Method and system for modelless scatterometry-based measurements of semiconductor structures

Abstract

Described herein are methods and systems for performing model-less measurements of semiconductor structures based on scatterometry measurement data. The scatterometry measurement data is processed directly without using conventional measurement models. Measurement sensitivity is defined by changes in detected diffraction images in one or more non-zero diffraction orders at at least two different illumination incidence angles. Discrete values ​​of a scalar function are determined directly from the measurement image at each incidence angle. A continuous mathematical function is fitted to the set of discrete values ​​of the scalar function determined at each incidence angle. Based on an analysis of the mathematical function, a value of the parameter of interest is determined. In some embodiments, the scalar function includes a weighting function, and weight values ​​associated with the weighting function are optimized to obtain an accurate fit of the mathematical function to the scalar values.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This patent application claims priority under 35 U.S.C. § 119 to U.S. Provisional Patent Application No. 63 / 404,973, filed September 9, 2022, the subject matter of which is incorporated herein by reference in its entirety.

[0002] The described embodiments relate to X-ray metrology systems and methods, and more particularly to methods and systems for improving measurement accuracy. [Background technology]

[0003] Semiconductor devices, such as logic and memory devices, are typically fabricated by a series of process steps applied to a specimen. These process steps form the various features and structural levels of the semiconductor device. Lithography, for example, is one semiconductor fabrication process that involves creating patterns on a semiconductor wafer. Additional examples of semiconductor fabrication processes include, but are not limited to, chemical-mechanical polishing, etching, deposition, and ion implantation. Multiple semiconductor devices can be fabricated on a single semiconductor wafer and then separated into individual semiconductor devices.

[0004] Metrology processes are used at various steps in the semiconductor manufacturing process to detect defects on wafers and promote higher yields. Several metrology-based techniques, including scatterometry and reflectometry implementations, and associated analysis algorithms are commonly used to characterize critical dimensions, film thickness, composition, and other parameters of nanoscale structures.

[0005] Traditionally, scatterometry-based critical dimension measurements are performed on targets consisting of thin films and / or repeating periodic structures. During device fabrication, these films and periodic structures typically represent the actual device geometry and material structure, or intermediate designs. As devices (e.g., logic and memory devices) progress to smaller nanometer-scale dimensions, 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 make it difficult for optical radiation to penetrate to the bottom layers. Optical metrology tools utilizing infrared to visible light can penetrate many layers of semitransparent materials, but do not provide sufficient sensitivity to small anomalies at the long wavelengths that provide good penetration depth. Additionally, the increasing number of parameters required to characterize complex structures (e.g., FinFETs) leads to increased parameter correlation. As a result, the parameters that characterize the target often cannot be reliably separated with available measurements.

[0006] In one example, longer wavelengths (e.g., near-infrared) have been used to attempt to overcome the penetration issues of 3D FLASH devices, which utilize polysilicon as one of the alternating materials in the stack. However, the specular structure of 3D FLASH inherently causes a drop in light intensity as the illumination propagates deeper into the film stack. This results in reduced sensitivity and correlation issues at depth. In this scenario, SCDs can only extract a reduced set of metrology dimensions with high sensitivity and low correlation.

[0007] In another example, opaque high-dielectric-constant (high-k) materials are increasingly used in modern semiconductor structures. Optical radiation is often unable to penetrate layers composed of these materials. As a result, measurements with thin-film scattering metrology tools such as ellipsometers or reflectometers become increasingly difficult.

[0008] To address these challenges, more sophisticated optical metrology tools have been developed, including those with multiple illumination angles, shorter illumination wavelengths, wider ranges of illumination wavelengths, and more complete information acquisition from the reflected signal (e.g., measuring multiple Mueller matrix elements in addition to the traditional reflectivity or ellipsometry signal). However, these approaches have not reliably overcome the fundamental challenges associated with measuring many advanced targets (e.g., complex 3D structures, structures smaller than 10 nm, and structures using opaque materials) and metrology applications (e.g., measuring line-edge roughness and linewidth roughness).

[0009] Atomic force microscopes (AFM) and scanning tunneling microscopes (STM) can achieve atomic resolution, but can only probe the surface of a sample. In addition, AFM and STM microscopes require long scanning times. Scanning electron microscopes (SEM) achieve moderate resolution levels but cannot penetrate deep enough into structures. As a result, high aspect ratio holes are not well characterized. In addition, the need to charge the sample negatively impacts imaging performance. X-ray reflectometers also suffer from penetration issues that limit their effectiveness when measuring high aspect ratio structures.

[0010] To overcome the penetration depth issue, conventional imaging techniques such as TEM and SEM are used in conjunction with destructive sample preparation techniques, such as focused ion beam (FIB) processing, ion milling, blanket etching, or selective etching. For example, transmission electron microscopy (TEM) can achieve high resolution levels and can observe to any depth, but TEM requires destructive cutting of the sample. Multiple iterations of material removal and measurement generally provide the information necessary to measure key metrology parameters across the entire three-dimensional structure. However, these techniques require sample destruction and long processing times. The complexity and time required to complete these types of measurements result in significant inaccuracies due to drift in the etching and metrology steps. Additionally, these techniques require multiple iterations, resulting in registration errors.

[0011] X-ray scatterometry systems have shown promise in addressing challenging measurement applications. Traditional X-ray scatterometry measurement techniques use indirect methods to measure the physical properties of the sample being measured. In some cases, a physics-based measurement model is created that attempts to predict the raw measurement signal based on assumed values ​​of one or more model parameters. The measurement model includes parameters related to the metrology tool itself, e.g., system parameters, and parameters related to the sample being measured. When solving for the parameters of interest, some sample parameters are treated as fixed values, while other sample parameters of interest are floating values, i.e., derived based on the raw measurement signal.

[0012] System parameters are parameters used to characterize the metrology tool. Exemplary system parameters include angle of incidence (AOI), azimuthal angle, beam divergence, etc. Sample parameters are parameters used to characterize the sample (e.g., material and geometric parameters that characterize the structure(s) being measured). For thin film samples, exemplary sample parameters include refractive index, dielectric function tensor, nominal layer thickness of all layers, layer order, etc. For CD samples, exemplary sample parameters include geometric parameter values ​​associated with different layers, refractive indices associated with different layers, etc. For measurement purposes, system parameters and many sample parameters are treated as known, fixed-value parameters. However, the values ​​of one or more sample parameters are treated as unknown, floating parameters of interest.

[0013] In some examples, the value of the floating parameter of interest is derived by an iterative process (e.g., regression) that results in the best fit between theoretical predictions and experimental data. The value of the unknown floating parameter of interest is varied, model output values ​​are calculated, and iteratively compared with the raw measured data until a set of sample parameter values ​​is determined that results in a sufficiently close match between the model output values ​​and the experimental measurements. In some other examples, the floating parameter is derived by searching a library of pre-calculated solutions to find the closest match.

