Methods and systems for x-ray scatterometry measurements employing a machine learning based electromagnetic response model

Abstract

This paper describes a method and system for estimating the value of a parameter of interest from X-ray scattering measurements with reduced computational effort. The value of the parameter of interest is estimated by regression using a trained machine learning (ML)-based electromagnetic (EM) response model. A training dataset contains design of experiments (DOE) values ​​for the parameter of interest and a set of corresponding DOE values ​​for a plurality of EM response measures. In some instances, the value of the parameter of interest is determined from the measured image based on regression using a series of trained ML-based EM response models. In other instances, the input values ​​used to train the ML-based EM response model are scaled according to variations in the model output.

Description

Technical Field

[0001] The described embodiments relate to metrology systems and methods, and more particularly, to methods and systems for improved measurement of semiconductor structures. Prior Art

[0002] Semiconductor devices, such as logic and memory devices, are typically manufactured through a series of processing steps applied to a sample. These processing steps form the various features and structural levels of the semiconductor device. For example, lithography is a particular type of semiconductor process that involves creating a pattern on a semiconductor wafer. Additional examples of semiconductor processes include (but are not limited to) chemical-mechanical polishing, etching, deposition, and ion implantation. Multiple semiconductor devices can be manufactured on a single semiconductor wafer and then separated into individual semiconductor devices.

[0003] Metrology processes are used at various steps during a semiconductor fabrication process to detect defects on the wafer to promote higher yields. Several metrology-based techniques, including scatterometry and reflectometry implementations and associated analysis algorithms, are commonly used to characterize critical dimensions, film thickness, composition, and other parameters of nanoscale structures.

[0004] Traditionally, scattering critical dimension (SCD) measurements are performed on targets composed of thin films and / or repeating periodic structures. During device fabrication, these films and periodic structures typically represent the actual device geometry and material structure or an intermediate design. As devices (e.g., logic and memory devices) progress toward smaller nanometer-scale dimensions, characterization becomes increasingly difficult. Devices incorporating complex three-dimensional geometries and materials with varying physical properties exacerbate this difficulty. For example, modern memory structures often feature high-aspect-ratio, three-dimensional structures that make it difficult for optical radiation to penetrate the underlying layers. Optical metrology tools utilizing infrared to visible light can penetrate many layers of semi-transparent materials, but the longer wavelengths that provide good penetration depth do not provide sufficient sensitivity for small anomalies. Furthermore, the increasing number of parameters required to characterize complex structures (e.g., FinFETs) leads to increased parameter dependencies. Consequently, the parameters of the characterized target often cannot be reliably decoupled.

[0005] In one example, longer wavelengths (e.g., near-infrared) have been used to attempt to overcome the penetration problem of 3D FLASH devices that utilize polysilicon as one of the alternating materials in the stack. However, the mirror-like structure of 3D FLASH inherently causes light intensity to decrease as illumination propagates deeper into the film stack. This leads to sensitivity loss and depth-dependency issues. In this scenario, SCD can only successfully extract a reduced set of metrology dimensions with high sensitivity and low correlation.

[0006] In another example, opaque high-k dielectric materials are increasingly used in modern semiconductor structures. Optical radiation is generally unable to penetrate layers constructed from these materials. Consequently, thin-film scatterometry tools such as ellipsometers or reflectometers are becoming increasingly challenging to measure.

[0007] In response to these challenges, more sophisticated optical metrology tools have been developed. For example, tools have been developed that feature multiple illumination angles, shorter illumination wavelengths, a wider illumination wavelength range, and more complete information extraction from the self-reflection signal (e.g., measuring multiple Mueller matrix elements in addition to the more conventional reflectivity or ellipsometric signals). Furthermore, X-ray scattering measurement systems, such as transmission small-angle X-ray scattering (T-SAXS) systems, have shown promise in addressing challenging measurement applications. These X-ray-based scattering measurement systems can also feature a wide range of illumination angles and wavelengths. While state-of-the-art optical and X-ray scattering measurement systems enable challenging measurement applications, the computational workload required to estimate the value of the parameter of interest has become a performance limiting issue.

[0008] Many metrology techniques, including X-ray scatterometry, are indirect methods for measuring the physical properties of a sample. In most cases, it is not possible to directly determine the physical properties of the sample using the raw measurement signal (e.g., a measured image). Instead, a measurement model or a pre-calculated library of model solutions is used to estimate the values ​​of one or more parameters of interest based on the raw measurement signal. For example, scatterometry is an indirect method for measuring the physical properties of a sample. Generally, a physics-based or machine learning-based measurement model is used to determine the physical properties of the sample based on the raw measurement signal (e.g., a measured image).

[0009] In some examples, a physics-based measurement model is created that attempts to predict the original measurement signal based on assumed values ​​for one or more model parameters. The physics-based measurement model includes parameters associated with the metrology tool itself (e.g., machine parameters) and parameters that characterize the sample being measured. Machine parameters are parameters used to characterize the metrology tool. Example machine parameters include angle of incidence (AOI), azimuth angle (Az), beam flux, beam divergence, etc. Sample parameters are parameters used to characterize the sample (e.g., material and geometric parameters of the measured structure(s)). For a CD sample, example sample parameters include geometric parameters associated with different layers, refractive indices associated with different layers, etc. For measurement purposes, the machine parameters and many sample parameters are treated as known fixed-value parameters, and the values ​​of one or more sample parameters of interest are treated as unknown floating parameter values.

[0010] In some examples, the value of the floating parameter of interest is solved for by an iterative process (e.g., regression) that produces the best fit between theoretical predictions and experimental data. The value of the unknown floating parameter of interest is varied, and model output values ​​(e.g., simulated pixelated images) are calculated and compared to the measured images in an iterative manner until a set of sample parameter values ​​is determined that results in a sufficiently close match between the model output values ​​(e.g., simulated images) and the experimental measurements (e.g., measured images). The matching process typically involves the use of a regression engine that adjusts the parameter values ​​that determine the shape and composition of the model until a fit cost function related to the difference between the measured and simulated levels is minimized. In some other examples, the floating parameter is solved by searching a library of pre-calculated solutions to find the closest match.

[0011] Directly using regression to estimate the value of one or more parameters of interest has proven successful, including parameters for characterizing memory structures. However, the computational cost associated with electromagnetic simulations, which underlie a physics-based measurement model, is a significant drawback. Typical memory structures have large, periodic structures with heights of several microns. Consequently, the number of parameters required to characterize complex structures is extremely large. Consequently, the computational effort required to construct the geometric model associated with a given set of parameters and calculate the electromagnetic scattering efficiency is limited. Furthermore, most regression engines require calculating parametric derivatives of the scattering efficiency, which is computationally intensive and increasingly impractical.

[0012] In some other examples, a trained machine learning-based measurement model is used to directly estimate the value of the parameter of interest based on the raw measurement data. In these examples, a machine learning-based measurement model takes the raw measurement signal (e.g., the measured image) as the model input and estimates the value of the parameter of interest as the model output.

[0013] Compared to regression based on a physics-based model, performing measurements based on a trained machine learning model requires much less computational effort. However, machine learning-based measurement models must be trained to produce useful estimates of the parameters of interest for a specific measurement application.

[0014] A machine learning-based measurement model is parameterized by a number of weight parameters. Traditionally, machine learning-based measurement models are trained using a regression procedure (e.g., ordinary least squares regression). Typically, model training is based on simulated images associated with known values ​​of the parameter of interest (i.e., design of experiment (DOE) data). The values ​​of the weight parameters are repeatedly adjusted to minimize the difference between the known DOE value of the parameter of interest and the value of the parameter of interest estimated by the machine learning-based measurement model based on the simulated DOE image data. In a typical measurement application, hundreds of thousands of images are simulated to train the machine learning-based model. Therefore, as model complexity increases, the computational workload required to train a machine learning-based measurement model can become prohibitive.

[0015] Furthermore, once trained, machine learning-based models often suffer from robustness and accuracy issues. Specifically, some variations in parameter values ​​result in similar images, and the trained machine learning-based measurement model cannot distinguish between these parameter values.

[0016] Future metrology applications present metrology challenges due to ever-smaller resolution requirements, multi-parameter dependencies, increasingly complex geometries, and the increased use of opaque materials. Therefore, methods and systems for generating and implementing highly accurate measurement models with reduced computational effort are desired. Summary of the Invention

[0017] Described herein are methods and systems for estimating the value of a parameter of interest from X-ray scattering measurements with reduced computational effort. The value of the parameter of interest is estimated by performing regression using a trained machine learning (ML)-based electromagnetic (EM) response model. The ML-based EM response model effectively replaces traditional three-dimensional structure discretization and physics-based EM response simulation in a measurement model based on regression of X-ray scattering measurement data.

[0018] The trained ML-based electromagnetic response model is computationally much more efficient than a physics-based electromagnetic response model, thus enabling accurate X-ray scattering measurements of complex semiconductor structures with less computational effort.

