Iterative metrology of product features

Abstract

Disclosed systems and techniques are directed to fast and accurate measurements of features manufactured in semiconductor processing chambers. In one example, the techniques include generating a plurality of nanoscale images of a feature of a manufacturing product, performing a plurality of iterations, each iterations identifying, using a respective nanoscale image, a respective dimension of the feature. At least a subset of the iterations determines the respective dimension by obtaining, using the respective nanoscale image, a measurement of the respective dimension, and adjusting, using two or more previously identified dimensions, the measurement of the respective dimension. Using the identified dimensions, a representation of a quality of the product.

Description

ITERATIVE METROLOGY OF PRODUCT FEATURESTECHNICAL FIELD

[0001] This instant specification generally relates to fabrication of product features in semiconductor materials and devices. More specifically, embodiments disclosed in the instant specification relate to iterative metrology of product features.BACKGROUND

[0002] Manufacturing of modern materials often includes various deposition, etching, plating, polishing, and cleaning techniques, including chemical vapor deposition (CVD) or physical vapor deposition (PVD) techniques, in which atoms of one or more selected types are deposited on a substrate (wafer) held in low or high vacuum environments that are provided by vacuum deposition chambers, plasma etching techniques, in which controlled amounts of materials are removed using chemically-active plasma, and / or the like. Materials manufactured in this manner include monocrystals, semiconductor films, fine coatings, and numerous other substances used in practical applications, such as electronic device manufacturing. Manufactured features, such as patterns, grooves, trenches, holes, ridges, and / or other raised or lowered portions of samples may need to be manufactured to a high degree of precision to ensure that the manufactured devices have correct characteristics. Various inspection techniques are typically deployed to for quality control monitoring and adherence of products to specifications of manufacturing processes. Such inspection techniques include optical inspections (e.g., to monitor larger-scale features and defects), scanning electron microscopy (SEM), tunneling electron microscopy (TEM) techniques, atomic force microscopy (AFM) techniques, etc., capable of measuring finer nanometer-sizes dimensions, and / or other techniques.BRIEF DESCRIPTION OF THE DRAWINGS

[0003] FIG. 1A illustrates an example SEM image of a feature produced as part of a manufacturing process, in accordance with at least one embodiment.

[0004] FIG. IB illustrates schematically application of a Kalman filter for tracking of a feature profile (e.g., a surface, boundary, or an interface of two materials), in accordance with at least one embodiment.

[0005] FIG. 2 is a block diagram illustrating an example system capable of tracking measurement of feature dimensions using Kalman filters for estimating and minimizing measurement errors, in accordance with at least one embodiment.

[0006] FIG. 3 is a diagram illustrating a schematic data flow associated with measurement tracking of feature dimensions using a Kalman filter, in accordance with at least one embodiment.

[0007] FIG. 4 is a schematic illustration of deployment of a dynamic time warping technique for efficient tracking of feature dimensions, in accordance with at least one embodiment.

[0008] FIG. 5 is a flow diagram of an example method of improving measurements of feature dimensions using a Kalman filter, in accordance with at least one embodiment.

[0009] FIG. 6 depicts a block diagram of an example computer system capable of supporting operations of the present disclosure, in accordance with at least one embodiment.SUMMARY

[0010] In one implementation, disclosed is a method that includes generating, by a processing device, a plurality of nanoscale images of a feature of a semiconductor manufacturing product and identifying a plurality of dimensions of the feature. Each dimension of at least a subset of the plurality of dimensions of the feature is identified by obtaining, by the processing device and using a respective nanoscale image of the plurality of nanoscale images, a measurement of a respective dimension, and adjusting, by the processing device and using two or more previously identified dimensions, the measurement of the respective dimension. The method further includes generating, using the plurality of dimensions, one or more representations of a quality of the semiconductor manufacturing product.

[0011] In another implementation, disclosed is a method that includes obtaining, by a processing device, a first set of one or more initial dimensions of a feature of a manufacturing product, wherein the one or more initial dimensions are extracted from one or more images of the feature and using a Kalman filter to determine, by the processing device, a second set of dimensions of the feature. Each of the second set of dimensions is obtained by applying, by the processing device, a state model to a state of the feature to obtain a predicted state of the feature, wherein the state of the feature includes a plurality of previously determined dimensions of the feature. The method further includes measuring, using the one or more images of the feature, a respective dimension of the feature of the second set of dimensions of the feature, and applying a Kalman gain to the predicted state of the feature and the measured respective dimension of the feature to obtain a respective dimension of the feature. Themethod further includes generating, using at least the second set of dimensions, one or more representations of a quality of the manufacturing product.

[0012] In yet another implementation, disclosed is a system that includes a memory storing a plurality of nanoscale images of a feature of a semiconductor manufacturing product, and a processing device communicatively coupled to the memory. The processing device is to identify a plurality of dimensions of the feature. Each dimension of at least a subset of the plurality of dimensions of the feature is identified by obtaining, by the processing device and using the respective nanoscale image, a measurement of the respective dimension, and adjusting, by the processing device and using two or more previously identified dimensions, the measurement of the respective dimension. The processing device is further to generate, using the plurality of dimensions, one or more representations of a quality of the semiconductor manufacturing product.DETAILED DESCRIPTION

[0013] A dimension, e.g., width w, of a particular manufactured feature (ridge, trench, etc.) measured at a specific elevation (height) z relative to a certain reference plane (e.g., the surface of a wafer or film) is often referred to as linewidth, feature width, or critical dimension (CD), especially if adherence of this dimension to a certain range of values near a target dimension vv0is important for a device’s characteristics. In many instances, a whole profile of the feature, w(zy), measured for multiple (e.g., equally spaced) elevations z15z2, . . can be determined. In one example, an SEM image can be generated that consists of multiple SEM slices acquired using a scanning electron beam with an energy associated with penetration of electrons to a given target elevation Zy. FIG. 1A illustrates an example SEM image 100 of a feature 102 produced as part of a manufacturing process, in accordance with at least one embodiment. The SEM image 100 can include an intensity map / (x, Zy) obtained for various lateral coordinates % (or multiple lateral coordinates x and y: I(x,y, Zj), e.g., in the instances of holes or other features localized in two dimensions). The intensity map / (%, Zy) can be used to determine coordinates of reference points xtand x2associated with a CD of feature 102 at a given elevation Zy, e.g., w(z;) = x2— xx. For example, points xxand x2can be associated with locations in the SEM image 100 where intensity I(x, Zj^ undergoes a change from low intensity (dark regions of SEM image 100) to high intensity (light regions of SEM image 100), indicative of a boundary between different materials.

[0014] Inaccuracies in the measurement of the profile w(z) may obscure serious errors in a manufacturing (e.g., etching, deposition, etc.) process or, conversely, indicate an error where no problem is actually present, therefore needlessly disrupting the process. Human operator analysis of SEM (or other types of) images may be accurate and reliable but is slow, given a large number of features that may need to be examined in each sample and a large number of samples. Furthermore, accuracy of human analysis is strongly operator-dependent and may be insufficient in the instances of an inexperienced operator. Automated measurements of feature dimensions are therefore important to maintain a high-quality yield in modern manufacturing processing.

[0015] The existing techniques of manufacturing feature metrology include machine learning models (MLMs) that may be trained using a number of training images. For example, ground truth reference points may be identified, e.g., by an experienced operator, in a training image, and the training image may be provided to an MLM as part of the training process. The MLM may process the training image and output (predict) reference points for the training image. A difference between the predicted reference points and the ground truth reference points may then be determined (e.g., quantified using a suitable loss function) and various parameters of the MLM may be adjusted to reduce this difference until the MLM learns to correctly identify reference points in the training image(s). The MLM may then be used for inference of new images not previously seen during the training process.

