predictions of the key parameters. The machine learning model 322 is trained to follow a skew pattern in which the predicted key parameter values are expected based on the process skew conditions. The accuracy data from the data 308 is measurement signals (e.g., including any of the measurement results from the first physical model 312, measurement signal 304, measurement signal 306, additional data signal 309, and measurement signal 302) from multiple runs from the same measurement tool but from the same sample. Similarly, the tool matching data from the data 308 is measurement signals (e.g., including any of the measurement results from the first physical model 312, measurement signal 304, measurement signal 306, additional data signal 309, and measurement signal 302) from different instances of the same type of measurement tool but from the same sample. The machine learning model 322 takes the accuracy and tool matching data as input features and makes predictions.The machine learning model 322 is trained such that the predicted values of the main parameters match for signals measured from the same sample but from different runs or different tools. The machine learning model 322 can be trained such that all criteria, matching to reference values, DOE skew conditions, high precision, and consistent tool matching are simultaneously met when all of these data are provided during training.

[0042] FIG. 4 illustrates, by way of example, a workflow 400 for in-line measurement for characterizing a sample based on one or more physical models and one or more machine learning models according to a first exemplary scenario using signals collected from a plurality of data sources, e.g., different tools and / or sources. The one or more physical models and the one or more machine learning models can be generated as discussed, e.g., with reference to FIG. 4. In FIG. 4, solid black arrows indicate processes used in the workflow 400, dashed black arrows indicate processes that are optional but at least one exists, and gray dotted arrows indicate optional processes.

[0043] As illustrated, a measurement signal 402 from the SOI of the sample is collected from a first data source or tool (source 1). The measurement signal 402 can be collected from any desired measurement device, such as the measurement tool 201 shown in FIG. 2, or from any other desired type of measurement device, and can be collected from the same measurement device or the same type of measurement device as used for source 1 in FIG. 3.

[0044] Additionally, the data is obtained from one or more additional data sources. For example, in some implementations, the measurement signals 404 and 406 can be collected from one or more additional sources or tools, illustrated as, for example, a second source or tool (Source 2) and a third source or tool (Source 3). The additional measurement signal 404 can be collected from a measurement device different from Source 1, such as the measurement tool 270 shown in FIG. 2, or from any other desired type of measurement device, and can be collected from the same measurement device or the same type of measurement device as that used for Source 2 in FIG. 3. The measurement signal 406 can be collected from a measurement device different from Source 1 and Source 2, and can be, for example, a different type of measurement from either the measurement tool 201 or 270 or any other desired type of measurement device, and can be collected from the same measurement device or the same type of measurement device as that used for Source 3 in FIG. 3. Further, in some implementations, additional data signals 409, process parameters, APC parameters, context data, and sensor data from production equipment that may be associated with the sources (e.g., Source 1, Source 2, and Source 3) can be obtained.

[0045] To extract measurement results from one or more physical models, signals and data from multiple data sources can be used. For example, as illustrated by the solid black arrow, the measurement signal 402 from the first source (Source 1) can be used to extract the measurement result of the SOI of the sample from the first physical model 412, which can be the same as the first physical model 312 in FIG. 3. In some implementations, additional data can be used to assist in extracting the measurement results from the first physical model 412. For example, as illustrated by the gray dotted arrow, the measurement signal 404 from the second source (Source 2) can be used to assist in extracting the measurement result from the first physical model 412 of the sample.

[0046] Additionally, as illustrated by the gray dotted arrow, an additional data signal 409 can be used to assist in extracting the measurement result of the sample from the first physical model 412.

[0047] In some implementations, multiple physical models can be used to extract measurement results of a sample. For example, as illustrated by the gray dotted arrows and the gray dotted box, a second physical model 414 can be used to extract the measurement results of the sample based on the measurement signal 404 from a second source (source 2). The second physical model 414 can be the same as, for example, the second physical model 314 in FIG. 3. In some implementations, additional data can be used to assist in extracting measurement results from the second physical model 414. For example, as illustrated by the gray dotted arrow, the measurement signal 406 from a third source (source 3) can be used to assist in extracting the measurement results of the sample from the second physical model 414. Additionally, as illustrated by the gray dotted arrow, an additional data signal 409 can be used to assist in extracting the measurement results of the sample from the second physical model 414. Further, the multiple physical models can be optimized independently or co-optimized. For example, in some implementations, as illustrated by the gray dotted line, the first physical model 412 and the second physical model 414 can be linked such that at least some parameters can be coupled across the physical models 412 and 414, and the combined parameter space can be searched to conform to the measurement signals from one or more data sources. The first physical model 412, and optionally the second physical model 414, can be configured to provide a goodness-of-fit 423 of the physical modeling.

[0048] One or more trained machine learning models 422 are used to predict a parameter of interest 425 based on multiple data sources. Machine learning measurement metrics 427 and fitness 423 from physical modeling may be reported to indicate the measurement quality of the synergistically applied recipe from physical modeling and machine learning. The trained machine learning model 422 can be, for example, the same as the machine learning model 322 of FIG. 3 after training. As illustrated by the solid black arrow, the trained machine learning model 422 uses the measurement results extracted by the first physical model 412 as input features. As indicated by the dashed black arrow, the trained machine learning model 422 further uses input features including at least one of the measurement signal 404 from a sample collected from a second source (source 2), the measurement signal 406 from a sample collected from a third source (source 3), an additional data signal 409, and the measurement results extracted by the second physical model 414 based on the additional measurement signals 404 and / or 406, or any combination thereof. In some implementations, as illustrated by the gray dotted arrow, the trained machine learning model 422 may optionally further use input features including the measurement signal 402 from a sample collected from a first source (source 1). In some implementations, the machine learning input features from the measurement signal 402 may include data channels or data chunks that are not used when extracting measurement results from the first physical model 412, as discussed with reference to FIG. 3.

[0049] FIG. 5 illustrates, as an example, a workflow 500 for offline recipe creation, e.g., the generation of one or more physical models and one or more machine learning models, according to a second exemplary scenario using signals collected from multiple data sources, e.g., different manufacturing process steps. In FIG. 5, the solid black arrows indicate the processes used in the workflow 500, the dashed black arrows indicate processes that are optional but at least one exists, and the dotted gray arrows indicate optional processes.

[0050] As illustrated, the post - processing step measurement signal 502 from one or more reference samples is measured from a measurement device. The reference sample can be, for example, an OCD target pad or a semiconductor device, and the post - processing step measurement signal 502 is acquired after the desired steps of sample fabrication are completed. The post - processing step measurement signal 502 can be collected from any desired measurement device such as the measurement tool 201 shown in FIG. 2, or from any other desired type of measurement device.