[0019] In one aspect, a machine learning-based electromagnetic response model is trained based on a training dataset comprising a set of design of experiments (DOE) values ​​for a parameter of interest and corresponding DOE values ​​for a plurality of electromagnetic response metrics. The training involves regressing the training dataset to minimize an objective function that minimizes the error between the DOE values ​​characterizing the plurality of electromagnetic response metrics and the values ​​of the plurality of electromagnetic response metrics determined using the machine learning-based electromagnetic response model.

[0020] In another aspect, the performance of a trained ML-based EM response model is evaluated to determine whether additional training is needed before implementing the trained model.

[0021] In another aspect, the value of a parameter of interest is determined from a measured image of a measured structure based on regression using a series of trained ML-based electromagnetic response models.

[0022] In another aspect, a value of a parameter of interest is determined from a measured image of a measured structure based on regression using a combination of a trained ML-based EM response model and a physics-based EM solver. More specifically, the goodness of fit associated with each EM response metric is evaluated to determine whether each particular EM response metric should be calculated using a trained ML-based EM response model or a physics-based EM solver.

[0023] In another aspect, model training speed and accuracy are improved by scaling DOE values ​​of parameters of interest based on corresponding values ​​of a plurality of electromagnetic response metrics determined during training using a machine learning-based electromagnetic response model.

[0024] The foregoing is a summary and therefore necessarily contains simplifications, generalizations, and omissions of detail; therefore, those skilled in the art will appreciate that the summary is illustrative only and not limiting in any way. Other aspects, inventive features, and advantages of the devices and / or processes described herein will become apparent from the non-limiting detailed description set forth herein. Simple diagram description

[0025] FIG1 is a diagram illustrating a metrology system 100 configured to measure properties of a sample according to the methods described herein.

[0026] FIG2 is a diagram illustrating a metrology system 200 in another embodiment configured to measure characteristics of a sample according to the methods presented herein.

[0027] FIG3 depicts x-ray illumination beam 117 incident on wafer 101 at a particular orientation described by angles φ and θ.

[0028] 4 is a diagram illustrating a measurement engine 150 configured to resolve sample parameter values ​​based on x-ray scattering measurement data according to the methods described herein.

[0029] FIG5 illustrates a diagram of a measurement model training engine 170 configured to train a machine learning-based electromagnetic response model according to the methods described herein.

[0030] FIG6 is a plot showing the R2 values ​​of various scattering level efficiencies after initial training of a machine learning based electromagnetic response model.

[0031] FIG7 is a plot showing the R 2 value of each scattering level efficiency after retraining of the machine learning based electromagnetic response model.

[0032] FIG8 is a histogram showing the number of image pixels having a residual value in different ranges after training a machine learning-based electromagnetic response model.

[0033] FIG9 is a histogram showing the number of image pixels having a residual value in different ranges after retraining of the machine learning based electromagnetic response model.

[0034] FIG. 10 is a diagram showing components of metrology systems 100 and 200 separated from a sample 101 contained within a vacuum environment.

[0035] 11A-11C depict an isometric view, a top view, and a cross-sectional view, respectively, of a typical 3D FLASH memory device 190 subjected to measurements in the manner described herein.

[0036] FIG12 depicts a flow diagram illustrating an exemplary method 300 of model-based measurement as described herein. Implementation Method

[0037] Reference will now be made in detail to background examples and some embodiments of the invention, examples of which are illustrated in the accompanying drawings.

[0038] Described herein are methods and systems for estimating the value of a parameter of interest from X-ray scattering measurements with reduced computational effort. More specifically, the value of the parameter of interest is estimated by performing regression using a trained machine learning-based electromagnetic response model. The ML-based electromagnetic response model effectively replaces traditional three-dimensional structure discretization and physics-based electromagnetic response simulation in a measurement model based on regression of X-ray scattering measurement data. The trained machine learning (ML)-based electromagnetic response model is computationally much more efficient than a physics-based electromagnetic response model. Consequently, accurate X-ray scattering measurements of complex semiconductor structures are achieved with less computational effort.

[0039] FIG1 illustrates an embodiment of a metrology system 100 for measuring characteristics of a sample according to exemplary methods presented herein. As shown in FIG1 , system 100 can be used to perform x-ray scattering measurements within a detection region 102 of a sample 101 positioned on a sample positioning system 140.

[0040] In the depicted embodiment, the metrology tool 100 includes an x-ray illumination source 110 configured to generate x-ray radiation suitable for x-ray scattering measurements. In some embodiments, the x-ray illumination system 110 is configured to generate wavelengths between 0.01 nanometers and 1 nanometer. The x-ray illumination source 110 generates an x-ray beam 117 that is incident on an inspection region 102 of the sample 101.

[0041] In general, any suitable high-brightness x-ray illumination source capable of producing high-brightness x-rays at a flux level sufficient to achieve high-throughput online metrology can be considered for providing x-ray illumination for x-ray scattering measurements. In some embodiments, an x-ray source includes a tunable monochromator that enables the x-ray source to deliver x-ray radiation at different selectable wavelengths.

[0042] In some embodiments, one or more x-ray sources emitting radiation with photon energies greater than 15 keV are used to ensure that the x-ray source supplies light of a wavelength that allows sufficient transmission throughout the device and the wafer substrate. By way of non-limiting example, any of a particle accelerator source, a liquid anode source, a rotating anode source, a stationary solid anode source, a microfocus source, a microfocus rotating anode source, and an inverse Compton source can be used as x-ray source 110. In one example, an inverse Compton source available from Lyncean Technologies, Inc. of Palo Alto, California (USA) can be considered. An inverse Compton source has the additional advantage of being able to generate x-rays over a range of photon energies, thereby enabling the x-ray source to deliver x-ray radiation of different selectable wavelengths.

[0043] Exemplary x-ray sources include electron beam sources configured to bombard solid or liquid targets to stimulate x-ray emission. FIG2 depicts a metrology system 200 for measuring properties of a sample according to the exemplary methods presented herein. Like-numbered elements of metrology tools 100 and 200 are similar. However, in the embodiment depicted in FIG2 , x-ray illumination source 110 is a liquid metal-based x-ray illumination system. A liquid metal jet 119 is generated from a liquid metal container 111 and collected in a liquid metal collector 112. A liquid metal circulation system (not shown) returns the liquid metal collected by collector 112 to liquid metal container 111. Liquid metal jet 119 comprises one or more elements. By way of non-limiting example, liquid metal jet 119 comprises any of aluminum, gallium, indium, tin, thallium, and bismuth. In this manner, liquid metal jet 119 generates x-rays corresponding to its constituent elements. In one embodiment, the liquid metal jet comprises a gallium and indium alloy. In some embodiments, the x-ray illumination system 110 is configured to generate wavelengths between 0.01 nanometers and 1 nanometer. An electron beam source 113 (e.g., an electron gun) generates an electron stream 118 that is directed by electron optics 114 toward a liquid metal jet 119. Suitable electron optics 114 include electromagnets, permanent magnets, or a combination of electromagnets and permanent magnets for focusing the electron beam and directing it toward the liquid metal jet. The coincidence of the liquid metal jet 119 and the electron stream 118 generates an x-ray beam 117 that is incident on the inspection region 102 of the sample 101.

[0044] Methods and systems for generating high-brightness liquid metal x-ray illumination are described in U.S. Patent No. 7,929,667, issued to KLA-Tencor Corporation on April 19, 2011, which is incorporated herein by reference in its entirety.

[0045] In one embodiment, the incident x-ray beam 117 is on the indium kα line at 24.2 keV. The x-ray beam is collimated down to less than 1 millirad divergence using multilayer x-ray optics for x-ray scattering measurements.

[0046] In some embodiments, the x-ray scattering measurements described herein are achieved without the use of a screen positioned between the x-ray source and the sample being measured. In these embodiments, the measured intensity of the incident beam over a range of incident angles, multiple wavelengths, or a combination thereof provides sufficient information to resolve a distribution map (i.e., an image) of a desired material property (e.g., complex refractive index, electron density, or absorptivity) of the measured structure. However, in some other examples, a pinhole or other aperture is positioned in a separate, opaque screen positioned between the x-ray source and the sample being measured to improve the collimation of the x-ray beam. The intensity of the diffraction pattern is measured for several locations of the aperture. In some other embodiments, a screen with a pseudo-random pattern of apertures is used, and the diffraction pattern is measured for multiple screens. These methods are also contemplated to provide additional information for resolving the three-dimensional distribution of the desired material property of the measured structure.

[0047] In some embodiments, the profile of the incident x-ray beam is controlled by two or more apertures, slits, or a combination thereof. In a further embodiment, the apertures, slits, or both are configured to rotate in coordination with the orientation of the sample to optimize the profile of the incident beam for each angle of incidence, azimuth, or both.

