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 priority and benefit from 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 which are assigned to the assignee of the present application and are incorporated herein by reference in their entireties.

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

[0003] In the semiconductor and other similar industries, metrology techniques such as optical metrology or X-ray metrology are often used to provide non-contact evaluation of samples during processing. In optical metrology, for example, a sample under test is irradiated with light of 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 structure under test. The model may be generated based on the physical properties of the structure, such as its material and nominal parameters, such as film thickness, optical properties of the material, lines, and spacing widths; therefore, it may also be referred to as a physical model. One or more parameters of the model may be varied, and predictive data may be calculated for each parameter variation based on the model, for example, using Rigorous Coupled Wave Analysis (RCWA) or other similar techniques. Measured data may be compared with the predicted data for each parameter variation, for example, in a nonlinear regression process, until a good fit is achieved between the predicted data and the measured data. At that point, the fitted parameters are considered to be an accurate representation of the parameters of the structure under test. However, modeling can be time-consuming, computationally intensive, and expensive, especially for small, complex features. [Overview of the project]

[0005] Physical modeling and machine learning modeling are combined to analyze signals from multiple data sources for hybrid measurement and ecosystems. Signals from data sources include measurement data that may be obtained from different toolsets or at different process steps, as well as additional data sensor data related to process equipment, such as process parameters, advanced process control (APC) parameters, and context data. The predictive capabilities of machine learning are 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 for key and non-key parameters of structures on a sample. Additionally, at least one machine learning model is built and trained to predict parameters of interest based on the extracted measurement results and additional data. Input data for machine learning models includes, for example, raw measurement signals used by one or more physical models, reference data and / or design of experiment (DOE) data, as well as data from different toolsets or the same tools used for physical modeling, such as additional data such as 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 acquiring a measurement signal about the structure on the sample from a first measuring device and extracting measurement results from a first physical model of the structure on the sample based on the measurement signal. The method further includes determining parameters of interest of the structure on the sample using a machine learning model based on the measurement results extracted from the first physical model. The machine learning model may determine parameters of interest based on at least one of the following: data from measurement signals from a first measuring device not used when extracting measurement results from the first physical model; a second measurement signal acquired about the structure on the sample from a second measuring device; process parameters used to generate the structure on the sample; advanced process control (APC) parameters used to generate the structure on the sample; contextual 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, the at least one processor configured to acquire a measurement signal of the structure on the sample from a first measuring device and to extract measurement results 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 parameters of interest of the structure on the sample using a machine learning model based on the measurement results extracted from the first physical model. The machine learning model may determine parameters of interest based on at least one of the following: data from a measurement signal from a first measuring device not used when extracting measurement results from the first physical model; a second measurement signal acquired from a second measuring device about 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; contextual 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, a system configured to characterize a structure on a sample includes means for acquiring a measurement signal of the structure on the sample from a first measuring device, and means for extracting measurement results from a first physical model of the structure on the sample based on the measurement signal. The system further includes means for determining parameters of interest of the structure on the sample using a machine learning model based on the measurement results extracted from the first physical model. The machine learning model may determine parameters of interest based on at least one of the following: data from measurement signals from a first measuring device not used when extracting measurement results from the first physical model, a second measurement signal acquired from a second measuring 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, contextual 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, a method for characterizing a structure on a sample includes, in a pre-processing step, acquiring a pre-processing step measurement signal for the structure on the sample from a measuring device, and in a post-processing step, acquiring a post-processing step measurement signal for the structure on the sample from a measuring device. The method further includes, based on the post-processing step measurement signal, extracting post-processing measurement results from a post-processing physical model of the structure on the sample, and generating pre-processing step data based on at least the pre-processing step measurement signal. The method further includes, based on the post-processing measurement results extracted from the post-processing physical model and the pre-processing step data, determining parameters of interest for the structure on the sample using a machine learning model.

[0010] In one implementation, a computer system configured to characterize a structure on a sample includes at least one processor, the at least one processor configured to acquire a pre-processing step measurement signal from a measuring device for the structure on the sample in a pre-processing step, and to acquire a post-processing step measurement signal from a measuring device for the structure on the sample in a post-processing step. The at least one processor is further configured to extract post-processing measurement results from a post-processing physical model of the structure on the sample based on the post-processing step measurement signal, and to generate pre-processing step data based on at least the pre-processing step measurement signal. The at least one processor is further configured to determine parameters of interest of the structure on the sample using a machine learning model, based on the post-processing measurement results extracted from the post-processing physical model and the pre-processing step data.

[0011] In one implementation, a system configured to characterize a structure on a sample includes, in a pre-processing step, means for acquiring a pre-processing step measurement signal from a measuring device for the structure on the sample, and in a post-processing step, means for acquiring a post-processing step measurement signal from a measuring device for the structure on the sample. The system further includes means for extracting post-processing measurement results from a post-processing physical model of the structure on the sample based on the post-processing step measurement signal, and means for generating pre-processing step data based on at least the pre-processing step measurement signal. The system further includes means for determining parameters of interest of the structure on the sample using a machine learning model based on the post-processing measurement results extracted from the post-processing physical model and the pre-processing step data.

[0012] In one implementation, a method for characterizing a structure on a sample includes acquiring measurement signals from one or more reference samples of the structure from a first measuring device, and generating a first physical model to extract measurement results of the structure on the sample, the first physical model being generated based on measurement signals from one or more reference samples from the first measuring device. The method further includes generating a machine learning model to predict parameters 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 further be generated based on at least one of the following: data from measurement signals from a first measuring device not used in generating the first physical model, second measurement signals acquired for one or more reference samples from a second measuring 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.

[0013] In one implementation, a computer system configured to characterize a structure on a sample includes at least one processor configured to acquire measurement signals from one or more reference samples of the structure from a first measuring device and to generate a first physical model to extract measurement results of the structure on the sample, the first physical model being generated based on measurement signals from one or more reference samples from the first measuring device. At least one processor is further configured to generate a machine learning model to predict parameters 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 the following: data from measurement signals from a first measuring device not used in generating the first physical model, second measurement signals acquired for one or more reference samples from a second measuring 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.

[0014] In one implementation, a system configured to characterize a structure on a sample includes means for acquiring measurement signals of one or more reference samples of the structure from a first measuring device, and means for generating a first physical model to extract measurement results of the structure on the sample, the first physical model being generated based on measurement signals of one or more reference samples from the first measuring device. The system further includes means for generating a machine learning model to predict parameters 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 further be generated based on at least one of the following: data from measurement signals from a first measuring device not used in generating the first physical model, second measurement signals acquired for one or more reference samples from a second measuring 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.