[0051] Additionally, the pre - processing step measurement signals 504 from one or more reference samples are measured using a measurement device, e.g., the same measurement device used to obtain the post - processing step measurement signal 502, and are used to generate pre - processing step data. The pre - processing step measurement signals 504 are obtained, for example, before the desired steps of sample fabrication are completed. In some implementations, the post - processing step measurement signal 502 and the pre - processing step measurement signal 504 can be combined (e.g., by addition, subtraction, multiplication, or division) to form a pre - adjusted signal 505. Additionally, data related to the reference sample, such as reference data of the sample, design of experiments (DOE), etc., 508 can be collected. In some implementations, the additional data 508 related to the reference sample can further include wafer state, accuracy, tool - matching data, etc. Additionally, data can be obtained from other sources, such as from the second measurement pad 506, from the fault - detection pad 509, or any combination thereof. The first exemplary scenario in FIGS. 3 and 4 highlighted multiple data sources collected from different measurement devices, while the second exemplary scenario illustrates that, for example, multiple data sources can be obtained from different measurement pads, or from the same pad at different processing steps. Different measurement pads can be measured from the same or different measurement devices. The pre - processing step measurement signal 504 and the post - processing step measurement signal 502 can be measured on either a designed OCD target or a device. The second measurement pad 506 refers to pre - processing step measurements and / or post - processing step measurements from a measurement pad that is not measured for the pre - processing step measurement signal 504 and the post - processing step measurement signal 502. For example, if the pre - processing step measurement signal 504 and the post - processing step measurement signal 502 are measured on an OCD target, the second measurement pad 506 can refer to signals from a device pad, or vice versa.

[0052] To generate one or more physical models, signals and data from multiple data sources can be used. For example, as illustrated by the solid black arrow, a post - processing step measurement signal 502 from a measurement device can be used to generate a post - processing physical model 512 of a sample. In some implementations, additional data can be used to assist in generating the post - processing physical model 512. For example, as illustrated by the gray dotted arrow, additional data 508 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool - matching data can be used to assist in generating the post - processing physical model 512. In another example, as illustrated by the dotted gray arrow, a pre - adjusted signal 505 can be used to assist in generating the post - processing physical model 512 of a sample. In another example, as illustrated by the gray dotted arrow, a signal from a second measurement pad 506 can be used to assist in generating the post - processing physical model 512 of a sample. In another example, as illustrated by the dotted gray arrow, a signal from a fault - detection pad 509 can be used to assist in generating the post - processing physical model 512 of a sample. In some implementations, all or any combination of the data 508 and signals from different measurement pads, e.g., a second measurement pad 506 and / or a fault - detection pad 509 can be used to assist in generating the post - processing physical model 512.

[0053] In some implementations, multiple physical models can be generated. For example, as illustrated by the gray dotted arrows and gray dotted boxes, the pre - processing physical model 514 can be generated based on the pre - processing step measurement signal 504 from the measurement device. In some implementations, additional data can be used to generate the pre - processing physical model 514. For example, as illustrated by the gray dotted arrows, additional data 508 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool matching data can be used to assist in the generation of the pre - processing physical model 514. In another example, as illustrated by the gray dotted arrows, signals from the second measurement pad 506 can be used to assist in the generation of the pre - processing physical model 514 of the sample. In another example, as illustrated by the gray dotted arrows, signals from the fault detection pad 509 can be used to assist in the generation of the pre - processing physical model 514 of the sample. In some implementations, all or any combination of the data 508, and signals from the second measurement pad 506 and the fault detection pad 509 can be used to assist in the generation of the pre - processing physical model 514. Further, the multiple physical models can be optimized independently or co - optimized. For example, in some implementations, as illustrated by the gray dotted lines, the post - processing physical model 512 and the pre - processing physical model 514 can be linked such that at least some parameters can be combined across the post - processing physical model 512 and the pre - processing physical model 514, and the combined parameter space can be searched to fit the measurement signals from one or more data sources. The post - processing physical model 512, and optionally the pre - processing physical model 514, can be configured to provide a goodness - of - fit 523 of the physical modeling.

[0054] Using multiple data sources, one or more machine learning models 522 are constructed and trained to predict parameters 525 of interest. Machine learning metrics 527 are developed and reported along with the goodness-of-fit 523 from physical modeling to indicate the measurement quality of the synergistic recipe from physical modeling and machine learning. As illustrated by the solid black arrows, the machine learning model 522 is constructed using the post-processing measurement results extracted by the post-processing physical model 512 as input features. As indicated by the dashed black arrows, the input features of the machine learning model 522 additionally include pre-processing step data generated based on the pre-processing step measurement signal 504. The pre-processing step data can be generated in multiple ways based on the pre-processing step measurement signal 504. For example, as illustrated in FIG. 5, the pre-processing step data can be generated in three different ways from the pre-processing step measurement signals 504 labeled 1, 2, and 3, where at least one of (1), (2), or (3), or any combination thereof can be used. As illustrated for the pre-processing step measurement signal 504 with label 1, the pre-processing step data can be generated by combining the pre-processing step measurement signal 504 with the post-processing step measurement signal 502 to form a pre-adjusted signal 505. As explained in FIG. 5, in some implementations, when the pre-adjusted signal 505 is generated, the pre-adjusted signal 505 is either (A) provided to the post-processing physical model 512 and the machine learning model 522 is constructed at least partially based on the post-processing measurement results extracted by the post-processing physical model 512, or (B) the pre-adjusted signal 505 is provided to the machine learning model 522 and the machine learning model 522 is constructed at least partially based on the pre-adjusted signal 505. Additionally, as further explained in FIG. 5, in some implementations, at least one of (A) or (B) can be used with the workflow 500.As illustrated by label 2 for the pre - processing step measurement signal 504, the pre - processing step data can be generated by providing the pre - processing step measurement signal 504 to the pre - processing physical model 514, and the machine learning model 522 is constructed at least in part based on the pre - processing measurement results extracted by the pre - processing physical model 514. As illustrated by label 3 for the pre - processing step measurement signal 504, the pre - processing step data can be generated by providing the pre - processing step measurement signal 504 to the machine learning model 522, and the machine learning model 522 is constructed at least in part based on the pre - processing step measurement signal 504.

[0055] Additionally, as indicated by the dashed black arrow, the machine learning model 522 is constructed using additional data including at least one of the pre - processing step measurement signals 504 (i.e., at least one of (1), (2), or (3) for the pre - processing step measurement signal 504, or any combination thereof), the signal from the second measurement pad 506, and the signal from the fault detection pad 509, or any combination thereof. In some implementations, as illustrated by the gray dotted arrow, the machine learning model 522 can optionally be further constructed using the post - processing step measurement signal 502, the pre - adjusted signal 505, the measurement results extracted by the pre - processing physical model 514, or some combination thereof.

[0056] The machine learning model 522 is trained using at least a portion of data 508 such as reference data and / or DOE, and optionally using wafer conditions, accuracy, and tool - matching data.

[0057] FIG. 6 illustrates, by way of example, a workflow 600 for in-line measurement for characterizing a sample based on, for example, one or more physical models and one or more machine learning models using a plurality of data sources, such as signals collected from different manufacturing process steps. The one or more physical models and the one or more machine learning models can be generated as discussed, for example, with reference to FIG. 5. In FIG. 6, solid black arrows indicate processes used in workflow 600, dashed black arrows indicate processes that are optional but at least one exists, and gray dotted arrows indicate optional processes.