[0048] As depicted in FIG1 , x-ray optics 115 shapes and directs incident x-ray beam 117 toward sample 101. In some examples, x-ray optics 115 includes an x-ray monochromator that monochromates the x-ray beam incident on sample 101. In one example, a crystal monochromator, such as a Loxley-Tanner-Bowen monochromator, is used to monochromatize the x-ray radiation beam. In some examples, x-ray optics 115 uses multilayer x-ray optics to collimate or focus x-ray beam 117 onto detection region 102 of sample 101 to a divergence of less than 1 millirad. In some embodiments, the x-ray optics 115 include one or more x-ray collimating mirrors, x-ray apertures, x-ray beam stops, refractive x-ray optics, diffractive optics (such as zone plates), mirror x-ray optics (such as grazing incidence elliptical mirrors), polycapillary optics (such as hollow capillary x-ray waveguides), multilayer optics or systems, or any combination thereof. Further details are described in U.S. Patent Publication No. 2015 / 0110249, the entire contents of which are incorporated herein by reference.

[0049] In general, the focal plane of the illumination optics system is optimized for each measurement application. In this way, the system 100 is configured to position the focal plane at various depths within the sample depending on the measurement application.

[0050] X-ray detector 116 collects x-ray radiation 125 scattered from sample 101 and generates an output signal 126 in accordance with an x-ray scattering measurement modality indicative of a property of sample 101 that is sensitive to incident x-ray radiation. In some embodiments, scattered x-rays 125 are collected by x-ray detector 116 while sample positioning system 140 positions and orients sample 101 to generate angularly resolved scattered x-rays.

[0051] In some embodiments, an x-ray scattering measurement system includes one or more photon-counting detectors with a high dynamic range (e.g., greater than 10 5 ) and a thick, highly absorptive crystalline substrate that absorbs the direct beam (i.e., the zero-order beam) without damage and with minimal parasitic backscatter. In some embodiments, a single photon-counting detector detects the position and number of detected photons.

[0052] Full-beam X-ray scattering measurements require the collection of the zero-order beam as well as higher diffraction orders. The zero-order beam is several orders of magnitude stronger than the other orders. If the zero-order beam is not completely absorbed in the X-ray-sensitive region of the detector, it will scatter and generate spurious signals. The intensity of these spurious signals limits the dynamic range of the measurement. For example, if the spurious signal is 10⁻¹⁴ of the maximum flux signal (i.e., the zero-order signal), the signals associated with many higher orders will be contaminated. Therefore, it is crucial that the detector (e.g., detector 116) exhibits high X-ray to electron-hole pair conversion efficiency and high X-ray absorption to increase the effective dynamic range of full-beam metrology.

[0053] Exemplary detector materials suitable for full-beam x-ray scattering measurements include cadmium telluride (CdTe), germanium (Ge), and gallium arsenide (GaAs) crystals, etc. In some embodiments, the detector material is selected to provide high conversion efficiency in a narrow energy band corresponding to the source energy.

[0054] In some embodiments, the thickness of the detector material is selected to achieve a desired absorption of incoming X-rays. In some embodiments, the detector is tilted relative to the incoming X-ray beam (various diffraction orders) to increase the path length of the X-ray beam through the detector material and thus increase the total absorption.

[0055] In some embodiments, a dual-threshold detector is used to improve the SNR.

[0056] In some embodiments, the x-ray detector 116 resolves one or more x-ray photon energies and generates a signal for each x-ray energy component that is indicative of a property of the sample. In some embodiments, the x-ray detector 116 comprises any of a CCD array, a microchannel plate, a photodiode array, a microstrip proportional counter, a gas-filled proportional counter, a scintillator, or a fluorescent material.

[0057] In this way, X-ray photon interactions within the detector are differentiated by energy, in addition to pixel location and count number. In some embodiments, X-ray photon interactions are differentiated by comparing their energy to a predetermined upper threshold and a predetermined lower threshold. In one embodiment, this information is communicated to a computing system 130 via output signal 126 for further processing and storage.

[0058] In some embodiments, the detector is scanned relative to the incoming X-rays to mitigate damage or overcharging from the incident zero-order beam. In some such embodiments, the detector is continuously scanned relative to the incoming X-rays to avoid dwelling the zero-order beam at a particular location on the detector surface for an extended period. In some other embodiments, the detector is periodically moved relative to the incoming X-rays to avoid dwelling the zero-order beam at a particular location on the detector surface for an extended period. In some embodiments, the scanning or periodic movement is approximately perpendicular to the incoming X-rays. In some embodiments, the movement is rotational (e.g., the detector is rotated so that a particular location on the detector surface describes a circle in space). In some embodiments, the movement is a combination of translational movements that move the point of incidence of the zero-order beam to various different locations on the detector surface.

[0059] In an X-ray scattering measurement, a structure (e.g., a high-aspect-ratio, vertically fabricated structure) diffracts a collimated X-ray beam into several diffraction orders. Each diffraction order travels in a specific, predictable direction. The angular spacing of the diffraction orders is inversely proportional to the sample's lattice constant divided by the wavelength. The diffraction orders are detected by a detector array positioned at a distance from the wafer. Each pixel of the detector outputs a signal indicating the number of photons that hit the pixel.

[0060] The intensities of the diffraction orders have the form I(m,n,θ,ϕ,λ), where {m,n} are integer indices of the diffraction orders, {θ,ϕ} are the elevation and azimuth angles of the incident beam (i.e., the polar coordinates of the incident chief ray relative to a coordinate system fixed to the wafer), and λ is the wavelength of the incident X-ray.

[0061] As the illumination light emerges from the illuminator and propagates toward the sample, it is perturbed by several noise sources. Exemplary interferences include beam current fluctuations, temperature-induced optical drift, and so on. The perturbed incident flux is denoted as F0(1+n1).

[0062] The target scatters the incident radiation in a manner that depends on the azimuth and elevation angles of the incident beam. The efficiency with which the light is scattered into a number of orders (m, n) can be defined as S mn(θ, ϕ). As the diffracted light propagates from the sample to the detector, the beam passes through other scattering media that similarly affect all orders with a certain variation (1 + n 2) and parasitic noise (n 3). In this way, the total intensity of each order, I mn, measured in a time t, can be expressed by Equation (1).

[0063] In some embodiments, it is desirable to perform measurements at different orientations, described by rotations about the x and y axes indicated by coordinate system 146 depicted in FIG1 . This increases the precision and accuracy of the measured parameters and reduces correlations among parameters by expanding the number and diversity of data sets available for analysis to include a variety of large-angle, out-of-plane orientations. Measuring sample parameters using a deeper, more diverse data set also reduces correlations among parameters and improves measurement accuracy. For example, in a normal orientation, x-ray scattering measurements can resolve a feature's critical dimension but are largely insensitive to a feature's sidewall angle and height. However, by collecting measurement data over a wide range of out-of-plane angular positions, a feature's sidewall angle and height can be resolved.

[0064] As shown in FIG1 , the metrology tool 100 includes a sample positioning system 140 configured to both align and orient the sample 101 within a wide range of out-of-plane angular orientations relative to the scatterometer. In other words, the sample positioning system 140 is configured to rotate the sample 101 over a wide range of angles about one or more rotation axes aligned in-plane with the surface of the sample 101. In some embodiments, the sample positioning system 140 is configured to rotate the sample 101 over a range of at least 90 degrees about one or more rotation axes aligned in-plane with the surface of the sample 101. In some embodiments, the sample positioning system is configured to rotate the sample 101 over a range of at least 120 degrees about one or more rotation axes aligned in-plane with the surface of the sample 101. In some other embodiments, the sample positioning system is configured to rotate the sample 101 over a range of at least 1 degree about one or more rotation axes aligned in-plane with the surface of the sample 101. In this manner, angularly resolved measurements of the sample 101 are collected by the metrology system 100 at any number of locations on the surface of the sample 101. In one example, the computing system 130 communicates a command signal indicating a desired position of the sample 101 to the motion controller 145 of the sample positioning system 140. In response, the motion controller 145 generates command signals to the various actuators of the sample positioning system 140 to achieve the desired position of the sample 101.

[0065] By way of non-limiting example, as illustrated in FIG. 1 , the sample positioning system 140 includes an edge clamping chuck 141 that fixedly attaches the sample 101 to the sample positioning system 140 . A rotary actuator 142 is configured to rotate the edge clamping chuck 141 and the attached sample 101 relative to a perimeter frame 143 . In the depicted embodiment, the rotary actuator 142 is configured to rotate the sample 101 about the x-axis of the coordinate system 146 depicted in FIG. As depicted in FIG. 1 , a rotation of the sample 101 about the z-axis is an in-plane rotation of the sample 101. Rotations about the x- and y-axes (not shown) are out-of-plane rotations of the sample 101, effectively tilting the surface of the sample relative to the metrology elements of the metrology system 100 . Although not illustrated, a second rotary actuator is configured to rotate the sample 101 about the y-axis. A linear actuator 144 is configured to translate the perimeter frame 143 in the x-direction. Another linear actuator (not shown) is configured to translate the perimeter frame 143 in the y-direction. In this way, every position on the surface of the sample 101 can be used to take measurements over a range of out-of-plane angular positions. For example, in one embodiment, a position of the sample 101 is measured within several angular increments within a range of -45 degrees to +45 degrees relative to the normal orientation of the sample 101.