[0014] Indirect methods for estimating the values ​​of parameters of interest are difficult to implement due to the complexity of the measurement models required to adequately represent the light scattered from complex semiconductor structures. The measurement model must adequately model both the device under test and the measurement system, and the physical interaction between them—i.e., the light scattered from the device under test. Generating accurate measurement models is computationally expensive and requires significant time. These costs are a significant barrier to the widespread adoption of scatterometry measurement techniques.

[0015] One promising method for X-ray scatterometry involves extracting critical dimensions without a metrology model. In this approach, measurements of semiconductor structures are achieved by directly processing measurement data without the use of a metrology model. This significantly reduces the effort required for developing metrology recipes and enables faster measurements. Exemplary methods for direct measurement include U.S. Patent No. 6,227,999 to Gellineau et al. and U.S. Patent No. 6,227,999 to Hench et al., the entire contents of which are incorporated herein by reference. [Prior art documents] [Patent documents]

[0016] [Patent Document 1] U.S. Patent No. 10,775,323 [Patent Document 2] U.S. Patent No. 10,545,104 Summary of the Invention [Problem to be solved by the invention]

[0017] To further improve device performance, the semiconductor industry continues to focus on vertical integration over lateral scaling. Therefore, accurate measurement of complex and complete three-dimensional structures is crucial to ensure the viability and continued scaling improvements. Future metrology applications present challenges to metrology due to ever-smaller resolution requirements, multi-parameter correlation, increasingly complex geometries including high aspect ratio structures, and the increasing use of opaque materials. Therefore, methods and systems for improving scatterometry-based measurements are desirable. [Means for solving the problem]

[0018] Described herein are methods and systems for performing model-less measurements of semiconductor structures based on scatterometry measurement data. The scatterometry measurement data is processed directly without the use of a measurement model. In general, the sensitivity of the model-less scatterometry-based measurements described herein is defined by changes in the detected diffraction image in one or more non-zero diffraction orders at at least two different illumination incidence angles. The changes in the diffraction image include changes in intensity, diffraction angle, or both. Thus, the model-less scatterometry-based measurements described herein can be used to estimate parameters of interest characterizing any semiconductor structure that scatters light in a non-specular manner.

[0019] In one aspect, discrete values ​​of the scalar function are determined directly from the measured image at each angle of incidence. A continuous mathematical function is fitted to the set of discrete values ​​of the scalar function determined at each angle of incidence. The value of the parameter of interest is determined based on an analysis of the mathematical function, e.g., minimum, maximum, inflection points, etc.

[0020] In some embodiments, the scalar function includes an image filter and a weighting function: the image filter function scales the value of each pixel in a particular image, and the weighting function scales the value of each image in a set of measurement images collected at different orientations of the structure being measured relative to the incoming illumination beam.

[0021] In another further aspect, the weighting values ​​associated with the weighting function are optimized to obtain an accurate fit of the mathematical function to the scalar values, hi some examples, the mathematical function is parameterized by one or more parameters that directly correspond to parameters of interest of the structure being measured.

[0022] In some examples, the weighting function, the image filter function, or both are implemented to minimize or maximize the signal from one-dimensional scattering. In these examples, the weighting function, the image filter function, or both are used to account for parameters related to one-dimensional or two-dimensional structures.

[0023] In another further aspect, different exposure times are used at different orientations of the structure being measured relative to the incident illumination beam. In these examples, the difference in exposure time between images collected at different orientations is accommodated by mathematically normalizing the image data based on the exposure time.

[0024] In another aspect, accurate model-less tilt measurements are used to improve system calibration, wafer shape models, and measurements of absolute wafer tilt.

[0025] In another aspect, an initial measurement of wafer tilt based on model-less scatterometry is performed, the orientation of the wafer being measured is repositioned to a desired orientation with respect to the incident illumination beam based on the measured wafer tilt, and then a precise model-less measurement is performed at the desired orientation and / or at a desired angle of incidence relative to the desired orientation.

[0026] In some embodiments, a model-less tilt measurement indicates an angular misalignment between the incident illumination beam and the hole structure. After measuring the misalignment, the AOI and azimuthal angle of the wafer relative to the illumination beam are adjusted to more accurately align the illumination beam with the hole structure based on the measured tilt. After aligning the illumination beam with the hole structure, one or more scattering images are collected and analyzed to estimate values ​​of one or more critical dimensions of the hole structure.

[0027] In some examples, the square of a Bessel function is used to determine the average critical dimension of the hole structures, and in some examples, the square of a modified Bessel function is used to determine the average shape of the elliptical-shaped hole structures that are typical of many memory structures.

[0028] In some embodiments, the AOI and azimuth angle of the wafer relative to the illumination beam are adjusted to a precise angle of incidence that is not aligned with the hole structure based on model-less tilt measurements. Scattered images are collected at precise off-axis angles of incidence and analyzed to estimate values ​​of critical dimensions of the hole structure. In some examples, a sinc function is used to estimate the height of the measured hole structure. In some other examples, scattered images are collected at precise off-axis angles of incidence to estimate overlay, e.g., the relative positioning of the hole structure and the contact layer below the hole.

[0029] In general, model-less scatterometry measurements can be used to measure the slope of multiple structural elements of a measurement target captured in a collected scatterometry image. In these examples, model-less techniques are applied to estimate values ​​of parameters of interest that characterize multiple different structural elements based on collected diffraction signals located in spatially distinct regions of the detector.

[0030] Measurement of the tilt of a semiconductor structure is often based on identifying individual peaks in the value of a mathematical function fitted to a locus of scalar values ​​obtained from the collected images, but typically multiple peak values ​​can be identified to estimate the value of a parameter that characterizes the semiconductor structure being measured.

[0031] In another aspect, an initial measurement of the parameter of interest is made using a model-less technique, and another measurement set is designated based on the initial measurement. In some examples, the design of subsequent measurement sets is based on the observed shape of a mathematical fit to the discrete values ​​of a scalar function evaluated at each orientation.

[0032] In some examples, the model-less measurements described herein are used to measure parameters of one or more structures, allowing for the verification or updating of measurement system calibration parameters. In some of these examples, the results of the model-less measurements allow for the calibration of the measurement tool used to perform the model-less measurements. However, in some other examples, information from the model-less measurements is used across multiple measurement tools. In one example, model-less tilt measurements are used to improve the results of optical measurements across multiple measurement tools.

