Method and system for x-ray scatterometry measurements using machine learning-based electromagnetic response models

Abstract

Described herein are methods and systems for estimating values ​​of parameters of interest from X-ray scatterometry measurements while reducing computational effort. The values ​​of the parameters of interest are estimated by regression using a trained machine learning (ML)-based electromagnetic (EM) response model. A training data set includes a set of design of experiments (DOE) values ​​for the parameters of interest and corresponding DOE values ​​of multiple electromagnetic response metrics. In some embodiments, the values ​​of the parameters of interest from the measured images are determined based on regression using a series of multiple trained ML-based electromagnetic response models. In some embodiments, input values ​​used to train the ML-based EM response model are scaled based on the variation range of the model output.

Description

[Technical Field]

[0001] FIELD OF THE INVENTION The embodiments described herein relate to metrology systems and methods, and more particularly to methods and systems for improving measurements of semiconductor structures. [Background technology]

[0002] Semiconductor devices, such as logic devices and memory devices, are typically fabricated by a series of processing steps performed on a specimen. These processing steps result in the creation of various features and multiple structural levels of the semiconductor device. For example, lithography is a semiconductor manufacturing process that involves creating patterns on a semiconductor wafer. Other examples of semiconductor manufacturing processes include, but are not limited to, chemical-mechanical polishing, etching, film deposition, and ion implantation. Multiple semiconductor devices can be fabricated on a single semiconductor wafer, which can then be separated into individual semiconductor devices.

[0003] Metrology is used at various stages of the semiconductor manufacturing process to detect defects on wafers and improve yield. Several metrology-based techniques, including implementations of scatterometry and reflectometry and associated analysis algorithms, are widely used to characterize minimum line widths, film thickness, composition, and other parameters of nanoscale structures.

[0004] Traditionally, scatterometry critical linewidth (SCD) measurements are performed on targets consisting of thin films and / or periodically repeating structures. During device fabrication, these thin films and periodic structures typically represent the actual device geometry and material composition, or intermediate designs. As devices (e.g., logic and memory devices) move to smaller dimensions on the nanometer scale, their characterization becomes more challenging. Devices incorporating complex three-dimensional shapes and materials with diverse physical properties contribute to the difficulty of characterization. For example, modern memory structures often have high-aspect-ratio three-dimensional structures that limit the penetration of optical radiation to the lowest layers. While optical metrology tools using infrared to visible light can penetrate many layers of semitransparent materials, the long wavelengths that enable good penetration depths do not provide sufficient sensitivity to small anomalies. Furthermore, the increasing number of parameters required to characterize complex structures (e.g., FinFETs) leads to high correlations between the parameters. As a result, it is often impossible to reliably separate these target-characterizing parameters from one another.

[0005] In one example, longer wavelengths (such as near-infrared) are used to overcome the transmission issues of 3D flash devices that use polysilicon as one of the alternating materials in the stack. However, the mirror-like structure of 3D flash inherently causes a decrease in light intensity as the illumination travels deeper into the thin-film stack. This leads to reduced sensitivity and correlation issues at depth. In this situation, SCDs are only good at extracting a narrow set of metrology dimensions with high sensitivity and low correlation.

[0006] In another example, modern semiconductor structures increasingly employ opaque, high-dielectric constant materials, which often prevent optical radiation from penetrating layers composed of these materials, making measurements with thin film scatterometry tools such as ellipsometers and reflectometers increasingly difficult.

[0007] To address these challenges, more complex optical metrology tools have been developed, including those with multiple illumination angles, shorter illumination wavelengths, wider illumination wavelength ranges, and the ability to obtain more complete information from the reflected signal (e.g., measuring multiple Mueller matrix elements in addition to the traditional reflectivity or ellipsometry signal). Furthermore, X-ray scatterometry systems, such as transmission small-angle X-ray scatterometry (T-SAXS) systems, have shown promise in addressing challenging metrology applications. These X-ray-based scatterometry systems also feature a wide range of illumination angles and wavelengths. While current state-of-the-art optical / X-ray scatterometry systems have enabled challenging metrology applications, the computational complexity required to estimate the values ​​of the parameters of interest has emerged as a performance-limiting issue.

[0008] Many metrology techniques, including X-ray-based scatterometry, are indirect methods for measuring the physical properties of a sample under test. In most cases, raw measurement signals (such as measured images) cannot be used to directly determine the physical properties of a sample. Instead, a measurement model or a pre-computed model solution library is used to estimate the values ​​of one or more parameters of interest based on the raw measurement signals. For example, scatterometry is an indirect method for measuring the physical properties of a sample under test. Typically, a physics-based or machine learning-based measurement model is used to determine the physical properties of a sample based on the raw measurement signals (such as measured images).

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

[0010] In some embodiments, values ​​of the floating parameters of interest that provide the best fit between theoretical predictions and experimental data are found through an iterative process (e.g., regression). The unknown floating parameters of interest are varied, and model output values ​​(e.g., a simulated image composed of pixels) are calculated and compared to the measured image. This process is repeated until a set of sample parameter values ​​is found that provides a sufficiently close fit between the model output values ​​(e.g., a simulated image) and experimentally measured values ​​(e.g., a measured image). This fitting process typically requires the use of a regression engine, which adjusts the parameter values ​​that determine the shape and configuration of the model until an appropriate cost function associated with the difference between the measured and simulated orders is minimized. In other embodiments, the floating parameters are found by searching a library of pre-computed solutions to find the closest fit.

[0011] Using regression to directly estimate the values ​​of one or more parameters of interest, including those characterizing memory structures, has proven successful. However, the computational cost associated with the electromagnetic simulations underlying physics-based measurement models is a significant drawback. Typical memory structures are large, periodic structures measuring several micrometers in height. Consequently, the number of parameters used to characterize complex structures is enormous. This limits the computational effort required not only to calculate the electromagnetic scattering efficiency but also to construct the geometric model associated with a given set of parameters. Furthermore, most regression engines require the calculation of derivatives of the parametric representation of the scattering efficiency, which is computationally intensive and increasingly impractical.

[0012] In some other embodiments, a trained machine learning-based measurement model is used to directly estimate values ​​of the parameters of interest based on raw measurement data. In these embodiments, the machine learning-based measurement model receives raw measurement signals (such as measured images) as model inputs and estimates values ​​of the parameters of interest as model outputs.

[0013] Performing measurements based on trained machine learning-based models requires much less computational effort than regression of physics-based models, but machine learning-based measurement models must be trained to produce estimates of parameters of interest that are useful for a particular measurement application.

[0014] A machine learning-based measurement model has several weight parameters. Traditionally, this machine learning-based measurement model is trained by a regression process (e.g., ordinary least squares regression). Typically, the model is trained based on simulated images associated with known values ​​of the parameters of interest (i.e., design of experiments (DOE) data). The values ​​of the weight parameters are iteratively adjusted to minimize the difference between the known DOE values ​​of the parameters of interest and the values ​​of the parameters of interest estimated by the machine learning-based measurement model based on the simulated image data of the DOE. In a typical measurement application, hundreds of thousands of images are simulated to train the machine learning-based model. Therefore, as the model's complexity increases, the computational effort required to train the machine learning-based measurement model can become excessive.

[0015] Furthermore, trained machine learning-based models often suffer from robustness and accuracy issues: several variations in parameter values ​​form similar images, and the trained machine learning-based measurement model is unable to distinguish between these parameter values. [Prior art documents] [Patent documents]

[0016] [Patent Document 1] U.S. Patent No. 7,929,667 [Patent Document 2] U.S. Patent Publication No. 2015 / 0110249 Summary of the Invention [Problem to be solved by the invention]

[0017] Future metrology applications present several challenges due to the need for higher resolution, multiple correlations between parameters, increasingly complex geometric structures, and the increasing use of opaque materials. Therefore, methods and systems are needed to generate and implement highly accurate metrology models while reducing computational complexity. [Means for solving the problem]

[0018] Described herein are methods and systems for estimating values ​​of parameters of interest from X-ray scatterometry measurements with reduced computational effort. The values ​​of the parameters of interest are estimated by regression using a trained machine learning (ML)-based electromagnetic (EM) response model. The ML-based electromagnetic response model effectively replaces traditional three-dimensional structure discretization and physics-based electromagnetic response simulation in regression based on measurement models to X-ray scatterometry data.