[0066] In general, the sample positioning system 140 may include any suitable combination of mechanical elements to achieve the desired linear and angular positioning performance, including but not limited to goniometer stages, hexapod stages, angular stages, and linear stages.

[0067] As described herein, x-ray scattering measurements are performed with multiple orientations of the illuminating x-ray beam relative to the surface normal of a semiconductor wafer. Each orientation is described by any two angular rotations of the wafer 101 relative to the x-ray illumination beam, or vice versa. In one example, the orientation can be described relative to a coordinate system fixed to the wafer. FIG3 depicts an x-ray illumination beam 117 incident on wafer 101 at a particular orientation described by angles φ and θ. A coordinate frame XYZ is fixed to a metrology system, and a coordinate frame X'Y'Z' is fixed to wafer 101. Z is aligned with an axis normal to the surface of wafer 101. X and Y lie in a plane aligned with the surface of wafer 101. Similarly, Z' is aligned with an axis normal to the surface of wafer 101, and X' and Y' lie in a plane aligned with the surface of wafer 101. As depicted in FIG3 , the x-ray illumination beam 117 lies in the X'Z' plane. Angle ϕ describes the orientation of x-ray illumination beam 117 relative to the surface normal of the wafer in the X'Z' plane. Furthermore, angle θ describes the orientation of the X'Z' plane relative to the XZ plane. Together, θ and ϕ uniquely define the orientation of x-ray illumination beam 117 relative to the surface of wafer 101. In this example, the orientation of the x-ray illumination beam relative to the surface of wafer 101 is described by a rotation about an axis normal to the surface of wafer 101 (i.e., the Z axis) and a rotation about an axis aligned with the surface of wafer 101 (i.e., the Y' axis). In some other examples, the orientation of the x-ray illumination beam relative to the surface of wafer 101 is described by a rotation about a first axis aligned with the surface of wafer 101 and another axis aligned with the surface of wafer 101 and perpendicular to the first axis, as described with reference to FIG. 1 .

[0068] In a further aspect, an x-ray scattering measurement system is used to determine a property of a sample (e.g., a structural parameter value) based on an x-ray scattering measurement image. As depicted in FIG1 , a metrology tool 100 includes a computing system 130 for acquiring a signal 126 generated by a detector 116 and determining a property of the sample based at least in part on the acquired signal.

[0069] In one aspect, the values ​​of one or more parameters of interest characterizing a semiconductor structure under measurement are estimated by regressing detected images using a trained machine learning-based electromagnetic response model. The detected images capture the spatial distribution of scattered diffraction orders at the detector plane of an x-ray scattering measurement system.

[0070] FIG4 illustrates a diagram of a measurement engine 150 configured to estimate sample parameter values ​​based on x-ray scattering measurement data using a trained machine learning-based electromagnetic response model. In one embodiment depicted in FIG1 , computing system 130 is configured as a measurement engine 150 to implement measurement functionality as described herein.

[0071] Generally, the values ​​of one or more parameters of interest (e.g., critical dimension, sidewall angle, height, overlay, etc.) are determined by inversely solving a predetermined trained ML-based electromagnetic response model. The values ​​of the one or more parameters of interest are provided as input to the trained ML-based electromagnetic model. An image determined based on the output of the trained ML-based electromagnetic model is compared with the actual measured image. The difference is used to iteratively adjust the values ​​of the one or more parameters of interest. In this way, target profile parameters are estimated that minimize the error between the measured scattered x-ray intensity and the modeled result.

[0072] As depicted in FIG4 , the measurement engine 150 includes a trained machine learning-based electromagnetic response module 152, a data decompression module 154, a metrology system model module 156, and an error estimation module 160. Initial values ​​of parameters of interest (POI initial 151) characterizing a measured structure are provided as input to the trained machine learning-based electromagnetic response module 152. In response, the trained machine learning-based electromagnetic response module 152 calculates the values ​​of principal components 153. Principal components 153 are communicated to the data decompression module 154. The data decompression module 154 maps the values ​​of principal components 153 to values ​​of electromagnetic response metrics 155. Exemplary electromagnetic response metrics include Q-space parameter values, scattering level efficiency, and scattering coefficient. The electromagnetic response metrics 155 are communicated to the metrology system module 156. The metrology system module 156 maps the values ​​of the electromagnetic response metrics 155 to a simulated image (IMG sim 157) at the detector surface. The simulated image IMG sim 157 and the measured image IMG meas 158 are transmitted to an error assessment module 160. Error assessment module 160 evaluates the difference between the measured and simulated images. If the difference is less than a threshold value THRES 159, the iteration stops and the current value of the parameter of interest (POI current 161) is transmitted as the estimated value of the parameter of interest and stored in memory 180. If the difference is greater than the threshold value, error assessment module 160 generates an updated value of the parameter of interest (POI undated 162). The updated value is transmitted to the trained ML-based electromagnetic response model to initiate another iteration of the regression.

[0073] In the embodiment depicted in FIG4 , a trained ML-based electromagnetic response model maps geometric parameter values ​​to principal components, a data decompression module maps the principal components to electromagnetic response metrics (e.g., scattering level efficiency), and a metrology system model maps the electromagnetic response metrics to detector images. However, in general, both the data decompression module 154 and the metrology system module 156 are optional.

[0074] In some examples, data compression is not used to train the ML-based EM response model. In these examples, data decompression is not used, and the trained ML-based EM response model directly maps geometric parameter values ​​to EM response metrics (such as scattering level efficiency).

[0075] In some cases, a metrology system model is not used. In these cases, a trained ML-based electromagnetic response model maps geometric parameter values ​​directly to the scattered image. This approach requires significantly more work to train the model, and the resulting trained model tends to be less accurate.

[0076] The metrology system model is a kinematic model that typically does not require significant computational effort. Separating the metrology system model from the trained ML-based electromagnetic response model provides several benefits. By separating the metrology system model from the ML-based electromagnetic response model, the size of the training sample is reduced from millions of detector pixels to thousands of scattering-level efficiencies. This significantly reduces the computational effort required to train the ML-based electromagnetic response model. Furthermore, separating the metrology system model from the ML-based electromagnetic response model decouples the trained ML-based electromagnetic response model from the metrology system hardware. This makes the trained ML-based electromagnetic response model less sensitive to hardware changes, such as long-term tool drift, environmental changes, system replacements, system maintenance, etc. These hardware changes only affect the metrology system model and can be compensated for by recalibrating the metrology system model without altering the trained ML-based electromagnetic response model.

[0077] In some examples, the electromagnetic response metrics are Q-space parameter values. In these examples, the trained ML-based electromagnetic response model maps the geometric parameter values ​​to Q-space parameter values, and the metrology system model maps the Q-space parameter values ​​to images.

[0078] In some other examples, the electromagnetic response metric is scattered level efficiency. In these examples, the trained ML-based electromagnetic response model maps geometric parameter values ​​to scattered level efficiency and the metrology system model maps scattered level efficiency to an image.

[0079] In some other examples, the electromagnetic response metric is a scattering coefficient (i.e., a complex scattering level value). In these examples, the trained ML-based electromagnetic response model maps geometric parameter values ​​to scattering coefficients and the metrology system model maps scattering level values ​​to images.

[0080] In some other examples, the electromagnetic response metric is a scattered image at the detector. In these examples, a trained machine learning-based electromagnetic response model maps the value of the parameter of interest to one or more images at the x-ray detector.

[0081] In a further aspect, a machine learning-based electromagnetic response model is trained based on a training dataset comprising a set of design of experiments (DOE) values ​​for a parameter of interest and corresponding DOE values ​​for a plurality of electromagnetic response metrics. The training involves regressing the training dataset to minimize an objective function that minimizes the error between the DOE values ​​characterizing the plurality of electromagnetic response metrics and the values ​​of the plurality of electromagnetic response metrics determined using the machine learning-based electromagnetic response model.

[0082] FIG5 illustrates a diagram of a measurement model training engine 170 configured to train a machine learning-based electromagnetic response model according to the methods described herein. In the embodiment depicted in FIG5 , a physics-based electromagnetic solver is used to generate DOE values ​​for an electromagnetic response metric (e.g., scattering level efficiency) for a wide range of DOE values ​​for a parameter of interest. The range of DOE values ​​spans the expected process range of the semiconductor structure being measured. This generates a large training dataset containing a large number of input-output pairs (e.g., DOE values ​​for the parameter of interest and corresponding DOE values ​​for scattering level efficiency).

[0083] Next, a machine learning-based electromagnetic response model is trained to match the input-to-output projection provided by the physics-based electromagnetic solver. In this way, the machine learning-based electromagnetic response model is trained to replicate the input-output characteristics of the physics-based electromagnetic solver, but with much less computational effort.

[0084] As depicted in FIG5 , a set of DOEs (POI DOE) 171 for the values ​​of the parameter of interest is communicated to a physics-based electromagnetic solver module 172. In response, the physics-based electromagnetic solver module 172 generates corresponding DOE values ​​for an electromagnetic response metric 173. The DOE values ​​for the electromagnetic response metric 173 are communicated to a data compression module 174, which maps the DOE values ​​for the electromagnetic response metric 173 to a set of principal components 175. This effectively reduces the size of the electromagnetic response metric.