[0016] MLM-based embodiments, however, have some limitations. In particular, proper training of an MLM may require large training datasets with maximal possible number of variations in feature dimensions. Such large training datasets may be difficult, expensive, and time-consuming to collect while various new types of defects and / or variations may result in inaccurate inferencing. MLM-based techniques may be incapable of estimating local (e.g., elevation-specific) measurement inaccuracies (errors) and may smooth out local profile changes while missing subtle profile changes / signatures. Additionally, MLM-based techniques typically provide little in the way of explanations of underlying mechanisms and reasons for various local profile changes (e.g., presence of structural defects, errors in etching process settings, and / or the like).

[0017] Aspects and embodiments of the present disclosure address these and other challenges of the existing manufacturing feature metrology by providing for systems and techniques that sequentially track feature dimensions w(z;) across a set of elevations z15z2,. . . using a Kalman filter to evaluate and minimize measurement errors. In some embodiments, a state of a feature profile w(z;) may be initiated by performing an initial measurement, e.g., for z — z0. FIG. IB illustrates schematically application 110 of a Kalman filter for tracking of a feature profile (e.g., a surface, boundary, or an interface of two materials), in accordance with at least one embodiment. More specifically, a set of two or more (three, in the example shown in FIG. IB) reference points (also referred to, for brevity, as simply points herein and depicted with black circles), x^z^, x(z2), and x(z3), obtained using previous measurements for elevations z1?z2, and z3, can be used to predict a new point x(z4) (a priori point, depicted with the white circle) for the next elevation, z4. For example, the prediction can be made using a polynomial interpolation model, e.g., by identifying a parabolic curve that passes through the three points %(z4), x(z2), and x(z3). The obtained parabolic function then predicts the new point x(z4) for the new elevation z4. An actual measurement taken for this elevation may identify point xm(z4) (depicted with the gray circle) that is different from the predicted point x(z4). The Kalman filter that tracks measurements and the measurement errors can then determine a relative weight given to the predicted point x(z4) and the measured point xm(zr) to determine the best approximation x(z4) that balances the model predictions with the actual measurements. This best (a posteriori) approximation is then taken as the next point of the feature profile. Numerous other embodiments of Kalman filterbased tracking of feature profiles are disclosed herein. In some embodiments, the measured points xmcan be identified using dynamic time warping (DTW) that maps measurement intensity data 7(x, z4) to one or more previous intensities 7(x, z3), 7(x, z2), etc., for improved accuracy of measured xm(z7).

[0018] The advantages of the disclosed systems and techniques include (but are not limited to) fast and accurate automated (or largely automated) measurements of complex features and structures encountered in product manufacturing. The use of Kalman filters further enables systematic estimation and statistical analysis of uncertainties of the measurement process, e.g., quantified via a difference between a posteriori estimates x and measured points xm(or between a posteriori estimates and a priori predictions x).

[0019] FIG. 2 is a block diagram illustrating an example system 200 capable of tracking measurement of feature dimensions using Kalman filters for estimating and minimizing measurement errors, in accordance with at least one embodiment. System 200 (e.g., using automated measurement component 214) can perform one or more of the methods describedherein (e.g., method 500 of FIG. 5). System 200 may include an automated measurement server 210, a client device 220, manufacturing equipment 224, sensors 226, metrology equipment 228, and / or data store 240.

[0020] In some embodiments, one or more of automated measurement server 210, client device 220, manufacturing equipment 224, sensors 226, metrology equipment 228, and / or data store 240 are coupled to each other via a network 230. In at least one embodiment, automated measurement server 210 trains one or more machine learning models to perform measurements of images of one or more target types (e.g., SEM images, TEM images, etc.). In at least one embodiment, automated measurement server 210 implements one or more trained machine learning models (e.g., deployed as part of location determiner 215) to determine locations in images where measurements are to be taken. In embodiments, images to be measured may be generated during and / or after product (e.g., wafer, substrate, film, etc.) manufacturing.

[0021] In some embodiments, network 230 is a public network that provides client device 220 with access to the automated measurement server 210, data store 240, and / or other publicly available computing devices. In some embodiments, network 230 is a private network that provides client device 220 access to manufacturing equipment 224, sensors 226, metrology equipment 228, data store 240, automated measurement server 210and / or other privately available computing devices. In some embodiments, network 230 includes one or more Wide Area Networks (WANs), Local Area Networks (LANs), wired networks (e.g., Ethernet network), wireless networks (e.g., an 802.11 network or a Wi-Fi network), cellular networks (e.g., a Long-Term Evolution (LTE) network), routers, hubs, switches, server computers, cloud computing networks, and / or a combination thereof.

[0022] In some embodiments, client device 220 includes a computing device such as Personal Computer (PC), laptop, mobile phone, smart phone, tablet computer, netbook computer, etc. In some embodiments, client device 220 includes a local automated measurement component 214, which can operate similarly to automated measurement component 214 of automated measurement server 210. Client device 220 includes an operating system that allows users to consolidate, generate, view, and / or edit data (e.g., image data), provide directives to the automated measurement server 210, and / or the like.

[0023] Manufacturing equipment 224 can produce products, such as substrates, wafers, semiconductors, electronic devices, etc., following execution of one or more recipes and / or processes to substrates over any appropriate period of time. Manufacturing equipment 224 can include one or more sensors configured to capture data (e.g., property data such as imagedata) for a substrate before, during and / or after a substrate processing operation. For example, the one or more sensors can be configured to capture image data and / or images of substrates (e.g., cross-sectional images, SEM images, TEM images, AFM images, optical images, overlay images, infrared images, reflectance images, transmittance images, etc.), spectral data, non-spectral data, and / or the like for a portion of a substrate before, during, or after a substrate processing operation.

[0024] Manufacturing equipment 224 can perform a process on a product at a processing chamber. Examples of processes include a deposition process to deposit one or more layers of film on a surface of the substrate, an etch process to form a pattern on the surface of the substrate, etc. Manufacturing equipment 224 can perform each process according to a process recipe. A process recipe defines a particular set of operations to be performed on the substrate during the process and can include one or more settings associated with each operation. One or more processes performed on a substrate form structures on the substrate. The structures may have one or more regions that may have one or more critical dimensions (e.g., that can be labeled). For example, an image of a structure may have labels designating locations of a coating, a gate, a drain, a mask, and / or other structures.

[0025] In some embodiments, manufacturing equipment 224 includes sensors 226 that are configured to generate data (e.g., image data) associated with a substrate processed by manufacturing equipment 224. For example, sensors 226 can include one or more scanning electron microscopy (SEM) sensors, optical sensors, atomic force microscopy sensors, overlay sensors, infrared sensors, reflectance / transmittance sensors, and / or the like. Sensors 226 may take measurements before, during, and / or after a processing operation, an etch operation, deposition operation, and / or the like.

[0026] Metrology equipment 228 can provide metrology data (e.g., image data) associated with substrates processed by manufacturing equipment 224. The metrology data can include one or more images of a processed substrate, such as cross-sectional images, top- down images, SEM images, optical images, atomic force microscopy images, overlay images, infrared images, reflectance images, transmittance images, and so on. In some embodiments, the metrology data can further include a value of one or more types of surface profile property data (e.g., a critical dimension of one or more features included on a surface of the substrate, a critical dimension uniformity across the surface of the substrate, an edge placement error, etc.). The metrology data can be of a finished or semi-finished product. The metrology data can be different for each substrate. Metrology data can be generated using, for example, reflectometry techniques, ellipsometry techniques, SEM, TEM, AFM techniques,and so forth. In some embodiments, metrology equipment 228 includes an instance of automated measurement component 214 and can generate automated measurements of generated images during and / or after generation of the images.

