System and method for estimating measurement uncertainty of characterization systems

Abstract

The invention discloses a characterization system. The system may include one or more controllers including one or more processors configured to execute a set of program instructions stored in a memory. The controller may be configured to train a machine learning based characterization library based on a set of training data. The controller may be configured to generate one or more characterization measurements based on real-time characterization data associated with one or more samples from a characterization subsystem using the trained machine learning-based characterization library. The controller may be configured to determine one or more additional characterization measurements based on a non-machine learning-based technique. The controller may be configured to compare the one or more characterization measurements to the one or more additional characterization measurements to monitor measurement uncertainty of the machine learning based characterization library.

Description

Technical Field

[0001] The present disclosure relates generally to characterizing systems, and more particularly, to a system and method for estimating measurement uncertainty of a characterizing system. Background Art

[0002] Characterization systems typically characterize (e.g., inspect or measure) various characteristics of a sample. For example, metrology systems typically characterize various characteristics of a sample, such as the superposition, angular tilt, etc. of a patterned structure on one layer of a sample relative to a patterned structure on another layer of the sample. As the size of the sample decreases and the sample density increases, the demand for the characterization system required for characterizing the sample increases. Various techniques have been developed to obtain sample measurement data (e.g., superposition, tilt measurement, inspection data), which are general and do not provide per-parameter uncertainty estimates. For example, when using regression to obtain measurements, spectral fitting (real and simulated spectra) can be used to estimate uncertainty, however, this method only gives an indication of how the entire model fits the spectrum rather than giving individual parameters. In this regard, in the case of large parameter errors, the modeled spectrum may overfit the spectrum. For another example, in the case of using a machine learning library to obtain measurements, the distance from the training set can be used for uncertainty estimation, however, the distance from the training set does not always indicate a large error of a well-extrapolated machine learning model. In addition, the method cannot estimate per-parameter uncertainty. Therefore, it is necessary to develop systems and methods to address the above-mentioned defects. Summary of the invention

[0003] According to one or more embodiments of the present disclosure, a characterization system is disclosed. In an embodiment, the characterization system includes one or more controllers, which include one or more processors configured to execute a set of program instructions stored in a memory. In an embodiment, the set of program instructions is configured to enable the one or more processors to train a machine learning-based characterization library based on a set of training data, the set of training data including at least known characterization data associated with one or more samples, theoretical characterization data, and real-time characterization data associated with the one or more samples from a characterization subsystem. In an embodiment, the set of program instructions is configured to enable the one or more processors to use the trained machine learning-based characterization library based on the real-time characterization data associated with the one or more samples from the characterization subsystem to generate one or more characterization measurements. In an embodiment, the set of program instructions is configured to enable the one or more processors to determine one or more additional characterization measurements based on a non-machine learning-based technique, the non-machine learning-based technique being configured to determine the one or more additional characterization measurements based on the real-time characterization data from the characterization subsystem or additional real-time characterization data from an additional characterization subsystem. In an embodiment, the set of program instructions is configured to cause the one or more processors to compare the one or more characterization measurements based on the generated machine learning-based characterization library with the one or more additional characterization measurements based on the non-machine learning-based technique to monitor measurement uncertainty of the machine learning-based characterization library.

[0004] According to one or more embodiments of the present disclosure, a characterization system is disclosed. In an embodiment, the characterization system includes a characterization subsystem configured to obtain real-time characterization data of one or more samples. In an embodiment, the characterization system includes one or more controllers, which include one or more processors configured to execute a set of program instructions stored in a memory. In an embodiment, the set of program instructions is configured to enable the one or more processors to train a machine learning-based characterization library based on a set of training data, and the set of training data includes at least known characterization data associated with one or more samples, theoretical characterization data, and real-time characterization data associated with the one or more samples from the characterization subsystem. In an embodiment, the set of program instructions is configured to enable the one or more processors to use the trained machine learning-based characterization library based on the real-time characterization data associated with the one or more samples from the characterization subsystem to generate one or more characterization measurements. In an embodiment, the set of program instructions is configured to cause the one or more processors to determine one or more additional characterization measurements based on non-machine learning based techniques, the non-machine learning based techniques being configured to determine the one or more additional characterization measurements based on the real-time characterization data from the characterization subsystem or additional real-time characterization data from an additional characterization subsystem. In an embodiment, the set of program instructions is configured to cause the one or more processors to compare the one or more characterization measurements based on the generated machine learning based characterization library with the one or more additional characterization measurements based on the non-machine learning based techniques to monitor measurement uncertainty of the machine learning based characterization library.

[0005] According to one or more embodiments of the present disclosure, a method is disclosed. In an embodiment, the method includes training a machine learning-based characterization library based on a set of training data, the set of training data including at least known characterization data associated with one or more samples, theoretical characterization data, and real-time characterization data associated with the one or more samples from a characterization subsystem. In an embodiment, the method includes using the trained machine learning-based characterization library to generate one or more characterization measurements based on the real-time characterization data associated with the one or more samples from the characterization subsystem. In an embodiment, the method includes determining one or more additional characterization measurements based on a non-machine learning-based technique, the non-machine learning-based technique being configured to determine the one or more additional characterization measurements based on the real-time characterization data from the characterization subsystem or the additional real-time characterization data from an additional characterization subsystem. In an embodiment, the method includes comparing the one or more characterization measurements based on the generated machine learning-based characterization library with the one or more additional characterization measurements based on the non-machine learning-based technique to monitor the measurement uncertainty of the machine learning-based characterization library.

[0006] It should be understood that both the above general description and the following detailed description are for illustration and explanation only and are not necessarily restrictive of the present invention.The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the present invention and together with the general description, serve to explain the principles of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0007] Those skilled in the art may better understand the numerous advantages of the present disclosure by referring to the accompanying drawings, in which:

[0008] Figure 1A A simplified schematic block diagram illustrating a characterization system in accordance with one or more embodiments of the present disclosure.

[0009] Figure 1B A simplified schematic diagram illustrating a characterization subsystem suitable for optical measurements in accordance with one or more embodiments of the present disclosure.

[0010] Figure 1C A simplified schematic diagram illustrating a characterization subsystem configured as an x-ray subsystem in accordance with one or more embodiments of the present disclosure.

[0011] Figure 1D A simplified schematic diagram illustrating a characterization subsystem configured as a particle beam characterization subsystem in accordance with one or more embodiments of the present disclosure.

[0012] Figure 2 Description A flowchart depicts a method or process for determining measurement uncertainty in accordance with one or more embodiments of the present disclosure.

[0013] Figure 3 Description A flowchart depicts a method or process for determining overlay measurement uncertainty in accordance with one or more embodiments of the present disclosure.

[0014] Figure 4 A plurality of overlay measurement uncertainty graphs illustrating a plurality of machine learning based overlay recipes according to one or more embodiments of the present disclosure.