[0085] For typical use cases in x-ray scattering measurements, the vector of electromagnetic response metrics 173 can be extremely large, for example, thousands of scattering levels multiplied by tens of angles (e.g., 100 angles). In one example, the training set contains 50,000 different values ​​of several input parameters and 50,000 corresponding values ​​of electromagnetic response metrics 173. Dimensionality reduction simplifies model training and, in some cases, is necessary to make the training process computationally feasible. In one example, principal component analysis (PCA) is used to compress the scattering level efficiencies, reducing the size of the dataset from 1e5 to 1e2. Exemplary data compression techniques include, but are not limited to, PCA, kernel PCA, and autoencoding. In general, any suitable data compression technique can be applied to reduce the size of the electromagnetic response metrics.

[0086] As depicted in FIG5 , a set of principal components 175 and a corresponding set of DOEs (POI DOEs) for parameters of interest 171 are transmitted to an ML-based electromagnetic response model training module 176 for training. The trained ML-based electromagnetic response model 177 is transmitted and stored in a memory 180. Generally speaking, the ML-based model is any suitable ML-based model, including, but not limited to, tensor product interpolation, radial basis interpolation, artificial neural networks, support vector machines, linear models, or any combination thereof.

[0087] In some embodiments, the ML-based electromagnetic response model training module 176 implements a linear or nonlinear regression that iteratively tunes model weighting parameters to achieve a best fit between the principal components generated by the physics-based electromagnetic solver and the principal components generated by the trained ML model. In some embodiments, the degree of fit is characterized by an objective function. The objective function includes, but is not limited to, a mathematical expression comprising a residual value associated with each of a plurality of electromagnetic response metrics. In some examples, the objective function represents the sum of the squared values ​​of the residual values. In other examples, the objective function represents the sum of the squared values ​​of the logarithms of the residual values, etc. In general, any objective function suitable for representing the error between the principal components generated by the physics-based electromagnetic solver and the principal components generated by the trained ML model is contemplated within the scope of this patent document.

[0088] In a further aspect, the performance of a trained ML-based EM response model is evaluated to determine whether additional training is needed before implementing the trained model. In some examples, the model is evaluated based on a library quality index ranging from 0 to 1. If the library quality index reaches a predetermined threshold (e.g., 0.9), the trained ML-based EM response model is considered sufficiently trained and ready for implementation. If the library quality index drops below the predetermined threshold, the trained ML-based EM response model undergoes additional training (e.g., further regression).

[0089] In other examples, the model is trained based on maximizing one of the R² values ​​for all scattered class efficiencies. If the R² value for each scattered class efficiency reaches a predetermined threshold (e.g., 0.9), the trained ML-based EM response model is considered sufficiently trained and ready for implementation. If the R² value for each scattered class efficiency drops below the predetermined threshold, the trained ML-based EM response model undergoes additional training (e.g., further regression).

[0090] FIG6 is a plot 191 showing the R² values ​​for various scattered level efficiencies after initial training of a machine learning-based electromagnetic response model. As depicted in FIG6 , a large number of scattered level efficiencies are characterized by an R² value greater than 0.9. However, a large number of scattered level efficiencies are characterized by an R² value less than 0.9.

[0091] FIG7 is a plot 192 showing the R2 values ​​of each scattering level efficiency after retraining the machine learning based electromagnetic response model. As depicted in FIG6, the fit of all scattering level efficiencies is characterized by an R2 value greater than 0.9 after training.

[0092] In another example, the model is trained to minimize a weighted sum of residual values ​​associated with each scattering level efficiency.

[0093] FIG8 is a histogram 193 showing the number of image pixels having residual values ​​in different ranges after initial training of a machine learning-based electromagnetic response model. In one example, the residual value is the difference between the intensity at each specific pixel as modeled by a physics-based electromagnetic solver and a machine learning-based electromagnetic response model. As depicted in FIG8 , the image pixel residual values ​​are distributed within a range from 0 to 1, with an average value of approximately 0.25.

[0094] FIG9 shows a histogram 194 of the number of image pixels characterized by residual values ​​within different ranges after retraining a machine learning-based electromagnetic response model. As depicted in FIG9 , image pixel residual values ​​are distributed within a range from 0 to 0.015, with an average value of approximately 0.0025. As depicted in FIG9 , the fit of all scattering level efficiencies is characterized by a much smaller residual value after retraining.

[0095] In addition to conventional regression, the ML-based electromagnetic response model training module 176 can use any number of advanced regression techniques, including but not limited to a multi-seed regression, a multi-pass regression, and a regularized regression.

[0096] In some examples, these advanced regression techniques improve regression robustness and eliminate multiple local minima. In one example of multi-seed regression, a measured scattered image is first compared with a generated image library to train an ML-based electromagnetic response model to identify a small number of relatively close matches. The DOE value of the parameter of interest corresponding to the selected image is used as the initial evaluation point (POI initial) in the subsequent regression analysis. In some of these examples, multiple regressions are initiated at each initial evaluation point and executed in parallel. Furthermore, the best fit is selected as the global minimum.

[0097] In one example, one hundred regressions were performed to test the performance of a trained ML-based EM response model compared to a conventional EM solver. The ML-based EM response model was trained using 500 principal components. A complex memory structure was measured, and 11 parameters of interest were varied in the regression. The average solution time using the EM solver was 77 seconds. Shape discretization and EM solution time consumed 64 seconds, and the metrology system model consumed 13 seconds of the combined 77 seconds. In contrast, the average solution time using the trained ML-based EM response model was 25 seconds. The trained ML-based EM response model solution time consumed 12 seconds, and the metrology system model consumed 13 seconds of the combined 25 seconds. Therefore, using the trained ML-based EM response model, the total regression time was reduced by a factor of 3, and the regression time associated with shape discretization and EM simulation was reduced by a factor of 5.

[0098] In the embodiment depicted in FIG5 , a physics-based electromagnetic solver is used to generate the training dataset. However, in some other embodiments, the training dataset is obtained from known reference data. In one example, several structures are measured to obtain the scattered level efficiency, and the same structures are measured by a trusted reference measurement system (e.g., a focused ion beam) to directly measure the value of the corresponding parameter of interest.

[0099] In addition, in the embodiment depicted in FIG5 , a data compression module is used to reduce the size of the training data used to train the ML-based EM response model. However, in general, data compression is optional. In these embodiments, the EM response metrics generated by the physics-based EM solver are directly used to train the ML-based EM response model.

[0100] In another further aspect, the value of the parameter of interest is determined from the measured image of the measured structure based on regression using a series of trained ML-based electromagnetic response models.

[0101] As described above, a first trained ML-based electromagnetic response model is used to estimate the values ​​of one or more parameters of interest based on measured X-ray scattering measurement images. In some embodiments, an additional set of DOE values ​​for the parameter of interest (e.g., 20 to 50 additional values) is selected that are very close to the value of the parameter of interest determined by the first trained ML-based electromagnetic response model.

[0102] A physics-based electromagnetic solver is used to determine DOE values ​​for a plurality of electromagnetic response metrics corresponding to each additional set of values ​​for the parameter of interest. The DOE values ​​for the parameter of interest and the additional sets of corresponding DOE values ​​for the plurality of electromagnetic response metrics comprise a second training dataset. A second machine learning-based electromagnetic response model is trained based on the second training dataset. Finally, refined values ​​of the parameter of interest characterizing one or more measured semiconductor structures are estimated by regressing the second trained machine learning-based electromagnetic response model on one or more detected images.

[0103] In another further aspect, a value of a parameter of interest is determined from a measured image of a measured structure based on regression using a combination of a trained ML-based EM response model and a physics-based EM solver. More specifically, the goodness of fit associated with each EM response metric is evaluated to determine whether each particular EM response metric should be calculated using a trained ML-based EM response model or a physics-based EM solver.

[0104] In one example, a goodness of fit (eg, R 2 , residual, etc.) is determined between a DOE value for each of a plurality of electromagnetic response metrics and a value for each of the plurality of electromagnetic response metrics determined using a machine learning-based electromagnetic response model.

[0105] If the goodness of fit for a particular electromagnetic response metric is within an acceptable range (e.g., R2 > 0.8), the regression uses the trained machine learning-based electromagnetic response model to calculate the value of the particular electromagnetic response metric. However, if the goodness of fit for a particular electromagnetic response metric is outside the acceptable range (e.g., R2 < 0.8), the regression uses a physics-based electromagnetic solver to calculate the value of the particular electromagnetic response metric.

[0106] In this way, a physics-based electromagnetic solver replaces a trained ML-based electromagnetic response model when the accuracy of the trained ML-based electromagnetic response model is insufficient to meet a specific electromagnetic response metric.

[0107] In another further aspect, model training speed and accuracy are improved by scaling DOE values ​​of parameters of interest based on corresponding values ​​of a plurality of electromagnetic response metrics determined during training using a machine learning-based electromagnetic response model.

