Measurement solutions for complex structures of interest

Abstract

We provide measurement solutions for complex structures of interest. [Solution] Complex structures in semiconductor devices, such as gate-all-around field-effect transistors or high-aspect-ratio channel-hole etchings, are measured using a combination of physical modeling and machine learning modeling. The measurement signal obtained in the preprocessing step is used, for example, to determine a first parameter of the structure of interest (SOI) using physical modeling and machine learning. This signal can be feedforward and used in the postprocessing step to generate a physical model of the SOI. A second parameter of the SOI in the postprocessing step is determined using physical modeling and machine learning, fed back, and used with the postprocessing signal to generate a physical model of the SOI in the postprocessing step and 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, filed on June 23, 2022, entitled "METROLOGY SOLUTIONS FOR GATE - ALL - AROUND TRANSISTORS", U.S. Provisional Application No. 63 / 498,475, filed on April 26, 2023, entitled "MULTIPLE SOURCES OF SIGNALS FOR HYBRID METROLOGY USING PHYSICAL MODELING AND MACHINE LEARNING", and U.S. Non - Provisional Application No. 18 / 339,971, filed on June 22, 2023, entitled "METROLOGY SOLUTIONS FOR COMPLEX STRUCTURES OF INTEREST", all of which have been 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 the 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, light of a single wavelength or multiple wavelengths is irradiated onto a test sample. After the light interacts with the sample, the resulting light is detected and analyzed to determine one or more characteristics of the sample.

[0004] The analysis typically involves modeling the structure under test. The model may be generated based on the physical properties of the structure, e.g., the material and nominal parameters of the structure, e.g., film thickness, optical properties of the material, lines, and spacing width; therefore, it is sometimes referred to as a physical model. One or more parameters of the model can be varied, and predictive data can be calculated for each parameter variation based on the model, for example, using Rigorous Coupled Wave Analysis (RCWA) or other similar techniques. Measured data may be compared with the predicted data for each parameter variation, for example, in a nonlinear 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 structure under test. However, modeling can be time-consuming, computationally intensive, and expensive, especially for small, complex features. [Overview of the project]

[0005] Complex structures in semiconductor devices, such as gate-all-around (GAA) field-effect transistors or high-aspect ratio (HAR) channel hole etchings, 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 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, to determine a first parameter of the SOI using physical modeling and machine learning. This signal can be feedforward and used in the post-processing step to generate a physical model of the SOI to improve accuracy. In the post-processing step, a second parameter of the SOI is 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 correlations.

[0006] In one implementation, a method for measuring multiple parameters of interest from a structure of interest (SOI) includes, in a post-processing step, acquiring a post-processing step measurement signal from a measurement device for SOIs on one or more samples. The method further includes extracting post-processing measurement results from a post-processing physical model of the SOI based on the post-processing step measurement signal and at least one of the values ​​of a first parameter of the SOI in a pre-processing step that is fed forward to the post-processing physical model, the values ​​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. The method further includes predicting the final value of the second parameter of the SOI in a post-processing step from a trained post-processing machine learning model based on the post-processing measurement results 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 multiple parameters of interest from a structure of interest (SOI) includes at least one processor, which is configured to acquire post-processing step measurement signals from a measurement device for SOIs on one or more samples in a post-processing step. The at least one processor is further configured to extract post-processing measurement results from a post-processing physical model of the SOI based on the post-processing step measurement signals and at least one of the values ​​of a first parameter of the SOI in a pre-processing step that is fed forward to the post-processing physical model, the values ​​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. The at least one processor is further configured to predict the final value of the second parameter of the SOI in a post-processing step from a trained post-processing machine learning model based on the post-processing measurement results extracted from the post-processing physical model, and to provide at least the final value of the second parameter of the SOI.

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

[0009] [Figure 1A] Examples of planar transistor architecture, fin-transistor architecture, and gate-all-around (GAA) field-effect transistor architecture are illustrated. [Figure 1B] Let's illustrate this with an example of a GAA transistor. [Figure 2] A schematic diagram illustrating a measuring device that may be used to characterize a sample, as discussed herein, is provided. [Figure 3] This illustrates a workflow for creating offline recipes using a first exemplary scenario that utilizes signals collected from multiple data sources, including different tools and / or sources. [Figure 4] This illustrates an inline measurement workflow using a first exemplary scenario with signals collected from multiple data sources, including different tools and / or sources. [Figure 5]This illustrates a workflow for creating offline recipes using a second exemplary scenario that utilizes signals collected from multiple data sources, including different manufacturing process steps. [Figure 6] This illustrates an inline measurement workflow using a second exemplary scenario that utilizes signals collected from multiple data sources, including different manufacturing process steps. [Figure 7] This illustrates a workflow for creating offline recipes using a third exemplary scenario that utilizes signals collected from multiple data sources, such as different manufacturing process steps. [Figure 8] This illustrates an inline measurement workflow using a third exemplary scenario that utilizes signals collected from multiple data sources, including different manufacturing process steps. [Figure 9] This document illustrates a flowchart that shows a method for characterizing a device on a sample based on multiple data sources. [Figure 10] This document illustrates a flowchart that shows a method for characterizing a device on a sample based on multiple data sources. [Modes for carrying out the invention]

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

[0011] Optical measurements, such as thin-film measurement and optical critical dimension (OCD) measurement, as well as other types of measurements, sometimes use physical modeling techniques to generate predicted data of the sample to be compared with measured data from the sample. Using physical modeling techniques, a model of the sample is generated, including major and minor parameters. The model may include one or more variable parameters, such as layer thickness, line width, spacing, sidewall angle, and material properties, which are derived based on the nominal parameters of the sample and may vary over a desired range depending on the process parameters used to fabricate the sample under test. The model may further include parameters related to the toolset, such as the characteristics of the optical system used by the measurement device. Predictive data can be calculated based on the parameters of a physical model, including variations in 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) / exact coupled wave analysis (RCWA), and finite element method (FEM). Measurement data obtained from a sample by the measurement device is compared with the predictive data for different parameter variations, for example, in a nonlinear regression process, until the best fit is achieved. At the point when the best fit is achieved, the values ​​of the fitted parameters are considered to be an accurate representation of the sample parameters.

[0012] Traditionally, modeling requires that preliminary structural and material information about a sample be known in order to generate an accurate representative model of the sample that includes one or more variable parameters. For example, preliminary structural and material information about a sample may include the type of structure of the sample and a physical description with nominal values ​​for various parameters, such as layer thickness, line width, spacing width, sidewall angle, and material properties, along with the range over which these parameters may change. The model may further include one or more non-variables, i.e., parameters that are not expected to change significantly in the sample during manufacturing. The variable parameters of the model can be adjusted, and predictive data can be generated in real time during a nonlinear regression process, or a library can be pre-generated. Thus, modeling applies physical constraints in the analysis and provides a high level of fidelity to the measurement results accordingly. However, modeling has a high computational cost due to the physical calculations required to generate predictive data. For example, modeling complex 3D structures suffers from slow time to solution (TTS), and modeling accuracy can be reduced due to the difficulty in fitting data for complex structures.