[0033] The foregoing is a summary and thus necessarily contains simplifications, generalizations, and omissions of detail; as a result, 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 processes described herein will become apparent in the non-limiting detailed description set forth herein. [Brief explanation of the drawings]

[0034] [Figure 1] FIG. 1 illustrates a metrology system 100 configured to perform model-less measurements of semiconductor structures based on scatterometry measurement data, according to methods described herein. [Figure 2] FIG. 1B is an end view of the beam-shaping slit mechanism 120 in one configuration. [Figure 3] FIG. 10 is an end view of the beam-shaping slit mechanism 120 in another configuration. [Figure 4] 1 shows an X-ray illumination beam 116 incident on a wafer 101 at an orientation described by specific angles φ and θ. [Figure 5] 1 shows the sample positioning system 140 with the wafer stage moved to a position where the illumination beam 116 is incident on the wafer 101. FIG. [Figure 6] FIG. 1 illustrates an example model-less measurement engine 180 configured to derive sample parameter values ​​based on scatterometry data according to model-less methods described herein. [Figure 7] FIG. 1 shows a tilted grating structure 171 measured by the metrology system 100 at an angle of incidence AOI. [Figure 8] 1 is a plot showing discrete values ​​172 of a scalar function S operating on measured images collected at detector 119 at various angles of incidence, and a mathematical function 173 fitted to those discrete values ​​172. [Figure 9] 2 is a flowchart illustrating an exemplary method 200 for performing model-less measurements of semiconductor structures based on scatterometry measurement data as described herein. DETAILED DESCRIPTION OF THE INVENTION

[0035] Reference will now be made in more detail to exemplary background and certain embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

[0036] Described herein are methods and systems for performing model-less measurements of semiconductor structures based on scatterometry measurement data. Measurement of the semiconductor structure is achieved by directly processing the scatterometry measurement data without the use of a measurement model. The scatterometry measurements are performed at various angles of incidence on the structure being measured. A detected image of light scattered from the structure being measured includes at least one higher diffraction order, i.e., one or more diffraction orders greater than the zeroth diffraction order.

[0037] In general, the sensitivity of the model-less scatterometry-based measurements described herein is defined by changes in the detected diffraction image in one or more non-zero diffraction orders at at least two different illumination incidence angles. The changes in the diffraction image include changes in intensity, diffraction angle, or both. Thus, the model-less scatterometry-based measurements described herein can be used to estimate parameters of interest characterizing any semiconductor structure that scatters light in a non-specular manner.

[0038] In one aspect, discrete values ​​of the scalar function are determined directly from the measured image at each angle of incidence. A continuous mathematical function is fitted to the set of discrete values ​​of the scalar function determined at each angle of incidence. The value of the parameter of interest is determined based on an analysis of the mathematical function, e.g., minimum, maximum, inflection points, etc.

[0039] In another aspect, an initial measurement of wafer tilt based on model-less scatterometry is performed, and the orientation of the wafer being measured is repositioned to a desired orientation relative to the incident illumination beam based on the measured wafer tilt. A refined model-less measurement is then performed at the desired orientation, or a desired angle of incidence relative to the desired orientation, or both. A value for the parameter of interest is determined based on the refined model-less measurement data.

[0040] The model-less scatterometry-based measurements of semiconductor structures described herein are used to determine values ​​of various parameters of interest from scatterometry measurement data, including, but not limited to, critical dimensions, tilt, average tilt, wafer bow, and other parametric measurements.

[0041] Measurements of semiconductor structures using the model-less scatterometry techniques described herein can be used in a variety of different ways as part of a semiconductor fabrication process. In some embodiments, model-less measurement results are used directly to control the fabrication process. In some examples, measurements of one or more parameters of interest, e.g., critical dimensions, are used directly to control one or more process parameters, e.g., focus, exposure dose, etch time, etc. In some embodiments, model-less measurement results are used to improve the accuracy of model-based measurements. In some examples, model-less measurement results are used to regularize model-based measurements, i.e., the model-less measurement results are used as part of one or more regularization terms in a regression analysis of the model-based measurements. In some examples, model-less measurement results are used to establish initial values ​​for one or more floating parameters of the model-based measurements. In some examples, model-less measurement results are used to establish values ​​for one or more fixed parameters of the model-based measurements. In some embodiments, model-based measurements are performed on the same structure measured by the model-less measurement technique. In some embodiments, model-based measurements are performed on a different structure measured by the model-less measurement technique. In some embodiments, model-based measurements are used to facilitate model-based measurements performed by the same metrology system. In some other embodiments, the model-based measurements are used to facilitate model-based measurements performed by a different metrology system, for example, a model-less measurement performed by an X-ray based scatterometry system may be used to facilitate a model-based measurement performed by an optical-based metrology system, such as a spectroscopic ellipsometer, spectroscopic reflectometer, etc.

[0042] In some embodiments, the structure being measured contains a degree of periodicity that scatters light into distinguishable, discrete diffraction orders. Diffraction from a structure that exhibits two-dimensional periodicity appears as discrete points on the detector's image plane. Diffraction from a structure that exhibits one-dimensional periodicity appears as discrete points along a line on the detector's image plane.

[0043] In some embodiments, the structure being measured is quasi-periodic in one or both in-plane dimensions, in these embodiments the diffraction pattern shows continuous lines of diffracted light.

[0044] In general, the model-less scatterometry-based measurements described herein can be used to measure any semiconductor structure that exhibits periodicity or quasi-periodicity in one or both in-plane dimensions, e.g., the x-direction, the y-direction, or both, as shown in FIG. 4 .

[0045] The model-less scatterometry-based measurements described herein can be performed using narrowband illumination light centered around any suitable illumination wavelength, for example, any wavelength within the optical range including the ultraviolet, visible, and infrared ranges, any wavelength within the X-ray range, or any wavelength within the infrared range. In a preferred embodiment, the illumination light is narrowband with low beam divergence to reduce smearing of diffraction orders at the detector due to changes in illumination wavelength. Order separation at an X-ray detector is a function of, among other factors, wavelength, target period, angle of incidence, divergence angle of uncollimated illumination light, detector resolution, and distance from the target. Nevertheless, in one dimension, it is fundamentally governed by the diffraction equation: d*sin(Δθ)=λ, where d is the period of the structure, λ is the illumination wavelength, and Δθ is the angular spacing between orders. From this equation or its two-dimensional equivalent, one skilled in the art can quickly determine the bandwidth and beam divergence required to resolve individual orders at the detector.

[0046] In general, model-less scatterometry-based measurements can be implemented with a wide variety of scatterometry-based measurement systems that use narrowband illumination, including, but not limited to, X-ray scatterometry-based systems such as small-angle X-ray scatterometry (SAXS) systems, angle-resolved light scatterometry systems such as one-dimensional (1-D) or two-dimensional (2-D) beam profile reflectometry (BPR) systems, and the like.

[0047] While useful measurements can be performed at two different angles of incidence, measurement sensitivity is generally improved by collecting measurement data over a larger and more diverse data set, whether that be over a longer period of time, over a wider range of different illumination angles of incidence, over a smaller interval between different illumination angles of incidence, or any combination thereof.

[0048] 1 illustrates one embodiment of a transmission small-angle X-ray scattering (T-SAXS) metrology tool 100 for measuring properties of a sample according to the exemplary methods presented herein. As shown in FIG. 1, the system 100 can be used to perform T-SAXS measurements over an examination area 102 of a sample 101 illuminated by an illumination beam spot.