[0108] Typically, the input values ​​are scaled according to their nominal range values. In one example, the input values ​​are scaled according to their nominal range values ​​such that after scaling, when training an ML-based model, the input values ​​are within a range between -1 and 1.

[0109] However, in some other examples, the input values ​​of the ML-based EM response model are proportionally adjusted based on changes in the corresponding output values ​​of the ML-based EM response model. More specifically, when the output residual value varies within a relatively large range for a given change in an input value, the input value is proportionally adjusted within the relatively large range. Furthermore, when the output residual value varies within a relatively small range for a given change in an input value, the input value is proportionally adjusted within the relatively small range. By proportionally adjusting the input values ​​based on the output change, the training explores a relatively large range of values ​​of an input variable to which the output is sensitive, and a relatively small range of values ​​of an input variable to which the output is relatively insensitive. In one example, the output change of a specific output variable is evaluated based on the extreme values ​​of each input variable, while the values ​​of all other input variables are maintained in the middle of their ranges. The value of the specific input variable is proportionally adjusted using the inverse of the resulting output change. This process is repeated for all input variables.

[0110] In another example, a range of residual values ​​associated with each of a plurality of electromagnetic response metrics is determined based on a corresponding range of DOE values ​​for each parameter of interest. A scaling factor is generated for each parameter of interest. The scaling factor associated with a particular parameter of interest is the range of residual values ​​determined over the full range of values ​​for the particular parameter of interest divided by the maximum range of residual values ​​determined over the full range of values ​​for each parameter of interest. During subsequent model training iterations (i.e., model retraining), the scaling factor associated with each parameter of interest is applied to the DOE value for each parameter of interest.

[0111] FIG12 illustrates a method 300 suitable for implementation by the metrology systems 100 and 200 of the present invention. In one aspect, it is recognized that the data processing blocks of method 300 can be performed via a pre-programmed algorithm executed by one or more processors of the computing system 130. While the following description is presented in the context of the metrology systems 100 and 200, it is recognized herein that the specific structural aspects of the metrology systems 100 and 200 are not intended to be limiting and should be construed as illustrative only.

[0112] In block 301, one or more semiconductor structures to be measured formed on a wafer surface are illuminated by a quantitative x-ray illumination radiation generated by an x-ray illumination source.

[0113] At block 302, one or more images of a plurality of diffraction orders of a quantity of radiation scattered from one or more structures in response to x-ray illuminating radiation incident on the one or more structures are detected by an x-ray detector.

[0114] In block 303 , values ​​of parameters of interest characterizing one or more semiconductor structures are estimated by regressing one or more detected images using a trained machine learning-based electromagnetic response model.

[0115] X-ray-based measurements of semiconductor structures as described herein may be performed on any number of different metrology systems, such as, but not limited to, x-ray transmission tools, x-ray reflection tools, infrared transmission tools, etc.

[0116] In a further aspect, x-ray scattering measurements are performed according to a measurement recipe comprising a range of incident angles, the x-ray scattering measurements providing sufficient resolution and penetration depth to characterize high aspect ratio structures throughout their depth.

[0117] In a further aspect, a measurement recipe is implemented on a metrology system by communicating control commands that cause a state of one or more components of the metrology system to change to implement an optimized measurement recipe.

[0118] In some examples, control commands are provided to the illumination source. In response, the electrical state of the illumination source is adjusted to change the scanning spot size and shape, illumination power, spot offset, incident angle, etc.

[0119] In some examples, control commands are provided to one or more positioning devices that control the position of one or more optical elements of the metrology system. In response, the one or more positioning devices change the position / orientation of the one or more optical elements to adjust the angle of incidence, the focal length between the illumination source and the illumination optics, beam positioning, the location of the beam spot on the optical element to minimize the effects of surface roughness, etc.

[0120] Metrology systems and techniques are used to measure structural and material properties associated with various semiconductor processes. In some examples, x-ray scattering measurements are performed to estimate critical dimensions, thicknesses, overlays, and material properties of high aspect ratio semiconductor structures, including but not limited to spin transfer torque random access memory (STT-RAM), three-dimensional NAND memory (3D-NAND) or vertical NAND memory (V-NAND), dynamic random access memory (DRAM), three-dimensional flash memory (3D-FLASH), resistive random access memory (Re-RAM), and phase change random access memory (PC-RAM).

[0121] In some embodiments, x-ray detector 116 is maintained in the same atmospheric environment as sample 101 (e.g., a gas-flushed environment). However, in some embodiments, the distance between sample 101 and x-ray detector 116 is long, and environmental disturbances (e.g., air turbulence) can cause noise in the detected signal. Therefore, in some embodiments, one or more x-ray detectors are maintained in a partial vacuum environment separated from the sample (e.g., sample 101) by a vacuum window.

[0122] Similarly, in some embodiments, x-ray illumination source 110, illumination optics 115, or both are maintained in the same atmospheric environment as sample 101 (e.g., a gas-flushed environment). However, in some embodiments, the optical path lengths between x-ray illumination source 110 and illumination optics 115, and between illumination optics 115 and sample 101, are long, and environmental disturbances (e.g., air turbulence) introduce noise into the illumination beam. Therefore, in some embodiments, x-ray illumination source, illumination optics 115, or both are maintained in a partial vacuum environment separated from the sample (e.g., sample 101) by a vacuum window.

[0123] FIG10 illustrates a diagram of a vacuum chamber 163 containing an x-ray illumination source 110 and illumination optics 115, and a vacuum chamber 164 containing an x-ray detector 116, in one embodiment. In a preferred embodiment, vacuum chamber 163 comprises a substantial portion of the optical path between x-ray illumination source 110 and sample 101, and vacuum chamber 164 comprises a substantial portion of the optical path between sample 101 and x-ray detector 116. The openings of vacuum chambers 163 and 164 are covered by vacuum windows 165 and 166, respectively. Vacuum windows 165 and 166 can be constructed of any suitable material that is substantially transparent to x-ray radiation, such as beryllium. Illumination beam 117 passes through vacuum window 165 as it propagates toward sample 101. After interacting with sample 101, scattered x-ray radiation 125 passes through vacuum window 166, enters vacuum chamber 164, and is incident on x-ray detector 116. A suitable vacuum environment 167 is maintained within vacuum chamber 163 to minimize disturbances to illumination beam 117, and a suitable vacuum environment 168 is maintained within vacuum chamber 164 to minimize disturbances to scattered x-ray radiation 125. A suitable vacuum environment can include any suitable vacuum level, any suitable flushing environment including an inert gas (e.g., helium), or any combination thereof. In this way, as much of the beam path as possible is positioned in vacuum to maximize throughput and minimize disturbances.

[0124] In some embodiments, the entire optical system including the sample 101 is maintained in a vacuum. However, in general, the costs associated with maintaining the sample 101 in a vacuum are high due to the complexity associated with the construction of the sample positioning system 140.

[0125] In some embodiments, a metrology target characterized by x-ray scattering measurements as described herein is positioned within a scribe street on the wafer being measured. In these embodiments, the metrology target is sized to fit the width of the scribe street. In some examples, the scribe street width is less than 80 microns. In some examples, the scribe street width is less than 50 microns. Generally, the scribe street widths used in semiconductor manufacturing tend to be smaller.

[0126] In some embodiments, the metrology target characterized by x-ray scattering measurements as described herein is located within an active die area of ​​the wafer being measured and is part of a functional integrated circuit (e.g., memory, image sensor, logic device, etc.).

[0127] Generally, a metrology target is characterized by an aspect ratio, which is defined as the maximum height dimension of the metrology target (i.e., the dimension normal to the wafer surface) divided by the maximum lateral extent (i.e., the dimension aligned with the wafer surface). In some embodiments, the metrology target has an aspect ratio of at least 20. In some embodiments, the metrology target has an aspect ratio of at least 40.

[0128] Figures 11A through 11C depict an isometric view, a top view, and a cross-sectional view, respectively, of a typical 3D FLASH memory device 190 subjected to measurements as described herein. The overall height (or equivalently, depth) of memory device 190 ranges from 1 micron to several microns. Memory device 190 is a vertical fabrication device. A vertical fabrication device such as memory device 190 essentially rotates a conventional planar memory device 90 degrees, orienting the bit lines and cell strings vertically (perpendicular to the wafer surface). To provide sufficient memory capacity, a large number of alternating layers of different materials are deposited on the wafer. This requires patterning processes to perform well at depths of several microns for structures with a maximum lateral extent of 100 nanometers or less. Consequently, aspect ratios of 25:1 or 50:1 are not uncommon.

[0129] Generally speaking, high-brightness x-ray scattering measurements enable high-flux x-ray radiation to penetrate into opaque areas of a target. Examples of geometric parameters that can be measured using x-ray scattering measurements include pore diameter, pore density, line edge roughness, line width roughness, sidewall angle, profile, critical dimension, overlay, edge placement error, and pitch. One example of a measurable material parameter includes electron density. In some examples, x-ray scattering measurements enable measurement of features smaller than 10 nm and advanced semiconductor structures requiring measurement of geometric and material parameters, such as STT-RAM, V-NAND, DRAM, PC-RAM, and Re-RAM.