[0015] Figure 5 Description A flowchart depicts a method or process for determining tilt measurement uncertainty in accordance with one or more embodiments of the present disclosure.

[0016] Fig. 6A A graph depicting an asymmetric signal per angle is illustrated in accordance with one or more embodiments of the present disclosure.

[0017] Figure 6B A graph depicting brightness per angle according to one or more embodiments of the present disclosure is illustrated. DETAILED DESCRIPTION

[0018] Reference is now made in detail to the subject matter illustrated in the accompanying drawings. The present disclosure has been particularly shown and described with respect to certain embodiments and specific features thereof. The embodiments described herein should be regarded as illustrative rather than restrictive. It should be readily apparent to one of ordinary skill in the art that various changes and modifications in form and detail may be made without departing from the spirit and scope of the present disclosure.

[0019] Embodiments of the present disclosure relate to systems and methods for estimating measurement uncertainty of a characterization system. In particular, embodiments of the present disclosure relate to a system and method for monitoring measurement uncertainty of a machine learning technique in a machine learning-based characterization library. For example, a system may be configured to generate a characterization measurement using a non-machine learning-based technique based on ground truth as a monitoring of measurement uncertainty of a machine learning technique. As an example, in the case of a superposition measurement, the generated superposition measurement may be generated based on an asymmetric signal, wherein the ground truth is: when the physical superposition is zero, the asymmetric signal is zero. In this regard, the superposition measurement generated based on the asymmetric signal may be compared with the superposition measurement obtained using a machine learning-based superposition library to monitor the measurement uncertainty of the machine learning technique of the superposition library. As another example, in the case of a tilt measurement, the generated angular tilt measurement may be generated based on an asymmetric signal or brightness per angle, wherein the ground truth is: at maximum intensity, the asymmetric signal is zero. In this regard, the superposition measurement generated based on the asymmetric signal may be compared with the superposition measurement obtained using a machine learning-based superposition library to monitor the measurement uncertainty of the machine learning technique of the superposition library.

[0020] For the purposes of this disclosure, the term superposition is used to describe the relative position of features on a sample manufactured by two or more lithographic patterning steps, where the term superposition error describes the deviation of features from the nominal arrangement. For example, a multilayer device may include features patterned on multiple sample layers using different lithographic steps for each layer, where the symmetry of features between layers must generally be tightly controlled to ensure proper performance of the resulting device. Thus, superposition measurements can characterize the relative position of features on two or more of the sample layers. As another example, multiple lithographic steps can be used to manufacture features on a single sample layer. Such techniques (commonly referred to as double patterning or multi-patterning techniques) can facilitate the manufacture of highly dense features near the resolution of the lithographic system. Superposition measurements in this context can characterize the relative position of features from different lithographic steps on this single layer. It should be understood that the examples and descriptions in this disclosure related to specific applications of superposition metrology are provided for illustrative purposes only and should not be construed as limiting the present disclosure.

[0021] Overlay measurements can generally be performed directly on features of the manufactured device (e.g., device features) or on dedicated overlay targets printed using the same lithography steps as the device features. Overlays on device features or device features within a die can beneficially provide measurements at or near locations of interest on a sample, but may require the use of overlay recipes involving complex models to correlate characterization data with measurements of physical overlays. In addition, overlay recipes may need to be retrained or adjusted over time to compensate for drift or deviations in processing equipment or sample variations. In contrast, dedicated overlay targets can generally be placed at any suitable location (e.g., within a die or within a scribe line) and may further include features with characteristics (e.g., size, density, orientation, etc.) that are specifically designed to facilitate overlay measurements. However, a key challenge in using dedicated overlay targets is to ensure that overlay measurements generated by dedicated overlay targets accurately represent the actual overlay of device features. Overlay measurements based on targets may deviate from the actual overlay of device features for a variety of reasons. For example, differences in size, orientation, density, or physical location between target features and device features may result in manufacturing deviations that manifest as systematic errors in overlay measurements. Additionally, different overlay techniques and target designs may have different tradeoffs between size, accuracy, illumination source requirements, and measurement complexity or speed.

[0022] Furthermore, superposition measurements of device features (e.g., preliminary superposition measurements) may be generated using various superposition recipes including, but not limited to, superposition libraries. For example, a superposition recipe for generating superposition measurements from device features may include, but not necessarily include, a superposition library generated by training a machine learning recipe with superposition data of device targets having known physical superposition values ​​and associated superposition data generated by a superposition metrology subsystem (e.g., Mueller ellipsometer, ARR, SAXS, SXR, etc.). In this manner, the trained machine learning library may provide superposition measurements of samples having unknown superposition values ​​based on superposition data from the superposition subsystem.

[0023] Additional embodiments of the present disclosure relate to a system and method for estimating angular tilt measurement uncertainty without any model. For example, the scattered x-ray intensity can be integrated over the region of interest at each angular position. Furthermore, the tilt values ​​can be calibrated based on the per-angle intensity values ​​and using ground truth, so that it can be used to measure the tilt uncertainty of a library based on tilt machine learning or to decide which library based on machine learning is more robust.

[0024] Reference Figures 1A to 6B , systems and methods for estimating measurement uncertainty of a characterization system are described in more detail according to one or more embodiments of the present disclosure.

[0025] Figure 1A A simplified schematic block diagram illustrating a characterization system 100 in accordance with one or more embodiments of the present disclosure.

[0026] In an embodiment, the characterization system 100 includes a characterization subsystem 102 that may be configured according to a characterization recipe (eg, an inspection recipe, an overlay recipe, a tilt recipe, etc.) to generate characterization data associated with a characterization target on a sample 104 .

[0027] In an embodiment, the characterization subsystem 102 includes one or more metrology subsystems. For example, the metrology subsystem 102 may include an overlay metrology subsystem configured to generate overlay data associated with various overlay targets distributed on the sample 104. As another example, the metrology subsystem 102 may include an x-ray metrology subsystem configured to generate tilt data associated with various metrology targets distributed on the sample 104.

[0028] In an embodiment, the characterization subsystem 102 includes one or more inspection subsystems. For example, the inspection subsystem 102 may include an optical inspection subsystem configured to generate optical inspection data associated with the sample 104. As another example, the inspection subsystem 102 may include a particle beam inspection subsystem configured to generate electron beam inspection data associated with the sample 104. As another example, the inspection subsystem 102 may include an x-ray inspection subsystem configured to generate x-ray inspection data associated with the sample 104.

[0029] In an embodiment, the sample 104 is disposed on a sample stage 106. The sample stage 106 may include any device suitable for positioning and / or scanning the sample 104 within the characterization subsystem 102. For example, the sample stage 106 may include a linear translation stage, a rotation stage, a flip / tilt stage, etc. In this manner, the sample stage 106 may be aligned with a selected target within the measurement field of view of the characterization subsystem 102 for measurement.

[0030] Reference Figures 1B to 1D , various configurations of the characterization subsystem 102 are described in more detail according to one or more embodiments of the present disclosure.

