Multiple Signal Sources for Hybrid Measurement Using Physical Modeling and Machine Learning

Abstract

Physical modeling and machine learning modeling are combined to analyze signals from multiple data sources, including measurement data obtained from different tool sets or at different process steps, and data related to process equipment such as sensor data, process parameters, advanced process control (APC) parameters, and context data. At least one physical model is generated and used to analyze measurement signals from measurement tools to extract measurement results of the main and non-main parameters of the structure on the sample. At least one machine learning model is constructed and trained to predict the parameters of interest based on the extracted measurement results and additional data including raw measurement signals, reference data and / or design of experiments (DOE) data, and data from different tool sets or the same tool used for physical modeling.

Description

Technical Field

[0001] (Cross - Reference to Related Applications) This application claims the priority and benefit of U.S. Provisional Application No. 63 / 355,053, entitled "METROLOGY SOLUTIONS FOR GATE - ALL - AROUND TRANSISTORS", filed on June 23, 2022; U.S. Provisional Application No. 63 / 498,475, entitled "MULTIPLE SOURCES OF SIGNALS FOR HYBRID METROLOGY USING PHYSICAL MODELING AND MACHINE LEARNING", filed on April 26, 2023; and U.S. Non - Provisional Application No. 18 / 339,973, entitled "MULTIPLE SOURCES OF SIGNALS FOR HYBRID METROLOGY USING PHYSICAL MODELING AND MACHINE LEARNING", filed on June 22, 2023. All of these are assigned to the assignee of this application and are hereby incorporated by reference in their entirety.

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

Background Art

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

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

SUMMARY OF THE INVENTION

[0005] Physical modeling and machine learning modeling are combined to analyze signals from multiple data sources for hybrid measurement and ecosystem. Signals from data sources can include measurement data that can be obtained from different tool sets or at different process steps, and additional data sensor data related to process equipment, such as process parameters, Advanced Process Control (APC) parameters, context data, etc. The predictive ability of machine learning is improved through data mining and data fusion of signals from multiple data sources. At least one physical model is generated and used to analyze measurement signals from one or more measurement tools to extract measurement results of the main and non-main parameters of the structure on the sample. Additionally, at least one machine learning model is constructed and trained to predict the parameters of interest based on the extracted measurement results and additional data. The input data for the machine learning model includes, for example, raw measurement signals used by one or more physical models, reference data and / or design of experiment (DOE) data, and data from a different tool set or the same tool that is different from that used for physical modeling, such as additional data like process parameters, Advanced Process Control (APC) parameters, context data, and sensor data from production equipment.

[0006] In one implementation, a method for characterizing a structure on a sample includes obtaining a measurement signal about the structure on the sample from a first measurement device and extracting a measurement result from a first physical model of the structure on the sample based on the measurement signal. The method further includes determining a parameter of interest of the structure on the sample using a machine learning model based on the measurement result extracted from the first physical model. The machine learning model can further determine the parameter of interest based on at least one of data from a measurement signal from the first measurement device not used when extracting the measurement result from the first physical model, a second measurement signal obtained about the structure on the sample from a second measurement device, a process parameter used to generate the structure on the sample, an advanced process control (APC) parameter used to generate the structure on the sample, context data of the structure on the sample, and sensor data from production equipment used to generate the structure on the sample.

[0007] In one implementation, a computer system configured to characterize a structure on a sample includes at least one processor configured to obtain a measurement signal of the structure on the sample from a first measurement device and extract a measurement result from a first physical model of the structure on the sample based on the measurement signal. The at least one processor is further configured to determine a parameter of interest of the structure on the sample using a machine learning model based on the measurement result extracted from the first physical model. The machine learning model can further determine the parameter of interest based on at least one of data from a measurement signal from the first measurement device not used when extracting the measurement result from the first physical model, a second measurement signal obtained about the structure on the sample from a second measurement device, a process parameter used to generate the structure on the sample, an advanced process control (APC) parameter used to generate the structure on the sample, context data of the structure on the sample, and sensor data from production equipment used to generate the structure on the sample.

[0008] In one implementation form, a system configured to evaluate the characteristics of a structure on a sample includes means for obtaining a measurement signal of the structure on the sample from a first measurement device, and means for extracting a measurement result from a first physical model of the structure on the sample based on the measurement signal. The system further includes means for determining a parameter of interest of the structure on the sample using a machine learning model based on the measurement result extracted from the first physical model. The machine learning model can further determine the parameter of interest based on at least one of data from a measurement signal from a first measurement device not used when extracting the measurement result from the first physical model, a second measurement signal obtained from the second measurement device for the structure on the sample, a process parameter used to generate the structure on the sample, an advanced process control (APC) parameter used to generate the structure on the sample, context data of the structure on the sample, and sensor data from production equipment used to generate the structure on the sample.

[0009] In one implementation form, a method for evaluating the characteristics of a structure on a sample includes, in a preprocessing step, obtaining a preprocessing step measurement signal from a measurement device for the structure on the sample, and in a postprocessing step, obtaining a postprocessing step measurement signal from a measurement device for the structure on the sample. The method further includes extracting a postprocessing measurement result from a postprocessing physical model of the structure on the sample based on the postprocessing step measurement signal, and generating preprocessing step data based on at least the preprocessing step measurement signal. The method further includes determining a parameter of interest of the structure on the sample using a machine learning model based on the postprocessing measurement result extracted from the postprocessing physical model and the preprocessing step data.

[0010] In one implementation form, a computer system configured to evaluate the characteristics of a structure on a sample includes at least one processor. The at least one processor is configured to, in a preprocessing step, acquire a preprocessing step measurement signal from a measurement device for the structure on the sample, and in a postprocessing step, acquire a postprocessing step measurement signal from the measurement device for the structure on the sample. The at least one processor is further configured to extract a postprocessing measurement result from a postprocessing physical model of the structure on the sample based on the postprocessing step measurement signal, and generate preprocessing step data based on at least the preprocessing step measurement signal. The at least one processor is further configured to determine a parameter of interest of the structure on the sample using a machine learning model based on the postprocessing measurement result extracted from the postprocessing physical model and the preprocessing step data.

[0011] In one implementation form, a system configured to evaluate the characteristics of a structure on a sample includes means for, in a preprocessing step, acquiring a preprocessing step measurement signal from a measurement device for the structure on the sample, and means for, in a postprocessing step, acquiring a postprocessing step measurement signal from the measurement device for the structure on the sample. The system further includes means for extracting a postprocessing measurement result from a postprocessing physical model of the structure on the sample based on the postprocessing step measurement signal, and means for generating preprocessing step data based on at least the preprocessing step measurement signal. The system further includes means for determining a parameter of interest of the structure on the sample using a machine learning model based on the postprocessing measurement result extracted from the postprocessing physical model and the preprocessing step data.

[0012] In one implementation, a method for characterizing a structure on a sample includes obtaining measurement signals of one or more reference samples of the structure from a first measurement device and generating a first physical model to extract measurement results of the structure on the sample, where the first physical model is generated based on the measurement signals of the one or more reference samples from the first measurement device. The method further includes generating a machine learning model to predict a parameter of interest of the structure on the sample. The machine learning model is generated based on the measurement results extracted by the first physical model and at least one of reference data and experimental design information. The machine learning model can be further generated based on at least one of data from measurement signals from the first measurement device not used in generating the first physical model, second measurement signals obtained for one or more reference samples from a second measurement device, process parameters used to generate the one or more reference samples, advanced process control (APC) parameters used to generate the one or more reference samples, context data of the one or more reference samples, and sensor data from production equipment used to generate the one or more reference samples.

[0013] In one implementation, a computer system configured to characterize a structure on a sample includes at least one processor. The at least one processor is configured to obtain measurement signals of one or more reference samples of the structure from a first measurement device and generate a first physical model to extract measurement results of the structure on the sample. The first physical model is generated based on the measurement signals of one or more reference samples from the first measurement device. The at least one processor is further configured to generate a machine learning model to predict a parameter of interest of the structure on the sample. The machine learning model is generated based on the measurement results extracted by the first physical model and at least one of reference data and experimental design information. The machine learning model can be further generated based on at least one of data from measurement signals from the first measurement device not used in generating the first physical model, second measurement signals obtained for one or more reference samples from a second measurement device, process parameters used to generate the one or more reference samples, advanced process control (APC) parameters used to generate the one or more reference samples, context data of the one or more reference samples, and sensor data from production equipment used to generate the one or more reference samples.

[0014] In one implementation, a system configured to characterize a structure on a sample includes means for obtaining measurement signals of one or more reference samples of the structure from a first measurement device, and means for generating a first physical model for extracting measurement results of the structure on the sample. The first physical model is generated based on measurement signals of one or more reference samples from the first measurement device. The system further includes means for generating a machine learning model for predicting a parameter of interest of the structure on the sample. The machine learning model is generated based on the measurement results extracted by the first physical model and at least one of reference data and experimental design information. The machine learning model may be further generated based on at least one of data from measurement signals from the first measurement device not used in generating the first physical model, second measurement signals obtained for one or more reference samples from a second measurement device, process parameters used to generate the one or more reference samples, advanced process control (APC) parameters used to generate the one or more reference samples, context data of the one or more reference samples, and sensor data from production equipment used to generate the one or more reference samples.

[0015] In one implementation, a method for characterizing a structure on a sample includes, in a preprocessing step, obtaining preprocessing step measurement signals from a measurement device for one or more reference samples of the structure, and in a postprocessing step, obtaining postprocessing step measurement signals from the measurement device for one or more reference samples of the structure. The method further includes generating a postprocessing physical model generated based on the postprocessing step measurement signals for extracting postprocessing measurement results for the structure on the reference sample, and generating preprocessing step data based on at least the preprocessing step measurement signals. The method further includes generating a machine learning model for predicting a parameter of interest of the structure on the sample. The machine learning model is generated based on the postprocessing measurement results extracted by the postprocessing physical model, at least one of reference data and experimental design information, and the preprocessing step data.

[0016] In one implementation form, a computer system configured to evaluate the characteristics of a structure on a sample includes at least one processor. The at least one processor is configured to obtain a preprocessing step measurement signal from a measurement device for one or more reference samples of the structure in a preprocessing step, and to obtain a postprocessing step measurement signal from the measurement device for one or more reference samples of the structure in a postprocessing step. The at least one processor is further configured to generate a postprocessing physical model generated based on the postprocessing step measurement signal to extract postprocessing measurement results for the structure on the reference sample, and to generate preprocessing step data based on at least the preprocessing step measurement signal. The at least one processor is further configured to generate a machine learning model to predict a parameter of interest of the structure on the sample. The machine learning model is generated based on the postprocessing measurement results extracted by the postprocessing physical model, at least one of the reference data and the experimental design information, and the preprocessing step data.

[0017] In one implementation form, a system configured to evaluate the characteristics of a structure on a sample includes means for obtaining a preprocessing step measurement signal from a measurement device for one or more reference samples of the structure in a preprocessing step, and means for obtaining a postprocessing step measurement signal from the measurement device for one or more reference samples of the structure in a postprocessing step. The system further includes means for generating a postprocessing physical model generated based on the postprocessing step measurement signal to extract postprocessing measurement results for the structure on the reference sample, and means for generating preprocessing step data based on at least the preprocessing step measurement signal. The system further includes means for generating a machine learning model to predict a parameter of interest of the structure on the sample. The machine learning model is generated based on the postprocessing measurement results extracted by the postprocessing physical model, at least one of the reference data and the experimental design information, and the preprocessing step data.