[0015] In one implementation, a method for characterizing a structure on a sample includes, in a pre-processing step, acquiring pre-processing step measurement signals from a measuring device for one or more reference samples of the structure; and in a post-processing step, acquiring post-processing step measurement signals from a measuring device for one or more reference samples of the structure. The method further includes generating a post-processing physical model generated based on the post-processing step measurement signals in order to extract post-processing measurement results for the structure on the reference samples; and generating pre-processing step data based on at least the pre-processing step measurement signals. The method further includes generating a machine learning model to predict parameters of interest for the structure on the sample. The machine learning model is generated based on the post-processing measurement results extracted by the post-processing physical model, at least one of the reference data and experimental design information, and the pre-processing step data.

[0016] In one implementation, a computer system configured to characterize a structure on a sample includes at least one processor, the at least one processor configured to acquire pre-processing step measurement signals from a measuring device for one or more reference samples of the structure in a pre-processing step, and to acquire post-processing step measurement signals from a measuring device for one or more reference samples of the structure in a post-processing step. The at least one processor is further configured to generate a post-processing physical model generated based on the post-processing step measurement signals in order to extract post-processing measurement results for the structure on the reference samples, and to generate pre-processing step data based on at least the pre-processing step measurement signals. The at least one processor is further configured to generate a machine learning model in order to predict parameters of interest for the structure on the sample. The machine learning model is generated based on the post-processing measurement results extracted by the post-processing physical model, at least one of the reference data and experimental design information, and the pre-processing step data.

[0017] In one implementation, a system configured to characterize a structure on a sample includes, in a pre-processing step, means for acquiring pre-processing step measurement signals from a measuring device for one or more reference samples of the structure, and in a post-processing step, means for acquiring post-processing step measurement signals from a measuring device for one or more reference samples of the structure. The system further includes means for generating a post-processing physical model generated based on the post-processing step measurement signals in order to extract post-processing measurement results for the structure on the reference samples, and means for generating pre-processing step data based on at least the pre-processing step measurement signals. The system further includes means for generating a machine learning model to predict parameters of interest for the structure on the sample. The machine learning model is generated based on the post-processing measurement results extracted by the post-processing physical model, at least one of the reference data and experimental design information, and the pre-processing step data. [Brief explanation of the drawing]

[0018] [Figure 1] A schematic diagram illustrating a measuring device that may be used to characterize a sample, as discussed herein, is provided. [Figure 2] This illustrates a workflow for creating offline recipes using a first exemplary scenario that utilizes signals collected from multiple data sources, including different tools and / or sources. [Figure 3] This illustrates an inline measurement workflow using a first exemplary scenario with signals collected from multiple data sources, including different tools and / or sources. [Figure 4] This illustrates a workflow for creating offline recipes using a second exemplary scenario that utilizes signals collected from multiple data sources, including different manufacturing process steps. [Figure 5] This illustrates an inline measurement workflow using a second exemplary scenario that utilizes signals collected from multiple data sources, including different manufacturing process steps. [Figure 6] This section illustrates a flowchart showing a method for characterizing the structure on a sample. [Figure 7] This section illustrates a flowchart showing a method for characterizing the structure on a sample. [Figure 8] This section illustrates a flowchart showing a method for characterizing the structure on a sample. [Figure 9] This section illustrates a flowchart showing a method for characterizing the structure on a sample. [Modes for carrying out 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 may use one or more wavelengths and may include, for example, polarization analysis, reflectivity measurement, and Fourier transform infrared spectroscopy (FTIR). Other types of measurement may also be used, including X-ray measurement, photoacoustic measurement, and electron beam (E-beam) measurement.

[0020] Optical metrology such as thin film measurement and Optical Critical Dimension (OCD) measurement, as well as other types of measurement, occasionally use physical modeling techniques to generate predicted data of a sample that is compared with measurement data obtained from the sample. Using physical modeling techniques, a model of the sample including main parameters and non-main parameters is generated. The model can be obtained based on nominal parameters of the sample, and may include, for example, one or more variable parameters such as layer thickness, line width, spacing width, sidewall angle, and material properties, which can vary over a desired range depending on process parameters used to fabricate the sample under test. The model may further include parameters associated with a tool set, for example, characteristics of an optical system used by a metrology device. The predicted data can be calculated based on parameters of the physical model including variations of variable parameters and characteristics of the metrology 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), and finite element method (FEM). Measurement data obtained from the sample by the metrology device is compared with the predicted data for different parameter variations, for example in a nonlinear regression process, until a best fit is achieved. When the best fit is achieved, the values of the fitted parameters are considered to be an accurate representation of the parameters of the sample.

[0021] Traditionally, modeling requires that preliminary structural and material information about a sample be known in order to generate an accurate representative model of the sample that includes one or more variable parameters. For example, preliminary structural and material information about a sample may include the type of structure of the sample and a physical description with nominal values ​​for various parameters, such as layer thickness, line width, spacing width, sidewall angle, and material properties, along with the range over which these parameters may vary. The model may further include one or more non-variables, i.e., parameters that are not expected to change significantly in the sample during manufacturing. The variable parameters of the model can be adjusted, and predictive data can be generated in real time during a nonlinear regression process, or a library can be pre-generated. Thus, modeling applies physical constraints in the analysis and provides a high level of fidelity to the measurement results accordingly. However, modeling has a high computational cost due to the physical calculations required to generate predictive data. For example, modeling complex 3D structures suffers from slow time to solution (TTS), and the accuracy of the model can be reduced due to the difficulty in fitting data for complex structures.

[0022] Another technique that can be used for generating prediction data of a sample based on measurement data obtained from the sample by a measurement device is machine learning. Machine learning algorithms that can be used for measurement may include, but are not limited to, for example, linear regression, neural networks, deep learning, convolution neural networks (CNN), ensemble methods, support vector machines (SVM), random forests, or a combination of a plurality of models in sequential mode and / or parallel mode. 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 values of structural parameters of interest, and is used to generate and train a machine learning model. The machine learning model is automatically trained using reference data and known values of structural parameters, to find relevant data features, and learns the inherent relationships and connections between input features and output features for making determinations and predictions on new data. The advantages of using machine learning are fast time-to-solution (TTS) and minimal computing resource requirements. However, machine learning requires a large amount of reference data, which is costly and time-consuming to acquire. Without a large amount of reference data, the machine learning model may suffer from overfitting due to lack of physical constraints.

[0023] As semiconductor devices continue to be miniaturized, metrology budgets become tighter. Additionally, complex three-dimensional structures are more frequently adopted to enable continuous device scaling. Advances in semiconductor technology, such as the use of complex three-dimensional structures, bring additional challenges to metrology due to increased modeling complexity, increased parameter correlation, and reduced sensitivity. For example, a signal from a single metrology tool or source may not have sufficient sensitivity to accurately measure parameters of interest for semiconductor process quality control. Ultimately, there may be no single metrology tool that can handle all metrology requirements for state-of-the-art semiconductor devices.