[0058] As illustrated, a post-processing step measurement signal 602 from the sample is collected from a measurement device. The sample can be, for example, an OCD target pad or a semiconductor device, and the post-processing step measurement signal 602 is obtained after a desired step of fabricating the sample is completed. The post-processing step measurement signal 602 can be collected from any desired measurement device, such as the measurement tool 201 shown in FIG. 2, or from any other desired type of measurement device, and can be collected from the same measurement device or the same type of measurement device used to obtain the post-processing step measurement signal 502 in FIG. 5.

[0059] Additionally, the pre - processing step measurement signal 604 from the sample is collected using a measurement device, e.g., the same measurement device used to obtain the post - processing step measurement signal 602 and / or the same measurement device or the same type of measurement device used to obtain the pre - processing step measurement signal 504 of FIG. 5. The pre - processing step measurement signal 604 is used to generate pre - processing step data. The pre - processing step measurement signal 604 is obtained, for example, before the desired step of sample fabrication is completed. In some implementations, the post - processing step measurement signal 602 and the pre - processing step measurement signal 604 can be combined (e.g., by addition, subtraction, multiplication, or division) to form a pre - adjusted signal 605. Additionally, data can be obtained from other sources such as from the second measurement pad 606, from the fault detection pad 609, or any combination thereof. The pre - processing step measurement signal 604 and the post - processing step measurement signal 602 can be measured at either the designed OCD target or device. The second measurement pad 606 refers to, for example, pre - processing step measurements and / or post - processing step measurements from measurement pads where the pre - processing step measurement signal 604 and the post - processing step measurement signal 602 are not measured. For example, if the pre - processing step measurement signal 604 and the post - processing step measurement signal 602 are measured on the OCD target, the second measurement pad 606 can refer to signals from the device pads or vice versa.

[0060] To extract measurement results from one or more physical models, signals and data from multiple data sources can be used. For example, as illustrated by the solid black arrow, a post - processing measurement signal 602 can be used to extract measurement results of a sample from a post - processing physical model 612 that can be the same as the post - processing physical model 512 of FIG. 5. In some implementations, additional data can be used to assist in extracting measurement results from the post - processing physical model 612. For example, as illustrated by the gray dotted arrow, a pre - adjusted signal 605 can be used to assist in extracting measurement results from the post - processing physical model 612 of the sample. In another example, as illustrated by the gray dotted arrow, a signal from a second measurement pad 606 can be used to assist in extracting measurement results from the post - processing physical model 612 of the sample. In another example, as illustrated by the gray dotted arrow, a signal from a fault - detection pad 609 can be used to assist in extracting measurement results from the post - processing physical model 612 of the sample. In some implementations, all or any combination of signals from the second measurement pad 606 and the fault - detection pad 609 can be used to assist in extracting measurement results from the post - processing physical model 612.

[0061] In some implementations, multiple physical models can be used to extract measurement results of a sample. For example, as illustrated by the black dotted arrows and the black dotted boxes, a preprocessing physical model 614 can be used to extract the measurement results of the sample based on the preprocessing step measurement signal 604. The preprocessing physical model 614 can be the same as the preprocessing physical model 614 in FIG. 5. Further, the multiple physical models can be optimized independently or co-optimized. For example, in some implementations, as illustrated by the gray dotted line, the postprocessing physical model 612 and the preprocessing physical model 614 can be linked such that at least some parameters can be coupled across the postprocessing physical model 612 and the preprocessing physical model 614, and the combined parameter space can be searched to fit the measurement signals from one or more data sources. The postprocessing physical model 612, and optionally the preprocessing physical model 614, can be configured to provide a goodness-of-fit 623 of the physical modeling.

[0062] One or more trained machine learning models 622 are used to predict a parameter 625 of interest based on multiple data sources. A machine learning measurement metric 627 can be developed and reported together with the goodness-of-fit 623 from the physical modeling to indicate the measurement quality of the synergistic recipe from the physical modeling and the machine learning. As illustrated by the solid black arrow, the trained machine learning model 622 uses the postprocessing measurement results extracted by the postprocessing physical model 612 as input data and also uses the preprocessing step data generated based on the preprocessing step measurement signal 604.

[0063] The preprocessing step data can be generated in multiple ways based on the preprocessing step measurement signal 604. For example, as illustrated in FIG. 6, the preprocessing step data can be generated in three different ways from the preprocessing step measurement signals 604 labeled 1, 2, and 3, where at least one of (1), (2), or (3), or any combination thereof can be used. As illustrated for the preprocessing step measurement signal 604 labeled 1, the preprocessing step data can be generated by combining the preprocessing step measurement signal 604 with the postprocessing step measurement signal 602 to form a pre-adjusted signal 605. As explained in FIG. 6, in some implementations, when the pre-adjusted signal 605 is generated, the pre-adjusted signal 605 is provided to the (A) postprocessing physical model 612, and the trained machine learning model 622 receives input data in the form of postprocessing measurement results extracted by the postprocessing physical model 612, or (B) the pre-adjusted signal 605 can be provided as input data to the trained machine learning model 622. Additionally, as further explained in FIG. 6, in some implementations, at least one of (A) or (B) can be used with the workflow 600. As illustrated for the preprocessing step measurement signal 604 labeled 2, the preprocessing step data can be generated by providing the preprocessing step measurement signal 604 to the preprocessing physical model 614, and the trained machine learning model 622 uses the measurement results extracted by the preprocessing physical model 614 as input data. As illustrated for the preprocessing step measurement signal 604 labeled 3, the preprocessing step data can be generated by providing the preprocessing step measurement signal 604 as input data to the trained machine learning model 622.

[0064] In some implementations, as illustrated by the gray dotted arrow, the trained machine learning model 622 can optionally further use input data including the postprocessing step measurement signal 602.

[0065] FIG. 7 illustrates, by way of example, a workflow 700 for offline recipe creation, e.g., generation of one or more physical models and one or more machine learning models, according to a third exemplary scenario using a plurality of data sources, e.g., signals collected from different manufacturing process steps. The workflow 700 according to the third exemplary scenario may be suitable for measuring complex 3D structures, including, but not limited to, GAA transistors or other devices, and using the hybrid measurement and ecosystem framework discussed herein, provides a way to independently measure different critical dimensions (CDs) of structures of interest in a logic GAA device, e.g., SiGe layer and internal spacer CDs, as discussed in FIGS. 1A and 1B. In FIG. 7, solid black arrows indicate processes used in the workflow 700 and dotted gray arrows indicate optional processes.

[0066] As illustrated, post - processing step measurement signals 702 from one or more reference samples are collected from a metrology device. The reference sample includes, for example, SOI, and the post - processing step measurement signals 702 are acquired after the desired steps of sample fabrication are completed. The post - processing step measurement signals 702 may be, for example, spectral data and may be collected from any desired metrology device, such as the metrology tool 201 shown in FIG. 2, or from any other desired type of metrology device.