Brief Description of the Drawings

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DETAILED DESCRIPTION OF THE INVENTION

[0019] During the fabrication of semiconductor devices and similar devices, it is often necessary to monitor the fabrication process by non-destructively measuring the devices. One type of measurement that can be used for non-destructive measurement of samples during processing is optical measurement, which can use a single wavelength or multiple wavelengths and can include, for example, polarization analysis, reflectivity measurement, Fourier Transform infrared spectroscopy (FTIR), etc. Other types of measurement, including X-ray measurement, photoacoustic measurement, electron beam (E-beam) measurement, etc., can also be used.

[0020] 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 a sample that is compared with measurement data from the sample. Using physical modeling techniques, a model of the sample including primary parameters and non-primary parameters is generated. The model can be based on the nominal parameters of the sample and can include, for example, one or more variable parameters such as layer thickness, line width, pitch width, sidewall angle, material properties, etc. that can vary over a desired range according to the process parameters used to fabricate the test sample. The model can further include parameters related to the tool set, for example, the characteristics of the optical system used by the measurement device. The predicted data can be calculated based on the parameters of the physical model including variations of the variable parameters and the characteristics of the measurement device using analytical or semi-analytical methods, such as effective medium theory (EMT), finite-difference time-domain (FDTD), transfer matrix method (TMM), Fourier modal method (FMM) / rigorous coupled-wave analysis (RCWA), finite element method (FEM), etc. The measurement data obtained from the sample by the measurement device is compared with the predicted data for different parameter variations, for example, in a non-linear regression process, until the best fit is achieved. At the time when the best fit is achieved, the value of the fitting parameter is regarded as an accurate representation of the parameter of the sample.

[0021] Conventionally, modeling requires that preliminary structural and material information be known about the sample 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 the sample can include the type of the sample's structure and a physical description having nominal values of various parameters, such as layer thickness, line width, pitch width, sidewall angle, material properties, etc., along with the ranges within which these parameters can vary. The model can further include one or more parameters that are not variable, i.e., not expected to vary in a significant amount in the sample during manufacturing. The variable parameters of the model can be adjusted and prediction data can be generated in real time during a non-linear regression process, or a library can be pre-generated. Thus, modeling applies physical constraints in the analysis and provides a high level of fidelity for the measurement results accordingly. However, modeling has a high computational cost due to the physical calculations required to generate the prediction data. For example, modeling a complex 3D structure is plagued by a slow time to solution (TTS), and the accuracy of the modeling can be reduced due to the difficulty in fitting data for complex structures.

[0022] Another technique that can be used to generate prediction data for a sample based on measurement data obtained from the sample by a measurement device is machine learning. Machine learning algorithms that can be used for measurement include, for example, linear regression, neural networks, deep learning, convolutional neural networks (CNNs), ensemble methods, support vector machines (SVMs), random forests, etc., or combinations of multiple models in sequential and / or parallel modes, but are not limited thereto. Machine learning does not require a physical model of the sample. Instead, reference data, for example, measurement data obtained from one or more reference samples by a measurement device, is acquired together with the values of the structural parameters of interest and used to generate and train a machine learning model. The machine learning model is automatically trained using the reference data and the known values of the structural parameters, finds the relevant data features, and learns the inherent relationships and connections between the input features and the output features in order to make decisions and predictions on new data. The advantage of using machine learning is that the time to solution (TTS) is fast and the computing resource requirements are minimal. However, machine learning requires a large amount of reference data, which is costly and time-consuming to obtain. Without a large amount of reference data, the machine learning model may suffer from overfitting due to the lack of physical constraints.

[0023] As semiconductor devices continue to shrink, the measurement budget becomes more stringent. Additionally, complex 3D structures are being adopted more frequently to enable continuous device scaling. Advancements in semiconductor technology, such as the use of complex 3D structures, pose additional challenges to measurement due to increased modeling complexity and parameter correlation, as well as reduced sensitivity. For example, the signal from a single measurement tool or source may not have sufficient sensitivity to accurately measure the parameters of interest for semiconductor process quality control. Ultimately, there may not be a single measurement tool that can handle all the measurement requirements for state-of-the-art semiconductor devices.

[0024] As contemplated herein, by using data collected from multiple data sources, e.g., from multiple tool sets and / or processing steps, and additional data such as sensor data related to samples collected from metrology and / or production equipment, a computationally efficient data analysis method can fuse multiple data sources and generate measurement results that are more accurate and consistent than those that can be provided by any individual data source. The analysis method can be flexible to accommodate various data of different natures, while at the same time maximizing the use of existing well-developed techniques such as physical modeling or machine learning for each type of data source and synergistically leveraging the strengths of individual measurement techniques.

[0025] As discussed herein, physical modeling and machine learning are combined to analyze multiple data sources for hybrid metrology and ecosystems. The methods described herein create predictive capabilities through data mining and data fusion from multiple data sources, such as multiple measurement tool sets, sample data from multiple processing steps, measurement instrument parameters, and production equipment parameters. By way of example, at least one physical model can be used to analyze measurement signals from one or more measurement tools, such as spectroscopic ellipsometers, spectroscopic reflectometers, X-ray measurements, photoacoustic measurements, Fourier transform infrared spectroscopy (FTIR), E-beam measurements, etc., to extract measurements of primary and non-primary parameters of a sample. Additionally, at least one machine learning model can be constructed and trained to predict parameters of interest. The machine learning model can use input data from one or more of the following data: measurements from one or more physical models (primary and non-primary parameters); one or more physical models and optionally raw signals used for misfit; data sources from different tool sets, or data sources from the same tool that are not included in the physical modeling; process parameters, advanced process control (APC) parameters, context data, and sensor data from production equipment. In-line measurements of a sample use one or more physical models and trained machine learning models to make predictions of sample parameters of interest based on data obtained from multiple data sources.

[0026] The proposed techniques can be used to combine and analyze multiple data sources in an efficient and flexible manner that synergistically combines physical modeling and machine learning with controllable computational cost and software and modeling complexity, thus providing the most feasible solution with time to solution (TTS) as well as improved final results and overall metrology performance. This approach is also versatile and applicable to measurements of any device, OCD, thin film, or other type of target.

[0027] FIG. 1 illustratively shows a schematic diagram of a measurement device 100 that can be used to characterize a structure on a sample, as described herein by way of example. The measurement device 100 can be configured to perform one or more types of measurements such as, for example, spectroscopic reflectance measurement, spectroscopic ellipsometry (including Mueller matrix ellipsometry), spectroscopic scattering measurement, overlay scattering measurement, interferometry, photoacoustic measurement, E-beam measurement, X-ray measurement, FTIR measurement, etc. of the sample 103. The measurement device 100 can include, for example, a first measurement tool 101 and a second measurement tool 170, but can include additional measurement tools or can be coupled to receive sample data measured by separate measurement tools. The measurement device 100 is illustrated as one exemplary configuration of a measurement device, and it should be understood that other configurations and other measurement devices can be used if desired.

[0028] The measurement device 100 includes an oblique incidence measurement tool 101 that includes a light source 110 that generates light 102. The light 102 can be, for example, UV-visible light having a wavelength such as 200 nm to 1000 nm. The light 102 generated by the light source 110 can include a range of wavelengths, i.e., a continuous range or a plurality of discrete wavelengths, or can be a single wavelength. The measurement device 100 includes condenser optical components 120 and 130 that collect and receive light and direct the light to obliquely incident on the uppermost surface of the sample 103. The optical components 120, 130 can be refractive, reflective, or a combination thereof, and can be objective lenses.

[0029] The reflected light can be focused by the lens 114 and received by the detector 150. The detector 150 can be a conventional charge coupled device (CCD), a photodiode array, a CMOS, or a detector of a similar type. The detector 150 can be, for example, a spectrometer when broadband light is used, and the detector 150 can generate a spectral signal as a function of wavelength, for example. The spectrometer can be used to disperse the entire spectrum of polarized light into spectral components across an array of detector pixels. One or more polarization elements can be present in the beam path of the optical measurement device 100. For example, the measurement device 100 can include one or both (or none at all) of one or more polarization elements 104 in the beam path before the sample 103 and a polarization element (analyzer) 112 in the beam path after the sample 103, and can include one or more additional elements 105a and 105b such as compensators or photoelastic modulators, which can be before, after, or both before and after the sample 103. By using a spectroscopic ellipsometer that uses a dual-rotation compensator between the polarization elements 104 and 112 and the sample, a complete Mueller matrix can be measured.

[0030] The measurement device 100 can include additional measurement devices or can be coupled to additional measurement devices. For example, as illustrated, the measurement device 100 can include a second normal incidence measurement tool 170. The second measurement tool 170 can be configured for, by way of example, spectroscopic reflectometry, spectroscopic scatterometry, overlay scatterometry, interferometry, e-beam measurement, x-ray measurement, FTIR measurement, and the like. In some implementations, the measurement device 100 can include additional tools, such as a third (or more) measurement tool. In some implementations, the additional measurement tool can be separate from the measurement device 100.

[0031] The measurement device 100 further includes at least one computing system 160 configured to characterize one or more parameters of the sample 103 using the methods described herein. The at least one computing system 160 is coupled to a first measurement tool 101, such as a detector 150, and a second measurement tool 170, and, if present, any additional measurement tools, to receive measurement data obtained during the measurement of the structure of the sample 103. Obtaining the data can be performed during pre-processing fabrication steps and post-processing fabrication steps. The at least one computing system 160 can be, for example, a workstation, a personal computer, a central processing unit, or other suitable computer system, or a plurality of systems.

[0032] The at least one computing system 160 can be a single computer system or a plurality of separate or linked computer systems, and it should be understood that herein it can be referred to interchangeably as the computing system 160 or the at least one computing system 160. The computing system 160 can be included in, connected to, or otherwise associated with the measurement device 100 and any additional measurement tools. Different subsystems of the measurement device 100 can each include a computing system configured to perform steps associated with the relevant subsystem. For example, the computing system 160 can control the positioning of the sample 103, for example, by controlling the movement of stage 109 coupled to the chuck. For example, stage 109 can be capable of horizontal movement in either Cartesian (i.e., X and Y) coordinates, or polar (i.e., R and θ) coordinates, or some combination of the two. The stage can also be capable of vertical movement along the Z coordinate. The computing system 160 can further control the operation of the chuck 108 to hold or release the sample 103. The computing system 160 can further control or monitor the rotation of one or more polarizing elements 104, 112, or additional elements 105a, 105b, etc.

[0033] The computing system 160 can be communicatively coupled to the detector 150 within the first measurement tool 101 and the detector (if present) within the second measurement tool 170 in any manner known in the art. For example, at least one computing system 160 can be coupled to a separate computing system associated with the detector 150. The computing system 160 can be configured to receive and / or obtain measurement data from, for example, the detector 150, and from the controller polarization elements 104, 112, and additional elements 105a, 105b, etc., and from components of the second measurement tool 170 via a transmission medium that can include a wired portion and / or a wireless portion. Thus, the transmission medium can function as a data link between the computing system 160 and other subsystems of the measurement device 100. The computing system 160 can be further configured to receive and / or obtain additional information regarding the sample and one or more subsystems of the first measurement tool 101 and the production equipment from, for example, a user interface (UI) 168 or via a transmission medium that can include a wired portion and / or a wireless portion.