[0024] As discussed herein, computationally efficient data analysis methods can merge multiple data sources and produce more accurate and consistent measurement results than any individual data source could provide, by using data collected from multiple data sources, for example, from multiple toolsets and / or processing steps, and additional data such as sensor data related to samples collected from measurement and / or production equipment. While the analysis method can be flexible to adapt to various data of different natures, it can also maximize the use of existing, well-developed techniques, such as physical modeling or machine learning, for each type of data source, thereby synergizing the strengths of individual measurement techniques.

[0025] As discussed herein, physical modeling and machine learning are combined to analyze multiple data sources for hybrid measurement and ecosystems. The methods described herein create predictive capabilities through data mining and data fusion from multiple data sources, e.g., multiple measurement toolsets, sample data from multiple processing steps, instrument parameters, and production equipment parameters. As an example, at least one physical model may be used to analyze measurement signals from one or more measurement tools, such as spectroscopic ellipsometers, spectroreflectometers, X-ray measurements, photoacoustic measurements, Fourier transform infrared spectroscopy (FTIR), and E-beam measurements, to extract measurement results for key and non-key parameters of a sample. In addition, at least one machine learning model may be constructed and trained to predict parameters of interest. The machine learning model may use input data from one or more of the following: Measurement results from one or more physical models (major and minor parameters); one or more physical models and raw signals used for optional misfitting; data sources from different toolsets, or from the same tools but not included in the physical modeling; process parameters, advanced process control (APC) parameters, contextual data, and sensor data from production equipment. In-line measurement of a sample uses one or more physical models and trained machine learning models to predict the sample parameters of interest based on data obtained from multiple data sources.

[0026] The proposed technique is an efficient and flexible method that synergizes physical modeling and machine learning, possessing controllable computational costs and software and modeling complexity. It can be used to combine and analyze multiple data sources, thus providing the most viable solution with a manageable time to a solution (TTS), improved final results, and overall measurement performance. This method is also versatile and can be applied to the measurement of any device, OCD, thin film, or other type of target.

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

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

[0029] The reflected light can be focused by the lens 114 and received by the detector 150. The detector 150 may be a conventional charge-coupled device (CCD), a photodiode array, a CMOS, or a similar type of detector. The detector 150 may be a spectrometer, for example, when broadband light is used, and the detector 150 may generate a spectral signal, for example, as a function of wavelength. The spectrometer may be used to disperse the entire spectrum of polarized light into spectral components across an array of detector pixels. One or more polarizing elements may be present in the beam path of the optical measurement device 100. For example, the measurement device 100 may include one or more polarizing elements 104 in the beam path in front of the sample 103 and one or both of a polarizing element (analyzer) 112 in the beam path after the sample 103 (or may not include any at all), and may include one or more additional elements 105a and 105b, such as compensators or photoelastic modulators, which may be in front of, after, or both of the sample 103. A complete Müller matrix can be measured by using a spectroscopic ellipsometer with a double rotation compensator between polarizing elements 104 and 112 and the sample.

[0030] The measuring device 100 may include additional measuring devices or be coupled with additional measuring devices. For example, as illustrated, the measuring device 100 may include a second perpendicular incidence measuring tool 170. The second measuring tool 170 may be configured, for example, spectral reflectance measurement, spectral scattering measurement, overlay scattering measurement, interferometry, E-beam measurement, X-ray measurement, FTIR measurement, etc. In some implementations, the measuring device 100 may include additional tools, such as a third (or more) measuring tool. In some implementations, the additional measuring tool may be separate from the measuring device 100.

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

[0032] At least one computing system 160 may be a single computer system or multiple separate or linked computer systems, and it should be understood that, as herein, computing system 160, or at least one computing system 160, may be interchangeably referred to. Computing system 160 may be included in, connected to, or otherwise associated with the measuring device 100 and any additional measuring tools. Each different subsystem of the measuring device 100 may include a computing system configured to perform steps associated with the relevant subsystem. For example, computing system 160 may control the positioning of the sample 103 by controlling the movement of a step 109 coupled to a chuck. For example, step 109 may be capable of horizontal movement in Cartesian (i.e., X and Y) coordinates, or polar (i.e., R and θ) coordinates, or any combination of the two. Step may also be capable of vertical movement along the Z coordinate. Computing system 160 may further control the movement of the chuck 108 to hold or release the sample 103. The computing system 160 may 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 in the first measuring tool 101 and the detector (if any) in the second measuring 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, for example, from the detector 150, as well as from the controller polarizing elements 104, 112, and additional elements 105a, 105b, etc., and from components of the second measuring tool 170 via a transmission medium which may include wired and / or wireless portions. Thus, the transmission medium can function as a data link between the computing system 160 and other subsystems of the measuring device 100. The computing system 160 may be further configured to receive and / or obtain additional information relating to the sample and one or more subsystems of the first measuring tool 101 and production equipment, for example, from a user interface (UI) 168 or via a transmission medium which may include wired and / or wireless components.

[0034] The computing system 160 includes at least one processor 162 together with memory 164, and a UI 168, which are communicatively coupled via a bus 161. Memory 164 or other non-temporary computer-readable storage medium may include its embodied computer-readable program code 166 and may be used by the computing system 160 to cause at least one computing system 160 to control the measurement device 100 and to perform functions including the techniques and analyses described herein. For example, as illustrated, memory 164 may include instructions for causing the processor 162 to perform both modeling and machine learning, and in some implementations, feedforward and / or feedback may be employed as considered herein. Data structures and software code for automatically implementing one or more actions described in this detailed description may be implemented by those skilled in the art in light of this disclosure and may be stored in computer-readable storage medium, such as memory 164, which may 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 may include, but are not limited to, magnetic and optical storage devices such as read-only memory, random-access memory, disk drives, and magnetic tapes. Additionally, the functions described herein may be embodied, in whole or in part, within the circuits of application-specific integrated circuits (ASICs) or programmable logic devices (PLDs), and the functions may be embodied in computer-readable descriptor languages ​​that can be used to create ASICs or PLDs that operate as described herein.