[0067] Additionally, the pre - processing step measurement signals 704 from one or more reference samples are collected using a measurement device, e.g., the same measurement device used to obtain the post - processing step measurement signal 702, and are used to generate pre - processing step data. For example, the pre - processing step measurement signal 704 is obtained from a reference sample containing, e.g., SOI, and the pre - processing step measurement signal 704 is obtained before the desired step of sample fabrication is completed. The pre - processing step measurement signal 704 can be, e.g., spectral data, and can be collected from the same or a different measurement device used to collect the post - processing step measurement signal 702. The measurement device can be any desired measurement device such as the measurement tool 201 or 270 shown in FIG. 2, or any other desired type of measurement device. In some implementations, the post - processing step measurement signal 702 and the pre - processing step measurement signal 704 can be combined (e.g., by addition, subtraction, multiplication, or division) to form a pre - adjusted signal 705.

[0068] Additionally, e.g., post - processing step data 708 related to the SOI of the reference sample in the post - processing step, e.g., after the desired step of sample fabrication is completed, can be collected, e.g., reference data of the sample and / or DOE. In some implementations, the additional post - processing step data 708 related to the reference sample can further include wafer conditions, accuracy, tool - matching data, etc. Additionally, e.g., pre - processing step data 709 related to the SOI of the reference sample in the pre - processing step, e.g., before the desired step of sample fabrication is completed, can be collected, e.g., reference data of the sample and / or DOE. In some implementations, the additional pre - processing step data 709 related to the reference sample can further include wafer conditions, accuracy, tool - matching data, etc.

[0069] To generate a plurality of physical models, such as a pre - processing physical model 714 and a post - processing physical model 712, signals and data from a plurality of data sources can be used. For example, as illustrated by the solid black arrow, to generate a pre - processing physical model 714 of SOI from a sample, a pre - processing step measurement signal 704 from a measurement device can be used. In some implementations, additional data can be used to assist in generating the pre - processing physical model 714. For example, as illustrated, to assist in generating the pre - processing physical model 714, additional pre - processing step data 709, such as reference data and / or DOE, and optionally wafer conditions, accuracy, tool - matching data can be used.

[0070] Additionally, the pre - processing machine - learning model 724 is constructed and trained to predict one or more parameters of interest (parameter #1) 725. The pre - processing machine - learning model 724 is constructed using, as input features, the pre - processing measurement results extracted by the pre - processing physical model 714, as illustrated by the solid black arrow. The pre - processing machine - learning model 724 can be further constructed using the pre - processing step measurement signal 704 as an input feature. The pre - processing machine - learning model 724 is trained using at least a portion of the pre - processing step data 709, such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool - matching data. The one or more parameters of interest (parameter #1) can include primary parameters, i.e., parameters to be measured in the current processing step, or non - primary parameters, i.e., parameters that are not the intended parameters to be measured, or both primary and non - primary parameters. The parameter of interest (parameter #1) can be the Si / SiGe thickness of a GAA transistor, but other parameters of interest, including primary or non - primary parameters, can be determined for GAA transistors or other devices being measured.

[0071] Additionally, as illustrated by the solid black arrows, post - process step measurement signals 702 from the measurement device can be used to generate a post - process physical model 712 of the SOI from the sample. In some implementations, additional data can be used to assist in generating the post - process physical model 712. For example, as illustrated, additional post - process step data 708, such as reference data and / or DOE, and optionally wafer conditions, accuracy, tool - matching data can be used to assist in generating the post - process physical model 712. The pre - process step measurement signal 704 contains rich information and sensitivity for one or more parameters of interest (parameter #1) 725, and thus such information can be used to improve accuracy. Thus, as illustrated, the post - process physical model 712 can receive feed - forward data from the pre - process physical model 714 and / or from the pre - process machine - learning model 724, for example, for one or more parameters of interest (parameter #1) 725, to facilitate the propagation of information in the pre - process fabrication step signal to the post - process physical model 712. In some implementations, feedback data generated based on the post - process step measurement signal 702 can be used to assist in generating the post - process physical model 712. As illustrated, the post - process physical model 712 can receive feedback data for one or more parameters of interest (parameter #2) 723, determined based on the post - process step measurement signal 702, by the post - process machine - learning model 722, as discussed below. The accuracy of one or more parameters of interest (parameter #2) 723 benefits from the more accurate one or more parameters of interest (parameter #1) 725 that are feed - forward to the post - process physical model 712. Further, the feedback of one or more parameters of interest (parameter #2) 723 can resolve high correlations of parameters of interest that have experienced the same fabrication step, for example, different etched SiGe CDs.For example, the post - processing physical model 712 or the post - processing machine learning model 722 may use feedback data and be retrained using additional post - processing step data 708, such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool - matching data to provide better predictions regarding other parameters of interest, such as (parameter #3) 713 or (parameter #2) 723.

[0072] The post - processing machine learning model 722 is constructed and trained to predict one or more parameters of interest (parameter #2) 723, which may include primary parameters, non - primary parameters, or both primary and non - primary parameters. The post - processing machine learning model 722 is constructed using the post - processing measurement results extracted by the post - processing physical model 712 as input features, as illustrated by the solid black arrow. The post - processing machine learning model 722 may be further constructed using the post - processing step measurement signal 702 as an input feature. Additionally, as illustrated by the gray dotted line, the post - processing machine learning model 722 may optionally be constructed using the pre - adjusted signal 705 and / or the pre - processing step measurement signal 704 as input features. The post - processing machine learning model 722 is trained using at least a portion of the post - processing step data 708, such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool - matching data. The parameters of the post - processing machine learning model 722 and the post - processing physical model 712, such as hyperparameters, weights, biases, etc., are provided for sample characterization and may be reported, for example.

[0073] As illustrated, the post - processing physical model 712 (or a separate machine - learning model) can be used to predict one or more additional parameters of interest, illustrated as parameter #3 713, which can include primary parameters, non - primary parameters, or both primary and non - primary parameters. The post - processing parameters of interest, e.g., (parameters #2 and #3) 723 and 713, can be, for example, SiGe CD1, SiGe CD2, SiGe CD3 for a GAA transistor (as illustrated in FIG. 1B), respectively, but other parameters of interest can be determined for a GAA transistor or for other devices being measured. For example, the workflow 700 illustrated in FIG. 7 can also be applied to other pre - processing and post - processing steps, e.g., multiple CD profile measurements in high aspect ratio (HAR) channel hole etching. Further, the additional parameter of interest (parameter #3) 713 from the post - processing physical model 712 can be further fed forward to the post - processing machine - learning model 722. The post - processing machine - learning model 722 can be retrained using at least a portion of the post - processing step data 708 to make a final prediction of the additional parameter of interest (parameter #3) 713.