[0027] In some embodiments, automated measurement server 210 includes one or more computing devices such as a rackmount server, a router computer, a server computer, a personal computer, a mainframe computer, a laptop computer, a tablet computer, a desktop computer, Graphics Processing Unit (GPU), accelerator Application-Specific Integrated Circuit (ASIC) (e.g., Tensor Processing Unit (TPU)), etc.

[0028] Automated measurement server 210 can include an automated measurement component 214, which can additionally (or alternatively) be included in client device 220 and / or metrology equipment 228. In some embodiments, automated measurement component 214 identifies image data 242 to be processed. In some embodiments, automated measurement component 214 automatically determines locations in image data 242 to be measured, and automatically generates measurements based on such determined locations. In some embodiments, automated measurement component 214 deploys location determiner 215, which includes one or more trained machine learning models to determine the locations to be measured, e.g., locations of patterned features in image data 242. In embodiments, location determiner 215 is trained using supervised or semi-supervised machine learning (e.g., historical image data labeled with locations to be measured, etc.).

[0029] In some embodiments, manufacturing equipment 224 (e.g., deposition chamber, cluster tool, wafer backgrind systems, wafer saw equipment, die attach machines, wirebonders, die overcoat systems, molding equipment, hermetic sealing equipment, metal can welders, deflash / trim / form / singulation (DTFS) machines, branding equipment, lead finish equipment, and / or the like) is part of a substrate processing system (e.g., integrated processing system). Manufacturing equipment 224 includes one or more of a controller, an enclosure system (e.g., substrate carrier, front opening unified pod (FOUP), autoteach FOUP, process kit enclosure system, substrate enclosure system, cassette, etc.), a side storage pod (SSP), an aligner device (e.g., aligner chamber), a factory interface (e.g., equipment front end module (EFEM)), a load lock, a transfer chamber, one or more processing chambers, a robot arm (e.g., disposed in the transfer chamber, disposed in the front interface, etc.), and / or the like. The enclosure system, SSP, and load lock mount to the factory interface and a robot arm disposed in the factory interface is to transfer content (e.g., substrates, process kit rings, carriers, validation wafer, etc.) between the enclosure system, SSP, load lock, and factory interface. The aligner device can be disposed in the factory interface to align substrates. Theload lock and the processing chambers may mount to the transfer chamber, and a robot arm disposed in the transfer chamber is to transfer content (e.g., substrates, process kit rings, carriers, validation wafer, etc.) between the load lock, the processing chambers, and the transfer chamber. In some embodiments, manufacturing equipment 224 includes components of substrate processing systems. In some embodiments, image data 242 of a substrate depicts results from the substrate undergoing one or more processes performed by components of the manufacturing equipment 224 (e.g., deposition, etching, heating, cooling, transferring, processing, flowing, etc.).

[0030] In some embodiments, sensors 226 provide image data 242 of a substrate processed by manufacturing equipment 224 and / or one or more structures of the substrate (e.g., transistors, interconnects, gates, contacts, memory cells, etc.). In some embodiments, sensors 226 include one or more of a metrology tool such as optical and imaging systems, imaging stations, and / or the like. In some embodiments, sensors 226 include one or more of a metrology tool such as ellipsometers (used to determine the properties and surfaces of thin films by measuring material characteristics such as layer thickness, optical constants, surface roughness, composition, and optical anisotropy), ion mills (used to prepare heterogeneous bulk materials when wide areas of material are to be uniformly thin), capacitance versus voltage (C-V) systems (used to measure the C-V and capacitance versus time (C-t) characteristics of semiconductor devices), interferometers (used to measure distances in terms of wavelength, and to determine wavelengths of particular light sources), source measure units (SME) magnetometers, profilometers, wafer probers (used to test a semiconductor wafer before it is separated into individual dies or chips), critical-dimension scanning electron microscope (CD-SEM, used to ensure the stability of the manufacturing process by measuring critical dimensions of substrates), reflectometers (used to measure the reflectivity and radiance from a surface), resistance probes (used to measure the resistivity of thin-films), resistance high-energy electron diffraction (REIEED) system (used to measure or monitor crystal structure or crystal orientation of epitaxial thin-films of silicon or other materials), X- ray diffractometers (used to unambiguously determine crystal structure, crystal orientation, film thickness and residual stress in silicon wafers, epitaxial films, or other substrates), and / or the like.

[0031] In some embodiments, image data 242 is used for assessment of equipment health and / or product health (e.g., product quality). For example, image data 242 may be image data used to take measurements of products (e.g., manufactured wafers). In some embodiments, , image data 242 is received over a period of time.

[0032] In some embodiments, sensors 226 and / or metrology equipment 228 provide image data 242, which may include one or more of scanning electron microscope (SEM) images, energy dispersive x-ray (EDX) images, spatial location data, chip layer data, chip layout data, edge data, gray level data, signal to noise data, spacing data, optical image data, and / or the like.

[0033] In some embodiments, image data 242 includes data that describes visual attributes of an image that may be organized in a matrix or multidimensional array. In some embodiments, image data allows for digital representation, processing, and analysis of pixellevel information of an image. In some embodiments, measurement data 244 is generated from image data 242. Measurement data 244 may relate to measurements of a substrate, such as critical dimension. In some embodiments, measurements of image data 242 includes size attribute data (e.g., data describing the size of attributes of a substrate). In some embodiments, measurements of image data 242 includes dimensional attribute data (e.g., data that describes the dimensions of attributes of a substrate). In some embodiments, image data 242 includes SEM images (e.g., images captured by a scanning electron microscope using a focused beam of electrons to scan a surface of a substrate to create a high-resolution image). In some embodiments, image data 242 includes EDX images (e.g., images generated from data that is collected using an x-ray technique to identify the elemental composition of materials). In some embodiments, measurements of image data 242 includes defect distribution data (e.g., data that describes the distribution, such as spatial, temporal, etc., of defects on a substrate). In some embodiments, measurements of image data 242 includes spatial location data (e.g., data that describes the spatial location of attributes, defects, elements, etc. of a substrate). In some embodiments, image data 242 includes grey level data (e.g., data that describes the brightness of a pixel of an image of a substrate) and signal to noise data (e.g., data that describes the signal to noise ratio of a substrate measure with, for example, spectrometry equipment).

[0034] In some embodiments, image data 242 is processed, e.g., by the client device 220 and / or by the automated measurement server 210. In some embodiments, processing of image data 242 includes generating features (e.g., measurements, critical dimensions, etc.). In some embodiments, the features are a measurement or a pattern in image data 242 (e.g., slope, width, height, peak, etc.) or a combination of values from image data 242.

[0035] In some embodiments, metrology equipment 228 can be included as part of manufacturing equipment 224. For example, metrology equipment 228 can be included inside of or coupled to a processing chamber and configured to generate metrology data such asimage data 242 of a substrate before, during, and / or after a process (e.g., a deposition process, an etch process, etc.) while the substrate remains in the processing chamber. In some instances, metrology equipment 228 can be referred to as in-situ metrology equipment. In another example, metrology equipment 228 can be coupled to another station of manufacturing equipment 224. For example, metrology equipment can be coupled to a transfer chamber, a load lock, or a factory interface.