[0035] The computing system 160 may be configured to acquire data about a reference sample from multiple data sources, including, for example, one or both of the measurement tools 101 and 170, and any additional desired measurement tools; data related to the sample, such as reference data and / or DOE data; and data related to the measurement tools and / or processing equipment, such as process parameters, Advanced Parameter Control (APC) parameters, context data, and sensor data from production equipment. The computing system 160 may be configured to generate one or more physical models (model 164pm) about the sample based on measurement data from one or more reference samples, and optionally additional information related to the sample and / or processing equipment; and, as considered herein, to generate and train one or more machine learning models (ML 164ml) about the sample based on one or more physical models and measurement results extracted from the data. In some implementations, measurement data and additional information can be obtained from training samples using different computing systems and / or different measurement devices to generate one or more physical models (model 164pm) and / or generate and train one or more machine learning models (ML164ml), and the resulting physical models and / or trained machine learning models (or parts thereof) can be provided to the computing system 160 via computer-readable program code 166 on a non-temporary computer-usable storage medium such as memory 164.

[0036] The computing system 160 may be used, additionally or alternatively, to obtain data from test samples from multiple data sources. The data may be of the same type as those used to generate physical models and to generate and train the machine learning models discussed above, and the test samples may have the same structure as the reference samples. The computing system 160 may be configured, as discussed herein, to determine one or more parameters 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 (ML164ml).

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

[0038] As discussed herein, in order to characterize a sample, (1) at least one physical-based model is constructed to analyze measurement signals from one or more tools such as spectroscopic ellipsometry (SE), spectroscopic reflectometry (SR), X-ray, E-beam, photoacoustic data, and Fourier transform infrared spectroscopy (FTIR), and from one or more sources, and to extract measurement results for major and minor parameters. In addition, (2) at least one machine learning model is constructed and trained to predict the parameters of interest. The machine learning model may take as input one of more of the following data: a) measurement results from the physical model from (1) (major and minor parameters); b) raw signals from the physical model from (1) and optionally misfits; data sources from different toolsets, or data sources from the same tools in (1) but not included in the physical modeling; process parameters, APC parameters, context data, and sensor data from production equipment. In addition, (3) inline measurements of the sample may be performed using offline-created and trained physical and machine learning models to predict parameters of interest based on data from multiple data sources.

[0039] Figure 2 illustrates, as an example, a workflow 200 for offline recipe creation, e.g., the generation of one or more physical models and one or more machine learning models, using a first exemplary scenario with multiple data sources, e.g., data collected from different tools and / or sources. In Figure 2, solid black arrows indicate processes used in workflow 200, dashed black arrows indicate optional processes where 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 may be collected from any desired measuring device, such as the measuring tool 101 shown in Figure 1, or from any other desired type of measuring device.

[0041] Additionally, data may be obtained from one or more additional data sources. For example, in some implementations, measurement signals 204 and 206 from one or more reference samples may be collected from one or more additional sources or tools, illustrated, for example, as a second source or tool (source 2) and a third source or tool (source 3). Additional measurement signals 204 may be collected from a different measuring device than source 1, such as measuring tool 170 shown in Figure 1, or from any other desired type of measuring device, and measurement signals 206 may be collected from a different measuring device than sources 1 and 2, such as a different type of measurement from either measuring tool 101 or 170, or from any other desired type of measuring device. Additional data 208 related to the reference sample may be collected and used as training data for one or more machine learning models 222, as illustrated by the block arrows. Additional data 208 may include, for example, reference data for sample and DOE data. Reference data may be measurement signals obtained from one or more reference samples by the measurement device, along with values ​​of structural parameters of interest, typically provided by CD-AFM (atomic force microscopy), CD-SEM (scanning electron microscopy), or TEM (transmission electron microscopy). DOE data may be data measured from a set of reference samples processed under intentionally introduced skew conditions, resulting in structural parameters of interest varying by the skewed process conditions in a known pattern. Reference data and / or DOE data may be used as training datasets to train machine learning models to identify relevant data features and learn the inherent relationships and connections between input and output features in order to determine and predict new data. In some implementations, additional data associated with the reference samples may further include wafer condition, precision, tool matching data, etc. Precision data may be data measured repeatedly from the same target multiple times from the same instance of the tool. Precision metrics are another key performance indicator (KPI) of the measurement that demonstrates 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 the same tool type. Tool matching metrics are another measurement KPI that demonstrates the consistency of results measured from different tools of the same type on the same sample. Measurement accuracy (evaluated by matching to a baseline provided by CD-AFM, CD-SEM, TEM, etc., and / or consistency to DOE conditions), precision, and tool matching are typical measurement KPIs. When precision and tool matching data are provided, physical modeling or machine learning models can be optimized not only to tightly match the baseline 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, additional data signals 209 may be used as inputs for physical models or as input features for machine learning models. The additional data signals 209 may relate to sources from which they can be obtained (e.g., Source 1, Source 2, and Source 3), such as process parameters, Advanced Process Control (APC) parameters, context data, and sensor data from production equipment. For example, some process control parameters, such as substrate temperature and chemical concentration for wet etching, can affect the etching rate (how quickly the material is removed from the wafer surface), and the etching rate is one of the important factors for determining the etching depth and CD profile. Some of these parameters, such as temperature, are measured by sensors from production equipment. Other parameters, such as etching time and etching chamber names, are user-controlled parameters. The etching chamber name is an example of context data. Since each etching chamber has its own characteristic distribution of etching profiles across the wafer, knowing this information can help machine learning predict the correct wafer map. An example of APC parameters is atomic force microscope (AFM) results measured from the same sample at different processing steps, including relevant information such as non-major parameters of the structure of interest. Adding non-major parameters as machine learning input features can help improve the machine learning robustness in predicting major parameters. Adding all these relevant parameters as machine learning input features can provide additional information that helps determine the structural parameters of interest controlled by these process parameters and conditions.

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

[0044] In some implementations, multiple physical models may be generated. For example, as illustrated by the gray dotted arrow and gray dotted box, a second physical model 214 may be generated based on a measurement signal 204 from a second source (source 2). In some implementations, additional data may 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, as well as optionally wafer conditions, precision, and tool matching data, may 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) may 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 may 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 may be used to assist in the generation of the second physical model 214. Furthermore, multiple physical models can be optimized independently or co-optimized. For example, in some implementations, as illustrated by the gray dotted lines, the first physical model 212 and the second physical model 214 can be linked such that at least some parameters are coupled across physical models 212 and 214, and the combined parameter space can be searched to fit 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 physical modeling fit 223.