[0034] Computing system 160 includes at least one processor 162, along with memory 164, and UI 168, which are communicatively coupled via bus 161. Memory 164 or other non-transitory computer-usable storage media includes its embodied computer-readable program code 166, which can be used by computing system 160 to cause at least one computing system 160 to control measurement device 100 and execute functions including the techniques and analysis described herein. For example, as illustrated, memory 164 may include instructions for causing processor 162 to perform both modeling and machine learning, and in some implementations, may employ feedforward and / or feedback as discussed herein. Data structures and software code for automatically implementing one or more of the acts described in this detailed description can be implemented by those skilled in the art in light of this disclosure and can be stored in a computer-usable storage medium, such as memory 164, which can be any device or medium capable of storing code and / or data for use by a computer system, such as computing system 160. Computer-usable storage media can include, but are not limited to, magnetic and optical storage devices such as read-only memory, random access memory, disk drives, magnetic tape, etc. Additionally, the functions described herein can be embodied, in whole or in part, within the circuitry of an application specific integrated circuit (ASIC) or a programmable logic device (PLD), and the functions can be embodied in a computer understandable descriptor language that can be used to create an ASIC or PLD that operates as described herein.

[0035] Computing system 160 can be configured to obtain data for reference samples from a plurality of data sources including, for example, one or both of measurement tools 101 and 170, and any desired additional measurement tools, data related to samples such as reference data and / or DOE data, and data related to measurement tools and / or processing equipment such as process parameters, Advanced Parameter Control (APC) parameters, context data, and sensor data from production equipment. Computing system 160 can be configured to generate one or more physical models (model 164pm) 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 contemplated herein, to generate and train one or more machine learning models (ML 164ml) for the sample based on the one or more physical models and measurement results extracted from the data. In some implementations, different computing systems and / or different measurement devices can be used to obtain measurement data and additional information from training samples, generate one or more physical models (model 164pm), and / or generate and train one or more machine learning models (ML 164ml), and the resulting physical models and / or trained machine learning models (or portions thereof) can be provided to computing system 160 via computer-readable program code 166 on a non-transitory computer-usable storage medium such as, for example, memory 164.

[0036] Computing system 160 can additionally or alternatively be used to obtain data from test samples from multiple data sources. The data can be of the same type as that used to generate physical models and to generate and train the machine learning models discussed above, and the test samples can have the same structure as the reference samples. Computing system 160 can be configured to determine parameters of one or more objects of interest of a sample using data from multiple sources, one or more physical models (Model 164pm), and one or more trained machine learning models (ML 164ml), as discussed herein.

[0037] Results from the analysis of the data can be reported, for example, stored in memory 164 associated with sample 103 and / or presented to the user via UI 168, an alarm, or other output device. Further, the results of the analysis can be reported and fed forward or fed back to process equipment to adjust appropriate manufacturing steps to correct any variations detected in the manufacturing process. Computing system 160 can include a communication port 169 that can be any type of communication connection, such as to the Internet or any other computer network. Communication port 169 is used to receive instructions for programming computing system 160 to perform any one or more of the functions described herein and / or to export, for example, signals with measurement results and / or instructions to another system, such as an external process tool, in a feed forward or feedback process to adjust process parameters associated with the manufacturing process steps of the sample based on the measurement results.

[0038] As considered herein, to characterize a sample, at least one physics-based model is constructed to analyze measurement signals from one or more tools, such as spectroscopic ellipsometry (SE), spectroscopic reflectometry (SR), X-rays, E-beams, photoacoustic data, Fourier transform infrared spectroscopy (FTIR), etc., and from one or more sources, and to extract measurement results of primary and non-primary parameters. Additionally, (2) at least one machine learning model is constructed and trained to predict a parameter of interest. The machine learning model can take as input more than one of the following data: a) measurement results (primary and non-primary parameters) from the physics model in (1); b) raw signals of the physics model in (1), and optionally misfits; data sources from different tool sets, or data sources from the same tool in (1) but not included in the physics modeling; process parameters, APC parameters, context data, and sensor data from production equipment. Additionally, (3) in-line measurements of the sample can be performed using the physics model and the machine learning model created and trained offline to predict the parameter of interest based on data from multiple data sources.

[0039] FIG. 2 illustrates, by way of example, a workflow 200 for offline recipe creation, e.g., generation of one or more physics models and one or more machine learning models, according to a first exemplary scenario using data collected from multiple data sources, e.g., different tools and / or sources. In FIG. 2, solid black arrows indicate processes used in workflow 200, dashed black arrows indicate processes that are optional but at least one exists, and gray dotted arrows indicate optional processes.

[0040] As illustrated, measurement signals 202 from one or more reference samples are collected from a first data source or tool (source 1). The measurement signals 202 can be collected from any desired measurement device, such as the measurement tool 101 shown in FIG. 1, or from any other desired type of measurement device.

[0041] Additionally, the data is obtained from one or more additional data sources. For example, in some implementations, the measurement signals 204 and 206 from one or more reference samples can be collected from one or more additional sources or tools, illustrated as, for example, a second source or tool (Source 2) and a third source or tool (Source 3). The additional measurement signal 204 can be collected from a measurement device different from Source 1, such as the measurement tool 170 shown in FIG. 1, or from any other desired type of measurement device, and the measurement signal 206 can be collected from a measurement device different from Sources 1 and 2, such as a different type of measurement from either measurement tool 101 or 170, or from any other desired type of measurement device. As illustrated by the block arrows, additional data 208 related to the reference sample is collected and can be used as training data for one or more machine learning models 222. The additional data 208 can include, for example, reference data for samples and DOE data. The reference data can be, for example, the measurement signals obtained from one or more reference samples by a measurement device, along with the values of the structural parameters of interest typically provided by CD-AFM (atomic force microscopy), CD-SEM (scanning electron microscopy), or TEM (transmission electron microscopy). The DOE data can be, for example, data measured from a set of reference samples processed under intentionally introduced skew conditions, such that the structural parameters of interest vary according to process conditions skewed in a known pattern. The reference data and / or DOE data can be used as a training data set to train a machine learning model to find relevant data features and learn the inherent relationships and connections between input features and output features for making decisions and predictions about new data. In some implementations, the additional data 208 related to the reference sample can further include wafer state, accuracy, tool matching data, etc. The accuracy data is, for example, data repeatedly measured from the same target multiple times from the same instance of a tool. The accuracy metric is another key performance indicator (KPI) of a measurement that indicates the consistency of measurement results from multiple runs on the same sample.Tool matching data is, for example, data measured from the same target from multiple instances of tools of the same tool type. A tool matching metric is another measurement KPI that indicates the consistency of results measured from different tools of the same type for the same sample. Measurement accuracy (evaluated by matching to a reference value provided by, e.g., CD-AFM, CD-SEM, TEM, etc. and / or consistency to DOE conditions), precision, and tool matching are typical measurement KPIs. When accuracy and tool matching data are provided, physical modeling or machine learning models can be optimized not only to match the reference value precisely 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.

[0042] Furthermore, in some implementations, the additional data signal 209 can be used as an input for a physical model or as an input feature for a machine learning model. The additional data signal 209 can be related to sources (e.g., source 1, source 2, and source 3) from which it can be obtained, such as, for example, process parameters, Advanced Process Control (APC) parameters, context data, and sensor data from production equipment. By way of example, some process control parameters, such as the substrate temperature and chemical concentration for wet etching, can affect the etching rate (how fast material is removed from the surface of the wafer), and the etching rate is one of the important factors for determining the etching depth and CD profile. Some of these parameters, such as temperature, are measured by sensors from production equipment. Other parameters, such as the etching time, the name of the etching chamber, are user control parameters. The name of the etching chamber is an example of context data. Since each etching chamber has its own characteristic distribution of the etching profile across the wafer, knowing this information can help the machine learning to predict the correct wafer map. An example of an APC parameter is the atomic force microscope (AFM) results measured from the same sample in different process steps including related information, such as non-critical parameters of the structure of interest. Adding non-critical parameters as machine learning input features can help improve the machine learning robustness in predicting critical parameters. Adding all of these related parameters as machine learning input features can provide additional information useful for determining the structure parameters of interest controlled by these process parameters and conditions.

[0043] To generate one or more physical models, measurement signals and data from multiple data sources can be used. For example, as illustrated by the solid black arrow, the measurement signal 202 from the first source (Source 1) can be used to generate the first physical model 212 of the sample. The physical model of the sample is created, for example, based on the known geometry, nominal values, and materials of the structure. The measurement signal 202 can be used to generate the first physical model 212 by providing the data from which the measurement results are extracted, and the first physical model 212 can be adjusted and optimized such that the calculated signal fits well to the measurement signal and a good matching is achieved between the extracted measurement results and the known parameters of the reference sample. In some implementations, additional data can be used to assist in the generation of the first physical model 212. For example, as illustrated by the gray dotted arrow, additional data 208 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool matching data can be used to assist in the generation of the first physical model 212. Additionally, as illustrated by the gray dotted arrow, a data signal 209 can be used to assist in the generation of the first physical model 212. In another example, as illustrated by the gray dotted arrow, the measurement signal 204 from the second source (Source 2) can be used to assist in the generation of the first physical model 212 of the sample. In some implementations, both the additional data 208 and the measurement signal 204 can be used to assist in the generation of the first physical model 212.

[0044] In some implementations, multiple physical models can be generated. For example, as illustrated by the gray dotted arrow and the gray dotted box, a second physical model 214 can be generated based on a measurement signal 204 from a second source (source 2). In some implementations, additional data can be used to generate the second physical model 214. For example, as illustrated by the gray dotted arrow, additional data 208 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool matching data can be used to assist in the generation of the second physical model 214. In another example, as illustrated by the gray dotted arrow, a measurement signal 206 from a third source (source 3) can be used to assist in the generation of the second physical model 214 of the sample. In some implementations, both the additional data 208 and the measurement signal 206 can be used to assist in the generation of the second physical model 214. Additionally, as illustrated by the gray dotted arrow, a data signal 209 can be used to assist in the generation of the second physical model 214. Further, the multiple physical models can be optimized independently or co-optimized. For example, in some implementations, as illustrated by the gray dotted line, the first physical model 212 and the second physical model 214 can be linked such that at least some parameters can be coupled across the physical models 212 and 214, and the combined parameter space can be searched to conform to measurement signals from one or more data sources. The first physical model 212, and optionally the second physical model 214, can be configured to provide a goodness of fit 223 of the physical modeling.

[0045] Using multiple data sources, one or more machine learning models 222 are constructed and trained to predict parameters 225 of interest. Machine learning metrics 227 are developed and reported together with the goodness-of-fit 223 from physical modeling to indicate the measurement quality of a synergistic recipe from physical modeling and machine learning. As illustrated by the solid black arrows, the machine learning model 222 is constructed using measurement results extracted by a first physical model 212 as input features. As shown by the dashed black arrows, the input features of the machine learning model 222 may additionally include at least one of measurement signals 204 from one or more reference samples collected from a second source (Source 2), measurement signals 206 from one or more reference samples collected from a third source (Source 3), additional data signals 209, measurement results extracted by a second physical model 214, or any combination thereof. In some implementations, as illustrated by the dotted gray arrows, the input features of the machine learning model 222 may optionally include measurement signals 202 from one or more reference samples collected from a first source (Source 1). In some implementations, the input features from the measurement signals 202 may include data from the measurement signals, e.g., at least one data channel or at least one data chunk not used in generating the first physical model 212. For example, generally, a data channel may be a measurement subsystem defined by at least one of an energy source such as a light source, an optical path directed by optical components, a detector, or any combination thereof, and a data chunk may be a wavelength (e.g., used in spectroscopic measurement), a frequency (e.g., used in frequency-resolved measurement), an angle (e.g., used in angle-resolved measurement), a time interval (e.g., used in time-resolved measurement), or a subset of any combination thereof from the complete data set provided by the data channel. For example, a first measurement device may collect normal incidence signals and oblique incidence spectroscopic ellipsometry (SE) signals. The SE signals may be used to generate the first physical model 212, but the normal incidence signals may not be used as it may be difficult to fit the normal incidence signals.Thus, the vertically incident signal can be a data channel that is used as data for the input features of the machine learning model 222, in addition to the physical modeling results generated from different data channels, e.g., SE signals. In another example, the same data channel can be split into multiple data chunks, e.g., signals from different wavelength ranges, and some data chunks may be difficult to fit using physical modeling but can be used as data for the input features of the machine learning model 222.