[0036] In some embodiments, sensors 226 can be included as part of the manufacturing equipment 224. For example, sensors 226 can be included inside of or coupled to a processing chamber and configured to generate sensor data of a substrate before, during, and / or after a process (e.g., a deposition process, an etch process, etc.) while the substrate remains in the processing chamber. In some instances, sensors 226 can be referred to as in- situ sensors. In another example, sensors 226 can be coupled to another station of manufacturing equipment 224. For example, sensors can be coupled to a transfer chamber, a load lock, or a factory interface.

[0037] In some embodiments, metrology equipment 228 (e.g., ellipsometry equipment, imaging equipment, spectroscopy equipment, etc.) is used to determine metrology data (e.g., image data, inspection data, spectroscopy data, ellipsometry data, material compositional, optical, or structural data, etc.) corresponding to substrates produced by manufacturing equipment 224 (e.g., substrate processing equipment). In some examples, after manufacturing equipment 224 processes substrates, the metrology equipment 228 is used to inspect portions (e.g., structures, regions, layers, etc.) of the substrates. In some embodiments, the metrology equipment 228 performs scanning acoustic microscopy (SAM), ultrasonic inspection, x-ray inspection, and / or computed tomography (CT) inspection.

[0038] In some examples, after manufacturing equipment 224 deposits one or more layers on a substrate, metrology equipment 228 is used to determine quality of the processed substrate (e.g., dimensions of features and / or structures, uniformity of features and / or structures, and / or the like). In some embodiments, metrology equipment 228 includes an imaging device (e.g., SAM equipment, ultrasonic equipment, x-ray equipment, CT equipment, and / or the like). In some embodiments, image data 242 includes sensor data from sensors 226 and / or metrology data from metrology equipment 228 located in-situ (inside the processing chamber).

[0039] In some embodiments, performance data 246 is measured by sensors 226 and / or metrology equipment 228 and may be associated with measurement consistency and accuracy for manufactured substrates.

[0040] In some embodiments, measurement data 244 can be generated for one or more images of image data 242. Measurement data 244 can include measurements of structures, critical dimensions, and / or other properties of features that appear in image data 242. In embodiments, measurement data 244 can be automatically generated for one or more target images by automated measurement component 214 responsive to automated measurement component 214 receiving and processing a labeled template image and the one or more target images.

[0041] In some embodiments, data store 240 is memory (e.g., random access memory), a drive (e.g., a hard drive, a flash drive), a database system, or another type of component or device capable of storing data. In some embodiments, data store 240 includes multiple storage components (e.g., multiple drives or multiple databases) that span multiple computing devices (e.g., multiple server computers). In some embodiments, data store 240 stores one or more of image data 242, measurement data 244, and / or performance data 246.

[0042] In some embodiments, performance data 246 can be associated with measurement consistency and accuracy for manufactured substrates (e.g., for measurement repetition between structurally similar images). For example, performance data 246 can be indicative of a critical dimension measurement. In some embodiments, at least a portion of the performance data 246 is associated with a quality of measurements of substrates produced by the manufacturing equipment 224. Performance data 246 can be indicative of whether a measurement is properly and / or accurately taken. For example, two images may be structurally similar but are not identical. Performance data 246 can indicate that a measurement taken of a first image is similarly taken of a second structurally similar but not identical image.

[0043] In some embodiments, at least a portion of performance data 246 is based on metrology data (e.g., image data) from metrology equipment 228 or sensors 226. In some embodiments, at least a portion of performance data 246 is based on inspection of the substrates. In some embodiments, performance data 246 includes user input (e.g., via client device 220) indicating a quality of the substrates. In some embodiments, performance data 246 includes an indication of an absolute value (e.g., inspection data of the substrates indicates missing the threshold data by a calculated value, drift value misses the threshold drift value by a calculated value) or a relative value (e.g., inspection data of the measurement data 244 indicates missing the threshold data by 5%, drift value misses threshold drift value by 5%). In some embodiments, performance data 246 is indicative of meeting a thresholdamount of error (e.g., at most 5% error in measurement data following a repeating a measurement, at most 5% error in production, etc.).

[0044] Measurement consistency and accuracy is beneficial to ensure reliable analysis and decision-making in semiconductor manufacturing processes. Taking manual measurements of each instance of a particular attribute in different images is time-consuming, labor-intensive, and prone to error. By providing image data 242 to automated measurement component 214 and receiving measurement data 244 from the automated measurement component 214, system 200 has the technical advantage of avoiding the time-consuming, labor-intensive, and error prone process of manually measuring each instance of a particular attribute in different images.

[0045] In some embodiments, automated measurement component 214 includes a Kalman filter-based profile tracker 216 to implement tracking of measurements of various manufactured features using Kalman filters. Operations of a Kalman filter (e.g., measurement stage) can be supported by dynamic time warping module 217 that maps image intensity data between images associated with different elevations, e.g.,Kalman filter-based profile tracker 216 (and DTW warping module 217) can operate on image data 242 and generate measurement data 244, including but not limited to profiles w(z;) of any product features of interest and consequence for one or more processes carried out using manufacturing equipment 224. Output of Kalman filter-based profile tracker 216 can be stored as measurement data 244. In some embodiments, outputs of Kalman filter-based profile tracker 216 are further processed using a statistics module 218, e.g., to compute various statistical metrics associated with measured features. The statistical metrics can include a minimum, maximum, range, average, median, mode, standard deviations, skewness, kurtosis, and / or any other suitable statistical metrics. Output of statistics module 218 can be stored as performance data 246 representative of a quality of processing operations carried out using manufacturing equipment 224.

[0046] Various operations of automated measurement component 214 can be performed by a suitable processor 21 1. Data input into processor 211 and data generated by processor 21 1 can be stored in memory 212 communicatively coupled to processor 21 1 . In some embodiments, processor 21 1 can be or include a central processing unit (CPU), a graphics processing unit (GPU), a parallel processing unit (PPU), field-programmable gate array (FPGA), application-specific integrated circuit (ASIC), and / or any other suitable processing device, or a combination thereof. Memory 212 can be or include a random-access memory(RAM), flash memory, dynamic random-access memory (DRAM), such as synchronous DRAM (SDRAM), etc.), a static memory, a static random access memory (SRAM), a flash memory, and / or any combination thereof. In some embodiments, instructions that are used to implement operations of Kalman filter-based profile tracker 216 (and DTW warping module 217) are stored in the read-only memory (ROM) portion of memory 212.

[0047] FIG. 3 is a diagram illustrating a schematic data flow associated with measurement tracking 300 of feature dimensions using a Kalman filter, in accordance with at least one embodiment. In some embodiments, measurement tracking 300 can be performed using one or more components of system 200 of FIG. 1, e.g., by automated measurement component 214 of automated measurement server 210, client device 220, metrology equipment 228, and / or other suitable components not shown in FIG. 2. Measurement tracking 300 can begin with receiving any suitable products for inspection, including but not limited to bare wafers, patterned wafers, chemically and / or mechanically polished wafers, wafers with one or more deposited films, wafers with one or more deposited and / or etched structures, which can include raised portions (e.g., ridges, terraces, etc.), lowered portions (e.g., holes, dips, trenches, grooves, etc.), or any combination thereof. Received products can include products that have undergone one or more processing operations, including but not limited to chemical mechanical polishing (CMP), chemical vapor deposition (CVD), physical vapor deposition (PVD), plasma-enhanced CVD, plasma-enhanced PVD, sputter deposition, atomic layer CVD, combustion CVD, catalytic CVD, evaporation deposition, molecular- beam epitaxy techniques, and / or the like. The processing operations can be performed under any applicable pressure, including high-vacuum pressure, low-vacuum pressure, atmospheric pressure, above-atmospheric pressure, and / or the like. The processing operations can be performed under any applicable temperature, e.g., above room temperature (including but not limited to plasma environment), room temperature, below room temperature, at or about liquid nitrogen temperature, below liquid nitrogen temperature, and / or the like.