[0031] In general, the characterization subsystem 102 can illuminate the sample 104 with at least one illumination beam and collect at least one measurement signal from the sample 104 in response to the illumination beam. The illumination beam can include, but is not limited to, an optical beam (e.g., an optical beam), an x-ray beam, an electron beam, or an ion beam of any wavelength or range of wavelengths. In this manner, the characterization subsystem 102 can operate as an optical characterization subsystem, an x-ray characterization subsystem, an electron beam (e.g., an e-beam) characterization subsystem, or an ion beam characterization subsystem.

[0032] Figure 1B A simplified schematic diagram illustrating a characterization subsystem 102 suitable for optical measurements according to one or more embodiments of the present disclosure. For example, Figure 1B Various configurations may generally be described, including but not limited to spectroscopic ellipsometers (SEs), SEs with multiple illumination angles, SE measurement Mueller matrix elements (e.g., using rotating compensators(s)), single wavelength ellipsometers, beam profile ellipsometers (angle resolved ellipsometers), beam profile reflectometers (angle resolved reflectometers), broadband reflectance spectrometers (spectral reflectometers), single wavelength reflectometers, angle resolved reflectometers, imaging systems, or scatterometers (e.g., speckle analyzers). The wavelength of the optical system may vary from about 120 nm to 3 microns. For non-ellipsometer systems, the collected signal may be polarization resolved or non-polarized.

[0033] In an embodiment, characterization subsystem 102 includes an illumination source 109 for generating an optical illumination beam 111. Illumination beam 111 may include one or more selected wavelengths of light including, but not limited to, ultraviolet (UV) radiation, visible radiation, or infrared (IR) radiation.

[0034] The illumination source 109 may be any type of illumination source known in the art suitable for producing the optical illumination beam 111. In an embodiment, the illumination source 108 comprises a broadband plasma (BBP) illumination source. In this regard, the illumination beam 111 may comprise radiation emitted by a plasma. For example, the BBP illumination source 109 may comprise, but need not necessarily comprise, one or more pump sources (e.g., one or more lasers) configured to focus into a gas volume so that energy is absorbed by the gas to produce or maintain a plasma suitable for emitting radiation. Furthermore, at least a portion of the plasma radiation may be used as the illumination beam 111.

[0035] In an embodiment, the illumination source 109 may include one or more lasers. For example, the illumination source 109 may include any laser system known in the art capable of emitting radiation in the infrared, visible, or ultraviolet portions of the electromagnetic spectrum.

[0036] The illumination source 109 may further generate an illumination beam 111 having any temporal profile. For example, the illumination source 108 may generate a continuous illumination beam 111, a pulsed illumination beam 111, or a modulated illumination beam 111. Additionally, the illumination beam 111 may be transmitted from the illumination source 109 via free space propagation or guided light (e.g., optical fiber, light pipe, etc.).

[0037] In an embodiment, the illumination source 109 directs an illumination beam 111 to the sample 104 via an illumination path 113. The illumination path 113 may include one or more illumination path lenses 116 or additional optical components 115 suitable for modifying and / or adjusting the illumination beam 111. For example, the one or more optical components 115 may include, but are not limited to, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers.

[0038] In an embodiment, the metrology subsystem 102 includes a detector 118 configured to capture photon or particle emissions (e.g., a collection signal 120) from the sample 104 through a collection path 122. The collection path 122 may include, but is not limited to, one or more collection path lenses 124 for directing at least a portion of the collection signal 120 to the detector 118. For example, the detector 118 may receive light collected, reflected, or scattered from the sample 104 (e.g., via specular reflection, diffuse reflection, etc.) via the one or more collection path lenses 124. As another example, the detector 118 may receive radiation of one or more diffraction orders (e.g., 0th order diffraction, ±1st order diffraction, ±2nd order diffraction, etc.) from the sample 104. As another example, the detector 118 may receive radiation generated by the sample 104 (e.g., luminescence associated with absorption of the illumination beam 110, etc.).

[0039] In some embodiments, the illumination beam 111 and the light collection signal 120 may pass through the same objective lens. For example, the illumination path 111 and the light collection path 122 may share the same objective lens.

[0040] The detector 118 may include any type of detector known in the art suitable for measuring the illumination received from the sample 104. For example, the detector 118 may include, but is not limited to, a charge coupled device (CCD) detector, a time delay integration (TDI) detector, a photomultiplier tube (PMT), an avalanche photodiode (APD), etc. In an embodiment, the detector 118 may include a spectral detector suitable for identifying the wavelength of light emitted from the sample 104.

[0041] The collection path 122 may further include any number of collection path lenses 132 or collection elements 126 for directing and / or modifying the illumination collected from the sample 104, including but not limited to one or more filters, one or more polarizers, one or more apodizers, or one or more beam stops.

[0042] Figure 1C A simplified schematic diagram illustrating a characterization subsystem 102 configured as an x-ray subsystem in accordance with one or more embodiments of the present disclosure. The metrology subsystem 102 may include any type of x-ray subsystem known in the art suitable for providing an x-ray illumination beam 110 and capturing an associated collection light signal 120, which includes but is not limited to x-ray emission, optical emission, or particle emission. Examples of x-ray configurations include but are not limited to a small angle x-ray scatterometer (SAXR) or a soft x-ray reflectometer (SXR).

[0043] In an embodiment, the characterization subsystem 102 includes an x-ray illumination path lens 116 adapted to collimate or focus the x-ray illumination beam 111 and a collection path lens (not shown) adapted to collect, collimate and / or focus x-rays from the sample 104. For example, the metrology subsystem 102 may include, but is not limited to, an x-ray collimating mirror, a mirrored x-ray optic such as a grazing incidence elliptical mirror, a polycapillary optic such as a hollow capillary x-ray waveguide, a multilayer optic or system, or any combination thereof. In an embodiment, the metrology subsystem 102 includes an x-ray detector 118, such as, but not limited to, an x-ray monochromator (e.g., a crystal monochromator such as a Loxley-Tanner-Bowen monochromator, etc.), an x-ray aperture, an x-ray beam stop, or a diffractive optic (e.g., such as a zone plate).

[0044] Figure 1D A simplified schematic diagram illustrates a characterization subsystem 102 configured as a particle beam metrology subsystem, such as an electron beam metrology subsystem, in accordance with one or more embodiments of the present disclosure.

[0045] In an embodiment, the characterization subsystem 102 includes one or more particle focusing elements (e.g., illumination path lens 116, collection path lens 124 (not shown), etc.). For example, the one or more particle focusing elements may include, but are not limited to, a single particle focusing element or one or more particle focusing elements forming a composite system. In addition, the one or more particle focusing elements may include any type of electron lens known in the art, including, but not limited to, electrostatic, magnetic, single potential, or dual potential lenses. It should be noted herein that Figure 1C The description of the voltage contrast imaging inspection system depicted in and the above associated descriptions are provided for illustrative purposes only and should not be construed as limiting. For example, the metrology subsystem 102 may include any excitation source known in the art suitable for generating inspection data on the sample 104. In an embodiment, the metrology subsystem 102 includes two or more particle beam sources (e.g., electron beam sources or ion beam sources) for generating two or more particle beams. In an embodiment, the metrology subsystem 102 includes one or more components (e.g., one or more electrodes) configured to apply one or more voltages to one or more locations of the sample 104. In this regard, the metrology subsystem 102 can generate voltage contrast imaging data.