[0019] The trained ML-based electromagnetic response model is much more computationally efficient than physics-based electromagnetic response models, thus enabling accurate X-ray scatterometry measurements of complex semiconductor structures with less computational effort.

[0020] In one aspect, the machine learning-based electromagnetic response model is trained based on a training dataset including a set of Design of Experiment (DOE) values ​​for the parameter of interest and corresponding DOE values ​​for a plurality of electromagnetic response metrics using regression on the training dataset to minimize an objective function characterizing the error between the DOE values ​​for the plurality of electromagnetic response metrics and values ​​of the plurality of electromagnetic response metrics determined using the machine learning-based electromagnetic response model.

[0021] In another embodiment, the performance of the trained ML-based EM response model is evaluated to determine whether additional training is required before implementation of the trained model.

[0022] In another aspect, determining the value of the parameter of interest from the measured image of the measured structure is based on regression using a plurality of successively trained ML-based electromagnetic response models.

[0023] In another aspect, determining values ​​of the parameters of interest from measured images of the measured structure is based on regression using a combination of a trained ML-based electromagnetic response model and a physics-based electromagnetic solver. More specifically, a goodness of fit associated with each electromagnetic response metric is evaluated to determine whether the individual electromagnetic response metric should be calculated using the trained ML-based electromagnetic response model or the physics-based electromagnetic solver.

[0024] In another aspect, the speed and accuracy of model training is improved by scaling the DOE value of a parameter of interest based on the corresponding values ​​of multiple electromagnetic response metrics determined during training using a machine learning-based electromagnetic response model.

[0025] The foregoing is a summary and contains, by definition, simplifications, generalizations, and omissions of detail. As such, those skilled in the art will appreciate that this summary is merely illustrative and is not intended to be in any way limiting. Other aspects, inventive features, and advantages of the devices and / or methods described herein will become apparent in the non-limiting detailed description set forth herein. [Brief explanation of the drawings]

[0026] [Figure 1] FIG. 1 illustrates a metrology system 100 configured to measure characteristics of a sample according to methods described herein. [Figure 2]FIG. 2 illustrates another embodiment of a metrology system 200 configured to measure characteristics of a specimen according to methods described herein. [Figure 3] 1 shows a beam of x-ray radiation 117 incident on a wafer 101 at a particular orientation represented by angles φ and θ. [Figure 4] FIG. 1 illustrates a measurement engine 150 configured to find specimen parameter values ​​based on x-ray scatterometry data according to methods described herein. [Figure 5] FIG. 1 illustrates a measurement model training engine 170 configured to train a machine learning-based electromagnetic response model according to methods described herein. [Figure 6] 10 is a chart showing the R2 values ​​of each scattering order efficiency after initial training of a machine learning-based electromagnetic response model. [Figure 7] 10 is a chart showing the R value of each scattering order efficiency after retraining of the machine learning-based electromagnetic response model. [Figure 8] This is a histogram showing the number of pixels in each range of residual values ​​after training of a machine learning-based electromagnetic response model. [Figure 9] 10 is a histogram showing the number of pixels in each range, with the residual values ​​for each pixel divided into ranges after retraining the machine learning-based electromagnetic response model. [Figure 10] 1 shows elements of metrology systems 100 and 200 contained in a vacuum environment separated from the sample 101. FIG. [Figure 11A] FIG. 1 is an isometric view of a typical 3D flash memory device 190 that may be measured using the methods described herein. [Figure 11B] FIG. 1 is a top view of a typical 3D flash memory device 190 measured with the methods described herein. [Figure 11C] 1 is a cross-sectional view of a typical 3D flash memory device 190 measured by the methods described herein. [Figure 12]3 is a flowchart illustrating an exemplary method 300 of model-based measurement described herein. DETAILED DESCRIPTION OF THE INVENTION

[0027] Reference will now be made in detail to background examples and certain embodiments of the invention, examples of which are illustrated in the accompanying drawings.

[0028] Described herein are methods and systems for estimating values ​​of parameters of interest from X-ray scatterometry measurements while reducing computational effort. More specifically, the values ​​of the parameters of interest are estimated by regression using a trained machine learning-based electromagnetic response model. This ML-based electromagnetic response model effectively replaces traditional three-dimensional structure discretization and physics-based electromagnetic response simulation in measurement model-based regression of X-ray scatterometry data. This trained machine learning (ML)-based electromagnetic response model is much more computationally efficient than physics-based electromagnetic response models. Thus, accurate X-ray scatterometry measurements of complex semiconductor structures are achieved with less computational effort.

[0029] 1 illustrates one embodiment of a metrology system 100 for measuring features of a specimen according to the exemplary methods described herein. As shown in FIG. 1, the system 100 can be used to perform x-ray scatterometry measurements across an examination area 102 of a specimen 101 positioned on a specimen positioning system 140.

[0030] In the illustrated embodiment, metrology tool 100 includes an x-ray radiation source 110 configured to generate x-ray radiation suitable for x-ray scatterometry measurements. In some embodiments, x-ray radiation source 110 is configured to generate wavelengths between 0.01 nanometers and 1 nanometer. X-ray radiation source 110 generates an x-ray beam 117 that is incident on examination region 102 of sample 101.

[0031] In general, any suitable high brightness x-ray radiation source capable of producing high brightness x-rays with a flux sufficient to enable high throughput line metrology can be envisioned for providing x-ray radiation for x-ray scatterometry measurements. In some embodiments, the x-ray source includes a tunable monochromator that allows x-ray radiation of different selectable wavelengths to be extracted from the x-ray source.

[0032] In some embodiments, one or more x-ray sources are used that emit radiation with photon energies greater than 15 keV, allowing the x-ray source to provide light at a wavelength that allows sufficient penetration throughout the device, not just the wafer substrate. Non-limiting examples of x-ray source 110 include particle accelerator sources, liquid anode sources, rotating anode sources, stationary solid anode sources, microfocus sources, microfocus rotating anode sources, and inverse Compton sources. In one example, an inverse Compton source available from Lyncean Technologies, Inc. (Palo Alto, California) may be considered. Another advantage of an inverse Compton source is that it can generate x-rays at a variety of photon energies, allowing for a variety of selectable wavelengths of x-ray radiation to be extracted from the x-ray source.

[0033] Examples of x-ray sources include electron beam sources configured to bombard a solid or liquid target and induce x-ray radiation. FIG. 2 illustrates a metrology system 200 for measuring characteristics of a specimen according to the exemplary methods described herein. Elements with the same number in metrology tools 100 and 200 are similar. However, in the embodiment illustrated in FIG. 2, x-ray irradiation source 110 is a liquid metal-based x-ray irradiation 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 includes one or more elements. By way of non-limiting example, liquid metal jet 119 may include any of aluminum, gallium, indium, tin, thallium, and bismuth. In this manner, liquid metal jet 119 generates x-ray emission lines corresponding to its constituent elements. In one embodiment, the liquid metal jet includes an alloy of gallium and indium. In some embodiments, the x-ray radiation source 110 is configured to produce wavelengths between 0.01 nanometers and 1 nanometer. An electron beam source 113 (e.g., an electron gun) generates an electron stream 118, which is directed toward a liquid metal jet 119 by electron-optics 114. Suitable electron-optics 114 include electromagnets, permanent magnets, or a combination of electromagnets and permanent magnets to focus and direct the electron beam toward the liquid metal jet. The liquid metal jet 119 and the electron stream 118 converge to produce an x-ray beam 117 that is incident on the examination region 102 of the sample 101.

[0034] A method and system for producing high brightness liquid metal x-ray radiation is described in US Pat. No. 6,223,999, the entirety of which is incorporated herein by reference.

[0035] In one embodiment, the incident x-ray beam 117 is a 24.2 keV indium kα beam, which is collimated to a divergence of less than 1 milliradian using multilayer x-ray optics for x-ray scatterometry measurements.

[0036] In some embodiments, the x-ray scattering measurements described herein are achieved without a screen between the x-ray source and the sample under test. In these embodiments, intensity measurements of beams incident at various angles of incidence, multiple wavelengths, or a combination of both, provide sufficient information to analyze a distribution map (i.e., image) of the material property of interest (e.g., complex refractive index, electron density, absorption coefficient, etc.) of the structure under test. However, in some other examples, a pinhole or other aperture is placed in a normally x-ray opaque screen between the x-ray source and the sample under test to improve the formation of a parallel x-ray beam. Measurements of the intensity of the diffraction pattern are made for several positions of this aperture. In other embodiments, a screen with a pseudo-random aperture pattern is used, and diffraction pattern measurements are made for multiple screen positions. It is conceivable that these techniques may provide additional information for analyzing the three-dimensional distribution of the material property of interest of the structure under test.