[0046] The machine learning model 222 is trained using at least a portion of the data 208 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool matching data. The data 208 is training data and is used for offline training. For example, the reference data can be a set of signals having labels (e.g., values of key parameters provided by other measurement systems such as CD-SEM, TEM, CD-AFM, etc.), including any of measurement results from the first physical model 212, measurement signal 204, measurement signal 206, additional data signal 209, and measurement signal 202. During the training of the machine learning model 222, 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 222 makes predictions of the key parameters. The machine learning model 222 is trained to learn and predict key parameters that match the labels of the reference data. The DOE from the data 208 is a set of signals measured from reference samples processed under intentionally introduced skew conditions, including any of measurement results from the first physical model 212, measurement signal 204, measurement signal 206, additional data signal 209, and measurement signal 202. During machine learning training, the machine learning model 222 takes the signals from the DOE data as input features and makes predictions of the key parameters. The machine learning model 222 is trained to follow a skew pattern in which the predicted key parameter values are expected based on the process skew conditions. The accuracy data from the data 208 is measurement signals (including any of measurement results from the first physical model 212, measurement signal 204, measurement signal 206, additional data signal 209, and measurement signal 202) from multiple runs of the same measurement tool on the same sample. Similarly, the tool matching data from the data 208 is measurement signals (including any of measurement results from the first physical model 212, measurement signal 204, measurement signal 206, additional data signal 209, and measurement signal 202) from different instances of the same type of measurement tool on the same sample. The machine learning model 222 takes the accuracy and tool matching data as input features and makes predictions.The machine learning model 222 is trained such that the predicted values of the main parameters match for signals measured from the same sample but from different runs or different tools. The machine learning model 222 can be trained such that all criteria, matching to reference values, DOE skew conditions, high precision, and consistent tool matching are simultaneously satisfied when all of these data are provided during training.

[0047] FIG. 3 illustrates, by way of example, a workflow 300 for in-line measurement for characterizing a sample based on one or more physical models and one or more machine learning models according to a first exemplary scenario using signals collected from a plurality of data sources, e.g., different tools and / or sources. The one or more physical models and the one or more machine learning models can be generated as discussed, e.g., with reference to FIG. 2. In FIG. 3, solid black arrows indicate processes used in the workflow 300, dashed black arrows indicate processes that are optional but at least one exists, and gray dotted arrows indicate optional processes.

[0048] As illustrated, a measurement signal 302 from the sample is collected from a first data source or tool (source 1). The measurement signal 302 can be collected from any desired measurement device, such as the measurement tool 101 shown in FIG. 1, or from any other desired type of measurement device, and can be collected from the same measurement device or the same type of measurement device as used for source 1 in FIG. 2.

[0049] Additionally, the data is obtained from one or more additional data sources. For example, in some implementations, the measurement signals 304 and 306 can be collected from one or more additional sources or tools, illustrated as a second source or tool (Source 2) and a third source or tool (Source 3), for example. The additional measurement signal 304 can be collected from a measurement device different from Source 1, such as the measurement tool 170 shown in FIG. 1, or from any other desired type of measurement device, and can be collected from the same measurement device or the same type of measurement device as that used for Source 2 in FIG. 2. The measurement signal 306 can be collected from a measurement device different from Source 1 and Source 2, and can be a different type of measurement from, for example, either of the measurement tools 101 or 170 or any other desired type of measurement device, and can be collected from the same measurement device or the same type of measurement device as that used for Source 3 in FIG. 2. Further, in some implementations, additional data signals 309, process parameters, APC parameters, context data, and sensor data from production equipment that can be associated with the sources (e.g., Source 1, Source 2, and Source 3) can be obtained.

[0050] Signals and data from multiple data sources can be used to extract measurement results from one or more physical models. For example, as illustrated by the solid black arrow, the measurement signal 302 from the first source (Source 1) can be used to extract the measurement results of the sample from a first physical model 312 that can be the same as the first physical model 212 in FIG. 2. In some implementations, additional data can be used to assist in extracting the measurement results from the first physical model 312. For example, as illustrated by the gray dotted arrow, the measurement signal 304 from the second source (Source 2) can be used to assist in extracting the measurement results of the sample from the first physical model 312. Additionally, as illustrated by the gray dotted arrow, an additional data signal 309 can be used to assist in extracting the measurement results of the sample from the first physical model 312.

[0051] In some implementations, multiple physical models can be used to extract measurement results of a sample. For example, as illustrated by the gray dotted arrows and the gray dotted box, a second physical model 314 can be used to extract the measurement results of the sample based on the measurement signal 304 from a second source (Source 2). The second physical model 314 can be the same as, for example, the second physical model 214 in FIG. 2. In some implementations, additional data can be used to assist in extracting measurement results from the second physical model 314. For example, as illustrated by the gray dotted arrow, the measurement signal 306 from a third source (Source 3) can be used to assist in extracting the measurement results of the sample from the second physical model 314. Additionally, as illustrated by the gray dotted arrow, an additional data signal 309 can be used to assist in extracting the measurement results of the sample from the second physical model 314. Further, the multiple physical models can be optimized independently or co-optimized. For example, in some implementations, as illustrated by the gray dotted line, the first physical model 312 and the second physical model 314 can be linked such that at least some parameters can be coupled across the physical models 312 and 314, and the combined parameter space can be searched to fit the 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 fitness 323 of the physical modeling.

[0052] To predict a parameter 325 of interest based on multiple data sources, one or more trained machine learning models 322 are used. To show the measurement quality of a synergistically-acted recipe from physical modeling and machine learning, a machine learning measurement metric 327 and a goodness of fit 323 from physical modeling may be reported. The trained machine learning model 322 can be, for example, the same as the machine learning model 222 of FIG. 2 after training. As illustrated by the solid black arrow, the trained machine learning model 322 uses the measurement results extracted by the first physical model 312 as input features. As shown by the dashed black arrow, the trained machine learning model 322 further uses as input features at least one of the measurement signals 304 from samples collected from a second source (Source 2), the measurement signals 306 from samples collected from a third source (Source 3), additional data signals 309, additional signals 304 and / or 306, and the measurement results extracted by the second physical model 314 based thereon, and optionally additional data signals 309, or any combination thereof. In some implementations, as illustrated by the gray dotted arrow, the trained machine learning model 322 may further optionally use as input features the measurement signals 302 from samples collected from a first source (Source 1). In some implementations, the machine learning input features from the measurement signals 302 may include at least one data channel or at least one data chunk of data from the measurement signals that is not used, for example, in extracting measurement results from the first physical model 312, as discussed with reference to FIG. 2.

[0053] FIG. 4 illustrates, by way of example, a workflow 400 for offline recipe creation, for example, the generation of one or more physical models and one or more machine learning models, according to a second exemplary scenario using signals collected from multiple data sources, for example, different manufacturing process steps. In FIG. 4, the solid black arrows indicate the processes used in the workflow 400, the dashed black arrows indicate processes that are optional but at least one exists, and the dotted gray arrows indicate optional processes.

[0054] As illustrated, post - processing step measurement signals 402 from one or more reference samples are measured from a measurement device. The reference sample can be, for example, an OCD target pad or a semiconductor device, and the post - processing step measurement signal 402 is obtained after a desired step of sample fabrication has been completed. The post - processing step measurement signal 402 can be collected from any desired measurement device, such as measurement tool 101 shown in FIG. 1, or from any other desired type of measurement device.

[0055] Additionally, the pre - processing step measurement signals 404 from one or more reference samples are measured using a measurement device, e.g., the same or a different measurement device used to obtain the post - processing step measurement signal 402, and are used to generate pre - processing step data. The pre - processing step measurement signals 404 are obtained, for example, before the desired step of sample fabrication is completed. In some implementations, the post - processing step measurement signal 402 and the pre - processing step measurement signal 404 can be combined (e.g., by addition, subtraction, multiplication, or division) to form a pre - adjusted signal 405. Additionally, data related to the reference sample, such as reference data of the sample, design of experiments (DOE), etc., 408 can be collected. In some implementations, the additional data 408 related to the reference sample can further include, for example, wafer state, accuracy, tool - matching data, etc. Additionally, the data can be obtained from other sources, such as from the second measurement pad 406, from the fault - detection pad 409, or any combination thereof. The first exemplary scenario of FIGS. 2 and 3 emphasizes multiple data sources collected from different measurement devices, while the second exemplary scenario illustrates that, for example, multiple data sources can be obtained from different measurement pads, or from the same pad at different processing steps. Different measurement pads can be measured from the same or different measurement devices. The pre - processing step measurement signal 404 and the post - processing step measurement signal 402 can be measured at either the designed OCD target or the device. The second measurement pad 406 refers to, for example, 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 404 and the post - processing step measurement signal 402. For example, if the pre - processing step measurement signal 404 and the post - processing step measurement signal 402 are measured on the OCD target, the second measurement pad 406 can refer to an auxiliary signal from the device pad, or vice versa.

[0056] To generate one or more physical models, signals and data from multiple data sources can be used. For example, as illustrated by the solid black arrow, a post - processing step measurement signal 402 from a measurement device can be used to generate a post - processing physical model 412 of a sample. In some implementations, additional data can be used to assist in the generation of the post - processing physical model 412. For example, as illustrated by the gray dotted arrow, additional data 408 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool - matching data can be used to assist in the generation of the post - processing physical model 412. In another example, as illustrated by the dotted gray arrow, a pre - adjusted signal 405 can be used to assist in the generation of the post - processing physical model 412 of a sample. In another example, as illustrated by the gray dotted arrow, a signal from a second measurement pad 406 can be used to assist in the generation of the post - processing physical model 412 of a sample. In another example, as illustrated by the dotted gray arrow, a signal from a fault - detection pad 409 can be used to assist in the generation of the post - processing physical model 412 of a sample. In some implementations, to assist in the generation of the post - processing physical model 412, all or any combination of the data 408 and signals from different measurement pads, such as the second measurement pad 406 and / or the fault - detection pad 409 can be used.

[0057] In some implementations, multiple physical models can be generated. For example, as illustrated by the gray dotted arrows and the gray dotted box, the pre - processing physical model 414 can be generated based on the pre - processing step measurement signal 404 from the measurement device. In some implementations, additional data can be used to generate the pre - processing physical model 414. For example, as illustrated by the gray dotted arrows, additional data 408 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool - matching data can be used to assist in the generation of the pre - processing physical model 414. In another example, as illustrated by the gray dotted arrows, signals from the second measurement pad 406 can be used to assist in the generation of the pre - processing physical model 414 of the sample. In another example, as illustrated by the gray dotted arrows, signals from the fault - detection pad 409 can be used to assist in the generation of the pre - processing physical model 414 of the sample. In some implementations, all or any combination of data 408, and signals from the second measurement pad 406 and the fault - detection pad 409 can be used to assist in the generation of the pre - processing physical model 414. Further, the multiple physical models can be optimized independently or co - optimized. For example, in some implementations, as illustrated by the gray dotted line, the post - processing physical model 412 and the pre - processing physical model 414 can be linked such that at least some parameters can be combined across the post - processing physical model 412 and the pre - processing physical model 414, and the combined parameter space can be searched to fit the measurement signals from one or more data sources. The post - processing physical model 412, and optionally the pre - processing physical model 414, can be configured to provide a goodness - of - fit 423 of the physical modeling.