[0049] In the illustrated embodiment, metrology tool 100 includes an X-ray illumination source 110 configured to generate X-ray radiation suitable for T-SAXS measurements. In some embodiments, X-ray illumination source 110 is configured to generate wavelengths between 0.01 nanometers and 1 nanometer. In general, any suitable high-brightness X-ray illumination source capable of generating high-brightness X-rays at flux levels sufficient to enable high-throughput in-line metrology can be envisioned for providing X-ray illumination for T-SAXS measurements. In some embodiments, the X-ray source includes a tunable monochromator that enables the X-ray source to output X-ray radiation at different selectable wavelengths.

[0050] In some embodiments, one or more X-ray sources emitting radiation with photon energies greater than 15 keV are used to ensure that the X-ray source provides light at a wavelength that allows sufficient penetration throughout the device and wafer substrate. By way of non-limiting example, any of the following may be used as the X-ray illumination source 110: a particle accelerator source, a liquid anode source, a rotating anode source, a stationary solid anode source, a microfocus source, a microfocus rotating anode source, a plasma-based source, and an inverse Compton source. In one example, an inverse Compton source available from Lyncean Technologies, Inc. of Palo Alto, California, USA, may be considered. An inverse Compton source has the added advantage of being capable of generating X-rays across a range of photon energies, thereby enabling the X-ray source to output X-ray radiation at different, selectable wavelengths.

[0051] Exemplary x-ray sources include electron beam sources configured to irradiate a solid or liquid target to stimulate x-ray emission. A method and system for producing high-brightness liquid metal x-ray illumination is described in U.S. Patent No. 7,929,667, issued April 19, 2011, to KLA-Tencor Corp., which is incorporated herein by reference in its entirety.

[0052] X-ray illumination source 110 generates X-ray emissions over a source region having a finite lateral dimension (i.e., a non-zero dimension orthogonal to the beam axis). Collection optics 111 focus the source radiation onto a metrology target located on sample 101. The finite lateral source dimension results in a finite spot size 102 on the target defined by rays 117 emerging from the end of the source. In some embodiments, collection optics 111 includes an ellipsoidally shaped collection optic.

[0053] The beam divergence control slit 112 is located in the beam path between the collection optics 111 and the beam shaping slit mechanism 120. The beam divergence control slit 112 limits the divergence of the illumination provided to the sample being measured. An additional intermediate slit 113 is located in the beam path between the beam divergence control slit 112 and the beam shaping slit mechanism 120. The intermediate slit 113 provides additional beam shaping. However, in general, the intermediate slit 113 is optional.

[0054] The beam-shaping slit mechanism 120 is located in the beam path just prior to the sample 101. In one embodiment, the slit of the beam-shaping slit mechanism 120 is located close to the sample 101 to minimize the expansion of the incident beam spot size due to the beam divergence defined by the finite source size. In one example, the expansion of the beam spot size due to the shadow caused by the finite source size is approximately 1 micrometer for an X-ray source size of 10 micrometers and a distance of 25 millimeters between the beam-shaping slit and the sample 101.

[0055] In some embodiments, the beam-shaping slit mechanism 120 includes multiple independently actuated beam-shaping slits (i.e., blades). In one embodiment, the beam-shaping slit mechanism 120 includes four independently actuated beam-shaping slits. These four beam-shaping slits effectively block a portion of the incoming beam 115 to produce an illumination beam 116 having a box-shaped illumination cross-section.

[0056] 2 and 3 show end views of the beam-shaping slit mechanism 120 shown in FIG. 1 in two different configurations. As shown in FIGS. 2 and 3, the beam axis is perpendicular to the drawing page. As shown in FIG. 2, the incoming beam 115 has a large cross-section. In some embodiments, the incoming beam 115 has a diameter of approximately 1 millimeter. Furthermore, the position of the incoming beam 115 within the beam-shaping slits 126-129 may have an uncertainty of approximately 3 millimeters due to beam pointing errors. To accommodate the uncertainty in the incoming beam size and beam position, each slit has a length L of approximately 6 millimeters. As shown in FIG. 2, each slit is movable in a direction perpendicular to the beam axis. In the view of FIG. 2, the slits 126-129 are positioned at a maximum distance from the beam axis (i.e., the slits are fully open and do not restrict light passing through the beam-shaping slit mechanism 120).

[0057] In the embodiment shown in FIG. 1, collection optics 111, slits 112 and 113, and beam-shaping slit mechanism 120 are maintained in a controlled environment (eg, vacuum) within flight tube 118.

[0058] Figure 3 shows slits 126-129 of beam-shaping slit mechanism 120 positioned to block a portion of incoming beam 115, resulting in a reduced size and well-defined shape of output beam 116 that is output to the sample being measured. As shown in Figure 3, each of slits 126-129 has been moved inward, toward the beam axis, to achieve the desired output beam shape.

[0059] The slits 126-129 are made of a material that minimizes scattering and effectively blocks the incident radiation. Exemplary materials include single-crystal materials such as germanium, gallium arsenide, and indium phosphide. Typically, the slit material is cleaved along a crystallographic direction rather than cut to minimize scattering at structural interfaces. Additionally, the slits are oriented with respect to the incoming beam to minimize scattering due to the interaction of the incoming radiation with the internal structure of the slit material. The crystal is attached to a slit fixture made of a high-density material (e.g., tungsten) to completely block the X-ray beam on one side of the slit. In some embodiments, each slit has a rectangular cross-section with a width of approximately 0.5 millimeters and a height of approximately 1-2 millimeters. As shown in Figure 2, the slit length L is approximately 6 millimeters.

[0060] Generally, the X-ray optics shapes and directs the X-ray radiation to the sample 101. In some examples, the X-ray optics includes an X-ray monochromator that monochromatizes the X-ray beam incident on the sample 101. In some examples, the X-ray optics uses multilayer X-ray optics to collimate or focus the X-ray beam onto the measurement region 102 of the sample 101 with a divergence of less than 1 milliradian. In these examples, the multilayer X-ray optics also function as a beam monochromator. In some embodiments, the X-ray optics 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, Montell optics, reflective X-ray optics such as grazing incidence elliptical mirrors, polycapillary optics such as hollow capillary X-ray waveguides, multilayer optics or systems, or any combination thereof. Further details are described in U.S. Patent Application Publication No. 2015 / 0110249, the contents of which are incorporated herein by reference in their entirety.

[0061] X-ray detector 119 collects X-ray radiation 114 scattered from sample 101 and generates output signal 135 indicative of a property of sample 101 sensitive to the incident X-ray radiation according to a T-SAXS measurement format. In some embodiments, scattered X-rays 114 are collected by X-ray detector 119 while sample positioning system 140 positions and orients sample 101 to generate angle-resolved scattered X-rays.

[0062] In some embodiments, the T-SAXS system has a high dynamic range (e.g., 10 5 In some embodiments, the single photon-counting detector detects the location and number of detected photons.

[0063] In some embodiments, the X-ray detector resolves one or more X-ray photon energies and outputs a signal for each X-ray energy component that is indicative of a characteristic of the sample. In some embodiments, the X-ray detector 119 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.