[0130] It should be appreciated that the various steps described throughout the present invention can be performed by a single computer system 130 or, alternatively, by multiple computer systems 130. Furthermore, various subsystems of system 100 (such as sample positioning system 140) may include a computer system suitable for performing at least a portion of the steps described herein. Therefore, the above description should not be construed as limiting the present invention but rather as merely illustrative. Furthermore, one or more computing systems 130 may be configured to perform any other step(s) of any of the method embodiments described herein.

[0131] Additionally, computer system 130 may be communicatively coupled to detector 116 and illumination optics 115 in any manner known in the art. For example, one or more computing systems 130 may be coupled to computing systems associated with detector 116 and illumination optics 115, respectively. In another example, either detector 116 or illumination optics 115 may be directly controlled by a single computer system coupled to computer system 130.

[0132] The computer system 130 can be configured to receive and / or retrieve data or information from subsystems of the system (e.g., the detector 116 and the illumination optics 115, and the like) via a transmission medium that can include wired and / or wireless components. In this manner, the transmission medium can serve as a data link between the computer system 130 and other subsystems of the system 100.

[0133] The computer system 130 of the metrology system 100 can be configured to receive and / or retrieve data or information (e.g., measurement results, modeling inputs, modeling results, etc.) from other systems via a transmission medium that can include wired and / or wireless components. In this manner, the transmission medium can serve as a data link between the computer system 130 and other systems (e.g., the internal memory of the metrology system 100, external memory, or an external system). For example, the computing system 130 can be configured to receive measurement data (e.g., signal 126) from a storage medium (e.g., memory 132 or 180) via a data link. For example, spectral results acquired using a spectrometer in one of the detectors 116 can be stored in a permanent or semi-permanent memory device (e.g., memory 132 or 180). In this regard, the measurement results can be imported from internal memory or from an external memory system. Furthermore, the computer system 130 can send data to other systems via a transmission medium. For example, the sample parameter value 170 determined by the computer system 130 may be stored in a permanent or semi-permanent memory device (eg, memory 180). In this regard, the measurement results may be exported to another system.

[0134] The computing system 130 may include, but is not limited to, a personal computer system, a mainframe computer system, a workstation, a video computer, a parallel processor, or any other device known in the art. Generally speaking, the term "computing system" may be broadly defined to encompass any device having one or more processors that execute instructions from a memory medium.

[0135] Program instructions 134 for implementing methods such as those described herein may be transmitted via a transmission medium such as a wire, cable, or wireless transmission link. For example, as shown in FIG1 , program instructions stored in memory 132 are transmitted to processor 131 via bus 133. Program instructions 134 are stored in a computer-readable medium (e.g., memory 132). Exemplary computer-readable media include read-only memory, random access memory, a magnetic or optical disk, or a magnetic tape.

[0136] In some embodiments, x-ray scattering measurements as described herein are implemented as part of a process tool. Examples of process tools include, but are not limited to, lithography tools, film deposition tools, implantation tools, and etching tools. In this manner, the results of a measurement are used to control a process. In one example, x-ray scattering measurement data collected from one or more targets is sent to a process tool. The x-ray scattering measurement data is analyzed as described herein, and the results are used to adjust the operation of the process tool.

[0137] Scatterometry as described herein can be used to determine the properties of various semiconductor structures. Exemplary structures include, but are not limited to, FinFETs, low-dimensional structures (such as nanowires or graphene), sub-10 nm structures, lithographic structures, through-substrate vias (TSVs), memory structures (such as DRAM, DRAM 4F2, FLASH, MRAM, and high aspect ratio memory structures). Exemplary structural characteristics include, but are not limited to, geometric parameters (such as line edge roughness, line width roughness, pore diameter, pore density, sidewall angle, profile, critical dimension, pitch) and material parameters (such as electron density, composition, grain structure, morphology, stress, strain, and element identification).

[0138] As used herein, the term "critical dimension" includes any critical dimension of a structure (e.g., bottom critical dimension, middle critical dimension, top critical dimension, sidewall angle, grating height, etc.), a critical dimension between any two or more structures (e.g., the distance between two structures), and an offset between two or more structures (e.g., the overlay offset between overlaid grating structures, etc.). Structures may include three-dimensional structures, patterned structures, overlaid structures, etc.

[0139] As used herein, the term "critical dimension application" or "critical dimension measurement application" includes any critical dimension measurement.

[0140] As used herein, the term "metrology system" encompasses any system used, at least in part, to characterize a sample in any manner, including measurement applications such as critical dimension metrology, overlay metrology, focus / dose metrology, and composition metrology. However, these technical terms do not limit the scope of the term "metrology system" as used herein. Furthermore, system 100 can be configured for measurement of patterned and / or unpatterned wafers. The metrology system can be configured as an LED inspection tool, an edge inspection tool, a backside inspection tool, a macro inspection tool, or a multi-mode inspection tool (involving data from one or more platforms simultaneously), as well as any other metrology or inspection tool that benefits from calibrating system parameters based on critical dimension data.

[0141] Various embodiments of a semiconductor measurement system that can be used to measure a sample within any semiconductor processing tool (e.g., an inspection system or a lithography system) are described herein. The term "sample" is used herein to refer to a wafer, a reticle, or any other sample that can be processed (e.g., printed or inspected for defects) by means known in the art.

[0142] As used herein, the term "wafer" generally refers to a substrate formed from a semiconductor or non-semiconductor material. Examples include, but are not limited to, single crystal silicon, gallium arsenide, and indium phosphide. These substrates are commonly found and / or processed in semiconductor manufacturing facilities. In some cases, a wafer may consist solely of a substrate (i.e., a bare wafer). Alternatively, a wafer may include one or more layers of different materials formed on a substrate. The one or more layers formed on a wafer may be "patterned" or "unpatterned." For example, a wafer may include a plurality of dies having repeatable pattern features.

[0143] A "reticle" can be a reticle at any stage of a reticle process, and may or may not be released for use as a finished reticle in a semiconductor manufacturing facility. A reticle or "mask" is generally defined as a substantially transparent substrate having substantially opaque regions formed thereon and configured in a pattern. The substrate may comprise, for example, a glass material such as amorphous SiO2. During an exposure step in a lithography process, a reticle can be placed over a photoresist-covered wafer so that the pattern on the reticle can be transferred to the photoresist.

[0144] One or more layers formed on a wafer may be patterned or unpatterned. For example, a wafer may contain multiple dies, each with repeatable pattern features. The formation and processing of these material layers ultimately yields a finished device. Many different types of devices can be formed on a wafer, and the term wafer, as used herein, is intended to encompass a wafer on which any type of device known in the art is fabricated.

[0145] In one or more exemplary embodiments, the described functions may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or transmitted via a computer-readable medium as one or more instructions or code. Computer-readable media includes both computer storage media and communication media, including any medium that facilitates transfer of a computer program from one location to another. A storage medium may be any available medium that can be accessed by a general-purpose or special-purpose computer. By way of example and not limitation, such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store the desired code components in the form of instructions or data structures and that can be accessed by a general-purpose or special-purpose computer or a general-purpose or special-purpose processor. Again, any connection is properly referred to as a computer-readable medium. For example, if software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair cable, digital subscriber line (DSL), or wireless technologies such as infrared, radio, and microwave, the coaxial cable, fiber optic cable, twisted pair cable, DSL, or wireless technologies such as infrared, radio, and microwave are included within the definition of medium. As used herein, magnetic disk and optical disc include compact disc (CD), laser disc, optical disc, digital versatile disc (DVD), floppy disk, and Blu-ray disc, where magnetic disks typically reproduce data magnetically, while optical discs use lasers to reproduce data optically. Combinations of the above should also be included within the scope of computer-readable media.

[0146] Although certain specific embodiments are described above for instructional purposes, the teachings of this patent document have general applicability and are not limited to the specific embodiments described above. Accordingly, various modifications, adaptations, and combinations of the various features of the described embodiments may be practiced without departing from the scope of the present invention as set forth in the appended claims.