[0058] Using multiple data sources, one or more machine learning models 422 are constructed and trained to predict parameters 425 of interest. Machine learning metrics 427 are developed and reported along with the goodness-of-fit 423 from physical modeling to indicate the measurement quality of a synergistic recipe from physical modeling and machine learning. As illustrated by the solid black arrows, the machine learning model 422 is constructed using the post-processing measurement results extracted by the post-processing physical model 412 as input features. As shown by the dashed black arrows, the input features of the machine learning model 422 additionally include pre-processing step data generated based on the pre-processing step measurement signal 404. The pre-processing step data can be generated in a plurality of ways based on the pre-processing step measurement signal 404. For example, as illustrated in FIG. 4, the pre-processing step data can be generated in three different ways from the pre-processing step measurement signals 404 labeled 1, 2, and 3, where at least one of (1), (2), or (3), or any combination thereof can be used. As illustrated by label 1 for the pre-processing step measurement signal 404, the pre-processing step data can be generated by combining the pre-processing step measurement signal 404 with the post-processing step measurement signal 402 to form a pre-adjusted signal 405. As explained in FIG. 4, in some implementations, when the pre-adjusted signal 405 is generated, the pre-adjusted signal 405 is either (A) provided to the post-processing physical model 412 and the machine learning model 422 is constructed at least in part based on the post-processing measurement results extracted by the post-processing physical model 412, or (B) the pre-adjusted signal 405 is provided to the machine learning model 422 and the machine learning model 422 is constructed at least in part based on the pre-adjusted signal 405. Additionally, as further explained in FIG. 4, in some implementations, at least one of (A) or (B) can be used with the workflow 400.As illustrated by label 2 for the pre - processing step measurement signal 404, the pre - processing step data can be generated by providing the pre - processing step measurement signal 404 to the pre - processing physical model 414, and the machine learning model 422 is constructed at least in part based on the pre - processing measurement results extracted by the pre - processing physical model 414. As illustrated by label 3 for the pre - processing step measurement signal 404, the pre - processing step data can be generated by providing the pre - processing step measurement signal 404 to the machine learning model 422, and the machine learning model 422 is constructed at least in part based on the pre - processing step measurement signal 404.

[0059] Additionally, as indicated by the dashed black arrow, the machine learning model 422 is constructed using at least one of the pre - processing step data (i.e., at least one of (1), (2), or (3) for the pre - processing step measurement signal 404, or any combination thereof), signals from the second measurement pad 406, and signals from the fault detection pad 409, or any combination of these additional data. In some implementations, as illustrated by the gray dotted arrow, the machine learning model 422 can optionally be further constructed using the post - processing step measurement signal 402, the pre - adjusted signal 405, the measurement results extracted by the pre - processing physical model 414, or some combination thereof.

[0060] The machine learning model 422 is trained using at least a portion of data 408 such as reference data and / or DOE, and optionally wafer conditions, accuracy, and tool matching data.

[0061] FIG. 5 illustrates, by way of example, a workflow 500 for in-line measurement for characterizing a sample based on, for example, one or more physical models and one or more machine learning models using a plurality of data sources, such as signals collected from different manufacturing process steps. The one or more physical models and the one or more machine learning models can be generated, for example, as discussed with reference to FIG. 4. In FIG. 5, the solid black arrows indicate the processes used in the workflow 500, the dashed black arrows indicate processes that are optional but at least one exists, and the dotted gray arrows indicate optional processes.

[0062] As illustrated, a post-processing step measurement signal 502 from the sample is collected from a measurement device. The sample can be, for example, an OCD target pad or a semiconductor device, and the post-processing step measurement signal 502 is obtained after a desired step of fabricating the sample is completed. The post-processing step measurement signal 502 can be collected from any desired measurement device, such as the measurement tool 101 shown in FIG. 1, or from any other desired type of measurement device, and can be collected from the same measurement device or the same type of measurement device used to obtain the post-processing step measurement signal 402 of FIG. 4.

[0063] Additionally, the pre - processing step measurement signal 504 from the sample is collected using a measurement device, for example, the same or a different measurement device as that used to obtain the post - processing step measurement signal 502, and the same measurement device or the same type of measurement device as that used to obtain the pre - processing step measurement signal 404 of FIG. 4. The pre - processing step measurement signal 504 is used to generate pre - processing step data. The pre - processing step measurement signal 504 is obtained, for example, before the desired step of sample fabrication is completed. In some implementations, the post - processing step measurement signal 502 and the pre - processing step measurement signal 504 may be combined (e.g., by addition, subtraction, multiplication, or division) to form a pre - adjusted signal 505. Additionally, data may be obtained from other sources such as the second measurement pad 506, the fault detection pad 509, or any combination thereof. The pre - processing step measurement signal 504 and the post - processing step measurement signal 502 may be measured at either a designed OCD target or device. The second measurement pad 506 refers to, for example, pre - processing step measurements and / or post - processing step measurements from a measurement pad where the pre - processing step measurement signal 504 and the post - processing step measurement signal 502 are not measured. For example, if the pre - processing step measurement signal 504 and the post - processing step measurement signal 502 are measured on an OCD target, the second measurement pad 506 may refer to an auxiliary signal from a device pad or vice versa.

[0064] To extract measurement results from one or more physical models, signals and data from multiple data sources can be used. For example, as illustrated by the solid black arrow, a post-processing measurement signal 502 can be used to extract measurement results of a sample from a post-processing physical model 512 that can be the same as the post-processing physical model 412 of FIG. 4. In some implementations, additional data can be used to assist in extracting measurement results from the post-processing physical model 512. For example, as illustrated by the gray dotted arrow, a pre-adjusted signal 505 can be used to assist in extracting measurement results from the post-processing physical model 512 of the sample. In another example, as illustrated by the gray dotted arrow, a signal from a second measurement pad 506 can be used to assist in extracting measurement results from the post-processing physical model 512 of the sample. In another example, as illustrated by the gray dotted arrow, a signal from a fault detection pad 509 can be used to assist in extracting measurement results from the post-processing physical model 512 of the sample. In some implementations, all or any combination of signals from the second pad 506 and the fault detection pad 509 can be used to assist in extracting measurement results from the post-processing physical model 512 of the sample.

[0065] In some implementations, multiple physical models may be used to extract measurement results of a sample. For example, as illustrated by the gray dotted arrows and the gray dotted box, a pre - processing physical model 514 may be used to extract the measurement results of the sample based on the pre - processing step measurement signal 504. The pre - processing physical model 514 may be the same as the pre - processing physical model 414 in FIG. 4. In some implementations, additional data may be used to assist in extracting the measurement results from the pre - processing physical model 514. For example, as illustrated by the gray dotted arrow, a signal from the second measurement pad 506 may be used to assist in extracting the measurement results from the pre - processing physical model 514 of the sample. In another example, as illustrated by the gray dotted arrow, a signal from the fault detection pad 509 may be used to assist in extracting the measurement results from the pre - processing physical model 514 of the sample. In some implementations, all or any combination of the signals from the second pad 506 and the fault detection pad 509 may be used to assist in extracting the measurement results from the pre - processing physical model 514 of the sample. Further, the 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 512 and the pre - processing physical model 514 may be linked such that at least some parameters may be coupled across the post - processing physical model 512 and the pre - processing physical model 514, and the combined parameter space may be searched to fit the measurement signals from one or more data sources. The post - processing physical model 512, and optionally the pre - processing physical model 514, may be configured to provide a goodness - of - fit 523 of the physical modeling.

[0066] One or more trained machine learning models 522 are used to predict a parameter 525 of interest based on multiple data sources. A machine learning metric 527 is developed and reported along with a goodness-of-fit 523 from physical modeling, which may indicate the measurement quality of a synergistically-acted recipe from physical modeling and machine learning. As illustrated by the solid black arrows, the trained machine learning model 522 uses the post-processed measurement results extracted by the post-process physical model 512 as input data and also uses the pre-process step data generated based on the pre-process step measurement signal 504.

[0067] The preprocessing step data can be generated in multiple ways based on the preprocessing step measurement signal 504. For example, as illustrated in FIG. 5, the preprocessing step data can be generated in three different ways from the preprocessing step measurement signals 504 labeled 1, 2, and 3, where at least one of (1), (2), or (3), or any combination thereof can be used. As illustrated by label 1 for the preprocessing step measurement signal 504, the 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-adjusted signal 505. As explained in FIG. 5, in some implementations, when the pre-adjusted signal 505 is generated, the pre-adjusted signal 505 is provided to the (A) postprocessing physical model 512, and the trained machine learning model 522 receives input data in the form of postprocessing measurement results extracted by the postprocessing physical model 512, or (B) the pre-adjusted signal 505 can be provided as input data to the trained machine learning model 522. Additionally, as further explained in FIG. 5, in some implementations, at least one of (A) or (B) can be used with the workflow 500. As illustrated by label 2 for the preprocessing step measurement signal 504, the preprocessing step data can be generated by providing the preprocessing step measurement signal 504 to the preprocessing physical model 514, and the trained machine learning model 522 uses the measurement results extracted by the preprocessing physical model 514 as input data. As illustrated by label 3 for the preprocessing step measurement signal 504, the preprocessing step data can be generated by providing the preprocessing step measurement signal 504 as input data to the trained machine learning model 522.

[0068] In some implementations, as illustrated by the gray dotted arrow, the trained machine learning model 522 can optionally further use input data including the postprocessing step measurement signal 502.

[0069] In some implementations, primary data, e.g., physical modeling, and in some implementations, measurement signals used in a machine learning model, as well as auxiliary data, e.g., a machine learning model, and in some implementations, captured data used in physical modeling, can be from different tool sets, or from the same tool set but different data channels, or from the same tool set and the same data channel but different wavelength ranges, time intervals, etc. Different data sources can collect data from, for example, the same OCD target on the same wafer or the same sample site on a device, from the same processing step, or from different processing steps. Different data sources can collect data from, for example, different sample sites of the same wafer from the same or different processing steps when the underlying structure has correlation parameters, and as a result, analyzing the combined data can improve the overall performance. As illustrated, at least one physical model can be created to analyze measurement signals from at least one data source. Further, when two or more physical models are used, the multiple physical models can be optimized independently or co-optimized. For example, the physical models can be linked such that at least some parameters can be coupled across the physical models and the combined parameter space can be searched to fit the measurement signals from one or more data sources. The primary data and the auxiliary data can have different natures. For example, some of the data can be measurement data collected from a tool set, while other data can be sensor data from process equipment, or wafer process parameters such as gas flow rate, APC parameters, or context data such as a specific process tool. Additionally, feature engineering and signal processing can be applied before data from all sources is provided to a machine learning model for training and prediction. Machine learning algorithms can include, for example, linear regression, neural networks, deep learning, convolutional neural networks (CNNs), ensemble methods, support vector machines (SVMs), random forests, etc., or combinations of multiple models in sequential mode and / or parallel mode, but are not limited thereto.