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

[0014] As semiconductor devices continue to miniaturize, measurement budgets become increasingly stringent. Additionally, complex 3D structures are being employed more frequently to enable continuous device scaling. Advances in semiconductor technology, such as the use of complex 3D structures, present additional challenges to measurement due to increased modeling complexity, parameter correlation, and reduced sensitivity. For example, signals from a single measurement tool or source may not be sensitive enough to accurately measure parameters of interest for semiconductor process quality control. Ultimately, there may be no single measurement tool that can handle all the measurement requirements for state-of-the-art semiconductor devices.

[0015] As discussed herein, computationally efficient data analysis methods can merge multiple data sources and produce more accurate and consistent measurement results than any individual data source could provide, by using data collected from multiple data sources, for example, from multiple toolsets and / or processing steps, and additional data such as sensor data related to samples collected from measurement and / or production equipment. While the analysis method can be flexible to adapt to various data of different natures, it can also maximize the use of existing, well-developed techniques, such as physical modeling or machine learning, for each type of data source, thereby synergizing the strengths of individual measurement techniques.

[0016] As discussed herein, physical modeling and machine learning are combined to analyze multiple data sources for hybrid measurement and ecosystems. The methods described herein create predictive capabilities through data mining and data fusion from multiple data sources, e.g., multiple measurement toolsets, sample data from multiple processing steps, instrument parameters, and production equipment parameters. As an example, a physical model may be used to analyze measurement signals from one or more measurement tools, such as spectroscopic ellipsometers, spectroreflectometers, X-ray measurements, photoacoustic measurements, Fourier transform infrared spectroscopy (FTIR), and E-beam measurements, to extract measurement results for key and non-key parameters of a sample in pre-processing and post-processing steps. Additionally, machine learning models may be built and trained to predict parameters of interest for a sample in pre-processing and post-processing steps. A post-processing physical model extracting post-processing measurement signals may, by feedforward, use predicted parameters of interest from the pre-processing step predicted by the pre-processing physical model or pre-processing machine learning model. Additionally or alternatively, the predicted parameters of the object of interest from the post-processing step can be fed back to a post-processing physical model or a post-processing machine learning model to determine parameters of other objects of interest.

[0017] The proposed technique is an efficient and flexible method that synergizes physical modeling and machine learning, possessing controllable computational costs and software and modeling complexity. It can be used to combine and analyze multiple data sources, thus providing the most viable solution with a manageable time to a solution (TTS), improved final results, and overall measurement performance. This method is also versatile and can be applied to the measurement of any device, OCD, thin film, or other type of target.

[0018] Figure 1A illustrates semiconductor devices 110, 120, and 130, respectively, which have planar, fin, and gate-all-around (GAA) field-effect transistor architectures. The planar transistor architecture used in device 110 uses a gate 112 positioned above a channel 114 to control the flow of current through the channel between the 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 coplanar and formed on the surface of the semiconductor wafer, with the gate positioned above the channel. To address effects such as increased leakage current that degrade their performance due to size reduction, a finFET is employed, as illustrated in device 120, in which the channel 124 has a fin shape surrounded on three sides by a gate 122. The use of gate 122 increases the effective area of ​​gate 122 adjacent to the channel 124. However, finFETs have limitations, and other more complex architectures have been employed. For example, device 130 uses a gate-all-around (GAA) design in which the gate 132 completely surrounds the channel 134. The GAA transistor device 130 contains multiple vertically stacked nanosheet channels 134 passing through a single gate 132. While the GAA device 130 promises continuous performance improvements, its three-dimensional features and small size significantly increase the complexity of the manufacturing process and require precise monitoring using non-destructive measurement.

[0019] FIG. 1B illustrates a more detailed view of a GAA transistor device 150 in fabrication, including, for example, 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 a 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 layers 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 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. These features are very small, but their dimensions are considered 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 measurement techniques.

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

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

[0024] The reflected light can be focused by the lens 214 and received by the detector 250. The detector 250 may be a conventional charge-coupled device (CCD), a photodiode array, a CMOS, or a similar type of detector. The detector 250 may be a spectrometer, for example, when broadband light is used, and the detector 250 may generate a spectral signal depending on the wavelength. The spectrometer may be used to disperse the entire spectrum of the received light into spectral components across an array of detector pixels. One or more polarizing elements may be present in the beam path of the measuring device 200. For example, the measuring device 200 may include one or more polarizing elements 204 in the beam path in front of the sample 203 and one or both of a polarizing element (analyzer) 212 in the beam path behind the sample 203 (or may not include any at all), and may include one or more additional elements 205a and 205b such as compensators or photoelastic modulators, which may be in front of, behind, or both of the sample 203. A complete Müller matrix can be measured by using a spectroscopic ellipsometer with a double rotation compensator between polarizing elements 204 and 212 and the sample.

[0025] The measuring device 200 may include additional measuring devices or may be coupled with additional measuring devices. For example, as illustrated, the measuring device 200 may include a second perpendicular incidence measuring tool 270. The second measuring tool 270 may be configured, for example, spectral reflectance measurement, spectral scattering measurement, overlay scattering measurement, interferometry, E-beam measurement, X-ray measurement, FTIR measurement, etc. In some implementations, the measuring device 200 may include additional tools, such as a third (or more) measuring tool. In some implementations, the additional measuring tool may be separate from the measuring device 200.

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

[0027] One or more computing systems 260 may be a single computer system or multiple separate or linked computer systems, and it should be understood that, as herein, computing systems 260, at least one computing system 260, and one or more computing systems 260 may be interchangeably referred to as computing systems 260. A computing system 260 may be included in, connected to, or otherwise associated with the measuring device 200 and any additional measuring tools. Each different subsystem of the measuring device 200 may include a computing system configured to perform steps associated with the relevant subsystem. For example, a computing system 260 may control the positioning of the sample 203 by controlling the movement of a step 209 coupled to a chuck. For example, the step 209 may be capable of horizontal movement in Cartesian (i.e., X and Y) coordinates, or polar (i.e., R and θ) coordinates, or any combination of the two. The step may also be capable of vertical movement along the Z coordinate. The computing system 260 may further control the movement of the chuck 208 to hold or release the sample 203. The computing system 260 may 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 in the first measurement tool 201 and the detector (if any) in the second measurement tool 270 in any manner known in the art. For example, one or more computing systems 260 can be coupled to separate computing systems associated with the detector 250. The computing system 260 can be 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 components of the second measurement tool 270 via a transmission medium which may include wired and / or wireless portions. 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 may be further configured to receive and / or obtain additional information relating to the sample and one or more subsystems of the first measuring tool 201 and production equipment, for example, from a user interface (UI) 268 or via a transmission medium which may include wired and / or wireless components.