[0147] 100: Measurement system 101: Wafer / Sample 102: Detection area 110: X-ray illumination source / X-ray illumination system 111:Liquid Metal Container 112:Liquid Metal Collector 113: Electron beam source 114:Electronic Optical Devices 115: X-ray optics 116: X-ray detector 117: X-ray illumination beam 118: Electron Flow 119: Liquid Metal Jet 125: X-ray radiation 126: output signal 130: Operational System 131: Processor 132: Memory 133: Bus 134: Program Instructions 140: Sample positioning system 141:Edge clamping chuck 142: Rotary actuator 143: Peripheral frame 144:Linear actuator 145: Motion Controller 146: Coordinate System 150: Measurement Engine 151: Initial value of the parameter of interest 152: Trained electromagnetic response module based on machine learning (ML) 153: Principal component 154:Data decompression module 155: Electromagnetic Response Measurement 156:Metrics and Weights System Module 157:Simulated Image 158:Measured image 159:Threshold value 160: Error assessment module 161: Current value of the parameter of interest 162: Updated value of the parameter of interest 163: Vacuum Chamber 164: Vacuum Chamber 165: Vacuum Window 166: Vacuum Window 167: Vacuum environment 168: Vacuum environment 170: Measurement Model Training Engine 171:Design of Experiments (DOE) Collection 172: Physics-based electromagnetic solver module 173: Electromagnetic Response Measurement 174:Data Compression Module 175: Principal component 176: Electromagnetic response model training module based on machine learning (ML) 177: Trained electromagnetic response model based on machine learning (ML) 180:Memory 190:Memory device 191: Plotting 192: Plotting 193: Histogram 194:Histogram 200: Measurement System 300: Method 301: Block 302: Block 303: Block

Claims

1. A system of weights and measures, comprising: An X-ray illumination source configured to generate quantitative X-ray illumination radiation directed to one or more measured semiconductor structures formed on a wafer surface; an X-ray detector configured to detect one or more images of a plurality of diffraction orders of quantitative radiation scattered from the one or more structures in response to the incident X-ray illumination radiation on the one or more structures; and a computing system configured to: The values ​​of parameters of interest characterizing one or more semiconductor structures are estimated by regressing one or more detected images using a trained machine learning-based electromagnetic response model, wherein the trained machine learning-based electromagnetic response model maps the values ​​of the parameters of interest to the values ​​of a plurality of electromagnetic response measures; and the machine learning-based electromagnetic response model is trained on a training dataset containing design of experiments (DOE) values ​​of the parameters of interest and corresponding DOE values ​​of the plurality of electromagnetic response measures, wherein the training involves regressing the training dataset to a target function that minimizes the error between the DOE values ​​characterizing the plurality of electromagnetic response measures and the values ​​of the plurality of electromagnetic response measures determined using the machine learning-based electromagnetic response model.

2. The measurement system of claim 1, wherein each of the plurality of electromagnetic response measures is any one of a pixel intensity, a scattering coefficient, a scattering level efficiency, and a scattering level value in Q space at the X-ray detector.

3. The measurement system of claim 1, wherein the regression of the one or more detected images includes a measurement system model, wherein the measurement system model maps the equivalent of the plurality of electromagnetic response measures to one or more images at the X-ray detector.

4. As in claim 1, the measurement system is further configured to: determine the DOE values ​​of the plurality of electromagnetic response measures corresponding to the sets of values ​​of the parameters of interest by means of simulation using a physics-based electromagnetic solver.

5. A measurement system as requested in item 1, wherein the training dataset is derived from measurements performed by a trusted reference measurement system.

6. The measurement system of claim 1, wherein the objective function is based on a residual value associated with each of the plurality of electromagnetic response measures.

7. The measurement system of claim 1, wherein the training involves reducing the size of one of the plurality of electromagnetic response measures.

8. As in request item 6, the measurement system is further configured to: proportionally adjust the DOE values ​​of the parameter of interest based on a range of residual values ​​associated with each of the plurality of electromagnetic response measures determined based on a range of DOE values ​​of the parameter of interest.

9. The measurement system of claim 1, wherein the regression involves any one of a multi-subgression, a multi-time regression, and a regularized regression.

10. The measurement system of claim 1, wherein the computing system is further configured to: select additional sets of DOE values ​​of the parameters of interest based on the estimates of the parameters of interest; determine the DOE values ​​of the plurality of electromagnetic response measures corresponding to the values ​​of the additional sets of the parameters of interest by performing simulation using a physics-based electromagnetic solver, wherein the DOE values ​​of the parameters of interest and the additional sets of the corresponding DOE values ​​of the plurality of electromagnetic response measures include a second training dataset; train a second machine learning-based electromagnetic response model based on the second training dataset; and estimate refined values ​​of the parameters of interest characterizing the one or more semiconductor structures by regressing the one or more detected images using the second trained machine learning-based electromagnetic response model.

11. The measurement system of claim 1, wherein the computing system is further configured to: estimate a goodness of fit between the DOE values ​​of the plurality of electromagnetic response measures and the values ​​of the plurality of electromagnetic response measures determined using a machine learning-based electromagnetic response model, wherein if the goodness of fit associated with the electromagnetic response measure is greater than a predetermined threshold, the regression of the one or more detected images is performed using the trained machine learning-based electromagnetic response model to determine a value of one of the plurality of electromagnetic response measures, and wherein if the goodness of fit associated with the electromagnetic response measure is less than a predetermined threshold, the regression of the one or more detected images is performed using a physics-based electromagnetic solver to determine the value of the electromagnetic response measure of the plurality of electromagnetic response measures.

12. A method of measurement, comprising: Illuminating one or more semiconductor structures formed on a wafer surface with a certain amount of X-ray illumination radiation generated by an X-ray illumination source; detecting one or more images of a plurality of diffraction levels of a certain amount of radiation scattered from the one or more structures to an X-ray detector, the certain amount of radiation being a response to the X-ray illumination radiation incident on the one or more structures and being scattered from the one or more structures; and estimating values ​​of parameters of interest characterizing the one or more semiconductor structures by regressing the one or more detected images using a trained machine learning-based electromagnetic response model, wherein the trained machine learning-based electromagnetic response model maps the values ​​of the parameters of interest to values ​​of a plurality of electromagnetic response measures; The machine learning-based electromagnetic response model is trained on a training dataset containing design of experiments (DOE) values ​​for the parameters of interest and corresponding DOE values ​​for a plurality of electromagnetic response measures. The training involves regressing the training dataset on an objective function to minimize the error between the DOE values ​​that characterize the plurality of electromagnetic response measures and the values ​​of the plurality of electromagnetic response measures determined using the machine learning-based electromagnetic response model.

13. The measurement method of claim 12, wherein each of the plurality of electromagnetic response measures is any one of a pixel intensity, a scattering coefficient, a scattering level efficiency, and a scattering level value in Q space at the X-ray detector.

14. The measurement method of claim 12, wherein the regression of the one or more detected images includes a measurement system model, wherein the measurement system model maps the equivalent of the plurality of electromagnetic response measures to one or more images at the X-ray detector.

15. The measurement method of claim 12, wherein the objective function is based on a residual value associated with each of the plurality of electromagnetic response measures.

16. The method of measurement as described in claim 12, further comprising: Reduce the size of one of the complex electromagnetic response metrics.

17. The method of measurement as described in claim 12, further comprising: The DOE values ​​of the parameter of interest are adjusted proportionally based on a range of residual values ​​associated with each of the plurality of electromagnetic response measures determined based on the range of DOE values ​​of the parameter of interest.

18. The method of measurement as described in claim 12, further comprising: Based on the estimated values ​​of the parameters of interest, an additional set of DOE values ​​for the parameters of interest is selected; the DOE values ​​of the plurality of electromagnetic response measures corresponding to the values ​​of the parameters of interest are determined by simulation using a physics-based electromagnetic solver, the DOE values ​​of the parameters of interest and the additional sets of the corresponding DOE values ​​of the plurality of electromagnetic response measures include a second training data set; a second machine learning-based electromagnetic response model is trained based on the second training data set; and refined values ​​of the parameters of interest for characterizing the one or more semiconductor structures are estimated by regression of the one or more detected images using the second trained machine learning-based electromagnetic response model.

19. The method of measurement as described in claim 12, further comprising: The goodness of fit between the DOE values ​​of the plurality of electromagnetic response measures and the values ​​of the plurality of electromagnetic response measures determined using a machine learning-based electromagnetic response model is estimated. If the goodness of fit associated with the electromagnetic response measure is greater than a predetermined threshold, the regression of the one or more detected images is performed using the trained machine learning-based electromagnetic response model to determine the value of one of the plurality of electromagnetic response measures. If the goodness of fit associated with the electromagnetic response measure is less than a predetermined threshold, the regression of the one or more detected images is performed using a physics-based electromagnetic solver to determine the value of the electromagnetic response measure.

20. A system of weights and measures, comprising: An X-ray illumination source configured to generate quantitative X-ray illumination radiation directed to one or more measured semiconductor structures formed on a wafer surface; an X-ray detector configured to detect one or more images of a plurality of diffraction orders of quantitative radiation scattered from the one or more structures in response to the incident X-ray illumination radiation; and a non-transitory computer-readable medium containing instructions that, when executed by one or more processors of a computing system, cause the computing system to: The values ​​of parameters of interest characterizing one or more semiconductor structures are estimated by regressing one or more detected images using a trained machine learning-based electromagnetic response model, wherein the trained machine learning-based electromagnetic response model maps the values ​​of the parameters of interest to the values ​​of a plurality of electromagnetic response measures; and the machine learning-based electromagnetic response model is trained on a training dataset containing design of experiments (DOE) values ​​of the parameters of interest and corresponding DOE values ​​of the plurality of electromagnetic response measures, wherein the training involves regressing the training dataset to a target function that minimizes the error between the DOE values ​​characterizing the plurality of electromagnetic response measures and the values ​​of the plurality of electromagnetic response measures determined using the machine learning-based electromagnetic response model.

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