[0045] Using multiple data sources, one or more machine learning models 222 are constructed and trained to predict parameters of interest 225. Machine learning metric indices 227 are developed and reported together with goodness-of-fit 223 from physical modeling to demonstrate the measurement quality of the 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 the 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 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 the second physical model 214, or at least one of any combination thereof. In some implementations, as illustrated by the dotted gray arrows, the input features of the machine learning model 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, a data channel may generally be a measurement subsystem defined by at least one of an energy source such as a light source, an optical path directed by an optical component, a detector, or any combination thereof, and a data chunk may be a subset of wavelength (e.g., used in spectroscopic measurements), frequency (e.g., used in frequency-resolved measurements), angle (e.g., used in angle-resolved measurements), time interval (e.g., used in time-resolved measurements), or any combination thereof from the complete dataset provided by the data channel. For example, the first measurement device may collect perpendicular incidence signals and oblique incidence spectroscopic ellipsometer (SE) signals. The SE signal may be used to generate the first physical model 212, but the Normal Incident signal may not be used because it can be difficult to adapt the Normal Incident signal.Therefore, the normally incident signal can be a data channel used as data for the input features of the machine learning model 222, in addition to physical modeling results generated from a different data channel, e.g., the SE signal. In another example, the same data channel may be divided into multiple data chunks, e.g., signals from different wavelength ranges, some of which may be difficult to fit using physical modeling but can be used as data for the input features of the machine learning model 222.

[0046] The machine learning model 222 is trained using reference data and / or at least a portion of data 208 such as DOE, and optionally wafer conditions, precision, and tool matching data. Data 208 is training data and is used for offline training. For example, the reference data may be a set of signals with labels (e.g., values ​​of key parameters provided by other measurement systems such as CD-SEM, TEM, CD-AFM) (e.g., including any of the measurement results from the first physical model 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 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 data 208 is a set of signals measured from a reference sample processed under intentionally introduced skew conditions (e.g., including any of the measurement results from the first physical model 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 for key parameters. Based on the process skew conditions, the machine learning model 222 is trained to ensure that the predicted key parameter values ​​follow an expected skew pattern. The precision data from data 208 is measurement signals from the same sample but from multiple runs using the same measurement tool (e.g., including any of the measurement results from the first physical model 212, measurement signal 204, measurement signal 206, additional data signal 209, and measurement signal 202). Similarly, the tool-matching data from data 208 consists of signals measured from the same sample but from different instances of the same type of measuring tool (e.g., including any of the measurement results from the first physical model 212, measurement signal 204, measurement signal 206, additional data signal 209, and measurement signal 202). 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 so that the predicted values ​​of the key parameters match signals measured from the same sample but from different runs or different tools. The machine learning model 222 can be trained so that all criteria, matching to reference values, DOE skew conditions, high accuracy, and consistent tool matching are simultaneously met during training, provided all such data are provided.

[0047] Figure 3 illustrates, as an example, a workflow 300 for inline measurement to characterize a sample based on one or more physical models and one or more machine learning models, using a first exemplary scenario with multiple data sources, e.g., signals collected from different tools and / or sources. The one or more physical models and one or more machine learning models may be generated as considered with reference to Figure 2, for example. In Figure 3, solid black arrows indicate processes used in workflow 300, dashed black arrows indicate optional processes where at least one exists, and gray dotted arrows indicate optional processes.

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

[0049] Additionally, data may be obtained from one or more additional data sources. For example, in some implementations, measurement signals 304 and 306 may be collected from one or more additional sources or tools, exemplified, for example, as a second source or tool (source 2) and a third source or tool (source 3). The additional measurement signal 304 may be collected from a different measuring device than source 1, such as the measuring tool 170 shown in Figure 1, or from any other desired type of measuring device, and may be collected from the same measuring device or the same type of measuring device used for source 2 in Figure 2. The measurement signal 306 may be collected from a different measuring device than sources 1 and 2, which may be a different type of measurement from either measuring tool 101 or 170 or any other desired type of measuring device, and may be collected from the same measuring device or the same type of measuring device used for source 3 in Figure 2. Furthermore, in some implementations, additional data signals 309, process parameters, APC parameters, context data, and sensor data from production equipment may be acquired, for example, related to the sources (e.g., source 1, source 2, and source 3).

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

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

[0052] One or more trained machine learning models 322 are used to predict the parameter of interest 325 based on multiple data sources. To demonstrate the measurement quality of the synergistic recipe from physical modeling and machine learning, machine learning measurement metrics 327 and goodness of fit 323 from physical modeling may be reported. The trained machine learning model 322 may be, for example, the same as the machine learning model 222 in Figure 2 after training. As illustrated by the solid black arrows, 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 arrows, the trained machine learning model 322 may further use input features including the measurement signal 304 from a sample collected from a second source (source 2), the measurement signal 306 from a sample collected from a third source (source 3), an additional data signal 309, the measurement results extracted by the second physical model 314 based on the additional signals 304 and / or 306, and optionally at least one of the additional data signal 309, or any combination thereof. In some implementations, as illustrated by the gray dotted arrows, the trained machine learning model 322 may optionally further use input features including a measurement signal 302 from a sample collected from a first source (source 1). In some implementations, the machine learning input features from the measurement signal 302 may include at least one data channel or at least one data chunk that is not used when extracting measurement results from the measurement signal, for example, as considered with reference to Figure 2.

[0053] Figure 4 illustrates, as an example, workflow 400 for offline recipe creation, e.g., for generating one or more physical models and one or more machine learning models, using a second exemplary scenario with multiple data sources, e.g., signals collected from different manufacturing process steps. In Figure 4, solid black arrows indicate processes used in workflow 400, dashed black arrows indicate optional processes where at least one exists, and 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 measuring device. The reference samples may be, for example, OCD target pads or semiconductor devices, and the post-processing step measurement signals 402 are acquired after a desired step in the fabrication of the sample is completed. The post-processing step measurement signals 402 may be collected from any desired measuring device, such as the measuring tool 101 shown in Figure 1, or from any other desired type of measuring device.

[0055] Additionally, pre-processing step measurement signals 404 from one or more reference samples are measured using the same or different measuring devices used to obtain post-processing step measurement signals 402 and used to generate pre-processing step data. The pre-processing step measurement signals 404 are acquired, for example, before the completion of a desired step in sample fabrication. In some implementations, the post-processing step measurement signals 402 and the pre-processing step measurement signals 404 may be combined (e.g., by addition, subtraction, multiplication, or division) to form a pre-adjusted signal 405. Additionally, data 408 related to the reference sample, such as sample reference data and design of experiments (DOE), may be collected. In some implementations, additional data 408 related to the reference sample may further include wafer condition, accuracy, tool matching data, etc. Additionally, data may be acquired from other sources, such as from a second measurement pad 406, from a fault detection pad 409, or any combination thereof. While the first exemplary scenario in Figures 2 and 3 highlighted multiple data sources collected from different measurement devices, the second exemplary scenario illustrates, for example, that multiple data sources may be obtained from different measurement pads or from the same pad at different processing steps. Different measurement pads may be measured from the same or different measurement devices. The pre-processing step measurement signal 404 and the post-processing step measurement signal 402 may be measured on either the designed OCD target or device. The second measurement pad 406 may refer to pre-processing step measurements and / or post-processing step measurements from a measurement pad that is not measured for the pre-processing step measurement signal 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 may refer to an auxiliary signal from a device pad, or vice versa.