[0029] The computing system 260 includes at least one processor 262 together with memory 264, and a UI 268, which are communicatively coupled via a bus 261. Memory 264 or other non-temporary computer-readable storage medium may include its embodied computer-readable program code 266 and may be used by the computing system 260 to cause at least one computing system 260 to control the measurement device 200 and to perform functions including the techniques and analyses described herein. For example, as illustrated, memory 264 may include instructions for causing the processor 262 to perform both modeling and machine learning, and in some implementations, feedforward and / or feedback may be employed as considered herein. Data structures and software code for automatically implementing one or more actions described in this detailed description may be implemented by those skilled in the art in light of this disclosure and may be stored in computer-readable storage medium, such as memory 264, which may be any device or medium capable of storing code and / or data for use by a computer system such as computing system 260. Computer-usable storage media may include, but are not limited to, magnetic and optical storage devices such as read-only memory, random-access memory, disk drives, and magnetic tapes. Additionally, the functions described herein may be embodied, in whole or in part, within the circuits of application-specific integrated circuits (ASICs) or programmable logic devices (PLDs), and the functions may be embodied in computer-readable descriptor languages ​​that can be used to create ASICs or PLDs that operate as described herein.

[0030] The computing system 260 may be configured to acquire data about reference samples, which may include structures of interest such as 3D composite structures, including, for example, GAA transistors, from multiple data sources, including one or both of the measurement tools 201 and 270 and any additional desired measurement tools, as well as sample-related data such as reference data and / or design of experiment (DOE) data, and measurement tool and / or processing equipment-related data such as process parameters, advanced parameter control (APC) parameters, context data, and sensor data from production equipment. DOE data may be, for example, data measured from a set of reference samples processed under intentionally introduced skew conditions, resulting in the structural parameters of interest changing with process conditions skewed in a known pattern. The computing system 260 may be configured to generate and use one or more physical models (model 264pm) for a 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 considered herein, to generate, train, and use one or more machine learning models (ML264ml) for a sample based on measurement results extracted from one or more physical models and data. In some implementations, measurement data and additional information can be obtained from training samples using different computing systems and / or different measurement devices to generate one or more physical models (model 264pm) and / or generate and train one or more machine learning models (ML264ml), and the resulting physical models and / or trained machine learning models (or parts thereof) may be provided to the computing system 260 via computer-readable program code 266 on a non-temporary computer-usable storage medium such as memory 264.

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

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

[0033] As discussed herein, in order to characterize a complex 3D structure, including but not limited to a measured SOI, such as a GAA transistor, (1) at least one physical-based model is constructed to extract measurement results for major and minor parameters by analyzing measurement signals from one or more tools and sources, such as spectroscopic ellipsometry (SE), spectroscopic reflectometry (SR), X-ray, E-beam, photoacoustic data, and Fourier transform infrared spectroscopy (FTIR). In addition, (2) at least one machine learning model is constructed and trained to predict the parameters of interest. The machine learning model may take as input one or more of the following data: a) measurement results from the physical model from (1) (major and minor parameters); b) raw signals from the physical model from (1) and optionally misfits; data sources from different toolsets, or from the same tools in (1) but not included in the physical modeling; process parameters, APC parameters, context data, and sensor data from production equipment. Additionally, (3) inline measurements of SOI may be performed using offline-created and trained physical and machine learning models to predict parameters of interest based on data from multiple data sources.

[0034] Figure 3 illustrates, as an example, a workflow 300 for offline recipe creation, e.g., the generation of one or more physical models and one or more machine learning models, using a first exemplary scenario with multiple data sources, e.g., data collected from different tools and / or sources. In Figure 3, solid black arrows indicate processes used in workflow 300, dashed black arrows indicate optional processes where 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). Measurement signals 302 from the SOI can be collected from any desired measuring device, such as the measuring tool 201 shown in Figure 2, or from any other desired type of measuring device.

[0036] Additionally, data may be obtained from one or more additional data sources. For example, in some implementations, measurement signals 304 and 306 from one or more reference samples may be collected from one or more additional sources or tools, illustrated, for example, as a second source or tool (source 2) and a third source or tool (source 3). Additional measurement signals 304 may be collected from a different measuring device than source 1, such as measuring tool 270 shown in Figure 2, or from any other desired type of measuring device, and measurement signals 306 may be collected from a different measuring device than sources 1 and 2, such as a different type of measurement from either measuring tool 201 or 270, or from any other desired type of measuring device. Additional data 308 related to SOI may be collected and used as training data for one or more machine learning models 322, as illustrated by the block arrows. Additional data 308 may include, for example, reference data for sample and DOE data. Reference data may be measurement data obtained from one or more reference samples by the measurement device, along with values ​​of structural parameters of interest, typically provided by CD-AFM (atomic force microscopy), CD-SEM (scanning electron microscopy), or TEM (transmission electron microscopy). Reference data and / or DOE data may be used as training datasets to train machine learning models to identify relevant data features and learn the inherent relationships and connections between input and output features in order to determine and predict new data. In some implementations, additional data related to the reference sample may further include wafer condition, precision, tool matching data, etc. Precision data are parameters based on data repeatedly measured from the same target multiple times from the same instance of the tool. Precision is another key performance indicator (KPI) of measurement that shows the consistency of measurement results from multiple runs on the same sample. Tool matching data are parameters based on data measured from the same sample from multiple instances of the same tool type.Tool matching is another measurement KPI that indicates the consistency of results measured from the same sample using different tools of the same type. 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 precision and tool matching data are provided, physical modeling or machine learning models can be optimized not only to tightly match reference values ​​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, additional data signals 309 may be used as inputs for a physical model or as input features for a machine learning model. The additional data signals 309 may relate to sources from which they can be obtained (e.g., Source 1, Source 2, and Source 3), such as process parameters, Advanced Process Control (APC) parameters, context data, and sensor data from production equipment. For example, some process control parameters, such as substrate temperature and chemical concentration for wet etching, can affect the etching rate (how quickly the material is removed from the wafer surface), 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 and etching chamber names, are user-controlled parameters. The etching chamber name is an example of context data. Since each etching chamber has its own characteristic distribution of etching profiles across the wafer, knowing this information can help machine learning predict the correct wafer map. An example of APC parameters is atomic force microscope (AFM) results measured from the same sample at different processing steps, including relevant information such as non-major parameters of the structure of interest. Adding non-major parameters as machine learning input features can help improve the machine learning robustness in predicting major parameters. Adding all these relevant parameters as machine learning input features can provide additional information that helps determine the structural parameters of interest controlled by these process parameters and conditions.