[0037] In some embodiments, the profile of the incident x-ray beam is controlled by two or more apertures, slits, or a combination thereof, while in other embodiments, the apertures, slits, or both are configured to rotate in coordination with the sample orientation, thereby optimizing the incident beam profile for different angles of incidence, different azimuthal angles, or both.

[0038] As shown in FIG. 1 , x-ray optics 115 shapes and directs incident x-ray beam 117 toward sample 101. In some embodiments, x-ray optics 115 includes an x-ray monochromator that monochromatizes the x-ray beam incident on sample 101. In one embodiment, a crystal monochromator, such as a Loxley-Tanner-Bowen monochromator, is used to monochromatize the beam of x-ray radiation. In some embodiments, x-ray optics 115 collimates or focuses x-ray beam 117 toward the inspection region 102 of sample 101 to a divergence angle of less than 1 milliradian using multilayer x-ray optics. In some embodiments, x-ray optics 115 includes one or more x-ray collimating mirrors, x-ray apertures, x-ray beam stops, refractive x-ray optics, diffractive optics such as zone plates, specular x-ray optics such as grazing incidence elliptical mirrors, poly-capillary optics such as hollow capillary x-ray waveguides, multilayer optics or systems, or any combination thereof. Further details are described in US Pat. No. 6,223,999, the entirety of which is incorporated herein by reference.

[0039] Typically, the focal plane of the illumination optics is optimized for each measurement application. In this manner, system 100 is configured to place the focal plane at different depths within the sample depending on the measurement application.

[0040] The x-ray detector 116 collects x-ray radiation 125 scattered from the sample 101 and generates an output signal 126 that is indicative of properties of the sample 101 that are responsive to the incident x-ray radiation according to an x-ray scatterometry measurement technique. In some embodiments, the scattered x-rays 125 are collected by the x-ray detector 116 in parallel with the sample positioning system 140 positioning and orienting the sample 101 to produce angularly resolved scattered x-rays.

[0041] In some embodiments, the x-ray scatterometry system has a wide dynamic range (10 5The photon-counting detector includes one or more photon-counting detectors (e.g., ultra-thin) and a thick, highly absorbing crystal substrate that absorbs the direct beam (i.e., the zeroth order beam) without damaging it and minimizes parasitic backscatter. In some embodiments, a single photon-counting detector detects the location and number of detected photons.

[0042] In full-beam x-ray scatterometry, the zeroth order beam must be collected in addition to the higher diffraction orders. The zeroth order beam has an intensity that is orders of magnitude greater than the other orders. If this zeroth order beam is not completely absorbed by the x-ray sensitive part of the detector, it will scatter and generate parasitic signals. The dynamic range of the measurement is limited by the intensity of these parasitic signals. For example, if the parasitic signals are 10 times the maximum flux signal (i.e., the zeroth order signal), -4 If the order is too large, then the signals associated with the many higher orders will be contaminated. Therefore, to increase the effective dynamic range of full-beam measurements, it is important that the detector (e.g., detector 116) has a high conversion efficiency of X-rays to electron-hole pairs and good absorption of X-rays.

[0043] Examples of detector materials suitable for full-beam x-ray scatterometry 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 within a narrow energy band corresponding to the energy to be converted.

[0044] In some embodiments, the thickness of the detector material is selected to achieve a desired absorption of incident X-rays, and in some embodiments, tilting the detector relative to the incident X-ray beam (various diffraction orders) increases the path length of the X-ray beam through the detector material, thereby increasing the total absorption.

[0045] In some embodiments, a dual threshold detector is used to improve the SNR.

[0046] In some embodiments, the x-ray detector resolves one or more x-ray photon energies and generates signals indicative of properties of the sample for each x-ray energy component. In some embodiments, the x-ray detector 116 includes 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.

[0047] 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 interaction energy to a predetermined upper threshold and a predetermined lower threshold. In one embodiment, this information is communicated via output signal 126 to computing system 130 for further processing and storage.

[0048] In some embodiments, the detector is scanned relative to the incident x-rays to mitigate damage or excessive charging from the incident zero-order beam. In some of these embodiments, the detector is continuously scanned relative to the incident x-rays to prevent the zero-order beam from dwelling for an extended period of time at a particular location on the detector surface. In other embodiments, the detector is periodically moved relative to the incident x-rays to prevent the zero-order beam from dwelling for an extended period of time at a particular location on the detector surface. In some embodiments, the scanning or periodic movement is approximately perpendicular to the incident x-rays. In some embodiments, the movement is rotational (e.g., the detector rotates so that a particular location on the detector surface traces a circle in space). In some embodiments, the movement is a combination of translational movement to move the point of incidence of the zero-order beam to various different locations on the detector surface.

[0049] In an x-ray scatterometry measurement, a structure (e.g., a high aspect ratio vertically fabricated structure) diffracts a parallel x-ray beam into multiple diffraction orders. Each diffraction order travels in a specific, predictable direction. The angular spacing between these diffraction orders is inversely proportional to the lattice constant of the sample divided by the wavelength. These diffraction orders are detected by a detector array placed some distance away from the wafer. Each pixel in this detector outputs a signal indicating the number of photons that strike that pixel.

[0050] The intensity of a diffraction order has the form I(m,n,θ,φ,λ), where {m,n} are the integer indexes 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 with respect to a coordinate system fixed on the wafer), and λ is the wavelength of the incident X-rays.

[0051] As the irradiated light travels from the source to the sample, it is subject to fluctuations due to several noise sources. Examples of disturbances include fluctuations in the electron beam current, optical drift due to temperature, etc. The fluctuating incident flux is denoted as F0(1+n1).

[0052] The behavior of incident light scattering by a target is determined by the azimuth and elevation angles of the incident beam. The efficiency of the (m,n)-order scattered light is S mn (θ,φ). This diffracted light passes through another scattering medium as it travels from the sample to the detector. All orders are similarly affected by some fluctuations (1 + n2) and parasitic noise (n3) from this scattering medium. Thus, the total intensity I of each order measured at time t is mn can be expressed by equation (1).

number

[0053] In some embodiments, it may be desirable to perform measurements at various orientations, expressed as rotations about the x- and y-axes of coordinate system 146 shown in FIG. 1 . This expands the number and diversity of data sets available for analysis to include a wide range of out-of-plane orientations, improving the precision and accuracy of measured parameters and reducing correlation between parameters. Measuring sample parameters using larger and more diverse data sets also reduces correlation between parameters and improves measurement accuracy. For example, in the normal orientation, x-ray scatterometry can resolve feature minimum linewidths but is less sensitive to feature sidewall angles and heights. However, collecting measurement data at a wide range of out-of-plane angular positions allows for feature sidewall angles and heights to be resolved.

[0054] As shown in Figure 1, the metrology tool 100 includes a sample positioning system 140 configured to position the sample 101 relative to the scatterometer and to orient the sample 101 relative to the scatterometer over a wide range of out-of-plane angles. That is, the sample positioning system 140 is configured to rotate the sample 101 over a wide range of angles about one or more in-plane rotational axes along 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 in-plane rotational axes along 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 in-plane rotational axes along the surface of the sample 101. In 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 in-plane rotational axes along the surface of the sample 101. In this manner, angle-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 embodiment, the computing system 130 communicates command signals indicating the 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 positioning of the sample 101.

[0055] As a non-limiting example, as shown in FIG. 1 , the specimen positioning system 140 includes an edge grip chuck 141. The edge grip chuck 141 is for fixedly mounting the specimen 101 to the specimen positioning system 140. A rotary actuator 142 is configured to rotate the edge grip chuck 141 and the attached specimen 101 relative to a perimeter frame 143. In the illustrated embodiment, the rotary actuator 142 is configured to rotate the specimen 101 about the x-axis of a coordinate system 146 shown in FIG. 1 . As shown in FIG. 1 , rotation of the specimen 101 about the z-axis is an in-plane rotation of the specimen 101. Rotation about the x- and y-axes (not shown) is an out-of-plane rotation of the specimen 101, which effectively tilts the surface of the specimen relative to the measurement elements of the metrology system 100. A second rotary actuator, not shown, is configured to rotate the specimen 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, any position on the surface of the sample 101 becomes available for measurement at various out-of-plane angular positions. For example, in one embodiment, one position of the sample 101 is measured over several steps at regular angle intervals within a range of -45 degrees to +45 degrees relative to the normal orientation of the sample 101.