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

[0057] In some implementations, multiple physical models may be generated. For example, as illustrated by the gray dotted arrows and gray dotted boxes, the pre-processing physical model 414 may be generated based on the pre-processing step measurement signal 404 from the measurement device. In some implementations, additional data may 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, as well as optionally wafer conditions, precision, and tool matching data, may be used to assist in the generation of the pre-processing physical model 414. In another example, as illustrated by the gray dotted arrows, a signal from a second measurement pad 406 may be used to assist in the generation of the sample pre-processing physical model 414. In yet another example, as illustrated by the gray dotted arrows, a signal from a fault detection pad 409 may be used to assist in the generation of the sample pre-processing physical model 414. In some implementations, data 408, as well as all or any combination of signals from the second measurement pad 406 and the fault detection pad 409, may be used to assist in the generation of the pre-processing physical model 414. Furthermore, multiple physical models can be optimized independently or co-optimized. For example, in some implementations, as illustrated by the gray dotted lines, the post-processing physical model 412 and the pre-processing physical model 414 can be linked so that at least some parameters are coupled 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 measured 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 for the physical modeling.

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

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

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

[0061] Figure 5 illustrates a workflow 500 for inline measurement to characterize a sample based on, for example, one or more physical models and one or more machine learning models, using, as an example, a second exemplary scenario that uses signals collected from multiple data sources, e.g., different manufacturing process steps. The one or more physical models and one or more machine learning models may be generated as discussed, for example, with reference to Figure 4. In Figure 5, solid black arrows indicate processes used in workflow 500, dashed black arrows indicate optional processes where at least one exists, and dotted gray arrows indicate optional processes.

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

[0063] Additionally, the pre-processing step measurement signal 504 from the sample is collected using a measuring device, for example, the same or a different measuring device used to obtain the post-processing step measurement signal 502, and the same or the same type of measuring device used to obtain the pre-processing step measurement signal 404 in Figure 4. The pre-processing step measurement signal 504 is used to generate pre-processing step data. The pre-processing step measurement signal 504 is acquired, 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 (for example, by addition, subtraction, multiplication, or division) to form a pre-adjusted signal 505. Additionally, data may be acquired from other sources, such as from a second measurement pad 506, from a fault detection pad 509, or any combination thereof. The pre-processing step measurement signal 504 and the post-processing step measurement signal 502 may be measured by either the designed OCD target or device. The second measurement pad 506 refers to pre-processing step measurements and / or post-processing step measurements from measurement pads that are not measured for, for example, the pre-processing step measurement signal 504 and the post-processing step measurement signal 502. For example, if the pre-processing step measurement signal 504 and the post-processing step measurement signal 502 are measured on the OCD target, the second measurement pad 506 may refer to auxiliary signals from the device pad, or vice versa.

[0064] Signals and data from multiple data sources may be used to extract measurement results from one or more physical models. For example, as illustrated by the solid black arrow, a post-processing step measurement signal 502 may be used to extract measurement results from a sample from a post-processing physical model 512, which may be the same as the post-processing physical model 412 in Figure 4. In some implementations, additional data may be used to assist in extracting measurement results from the post-processing physical model 512. For example, a pre-tuned signal 505 may be used to assist in extracting measurement results from the post-processing physical model 512 of the sample, as illustrated by the gray dotted arrow. In another example, a signal from a second measurement pad 506 may be used to assist in extracting measurement results from the post-processing physical model 512 of the sample, as illustrated by the gray dotted arrow. In yet another example, a signal from a fault detection pad 509 may be used to assist in extracting measurement results from the post-processing physical model 512 of the sample, as illustrated by the gray dotted arrow. In some implementations, all or any combination of signals from the second pad 506 and the fault detection pad 509 may 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 from a sample. For example, a pre-processing physical model 514 may be used to extract measurement results from a sample based on a pre-processing step measurement signal 504, as illustrated by the gray dotted arrow and gray dotted box. The pre-processing physical model 514 may be the same as the pre-processing physical model 414 in Figure 4. In some implementations, additional data may be used to assist in extracting measurement results from the pre-processing physical model 514. For example, a signal from a second measurement pad 506 may be used to assist in extracting measurement results from the sample pre-processing physical model 514, as illustrated by the gray dotted arrow. In another example, a signal from a fault detection pad 509 may be used to assist in extracting measurement results from the sample pre-processing physical model 514, as illustrated by the gray dotted arrow. In some implementations, all or any combination of signals from the second pad 506 and the fault detection pad 509 may be used to assist in extracting measurement results from the sample pre-processing physical model 514. Furthermore, multiple physical models may be optimized independently or co-optimized. For example, in some implementations, as illustrated by the gray dotted lines, the post-processing physical model 512 and the pre-processing physical model 514 may be linked so that at least some parameters are coupled across the post-processing physical model 512 and the pre-processing physical model 514, and the combined parameter space may be searched to fit the measured signals from one or more data sources. The post-processing physical model 512, and optionally the pre-processing physical model 514, may be configured to provide a goodness of fit 523 for the physical modeling.

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

[0067] Preprocessing step data can be generated in multiple ways based on the preprocessing step measurement signal 504. For example, as illustrated in Figure 5, preprocessing step data can be generated in three different ways from preprocessing step measurement signals 504 labeled 1, 2, and 3, where at least one of (1), (2), or (3), or any combination thereof, may be used. As illustrated by label 1 for the preprocessing step measurement signal 504, preprocessing step data can be generated by combining the preprocessing step measurement signal 504 with a postprocessing step measurement signal 502 to form a pre-tuned signal 505. As illustrated in Figure 5, in some implementations, if a pre-tuned signal 505 is generated, the pre-tuned signal 505 may be (A) provided to 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-tuned signal 505 may be provided to the trained machine learning model 522 as input data. Additionally, as further illustrated in Figure 5, in some implementations, at least one of (A) or (B) may be used with workflow 500. Preprocessing step data may be generated by providing the preprocessing step measurement signal 504 to a preprocessing physical model 514, as illustrated by label 2 for the preprocessing step measurement signal 504, and the trained machine learning model 522 uses the measurement results extracted by the preprocessing physical model 514 as input data. Preprocessing step data may be generated by providing the preprocessing step measurement signal 504 to a trained machine learning model 522 as input data, as illustrated by label 3 for the preprocessing step measurement signal 504.