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

[0039] In some implementations, multiple physical models may be generated. For example, as illustrated by the gray dotted arrow and gray dotted box, a second physical model 314 may be generated based on a measurement signal 304 from a second source (source 2). In some implementations, additional data may 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, as well as optionally wafer conditions, precision, and tool matching data, may 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) may be used to assist in the generation of the second physical model 314 of the sample. In some implementations, both the additional data 308 and the measurement signal 306 may 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 may be used to assist in the generation of the second physical model 314. Furthermore, multiple physical models can be optimized independently or co-optimized. For example, in some implementations, as illustrated by the gray dotted lines, the first physical model 312 and the second physical model 314 can be linked such that at least some parameters are coupled across physical models 312 and 314, and the combined parameter space can be searched to fit 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 physical modeling fit 323.

[0040] Using multiple data sources, one or more machine learning models 322 are constructed and trained to predict parameters of interest 325. Machine learning measurement metrics 327 are developed and reported along with the goodness of fit from physical modeling to demonstrate the measurement quality of a recipe synergistically derived 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 the first physical model 312 as input features. As shown by the dashed black arrows, the input features of the machine learning model 322 may additionally include 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 the second physical model 314, or at least one of 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 an optical component, a detector, or any combination thereof, and a data chunk may be a subset of wavelength (e.g., used in spectroscopic measurements), frequency (e.g., used in frequency-resolved measurements), angle (e.g., used in angle-resolved measurements), time interval (e.g., used in time-resolved measurements), or any combination thereof from a complete dataset provided by the data channel. For example, the first measurement device may collect perpendicular incidence signals and oblique incidence spectroscopic ellipsometer (SE) signals. The SE signal may be used to generate the first physical model 312, but the Normal Incident signal may not be used because it can be difficult to adapt the Normal Incident signal.Therefore, the normally incident signal can be a data channel used as data for the input features of the machine learning model 322, in addition to physical modeling results generated from a different data channel, e.g., the SE signal. In another example, the same data channel may be divided into multiple data chunks, e.g., signals from different wavelength ranges, some of which 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 reference data and / or at least a portion of data 308 such as DOE, and optionally wafer conditions, precision, and tool matching data. Data 308 is training data and is used for offline training. For example, the reference data may be a set of signals with labels (e.g., values ​​of key parameters provided by other measurement systems such as CD-SEM, TEM, CD-AFM) (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 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 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 data 308 is a set of signals measured from a reference sample 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 for key parameters. Based on the process skew conditions, the machine learning model 322 is trained to ensure that the predicted key parameter values ​​follow an expected skew pattern. The precision data from data 308 is measurement signals from the same sample but from multiple runs using the same measurement tool (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). Similarly, the tool-matching data from data 308 consists of signals measured from the same sample but from different instances of the same type of measuring tool (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). 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 so that the predicted values ​​of the key parameters match signals measured from the same sample but from different runs or different tools. The machine learning model 322 can be trained so that all criteria, matching to reference values, DOE skew conditions, high accuracy, and consistent tool matching are simultaneously met during training, provided all such data are provided.

[0042] Figure 4 illustrates, as an example, a workflow 400 for inline measurement to characterize a sample based on one or more physical models and one or more machine learning models, using a first exemplary scenario with multiple data sources, e.g., signals collected from different tools and / or sources. The one or more physical models and one or more machine learning models may be generated as considered with reference to Figure 4, for example. In Figure 4, solid black arrows indicate processes used in workflow 400, dashed black arrows indicate optional processes where at least one exists, and gray dotted arrows indicate optional processes.

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

[0044] Additionally, data may be obtained from one or more additional data sources. For example, in some implementations, measurement signals 404 and 406 may be collected from one or more additional sources or tools, exemplified, for example, as a second source or tool (source 2) and a third source or tool (source 3). The additional measurement signal 404 may be collected from a different measuring device than source 1, such as the measuring tool 270 shown in Figure 2, or from any other desired type of measuring device, and may be collected from the same measuring device or the same type of measuring device used for source 2 in Figure 3. The measurement signal 406 may be collected from a different measuring device than sources 1 and source 2, for example, a different type of measurement from either measuring tool 201 or 270 or any other desired type of measuring device, and may be collected from the same measuring device or the same type of measuring device used for source 3 in Figure 3. Furthermore, in some implementations, additional data signals 409, process parameters, APC parameters, context data, and sensor data from production equipment may be acquired, for example, related to the sources (e.g., source 1, source 2, and source 3).

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

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

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

[0048] One or more trained machine learning models 422 are used to predict the parameter of interest 425 based on multiple data sources. To demonstrate the measurement quality of the synergistic recipe from physical modeling and machine learning, machine learning measurement metrics 427 and goodness of fit 423 from physical modeling may be reported. The trained machine learning model 422 may be, for example, the same as the machine learning model 322 in Figure 3 after training. As illustrated by the solid black arrows, the trained machine learning model 422 uses the measurement results extracted by the first physical model 412 as input features. As shown by the dashed black arrows, the trained machine learning model 422 may further use input features including at least one of the following: measurement signal 404 from a sample collected from a second source (source 2), measurement signal 406 from a sample collected from a third source (source 3), additional data signal 409, and 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 arrows, the trained machine learning model 422 may optionally further use input features including measurement signals 402 from a sample collected from a first source (source 1). In some implementations, the machine learning input features from measurement signals 402 may include data channels or data chunks that are not used when extracting measurement results from the first physical model 412, as considered with reference to Figure 3.

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

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

[0051] Additionally, pre-processing step measurement signals 504 from one or more reference samples are measured using the same measuring device used to obtain the post-processing step measurement signals 502 and used to generate pre-processing step data. The pre-processing step measurement signals 504 are acquired, for example, before the desired steps of sample fabrication are completed. In some implementations, the post-processing step measurement signals 502 and the pre-processing step measurement signals 504 may be combined (e.g., by addition, subtraction, multiplication, or division) to form a pre-adjusted signal 505. Additionally, data 508 related to the reference sample, such as sample reference data and design of experiments (DOE), may be collected. In some implementations, additional data 508 related to the reference sample may further include wafer condition, accuracy, tool matching data, etc. Additionally, data may be acquired from other sources, such as from a second measurement pad 506, from a fault detection pad 509, or any combination thereof. While the first exemplary scenario in Figures 3 and 4 highlighted multiple data sources collected from different measuring devices, the second exemplary scenario illustrates, for example, that multiple data sources may be obtained from different measurement pads or from the same pad at different processing steps. Different measurement pads may be measured from the same or different measuring devices. The pre-processing step measurement signal 504 and the post-processing step measurement signal 502 may be measured on either the designed OCD target or device. The second measurement pad 506 may refer 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 the OCD target, the second measurement pad 506 may refer to signals from a device pad, or vice versa.