[0056] In general, the sample positioning system 140 may include any suitable combination of mechanical elements that achieve the desired linear and angular positioning performance, including, but not limited to, goniometer stages, hexapod stages, angular stages, and linear stages.

[0057] The x-ray scatterometry measurements described herein are performed at multiple orientations of the illuminating x-ray beam relative to the normal to the surface of the semiconductor wafer. Each orientation is represented by any two angular rotations of the wafer 101 relative to the x-ray illumination beam (or vice versa). In one embodiment, these orientations may be represented relative to a coordinate system fixed to the wafer. FIG. 3 shows the x-ray illumination beam 117 incident on the wafer 101 at a specific orientation represented by angles φ and θ. The coordinate frame XYZ is fixed to the metrology system, and the coordinate frame X'Y'Z' is fixed to the wafer 101. Z coincides with the axis normal to the surface of the wafer 101. X and Y lie in a plane coincident with the surface of the wafer 101. Similarly, Z' coincides with the axis normal to the surface of the wafer 101, and X' and Y' lie in a plane coincident with the surface of the wafer 101. As shown in FIG. 3, the x-ray illumination beam 117 lies in the X'Z' plane. The angle φ represents the orientation of the x-ray illumination beam 117 relative to the normal to the surface of the wafer in the X'Z' plane. Furthermore, the angle θ represents the orientation of the X'Z' plane relative to the XZ plane. The combination of θ and φ uniquely defines the orientation of the x-ray illumination beam 117 relative to the surface of the wafer 101. In this example, the orientation of the x-ray illumination beam relative to the surface of the wafer 101 is represented by a rotation about an axis normal to the surface of the wafer 101 (i.e., the Z axis) and a rotation about an axis along the surface of the wafer 101 (i.e., the Y' axis). In some other embodiments, the orientation of the x-ray illumination beam relative to the surface of the wafer 101 is represented by a rotation about a first axis along the surface of the wafer 101 and another axis along the surface of the wafer 101 that is perpendicular to the first axis, as described with reference to FIG. 1 .

[0058] In other embodiments, an x-ray scatterometry system is used to determine a property (e.g., a structural parameter value) of the sample based on the x-ray scatterometry image. As shown in Figure 1, the metrology tool 100 includes a computing system 130 that is used to acquire signals 126 generated by the detector 116 and to determine a property of the sample based at least in part on the acquired signals.

[0059] In one aspect, values ​​of parameters of interest characteristic of one or more measured semiconductor structures are estimated by regression using a trained machine learning-based electromagnetic response model on a detected image capturing the spatial distribution of multiple diffraction orders scattered at a detector plane of an x-ray scatterometry system.

[0060] 4 illustrates a measurement engine 150. The measurement engine 150 is configured to estimate specimen parameter values ​​based on x-ray scatterometry data using trained machine learning-based electromagnetic response models. In one embodiment shown in FIG. 1, the computing system 130 is configured as the measurement engine 150 to implement the measurement functionality described herein.

[0061] Typically, values ​​of one or more parameters of interest (e.g., minimum line width, sidewall angle, height, overlay, etc.) are determined by an inverse analysis solution of a pre-established, 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, desired shape parameters are estimated that minimize the error between the measured scattered x-ray intensity and the modeled results.

[0062] 4, the measurement engine 150 includes a trained machine learning-based electromagnetic response module 152, a data recovery module 154, a measurement system model module 156, and an error estimation module 160. Initial values ​​of parameters of interest (POI) that characterize the structure under test are used to estimate the initial values ​​of the parameters of interest (POI). initial151 is provided as an input to a trained ML-based electromagnetic response module 152. In response, the trained ML-based electromagnetic response module 152 calculates values ​​of principal components 153. The principal components 153 are communicated to a data reconstruction module 154. The data reconstruction module 154 maps the values ​​of the principal components 153 to values ​​of electromagnetic response indices 155. Examples of electromagnetic response indices include Q-space parameter values, scattering order efficiencies, scattering coefficients, etc. The electromagnetic response indices 155 are communicated to a measurement system module 156. The measurement system module 156 maps the values ​​of the electromagnetic response indices 155 to a simulated image IMG of the detector surface. sim Mapped to 157. Simulation image IMG sim 157 and actual measurement image IMG meas 158 is transmitted to an error estimation module 160, which estimates the difference between the measured image and the simulated image. If the difference is less than a threshold THRES 159, the iteration stops and the current value of the parameter of interest POI current 161 is communicated to memory 180 and stored as an estimate of the parameter of interest. If the difference is greater than the threshold, the error estimation module 160 updates the parameter of interest POI undated 162. The updated values ​​are propagated to the trained ML-based electromagnetic response model to start a new iteration of the regression.

[0063] 4, the trained ML-based electromagnetic response model maps geometric parameter values ​​to principal components, which the data reconstruction module maps to electromagnetic response metrics (such as scattering order efficiencies), which the metrology system model maps to detector images, although in general both the data reconstruction module 154 and the metrology system module 156 are optional.

[0064] In some examples, no data compression is used to train the ML-based electromagnetic response module. In these embodiments, no data decompression is used and the trained ML-based electromagnetic response model directly maps geometric parameter values ​​to electromagnetic response metrics such as scattering order efficiencies.

[0065] In some embodiments, the measurement system model is not used. In these embodiments, the trained ML-based electromagnetic response model directly maps geometric parameter values ​​to the scattering image. This approach requires significant effort to train the model and tends to result in lower accuracy of the resulting trained model.

[0066] The measurement system model is a kinematic model, and kinematic models typically do not require significant computational effort. Separating the measurement system model from the trained ML-based electromagnetic response model has several advantages. By separating the measurement system model from the ML-based electromagnetic response model, the dimensionality of the training samples is reduced from millions of detector pixels to thousands of scattering order efficiencies. This significantly reduces the amount of computation required to train the ML-based electromagnetic response model. Furthermore, by separating the measurement system model from the ML-based electromagnetic response model, the trained ML-based electromagnetic response model is decoupled from the measurement system hardware. This makes the trained ML-based electromagnetic response model insensitive to hardware changes, such as long-term tool drift, environmental changes, system replacement, and system maintenance. These hardware changes only affect the measurement system model and can be compensated for by recalibrating the measurement system model without modifying the trained ML-based electromagnetic response model.

[0067] In some embodiments, the electromagnetic response metrics are Q-space parameter values. In these embodiments, the trained ML-based electromagnetic response model maps geometric parameter values ​​to Q-space parameter values ​​that the measurement system model maps to images.

[0068] In some other embodiments, the electromagnetic response metric is scattering order efficiency. In these embodiments, the trained ML-based electromagnetic response model maps geometric parameter values ​​to scattering order efficiencies, which the measurement system model maps to images.

[0069] In some other embodiments, the electromagnetic response indices are scattering coefficients, i.e., complex scattering order values, in these embodiments, the trained ML-based electromagnetic response model maps geometric parameter values ​​to scattering coefficients, which the measurement system model maps to images.

[0070] In some other embodiments, the electromagnetic response indicator is a scatter image at the detector. In these embodiments, the trained machine learning based electromagnetic response model maps values ​​of a parameter of interest to one or more images of the x-ray detector.

[0071] In another aspect, the machine learning-based electromagnetic response model is trained based on a training dataset including a set of Design of Experiment (DOE) values ​​for the parameter of interest and corresponding DOE values ​​for a plurality of electromagnetic response metrics using regression on the training dataset to minimize an objective function characterizing the error between the DOE values ​​for the plurality of electromagnetic response metrics and values ​​of the plurality of electromagnetic response metrics determined using the machine learning-based electromagnetic response model.

[0072] FIG. 5 illustrates a measurement model training engine 170. The measurement model training engine 170 is configured to train a machine learning-based electromagnetic response model according to the methods described herein. In the embodiment illustrated in FIG. 5, a physics-based electromagnetic solver is used to generate DOE values ​​of electromagnetic response metrics (e.g., scattering order efficiency) for a wide range of DOE values ​​of the parameter of interest. The range of DOE values ​​spans the expected processing range of the semiconductor structure being measured. This generates a large training data set containing a large number of input-output pairs. An example of an input-output pair may include a DOE value of the parameter of interest and a corresponding scattering order efficiency DOE value.