[0048] The received sample can undergo feature location 302 (e.g., performed using location determiner 215). In some embodiments, feature location 302 can be performed manually by a human operator. In some embodiments, feature location 302 can be performed automatically, e.g., using a mask of features associated with a type of the received product, a trained machine learning model, a set of heuristics, and / or using some other tools or a combination of the tools. In some embodiments, feature location 302 can be performed via a combination of manual and automatic operations. For example, a human operator can identify regions of the product that are to undergo inspection and the one or more automated featurelocation tools can identify individual features to be inspected. The subsequent description will refer to inspection of a single feature, for conciseness, but it should be understood that multiple features (including features of different types) can be similarly inspected within any particular received product.

[0049] A location identified by feature location 302 can undergo initial profile measurement 310, which can include obtaining one or more SEM images, TEM images, EDX images, AFM images, ion beam images, and / or any other type of high-resolution measurements. In some embodiments, initial profile measurement 310 can include lower- resolution images, e.g., one or more optical images. As depicted schematically in FIG. 3, initial profile measurement 310 of a feature 312 (e.g., a trench) can include an intensity map, e.g., SEM intensity, or any other suitable measurement for an initial measurementlocation z0(e.g., elevation relative to a specific reference plane, e.g., surface of the product, such as a surface of wafer or film). Initial profile measurement 310 can be used to identify one or more target characteristics of feature 312, including but not limited to a feature profile w(z0) for the initial location. In some embodiments, identifying feature profile w(z0) can include identifying multiple reference points, For example, in theinstance of a simple trench or hole, the feature profile can be defined by two reference points, In m°re complex features, e.g., a hole partially filled with adifferent material (e.g., of the type illustrated in FIG. 1A), more than two reference points can be identified, e.g., as many reference points as there are material boundaries across the elevation z0. Correspondingly, each of the reference points can serve as a seed for(start of) a respective curve with the full set of all curves referred to,collectively, as the feature profile. In some embodiments, the reference points for the initial location z0can be obtained manually, by a human operator, or using any suitable automated tools, e.g., one or more machine learning models.

[0050] For brevity and conciseness, operations of measurement tracking 300 will be described with respect to a single curve, referenced as simply x(z) herein (subscript omitted). Initial profile measurement 310 initializes a state to be tracked using a Kalman filter across multiple additional measurement locations etc. For each of these locations, thestate may depend on the history of previous measurements made for the same feature 312. This history captures preceding evolution of the feature profile and can be used to predict the next data point or a set of data points, as part of a state model. More specifically, in one embodiment of a state model, the state after j-th measurement can depend on the most recentcoordinate x(z7) and on the rate of change (e.g., represented by the derivative) of this coordinate x'(z7):The derivative can be determined based on at least two recent coordinates of the reference points,

[0051] In the above example, profile state prediction 320 (a priori state estimate, indicated with the bar) can be obtained using the linear model as,In other embodiments, the state of feature profile can include more than two previous coordinates, e.g., n + 1 the most recent values,StateIn such embodiments, profile state prediction 320 can be performed as follows. A degree-n polynomial can be defined with n + 1 coefficients {ak} that aredetermined using the system of linear equations(In some embodiments, finding a vector of the polynomial coefficients {ak} can be performed using a matrix multiplication with asuitably chosen (and precomputed) matrix M and the vecto of the previous n + 1coordinates tracked as part of the feature state). Profile state prediction 320 is then obtained by extrapolating the obtained polynomial to the next elevation

[0052] In some embodiments, profile state prediction 320 can further account for an uncertainty q of the state model, e.g.,fe fc ) (^ )For example, the model uncertainty q(z) can be a white noise with the varianceQ, where Q is an empirically selected parameter, which can be specific to a particular type of features being inspected.[00531 Operations of measurement tracking 300 can continue with performing a state measurement 330 that uses one or more techniques to measure ), e.g., as illustratedschematically in FIG. 1A. In some embodiments, a measurement o ) can beperformed by simply identifying a point x where the intensity map crosses a predetermined threshold hand then taking that point a In some embodiments,measurement of can be performed by using a trained machine learning modelwhose input includes the intensity map and the output is the position of the boundary between two regions of different intensity In some embodiments,the same MLM can simultaneously output coordinates of multiple curves (e.g., corresponding to various boundaries between different materials of feature 312). In some embodiments, measured points can be identified using additional techniques, such as dynamictime warping (DTW) 332 that maps measurement intensity data7to one or more previous intensities , and so on, for improved accuracy of measured, as disclosed in more detail in conjunction with FIG. 4 below.

[0054] The obtained a priori estimate (prediction) of the coordinate and themeasured coordinate is then used to generate a posteriori estimate that isbased on Kalman gain computation 340. For example, a posteriori estimate x(z7 +1) can be a weighted average of the a priori estimate of the position7and the measured positionwhere the weight Z is the Kalman gain selected to minimize the statisticalmeasurement error ] between a posteriori estimate7whichis accepted as the most likely actual coordinate, and its measured value x

[0055] The Kalman gaincan be computed by tracking, across different elevations zJa measurement uncertainty (also known as covariance) PIn one embodiment, the Kalman gain K(Z7 + 1) can be computedas follows:where R is a measurement noise parameter characterizing intrinsic accuracy of the measurement process, which can also be approximated with a white noise, e.g., similar to how the model uncertainty is characterized with parameter Q. The measurement noise parameter R can also be empirically selected, e.g., based on a specific type of measurements being used, and can be different for SEM measurements than for TEM measurements, in one example.

[0056] The measurement uncertainty1can be tracked, by a covariance update 350,across different elevations , e.g., using the following recursive condition,based on the measurement uncertaintyfrom the previous tracking iteration. The updated measurement uncertainty can then be stored for the next7iteration. Profile state update 360 then adds the new determined location to the stateof the feature. The oldest location can then be dropped from the state: Updated State =Further iterations of measurement tracking 300 can continue — as depicted schematically with the dashed arrow — for further elevations , until the final elevation zNof feature312 has been processed. The output of measurement tracking 300 then includes a set of all a posteriori locations collectively representing the feature profile (or aportion of the feature profile when the feature profile includes multiple curves).[0057J In some embodiments, the set of elevations z can be equally spacedwith the spacing fixed prior to the start of tracking 300. In someembodiments, the elevations need not be equally spaced and can be setdynamically, with finer spacings (smaller values Az) used in regions where feature profile changes quickly with the elevation z and coarser spacings (larger values A) used inregions where profile x(z) changes more smoothly with the elevation z.

[0058] The example deployment of the Kalman filter disclosed in conjunction with FIG.3 should be considered as a way of illustration and not limitation. Numerous other similar ways of deploying Kalman filters (e.g., setting up a state model for predicting a prioricoordinates / locations / dimensions) that lead to the same or similar functionality, are within the scope of this disclosure.

[0059] FIG. 4 is a schematic illustration 400 of deployment of a dynamic time warping technique for efficient tracking of feature dimensions, in accordance with at least one embodiment. In some embodiments, DTW technique can be used in conjunction with operations of measurement tracking 300 of FIG. 3, e.g., as part of state measurement 330. In particular, DTW (e.g., DTW 332 in FIG. 3) can be used to determine measured positions for various iterations (elevations Zj). In some embodiments, determining measured agiven position, may be performed based on a number, e.g., n, previousmeasurements, including measured positions etc., andcorresponding intensity maps.