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

[0053] In some implementations, multiple physical models may be generated. For example, as illustrated by the gray dotted arrows and gray dotted boxes, the pre-processing physical model 514 may be generated based on the pre-processing step measurement signal 504 from the measurement device. In some implementations, additional data may 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, as well as optionally wafer conditions, precision, and tool matching data, may be used to assist in the generation of the pre-processing physical model 514. In another example, as illustrated by the gray dotted arrows, a signal from a second measurement pad 506 may be used to assist in the generation of the pre-processing physical model 514 of a sample. In yet another example, as illustrated by the gray dotted arrows, a signal from a fault detection pad 509 may be used to assist in the generation of the pre-processing physical model 514 of a sample. In some implementations, all or any combination of the data 508, as well as the signals from the second measurement pad 506 and the fault detection pad 509, may be used to assist in the generation of the pre-processing physical model 514. Furthermore, multiple physical models can be optimized independently or co-optimized. For example, in some implementations, as illustrated by the gray dotted line, the post-processing physical model 512 and the pre-processing physical model 514 can be linked so that at least some parameters are coupled across the post-processing physical model 512 and the pre-processing physical model 514, and the combined parameter space can be retrieved to fit the measured 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 for the physical modeling.

[0054] Using multiple data sources, one or more machine learning models 522 are constructed and trained to predict parameters of interest 525. Machine learning metric indices 527 are developed and reported together with goodness-of-fit 523 from physical modeling to demonstrate the synergistic quality of the recipe from physical modeling and machine learning. As illustrated by the solid black arrows, the machine learning model 522 is constructed using post-processing metric 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 metric signals 504. The pre-processing step data can be generated in multiple ways based on the pre-processing step metric signals 504. For example, as illustrated in Figure 5, the pre-processing step data can be generated in three different ways from the pre-processing step metric signals 504 labeled 1, 2, and 3, where at least one of (1), (2), or (3), or any combination thereof, may be used. As illustrated by label 1 for the preprocessing step measurement signal 504, preprocessing step data can be generated by combining the preprocessing step measurement signal 504 with the postprocessing step measurement signal 502 to form a pre-tuned signal 505. As illustrated in Figure 5, in some implementations, if a pre-tuned signal 505 is generated, the pre-tuned signal 505 is either (A) provided to a postprocessing physical model 512, and the machine learning model 522 is built at least partially on the postprocessing measurement results extracted by the postprocessing physical model 512, or (B) the pre-tuned signal 505 is provided to a machine learning model 522, and the machine learning model 522 is built at least partially on the pre-tuned signal 505. Additionally, as further illustrated in Figure 5, in some implementations, at least one of (A) or (B) may be used in conjunction with the workflow 500.As illustrated by label 2 for the preprocessing step measurement signal 504, preprocessing step data can be generated by providing the preprocessing step measurement signal 504 to a preprocessing physical model 514, and the machine learning model 522 is built at least partially on the preprocessing measurement results extracted by the preprocessing physical model 514. As illustrated by label 3 for the preprocessing step measurement signal 504, preprocessing step data can be generated by providing the preprocessing step measurement signal 504 to a machine learning model 522, and the machine learning model 522 is built at least partially on the preprocessing 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 preprocessing step measurement signals 504 (i.e., at least one of (1), (2), or (3) for the preprocessing 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 may optionally be constructed using further postprocessing step measurement signals 502, pre-tuned signals 505, measurement results extracted by the preprocessing physical model 514, or any combination thereof.

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

[0057] Figure 6 illustrates a workflow 600 for inline measurement to characterize a sample based on, for example, one or more physical models and one or more machine learning models, using, as an example, a second exemplary scenario that uses signals collected from multiple data sources, e.g., different manufacturing process steps. The one or more physical models and one or more machine learning models may be generated as discussed, for example, with reference to Figure 5. In Figure 6, solid black arrows indicate processes used in workflow 600, dashed black arrows indicate optional processes where at least one exists, and gray dotted arrows indicate optional processes.

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

[0059] Additionally, the pre-processing step measurement signal 604 from the sample is collected using a measuring device, e.g., the same measuring device used to obtain the post-processing step measurement signal 602, and the same or the same type of measuring device used to obtain the pre-processing step measurement signal 504 in Figure 5. The pre-processing step measurement signal 604 is used to generate pre-processing step data. The pre-processing step measurement signal 604 is acquired, 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 may be combined (e.g., by addition, subtraction, multiplication, or division) to form a pre-adjusted signal 605. Additionally, data may be acquired from other sources, such as from a second measurement pad 606, from a fault detection pad 609, or any combination thereof. The pre-processing step measurement signal 604 and the post-processing step measurement signal 602 may be measured by either the designed OCD target or device. The second measurement pad 606 may refer to pre-processing step measurements and / or post-processing step measurements from measurement pads that are not measured, for example, for the pre-processing step measurement signal 604 and the post-processing step measurement signal 602. 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 may refer to signals from the device pad, or vice versa.

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

[0061] In some implementations, multiple physical models may be used to extract measurement results from a sample. For example, a pre-processing physical model 614 may be used to extract measurement results from a sample based on a pre-processing step measurement signal 604, as illustrated by the black dotted arrow and black dotted box. The pre-processing physical model 614 may be the same as the pre-processing physical model 614 in Figure 5. Furthermore, multiple physical models may be optimized independently or co-optimized. For example, in some implementations, as illustrated by the gray dotted line, the post-processing physical model 612 and the pre-processing physical model 614 may be linked so that at least some parameters are combined across the post-processing physical model 612 and the pre-processing physical model 614, and the combined parameter space may be searched to fit measurement signals from one or more data sources. The post-processing physical model 612, and optionally the pre-processing physical model 614, may be configured to provide a goodness of fit 623 for the physical modeling.

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

[0063] Preprocessing step data can be generated in multiple ways based on the preprocessing step measurement signal 604. For example, as illustrated in Figure 6, preprocessing step data can be generated in three different ways from preprocessing step measurement signals 604 labeled 1, 2, and 3, where at least one of (1), (2), or (3), or any combination thereof, may be used. As illustrated by label 1 for the preprocessing step measurement signal 604, preprocessing step data can be generated by combining the preprocessing step measurement signal 604 with a postprocessing step measurement signal 602 to form a pre-tuned signal 605. As illustrated in Figure 6, in some implementations, if a pre-tuned signal 605 is generated, the pre-tuned signal 605 may be (A) provided to 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-tuned signal 605 may be provided to the trained machine learning model 622 as input data. Additionally, as further illustrated in Figure 6, in some implementations, at least one of (A) or (B) may be used with workflow 600. Preprocessing step data may be generated by providing the preprocessing step measurement signal 604 to a 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 by label 3 for the preprocessing step measurement signal 604. Preprocessing step data may 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 arrows, the trained machine learning model 622 may optionally further use input data including post-processing step measurement signals 602.