[0074] FIG. 8 illustrates, by way of example, a workflow 800 for in - line measurement for characterizing a sample based on one or more physical models and one or more machine - learning models, according to a third exemplary scenario that uses multiple data sources, e.g., signals collected from different manufacturing process steps. The one or more physical models and one or more machine - learning models can be generated, for example, as discussed with reference to FIG. 7. In FIG. 8, the solid black arrows indicate the processes used in the workflow 800, and the gray arrows indicate optional processes.

[0075] As illustrated, post - processing step measurement signals 802 from one or more reference samples are collected from a measurement device. The reference sample includes, for example, SOI, and the post - processing step measurement signal 802 is obtained after a desired step of sample fabrication is completed. The post - processing step measurement signal 802 can be, for example, spectral data and can be collected from any desired measurement device such as measurement tool 201 shown in FIG. 2, or from any other desired type of measurement device, and can be collected from the same measurement device or the same type of measurement device as that used to obtain the post - processing step measurement signal 702 in FIG. 7.

[0076] Additionally, pre - processing step measurement signals 804 from one or more reference samples are collected using a measurement device, for example, the same measurement device used to obtain the post - processing step measurement signal 802, and are used to generate pre - processing step data. For example, the pre - processing step measurement signal 804 is obtained from a reference sample that includes, for example, SOI, and the pre - processing step measurement signal 804 is obtained before a desired step of sample fabrication is completed. The pre - processing step measurement signal 804 can be, for example, spectral data and can be collected from the same or a different measurement device used to collect the post - processing step measurement signal 802, and the measurement device can be any desired measurement device such as measurement tool 201 or 270 shown in FIG. 2, or the pre - processing step measurement signal 804 can be collected from any other desired type of measurement device, and can be the same measurement device or the same type of measurement device as that used to obtain the pre - processing step measurement signal 704 in FIG. 7. In some implementations, the post - processing step measurement signal 802 and the pre - processing step measurement signal 804 can be combined (e.g., combined by addition, subtraction, multiplication, or division) to form a pre - adjusted signal 805.

[0077] To extract measurement results from multiple physical models, such as the pre-processing physical model 814 and the post-processing physical model 812, signals and data from multiple data sources can be used. For example, as illustrated by the solid black arrow, to extract measurement results from the pre-processing physical model 814 of SOI from a sample, the pre-processing step measurement signal 804 from the measurement device can be used.

[0078] Additionally, a trained pre-processing machine learning model 824 can be used to predict one or more parameters of interest (parameter #1) 825. As illustrated by the solid black arrow, the trained pre-processing machine learning model 824 uses the pre-processing measurement results extracted by the pre-processing physical model 814 as input features. The trained pre-processing machine learning model 824 can further use the pre-processing step measurement signal 804 as input features. The one or more parameters of interest (parameter #1) can include primary parameters, non-primary parameters, or both primary and non-primary parameters, and by way of example, can be the Si / SiGe thickness of a GAA transistor, although other parameters of interest can be determined for GAA transistors or other devices being measured.

[0079] Additionally, as illustrated by the solid black arrows, the post - processing step measurement signal 802 from the measurement device can be used to extract measurement results from the post - processing physical model 812 of the SOI from the sample. In some implementations, additional data can be used to assist in extracting measurement results from the post - processing physical model 812. For example, as illustrated, the post - processing physical model 812 can receive feed - forward data from the pre - processing physical model 814 and / or from the pre - processing machine - learning model 824, for example, about the values of one or more parameters of interest (parameter #1) 825, to facilitate the propagation of information within the pre - processing fabrication step signal to the post - processing physical model 812. In some implementations, feedback data generated based on the post - processing step measurement signal 802 can be used to assist in extracting measurement results from the post - processing physical model 812. As illustrated, the post - processing physical model 812 can receive feedback data about the initial values of one or more parameters of interest (parameter #2) 823, determined, for example, based on the post - processing step measurement signal 802 by the post - processing machine - learning model 822, as discussed below. Due to the accuracy of the one or more parameters of interest (parameter #2) 823, the post - processing physical model 812 benefits from more accurate one or more parameters of interest (parameter #1) 825 being feed - forward to it. Further, the feedback of the one or more parameters of interest (parameter #2) 823 can resolve high correlations of parameters of interest that have experienced the same fabrication step, for example, different etched SiGe CDs.

[0080] After being trained, the post - processing machine learning model 822 is used to predict the final values of one or more parameters of interest (parameter #2) 823 (and, if feedback is used, one or more initial values of one or more parameters of interest (parameter #2) 823), which may include primary parameters, non - primary parameters, or both primary and non - primary parameters. As illustrated by the solid black arrow, the trained post - processing machine learning model 822 uses the post - processing measurement results extracted by the post - processing physical model 812 as input features. The trained post - processing machine learning model 822 may further use the post - processing step measurement signal 802 as an input feature. Additionally, as illustrated by the gray dotted line, the trained post - processing machine learning model 822 may optionally use the pre - adjusted signal 805 and / or the pre - processing step measurement signal 804 as input features. The final values of the one or more parameters of interest are provided for characterizing the sample and may be reported, for example.

[0081] As illustrated, the post - processing physical model 812 (or a separate machine learning model) may be used to predict one or more additional parameters of interest, illustrated as parameter #3 813, which may include primary parameters, non - primary parameters, or both primary and non - primary parameters. The post - processing parameters of interest, e.g., (parameter #2 and #3) 823 and 813, may be, by way of example, SiGe CD1, SiGe CD2, SiGe CD3 for a GAA transistor, respectively, but other parameters of interest may be determined for a GAA transistor or other devices being measured. For example, the workflow 800 illustrated in FIG. 8 may also be applied to other pre - processing and post - processing steps, e.g., multiple CD profile measurements in high aspect ratio (HAR) channel hole etching. Further, the additional parameters of interest (parameter #3) 813 from the post - processing physical model 812 can be further fed forward to the post - processing machine learning model 822.

[0082] In some implementations, primary data, such as measurement signals used in physical modeling, and auxiliary data, such as data used only in machine learning, can be from different tool sets, or from the same tool set but different data channels, or from the same tool set and the same data channel but different wavelength ranges, time intervals, etc. Different data sources can collect data from the same OCD target on the same wafer or the same sample site on a device, from the same processing step, or from different processing steps. Different data sources can collect data from different sample sites on the same wafer from the same or different processing steps, for example, when the underlying structure has correlation parameters, and as a result, analyzing the combined data can improve overall performance. As illustrated, at least one physical model can be created to analyze measurement signals from at least one data source. Further, when two or more physical models are used, the multiple physical models can be optimized independently or co-optimized. For example, the physical models can be linked such that at least some parameters can be coupled across the physical models and the combined parameter space can be searched to fit the measurement signals from one or more data sources. The primary data and the auxiliary data can have different natures. For example, some of the data can be measurement data collected from a tool set, and other data can be sensor data from process equipment, or wafer process parameters such as gas flow rate, APC parameters, or context data, such as specific process tools. Additionally, feature engineering and signal preprocessing can be applied before data from all sources is provided to a machine learning model for training. Machine learning algorithms can include, for example, linear regression, neural networks, deep learning, convolutional neural networks (CNNs), ensemble methods, support vector machines (SVMs), random forests, etc., or combinations of multiple models in sequential mode and / or parallel mode, but are not limited thereto.