[0070] The illustrated workflow efficiently combines various measurement techniques and the use of multiple data sources by synergistically applying physical modeling and machine learning to generate more usable information than provided by individual measurement techniques or a single data source. Physical modeling can be performed using previously well-established modeling solutions with a desired measurement device, and the physical modeling results can be combined with other modeling-difficult or impossible data, which can be referred to as auxiliary data, for machine learning training and prediction. Thus, the resulting process provides an executable solution that has the advantages of both physical modeling and machine learning while controlling the computational cost, enables an acceptable TTS for generation, is easily implemented, and is actually used. Additionally, the prediction ability can be increased through the use of data such as process parameters and sensor data from production equipment, which is combined with measurement data through data mining and data fusion as considered herein. The proposed method is flexible to adapt to various signals of different natures and, at the same time, maximizes the use of existing well-developed algorithms for each type of data source. Furthermore, the techniques considered herein have general-purpose applications and can be applied, for example, to the measurement of any device, OCD, thin film, or other type of target.

[0071] FIG. 6 shows an illustrative flow diagram depicting an exemplary method 600 for characterizing a structure on a sample according to some implementations. In some implementations, the exemplary method 600 is configured to store a measurement signal, measurement results, one or more physical models, one or more machine learning models, and parameters of interest of the structure, and to implement the workflow 300 illustrated in FIG. 3, and can be executed by at least one memory, such as the memory 164, coupled to one or more processors, such as the processor 162 within the computing system 160 of FIG. 1.

[0072] One or more processors may obtain a measurement signal about a structure on a sample from a first measurement device (602). For example, the measurement signal about the structure on the sample may be obtained by the measurement device 100 shown in FIG. 1. The measurement signal about the structure on the sample may be, for example, the measurement signal 302 shown in FIG. 3. The means for obtaining a measurement signal about a structure on a sample from a first measurement device may be, for example, the measurement device 100 shown in FIG. 1, and at least one memory 164 and at least one processor 162 within the computing system 160 shown in FIG. 1.

[0073] One or more processors may extract a measurement result from a first physical model of a structure on a sample based on the measurement signal (604). For example, the first physical model may be the first physical model 312 shown in FIG. 3. The means for extracting a measurement result from a first physical model of a structure on a sample based on the measurement signal may be, for example, based on instructions for the model 164pm from computer-readable program code 166 on a non-transitory computer-usable storage medium such as the memory 164 shown in FIG. 1, and may be at least one processor 162 configured to implement one or more physical models.

[0074] One or more processors may further determine a parameter of interest of a structure on a sample using a machine learning model based on measurement results extracted from a first physical model and data from a measurement signal from a first measurement device that was not used to extract the measurement results from the first physical model, a second measurement signal obtained from a second measurement device regarding the structure on the sample, process parameters used to generate the structure on the sample, advanced process control (APC) parameters used to generate the structure on the sample, context data of the structure on the sample, and sensor data from production equipment used to generate the structure on the sample (606). The machine learning model may be, for example, a trained machine learning model 322 that receives measurement results extracted from the first physical model 312 in FIG. 3. Additionally, the second measurement signal obtained from the second measurement device regarding the structure on the sample may be the measurement signal 304, and the process parameters used to generate the structure on the sample, the APC parameters used to generate the structure on the sample, the context data of the structure on the sample, and the sensor data from production equipment used to generate the structure on the sample may be the additional data signal 309 shown in FIG. 3. Means for determining a parameter of interest of a structure on a sample using a machine learning model based on measurement results extracted from a first physical model and data from a measurement signal from a first measurement device that was not used to extract the measurement results from the first physical model, a second measurement signal obtained from a second measurement device regarding the structure on the sample, process parameters used to generate the structure on the sample, advanced process control (APC) parameters used to generate the structure on the sample, context data of the structure on the sample, and sensor data from production equipment used to generate the structure on the sample may be, for example, at least one processor 162 configured to implement one or more physical models based on instructions for a model 164ml from computer-readable program code 166 on a non-transitory computer-usable storage medium such as the memory 164 shown in FIG. 1.

[0075] In some implementations, data from the measurement signal can be at least one data channel that can be a measurement subsystem defined by at least one of an energy source such as a light source, an optical path directed by optical components, a detector, or a combination thereof, and, for example, at least one data chunk that can be a subset of wavelength, frequency, angle, time interval, or any combination of the above, from the complete data set provided by the at least one data channel, as considered with reference to the data provided from the measurement signal 302 to the machine learning model 322 in FIG. 3.

[0076] In some implementations, the machine learning model can be generated based on measurement results extracted by the first physical model for one or more reference samples of the structure, and at least one of reference data and experimental design information, as illustrated, for example, by the black arrow from the first physical model 212 in FIG. 2 and the block arrow from the additional data 208 to the machine learning model 222. The machine learning model can be further generated based on at least one of data from the measurement signal not used in generating the first physical model, a second measurement signal obtained for one or more reference samples from a second measurement device, process parameters used to generate the one or more reference samples, APC parameters used to generate the one or more reference samples, context data of the one or more reference samples, and sensor data from production equipment used to generate the one or more reference samples, as illustrated by the black dashed line from the measurement signal 204 to the machine learning model 222 and the additional data signal 209 in FIG. 2.

[0077] In some implementations, the measurement results can be further extracted from the first physical model of the structure on the sample, based on a second measurement signal for the structure on the sample from a second measurement device, as illustrated by the gray dotted line from the measurement signal 304 to the first physical model 312 shown in FIG. 3.

[0078] In some implementations, the first measurement result can be extracted from a first physical model of a structure on a sample, based further on at least one of process parameters, APC parameters, context data, and sensor data from production equipment, as illustrated, for example, by the gray dotted line from the additional data signal 309 to the first physical model 312 in FIG. 3.

[0079] In some implementations, one or more processors may further extract a second measurement result from a second physical model of the structure on the sample based on a second measurement signal from a second measurement device, and the machine learning model may, for example, be illustrated by the second physical model 314 in FIG. 3, the gray dotted line from the measurement signal 304 to the second physical model 314, and the gray dotted line from the second physical model 314 to the trained machine learning model 322. Based on the second measurement result extracted from the second physical model, the parameter of interest of the structure on the sample is determined. As an example, in some implementations, the second measurement result is further based on a third measurement signal for the structure on the sample from a third measurement device, as illustrated by the gray dotted line from the measurement signal 306 to the second physical model 314 in FIG. 3, and is extracted from the second physical model of the structure on the sample. As an example, in some implementations, the second measurement result may be further based on at least one of process parameters, APC parameters, context data, and sensor data from production equipment, as illustrated by the black dashed line from the additional data signal 309 in FIG. 3 to the second physical model 314, and may be extracted from the second physical model of the structure on the sample. The means for extracting the second measurement result from the second physical model of the structure on the sample based on the second measurement signal from the second measurement device, where the machine learning model further determines the parameter of interest of the structure on the sample based on the second measurement result extracted from the second physical model, may be, for example, at least one processor 162 configured to implement one or more physical models, based on instructions for the model 164pm from computer-readable program code 166 on a non-transitory computer-usable storage medium such as the memory 164 shown in FIG. 1.

[0080] In some implementations, the machine learning model determines the parameter of interest of the structure on the sample further based on a second measurement signal from a second measurement device and further based on a third measurement signal regarding the structure on the sample from a third measurement device, as illustrated, for example, by the black dashed line from the measurement signals 304 and 306 in FIG. 3 to the machine learning model 322 trained thereby.

[0081] FIG. 7 shows an illustrative flowchart depicting an exemplary method 700 for characterizing a structure on a sample according to some implementations. In some implementations, the exemplary method 700 can be implemented by at least one memory, such as memory 164, coupled to one or more processors, such as processor 162 in computing system 160 of FIG. 1, configured to store measurement signals, measurement results, one or more physical models, one or more machine learning models, and parameters of interest of the structure and to implement the workflow 500 illustrated in FIG. 5.

[0082] In a preprocessing step, one or more processors can obtain a preprocessing step measurement signal regarding the structure on the sample from a measurement device (702). For example, the preprocessing step measurement signal can be obtained by the measurement device 100 shown in FIG. 1. The preprocessing step measurement signal can be, for example, the preprocessing step measurement signal 504 shown in FIG. 5. In the preprocessing step, means for obtaining a preprocessing step measurement signal regarding the structure on the sample from a measurement device can be, for example, the measurement device 100 shown in FIG. 1 and at least one memory 164 and at least one processor 162 within the computing system 160 shown in FIG. 1.

[0083] One or more processors may obtain a post - processing step measurement signal for a structure on a sample from a measurement device in a post - processing step (704). For example, the post - processing step measurement signal may be obtained by the measurement device 100 shown in FIG. 1. The post - processing step measurement signal for the structure on the sample may be, for example, the post - processing step measurement signal 502 shown in FIG. 5. In the post - processing step, means for obtaining a post - processing step measurement signal for a structure on a sample from a measurement device may be, for example, the measurement device 100 shown in FIG. 1, and at least one memory 164 and at least one processor 162 within the computing system 160 shown in FIG. 1.

[0084] One or more processors may extract a post - processing measurement result from a post - processing physical model of the sample based on the post - processing step measurement signal (706). For example, the post - processing physical model may be the post - processing physical model 512 shown in FIG. 5. Means for extracting a post - processing measurement result from a post - processing physical model of the sample based on the post - processing step measurement signal may be, for example, based on instructions for model 164pm from computer - readable program code 166 on a non - transitory computer - usable storage medium such as the memory 164 shown in FIG. 1, and at least one processor 162 configured to implement one or more physical models.

[0085] One or more processors may generate pre - processing step data based at least on the pre - processing step measurement signal (708). For example, the pre - processing step data generated based at least on the pre - processing step measurement signal may be any one of labels 1, 2, and 3 from the pre - processing step measurement signal 504 shown in FIG. 5. Means for generating pre - processing step data based at least on the pre - processing step measurement signal may be, for example, the measurement device 100 shown in FIG. 1, and at least one memory 164 and at least one processor 162 within the computing system 160 shown in FIG. 1.

[0086] One or more processors may determine a parameter of interest of a sample using a machine learning model based on post - processing measurement results extracted from a post - processing physical model and pre - processing step data (710). The trained machine learning model can be, for example, a trained machine learning model 522 that receives post - processing measurement results extracted by a post - processing physical model 512 and pre - processing step data, such as any one of labels 1, 2, and 3 from the pre - processing step measurement signal 504 shown in FIG. 5. The means for determining a parameter of interest of a sample using a machine learning model based on post - processing measurement results extracted from a post - processing physical model and pre - processing step data can be, for example, at least one processor 162 configured to implement one or more physical models, based on instructions for a model 164ml from computer - readable program code 166 on a non - transitory computer - usable storage medium such as the memory 164 shown in FIG. 1.

[0087] In some implementations, the machine learning model may further determine a parameter of interest of a structure on the sample based on at least one of a pre - processing step measurement signal, a second measurement signal obtained from a measurement pad, and a third measurement signal obtained from a fault - detection pad, as illustrated, for example, by the black dashed - line arrow from the pre - processing step measurement signal 504 shown in FIG. 5, the signal from the second measurement pad 506, and the signal from the fault - detection pad 509 to the machine learning model 522. The pre - processing step measurement signal, the second measurement signal obtained from a measurement pad, and the third measurement signal obtained from a fault - detection pad may be from different measurement pads or from the same pad at different processing steps and can be measured from the same or different measurement devices.