[0065] Figure 7 illustrates, as an example, a workflow 700 for offline recipe creation, e.g., for the generation of one or more physical models and one or more machine learning models, using a third exemplary scenario with multiple data sources, e.g., signals collected from different manufacturing process steps. The workflow 700 based on the third exemplary scenario may be suitable for measuring complex 3D structures, including, but not limited to, GAA transistors or other devices, and provides a method for independently measuring different limit dimensions (CD) of a structure of interest in a logic GAA device, e.g., SiGe layer and internal spacer CD, using the hybrid measurement and ecosystem framework discussed herein, as discussed in Figures 1A and 1B. In Figure 7, solid black arrows indicate processes used in 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 measuring device. The reference samples include, for example, SOI, and the post-processing step measurement signals 702 are acquired after the desired steps of sample preparation are completed. The post-processing step measurement signals 702 may be, for example, spectral data and may be collected from any desired measuring device, such as the measuring tool 201 shown in Figure 2, or from any other desired type of measuring device.

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

[0068] Additionally, for example, post-processing step data 708 related to the SOI of the reference sample in a post-processing step after the desired steps of sample fabrication are completed, such as reference data of the sample and / or DOE, may be collected. In some implementations, additional post-processing step data 708 related to the reference sample may further include wafer conditions, precision, tool matching data, etc. Additionally, for example, pre-processing step data 709 related to the SOI of the reference sample in a pre-processing step before the desired steps of sample fabrication are completed, such as reference data of the sample and / or DOE, may be collected. In some implementations, additional pre-processing step data 709 related to the reference sample may further include wafer conditions, precision, tool matching data, etc.

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

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

[0071] Additionally, as illustrated by the solid black arrows, a post-processing step measurement signal 702 from the measuring device may be used to generate a post-processing physical model 712 of SOI from the sample. In some implementations, additional data may be used to assist in the generation of the post-processing physical model 712. For example, as illustrated, additional post-processing step data 708, e.g., reference data and / or DOE, as well as optionally wafer conditions, precision, and tool matching data, may be used to assist in the generation of the post-processing physical model 712. The pre-processing step measurement signal 704 contains rich information and sensitivity to one or more parameters of interest (parameter #1) 725, and such information can therefore be used to improve accuracy. Thus, as illustrated, the post-processing physical model 712 may receive feedforward data from the pre-processing physical model 714 and / or the pre-processing machine learning model 724, e.g., for one or more parameters of interest (parameter #1) 725, to facilitate the propagation of information in the pre-processing fabrication step signal to the post-processing physical model 712. In some implementations, feedback data generated based on the post-processing step measurement signal 702 may be used to assist in the generation of the post-processing physical model 712. As illustrated, the post-processing physical model 712 may receive feedback data on one or more parameters of interest (parameter #2) 723 from a post-processing machine learning model 722, which is determined based on the post-processing step measurement signal 702, as discussed below. The accuracy of one or more parameters of interest (parameter #2) 723 benefits from more accurate one or more parameters of interest (parameter #1) 725 that are fed forward to the post-processing physical model 712. Furthermore, the feedback of one or more parameters of interest (parameter #2) 723 can resolve high correlations between parameters of interest that have experienced the same fabrication step, e.g., different etched SiGe CDs.For example, the post-processing physical model 712 or post-processing machine learning model 722 may use feedback data and be retrained with additional post-processing step data 708, e.g., reference data and / or DOE, and optionally wafer conditions, accuracy, and tool matching data, to provide better predictions regarding other parameters of interest, e.g., (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 post-processing measurement results extracted by the post-processing physical model 712 as input features, as illustrated by the solid black arrows. 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 be optionally constructed using the pre-tuned 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, as well as 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, and biases, are provided for the characterization of the sample and may, for example, be reported.

[0073] As illustrated, a post-processing physical model 712 (or a separate machine learning model) may be used to predict one or more additional parameters of interest, illustrated as parameter #3 713, which may include primary parameters, non-primary parameters, or both primary and non-primary parameters. Post-processing parameters of interest, e.g. (parameters #2 and #3) 723 and 713, may, for example, be SiGe CD1, SiGe CD2, and SiGe CD3, respectively, for a GAA transistor (as illustrated in Figure 1B), but other parameters of interest may be determined for the GAA transistor or for other devices being measured. For example, the workflow 700 illustrated in Figure 7 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. Furthermore, additional parameters of interest (parameter #3) 713 from the post-processing physical model 712 can be further fedforward to a 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 final predictions for an additional parameter of interest (parameter #3) 713.

[0074] Figure 8 illustrates a workflow 800 for inline measurement to characterize a sample based on, for example, one or more physical models and one or more machine learning models, using, as an example, a third exemplary scenario that uses signals collected from multiple data sources, e.g., different manufacturing process steps. The one or more physical models and one or more machine learning models may be generated as discussed, for example, with reference to Figure 7. In Figure 8, solid black arrows indicate processes used in workflow 800, and gray arrows indicate optional processes.

[0075] As illustrated, post-processing step measurement signals 802 from one or more reference samples are collected from a measuring device. The reference samples include, for example, SOI, and the post-processing step measurement signals 802 are acquired after the desired steps of sample preparation are completed. The post-processing step measurement signals 802 may be, for example, spectral data and may be collected from any desired measuring device such as the measuring tool 201 shown in Figure 2, or from any other desired type of measuring device, and may be collected from the same measuring device or the same type of measuring device used to obtain the post-processing step measurement signals 702 in Figure 7.

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

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

[0078] Additionally, a trained preprocessing machine learning model 824 may be used to predict one or more parameters of interest (parameter #1) 825. As illustrated by the solid black arrows, the trained preprocessing machine learning model 824 uses preprocessing measurement results extracted by the preprocessing physical model 814 as input features. The trained preprocessing machine learning model 824 may further use preprocessing step measurement signals 804 as input features. One or more parameters of interest (parameter #1) may include primary parameters, non-primary parameters, or both primary and non-primary parameters, and may, for example, be the Si / SiGe thickness of a GAA transistor, but other parameters of interest may be determined for the GAA transistor 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 may be used to extract measurement results from the post-processing physical model 812 of the SOI from the sample. In some implementations, additional data may 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 may receive feedforward data from the pre-processing physical model 814 and / or the pre-processing machine learning model 824, for example, the values ​​of one or more parameters of interest (parameter #1) 825, to facilitate the propagation of information in 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 may be used to assist in extracting measurement results from the post-processing physical model 812. As illustrated, the post-processing physical model 812 may receive feedback data from the post-processing machine learning model 822, for example, determined based on the post-processing step measurement signal 802, as considered below. The accuracy of one or more parameters of interest (parameter #2) 823 benefits from more accurate parameters of one or more objects of interest (parameter #1) 825, which are fed forward to the post-processing physical model 812. Furthermore, feedback of one or more parameters of interest (parameter #2) 823 can resolve high correlations between parameters of interest that have experienced the same fabrication step, for example, different etched SiGe CDs.