[0046] In an embodiment, the characterization subsystem 102 includes one or more particle detectors 118 for imaging or otherwise detecting particles emitted from the sample 104. In an embodiment, the one or more particle detectors 118 include an electron collector (e.g., a secondary electron collector, a backscattered electron detector, etc.). In an embodiment, the one or more particle detectors 118 include a photon detector (e.g., a photodetector, an x-ray detector, a scintillation element coupled to a photomultiplier tube (PMT) detector, etc.) for detecting electrons and / or photons from the sample surface.

[0047] Some embodiments of the present disclosure relate to providing recipes for configuring the characterization subsystem 102 to facilitate characterization measurements. The characterization recipe may include a set of parameters for controlling various aspects of the characterization measurement, such as, but not limited to, a characterization library, illumination of the sample 104, collection of light from the sample 104, or the position of the sample 104 during measurement. In this way, the characterization subsystem 102 may be configured to provide a selected type of measurement for a selected metrology target design. For example, the characterization recipe may include a characterization library, such as, but not limited to, a machine learning-based characterization recipe. As another example, the characterization recipe may include parameters of the illumination beam 110, such as, but not limited to, illumination wavelength, illumination pupil distribution (such as distribution of illumination angles and associated illumination intensities at the angles), polarization of incident illumination, or spatial distribution of illumination. As another example, the characterization recipe may include collection parameters, such as, but not limited to, collection pupil distribution (such as desired distribution of angular light from the target for measurement and associated filtering intensities at the angles), collection field stop settings for selecting portions of the metrology target of interest, polarization of the collection light, wavelength filters, or parameters for controlling one or more detectors. As another example, the characterization recipe may include various parameters associated with the design of the target, such as, but not limited to, the location and orientation of sample features, such as the pitch of grating features along a particular direction. As another example, the characterization recipe may include various parameters associated with the location of the sample 104 during measurement, such as, but not limited to, sample height, sample orientation, whether the sample 104 is static during measurement, or whether the sample 104 is in motion during measurement (and associated parameters describing speed, scanning pattern, etc.).

[0048] Now generally refer to Figures 1A to 1D, various hardware configurations may be separated into discrete operating systems or integrated into a single subsystem. For example, a metrology subsystem may combine a combination of multiple hardware configurations into a single subsystem, as generally described in U.S. Pat. No. 7,933,026, which is hereby incorporated by reference in its entirety. As another example, multiple metrology subsystems may be used for measurement of a single or multiple metrology targets, as generally described in U.S. Pat. No. 7,478,019, which is hereby incorporated by reference in its entirety. Various hardware configurations are generally described in U.S. Pat. Nos. 5,608,526, 5,859,424, and 6,429,943, which are hereby incorporated by reference in their entirety.

[0049] Characterization subsystem 102 may be further configured in various hardware configurations to measure various structural and / or material properties of one or more layers of sample 104, including but not limited to overlay, tilt, critical dimension (CD) of one or more structures, film thickness, or film composition after one or more fabrication steps.

[0050] Reference Figure 2 , 3 5, various method steps for estimating measurement uncertainty of a characterization system are described in more detail according to one or more embodiments of the present disclosure. Applicants should note that the embodiments and implementation techniques previously described herein in the context of the overlay characterization system 100 should be interpreted as extending to the following steps. However, it should be further noted that the following steps are not limited to the architecture of the overlay characterization system 100.

[0051] Figure 2 Description A flow chart depicts a method 200 for determining measurement uncertainty for characterizing a system, in accordance with one or more embodiments of the present disclosure.

[0052] In step 202, a characterization library may be generated. For example, a machine learning-based characterization library may be generated. In an embodiment, the machine learning-based characterization library includes a machine learning-based superposition measurement library. For example, the machine learning-based superposition measurement library may be generated based on a set of superposition metrology data (e.g., real data, synthetic data, reference data, etc.). In this regard, the trained machine learning-based superposition measurement library may be configured to operate in concert with the superposition metrology subsystem 102 to predict superposition measurements, as further discussed herein. In an embodiment, the machine learning-based characterization library includes a machine learning-based tilt measurement library. For example, the machine learning-based tilt measurement library may be generated based on a set of tilt metrology data (e.g., real data, synthetic data, reference data, etc.). In this regard, the trained machine learning-based tilt measurement library may be configured to operate in concert with the x-ray metrology subsystem 102 to predict tilt measurements, as further discussed herein.

[0053] In an embodiment, a machine learning-based characterization library may be generated based on one or more training data sets. When generating a machine learning-based characterization library, the system 100 may be configured to acquire one or more training images of the sample 104. For example, the controller 108 may be configured to receive training data of the sample 104 from the characterization subsystem 102. The training data set may include, but is not limited to, data from a physical sample with known characterization values, theoretical data, real-time characterization data from a physical sample, etc. For the purposes of this disclosure, the term "training data set" may be considered as data that will be used as input to train a machine learning algorithm of a machine learning-based characterization library.

[0054] The controller 108 may be configured to generate a machine learning-based characterization library via any technique known in the art including, but not limited to, supervised learning, unsupervised learning, etc. For example, in the context of supervised learning, the training data may include data from a physical sample with known characterization values, theoretical data, real-time characterization data from a physical sample, etc. Thus, the training data set may be used as input for training the machine learning-based characterization library. The controller 108 may be further configured to generate a machine learning classifier in the memory 112.

[0055] It should be noted that the machine learning based characterization library may include any type of machine learning algorithm and / or deep learning technique known in the art, including but not limited to linear models, artificial neural networks (ANNs), convolutional neural networks (CNNs), etc.

[0056] In step 204, the characterization library (generated in step 202) may be used to obtain one or more characterization measurements. For example, according to the characterization recipe, the characterization subsystem 102 may be configured to use the trained machine learning-based characterization library to generate one or more characterization measurements based on real-time characterization data associated with one or more samples 104 from the characterization subsystem 102. In an embodiment, the trained machine learning-based characterization library may be configured to run in concert with the characterization subsystem 102 to predict the one or more characterization measurements. For example, the controller 108 may be configured to receive real-time characterization data from the characterization subsystem 102 to generate characterization values ​​using the trained machine learning-based characterization library.

[0057] In an embodiment, the characterization subsystem 102 may include an overlay metrology subsystem 102 configured to generate one or more overlay measurements. For example, the overlay metrology subsystem 102 may be configured to determine overlay by obtaining spectra using the metrology subsystem 102 and using the trained machine learning-based metrology library (generated in step 202) to generate overlay values.