[0083] The illustrated workflow efficiently combines various measurement techniques and the use of multiple data sources by synergistically applying physical modeling and machine learning to generate more usable information than provided by individual measurement techniques or a single data source. Physical modeling can be performed using previously well-established modeling solutions with a desired measurement device, and the physical modeling results can be combined with other modeling-difficult or impossible data, referred to as auxiliary data, for machine learning training and prediction. Thus, the resulting process provides an executable solution with the advantages of both physical modeling and machine learning while controlling the computational cost, enables an acceptable TTS for generation, is easily implemented, and is actually used. Additionally, the predictive ability can be increased through the use of data such as process parameters and sensor data from production equipment, which is combined with measurement data through data mining and data fusion as considered herein. The proposed method is flexible to adapt to various signals of different natures and, at the same time, maximizes the use of existing well-developed algorithms for each type of data source. Further, the techniques considered herein have general-purpose applications and can be applied, for example, to the measurement of any device, OCD, thin film, or other type of target.

[0084] FIG. 9 shows an illustrative flow diagram depicting an exemplary method 900 for measuring parameters of at least one object of interest from an SOI according to some implementations. In some implementations, the exemplary method 900 can be executed by at least one processor, such as processor 262 within computing system 260 of FIG. 2, which implements the workflow 700 illustrated in FIG. 7.

[0085] At least one processor may obtain a post - processing step measurement signal from a measurement device for SOI on one or more samples in a post - processing step (902). For example, the means for obtaining the post - processing step measurement signal may be an interface with the measurement device 200 and the processor 262 within the computing system 260 shown in FIG. 2. The post - processing step measurement signal of SOI on one or more samples in the post - processing step may be, for example, the post - processing step measurement signal 702 shown in FIG. 7.

[0086] At least one processor may generate a post - processing physical model (904) for extracting post - processing measurement results of the SOI based on at least one of a post - processing step measurement signal, a first parameter of the SOI in a pre - processing step that is fed forward to the post - processing physical model, a second parameter of the SOI in a post - processing step that is fed back to the post - processing physical model, and combinations thereof. The first parameter of the SOI may be determined, for example, by at least one of a pre - processing physical model and a pre - processing machine learning model for the pre - processing step measurement signal obtained from the SOI on one or more samples in the pre - processing step. For example, the post - processing measurement results of the SOI may be extracted based on the post - processing step measurement signal and at least one of the first parameter or the second parameter, or both the first parameter and the second parameter. Further, in some implementations, one or more first parameters may be used. In some implementations, one or more second parameters may be used. The means for generating the post - processing physical model may be a measurement device 200 including a computing system 260 configured to generate one or more physical models (model 264pm) by computer - readable program code 266 shown in FIG. 2. The post - processing physical model may be, for example, a post - processing physical model 712 generated using at least one of a feed - forward parameter from a pre - processing physical model 714, or a first parameter 725 determined from the pre - processing physical model 714 and a pre - processing machine learning model 724, or a feedback of a second parameter 723, as illustrated in FIG. 7. In some implementations, each of the first parameter and the second parameter may be a primary parameter or a non - primary parameter.

[0087] At least one processor may generate a post - processing machine - learning model to predict a second parameter of the SOI in a post - processing step, and the post - processing machine - learning model is generated based on post - processing measurement results extracted from a post - processing physical model (906). The post - processing machine - learning model may be further generated based on a post - processing measurement signal and post - processing step data including at least one of reference data and experimental design information for the SOI in the post - processing step. For example, the means for generating the post - processing machine - learning model may be a measurement device 200 including a computing system 260 configured to generate and train one or more machine - learning models (ML264ml) by computer - readable program code 266 shown in FIG. 2. The post - processing machine - learning model may be, for example, a post - processing step machine - learning model 722 generated based on post - processing measurement results extracted from a post - processing physical model 712, a post - processing measurement signal 702, and post - processing step data 708.

[0088] At least one processor may provide parameters of a post - processing physical model and a post - processing machine - learning model to measure at least one parameter of interest of the SOI (908). For example, the means for providing parameters for a post - processing physical model and a post - processing machine - learning model to measure at least one parameter of interest of the SOI may be an interface within the computing system 260 shown in FIG. 2, the measurement device 200, as well as the processor 262 and the memory 264.

[0089] In some implementations, the post - processing physical model may be further generated based on the post - processing step data, as illustrated, for example, by the arrow from the post - processing step data 708 to the post - processing physical model 712 shown in FIG. 7.

[0090] In some implementations, at least one processor may further obtain a preprocessing step measurement signal from a measurement device for SOI on one or more samples in a preprocessing step, as illustrated, for example, by the preprocessing step measurement signal 704 shown in FIG. 7. At least one processor may further generate a preprocessing physical model to extract preprocessing measurement results of the SOI based on the preprocessing step measurement signal, as illustrated, for example, by the preprocessing physical model 714 shown in FIG. 7. At least one processor may further generate a preprocessing machine learning model to predict a first parameter of the SOI in the preprocessing step, as illustrated, for example, by the preprocessing machine learning model 724 shown in FIG. 7. The preprocessing machine learning model may be generated based on the preprocessing measurement results extracted from the preprocessing physical model and the preprocessing step data including at least one of the reference data of the SOI and the design of experimental information in the preprocessing step, as illustrated by the arrows from the preprocessing physical model 714 to the preprocessing machine learning model 724 and from the preprocessing step data 709 to the preprocessing machine learning model 724 shown in FIG. 7.

[0091] In some implementations, the preprocessing physical model may be further generated based on the preprocessing step data, as illustrated, for example, by the arrow from the preprocessing step data 709 to the preprocessing physical model 714 shown in FIG. 7.

[0092] In some implementations, the postprocessing machine learning model may be further generated based on the preprocessing step measurement signal from the SOI in the preprocessing step, as illustrated, for example, by the arrow from the preprocessing step measurement signal 704 to the postprocessing machine learning model 722 shown in FIG. 7.

[0093] In some implementations, at least one processor may further generate a pre-adjusted signal by combining a pre-processing step measurement signal from the SOI in a pre-processing step and a post-processing step measurement signal from the SOI in a post-processing step, where the post-processing machine learning model is further generated based on the pre-adjusted signal, as illustrated, for example, by the pre-adjusted signal 705 shown in FIG. 7 and the arrow from the pre-adjusted signal 705 to the post-processing machine learning model 722.

[0094] In some implementations, at least one processor may further determine one or more additional parameters of the SOI using at least one of a post-processing physical model or a post-processing machine learning model, as illustrated, for example, by the prediction of parameter #3 713. In some implementations, the one or more additional parameters may include a primary parameter, a non-primary parameter, or a combination of a primary parameter and a non-primary parameter.