[0080] The trained post-processing machine learning model 822 is used to predict the final values ​​(and, if feedback is used, one or more initial values ​​of the one or more parameters of interest (parameter #2) 823) of one or more parameters of interest, which may include primary parameters, non-primary parameters, or both primary and non-primary parameters. As illustrated by the solid black arrows, 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-tuned 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, for example, be reported.

[0081] As illustrated, a 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. Post-processing parameters of interest, e.g. (parameters #2 and #3) 823 and 813, may, for example, be SiGe CD1, SiGe CD2, and SiGe CD3 for a GAA transistor, but other parameters of interest may be determined for the GAA transistor or for other devices being measured. For example, the workflow 800 illustrated in Figure 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. Furthermore, additional parameters of interest (parameter #3) 813 from the post-processing physical model 812 can be further fedforward to a post-processing machine learning model 822.

[0082] In some implementations, primary data, e.g., measurement signals used in physical modeling, and auxiliary data, e.g., data used only in machine learning, may originate from different toolsets, from the same toolset but from different data channels, or from the same toolset and data channels but from different wavelength ranges, time intervals, etc. Different data sources may collect data from the same sample location on the same wafer OCD target or device, from the same processing step, or from different processing steps. Different data sources may collect data from different sample locations on the same wafer from the same or different processing steps, for example, if the underlying structure has correlated parameters, and as a result, analyzing the combined data may improve overall performance. As illustrated, at least one physical model may be created to analyze measurement signals from at least one data source. Furthermore, if two or more physical models are used, the multiple physical models may be optimized independently or co-optimized, for example, the physical models may be linked so that at least some parameters are coupled across the physical models, and the combined parameter space can be searched to fit measurement signals from one or more data sources. Primary and auxiliary data may have different characteristics; for example, some data may be measurement data collected from a toolset, while other data may be sensor data from process equipment, or wafer process parameters such as gas flow rates and APC parameters, or contextual data such as specific process tools. Additionally, feature engineering and signal preprocessing may be applied before data from all sources is provided to the machine learning model for training. Machine learning algorithms may include, but are not limited to, linear regression, neural networks, deep learning, convolutional neural networks (CNNs), ensemble methods, support vector machines (SVMs), random forests, or combinations of multiple models in sequential and / or parallel modes.

[0083] The illustrated workflow efficiently combines various measurement techniques and the use of multiple data sources by synergizing physical modeling and machine learning to generate more usable information than would be provided by individual measurement techniques or a single data source. Physical modeling can be performed using the desired measurement device with previously well-established modeling solutions, and the physical modeling results can be combined with other data that is difficult or impossible to model, referred to as auxiliary data, for machine learning training and prediction. Thus, the resulting process provides a viable solution that has the advantages of both physical modeling and machine learning while controlling computational costs, enabling an acceptable TTS for generation, and is easy to implement and use in practice. Additionally, predictive capability can be increased through the use of data such as process parameters and sensor data from production equipment, which are 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. Furthermore, the techniques considered herein have general applications and can be applied, for example, to the measurement of any device, OCD, thin film, or other type of target.

[0084] Figure 9 shows an illustrative flowchart illustrating exemplary methods 900 for measuring at least one parameter of interest from a SOI in several implementation forms. In some implementation forms, exemplary methods 900 may be executed by at least one processor, such as processor 262 in the computing system 260 in Figure 2, which implements the workflow 700 illustrated in Figure 7.

[0085] At least one processor may acquire post-processing step measurement signals from a measuring device for one or more SOIs on a sample during the post-processing step (902). For example, means for acquiring post-processing step measurement signals may be an interface between a measuring device 200 and a processor 262 in the computing system 260 shown in Figure 2. Post-processing step measurement signals for one or more SOIs on a sample during the post-processing step may be, for example, the post-processing step measurement signals 702 shown in Figure 7.

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

[0087] At least one processor may generate a post-processing machine learning model to predict a second parameter of SOI in a post-processing step, the post-processing machine learning model being generated based on post-processing measurement results extracted from the post-processing physical model (906). The post-processing machine learning model may be further generated based on the post-processing step measurement signal and post-processing step data including at least one of reference data and experimental design information for SOI in the post-processing step. For example, means for generating a 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 Figure 2. The post-processing machine learning model may be, for example, a post-processing step machine learning model 722 generated based on the post-processing measurement results extracted from the post-processing physical model 712 and the post-processing measurement signal 702 and post-processing step data 708.

[0088] At least one processor may provide 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 (908). For example, 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 with a measurement device 200 and processors 262 and memory 264 in the computing system 260 shown in Figure 2.

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

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

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

[0092] In some implementations, the post-processing machine learning model may be generated based on the pre-processing step measurement signal from the SOI in the pre-processing step, as illustrated by the arrow from the pre-processing step measurement signal 704 to the post-processing machine learning model 722 shown in Figure 7.

[0093] In some implementations, at least one processor may further generate a pre-tuned 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-tuned signal, as illustrated, for example, by the pre-tuned signal 705 and the arrow from the pre-tuned signal 705 to the post-processing machine learning model 722 shown in Figure 7.

[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, for example, as illustrated by the prediction of parameter #3 713. In some implementations, the one or more additional parameters may include primary parameters, non-primary parameters, or combinations of primary and non-primary parameters.

[0095] Figure 10 shows an illustrative flowchart illustrating exemplary method 1000 for measuring at least one parameter of interest from a SOI in several implementation forms. In some implementation forms, exemplary method 1000 may be executed by at least one processor, such as processor 262 in the computing system 260 in Figure 2, which implements the workflow 800 illustrated in Figure 8.

[0096] At least one processor may acquire post-processing step measurement signals from a measuring device for one or more SOIs on a sample during the post-processing step (1002). For example, means for acquiring post-processing step measurement signals may be an interface between a measuring device 200 and a processor 262 in the computing system 260 shown in Figure 2. Post-processing step measurement signals for one or more SOIs on a sample during the post-processing step may be, for example, the post-processing step measurement signals 802 shown in Figure 8.