[0073] A machine learning-based electromagnetic response model is then trained to match the inferences derived from the inputs with the outputs provided by the physics-based electromagnetic solver. In this way, the machine learning-based electromagnetic response model is trained to reproduce the input-output characteristics of the physics-based electromagnetic solver with much less computational effort.

[0074] As shown in Figure 5, the DOE value set POI for the parameter of interest DOE 171 is communicated to a physics-based electromagnetic solver module 172. In response, the physics-based electromagnetic solver module 172 generates corresponding electromagnetic response index DOE values ​​173. The electromagnetic response index DOE values ​​173 are communicated to a data compression module 174, which maps the electromagnetic response index DOE values ​​173 to a principal component set 175, thereby effectively reducing the dimensionality of the electromagnetic response index.

[0075] In a typical use case in x-ray scatterometry, the dimension of the vector of the electromagnetic response index 173 can be very large, such as thousands of scattering orders times tens (e.g., hundreds) of angles. In one example, the training set includes 50,000 distinct values ​​of multiple input parameters and 50,000 corresponding values ​​of the electromagnetic response index 173. Dimensionality reduction can be necessary to make model training more efficient and, in some cases, to make the training process more computationally feasible. In one example, principal component analysis (PCA) is used to compress the scattering order indexes, reducing the dimensionality of the data set from 1e5 to 1e2. Examples of 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 dimensionality of the electromagnetic response index.

[0076] As shown in FIG. 5, a set of principal components 175 and a corresponding DOE set of parameters of interest POI DOE 171 is communicated to an ML-based electromagnetic response model training module 176 for training. The trained ML-based electromagnetic response model 177 is communicated to and stored in memory 180. In general, the ML-based electromagnetic response model may be 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.

[0077] In some embodiments, the ML-based electromagnetic response model training module 176 implements linear or nonlinear regression, which iteratively adjusts model weighting parameters to achieve the best fit between the principal components generated from the physics-based electromagnetic solver and the principal components generated by the ML model being trained. In some embodiments, this fit is characterized by an objective function, which may include, but is not limited to, a mathematical expression that includes residual values ​​associated with each of a plurality of electromagnetic response metrics. In some examples, the objective function represents the sum of the squares of the residual values. In other examples, the objective function represents the sum of the squares of the logarithms of the residual values, or the like. In general, any objective function suitable for representing the error between the principal components generated from the physics-based electromagnetic solver and the principal components generated by the ML model being trained may be envisioned within the scope of this patent document.

[0078] In other aspects, the performance of a trained ML-based EM response model is evaluated to determine whether additional training is required before implementing the trained model. In some embodiments, 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 properly trained and ready for implementation. If the library quality index falls below the predetermined threshold, the trained ML-based EM response model undergoes additional training (e.g., additional regressions).

[0079] In another embodiment, the model is based on the R 2 It is trained based on maximizing the value of R for each scattering order efficiency. 2 Once the value reaches a predetermined threshold (e.g., 0.9), the trained ML-based EM response model is considered properly trained and ready for implementation. 2If the value falls below a predetermined threshold, the trained ML-based EM response model undergoes further training (such as additional regressions).

[0080] Figure 6 shows the R of each scattering order efficiency after the initial training of the machine learning-based electromagnetic response model. 2 As shown in Figure 6, the goodness of fit of multiple scattering order efficiencies is R 2 However, R 2 There are significant scattering order efficiencies characterized by values ​​less than 0.9.

[0081] Figure 7 shows the R of each scattering order efficiency after retraining the above machine learning-based electromagnetic response model. 2 As shown in Figure 7, after retraining, the goodness of fit for all scattering order efficiencies is R 2 Indicates a feature with a value greater than 0.9.

[0082] In another embodiment, the model is trained to minimize a weighted sum of the residual values ​​associated with each scattering order efficiency.

[0083] Figure 8 shows a histogram 193 of the residual values ​​for each pixel after initial training of the machine learning-based electromagnetic response model, with the number of pixels in each range divided into ranges. In one example, the residual values ​​are the difference between the intensity output from the physics-based electromagnetic solver and the intensity output from the machine learning-based electromagnetic response model for each pixel. As shown in Figure 8, the residual values ​​for these pixels range from 0 to 1, with a mean value of approximately 0.25.

[0084] Figure 9 is a histogram 194 showing the residual values ​​for each pixel after retraining of the machine learning-based electromagnetic response model, divided into ranges, and the number of pixels in each range. As shown in Figure 9, the residual values ​​of these pixels are distributed in the range of 0 to 0.015, with an average value of approximately 0.0025. As shown in Figure 9, a characteristic is observed in which the residual values ​​are much smaller after retraining for all scattering order efficiency fitnesses.

[0085] In addition to traditional regression, the ML-based electromagnetic response model training module 176 can use any number of advanced regression techniques, including, but not limited to, multi-seed regression, multi-path regression, regularized regression, etc.

[0086] In some embodiments, these advanced regression techniques improve the robustness of the regression and eliminate multiple local minima. In one embodiment of multi-seed regression, measured scattered images are first compared to a library of images generated to train an ML-based electromagnetic response model to identify a small number of relatively good matches. The DOE values ​​of the parameters of interest corresponding to these selected images are used as initial points of interest (POIs) in subsequent regression analyses. initial In some of these embodiments, multiple regressions are started at each initial evaluation point and run in parallel, and the best fit is selected as the global minimum.

[0087] In one example, 100 regressions were performed to test the performance of the trained ML-based electromagnetic response model compared to a conventional electromagnetic solver. The ML-based electromagnetic response model was trained using 500 principal components. A complex memory structure was measured, and 11 parameters of interest were left as floating parameters in the regression. The average solution time using the electromagnetic solver was 77 seconds. Of this total, 64 seconds were spent on geometry discretization and EM solution, and 13 seconds were spent on the measurement system model. In contrast, the average solution time using the trained ML-based electromagnetic response model was 25 seconds. Of this total, 12 seconds were spent on the trained ML-based EM response model, and 13 seconds were spent on the measurement system model. Therefore, using the trained ML-based EM response model reduced the total regression time by one-third, and reduced the regression time associated with geometry discretization and EM simulation by one-fifth.

[0088] In the embodiment shown in Figure 5, a physics-based electromagnetic solver is used to generate the training data set. However, in some other embodiments, this training data set is obtained from known reference data. In one example, a number of structures are measured to obtain scattering order efficiencies. These same structures are then measured with a trusted reference measurement system (e.g., a focused ion beam) to directly measure the values ​​of the corresponding parameters of interest.

[0089] 5, a data compression module is used to reduce the dimensionality of the training data used to train the ML-based electromagnetic response model. However, data compression is generally optional. In such an embodiment, the electromagnetic response metrics generated by the physics-based electromagnetic solver are used directly to train the ML-based electromagnetic response model.

[0090] In another aspect, determining the value of the parameter of interest from the measured image of the measured structure is based on regression using a plurality of successively trained ML-based electromagnetic response models.

[0091] Similar to the above, a first trained ML-based electromagnetic response model is used to estimate values ​​of one or more parameters of interest based on the measured X-ray scatterometry images. In some embodiments, an additional set of DOE values ​​(e.g., 20-50 additional values) of the parameters of interest are selected near the values ​​of the parameters of interest determined by the first trained ML-based electromagnetic response model.

[0092] A physics-based electromagnetic solver is used to determine DOE values ​​of a plurality of electromagnetic response indices corresponding to each additional set of values ​​for the parameters of interest. The additional sets of DOE values ​​for the parameters of interest and the corresponding DOE values ​​of the plurality of electromagnetic response indices constitute a second training data set. A second machine learning-based electromagnetic response model is trained based on the second training data set. Finally, values ​​of the refined parameters of interest characteristic of one or more measured semiconductor structures are estimated by regression on one or more detected images using the second trained machine learning-based electromagnetic response model.

[0093] In another aspect, the determination of values ​​of the parameters of interest from measured images of the measured structure is based on regression using a combination of a trained ML-based electromagnetic response model and a physics-based electromagnetic solver. More specifically, a goodness of fit associated with each electromagnetic response metric is evaluated to determine whether the individual electromagnetic response metric should be calculated using the trained ML-based electromagnetic response model or the physics-based electromagnetic solver.