[0058] In an embodiment, the characterization subsystem 102 may include an x-ray metrology subsystem 102 configured to generate one or more tilt measurements. For example, the x-ray metrology subsystem 102 may be configured to determine tilt by obtaining a spectrum using the metrology subsystem 102 and using a training machine learning based metrology library (generated in step 202) to generate a tilt value.

[0059] In step 206, additional characterization measurements may be generated using techniques other than machine learning. For example, a superposition measurement may be generated based on an asymmetric signal (e.g., relative to Figure 3 For example, the ground truth may be based on an asymmetric signal and used as a monitoring of measurement uncertainty for a machine learning based technique with a machine learning based overlay library. As another example, angular tilt measurements may be generated based on an asymmetric signal or per-angle brightness values ​​(e.g., relative to Figure 5 For example, the ground truth can be based on an asymmetric signal or brightness per angle and used as a monitoring of measurement uncertainty for machine learning based techniques using a machine learning based tilt library.

[0060] In step 208, the additional characterization measurements (generated in step 206) may be compared to the characterization measurements (generated in step 204) to monitor the measurement uncertainty of the trained machine learning-based characterization library (generated in step 202). For example, an asymmetric signal-based superposition measurement may be compared to a superposition measurement according to the machine learning-based superposition library to identify measurement bias, measurement error, measurement uncertainty, etc., or a combination thereof. As another example, an asymmetric signal / per-angle brightness-based tilt measurement may be compared to a tilt measurement according to the machine learning-based tilt library to identify measurement bias, measurement error, measurement uncertainty, etc., or a combination thereof.

[0061] In optional step 210, the machine learning based library is adjusted based on the additional characterization measurements generated (generated in step 206 using non-machine learning based techniques). For example, the machine learning based overlay library can be adjusted based on the additional characterization measurements generated. For example, the machine learning based overlay library (or recipe) can be retrained based on the additional characterization measurements generated. As another example, the machine learning based tilt library can be adjusted based on the additional angular tilt measurements generated (generated in step 206 using non-machine learning based techniques). For example, the machine learning based tilt library can be retrained based on the additional tilt measurements generated.

[0062] It is prudent that the additional characterization measurements generated in step 206 may be periodically generated to monitor the measurement uncertainty of the machine learning based characterization library. In this regard, the system may be configured to periodically check the machine learning based characterization library to determine whether the machine learning based characterization library needs to be adjusted (or optimized).

[0063] Figure 3 Flowchart depicting a method or process 300 for generating additional overlay measurements based on non-machine learning based techniques in accordance with one or more embodiments of the present disclosure.

[0064] In step 302, an asymmetric signal may be calculated. For example, the asymmetric signal may be calculated based on Mueller components. For example, the asymmetric signal may be calculated based on signal selection of non-diagonal Mueller elements over a wavelength range that is only sensitive to superposition variations.

[0065] As another example, the asymmetric signal can be calculated based on different azimuth angles. For example, the asymmetric signal can be calculated based on a signal combination (e.g., sum square, sum, or principal component) of the difference signal between opposite azimuth angles (e.g., AZ180-AZ0) in a wavelength region sensitive to superposition.

[0066] In step 304, a zero overlay location for each sample may be determined based on the calculated asymmetry signal. For example, the zero overlay location may be determined for each sample (e.g., wafer) based on the location where the asymmetry signal becomes zero. For example, the zero overlay location may be determined by determining where on each sample the actual overlay on the sample is zero. In this regard, when the actual overlay is zero, the asymmetry signal is zero, such that this asymmetry signal may be ground truth.

[0067] In step 306, an overlay function that relates the asymmetric signal to the additional overlay measurements may be determined. For example, the overlay function may be shown and described by the following equation 1:

[0068] OVL2 = f(AsymSignal) Equation 1

[0069] When AsymSignal = 0, OVL2 = 0

[0070] In step 308, the determined overlay function may be applied to each site of the sample to determine an additional overlay measurement. For example, the additional overlay measurement may be determined using a linear transformation. For example, the asymmetric signal plot may be linearly transformed using Equation 1 so that the standard deviation (STD) of the residual signal is the same as the expected standard deviation of the overlay within the sample (e.g., a wafer). In this regard, when the asymmetric signal is zero, OVL2 is forced to be zero, and further forced to have the expected overlay standard deviation across the sample. It should be noted that the standard deviation of the asymmetric signal may not match the expected overlay standard deviation. It should be further noted that the overlay calculated from the asymmetric signal may not be subject to extrapolation robustness issues because it is anchored by zero asymmetry. This allows the system to detect shifts in the performance of the main overlay library due to extrapolation robustness issues.

[0071] It should be noted that the systems and methods may use any type of non-machine learning based techniques to derive additional overlay measurements.The above examples are provided for illustrative purposes only and should not be construed as limiting the scope of the present disclosure.

[0072] In optional step 310, a stacking error may be calculated based on the calculated stack (from step 308) to determine the stack library measurement uncertainty. For example, the calculated stack (from step 308) may be used as ground truth. The stacking error may be determined based on the difference between the stack (OVL) calculated in step 204 and the asymmetric signal-based stack (OVL2) calculated in step 308, as shown in Equation 2 below:

[0073] OVL error = OVL - OVL2 Equation 2

[0074] In an additional / optional step 312, one or more key performance indicators (KPIs) may be defined to monitor process shifts. For example, as previously discussed herein, when process variations are significant, existing machine learning-based characterization recipes may not be robust on extrapolated data sets. It is critical to determine when a machine learning-based characterization recipe is subject to robustness issues. Once additional overlay measurements (OVL2) are obtained for each sample (e.g., wafer), various sample (e.g., wafer) level metrics may be defined to detect process shifts and trigger a refresh of the existing machine learning-based recipe online run. In one example, KPIs may be defined at the sample level to monitor process shifts, including but not limited to correlation (R2), slope, shift between the calibrated overlay from the asymmetric signal and the overlay prediction from the existing machine learning-based characterization recipe, zero overlay point error (e.g., overlay prediction at the zero overlay site determined from the asymmetric signal), etc.

[0075] In another example, KPIs can be defined at the site level and used for recipe optimization to determine which machine learning-based library is more robust. Site-level KPIs can be determined based on Equation 3 shown and described below:

[0076] Site-level KPI

[0077] | Calibrated OVL at site i - OVL prediction from existing formulation at site i | Equation 3

[0078] Figure 4 A plurality of overlay measurement uncertainty graphs for a plurality of machine learning based overlay recipes according to one or more embodiments of the present disclosure are illustrated. In an embodiment, the measurement uncertainty graph may be generated by subtracting an overlay (OVL2) from an asymmetric signal from an overlay (OVL) from a machine learning based recipe.