[0064] In this way, X-ray photon interactions within the detector are identified by energy in addition to pixel location and count number. In some embodiments, X-ray photon interactions are identified by comparing the energy of the X-ray photon interaction with a predetermined upper threshold and a predetermined lower threshold. In one embodiment, this information is communicated via output signal 135 to computing system 130 for further processing and storage.

[0065] In a further embodiment, the T-SAXS system is used to determine a property (e.g., a structural parameter value) of the sample based on one or more diffraction orders of the scattered light. As shown in Figure 1, the metrology tool 100 includes a computing system 130 that is used to acquire a signal 135 generated by the detector 119 and determine a property of the sample based at least in part on the acquired signal in accordance with the model-less scatterometry techniques described herein.

[0066] To improve the precision and accuracy of measured parameter values, it is desirable to perform measurements over a wide range of incidence and azimuthal angles. This technique reduces correlation between parameters by expanding the number and diversity of data sets available for analysis to include a variety of large-angle out-of-plane orientations. For example, at normal orientations, T-SAXS can resolve the critical dimensions of features but has little sensitivity to the feature's sidewall angle and height. However, by collecting measurement data over a wide range of out-of-plane angular orientations, the feature's sidewall angle and height can be resolved. In another example, measurements performed over a wide range of incidence and azimuthal angles provide sufficient resolution and penetration depth to characterize high-aspect-ratio structures throughout their entire depth.

[0067] Measurements of the intensity of diffracted radiation are collected as a function of the angle of incidence of X-rays relative to the wafer surface normal. The information contained in multiple diffraction orders is typically unique for each model parameter considered. In this way, X-ray scattering provides estimates for the values ​​of the parameters of interest with small errors and reduced parameter correlation.

[0068] Each orientation of the illuminating X-ray beam 116 relative to the surface normal of the semiconductor wafer 101 is described by any two angular rotations of the wafer 101 relative to the X-ray illumination beam 115, or vice versa. In one example, the orientation can be described relative to a coordinate system fixed to the wafer. FIG. 4 shows the X-ray illumination beam 116 incident on the wafer 101 at a particular orientation described by the incidence angle θ and the azimuthal angle φ. The coordinate frame XYZ is fixed to the measurement system (e.g., the illumination beam 116), and the coordinate frame X'Y'Z' is fixed to the wafer 101. The Y axis is aligned in-plane with the surface of the wafer 101. X and Z are not aligned with the surface of the wafer 101. Z' is aligned with an axis normal to the surface of the wafer 101, and X' and Y' are aligned in-plane with the surface of the wafer 101. As shown in FIG. 4, the X-ray illumination beam 116 is aligned with the Z axis and therefore lies in the XZ plane. The angle of incidence θ represents the orientation of the X-ray illumination beam 116 relative to the wafer's surface normal in the XZ plane. Furthermore, the azimuthal angle φ represents the orientation of the XZ plane relative to the X'Z' plane. Together, θ and φ uniquely define the orientation of the X-ray illumination beam 116 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 described 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 aligned with the surface of the wafer 101 (i.e., the Y axis). In some other examples, the orientation of the X-ray illumination beam relative to the surface of the wafer 101 is described by a rotation about a first axis aligned with the surface of the wafer 101 and another axis aligned with the surface of the wafer 101 and orthogonal to the first axis.

[0069] 1 , the metrology tool 100 includes a sample positioning system 140 configured to align and orient the sample 101 over a wide range of incidence and azimuthal angles relative to the illumination beam 116. In some embodiments, the sample positioning system 140 is configured to rotate the sample 101 over a wide range of rotation angles (e.g., at least 60 degrees) aligned in-plane with the surface of the sample 101. In this manner, angle-resolved measurements of the sample 101 are collected by the metrology system 100 over any number of positions and orientations on the surface of the sample 101. In one example, the computing system 130 communicates command signals (not shown) to the sample positioning system 140 indicating a desired position of the sample 101. In response, the sample positioning system 140 generates command signals to various actuators of the sample positioning system 140 to achieve the desired positioning of the sample 101.

[0070] Figure 5 illustrates a sample positioning system 140 in one embodiment. As shown in Figure 5, the sample positioning system 140 includes a base frame 141, a lateral alignment stage 142, a stage reference frame 143, and a wafer stage 144. For reference, {X BF ,Y BF ,Z BF} coordinate frame is the base frame 141, NF ,Y NF ,Z NF} coordinate frame is aligned with the lateral alignment stage 142, RF ,Y RF ,Z RF} coordinate frame to the stage reference frame 143, SF ,Y SF ,Z SFThe} coordinate frame is mounted on wafer stage 144. Wafer 101 is supported on wafer stage 144 by tip-tilt Z-stage 156, which includes actuators 150A-C. A rotational stage 158 mounted on tip-tilt Z-stage 156 orients wafer 101 over a range of azimuthal angles φ relative to illumination beam 116. In the illustrated embodiment, three linear actuators 150A-C are mounted on wafer stage 144 and support rotational stage 158, which in turn supports wafer 101.

[0071] The actuator 145 moves the lateral alignment stage 142 in the X direction. BF The rotational actuator 146 translates the stage reference frame 143 relative to the base frame 141 along the Y axis. NF The wafer stage 144 rotates relative to the lateral alignment stage 142 about a rotation axis 153 aligned with the X axis. The rotation actuator 146 orients the wafer 101 with respect to the illumination beam 116 over a range of angles of incidence θ. The wafer stage actuators 147 and 148 rotate the wafer stage 144 at angles X, X, and X, respectively. RF axis and Y RF The actuators 150A-C operate in coordination to translate the rotation stage 158 and the wafer 101 relative to the wafer stage 144 along the Z axis. SF and the rotation stage 158 and the wafer 101 relative to the wafer stage 144 are translated in the X direction. SF -Y SF The rotation stage 158 rotates the wafer 101 around an axis normal to the surface of the wafer 101.

[0072] In summary, the wafer stage 144 allows the illumination beam 116 to be positioned at any point (i.e., X RF and Y RFThe wafer 101 can be moved relative to the illumination beam 116 so that the illumination beam 116 can be incident on the surface of the wafer 101 at any wide range of azimuthal angles (e.g., a range of at least 300 millimeters in the azimuthal direction). The rotational actuator 146 can rotate the stage reference frame 143 relative to the illumination beam 116 so that the illumination beam 116 can be incident on the surface of the wafer 101 at any wide range of azimuthal angles (e.g., greater than 2 degrees). In one embodiment, the rotational actuator 146 is configured to rotate the stage reference frame 143 over a range of at least 60 degrees. The rotational actuator 149 attached to the wafer stage 144 can rotate the wafer 101 relative to the illumination beam 116 so that the illumination beam 116 can be incident on the surface of the wafer 101 at any wide range of azimuthal angles (e.g., a rotational range of at least 90 degrees).