[0094] In one embodiment, a goodness of fit (e.g., R ) between the DOE values ​​of each of the plurality of electromagnetic response indices and the values ​​of each of the plurality of electromagnetic response indices determined using the machine learning-based electromagnetic response model may be measured. 2 Determine the residuals, etc.

[0095] The goodness of fit of a particular electromagnetic response index is within an acceptable range (e.g., R 2 >0.8), the regression uses the trained machine learning-based electromagnetic response model to calculate the value of that particular electromagnetic response index. However, if the goodness of fit of a particular electromagnetic response index is outside the acceptable range (e.g., R 2 <0.8), the regression uses a physics-based electromagnetic solver to calculate the value of that particular electromagnetic response index.

[0096] In this way, if the accuracy of the trained ML-based electromagnetic response model is insufficient for a particular electromagnetic response metric, a physics-based electromagnetic solver is used in place of the trained ML-based electromagnetic response model.

[0097] In another aspect, the speed and accuracy of model training is improved by scaling the DOE values ​​of the parameters of interest based on corresponding values ​​of a plurality of electromagnetic response metrics determined during training using the machine learning-based electromagnetic response model.

[0098] Typically, the input values ​​are scaled according to their nominal range of values. In one embodiment, the scaling of the input values ​​according to their nominal range of values ​​is performed such that the input values ​​during training of the ML-based model are each within the range of -1 to 1 after scaling.

[0099] However, in some other embodiments, the input values ​​of the ML-based EM response model are scaled according to the range of variation of the corresponding output value of the ML-based EM response model. More specifically, if the output value fluctuates over a relatively wide range for a given change in an input value, the input value is scaled to a relatively wide range. Furthermore, if the output value fluctuates over a relatively narrow range for a given change in an input value, the input value is scaled to a relatively narrow range. By scaling the input values ​​according to the range of variation of the output, the training explores a relatively wide range of values ​​for the input variable when the output is more variable relative to the value of the input variable, and explores a relatively narrow range of values ​​for the input variable when the output is less variable relative to the value of the input variable. In one embodiment, the output range of one particular output variable is evaluated at the extreme values ​​of each input variable while maintaining the values ​​of all other input variables in the middle of their ranges. The inverse of the resulting output range is used to scale the value of that particular input variable. This is repeated for all input variables.

[0100] In another embodiment, a range of residual values ​​associated with each of the plurality of electromagnetic response metrics is determined based on the range of DOE values ​​for each corresponding 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 variation in the residual values ​​over the full range of values ​​for that particular parameter of interest divided by the maximum variation in the residual values ​​over the full range of values ​​for each parameter of interest. The scaling factor associated with each parameter of interest is applied to the DOE values ​​for each parameter of interest during subsequent iterations of model training, i.e., model retraining.

[0101] 12 illustrates a method 300 suitable for implementation by metrology systems 100 and 200 of the present invention. It should be appreciated that, in one aspect, each data processing block of method 300 may be implemented by a pre-programmed algorithm, which is executed by one or more processors of computing system 130. While the following description is provided in the context of metrology systems 100 and 200, it should be appreciated herein that the particular structural aspects of metrology systems 100 and 200 should be construed as illustrative only, and not limiting.

[0102] In block 301, one or more semiconductor structures under test formed on a wafer surface are irradiated with a dose of x-ray radiation generated by an x-ray radiation source.

[0103] At block 302, one or more images of multiple diffraction orders of a quantity of radiation scattered from the one or more structures in response to the x-ray illumination radiation incident on the one or more structures are detected by an x-ray detector.

[0104] At block 303, values ​​of parameters of interest characteristic of the one or more semiconductor structures are estimated by regression on the one or more detected images using a trained machine learning based electromagnetic response model.

[0105] The x-ray based measurements of semiconductor structures described herein can be performed with any number of different metrology systems, including, but not limited to, x-ray transmission tools, x-ray reflectance tools, infrared transmission tools, and the like.

[0106] In another aspect, x-ray scatterometry measurements are performed according to a measurement recipe that includes a variety of angles of incidence that allow sufficient resolution and penetration depth to characterize high aspect ratio structures throughout their depth.

[0107] In another aspect, the implementation of the metrology recipe to the metrology system is performed by communicating control commands that result in changes to the state of one or more elements of the metrology system to implement the optimized metrology recipe.

[0108] In some embodiments, the control commands are provided to the illumination source, and in response, the electrical state of the illumination source is adjusted to change the scanning spot size and shape, illumination power, spot offset, angle of incidence, etc.

[0109] In some embodiments, the control commands are provided to one or more positioning devices that control the position of one or more optical elements of the metrology system, and in response, the one or more positioning devices change the position / orientation of one or more optical elements to adjust the angle of incidence, the focal length between the illumination source and illumination optics, beam positioning, position of the beam spot relative to an optical component to minimize the effects of surface roughness, etc.

[0110] Metrology systems and techniques are used to measure structural and material features associated with various semiconductor manufacturing processes. In some embodiments, x-ray scatterometry measurements are performed to estimate minimum linewidth, thickness, overlay, and material property values ​​for 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).

[0111] In some embodiments, the x-ray detector 116 is maintained in the same atmospheric environment (e.g., a gas-purged environment) as the sample 101. However, in some embodiments, the distance between the sample 101 and the x-ray detector 116 is long, and environmental disturbances (e.g., air turbulence) introduce noise into the detected signal. Therefore, in some embodiments, one or more x-ray detectors are maintained in a local vacuum environment separated from the sample (e.g., sample 101) by a vacuum window.

[0112] Similarly, in some embodiments, the x-ray irradiation source 110, the illumination optics 115, or both, are maintained in the same atmospheric environment (e.g., a gas-purged environment) as the sample 101. However, in some embodiments, the optical path lengths between the x-ray irradiation source 110 and the illumination optics 115, and between the illumination optics 115 and the sample 101 are long, and environmental disturbances (e.g., air turbulence) introduce noise into the illumination beam. Therefore, in some embodiments, the x-ray irradiation source, the illumination optics 115, or both, are maintained in a local vacuum environment separated from the sample (e.g., sample 101) by a vacuum window.

[0113] FIG. 10 illustrates vacuum chambers 163 and 164 in one embodiment. The vacuum chamber 163 includes the x-ray irradiation source 110 and irradiation optics 115, while the vacuum chamber 164 includes the x-ray detector 116. In a preferred embodiment, the vacuum chamber 163 includes most of the optical path between the x-ray irradiation source 110 and the sample 101, and the vacuum chamber 164 includes most of the optical path between the sample 101 and the x-ray detector 116. The openings of the vacuum chambers 163 and 164 are covered by vacuum windows 165 and 166, respectively. The vacuum windows 165 and 166 may be made of any suitable material that is substantially transparent to x-ray radiation, such as beryllium. The irradiation beam 117 passes through the vacuum window 165 as it propagates toward the sample 101. After interacting with the sample 101, scattered x-ray radiation 125 passes through the vacuum window 166, enters the vacuum chamber 164, and is incident on the 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 may include any suitable level of vacuum, any suitable purged environment including an inert gas (such as helium), or any combination thereof. In this way, the beam path is placed in as much vacuum as possible to maximize flux and minimize fluctuations.

[0114] In some embodiments, the entire optical system, including the sample 101, is maintained under vacuum. However, the costs associated with maintaining the sample 101 under vacuum are generally high due to the complexities associated with the construction of the sample positioning system 140.

[0115] In some embodiments, a metrology target characterized by the x-ray scatterometry measurements described herein is positioned within a scribe line of a wafer under test. In these embodiments, the metrology target is sized to fit within the width of the scribe line. In some examples, the width of the scribe line is less than 80 micrometers. In some examples, the width of the scribe line is less than 50 micrometers. In general, the width of scribe lines used in semiconductor manufacturing tends to be smaller.

[0116] In some embodiments, the metrology target whose characteristics are evaluated by the x-ray scatterometry measurements described herein is located within the die active area of ​​the wafer under test and is part of an integrated circuit with a specific function (e.g., memory, image sensor, logic device, etc.).