[0060] FIG. 4 illustrates an example non-limiting embodiment in which n = 3. Correspondingly, three intensity maps 406 areshown in FIG. 4. Values of the intensity are defined within the range of I = 0 (dark pixels) to 7 = 1 (bright pixels) and a specific measured (boundary) location is associated with atransition between a dark region and a bright region (but not necessarily with a certain rigid threshold value IT). When a new intensity map 408 is obtained for the nextelevation the new intensity map 408 can be DTW-mapped onto each ofintensity maps 402, 404, and 406 stored from the previous elevation iterations. DTW may deploy one or more algorithms for identifying similarity between two intensity maps, e.g., 408 and 402, as illustrated with the top panels of FIG. 4. For example,DTW can match various coordinates x from intensity map 402 to one or morecoordinates x from intensity map408 and vice versa. The mapping of the coordinates x from intensity map402 to the coordinates x from intensity map408 is monotonic but not necessarily single-valued (meaning that if coordinate x^ from intensity map) 402 is mapped to coordinate x\ from intensity map408, then another pointx) can be mapped to one or more points x'2, x"2, etc., from intensity map408, such that , etc. (and vice versa). Insome embodiments, the DTM mapping can be determined by minimizing distances in a suitable space (e.g., the x-l plane or some other space obtained by transforming the x-1 plane using a suitable transformation). Dotted curves 410 illustrate respective warped intensities after DTW transformations.|0061] The obtained DTM mapping determines a (new) candidate point xm(zj+1; Zj~) of the intensity map / 408 that corresponds to (previously identified) point xm(zj) of the intensity map I 408. Similar DTM mappings can be obtained for the other intensity406, as illustrated with the middle and bottom panels of FIG. 4, respectively. These mappings determine additional candidate pointsm(j+1j2)

[0062] As illustrated with block 420, the determined candidate points,and so on (if more than three mappings are being used) can be aggregated to obtain a point hat is then taken as the measured location forelevation In some embodiments, the aggregation can be an average (e.g., arithmeticaverage) of the determined candidate points.

[0063] FIG. 5 is a flow diagram of an example method 500 of improving measurements of feature dimensions using a Kalman filter, in accordance with at least one embodiment. In some embodiments, method 500 is performed using systems and components disclosed in conjunction with FIGs. 1-4 or any combination thereof, e.g., automated measurement component 214, which can be deployed as part of of automated measurement server 210, client device 220, metrology equipment 228 of FIG. 2, and / or other similar systems and components. Performance of method 500 can be supported by various computing devices, having one or more processors (e.g., processors 21 1), such as central processing units (CPUs), microprocessors, digital signal processors (DSP), application-specific integrated circuits (ASIC), finite-state machines, field-programmable gate arrays (FPGA), and so on, which can be coupled to one or more memory devices (e.g., memory 212), such as a randomaccess memory, a read-only memory, a flash memory, a static memory, and so on). In some embodiments, the processors execute software or firmware instructions of method 500 stored in the memory device(s) and / or on any suitable non-transitory computer-readable media. In some embodiments, some of the blocks of method 500 are optional.

[0064] Method 500 can be used to perform measurement of a plurality of dimensions of a feature of a product, e.g., a semiconductor manufacturing product. The product can previously undergo one or more processing operations, including but not limited to deposition, etching, plating, polishing, chemical cleaning, drilling, ion beam etching / deposition, laser-enhanced etching or plating, and / or the like. “Feature,” as usedherein, should be understood as any local or extended structure that departs from a uniform medium and can include a surface of a single medium / material, an interface between two uniform media / materials (or multiple interfaces between two or more media), any type of defect, hole, trench, depression, groove, and / or any other recessed structure, a notch, ridge, bump, and / or any other raised structure, the aforementioned recessed and / or raised structure(s) extending over one or more materials, and / or any other suitable structure, the like. “Feature” can be purposely manufactured (e.g., drilled, etched, plated, deposited, etc.) or accidentally occurring (e.g., a dent, crack, crystal defect, impurity, dislocation, and / or the like). “Dimension,” as used herein, should be understood as any size or location (e.g., one or more coordinates) characterizing a spatial extent of the feature. For example, “dimension” can refer to a coordinate of any point associated with a feature, e.g., a surface of the feature, a boundary associated with the feature, and / or a combination of (e.g., distance between) any points associated with the feature. “Dimension” can further refer to any extent or size of the feature along any spatial dimension, e.g., a width, length, depth, area, radius, curvature, and / or the like. Furthermore, “dimension” can include multiple sizes. For example, plane z = Zj in FIG. 1A intersects six boundaries; correspondingly, a dimension corresponding to the plane z = Zy can include six (or more) sizes / coordinates associated with these boundaries.

[0065] In one example non-limiting embodiment, the feature is manufactured in a semiconducting wafer (e.g., silicon wafer, etc.), a dielectric wafer (e.g., silicon oxide wafer, quartz wafer, sapphire wafer, etc.), or in one or more films deposited on the semiconducting wafer or the dielectric wafer. Method 500 can be used to determine a plurality of dimensions of the feature, e.g., a plurality of width dimensions w(z) at different elevations z of the feature (see, e.g., FIG. 1A).

[0066] At block 510, method 500 can include generating, by a processing device, a plurality of nanoscale images of the feature. The term “nanoscale image” should be understood as any image having a resolution of 0.1-10 nm, e.g., substantially higher than the optical resolution (e.g., 100 nm and up). Nanoscale images of the feature can include one or more SEM images, one or more TEM, one or more X-ray images (e.g., EDX images), one or more neutron scattering images, one or more AFM images, and / or other suitable nanoscale images.

[0067] Method 500 can include performing a plurality of iterations. Each iteration (e.g., for a given elevation z;) can identify a respective dimension (e.g., one or more coordinates / locations ) of the plurality of dimensions of the feature. Eachiteration can use a respective nanoscale image of the plurality of nanoscale images. Although referred to via a singular noun, “a nanoscale image” can include multiple images (e.g., several images corresponding to different portions of the feature).|0068] Various iterations can be performed as illustrated with blocks 520 -530. More specifically, at block 520, method 500 can include obtaining, using a respective nanoscale image, a measurement of the respective dimension. In some embodiments, operations of block 520 can be performed as illustrated with the top callout portion of FIG. 5. In particular, the nanoscale image (e.g., used in a given iteration z,) can include an intensity map (e.g., as illustrated in FIG. 4) for at least a portion of the feature.

[0069] Obtaining the measurement of the respective dimension can include, at block 522, identifying a dynamic time warping (DTW) mapping of the intensity map to one or more additional intensity maps for the feature. The one or more additional intensity maps can be associated with one or more previous iterations of the plurality of iterations. For example, the DTW mapping can map etc. At block 524, method 500 caninclude using the DTW mapping to obtain the measurement of the respective dimension (e.g.,illustrated with block 420 of FIG. 4).

[0070] In some embodiments, obtaining the measurements for one or more initial iterations (e.g., z0, z15etc.) can be performed differently than obtaining the measurements for subsequent iterations. For example, a first dimension of the plurality of dimensions (e.g., determined as part of the first iteration) can include receiving the measurement of the first dimension from a different source. For example, such a source can include a machine learning model that uses, as input, a first image of the plurality of nanoscale images of the feature. In some embodiments, the measurement of the first dimension can be performed by a human user (operator, process engineer, etc.). In such embodiments, such a source can include a software that displays the first image to a user and generates the first dimension responsive to a user input. For example, the user can select a point within the intensity map of the first image using the software (e.g., imaging software) that presents the intensity map to the user.