[0088] In some implementations, the post - processing measurement results are extracted from the post - processing physical model based on at least one of a second measurement signal from a measurement pad and a third measurement signal from a fault - detection pad, as illustrated, for example, by the gray dotted - line arrows from the second measurement pad 506 and the fault - detection pad 509 to the post - processing physical model 512.

[0089] In some implementations, the preprocessing step data may include a pre-adjusted signal generated based on a combination of the preprocessing step measurement signal and the postprocessing step measurement signal, as illustrated, for example, by the pre-adjusted signal 505 shown in FIG. 5 and the gray dotted line from the pre-adjusted signal 505 to the machine learning model 522.

[0090] In some implementations, one or more processors may further generate a pre-adjusted signal based on a combination of the preprocessing step measurement signal and the postprocessing step measurement signal, where the postprocessing measurement result is extracted from the postprocessing physical model based further on the pre-adjusted signal, as illustrated, for example, by the pre-adjusted signal 505 shown in FIG. 5 and the gray dotted line from the pre-adjusted signal 505 to the postprocessing physical model 512. The means for generating a pre-adjusted signal based on a combination of the preprocessing step measurement signal and the postprocessing step measurement signal, where the postprocessing measurement result is extracted from the postprocessing physical model based further on the pre-adjusted signal, may be, for example, the measurement device 100 shown in FIG. 1, and at least one memory 164 and at least one processor 162 within the computing system 160 shown in FIG. 1.

[0091] In some implementations, one or more processors may further extract pre - processing measurement results from a pre - processing physical model based on a pre - processing step measurement signal, and the pre - processing step data may include, for example, as illustrated by the pre - processing physical model 514 shown in FIG. 5, the gray dotted line from the pre - processing step measurement signal 504 to the pre - processing physical model 514, and the gray dotted line from the pre - processing physical model 514 to the machine learning model 522, the pre - processing measurement results extracted from the pre - processing physical model. The means for extracting pre - processing measurement results from the pre - processing physical model based on the pre - processing step measurement signal, where the pre - processing step data includes the pre - processing measurement results extracted from the pre - processing physical model, may be, for example, at least one processor 162 configured to implement one or more physical models based on instructions for the model 164pm from computer - readable program code 166 on a non - transitory computer - usable storage medium such as the memory 164 shown in FIG. 1.

[0092] As an example, in some implementations, the pre - processing measurement results are further extracted from the pre - processing physical model based on at least one of a second measurement signal obtained from a measurement pad and a third measurement signal obtained from a fault - detection pad, as illustrated by the gray dotted lines from the second measurement pad 506 to the pre - processing physical model 514 and from the fault - detection pad 509 to the pre - processing physical model 514 shown in FIG. 5.

[0093] In some implementations, the pre - processing step data may include the pre - processing step measurement signal, as illustrated by the black dashed line from the pre - processing step measurement signal 504 to the machine learning model 522 shown in FIG. 5.

[0094] FIG. 8 shows an illustrative flow diagram depicting an exemplary method 800 for characterizing a structure on a sample according to some implementations. In some implementations, the exemplary method 800 is configured to store a measurement signal, a measurement result, one or more physical models, one or more machine learning models, and parameters of a structure of interest, and implement the workflow 200 illustrated in FIG. 2, and can be executed by at least one memory, such as the memory 164, coupled to one or more processors, such as the processor 162 within the computing system 160 of FIG. 1.

[0095] One or more processors may obtain (802) a measurement signal for one or more reference samples of a structure from a first measurement device. For example, the measurement signal for one or more reference samples may be obtained by the measurement device 100 shown in FIG. 1. The measurement signal for one or more reference samples may be, for example, the measurement signal 202 shown in FIG. 2. The means for obtaining a measurement signal for one or more reference samples of a structure from a first measurement device may be, for example, the measurement device 100 shown in FIG. 1, and at least one memory 164 and at least one processor 162 within the computing system 160 shown in FIG. 1.

[0096] One or more processors may generate a first physical model to extract measurement results about a structure on a sample, and the first physical model is generated based on measurement signals about one or more reference samples from a first measurement device (804). For example, the first physical model generated based on the measurement signals of one or more reference samples from the first measurement device may be the first physical model 212 shown in FIG. 2. Means for generating a first physical model to extract measurement results about a structure on a sample, wherein the first physical model is generated based on measurement signals of one or more reference samples from a first measurement device, the means may be, for example, based on instructions for a model 164pm from computer-readable program code 166 on a non-transitory computer-usable storage medium such as the memory 164 shown in FIG. 1, for example, at least one processor 162 configured to implement one or more physical models.

[0097] One or more processors may generate a machine learning model to predict parameters of interest of a structure on a sample, the machine learning model being based on measurement results extracted by a first physical model and at least one of reference data and experimental design information, and further based on data from a measurement signal from a first measurement device not used in generating the first physical model, a second measurement signal obtained for one or more reference samples from a second measurement device, process parameters used to generate one or more reference samples, advanced process control (APC) parameters used to generate one or more reference samples, context data for one or more reference samples, and sensor data from production equipment used to generate one or more reference samples (806). A machine learning model for predicting parameters of interest of a structure on a sample may be, for example, a machine learning model 222 generated based on measurement results extracted by a first physical model 212 and at least one of reference data and experimental design information within additional data 208 shown in FIG. 2. Additionally, the data from the measurement signal may be at least one data channel or at least one data chunk from a first measurement device not used by the first physical model 212, the second measurement signal obtained for one or more reference samples from a second measurement device may be measurement signal 204, the process parameters used to generate one or more reference samples, the APC parameters used to generate one or more reference samples, the context data for one or more reference samples, and the sensor data from production equipment may be additional data signals 209 shown in FIG. 2.A means for generating a machine learning model to predict parameters of interest of a structure on a sample, wherein the machine learning model is based on measurement results extracted by a first physical model and at least one of reference data and experimental design information, and further based on data from a measurement signal from a first measurement device not used when generating the first physical model, a second measurement signal obtained for one or more reference samples from a second measurement device, process parameters used to generate one or more reference samples, advanced process control (APC) parameters used to generate one or more reference samples, context data of one or more reference samples, and sensor data from production equipment used to generate one or more reference samples. The means can be, for example, at least one processor 162 configured to implement one or more physical models, based on instructions for a model 164ml from computer-readable program code 166 on a non-transitory computer-usable storage medium such as memory 164 shown in FIG. 1.

[0098] In some implementations, the data from the measurement signal can be at least one data channel defined by a measurement subsystem that can be at least one of an energy source such as a light source, an optical path directed by optical components, a detector, or a combination thereof, and at least one data chunk that can be a subset of wavelength, frequency, angle, time interval, or any combination of the above, from a complete data set provided by at least one data channel, as considered with reference to the data provided from measurement signal 202 to machine learning model 222 in FIG. 2, for example.

[0099] In some implementations, the first physical model can be further generated based on a second measurement signal for one or more reference samples from a second measurement device, as illustrated by the gray dotted line from measurement signal 204 to the first physical model 212 shown in FIG. 2, for example.

[0100] In some implementations, the first physical model can be further generated based on at least one of process parameters, APC parameters, context data, and sensor data from production equipment, as illustrated, for example, by the gray dotted line from the additional data signal 209 to the first physical model 212 in FIG. 2.

[0101] In some implementations, one or more processors may further generate a second physical model to extract second measurement results about the structure on the sample, the second physical model being generated based on second measurement signals about one or more reference samples from a second measurement device, and the machine learning model may be generated further based on the second measurement results extracted by the second physical model, as illustrated, for example, by the second physical model 214 in FIG. 2, the gray dotted line from the measurement signal 204 to the second physical model 214, and the gray dotted line from the second physical model 214 to the machine learning model 222. As an example, in some implementations, the second physical model is generated further based on third measurement signals about one or more reference samples from a third measurement device, as illustrated, for example, by the gray dotted line from the measurement signal 206 in FIG. 2 to the second physical model 214. As an example, in some implementations, the second physical model is generated further based on at least one of process parameters, APC parameters, context data, and sensor data from production equipment, as illustrated, for example, by the gray dotted line from the additional data signal 209 in FIG. 2 to the second physical model 214. The means for generating a second physical model to extract second measurement results about the structure on the sample, wherein the second physical model is generated based on second measurement signals regarding one or more reference samples from a second measurement device, and wherein the machine learning model may be generated further based on the second measurement results extracted by the second physical model, may be, for example, at least one processor 162 configured to implement one or more physical models, based on instructions for the model 164pm from computer-readable program code 166 on a non-transitory computer-usable storage medium such as the memory 164 shown in FIG. 1.

[0102] In some implementations, the machine learning model can be generated based further on a second measurement signal from a second measurement device and further on a third measurement signal for one or more reference samples from a third measurement device, as illustrated, for example, by the black dashed lines from the measurement signals 204 and 206 in FIG. 2 to the machine learning model 222.

[0103] FIG. 9 shows an illustrative flow diagram depicting an exemplary method 900 for characterizing a structure on a sample according to some implementations. In some implementations, the exemplary method 900 can be implemented by at least one memory, such as memory 164, coupled to one or more processors, such as processor 162 in the computing system 160 of FIG. 1, configured to store measurement signals, measurement results, one or more physical models, one or more machine learning models, and parameters of interest of the structure, and to implement the workflow 400 illustrated in FIG. 4.

[0104] In a preprocessing step, one or more processors can obtain a preprocessing step measurement signal for one or more reference samples of the structure from a measurement device (902). For example, the preprocessing step measurement signal for one or more reference samples can be obtained by the measurement device 100 shown in FIG. 1. The preprocessing step measurement signal for one or more reference samples can be, for example, the preprocessing step measurement signal 404 shown in FIG. 4. In the preprocessing step, means for obtaining a preprocessing step measurement signal for one or more reference samples of the structure from a measurement device can be, for example, the measurement device 100 shown in FIG. 1, and at least one memory 164 and at least one processor 162 within the computing system 160 shown in FIG. 1.

[0105] One or more processors may obtain post - processing step measurement signals for one or more reference samples from a measurement device in a post - processing step (904). For example, the post - processing step measurement signals for one or more reference samples may be obtained by the measurement device 100 shown in FIG. 1. The post - processing step measurement signals for one or more reference samples may be, for example, the post - processing step measurement signals 402 shown in FIG. 4. In the post - processing step, the means for obtaining post - processing step measurement signals for one or more reference samples from a measurement device may be, for example, the measurement device 100 shown in FIG. 1, and at least one memory 164 and at least one processor 162 within the computing system 160 shown in FIG. 1.

[0106] One or more processors may generate a post - processing physical model to extract post - processing measurement results for one or more reference samples, and the post - processing physical model is generated based on the post - processing step measurement signals (906). For example, the post - processing physical model generated based on the post - processing step measurement signals may be the post - processing physical model 412 shown in FIG. 4. The means for generating a post - processing physical model to extract post - processing measurement results for one or more reference samples, where the post - processing physical model is generated based on the post - processing step measurement signals, may be, for example, at least one processor 162 configured to implement one or more physical models based on instructions for a model 164pm from computer - readable program code 166 on a non - transitory computer - usable storage medium such as the memory 164 shown in FIG. 1.

[0107] One or more processors may generate pre - processing step data based at least on the pre - processing step measurement signal (908). For example, the pre - processing step data generated based at least on the pre - processing step measurement signal may be any of labels 1, 2, and 3 from the pre - processing step measurement signal 404 shown in FIG. 4. The means for generating pre - processing step data based at least on the pre - processing step measurement signal may be, for example, the measurement device 100 shown in FIG. 1, and at least one memory 164 and at least one processor 162 within the computing system 160 shown in FIG. 1.