[0117] Metrology targets are typically characterized by their aspect ratio, which is defined as the metrology target's largest height dimension (i.e., the dimension normal to the wafer surface) divided by the metrology target's largest lateral dimension (i.e., the dimension along the wafer surface). In some embodiments, the metrology target being measured has an aspect ratio of at least 20. In some embodiments, the metrology target has an aspect ratio of at least 40.

[0118] 11A-11C show isometric, top, and cross-sectional views, respectively, of a typical 3D flash memory device 190 measured using the methods described herein. The overall height (or equivalently, depth) of memory device 190 ranges from one micrometer to several micrometers. Memory device 190 is a vertically fabricated device. Vertically fabricated devices such as memory device 190 essentially rotate a traditional planar memory device by 90 degrees, with the bit lines and cell strings oriented vertically (perpendicular to the wafer surface). To provide sufficient memory capacity, multiple alternating layers of different materials are deposited on the wafer. This requires patterning recipes that work well down to a depth of several micrometers for structures with maximum lateral widths of 100 nanometers or less. As a result, aspect ratios of 25:1 or 50:1 are not uncommon.

[0119] Generally, high-brilliance x-ray scatterometry allows a high flux of x-ray radiation to penetrate opaque areas of a target. Examples of geometric parameters that can be measured using x-ray scatterometry include pore size, pore density, line-edge roughness, linewidth roughness, sidewall angle, profile, minimum linewidth, overlay, edge placement error, and pitch. Examples of material parameters that can be measured include electron density. In some embodiments, x-ray scatterometry enables measurement of sub-10 nm features and advanced semiconductor structures such as STT-RAM, V-NAND, DRAM, PC-RAM, and Re-RAM, which require measurement of geometric and material parameters.

[0120] It should be appreciated that the various steps described throughout this disclosure may be performed by a single computer system 130 or by multiple computer systems 130. Furthermore, individual subsystems of the system 100, such as the sample positioning system 140, may include computer systems suitable for performing at least some of the steps described herein. Therefore, the foregoing 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 steps of any of the method embodiments described herein.

[0121] Additionally, computer system 130 may be coupled to communicate with 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 each computing system associated with detector 116 and illumination optics 115, respectively. In another example, detector 116 and illumination optics 115 may both be directly controlled by a single computer system coupled to computer system 130.

[0122] Computer system 130 may be configured to receive and / or acquire data or information from its subsystems (e.g., detector 116, illumination optics 115, etc.) by way of a transmission medium that may include wired and / or wireless portions. In this manner, the transmission medium may act as a data link between computer system 130 and other subsystems of system 100.

[0123] The computer system 130 of the measurement system 100 may be configured to receive and / or acquire data or information (e.g., measurement results, modeling inputs, modeling results, etc.) from other systems via a transmission medium, which may include wired and / or wireless portions. In this manner, the transmission medium may serve as a data link between the computer system 130 and other systems (e.g., memory onboard the measurement system 100, external memory, or external systems). For example, the computing system 130 may be configured to receive measurement data (e.g., signal 126) from a storage medium (i.e., memory 132 or 180) via a data link. For example, spectral results acquired using the spectrometer of either detector 116 may be stored in a permanent or semi-permanent memory device (e.g., memory 132 or 180). Thus, measurement results may be imported from on-board memory or from an external memory system. Additionally, the computer system 130 may transmit data to other systems via the transmission medium. For example, the sample parameter values ​​170 determined by the computer system 130 may be stored in a permanent or semi-permanent memory device (such as memory 180) so that the measurement results can be exported to another system.

[0124] Computing system 130 may include, but is not limited to, a personal computer system, a mainframe computer system, a workstation, an image computer, a parallel processor, or any other device known in the art. In general, the term "computing system" may be broadly defined to encompass any device with one or more processors that execute instructions from a memory medium.

[0125] Program instructions 134 implementing the methods as described herein may be transmitted over a transmission medium such as a wire, cable, or wireless transmission link. For example, as shown in Figure 1, program instructions stored in memory 132 are transmitted to processor 131 over bus 133. Program instructions 134 are stored in a computer-readable medium (such as memory 132). Examples of computer-readable media include read-only memory, random-access memory, magnetic / optical disks, or magnetic tape.

[0126] In some embodiments, the x-ray scatterometry measurements described herein are implemented as part of a manufacturing process tool. Examples of manufacturing process tools include, but are not limited to, lithography exposure tools, thin film deposition tools, implant tools, and etch tools. In this manner, the measurement results are used to control the manufacturing process. In one example, x-ray scatterometry measurement data collected from one or more targets is sent to a manufacturing process tool. The x-ray scatterometry measurement data is analyzed as described herein, and the results are used to adjust the operation of the manufacturing process tool.

[0127] The scatterometry measurements described herein can be used to characterize various semiconductor structures. Examples of structures include, but are not limited to, FinFETs, low-dimensional structures such as nanowires and graphene, sub-10 nm structures, lithographic structures, through-substrate vias (TSVs), memory structures such as DRAM, DRAM 4F2, flash, and MRAM, and high-aspect-ratio memory structures. Examples of structural characteristics include, but are not limited to, geometric parameters such as line-edge roughness, linewidth roughness, pore size, pore density, sidewall angle, profile, minimum linewidth, and pitch, and material parameters such as electron density, composition, grain structure, morphology, stress, strain, and elemental identity.

[0128] As used herein, the term "minimum line width" includes any minimum line width of a structure (e.g., minimum bottom line width, minimum middle line width, minimum top line width, sidewall angle, grating height, etc.), the minimum line width between two or more structures (e.g., the distance between two structures), and the displacement between two or more structures (e.g., the overlay displacement between overlapping grating structures, etc.). Structures can include three-dimensional structures, pattern structures, overlay structures, etc.

[0129] As used herein, the terms "minimum line width application" or "minimum line width measurement application" include any minimum line width measurement.

[0130] As used herein, the term "metrology system" includes any system used at least in part to characterize a specimen in any manner, including metrology applications such as minimum linewidth metrology, overlay metrology, focus / exposure metrology, and composition metrology. However, such terminology does not limit the scope of the term "metrology system" as used herein. Furthermore, system 100 may be configured to measure patterned and / or unpatterned wafers. The metrology system may 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 (handling data from one or more platforms simultaneously), as well as any other metrology or inspection tool that benefits from calibrating system parameters based on minimum linewidth data.

[0131] Described herein are various embodiments of semiconductor metrology systems that can be used to measure specimens within any semiconductor processing tool (such as an inspection system or a lithography system). As used herein, the term "specimen" refers to a wafer, reticle, or other specimen that may be processed (such as printed or inspected for defects) by means known in the art.

[0132] As used herein, the term "wafer" typically refers to a substrate formed of a semiconductor or non-semiconductor material. Examples include, but are not limited to, monocrystalline silicon, gallium arsenide, and indium phosphide. Such substrates may be commonly used and / or processed in semiconductor manufacturing facilities. In some cases, a wafer may include only the substrate (i.e., a bare wafer). Alternatively, a wafer may include one or more layers of various 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 multiple dies having repeatable pattern features.

[0133] A "reticle" can be a reticle at any stage in the reticle manufacturing process or a finished reticle, whether ready for use in a semiconductor manufacturing facility. A reticle or "mask" is generally defined as a substantially transparent substrate with a pattern of substantially opaque areas formed thereon. The substrate may comprise, for example, a glass material such as amorphous SiO2. During the exposure stage of the lithography process, the reticle is placed over a resist-coated wafer, allowing the pattern on the reticle to be transferred to the resist.

[0134] One or more layers formed on a wafer may be patterned or unpatterned. For example, a wafer may include multiple dies, each with repeatable pattern features. These layers of material may be formed and processed to ultimately yield a completed device. Many different types of devices may be formed on a wafer. As used herein, the term wafer is intended to encompass wafers undergoing the fabrication of any type of device known in the art.

[0135] In one or more exemplary embodiments, the functions described herein may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes computer storage media and communication media. Communication media includes any medium that facilitates transfer of a computer program from one place to another. Storage media may be any available medium that can be accessed by a general-purpose or special-purpose computer. Such computer-readable media include, by way of non-limiting example, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or other media that can be used to hold or store the necessary program code means 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. Additionally, any connection may qualify as a computer-readable medium. For example, if the software is transmitted from a website, server, or other remote source using coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technologies such as infrared, radio, or microwave, the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, or microwave are included within the definition of medium. As used herein, "disk" and "disc" include compact discs (CDs), laser discs, optical discs, digital versatile discs (DVDs), floppy disks, and Blu-ray discs. Disks typically reproduce data magnetically, while discs reproduce data optically using lasers. Combinations of the above should also be included within the scope of computer-readable media.