[0095] FIG. 10 shows an illustrative flow diagram depicting an exemplary method 1000 for measuring at least one parameter of interest from an SOI according to some implementations. In some implementations, the exemplary method 1000 may be executed by at least one processor, such as processor 262 within computing system 260 illustrated in FIG. 2, which implements the workflow 800 illustrated in FIG. 8.

[0096] At least one processor may obtain a post-processing step measurement signal from a measurement device for the SOI on one or more samples in a post-processing step (1002). For example, the means for obtaining the post-processing step measurement signal may be an interface between the measurement device 200 and the processor 262 within the computing system 260 shown in FIG. 2. The post-processing step measurement signal for the SOI on one or more samples in the post-processing step may be, for example, the post-processing step measurement signal 802 shown in FIG. 8.

[0097] At least one processor can extract post - processing measurement results (1004) based on at least one of a post - processing step measurement signal, a value of a first parameter of the SOI in a pre - processing step that is fed forward to the post - processing physical model, a value of a second parameter of the SOI in a post - processing step that is fed back to the post - processing physical model, and combinations thereof, from the post - processing physical model of the SOI. For example, the post - processing measurement results of the SOI can be extracted based on the post - processing step measurement signal, the value of the first parameter or the second parameter, or both the first parameter and the second parameter. Further, in some implementations, one or more first parameters can be used. In some implementations, one or more second parameters can be used. The means for generating the post - processing measurement results extracted from the post - processing physical model can be the measurement device 200 including a computing system 260 configured to generate one or more physical models (model 264pm) by computer - readable program code 266 shown in FIG. 2. The post - processing measurement results can be extracted from the post - processing physical model based on, for example, the post - processing step measurement signal 802 and at least one of the feedback of the feed - forward first parameter 825 determined from the pre - processing physical model 814 and the pre - processing machine - learning model 824 or the second parameter 823 as illustrated in FIG. 8, as illustrated by the arrow from the post - processing physical model 812. In some implementations, each of the first parameter and the second parameter can be a major parameter or a non - major parameter.

[0098] At least one processor predicts (1006) a final value of a possible second parameter of the SOI in a post-processing step from a trained post-processing machine learning model based on post-processing measurement results extracted from a post-processing physical model. The final value of the second parameter of the SOI can be predicted from the trained post-processing machine learning model further based on a post-processing step measurement signal. For example, means for predicting the final value of the second parameter of the SOI from the trained post-processing machine learning model can be a measurement device 200 including a computing system 260 configured to generate and train one or more machine learning models (ML264ml) by computer-readable program code 266 shown in FIG. 2. The final value of the second parameter of the SOI can be predicted by a trained post-processing machine learning model based on, for example, post-processing measurement results extracted from a post-processing physical model and a post-processing step measurement signal, as illustrated by an arrow from the post-processing physical model 812 to the post-processing machine learning model 822 and the post-processing step measurement signal 802 to the post-processing machine learning model 822, and, for example, a parameter #2 823 predicted by the post-processing machine learning model 822.

[0099] At least one processor can provide (1008) at least the final value of the second parameter of the SOI. For example, means for providing at least the final value of the second parameter of the SOI can be a measurement device 200, which can interface with a processor 262 and a memory 264 within the computing system 260 and the UI 268 shown in FIG. 2.

[0100] In some implementations, the value of the first parameter of the SOI can be determined from at least one of, for example, a pre - processing physical model and a trained pre - processing machine learning model for pre - processing measurement signals obtained from the SOI on one or more samples in a pre - processing step. For example, at least one processor can obtain a pre - processing measurement signal from a measurement device for the SOI on one or more samples in a pre - processing step, as illustrated by the pre - processing measurement signal 804 shown in FIG. 8. At least one processor can determine the value of the first parameter from the extracted pre - processing measurement results of the SOI from the pre - processing physical model based on the pre - processing measurement signal, as illustrated by the arrow from the pre - processing physical model 814 shown in FIG. 8. In another example, at least one processor extracts the pre - processing measurement results of the SOI from the pre - processing physical model based on the pre - processing measurement signal, as illustrated by the predicted parameter #1 825 predicted by the pre - processing machine learning model 824 shown in FIG. 8, and can predict the value of the first parameter of the SOI in the pre - processing step from the trained pre - processing machine learning model based on the pre - processing measurement results extracted from the pre - processing physical model.

[0101] In some implementations, the value of the second parameter of the SOI in a post - processing step can be predicted from a trained post - processing machine learning model based on initial post - processing measurement results extracted from a post - processing physical model, as illustrated by the arrow from the post - processing physical model 812 to the post - processing machine learning model 822 shown in FIG. 8.

[0102] In some implementations, the final value of the second parameter of the SOI in a post - processing step can be predicted from a trained post - processing machine learning model based further on the pre - processing measurement signal from the SOI in a pre - processing step, as illustrated by the arrow from the pre - processing measurement signal 804 shown in FIG. 8 to the post - processing machine learning model 822.

[0103] In some implementations, at least one processor may further generate a pre-adjusted signal by combining a pre-processing step measurement signal from the SOI in a pre-processing step and a post-processing step measurement signal from the SOI in a post-processing step, where the final value of the second parameter of the SOI in the post-processing step is predicted from a trained post-processing machine learning model based further on the pre-adjusted signal, as illustrated, for example, by the pre-adjusted signal 805 shown in FIG. 8 and the arrow from the pre-adjusted signal 805 to the post-processing machine learning model 822.

[0104] In some implementations, at least one processor may further determine one or more additional parameters of the SOI using at least one of a post-processing physical model or a post-processing machine learning model, as illustrated, for example, by the prediction of parameter #3 813 shown in FIG. 8. In some implementations, the one or more additional parameters may include a primary parameter, a non-primary parameter, or a combination of a primary parameter and a non-primary parameter.

[0105] The above description is intended to be illustrative and not restrictive. For example, the above examples (or one or more aspects thereof) may be used in combination with each other. Other implementations may be used by, for example, those skilled in the art when considering the above description. Also, various features may be grouped together and fewer features than all the features of a particular disclosed implementation may be used. Accordingly, the following aspects are incorporated by this specification into the above description as examples or implementations, each aspect standing on its own as a separate implementation, and such implementations are intended to be combinable with each other in various combinations or permutations. Accordingly, the spirit and scope of the appended claims should not be limited to the foregoing description.