[0097] At least one processor may extract post-processing measurement results from the post-processing physical model of the SOI based on a post-processing step measurement signal and at least one of the values ​​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 (1004). For example, the post-processing measurement results of the SOI may be extracted based on a post-processing step measurement signal and the value of the first parameter or the second parameter, or both the first parameter and the second parameter. Furthermore, in some implementations, one or more first parameters may be used. In some implementations, one or more second parameters may be used. Means for generating post-processing measurement results extracted from the post-processing physical model may include 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 Figure 2. Post-processing measurement results can be extracted from the post-processing physical model based on the post-processing step measurement signal 802 and at least one of the feedforward first parameter 825 determined from the pre-processing physical model 814 and the pre-processing machine learning model 824, or a second parameter 823 as illustrated in Figure 8, as illustrated in Figure 8, for example, as illustrated by the arrow from the post-processing physical model 812. In some implementations, each of the first and second parameters may be a primary or secondary parameter.

[0098] At least one processor predicts 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 post-processing measurement results extracted from the post-processing physical model (1006). The final value of the second parameter of the SOI can be predicted from the trained post-processing machine learning model based on the post-processing step measurement signal. For example, a means for predicting the final value of the second parameter of the SOI from a trained 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 Figure 2. The final value of the second parameter of the SOI can be predicted from the trained post-processing machine learning model, for example, as illustrated by parameter #2 823 predicted by the post-processing machine learning model 822, based on the post-processing measurement results extracted from the post-processing physical model and the post-processing step measurement signal 802 to the post-processing machine learning model 822, as illustrated by the 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.

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

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

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

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

[0103] In some implementations, at least one processor may further generate a pre-tuned 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 post-processing machine learning model trained on the pre-tuned signal, as illustrated, for example, by the pre-tuned signal 805 shown in Figure 8 and the arrow from the pre-tuned 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 Figure 8. In some implementations, one or more additional parameters may include primary parameters, non-primary parameters, or combinations of primary and non-primary parameters.

[0105] The above description is intended to be illustrative and not restrictive. For example, the above examples (or one or more of them) may be used in combination with each other. Other implementations may be used, for example, by those skilled in the art when considering the above description. Also, various features may be grouped together, and fewer features may be used than all the features of a particular disclosed implementation. Accordingly, the following embodiments are incorporated herein as examples or implementations, and each embodiment stands on its own as a separate implementation, and such implementations are intended to be combined with each other in various combinations or rearrangements. Accordingly, the intent and scope of the appended claims should not be limited to the above description.

Claims

1. A method for measuring at least one parameter of an object of interest from the structure of an object of interest (SOI), The computer system acquires post-processing step measurement signals from a measuring device for one or more SOIs on a sample during the post-processing step. The computer system generates a post-processing physical model and extracts post-processing measurement results for the SOI based on the post-processing step measurement signal, the value of a first parameter of the SOI in the pre-processing step which is fed forward to the post-processing physical model by the computer system, the value of a second parameter of the SOI in the post-processing step which is fed back to the post-processing physical model by the computer system, and at least one combination thereof. The computer system generates a post-processing machine learning model based on the post-processing measurement results extracted from the post-processing physical model, and predicts the value of the second parameter of the SOI in the post-processing step. A method comprising the computer system providing values ​​for the post-processed physical model and the post-processed machine learning model in order to measure the parameters of at least one object of interest of the SOI.

2. The method according to claim 1, wherein the value of the first parameter of the SOI is determined by at least one of a pretreatment physical model and a trained pretreatment machine learning model based on pretreatment step measurement signals obtained from the SOI on one or more samples in the pretreatment step.

3. The method according to claim 1, wherein the post-processing physical model is further generated based on the post-processing step data.

4. In the aforementioned pretreatment step, the measurement signal of the pretreatment step is obtained from the measurement device for the SOI on one or more samples, The process involves generating the aforementioned preprocessing physical model and extracting the preprocessing measurement results of the SOI based on the preprocessing step measurement signals, The method according to claim 1, further comprising generating the preprocessing machine learning model and predicting the value of the first parameter of the SOI in the preprocessing step.

5. The method according to claim 1, wherein the post-processing machine learning model is generated based on the post-processing step measurement signal and post-processing step data which includes at least one of reference data and experimental design information for the SOI in the post-processing step.

6. The method according to claim 1, wherein the post-processing machine learning model is generated based on the 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-tuned signal by combining the pre-treatment step measurement signal from the SOI in the pre-treatment step and the post-treatment step measurement signal from the SOI in the post-treatment step, wherein the post-treatment machine learning model is further generated based on the pre-tuned signal.

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

9. A computer system configured to measure at least one parameter of an object of interest from a structure of interest (SOI), It comprises at least one processor, and the at least one processor is In the post-processing step, a post-processing step measurement signal is acquired from the measurement device for one or more SOIs on the sample. A post-processing physical model is generated, and post-processing measurement results for the SOI are extracted based on the post-processing step measurement signal, the value of the first parameter of the SOI in the pre-processing step which is fed forward to the post-processing physical model, the value of the second parameter of the SOI in the post-processing step which is fed back to the post-processing physical model, and at least one combination thereof. A post-processing machine learning model is generated based on the post-processing measurement results extracted from the post-processing physical model, and the value of the second parameter of the SOI in the post-processing step is predicted. To measure the parameters of at least one object of interest of the SOI, the values ​​of the parameters for the post-processed physical model and the post-processed machine learning model are provided. A computer system configured in such a way.

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

11. The computer system according to claim 9, wherein the at least one processor is configured to generate the post-processing physical model based on the post-processing step data.

12. The aforementioned at least one processor is In the pretreatment step, the pretreatment step measurement signal is acquired from the measurement device for the SOI on one or more samples. The preprocessing physical model is generated, and the preprocessing measurement results of the SOI are extracted based on the preprocessing step measurement signals. The computer system according to claim 9, further configured to generate the preprocessing machine learning model and predict the value of the first parameter of the SOI in the preprocessing step.

13. The computer system according to claim 9, wherein the at least one processor is configured to generate the post-processing machine learning model based on the post-processing step measurement signal and post-processing step data, which includes at least one of reference data and experimental design information for the SOI in the post-processing step.

14. The computer system according to claim 9, wherein the at least one processor is configured to generate the post-processing machine learning model based on the pre-processing step measurement signal from the SOI in the pre-processing step.

15. The computer system according to claim 9, wherein the at least one processor is further configured to generate a pre-tuned signal by combining the pre-treatment step measurement signal from the SOI in the pre-treatment step and the post-treatment step measurement signal from the SOI in the post-treatment step, and the at least one processor is further configured to generate the post-treatment machine learning model based on the pre-tuned signal.

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