[0073] In some other embodiments, the lateral alignment stage 142 is removed and the stage reference frame 143 is rotated relative to the base frame 141 by a rotational actuator 146. In these embodiments, the X-ray illumination system rotates the X-ray illumination beam 116 relative to the base frame 141, e.g., BF and one or more actuators for moving one or more optical elements of the X-ray illumination system in a direction.

[0074] Although a specific embodiment is shown in FIG. 5, in general, the sample positioning system 140 may include any suitable combination of mechanical elements, including but not limited to, goniometer stages, hexapod stages, angular stages, and linear stages, to achieve the desired linear and angular positioning performance.

[0075] In another further aspect, computing system 130 is configured to generate a scalar signal associated with each measured scatterometry image, fit the discrete set of scalar signals to a mathematical function, and extract values ​​of one or more parameters of interest based on one or more characteristics of the mathematical function. In the embodiment shown in Figure 1, computing system 130 is configured as a model-less measurement engine configured to implement the model-less measurement functionality described herein.

[0076] 6 illustrates an exemplary model-less measurement engine 180 implemented by computing system 130. As shown in FIG. 6, model-less measurement engine 180 includes a scalar signal generation module 181, a fitting analysis module 183, and a parameter-of-interest extraction module 185.

[0077] In one aspect, discrete values ​​of the scalar function are obtained for each orientation of the structure to be measured relative to the incoming illumination beam.

number

[0078] As shown in FIG. 6, the measurement images 135 are communicated to a scalar signal generation module 181. The scalar signal generation module 181 determines a scalar value associated with each captured image based on a scalar function. In some embodiments, the scalar function includes an image filter and a weighting function. The image filter function scales the value of each pixel in a particular image. The weighting function scales the value of each image in a set of measurement images collected at different orientations of the structure being measured relative to the incoming illumination beam. In other words, the weighting function scales the value of each image in a set of measurement images collected at different orientations of the structure being measured relative to the incoming illumination beam.

number

[0079] In one example, the scalar function S is expressed by equation (1), where:

number

number

[0080] P is a weighting function that operates on each vector of filtered pixel values. In general, the coefficients of the weighting function P depend on the orientation of the structure being measured relative to the incident illumination beam.

number

[0081] As shown by equation (1), the resulting filtered and weighted pixel values ​​associated with each acquired image are summed to obtain a scalar measurement value 182 associated with each measurement image 135 .

number

[0082] In a further aspect, a continuous mathematical function is fitted to a set of discrete values ​​182 of a scalar function relating measurement images collected at different orientations of the structure being measured relative to the incident illumination beam.

[0083] 6, a set of discrete values ​​182 is communicated to a fitting analysis module 183. The fitting analysis module 183 fits a continuous mathematical function 184 to the set of discrete values ​​182 and communicates the continuous mathematical function to a parameter of interest (POI) extraction module 185. In some embodiments, the continuous mathematical function is a quadratic function. However, in general, any suitable mathematical function may be envisioned within the scope of this patent specification.

[0084] In another further embodiment, values ​​of the parameters of interest are determined based on an analysis of the continuous mathematical function 184. As shown in Figure 6, a POI extraction module 185 analyzes the continuous mathematical function 184 to extract values ​​of one or more parameters of interest related to parameters characterizing the continuous mathematical function, e.g., minimum values, maximum values, inflection points, values ​​where the first derivative of the mathematical function is zero, etc. Estimates 186 of each POI are stored in a memory, e.g., memory 190.

[0085] In another further aspect, the weighting values ​​associated with the weighting function P are optimized to obtain an accurate fit of the mathematical function to the scalar values. In some examples, the mathematical function is parameterized by one or more parameters that directly correspond to parameters of interest of the structure being measured.

[0086] In some examples, optimal weight values ​​associated with the weighting array P are determined using an optimization procedure. For a fixed value of P, the critical dimension q is determined by the orientation set as shown by equation (2).

number

number

[0087] The estimate of the scalar parameter of interest q is then calculated using the scalar reference function r(u * ,P) to find the optimal parameterization value u * In one example, using a two-stage optimization technique, a higher-level optimization can be used to optimize a lower-level optimization from which critical dimensions are extracted. In this example, the two-stage optimization is expressed as a top-level optimization shown by equation (2) and a bottom-level optimization shown by equation (4) or equation (5).

[0088] Top-level optimization involves optimizing the fitting function F over multiple measurements. This is achieved by defining the reference function R as a vector of critical dimension estimates r and U* as the set of optimal values ​​of the curve parameterization u, as shown by equation (3).

number

number

number

[0089] As shown by equation (2), the curve function C is the vector of the measurement orientation

number

[0090] In some examples, the optimization used to solve the mathematical function C shown in equation (2) is weighted by the signal-to-noise ratio of the measurement image at each orientation. In this way, measurement images with the highest signal-to-noise ratios are weighted more heavily than measurement images with relatively low signal-to-noise ratios.

[0091] The reference function R matches the reference values ​​Q of one or more POIs with the extraction function R(UI). The extraction function estimates the values ​​Q of the POIs given the values ​​of the curve fitting parameters U. In some examples, the reference function includes a regularization term. In the example shown by Equation (3), the regularization term is the ratio of the current values ​​μ of the parameters characterizing the curve function C to the initial values ​​μ of the parameters estimated by the complement of the reference function. υ The square of the distance between Π This includes multiplied by

[0092] In general, the initial values ​​u0 and P0 can be treated as fixed values ​​that are repeated in each iteration cycle, as constant values ​​that are updated in each iteration cycle based on the optimal results obtained in the previous iteration cycle, or as a combination thereof.

[0093] In some other examples, optimal weight values ​​associated with weighting function P are determined using a joint optimization on P and u. In these examples, the topology resembles a neural network and is suitable for backpropagation.

[0094] In some cases, the parameter of interest is the tilt angle of the structure being measured relative to the incident illumination beam, for example, at a fixed azimuthal angle.

[0095] In one of these examples, a quadratic curve fitting function shown by equation (6) is fitted to discrete values ​​of a scalar function S.

number

[0096] Furthermore, the extraction function shown by equation (7) is used to extract the value of the slope T from the coefficients characterizing the quadratic curve fitting function.

number

[0097] Optimization identifies values ​​for the weighting function P such that the scalar signal curve S is as close to a quadratic curve as possible. This is achieved by using a finite difference operator to take the second derivative of the data as a function of orientation. Two quantities, U and V, are then calculated, where U is the second moment of the data on a pixel-by-pixel basis and V is the variance of the data on a pixel-by-pixel basis. The ratio W = V / U provides an inverse measure of how well the pixel signal fits the quadratic function across the entire data set. The pixel weight value P is a function of the ratio, e.g., P = 1 - W / max(W).

[0098] As shown in Figure 7, the grating structure 171 is measured by the T-SAXS system 100 at an azimuthal angle of zero and an angle of incidence AOI. As shown in Figure 7, the grating structure itself is tilted at an oblique angle α relative to the wafer surface.