[0136] Although certain specific embodiments have been described above for purposes of illustration, the teachings of this patent document are general in nature and are not limited to the specific embodiments described above. Accordingly, various modifications, adaptations, and combinations of the various features of the embodiments described herein can be made without departing from the scope of the invention as set forth in the claims.

Claims

1. an x-ray radiation source configured to generate a quantity of x-ray radiation directed toward one or more semiconductor structures under test formed on the wafer surface; an x-ray detector configured to detect one or more images of a plurality of diffraction orders of an amount of radiation scattered from the one or more structures in response to the x-ray illumination radiation incident on the one or more structures; 1. A computing system comprising: a computing system configured to estimate values ​​of parameters of interest characteristic of the one or more semiconductor structures by regression on the one or more detected images using a trained machine learning based electromagnetic response model, the trained machine learning based electromagnetic response model mapping values ​​of the parameters of interest to values ​​of a plurality of electromagnetic response metrics; A measurement system comprising:

2. The metrology system of claim 1 , wherein each of the plurality of electromagnetic response indices is one of a pixel intensity in the x-ray detector, a scattering coefficient, a scattering order efficiency, and a scattering order value in Q-space.

3. The metrology system of claim 1 , wherein the regression for the one or more detected images includes a metrology system model, the metrology system model mapping values ​​of the plurality of electromagnetic response indices to one or more images at the x-ray detector.

4. the computing system further comprising:

2. The measurement system of claim 1, wherein the machine learning-based electromagnetic response model is configured to be trained based on a training dataset, the training dataset including a set of Design of Experiments (DOE) values ​​for the parameter of interest and corresponding DOE values ​​for a plurality of electromagnetic response metrics, and the training uses regression on the training dataset to minimize an objective function that characterizes an error between the DOE values ​​for the plurality of electromagnetic response metrics and values ​​of the plurality of electromagnetic response metrics determined using the machine learning-based electromagnetic response model.

5. the computing system further comprising:

5. The metrology system of claim 4, configured to determine the DOE values ​​of the plurality of electromagnetic response measures corresponding to each set of values ​​of the parameter of interest by simulation using a physics-based electromagnetic solver.

6. The metrology system of claim 4 , wherein the training data set is obtained from measurements performed by a trusted reference metrology system.

7. The measurement system of claim 4 , wherein the objective function is based on a residual value associated with each of the plurality of electromagnetic response metrics.

8. The measurement system of claim 4 , wherein the training comprises reducing the dimensionality of the plurality of electromagnetic response indices.

9. the computing system further comprising:

8. The measurement system of claim 7, configured to scale a DOE value of a parameter of interest based on the 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.

10. The measurement system of claim 4 , wherein the regression comprises one of a multi-seed regression, a multi-path regression, and a regularized regression.

11. the computing system further comprising: selecting an additional set of DOE values ​​for the parameter of interest based on the estimated value of the parameter of interest; determining, by simulation using a physics-based electromagnetic solver, DOE values ​​of the plurality of electromagnetic response indices corresponding to each additional set of values ​​of the parameters of interest, the additional sets of DOE values ​​of the parameters of interest and the corresponding DOE values ​​of the plurality of electromagnetic response indices constituting a second training data set; training a second machine learning based electromagnetic response model based on the second training data set; estimating refined values ​​of the parameters of interest characteristic of the one or more semiconductor structures by regression on the one or more detected images using the second trained machine learning based electromagnetic response model. The measurement system of claim 1 , configured as follows:

12. the computing system further comprising:

5. The measurement system of claim 4, configured to evaluate a goodness of fit between the DOE value for each of the plurality of electromagnetic response indicators and the value for each of the plurality of electromagnetic response indicators determined using the machine learning based electromagnetic response model, wherein if the goodness of fit associated with an electromagnetic response indicator is greater than a predetermined threshold, the regression for the one or more detected images uses the trained machine learning based electromagnetic response model to determine the value of one of the plurality of electromagnetic response indicators, and if the goodness of fit associated with an electromagnetic response indicator is less than a predetermined threshold, the regression for the one or more detected images uses a physics-based electromagnetic solver to determine the value of the one of the plurality of electromagnetic response indicators.

13. irradiating one or more semiconductor structures formed on a wafer surface with a dose of x-ray radiation produced by an x-ray radiation source; detecting one or more images of a plurality of diffraction orders of a quantity of radiation scattered from the one or more structures onto an x-ray detector, the quantity of radiation scattered from the one or more structures in response to the x-ray illumination radiation incident on the one or more structures; estimating values ​​of parameters of interest characteristic of the one or more semiconductor structures by regression on the one or more detected images using a trained machine learning based electromagnetic response model, the trained machine learning based electromagnetic response model mapping values ​​of the parameters of interest to values ​​of a plurality of electromagnetic response metrics; A method comprising:

14. 14. The method of claim 13, wherein each of the plurality of electromagnetic response indices is one of a pixel intensity in the x-ray detector, a scattering coefficient, a scattering order efficiency, and a scattering order value in Q-space.

15. 14. The method of claim 13, wherein the regression for the one or more detected images includes a metrology system model, the metrology system model mapping values ​​of the plurality of electromagnetic response indices to one or more images at the x-ray detector.

16. 14. The method of claim 13, further comprising training the machine learning-based electromagnetic response model based on a training dataset, the training dataset including a set of Design of Experiments (DOE) values ​​for the parameter of interest and corresponding DOE values ​​for a plurality of electromagnetic response indices, wherein the training uses regression on the training dataset to minimize an objective function characterizing an error between the DOE values ​​for the plurality of electromagnetic response indices and values ​​of the plurality of electromagnetic response indices determined using the machine learning-based electromagnetic response model.

17. The method of claim 16 , wherein the objective function is based on a residual value associated with each of the plurality of electromagnetic response measures.

18. The method of claim 16 , further comprising reducing the dimensionality of the plurality of electromagnetic response indices.

19. 17. The method of claim 16, further comprising scaling a DOE value for a parameter of interest based on the range of residual values ​​associated with each of the plurality of electromagnetic response measures determined based on a range of DOE values ​​for the parameter of interest.

20. selecting an additional set of DOE values ​​for the parameter of interest based on the estimated value of the parameter of interest; determining, by simulation using a physics-based electromagnetic solver, DOE values ​​of the plurality of electromagnetic response indices corresponding to each additional set of values ​​of the parameters of interest, wherein the additional sets of DOE values ​​of the parameters of interest and their corresponding DOE values ​​of the plurality of electromagnetic response indices constitute a second training data set; training a second machine learning based electromagnetic response model based on the second training data set; estimating refined values ​​of the parameters of interest characteristic of the one or more semiconductor structures by regression on the one or more detected images using the second trained machine learning based electromagnetic response model; and 14. The method of claim 13, further comprising:

21. 17. The method of claim 16, further comprising evaluating a goodness of fit between the DOE value for each of the plurality of electromagnetic response indices and the value for each of the plurality of electromagnetic response indices determined using the machine learning based electromagnetic response model, wherein if the goodness of fit associated with an electromagnetic response index is greater than a predetermined threshold, the regression for the one or more detected images uses the trained machine learning based electromagnetic response model to determine the value of one of the plurality of electromagnetic response indices, and if the goodness of fit associated with an electromagnetic response index is less than a predetermined threshold, the regression for the one or more detected images uses a physics-based electromagnetic solver to determine the value of the one of the plurality of electromagnetic response indices.

22. an x-ray radiation source configured to generate a quantity of x-ray radiation directed toward one or more semiconductor structures under test formed on the wafer surface; an x-ray detector configured to detect one or more images of a plurality of diffraction orders of an amount of radiation scattered from the one or more structures in response to the x-ray illumination radiation incident on the one or more structures; A non-transitory computer-readable medium containing instructions, When the instructions are executed by one or more processors of a computing system, the computing system: a non-transitory computer-readable medium for estimating values ​​of parameters of interest characteristic of the one or more semiconductor structures by regression on the one or more detected images using a trained machine learning based electromagnetic response model, the trained machine learning based electromagnetic response model mapping values ​​of the parameters of interest to values ​​of a plurality of electromagnetic response metrics; A measurement system comprising:

Images