[0068] In some implementations, as illustrated by the gray dotted arrows, the trained machine learning model 522 may optionally further use input data including post-processing step measurement signals 502.

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

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

[0071] Figure 6 shows an illustrative flowchart illustrating exemplary methods 600 for characterizing structures on a sample in several implementation configurations. In some implementation configurations, exemplary methods 600 may be executed 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 Figure 1, which is 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 implements the workflow 300 illustrated in Figure 3.

[0072] One or more processors may acquire measurement signals about the structure on the sample from the first measuring device (602). For example, measurement signals about the structure on the sample may be acquired by the measuring device 100 shown in Figure 1. Measurement signals about the structure on the sample may be, for example, measurement signal 302 shown in Figure 3. Means for acquiring measurement signals about the structure on the sample from the first measuring device may be, for example, the measuring device 100 shown in Figure 1, as well as at least one memory 164 and at least one processor 162 in the computing system 160 shown in Figure 1.

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

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

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

[0076] In some implementations, a machine learning model may be generated based on measurement results extracted by the first physical model for one or more reference samples of a 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 and the block arrow from additional data 208 to the machine learning model 222 in Figure 2. The machine learning model may further be generated based on at least one of the following, as illustrated by the black dashed line from the measurement signal 204 to the machine learning model 222 in Figure 2 and the additional data signal 209: data from measurement signals not used in generating the first physical model, second measurement signals acquired for one or more reference samples from a second measuring device, process parameters used to generate one or more reference samples, 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.

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

[0078] In some implementations, the first measurement result can be extracted from a first physical model of the structure on the sample, 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 309 to the first physical model 312 in Figure 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 measuring device, and a machine learning model may determine the parameters of interest of the structure on the sample based on the second measurement result extracted from the second physical model, as illustrated, for example, by the second physical model 314, 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 in Figure 3. For example, in some implementations, the second measurement result is further extracted from the second physical model of the structure on the sample based on a third measurement signal about the structure on the sample from a third measuring device, as illustrated, for example, by the gray dotted line from the measurement signal 306 to the second physical model 314 in Figure 3. For example, in some implementations, the second measurement result may be extracted from a second physical model of the structure on the sample based on at least one of process parameters, APC parameters, context data, and sensor data from production equipment, as illustrated, for example, by the black dashed line from the additional data signal 309 to the second physical model 314 in Figure 3. A means for extracting a second measurement result from a second physical model of the structure on the sample based on a second measurement signal from a second measuring device, wherein a machine learning model further determines parameters 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 model 164pm from computer-readable program code 166 on a non-temporary computer-usable storage medium such as memory 164 shown in Figure 1.

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

[0081] Figure 7 shows an illustrative flowchart illustrating exemplary methods 700 for characterizing structures on a sample in several implementation configurations. In some implementation configurations, exemplary methods 700 may be executed 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 Figure 1, which is 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 implements the workflow 500 illustrated in Figure 5.

[0082] One or more processors may acquire a pre-processing step measurement signal about the structure on the sample from a measuring device during the pre-processing step (702). For example, the pre-processing step measurement signal may be acquired by the measuring device 100 shown in Figure 1. The pre-processing step measurement signal may be, for example, the pre-processing step measurement signal 504 shown in Figure 5. Means for acquiring a pre-processing step measurement signal about the structure on the sample from a measuring device during the pre-processing step may be, for example, the measuring device 100 shown in Figure 1, as well as at least one memory 164 and at least one processor 162 in the computing system 160 shown in Figure 1.

[0083] One or more processors may, in the post-processing step, acquire a post-processing step measurement signal about the structure on the sample from a measuring device (704). For example, the post-processing step measurement signal may be acquired by the measuring device 100 shown in Figure 1. The post-processing step measurement signal about the structure on the sample may be, for example, the post-processing step measurement signal 502 shown in Figure 5. Means for acquiring the post-processing step measurement signal about the structure on the sample from a measuring device in the post-processing step may be, for example, the measuring device 100 shown in Figure 1, and at least one memory 164 and at least one processor 162 in the computing system 160 shown in Figure 1.

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

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

[0086] One or more processors may use a machine learning model to determine parameters of interest for a sample based on post-processing measurement results and pre-processing step data extracted from a post-processing physical model (710). A trained machine learning model could 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, for example, any of labels 1, 2, and 3 from the pre-processing step measurement signal 504 shown in Figure 5. Means for determining parameters of interest for a sample using a machine learning model based on post-processing measurement results and pre-processing step data extracted from a post-processing physical model could be, for example, at least one processor 162 configured to implement, for example, one or more physical models based on instructions for model 164ml from computer-readable program code 166 on a non-temporary computer-available storage medium such as memory 164 shown in Figure 1.

[0087] In some implementations, a machine learning model can determine parameters of interest in the structure on a sample based on at least one of the 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 arrow from the pre-processing step measurement signal 504, the signal from the second measurement pad 506, and the signal from the fault detection pad 509 to the machine learning model 522 shown in Figure 5. 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 originate from different measurement pads or from the same pad in different processing steps, and may be measured from the same or different measuring devices.

[0088] In some implementations, the post-processing measurement results are extracted from the post-processing physical model based on at least one of the second measurement signals from the measurement pads and the third measurement signal from the fault detection pad, as illustrated, for example, by the gray dotted 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-tuned signal generated based on a combination of a preprocessing step measurement signal and a postprocessing step measurement signal, as illustrated, for example, by the pre-tuned signal 505 and the gray dotted line from the pre-tuned signal 505 to the machine learning model 522 shown in Figure 5.

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

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

[0092] For example, in some implementations, the preprocessing measurement results are extracted from the preprocessing physical model based on at least one of the second measurement signal obtained from the measurement pads and the third measurement signal obtained from the fault detection pads, as illustrated, for example, by the gray dotted lines from the second measurement pad 506 to the preprocessing physical model 514 and from the fault detection pad 509 shown in Figure 5.

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

[0094] Figure 8 shows an illustrative flowchart illustrating exemplary methods 800 for characterizing structures on a sample in several implementation configurations. In some implementation configurations, exemplary methods 800 may be executed 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 Figure 1, which is 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 implements the workflow 200 illustrated in Figure 2.

[0095] One or more processors may acquire measurement signals for one or more reference samples of the structure from the first measuring device (802). For example, measurement signals for one or more reference samples may be acquired by the measuring device 100 shown in Figure 1. Measurement signals for one or more reference samples may be, for example, measurement signals 202 shown in Figure 2. Means for acquiring measurement signals for one or more reference samples of the structure from the first measuring device may be, for example, the measuring device 100 shown in Figure 1, as well as at least one memory 164 and at least one processor 162 in the computing system 160 shown in Figure 1.