[0099] 8 is a plot showing discrete values ​​172 of a scalar function S that operates on measured images collected at various angles of incidence on detector 119. Additionally, a mathematical function 173, i.e., a curve C, is fitted to the discrete values ​​172. As shown in FIG. 8, the maximum value of mathematical function 173 indicates the orientation of grating structure 171 relative to incident illumination beam 116 where incident illumination beam 116 is aligned with the holes in grating structure 171, i.e., there is zero tilt.

[0100] In some examples, the weighting function P, the image filter function Q, or both are implemented to minimize or maximize the signal from one-dimensional scattering. In these examples, the weighting function P, the image filter function Q, or both are used to account for parameters related to one-dimensional or two-dimensional structures.

[0101] In another further aspect, different exposure times are used at different orientations of the structure being measured relative to the incident illumination beam. In these examples, increasing the exposure time at a particular orientation is used to reduce measurement noise for a given time required to estimate one or more parameters of interest. In other words, simply increasing the exposure time at all orientations would increase the total measurement time required to estimate one or more parameters of interest. However, in some examples, collecting image data at different orientations for different lengths of time maximizes the information content of the scalar signal. In these examples, differences in exposure time between images collected at different orientations are accommodated by mathematically normalizing the image data based on the exposure time, e.g., scaling the measured pixel intensities between different images based on the exposure time.

[0102] In another aspect, accurate model-less tilt measurements are used to improve system calibration, wafer shape models, and measurements of absolute wafer tilt.

[0103] In some embodiments, the AOI offset value is determined based on model-less tilt measurements of a calibration grating at two azimuthal angles 180 degrees apart. In this way, calibration of the AOI offset is decoupled from the angular offset of the target structure itself by measuring tilt over a range of incidence angles and two azimuthal angles 180 degrees apart. Similarly, multiple tilt measurements allow calibration of the absolute tilt of the wafer.

[0104] In another aspect, the model-less tilt measurements are used to define a subsequent measurement set of the structure of interest. The subsequent measurement set allows for improved measurement accuracy, measurement of an expanded set of parameters of interest, or both. In some examples, the subsequent measurement set allows for improved measurement accuracy, measurement of an expanded set of parameters of interest, or both when measuring deep hole memory structures.

[0105] In some embodiments, a model-less measurement of the tilt of the hole structure is performed as described herein. The measured tilt indicates an angular misalignment between the incident illumination beam and the hole structure. After measuring the misalignment, the AOI and azimuthal angle of the wafer relative to the illumination beam are adjusted to more precisely align the illumination beam with the hole structure based on the measured tilt. After aligning the illumination beam with the hole structure, one or more scattering images are collected while the illumination beam is more precisely aligned with the hole structure. The measured scattering pattern is analyzed to estimate values ​​of one or more critical dimensions of the hole structure.

[0106] In some examples, the square of a Bessel function is used to determine the average critical dimension of a hole structure. When an illumination beam is aligned with a circular hole structure, the scattered light pattern captured at the detector is approximated by a Bessel function. Visually, the intensity pattern at the detector appears as a series of concentric rings. The larger the spacing between adjacent rings, the smaller the hole diameter, and vice versa. In some examples, the square of a Bessel function is fitted to the measured scattering pattern in an iterative manner. The values ​​of the parameters characterizing the Bessel function fitted to the measured scattering pattern directly correlate to the values ​​of the critical dimensions of the measured hole structure.

[0107] In some examples, the square of a modified Bessel function is used to determine the average shape of elliptical hole structures, which are typical in many memory structures. When the cross-sectional shape of a hole structure is elliptical rather than circular, the scattering pattern differs from the ideal Bessel function. In these examples, the elliptical hole shape is modeled with a modified Bessel square function and transformed using a Fourier transform to predict the scattered light pattern at the detector. In an iterative manner, parameters describing the elliptical shape, such as the magnitude and orientation of the major and minor axes, are adjusted until the predicted scattering pattern matches the actual scattering pattern. In this way, the shape and orientation of non-circular hole structures can be estimated with high accuracy.

[0108] In some embodiments, a model-less measurement of the tilt of a hole structure is performed as described herein. The measured tilt indicates the angular misalignment between the incident illumination beam and the hole structure. The AOI and azimuthal angle of the wafer relative to the illumination beam are adjusted to a precise angle of incidence that is not aligned with the hole structure, i.e., a precise off-axis angle, based on the measured tilt. Scattering images are collected at the precise off-axis angle of incidence. The measured scattering pattern is analyzed to estimate the value of the critical dimension of the hole structure. In some examples, a sinc function is used to estimate the height of the measured hole structure. In some other examples, scattering images are collected at the precise off-axis angle of incidence to estimate the overlay, e.g., the relative positioning of the hole structure and the contact layer below the hole. Further details are described in U.S. Pat. No. 10,545,104 to KLA-Tencor Corporation (USA), the entire contents of which are incorporated herein by reference.

[0109] As previously described, model-less scatterometry measurements are used to measure the slope of hole structures. However, in general, model-less scatterometry measurements can be used to measure the slope of multiple structural elements of a measurement target captured in a collected scatterometry image. In some examples, the measurement target includes multiple layer hole structures, each characterized by a different slope. In some of these examples, one layer has a stronger diffraction signal than another layer, e.g., an underlying layer. In such examples, a strong diffraction signal may appear away from the center of the image, while a weak diffraction signal may appear only near the center of the image. In these examples, the slope associated with the strong diffraction signal is determined by a model-less measurement associated with a scatterometry signal near the edge of the image, rather than the signal near the center of the image. After determining the slope associated with the strong diffraction signal, the known slope value is used to estimate the slope of the underlying layer using a model-less technique based on the signal near the center of the image. In some examples, the measurement target includes a hole structure and a word line cut structure, each characterized by a different slope. In some of these examples, the diffraction signal associated with the hole structure and the diffraction signal associated with the word line cut structure appear in different regions of the collected image. In these examples, the slope associated with the hole structure is determined by a model-less measurement technique based on the signal in one region of the collected image, and the slope associated with the word line cut structure is determined by a model-less measurement technique based on the signal in a different region of the collected image.

[0110] Measurement of the slope of a semiconductor structure is often based on identifying individual peaks in the value of a mathematical function fitted to a locus of scalar values ​​derived from the collected images, although typically multiple peaks may be identified to estimate the value of a parameter characterizing the semiconductor structure being measured. In some examples, scatterometry measurements of hole structures using model-less techniques result in two peaks in the value of a mathematical function fitted to a locus of scalar values ​​derived from the collected images. In these examples, the hole structures are characterized by both slope and taper, i.e., the change in critical dimension as a function of height. As a result, one peak is associated with the slope associated with one side of the hole structure, and a second peak is associated with the slope associated with the opposite side of the hole structure. In this manner, the overall slope of the hole structure and the taper of the hole structure are determined based on the values ​​of the two peaks.