[0071] At block 530, method 500 can continue with adjusting, using two or more previously identified dimensions, the measurement of the respective dimension. In some embodiments, operations of block 530 can be performed as illustrated with the bottom callout portion of FIG. 5. In particular, adjusting the measurement of the respective dimension includes, at block 532, obtaining an estimate of the respective dimension (e.g., %(z7), asdescribed in conjunction with FIG. 3). The estimate of the respective dimension can be interpolated from the two or more previously identified dimensions. In some embodiments, the estimate of the respective dimension can be interpolated using a polynomial interpolation from the two or more previously identified dimensions. The polynomial interpolation can include linear interpolation (that is based on two previously identified dimensions), quadratic interpolation (three previously identified dimensions), and so on. The polynomial interpolation should be understood to also include basis spline (B-spline) interpolations, in some embodiments.

[0072] At block 534, method 500 can include obtaining a weighted combination of the measurement of the respective dimension and the estimate of the respective dimension, e.g., using a Kalman gain as a weight, for example, as disclosed in more detail in conjunction with FIG. 3. For example, the weighted combination can be obtained using the weight factor that characterizes a measurement uncertainty and is updated for each of the subset of the plurality of iterations.

[0073] At block 540, method 500 can continue with generating, using the plurality of dimensions, one or more representations of a quality of the semiconductor manufacturing product. In some embodiments, generating the one or more representations of the quality of the semiconductor manufacturing product can include generating, using a plurality of measurement errors, one or more statistical characteristics representative of an uncertainty of the plurality of dimensions. The measurements errors can be representative of a difference (e.g., — x(z;), between the measurement of the respective dimension (e.g., %7n(z / )) and the determined dimension (e.g., x(z7)) for the respective iteration (e.g., z7), of the plurality of iterations. The statistical characteristics can include an average measurement error, a standard deviation of the measurement error, and / or any other similar statistical characteristics.

[0074] At block 550, method 500 can include configuring, responsive to the plurality of dimensions, one or more processing operations on the semiconductor manufacturing product or an additional product. For example, configuring the processing operation(s) can include performing some remedial processing of the product, e.g., performing additional polishing of the product, etching, drilling, and / or deposition. In some instances, adjustments can be applied to subsequent products processed by the manufacturing system. For example, the adjustments can include modifying chemical composition, pressure, temperature, etc., of anenvironment of some portion of the manufacturing system, such as a processing chamber, a transfer chamber, a loading chamber, and / or the like.

[0075] FIG. 6 depicts a block diagram of an example computer system 600 capable of supporting methods and techniques of the present disclosure, in accordance with at least one embodiment. In various illustrative examples, computer system 600 may be a computer system supporting operations of automated measurement server 210, computer system of client device 220, and / or computer system supporting operations of manufacturing equipment 224 of FIG. 2. Example computer system 600 may be connected to other computer systems in a LAN, an intranet, an extranet, and / or the Internet. Computer system 600 may operate in the capacity of a server in a client-server network environment. Computer system 600 may be a personal computer (PC), a set-top box (STB), a server, a network router, switch or bridge, or any device capable of executing a set of instructions (sequential or otherwise) that specify actions to be taken by that device. Further, while only a single example computer system is illustrated, the term “computer” shall also be taken to include any collection of computers that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methods discussed herein.

[0076] Example computer system 600 may include a processing device 602 (also referred to as a processor or CPU), a main memory 604 (e.g., read-only memory (ROM), flash memory, dynamic random access memory (DRAM) such as synchronous DRAM (SDRAM), etc.), a static memory 606 (e.g., flash memory, static random access memory (SRAM), etc.), and a secondary memory (e.g., a data storage device 618), which may communicate with each other via a bus 630.

[0077] Processing device 602 represents one or more general-purpose processing devices such as a microprocessor, central processing unit, or the like. More particularly, processing device 602 may be a complex instruction set computing (CISC) microprocessor, reduced instruction set computing (RISC) microprocessor, very long instruction word (VLIW) microprocessor, processor implementing other instruction sets, or processors implementing a combination of instruction sets. Processing device 602 may also be one or more specialpurpose processing devices such as an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), network processor, or the like. In accordance with one or more aspects of the present disclosure, processing device 602 may include a processing logic 626 configured to execute instructions (e.g., instructions 622) implementing example method 500 of improving measurements of feature dimensions using a Kalman filter.

[0078] Example computer system 600 may further comprise a network interface device 608, which may be communicatively coupled to a network 620. Example computer system 600 may further comprise a video display 610 (e.g., a liquid crystal display (LCD), a touch screen, or a cathode ray tube (CRT)), an alphanumeric input device 612 (e.g., a keyboard), a cursor control device 614 (e.g., a mouse), and an acoustic signal generation device 616 (e.g., a speaker).

[0079] Data storage device 618 may include a computer-readable storage medium (or, more specifically, a non-transitory computer-readable storage medium) 624 on which is stored one or more sets of executable instructions 622. In accordance with one or more aspects of the present disclosure, executable instructions 622 may comprise executable instructions implementing example method 500 of improving measurements of feature dimensions using a Kalman filter.

[0080] Executable instructions 622 may also reside, completely or at least partially, within main memory 604 and / or within processing device 602 during execution thereof by example computer system 600, main memory 604 and processing device 602 also constituting computer-readable storage media. Executable instructions 622 may further be transmitted or received over a network via network interface device 608.

[0081] While the computer-readable storage medium 624 is shown in FIG. 6 as a single medium, the term “computer-readable storage medium” should be taken to include a single medium or multiple media (e.g., a centralized or distributed database, and / or associated caches and servers) that store the one or more sets of operating instructions. The term “computer-readable storage medium” shall also be taken to include any medium that is capable of storing or encoding a set of instructions for execution by the machine that cause the machine to perform any one or more of the methods described herein. The term “computer-readable storage medium” shall accordingly be taken to include, but not be limited to, solid-state memories, and optical and magnetic media.

[0082] It should be understood that the above description is intended to be illustrative, and not restrictive. Many other embodiment examples will be apparent to those of skill in the art upon reading and understanding the above description. Although the present disclosure describes specific examples, it will be recognized that the systems and methods of the present disclosure are not limited to the examples described herein, but may be practiced with modifications within the scope of the appended claims. Accordingly, the specification and drawings are to be regarded in an illustrative sense rather than a restrictive sense. The scopeof the present disclosure should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.

[0083] The embodiments of methods, hardware, software, firmware or code set forth above may be implemented via instructions or code stored on a machine-accessible, machine readable, computer accessible, or computer readable medium which are executable by a processing element. “Memory” includes any mechanism that provides (i.e., stores and / or transmits) information in a form readable by a machine, such as a computer or electronic system. For example, “memory” includes random-access memory (RAM), such as static RAM (SRAM) or dynamic RAM (DRAM); ROM; magnetic or optical storage medium; flash memory devices; electrical storage devices; optical storage devices; acoustical storage devices, and any type of tangible machine-readable medium suitable for storing or transmitting electronic instructions or information in a form readable by a machine (e.g., a computer).

[0084] Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the disclosure. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0085] In the foregoing specification, a detailed description has been given with reference to specific exemplary embodiments. It will, however, be evident that various modifications and changes may be made thereto without departing from the broader spirit and scope of the disclosure as set forth in the appended claims. The specification and drawings are, accordingly, to be regarded in an illustrative sense rather than a restrictive sense.Furthermore, the foregoing use of embodiment, embodiment, and / or other exemplary language does not necessarily refer to the same embodiment or the same example, but may refer to different and distinct embodiments, as well as potentially the same embodiment.