[0079] like Figure 4 As shown in , the measurement uncertainty graphs of different machine learning-based recipes can be analyzed to determine which machine learning-based recipe is more robust. For example, the superposition calculated from the asymmetric signal can be used to compare different machine learning-based recipes to determine which one has a greater uncertainty or is a more robust recipe. Figure 4 As shown in , Formulation 2 has significantly greater uncertainty and is less robust than Formulation 1.

[0080] Reference again Figure 3 In an additional / optional step 314, the characterized library measurement performance degradation may be determined. For example, the machine learning based library measurement performance degradation (without adding uncertainty) may be determined using the mean and σ of the error across samples (calculated in step 310).

[0081] Figure 5 The illustration depicts a flow chart of a method or process 500 for generating additional angular tilt measurements based on non-machine learning based techniques in accordance with one or more embodiments of the present disclosure.

[0082] In optional step 502, an asymmetric signal may be calculated. Fig. 6A , the asymmetric signal may be calculated based on the integrated intensity difference between the left and right portions of the image for each angular position based on graph 600. For example, the scattered x-ray intensity from the x-ray characterization subsystem 102 may be integrated within the region of interest for each angular position and used to calculate the asymmetric signal.

[0083] In optional step 504, the brightness per angle may be calculated. Figure 6B , the asymmetric signal may be calculated from the brightness per angular position based on graph 610. For example, the scattered x-ray intensity from the x-ray characterization subsystem 102 may be integrated within the region of interest at each angular position and used to calculate the brightness per angle.

[0084] In step 506, a tilt function that relates one of the asymmetry signal or the per-angle brightness to additional tilt measurements may be determined. For example, where the asymmetry signal is determined (step 502), the most symmetric image may be obtained when the asymmetry signal is zero. In this regard, the corresponding angle of incidence at zero asymmetry may be considered ground truth and used to measure angular tilt.

[0085] As another example, in the case of calculating the brightness per angle (step 504), the brightest image may be obtained as the maximum value of the integrated scattered x-ray intensity. For example, at each angle, the scattered x-ray intensity of the x-ray scatter image from the x-ray characterization subsystem 102 may be integrated. In this regard, Figure 6B As shown in , the integrated intensity (as the brightness of the image) along the angle with an empirical peak function can be non-linear, and the angular position of the maximum of the scattered intensity can be directly related to the tilt measurement.

[0086] In step 508, the determined tilt function may be applied to determine additional tilt measurements. For example, the tilt function may be considered ground truth and used to measure tilt uncertainty for a tilt library based on tilt machine learning. As another example, the tilt function may be used to decide which machine learning library is more robust.

[0087] Reference again Figure 1A , additional components of characterization system 100 are described in more detail according to one or more embodiments of the present disclosure.

[0088] In an embodiment, the characterization system 100 includes a controller 128 that is communicatively coupled to the characterization subsystem 102 and / or any components therein. In an embodiment, the controller 128 includes one or more processors 130. For example, the one or more processors 130 may be configured to execute a set of program instructions maintained in a memory device 132 (or memory). The one or more processors 130 of the controller 128 may include any processing element known in the art. In this sense, the one or more processors 130 may include any microprocessor-type device configured to execute algorithms and / or instructions.

[0089] The one or more processors 130 of the controller 128 may include any processor or processing element known in the art. For the purposes of this disclosure, the term "processor" or "processing element" may be broadly defined to encompass any device having one or more processing or logic elements, such as one or more microprocessor devices, one or more application specific integrated circuit (ASIC) devices, one or more field programmable gate arrays (FPGAs), or one or more digital signal processors (DSPs). In this sense, the one or more processors 130 may include any device configured to execute algorithms and / or instructions, such as program instructions stored in a memory. In an embodiment, the one or more processors 130 may be embodied as a desktop computer, a mainframe computer system, a workstation, an image computer, a parallel processor, a networked computer, or any other computer system configured to execute a program that is configured to operate the characterization system 100 or operate in conjunction with the characterization system 100, as described in this disclosure. In addition, different subsystems of the characterization system 100 may include processors or logic elements suitable for implementing at least a portion of the steps described in this disclosure. Therefore, the above description should not be interpreted as limiting the embodiments of the present disclosure, but is merely illustrative. In addition, the steps described in the present disclosure may be performed by a single controller or, alternatively, multiple controllers. In addition, the controller 128 may include one or more controllers housed in a common housing or multiple housings. In this way, any controller or combination of controllers may be individually packaged as a module suitable for integration into the characterization system 100.

[0090] The memory device 132 may include any storage media known in the art suitable for storing program instructions executable by the associated one or more processors 130. For example, the memory device 132 may include a non-transitory memory medium. As another example, the memory device 132 may include, but is not limited to, a read-only memory (ROM), a random access memory (RAM), a magnetic or optical storage device (e.g., a disk), a tape, a solid-state drive, etc. It should be further noted that the memory device 132 may be housed in a common controller housing with the one or more processors 130. In an embodiment, the memory device 132 may be remotely located relative to the physical location of the one or more processors 130 and the controller 128. For example, the one or more processors 130 of the controller 128 may access a remote memory (e.g., a server) that is accessible via a network (e.g., the Internet, an intranet, etc.).

[0091] The controller 128 may direct (eg, via control signals) or receive data from the characterization subsystem 102 or any component therein. The controller 128 may be further configured to perform any of the various process steps described in this disclosure.

[0092] In an embodiment, the memory device 132 includes a data server. For example, the data server may collect data from the characterization subsystem 102 or other external subsystems associated with the characterization target at any one or more processing steps (e.g., ADI step, AEI step, ACI step, etc.). The data server may also store training data associated with training or otherwise generating a characterization recipe (e.g., an overlay recipe or a tilt recipe). The controller 128 may then utilize any of this data to generate, update, retrain, or modify a characterization recipe (e.g., a machine learning characterization recipe) for generating a characterization measurement using the characterization data from the device target.

[0093] In an embodiment, the characterization system 100 includes a user interface 134 that is communicatively coupled to the controller 128. In an embodiment, the user interface 134 may include, but is not limited to, one or more desktop computers, laptop computers, tablet computers, etc. In an embodiment, the user interface 134 includes a display for displaying data of the characterization system 100 to a user. The display of the user interface 134 may include any display known in the art. For example, the display may include, but is not limited to, a liquid crystal display (LCD), an organic light emitting diode (OLED)-based display, or a CRT display. Those skilled in the art will recognize that any display device capable of being integrated with the user interface 134 is suitable for implementation in the present disclosure. In an embodiment, a user may enter selections and / or instructions via a user input device of the user interface 134 in response to data displayed to the user.

[0094] All methods described herein may include storing the results of one or more steps of the method embodiment in a memory. The result may include any of the results described herein and may be stored in any manner known in the art. The memory may include any memory described herein or any other suitable storage medium known in the art. After the results are stored, the results may be accessed in the memory and used by any of the method or system embodiments described herein, formatted to display to a user, used by another software module, method or system, etc. In addition, the results may be "permanent", "semi-permanent", "temporary" or stored within a certain period of time. For example, the memory may be a random access memory (RAM), and the results may not be stored in the memory indefinitely.