[0108] One or more processors generate a machine - learning model to predict a parameter of interest of a structure on a sample, and the machine - learning model is generated based on at least one of post - processing measurement results extracted by a post - processing physical model, reference data and experimental design information, and pre - processing step data (910). The machine - learning model may be, for example, a machine - learning model 422 generated based on at least one of post - processing measurement results extracted by a post - processing physical model 412, at least one of reference data and experimental design information within the additional data 408 shown in FIG. 4, and pre - processing step data (e.g., any of labels 1, 2, 3) from the pre - processing step measurement signal 404 shown in FIG. 4. The means for generating a machine - learning model to predict a parameter of interest of a structure on a sample, wherein the machine - learning model is generated based on at least one of post - processing measurement results extracted by a post - processing physical model, reference data and experimental design information, and pre - processing step data, may be, for example, based on instructions for a model 164ml from computer - readable program code 166 on a non - transitory computer - usable storage medium such as the memory 164 shown in FIG. 1, and may be, for example, at least one processor 162 configured to implement one or more physical models.

[0109] In some implementations, the machine learning model can be further generated based on at least one of a preprocessing step measurement signal, a second measurement signal obtained from a measurement pad, and a third measurement signal obtained from a fault detection pad, as illustrated by the black dashed arrows from the preprocessing step measurement signal 404, from the second measurement pad 406, and from the fault detection pad 409 to the machine learning model 422 shown in FIG. 4, for example. The preprocessing step measurement signal, the second measurement signal obtained from the measurement pad, and the third measurement signal obtained from the fault detection pad can be derived from different measurement pads or the same pad at different processing steps and can be measured from the same or different measurement devices.

[0110] In some implementations, the post-processing physical model can be further generated based on at least one of the second measurement signal from the measurement pad and the third measurement signal from the fault detection pad, as illustrated by the gray dotted arrows from the second measurement pad 406 and the fault detection pad 409 to the post-processing physical model 412 shown in FIG. 4, for example.

[0111] In some implementations, the preprocessing step data can include a pre-adjusted signal generated based on a combination of the preprocessing step measurement signal and the postprocessing step measurement signal, as illustrated by the gray dotted line from the pre-adjusted signal 405 and the pre-adjusted signal 405 to the machine learning model 422 shown in FIG. 4, for example.

[0112] In some implementations, one or more processors may further generate a pre-adjusted signal based on a combination of a pre-processing step measurement signal and a post-processing step measurement signal, where the post-processing physical model is generated further based on the pre-adjusted signal, as illustrated, for example, by the pre-adjusted signal 405 shown in FIG. 4 and the gray dotted line from the pre-adjusted signal 405 to the post-processing physical model 412. Means for generating a pre-adjusted signal based on a combination of a pre-processing step measurement signal and a post-processing step measurement signal, where the post-processing physical model is generated further based on the pre-adjusted signal, may be, for example, the measurement device 100 shown in FIG. 1, and at least one memory 164 and at least one processor 162 within the computing system 160 shown in FIG. 1.

[0113] In some implementations, one or more processors may further generate a pre-processing physical model to extract pre-processing measurement results for a sample, the pre-processing physical model being generated based on pre-processing step measurement signals for one or more reference samples, and the pre-processing step data including pre-processing measurement results extracted from the pre-processing physical model, as illustrated, for example, by the pre-processing physical model 414 shown in FIG. 4, the gray dotted line from the pre-processing step measurement signal 404 to the pre-processing physical model 414, and the gray dotted line from the pre-processing physical model 414 to the machine learning model 422. Means for generating a pre-processing physical model to extract pre-processing measurement results for a sample, where the pre-processing physical model is generated based on pre-processing step measurement signals for one or more reference samples, and the pre-processing step data includes pre-processing measurement results extracted from the pre-processing physical model, may be, for example, at least one processor 162 configured to implement one or more physical models based on instructions of a model 164pm from computer-readable program code 166 on a non-transitory computer-usable storage medium such as the memory 164 shown in FIG. 1.

[0114] As an example, in some implementations, the preprocessing physical model can be further generated based on at least one of a second measurement signal obtained from a measurement pad and a third measurement signal obtained from a fault detection pad, as illustrated, for example, by the gray dotted lines from the second measurement pad 406 to the preprocessing physical model 414 and from the fault detection pad 409 to the preprocessing physical model 414 shown in FIG. 4.

[0115] In some implementations, the preprocessing step data can include a preprocessing step measurement signal, as illustrated, for example, by the black dashed line from the preprocessing step measurement signal 404 to the machine learning model 422 shown in FIG. 4.

[0116] The above description is intended to be illustrative and not limiting. For example, the above examples (or one or more aspects thereof) can be used in combination with each other. Other implementations can be used by, for example, those skilled in the art when considering the above description. Also, various features can be grouped together, and fewer features than all the features of a particular disclosed implementation can be used. Accordingly, the following aspects are incorporated into the above description by this specification as examples or implementations, each aspect standing on its own as a separate implementation, and such implementations are intended to be combinable with each other in various combinations or permutations. Accordingly, the spirit and scope of the appended claims should not be limited to the foregoing description.

Claims

1. A method for characterizing a structure on a sample, comprising: obtaining a measurement signal for the structure on the sample from a first measurement device; extracting a measurement result from a first physical model of the structure on the sample based on the measurement signal; determining a parameter of interest of the structure on the sample using a machine learning model based on the measurement result extracted from the first physical model and further based on at least one of data from the measurement signal of the first measurement device not used in extracting the measurement result from the first physical model, a second measurement signal obtained from the second measurement device for the structure on the sample, a process parameter used to generate the structure on the sample, an advanced process control (APC) parameter used to generate the structure on the sample, context data of the structure on the sample, and sensor data from production equipment used to generate the structure on the sample.

2. The method of claim 1, wherein the data from the measurement signal includes at least one data channel including a measurement subsystem defined by at least one of a light source, an optical path directed by optical components, a detector, or a combination thereof, and at least one data chunk including a subset of wavelength, frequency, angle, time interval, or any combination thereof from a complete data set provided by the at least one data channel.

3. The method of claim 1, wherein the machine learning model is generated based on the measurement result extracted by the first physical model of one or more reference samples of the structure and at least one of reference data and experimental design information, and at least one of data from the measurement signal not used in generating the first physical model, a second measurement signal obtained from the second measurement device for the one or more reference samples, a process parameter used to generate the one or more reference samples, an APC parameter used to generate the one or more reference samples, context data for the one or more reference samples, and sensor data from production equipment used to generate the one or more reference samples.

4. The method according to claim 1, wherein the measurement result is extracted from the first physical model for the structure on the sample, further based on the second measurement signal for the structure on the sample from the second measurement device.

5. The method according to claim 1, wherein the measurement result extracted from the first physical model for the structure on the sample is further based on at least one of the process parameters, the APC parameters, the context data, and the sensor data from the production equipment.

6. The method according to claim 1, further comprising extracting a second measurement result from a second physical model of the structure on the sample based on the second measurement signal from the second measurement device, wherein the machine learning model determines the parameter of interest of the structure on the sample further based on the second measurement result extracted from the second physical model.

7. The method according to claim 6, wherein the second measurement result is extracted from the second physical model of the structure on the sample, further based on a third measurement signal for the structure on the sample from a third measurement device.

8. The method according to claim 6, wherein the second measurement result is extracted from the second physical model of the structure on the sample, further based on at least one of the process parameters, the APC parameters, the context data, and the sensor data from the production equipment.

9. The method according to claim 1, wherein the machine learning model determines the parameter of interest of the structure on the sample further based on the second measurement signal from the second measurement device and further based on a third measurement signal for the structure on the sample from a third measurement device.

10. A computer system configured to characterize a structure on a sample, comprising: at least one memory configured to store a measurement signal, a measurement result, a first physical model, a machine learning model, and a parameter of interest of the structure; at least one processor coupled to the at least one memory, the at least one processor being configured to: acquire a measurement signal for the structure on the sample from a first measurement device; extract a measurement result from a first physical model of the structure on the sample based on the measurement signal; Based on the measurement results extracted from the first physical model, and further based on at least one of data from measurement signals from the first measurement device that is not used when extracting the measurement results from the first physical model, second measurement signals acquired from the second measurement device for the structure on the sample, process parameters used to generate the structure on the sample, advanced process control (APC) parameters used to generate the structure on the sample, context data of the structure on the sample, and sensor data from production equipment used to generate the structure on the sample, a computer system configured to determine a parameter of interest of the structure on the sample using a machine learning model.

11. The data from the measurement signal includes at least one data channel including a measurement subsystem defined by at least one of a light source, an optical path directed by optical components, a detector, or a combination thereof, and at least one data chunk including a subset of wavelength, frequency, angle, time interval, or any combination thereof from a complete data set provided by the at least one data channel, the computer system according to claim 10.

12. The machine learning model is generated based on measurement results extracted by the first physical model of one or more reference samples of the structure, at least one of reference data and experimental design information, and at least one of data from measurement signals not used when generating the first physical model, second measurement signals acquired from the second measurement device for the one or more reference samples, process parameters used to generate the one or more reference samples, APC parameters used to generate the one or more reference samples, context data for the one or more reference samples, and sensor data from production equipment used to generate the one or more reference samples, the computer system according to claim 10.

13. The computer system according to claim 10, wherein the measurement result is extracted from the first physical model for the structure on the sample, further based on the second measurement signal for the structure on the sample from the second measurement device.

14. The computer system according to claim 10, wherein the measurement result extracted from the first physical model for the structure on the sample is further based on at least one of the process parameter, the APC parameter, the context data, and the sensor data from the production equipment.

15. The at least one processor is further configured to extract a second measurement result from a second physical model of the structure on the sample based on the second measurement signal from the second measurement device, and the machine learning model determines the parameter of interest of the structure on the sample further based on the second measurement result extracted from the second physical model. The computer system according to claim 10.

16. The computer system according to claim 15, wherein the second measurement result is extracted from the second physical model of the structure on the sample, further based on a third measurement signal for the structure on the sample from a third measurement device.

17. The computer system according to claim 15, wherein the second measurement result is extracted from the second physical model of the structure on the sample, further based on at least one of the process parameter, the APC parameter, the context data, and the sensor data from the production equipment.

18. The machine learning model determines the parameter of interest of the structure on the sample further based on the second measurement signal from the second measurement device and further based on a third measurement signal for the structure on the sample from a third measurement device. The computer system according to claim 10.

19. A system configured to characterize a structure on a sample, means for obtaining a measurement signal for the structure on the sample from a first measurement device; means for extracting a measurement result from a first physical model of the structure on the sample based on the measurement signal; Means for determining a parameter of interest of the structure on the sample using a machine learning model, based on the measurement results extracted from the first physical model and further based on at least one of data from a measurement signal from the first measurement device not used when extracting the measurement results from the first physical model, a second measurement signal acquired from the second measurement device regarding the structure on the sample, process parameters used to generate the structure on the sample, advanced process control (APC) parameters used to generate the structure on the sample, context data of the structure on the sample, and sensor data from production equipment used to generate the structure on the sample. A system comprising:

20. The system according to claim 19, further comprising means for extracting a second measurement result from a second physical model of the structure on the sample based on the second measurement signal from the second measurement device, wherein the machine learning model determines the parameter of interest of the structure on the sample further based on the second measurement result extracted from the second physical model.

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