[0086] The words “example” or “exemplary” are used herein to mean serving as an example, instance, or illustration. Any aspect or design described herein as “example’ or “exemplary” is not necessarily to be construed as preferred or advantageous over other aspects or designs. Rather, use of the words “example” or “exemplary” is intended to present concepts in a concrete fashion. As used in this application, the term “or” is intended to mean an inclusive “or” rather than an exclusive “or.” That is, unless specified otherwise, or clearfrom context, “X includes A or B” is intended to mean any of the natural inclusive permutations. That is, if X includes A; X includes B; or X includes both A and B, then “X includes A or B” is satisfied under any of the foregoing instances. In addition, the articles “a” and “an” as used in this application and the appended claims should generally be construed to mean “one or more” unless specified otherwise or clear from context to be directed to a singular form. Moreover, use of the term “an embodiment” or “one embodiment” or “an embodiment” or “one embodiment” throughout is not intended to mean the same embodiment or embodiment unless described as such. Also, the terms “first,” “second,” “third,” “fourth,” etc. as used herein are meant as labels to distinguish among different elements and may not necessarily have an ordinal meaning according to their numerical designation.

Claims

CLAIMSWhat is claimed is:

1. A method comprising: generating, by a processing device, a plurality of nanoscale images of a feature of a semiconductor manufacturing product; identifying a plurality of dimensions of the feature, wherein each dimension of at least a subset of the plurality of dimensions of the feature is identified by: obtaining, by the processing device and using a respective nanoscale image of the plurality of nanoscale images, a measurement of a respective dimension, and adjusting, by the processing device and using two or more previously identified dimensions, the measurement of the respective dimension; and generating, using the plurality of dimensions, one or more representations of a quality of the semiconductor manufacturing product.

2. The method of claim 1, wherein adjusting the measurement of the respective dimension comprises: obtaining an estimate of the respective dimension, wherein the estimate of the respective dimension is interpolated from the two or more previously identified dimensions.

3. The method of claim 2, wherein the estimate of the respective dimension is interpolated using a polynomial interpolation from the two or more previously identified dimensions.

4. The method of claim 2, wherein adjusting the measurement of the respective dimension further comprises: obtaining a weighted combination of the measurement of the respective dimension and the estimate of the respective dimension.

5. The method of claim 4, wherein the weighted combination is obtained using a weight factor that characterizes a measurement uncertainty and is updated for each of the subset of the plurality of dimensions of the feature.

6. The method of claim 1 , wherein the respective nanoscale image comprises an intensity map for at least a portion of the feature, and wherein obtaining the measurement of the respective dimension comprises: identifying a dynamic time warping (DTW) mapping of the intensity map to one or more additional intensity maps for the feature, the one or more additional intensity maps being associated with one or more previously identified dimensions of the plurality of dimensions of the feature; and using the DTW mapping to obtain the measurement of the respective dimension.

7. The method of claim 1 , wherein obtaining the measurement of a first dimension of the plurality of dimensions comprises: receiving the measurement of the first dimension from at least one of: a machine learning model that uses, as input, a first image of the plurality of nanoscale images of the feature, or a software that displays the first image to a user and generates the first dimension responsive to a user input.

8. The method of claim 1, wherein the plurality of nanoscale images of the feature comprise at least one of: a scanning electron microscopy (SEM) image, a tunneling electron microscopy (TEM) image, or an atomic force microscopy (AFM) image.

9. The method of claim 1 , wherein the feature is manufactured in one or more of: a semiconducting wafer, a dielectric wafer, or one or more films deposited on the semiconducting wafer or the dielectric wafer.

10. The method of claim 1 , wherein the plurality of dimensions of the feature comprises a plurality of width dimensions at different elevations of the feature.1 1 . The method o f claim 1 , wherein generating the one or more representations of the quality of the semiconductor manufacturing product comprises:generating, using a plurality of measurement errors, one or more statistical characteristics representative of an uncertainty of the plurality of dimensions, wherein each measurement error of the plurality of measurement errors is representative of a difference between the measurement of the respective dimension and an identified dimension of the plurality of dimensions of the feature.

12. The method of claim 1 , further comprising: configuring, responsive to the plurality of dimensions, one or more processing operations on at least the semiconductor manufacturing product or an additional product.

13. A method comprising: obtaining, by a processing device, a first set of one or more initial dimensions of a feature of a manufacturing product, wherein the one or more initial dimensions are extracted from one or more images of the feature; using a Kalman filter to determine, by the processing device, a second set of dimensions of the feature, wherein each of the second set of dimensions is obtained by: applying, by the processing device, a state model to a state of the feature to obtain a predicted state of the feature, wherein the state of the feature comprises a plurality of previously determined dimensions of the feature; measuring, using the one or more images of the feature, a respective dimension of the feature of the second set of dimensions of the feature, and applying a Kalman gain to the predicted state of the feature and the measured respective dimension of the feature to obtain a respective dimension of the feature; and generating, using at least the second set of dimensions, one or more representations of a quality of the manufacturing product.

14. The method of claim 13, wherein applying the state model comprises: applying a polynomial interpolation to the plurality of previously determined dimensions of the feature to obtain a predicted dimension of the feature.

15. The method of claim 13, wherein measuring the respective dimension of the feature comprises:obtaining a respective image of the one or more images of the feature, the respective image comprising an intensity map for at least a portion of the feature; identifying a dynamic time warping (DTW) mapping of the intensity map to one or more additional intensity maps for the feature, the one or more additional intensity maps being associated with one or more previously obtained dimensions of the feature; and using the DTW mapping to obtain the measured respective dimension of the feature.

16. A system comprising: a memory storing a plurality of nanoscale images of a feature of a semiconductor manufacturing product; and a processing device communicatively coupled to the memory, the processing device to: identify a plurality of dimensions of the feature, wherein each dimension of at least a subset of the plurality of dimensions of the feature is identified by: obtaining, by the processing device and using the respective nanoscale image, a measurement of the respective dimension, and adjusting, by the processing device and using two or more previously identified dimensions, the measurement of the respective dimension; and generate, using the plurality of dimensions, one or more representations of a quality of the semiconductor manufacturing product.

17. The system of claim 16, wherein the adjusting the measurement of the respective dimension comprises: obtaining an estimate of the respective dimension, wherein the estimate of the respective dimension is interpolated, using a polynomial interpolation, from the two or more previously identified dimensions.

18. The system of claim 17, wherein adjusting the measurement of the respective dimension further comprises: obtaining a weighted combination of the measurement of the respective dimension and the estimate of the respective dimension, wherein the weighted combination is obtained using a weight factor that characterizes a measurement uncertainty and is updated for each of the subset of the plurality of dimensions of the feature.

19. The system of claim 16, wherein obtaining the measurement of the respective dimension comprises: obtaining a respective image of the plurality of nanoscale images of the feature, the respective image comprising an intensity map for at least a portion of the feature; identifying a dynamic time warping (DTW) mapping of the intensity map to one or more additional intensity maps for the feature, the one or more additional intensity maps being associated with one or more previously identified dimensions of the plurality of dimensions of the feature; and using the DTW mapping to obtain the measurement of the respective dimension.

20. The system of claim 16, wherein obtaining the measurement of a first dimension of the plurality of dimensions comprises: receiving the measurement of the first dimension from at least one of: a machine learning model that uses, as input, a first image of the plurality of nanoscale images of the feature, or a software that displays the first image to a user and generates the first dimension responsive to a user input.

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