[0095] Upon further careful consideration, each of the embodiments of the method described above may include any other steps of any other method(s) described herein. In addition, each of the embodiments of the method described above may be performed by any of the systems described herein.

[0096] Those skilled in the art will recognize that, for conceptual clarity, the components, operations, devices, objects, and accompanying discussions described herein are used as examples and that various configuration modifications are contemplated. Therefore, as used herein, the specific examples and accompanying discussions set forth are intended to represent their more general class. In general, the use of any specific example is intended to represent its class, and the non-inclusion of specific components, operations, devices, and objects should not be considered limiting.

[0097] As used herein, directional terms such as "top", "bottom", "above", "below", "up", "upward", "down", "downward", and "downward" are intended to provide relative relationships for descriptive purposes and are not intended to specify an absolute reference system. Various modifications to the described embodiments will be apparent to those skilled in the art, and the general principles defined herein may be applied to other embodiments.

[0098] With respect to the use of substantially any plural and / or singular terms herein, those skilled in the art may translate from the plural to the singular and / or from the singular to the plural, as appropriate to the context and / or application. For clarity, the various singular / plural arrangements are not explicitly set forth herein.

[0099] The subject matter described herein sometimes illustrates different components contained in or connected to other components. It should be understood that such depicted architectures are exemplary only, and in fact, many other architectures can be implemented to achieve the same functionality. Conceptually, any arrangement of components for achieving the same functionality is effectively "associated" so that the desired functionality is achieved. Therefore, any two components combined to achieve a specific functionality herein can be considered to be "associated" with each other to achieve the desired functionality regardless of the architecture or intermediate components. Similarly, any two components so associated can be considered to be "connected" or "coupled" to achieve the desired functionality, and any two components that can be so associated can also be considered to be "coupleable" to each other to achieve the desired functionality. "Coupleable" specific examples include but are not limited to physically matable and / or physically interactive components and / or wirelessly interactive and / or wirelessly interactive components and / or logically interactive and / or logically interactive components.

[0100] Furthermore, it should be understood that the present invention is defined by the appended claims. It should be understood by those skilled in the art that, in general, the terms used herein and particularly in the appended claims (e.g., the body of the appended claims) are generally intended to be "open" terms (e.g., the term "comprising" should be interpreted as "including but not limited to", the term "having" should be interpreted as "having at least", etc.). It should be further understood by those skilled in the art that if a specific number of claim recitations is intended to be introduced, then such intention is to be explicitly stated in the claim, and if such statement is not made, then such intention does not exist. For example, as an aid to understanding, the following appended claims may contain the use of the introductory phrases "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be interpreted as implying that the introduction of a claim recitation by the indefinite article "a" or "an" limits any particular claim containing such introduced claim recitation to an invention containing only one such recitation, even if the same claim contains the introductory phrase "one or more" or "at least one" and an indefinite article such as "a" or "an" (e.g., "a" and / or "an" should generally be interpreted as meaning "at least one" or "one or more"); the same applies to the use of definite articles used to introduce claim recitations. In addition, even if a specific number of introduced claim recitations is explicitly recited, those skilled in the art will recognize that such recitation should generally be interpreted as meaning at least the number of recitations (e.g., the bare recitation "two recitations" without other modifiers generally means at least two recitations or two or more recitations). Furthermore, in examples where a convention similar to “at least one of A, B, and C, etc.” is used, this construction is generally intended to be what one of ordinary skill in the art would understand (e.g., “a system having at least one of A, B, and C” would include, but not be limited to, systems having only A, only B, only C, both A and B, both A and C, both B and C, and / or both A, B, and C, etc.). In examples where a convention similar to “at least one of A, B, or C, etc.” is used, this construction is generally intended to be what one of ordinary skill in the art would understand (e.g., “a system having at least one of A, B, or C” would include, but not be limited to, systems having only A, only B, only C, both A and B, both A and C, both B and C, and / or both A, B, and C, etc.). One of ordinary skill in the art would further understand that virtually any disjunctive word and / or phrase presenting two or more alternatives, whether in the detailed description, claims, or drawings, would be understood to contemplate the possibility of including one of the terms, either of the terms, or both of the terms. For example, the phrase "A or B" should be understood to include the possibilities of "A" or "B" or "A and B."

[0101] It is believed that the present disclosure and its many attendant advantages will be understood from the foregoing description, and it should be appreciated that various changes may be made to the form, construction and arrangement of components without departing from the disclosed objects or sacrificing all of its material advantages. The forms described are for illustration only, and the appended claims are intended to cover and encompass such changes. Furthermore, it should be understood that the invention is defined by the appended claims.

Claims

1. A characterization system, comprising: One or more controllers including one or more processors configured to execute a set of program instructions stored in a memory, the set of program instructions configured to cause the one or more processors to: training a machine learning-based characterization library based on a set of training data, the set of training data comprising at least known characterization data associated with one or more samples, theoretical characterization data, and real-time characterization data associated with the one or more samples from a characterization subsystem; generating one or more characterization measurements based on the real-time characterization data associated with the one or more samples from the characterization subsystem using the trained machine learning-based characterization library; determining one or more additional characterization measurements based on a non-machine learning based technique configured to determine the one or more additional characterization measurements based on the real-time characterization data from the characterization subsystem or additional real-time characterization data from an additional characterization subsystem; and The one or more characterization measurements based on the generated machine learning based characterization library are compared to the one or more additional characterization measurements based on the non-machine learning based technique to monitor measurement uncertainty of the machine learning based characterization library.

2. The system of claim 1 , wherein the set of program instructions is further configured to cause the one or more processors to: The generated machine learning-based characterization library is adjusted based on the comparison of the one or more characterization measurements and the one or more additional characterization measurements.

3. The system of claim 1, wherein the machine learning based characterization library comprises a machine learning based overlay measurement library.

4. The system of claim 1, wherein the machine learning based characterization library comprises a machine learning based angular tilt measurement library.

5. The system of claim 1, wherein the one or more characterization measurements comprise one or more overlay metrology measurements.

6. The system of claim 1, wherein the one or more characterization measurements include one or more angular tilt metrology measurements.

7. The system of claim 1, wherein the non-machine learning based technique to determine one or more additional characterization measurements further comprises: Calculate asymmetric signals; determining a zero-overlap position for each sample based on the calculated asymmetric signal; determining a superposition function correlating the calculated asymmetric signal with an additional superposition measurement; determining the additional overlay measurement by applying the determined overlay function to the sample; and An overlay error value is calculated based on the one or more characterization measurements and the additional overlay measurement.

8. The system of claim 7, wherein the calculating the asymmetric signal comprises: The asymmetric signal is calculated based on the Mueller component.