Claims

**Claim 1** A method for measuring at least one parameter of interest from a structure of interest (SOI), comprising: In a post-processing step, obtaining a post-processing step measurement signal from a measurement device for the SOI on one or more samples; Extracting a post-processing measurement result from the post-processing physical model of the SOI based on at least one of the post-processing step measurement signal, the value of the first parameter of the SOI in a pre-processing step fed forward to the post-processing physical model, the value of the second parameter of the SOI in the post-processing step fed back to the post-processing physical model, and combinations thereof; Predicting a final value of the second parameter of the SOI in the post-processing step from a trained post-processing machine learning model based on the post-processing measurement result extracted from the post-processing physical model; Providing at least the final value of the second parameter of the SOI. **Claim 2** The method according to claim 1, wherein the value of the first parameter of the SOI is determined from at least one of a pre-processing physical model and a trained pre-processing machine learning model based on a pre-processing step measurement signal obtained from the SOI on the one or more samples in the pre-processing step. **Claim 3** The method according to claim 2, further comprising, in the pre-processing step, obtaining the pre-processing step measurement signal from the measurement device for the SOI on the one or more samples; Determining the value of the first parameter from the extracted pre-processing measurement result of the SOI from the pre-processing physical model based on the pre-processing step measurement signal. **Claim 4** The method according to claim 2, further comprising, in the pre-processing step, obtaining the pre-processing step measurement signal from the measurement device for the SOI on the one or more samples; Extracting a pre-processing measurement result of the SOI from the pre-processing physical model based on the pre-processing step measurement signal; Predicting the value of the first parameter of the SOI in the pre-processing step from the trained pre-processing machine learning model based on the pre-processing measurement result extracted from the pre-processing physical model. **Claim 5** The method according to claim 1, wherein the value of the second parameter of the SOI in the post-processing step is predicted from the trained post-processing machine learning model based on an initial post-processing measurement result extracted from the post-processing physical model and the post-processing step measurement signal.

6. The method according to claim 1, wherein the final value of the second parameter of the SOI in the post-processing step is predicted from the trained post-processing machine learning model further based on a pre-processing step measurement signal from the SOI in the pre-processing step.

7. The method according to claim 1, further comprising generating a pre-adjusted signal by combining a pre-processing step measurement signal from the SOI in the pre-processing step and a post-processing step measurement signal from the SOI in the post-processing step, wherein the final value of the second parameter of the SOI in the post-processing step is predicted from the trained post-processing machine learning model further based on the pre-adjusted signal.

8. The method according to claim 1, further comprising determining one or more additional parameters of the SOI using at least one of the post-processing physical model or the trained post-processing machine learning model.

9. A computer system configured to measure at least one parameter of interest from a structure of interest (SOI), comprising at least one processor, the at least one processor in a post-processing step, for an SOI on one or more samples, obtaining a post-processing step measurement signal from a measurement device, extracting a post-processing measurement result from the post-processing physical model based on at least one of the post-processing step measurement signal, a value of a first parameter of the SOI in a pre-processing step fed forward to the post-processing physical model, a value of a second parameter of the SOI in the post-processing step fed back to the post-processing physical model, and combinations thereof, predicting a final value of the second parameter of the SOI in the post-processing step from a trained post-processing machine learning model based on the post-processing measurement result extracted from the post-processing physical model. A computer system configured to provide at least the final value of the second parameter of the SOI.

10. The value of the first parameter of the SOI is determined from at least one of a preprocessing physical model and a trained preprocessing machine learning model based on a preprocessing step measurement signal obtained from the SOI on the one or more samples in the preprocessing step, the computer system according to claim 9.

11. The at least one processor In the preprocessing step, for the SOI on the one or more samples, obtain the preprocessing step measurement signal from the measurement device, Based on the preprocessing step measurement signal, further configured to determine the value of the first parameter from the extracted preprocessing measurement results of the SOI from the preprocessing physical model, the computer system according to claim 10.

12. The at least one processor In the preprocessing step, for the SOI on the one or more samples, obtain the preprocessing step measurement signal from the measurement device, Based on the preprocessing step measurement signal, extract the preprocessing measurement results of the SOI from the preprocessing physical model, Based on the preprocessing measurement results extracted from the preprocessing physical model, predict the value of the first parameter of the SOI in the preprocessing step from the trained preprocessing machine learning model, the computer system according to claim 10.

13. The at least one processor is configured to predict the value of the second parameter of the SOI in the postprocessing step from the trained postprocessing machine learning model based on an initial postprocessing measurement result extracted from the postprocessing physical model and the postprocessing step measurement signal, the computer system according to claim 9.

14. The at least one processor is further configured to predict the final value of the second parameter of the SOI in the postprocessing step from the trained postprocessing machine learning model based on the preprocessing step measurement signal from the SOI in the preprocessing step, the computer system according to claim 9.

15. The at least one processor is further configured to generate a pre-adjusted signal by combining the pre-processing step measurement signal from the SOI in the pre-processing step and the post-processing step measurement signal from the SOI in the post-processing step, and the at least one processor is further configured to predict the final value of the second parameter of the SOI in the post-processing step from the trained post-processing machine learning model based further on the pre-adjusted signal. The computer system according to claim 9.

16. The at least one processor is further configured to determine one or more additional parameters of the SOI using at least one of the post-processing physical model or the trained post-processing machine learning model. The computer system according to claim 9.

17. A system configured to measure at least one parameter of interest from a structure of interest (SOI), In a post-processing step, means for obtaining a post-processing step measurement signal from a measurement device for the SOI on one or more samples, Means for extracting a post-processing measurement result based on the post-processing step measurement signal and at least one of the value of the first parameter of the SOI in the pre-processing step fed forward to the post-processing physical model, the value of the second parameter of the SOI in the post-processing step fed back to the post-processing physical model, and combinations thereof, from the post-processing physical model of the SOI, Means for predicting the final value of the second parameter of the SOI in the post-processing step from a trained post-processing machine learning model based on the post-processing measurement result extracted from the post-processing physical model, A system comprising means for providing at least the final value of the second parameter of the SOI.

18. The value of the first parameter of the SOI is determined from at least one of a pre-processing physical model and a trained pre-processing machine learning model based on a pre-processing step measurement signal obtained from the SOI on the one or more samples in the pre-processing step. The system according to claim 17.

19. The value of the second parameter of the SOI in the post - processing step is predicted from the trained post - processing machine learning model based on an initial post - processing measurement result extracted from the post - processing physical model and the post - processing step measurement signal, the system according to claim 17.

20. The final value of the second parameter of the SOI in the post - processing step is predicted from the trained post - processing machine learning model further based on a pre - processing step measurement signal from the SOI in the pre - processing step, the system according to claim 17.

21. The value of the second parameter of the SOI in the post - processing step is predicted from the trained post - processing machine learning model based on an initial post - processing measurement result extracted from the post - processing physical model and the post - processing step measurement signal, the system according to claim 17.

22. The final value of the second parameter of the SOI in the post - processing step is predicted from the trained post - processing machine learning model further based on a pre - processing step measurement signal from the SOI in the pre - processing step, the system according to claim 17.

23. The system according to claim 17, further comprising means for generating a pre - adjusted signal that combines a pre - processing step measurement signal from the SOI in the pre - processing step and a post - processing step measurement signal from the SOI in the post - processing step, wherein the final value of the second parameter of the SOI in the post - processing step is predicted from the trained post - processing machine learning model further based on the pre - adjusted signal.

24. The system according to claim 17, further comprising means for determining one or more additional parameters of the SOI using at least one of the post - processing physical model or the trained post - processing machine learning model.

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