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

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

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

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

[0100] In some implementations, the first physical model may be 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 Figure 2.

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

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

[0103] Figure 9 shows an illustrative flowchart illustrating exemplary methods 900 for characterizing structures on a sample in several implementation configurations. In some implementation configurations, exemplary methods 900 may be executed 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 Figure 1, which is 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 implements the workflow 400 illustrated in Figure 4.

[0104] One or more processors may, in the preprocessing step, acquire preprocessing step measurement signals from a measuring device for one or more reference samples of the structure (902). For example, preprocessing step measurement signals for one or more reference samples may be acquired by the measuring device 100 shown in Figure 1. Preprocessing step measurement signals for one or more reference samples may be, for example, preprocessing step measurement signals 404 shown in Figure 4. Means for acquiring preprocessing step measurement signals from a measuring device for one or more reference samples of the structure in the preprocessing step may be, for example, the measuring device 100 shown in Figure 1, and at least one memory 164 and at least one processor 162 in the computing system 160 shown in Figure 1.

[0105] One or more processors may acquire post-processing step measurement signals from a measuring device for one or more reference samples during the post-processing step (904). For example, post-processing step measurement signals for one or more reference samples may be acquired by the measuring device 100 shown in Figure 1. Post-processing step measurement signals for one or more reference samples may be, for example, post-processing step measurement signals 402 shown in Figure 4. Means for acquiring post-processing step measurement signals from a measuring device for one or more reference samples during the post-processing step may be, for example, the measuring device 100 shown in Figure 1, and at least one memory 164 and at least one processor 162 in the computing system 160 shown in Figure 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, the post-processing physical model being generated based on a post-processing step measurement signal (906). For example, a post-processing physical model generated based on a post-processing step measurement signal may be the post-processing physical model 412 shown in Figure 4. Means for generating a post-processing physical model to extract post-processing measurement results for one or more reference samples, wherein the post-processing physical model is generated based on a post-processing step measurement signal, may be at least one processor 162 configured to implement, for example, one or more physical models based on instructions for model 164pm from computer-readable program code 166 on a non-temporary computer-usable storage medium such as memory 164 shown in Figure 1.

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

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

[0109] In some implementations, the machine learning model may be generated based on at least one of 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, as illustrated by the black dashed arrows from the preprocessing step measurement signal 404, the second measurement signal obtained from the second measurement pad 406, and the fault detection pad 409 shown in Figure 4. 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 may originate from different measurement pads or from the same pad in different processing steps, and may be measured from the same or different measuring devices.

[0110] In some implementations, the post-processing physical model may be 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, for example, by the gray dotted arrows from the second measurement pad 406 and fault detection pad 409 to the post-processing physical model 412 shown in Figure 4.

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

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

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

[0114] For example, in some implementations, the preprocessing physical model may be 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 shown in Figure 4.

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

[0116] The above description is intended to be illustrative and not restrictive. For example, the above examples (or one or more of them) may be used in combination with each other. Other implementations may be used, for example, by those skilled in the art when considering the above description. Also, various features may be grouped together, and fewer features may be used than all the features of a particular disclosed implementation. Accordingly, the following embodiments are incorporated herein as examples or implementations, and each embodiment stands on its own as a separate implementation, and such implementations are intended to be combined with each other in various combinations or rearrangements. Accordingly, the intent and scope of the appended claims should not be limited to the above description.

Claims

1. A method for characterizing the structure on a sample, Obtaining a measurement signal for the structure on the sample from the first measuring device, Based on the measurement signal, the measurement results are extracted from a first physical model of the structure on the sample. A method comprising determining parameters of interest of the structure on a 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 the following: data from measurement signals from a first measuring device not used when extracting the measurement results from the first physical model; a second measurement signal obtained from a second measuring 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.

2. The method according to claim 1, wherein the data from the measurement signal comprises one of the following: at least one data channel comprising a measurement subsystem defined by at least one of a light source, an optical path directed by an optical component, a detector, or a combination thereof; and at least one data chunk comprising a subset of wavelength, frequency, angle, time interval, or any combination thereof from a complete dataset provided by the at least one data channel.

3. The method according to claim 1, wherein 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 in generating the first physical model, a second measurement signal obtained from the second measuring 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.

4. The method according to claim 1, wherein the measurement results are extracted from a first physical model for the structure on the sample, based on a second measurement signal for the structure on the sample from the second measuring device.

5. The method according to claim 1, wherein the measurement results extracted from the first physical model with respect to the structure on the sample are 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 measuring device, wherein the machine learning model determines the parameter of interest of the structure on the sample 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 based on at least one of the following: a third measurement signal for the structure on the sample from a third measuring device, the process parameters, the APC parameters, the context data, and the sensor data from the production equipment.

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

9. A computer system configured to characterize the structure on a sample, At least one memory configured to store measurement signals, measurement results, a first physical model, a machine learning model, and parameters of interest of the structure, The system comprises at least one processor coupled to the at least one memory, and the at least one processor is A measurement signal for the structure on the sample is acquired from the first measuring device. Based on the measurement signal, the measurement result is extracted from the first physical model of the structure on the sample. A computer system configured to determine parameters of interest of the structure on a 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 the following: data from measurement signals from a first measuring device not used when extracting the measurement results from the first physical model; a second measurement signal obtained from a second measuring 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.

10. The computer system according to claim 9, wherein the data from the measurement signal includes at least one data channel comprising a measurement subsystem defined by at least one of a light source, an optical path directed by an optical component, a detector, or a combination thereof, and at least one data chunk comprising a subset of wavelength, frequency, angle, time interval, or any combination thereof from a complete dataset provided by the at least one data channel.

11. The computer system according to claim 9, wherein 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, data from measurement signals not used in generating the first physical model, a second measurement signal obtained from the second measuring 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.

12. The computer system according to claim 9, wherein the measurement results are extracted from a first physical model for the structure on the sample, based on a second measurement signal for the structure on the sample from the second measuring device.

13. The computer system according to claim 9, wherein the measurement results extracted from the first physical model with respect to the structure on the sample are further based on at least one of the process parameters, the APC parameters, the context data, and the sensor data from the production equipment.

14. The computer system according to claim 9, wherein 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 measuring device, the machine learning model determines the parameters of interest of the structure on the sample based on the second measurement result extracted from the second physical model, and the second measurement result is extracted from the second physical model of the structure on the sample based on at least one of a third measurement signal for the structure on the sample from a third measuring device, the process parameters, the APC parameters, the context data, and the sensor data from production equipment.

15. The computer system according to claim 9, wherein the machine learning model determines the parameters of interest of the structure on the sample based on the second measurement signal from the second measuring device and on the third measurement signal for the structure on the sample from the third measuring device.

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