9. The system of claim 7, wherein the calculating the asymmetric signal comprises: The asymmetric signal is calculated based on the opposite azimuth angle.

10. The system of claim 7, wherein the comparing the one or more characterization measurements based on the generated machine learning based characterization library with the one or more additional characterization measurements based on the non-machine learning based technique to monitor measurement uncertainty of the machine learning based characterization library further comprises: One or more key performance indicators are defined at one of the sample level or the site level.

11. The system of claim 7, wherein the comparing the one or more characterization measurements based on the generated machine learning based characterization library with the one or more additional characterization measurements based on the non-machine learning based technique to monitor measurement uncertainty of the machine learning based characterization library further comprises: A measurement performance degradation of the machine learning based characterization library is determined using one of a mean of the calculated overlay errors across the samples or a sigma of the calculated overlay errors across the samples.

12. The system of claim 1, wherein the non-machine learning based technique to determine one or more additional characterization measurements further comprises: Calculate asymmetric signals; determining a tilt function correlating the calculated asymmetric signal with an additional tilt measurement; and The additional tilt measurement is determined by applying the determined tilt function to the samples.

13. The system of claim 1, wherein the non-machine learning based technique to determine one or more additional characterization measurements further comprises: Calculate the brightness at each angle; determining a tilt function relating said calculated per-angle brightness to an additional tilt measurement; and The additional tilt measurement is determined by applying the determined tilt function to the samples.

14. A characterization system, the characterization system comprising: a characterization subsystem configured to obtain real-time characterization data of one or more samples; and One or more controllers including one or more processors configured to execute a set of program instructions stored in a memory, the set of program instructions configured to cause the one or more processors to: training a machine learning-based characterization library based on a set of training data, the set of training data comprising at least known characterization data associated with the one or more samples, theoretical characterization data, and the real-time characterization data associated with the one or more samples from the characterization subsystem; generating one or more characterization measurements based on the real-time characterization data associated with the one or more samples from the characterization subsystem using the trained machine learning-based characterization library; determining one or more additional characterization measurements based on a non-machine learning based technique configured to determine the one or more additional characterization measurements based on the real-time characterization data from the characterization subsystem or additional real-time characterization data from an additional characterization subsystem; and The one or more characterization measurements based on the generated machine learning based characterization library are compared to the one or more additional characterization measurements based on the non-machine learning based technique to monitor measurement uncertainty of the machine learning based characterization library.

15. The system of claim 14, wherein the set of program instructions is further configured to cause the one or more processors to: The generated machine learning-based characterization library is adjusted based on the comparison of the one or more characterization measurements and the one or more additional characterization measurements.

16. The system of claim 14, wherein the characterization subsystem comprises a superposition metrology subsystem.

17. The system of claim 16, wherein the machine learning based characterization library comprises a machine learning based overlay measurement library.

18. The system of claim 14, wherein the characterization subsystem comprises an x-ray metrology subsystem.

19. The system of claim 18, wherein the machine learning based characterization library comprises a machine learning based angular tilt measurement library.

20. The system of claim 16, wherein the non-machine learning based technique to determine one or more additional characterization measurements further comprises: Calculate asymmetric signals; determining a zero-overlap position for each sample based on the calculated asymmetric signal; determining a superposition function correlating the calculated asymmetric signal with an additional superposition measurement; determining the additional overlay measurement by applying the determined overlay function to the sample; and An overlay error value is calculated based on the one or more characterization measurements and the additional overlay measurement.

21. The system of claim 20, wherein said calculating an asymmetric signal comprises: The asymmetric signal is calculated based on the Mueller component.

22. The system of claim 20, wherein said calculating an asymmetric signal comprises: The asymmetric signal is calculated based on the opposite azimuth angle.

23. The system of claim 20, wherein the comparing the one or more characterization measurements based on the generated machine learning based characterization library with the one or more additional characterization measurements based on the non-machine learning based techniques to monitor measurement uncertainty of the machine learning based characterization library further comprises: One or more key performance indicators are defined at one of the sample level or the site level.

24. The system of claim 20, wherein the comparing the one or more characterization measurements based on the generated machine learning based characterization library with the one or more additional characterization measurements based on the non-machine learning based techniques to monitor measurement uncertainty of the machine learning based characterization library further comprises: A measurement performance degradation of the machine learning based characterization library is determined using one of a mean of the calculated overlay errors across the samples or a sigma of the calculated overlay errors across the samples.

25. The system of claim 18, wherein the determining one or more additional characterization measurements based on the non-machine learning based technique further comprises: Calculate asymmetric signals; and determining a tilt function correlating the calculated asymmetric signal with an additional tilt measurement; and The additional tilt measurement is determined by applying the determined tilt function to the samples.

26. The system of claim 18, wherein the non-machine learning based technique to determine one or more additional characterization measurements further comprises: Calculate the brightness at each angle; and determining a tilt function relating said calculated per-angle brightness to an additional tilt measurement; and The additional tilt measurement is determined by applying the determined tilt function to the samples.

27. A method comprising: training a machine learning-based characterization library based on a set of training data, the set of training data comprising at least known characterization data associated with one or more samples, theoretical characterization data, and real-time characterization data associated with the one or more samples from a characterization subsystem; generating one or more characterization measurements based on the real-time characterization data associated with the one or more samples from the characterization subsystem using the trained machine learning-based characterization library; determining one or more additional characterization measurements based on a non-machine learning based technique configured to determine the one or more additional characterization measurements based on the real-time characterization data from the characterization subsystem or additional real-time characterization data from an additional characterization subsystem; and The one or more characterization measurements based on the generated machine learning based characterization library are compared to the one or more additional characterization measurements based on the non-machine learning based technique to monitor measurement uncertainty of the machine learning based characterization library.

28. The method of claim 27, further comprising: The generated machine learning-based characterization library is adjusted based on the comparison of the one or more characterization measurements and the one or more additional characterization measurements.

29. The method of claim 27, wherein the determining one or more additional characterization measurements based on a non-machine learning based technique further comprises: Calculate asymmetric signals; determining a zero-overlap position for each sample based on the calculated asymmetric signal; determining a superposition function correlating the calculated asymmetric signal with an additional superposition measurement; determining the additional overlay measurement by applying the determined overlay function to the samples; and An overlay error value is calculated based on the obtained one or more characterization measurements and the additional overlay measurement.

30. The method of claim 27, wherein the non-machine learning based technique to determine one or more additional characterization measurements further comprises: Calculate asymmetric signals; determining a tilt function correlating the asymmetric signal with an additional tilt measurement; and The additional tilt measurement is determined by applying the determined tilt function to the samples.

31. The method of claim 27, wherein the determining one or more additional characterization measurements based on a non-machine learning based technique further comprises: Calculate the brightness at each angle; determining a tilt function relating said calculated per-angle brightness to an additional tilt measurement; and The additional tilt measurement is determined by applying the determined tilt function to the samples.

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