[0111] In some embodiments, a model-less measurement of the tilt of a hole structure is performed as described herein based on a relatively small set of images. The measured tilt indicates an angular misalignment between an incident illumination beam and the hole structure with relatively low precision. The AOI and azimuthal angle of the wafer relative to the illumination beam are adjusted to a precise angle of incidence that is not aligned with the hole structure based on the measured tilt. Scattering images are collected at a precise off-axis angle of incidence. The measured scattering pattern is analyzed to estimate the value of the tilt of the hole structure with relatively high precision.

[0112] In these embodiments, an initial estimate of the hole tilt is performed with a relatively small set of images collected with short exposure times to minimize the time required to estimate the hole tilt. Based on the initial estimate, another set of measurements, e.g., incidence angle, azimuth angle, and exposure time, is specified to maximize the precision of the tilt measurement relative to the total measurement time. In some examples, the design of subsequent measurement sets is based on sensitivity analysis derived from initial geometric and electromagnetic modeling of the structure to be measured.

[0113] In some other examples, the design of subsequent measurement sets is based on the observed shape of the mathematical fit to the discrete values ​​of the scalar function evaluated at each orientation. In some examples, it is observed that the highest signal information is found where the derivative of the mathematical function is highest. In these examples, subsequent measurement sets are designed to measure structures at orientations clustered in regions of the mathematical function with the highest values ​​of the first derivative, measure for longer periods of time at these orientations, or both. If different exposure times are used at different orientations, the resulting images are normalized based on the exposure time; for example, the measured intensity at each pixel in each image is scaled by the exposure time associated with each image.

[0114] In some cases, a symmetric kernel is used to fit data from measurements collected from various angles of incidence, however, in general, many different kernel functions can be used to estimate many different tilt parameters, e.g., mean tilt, wafer bow, etc.

[0115] In some examples, the model-less measurements described herein are used to measure parameters of one or more structures that allow for verifying or updating measurement system calibration parameters.

[0116] In some of these examples, the results of the model-less measurements allow for calibration of the metrology tool used to perform the model-less measurements. However, in some other examples, information from the model-less measurements is used across multiple metrology tools. In one example, model-less tilt measurements are used to improve the results of optical measurements across multiple metrology tools, for example, Mueller matrix elements.

[0117] It should be appreciated that the various steps described throughout this disclosure may be performed by a single computer system 130, or alternatively, by multiple computer systems 130. Furthermore, different 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 above description should not be construed as limiting on the present invention, but merely as illustrative. Furthermore, one or more computing systems 130 may be configured to perform any other step(s) of any method, embodiment, described herein.

[0118] Additionally, computer system 130 may be communicatively coupled to X-ray illumination source 110, beam-forming slit mechanism 120, sample positioning system 140, and detector 119 in any manner known in the art. For example, one or more computing systems 130 may be coupled to computing systems associated with X-ray illumination source 110, beam-forming slit mechanism 120, sample positioning system 140, and detector 119, respectively. In another example, X-ray illumination source 110, beam-forming slit mechanism 120, sample positioning system 140, and detector 119 may all be directly controlled by a single computer system coupled to computer system 130.

[0119] Computer system 130 may be configured to receive and / or acquire data or information from the system's subsystems (e.g., X-ray illumination source 110, beam-shaping slit mechanism 120, sample positioning system 140, detector 119, etc.) via a transmission medium, which 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.

[0120] 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 act as a data link between the computer system 130 and other systems (e.g., memory onboard the measurement system 100, external memory, or an external system). For example, the computing system 130 may be configured to receive measurement data (e.g., signal 135) from a storage medium (i.e., memory 132 or 190) via the data link. For example, spectral results obtained using the detector 119 may be stored in a permanent or semi-permanent memory device (e.g., memory 132 or 190). In this regard, measurement results may be imported from onboard 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 ​​186 determined by the computer system 130 may be stored in a permanent or semi-permanent memory device (e.g., memory 190). At this point, the measurement results may be exported to another system.

[0121] 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 having one or more processors that execute instructions from a memory medium.

[0122] Program instructions 134 implementing methods such as those 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 on a computer-readable medium (e.g., memory 132). Exemplary computer-readable media include read-only memory, random-access memory, a magnetic or optical disk, or magnetic tape.

[0123] 9 illustrates a method 200 suitable for implementation by the metrology system 100 of the present invention. It is recognized that, in one aspect, the data processing blocks of method 200 may be performed via pre-programmed algorithms executed by one or more processors of computing system 130. While the following description is presented in the context of metrology system 100, it is recognized that the specific structural aspects of metrology system 100 herein do not represent limitations and should be construed as illustrative only.

[0124] In block 201, an illumination source generates a narrowband illumination light beam that is incident on a structure to be measured.

[0125] In block 202, a structure to be measured is oriented relative to an incident illumination beam at each of a plurality of angular orientations, each of the plurality of angular orientations being associated with a different measurement instance of the plurality of measurement instances.

[0126] In block 203, an image of light scattered from the structure to be measured in response to the incident illumination beam is detected at each of a plurality of measurement instances, each detected image including multiple diffraction orders of the scattered light.

[0127] At block 204, a plurality of discrete values ​​of the scalar function are determined, each of the plurality of discrete values ​​being based on the detected image at each of the plurality of measurement instances.

[0128] In block 205, values ​​of parameters that characterize a continuous mathematical function that fits a plurality of discrete values ​​of the scalar function are determined.

[0129] In block 206, values ​​of parameters of interest characterizing the structure being measured are estimated based on one or more properties of the mathematical function.

[0130] 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 its largest lateral extent (i.e., the dimension aligned to the wafer surface). In some embodiments, metrology targets to be measured have an aspect ratio of at least 20. In some embodiments, metrology targets have an aspect ratio of at least 40.

[0131] In some embodiments, the scatterometry measurements described herein are implemented as part of a fabrication process tool. Examples of fabrication process tools include, but are not limited to, lithography exposure tools, film deposition tools, implant tools, and etch tools. In this manner, the results of the T-SAXS analysis are used to control the fabrication process. In one example, T-SAXS measurement data collected from one or more targets is transmitted to the fabrication process tool. The T-SAXS measurement data is analyzed as described herein, and the results are used to adjust the operation of the fabrication process tool.

[0132] The scatterometry measurements described herein can be used to determine the properties of various semiconductor structures. Exemplary structures include, but are not limited to, low-dimensional structures such as FinFETs, nanowires, or graphene, sub-10 nm structures, lithographic structures, through-substrate vias (TSVs), memory structures such as DRAM, DRAM 4F2, FLASH, MRAM, and high-aspect-ratio memory structures. Exemplary structural characteristics include, but are not limited to, geometric parameters such as line-edge roughness, line-width roughness, pore size, pore density, sidewall angle, profile, critical dimension, pitch, thickness, and overlay, and material parameters such as electron density, composition, grain structure, morphology, stress, strain, and elemental identity. In some embodiments, the metrology target is a periodic structure. In some other embodiments, the metrology target is aperiodic.

[0133] In some examples, measurements of critical dimensions, thickness, overlay, and material properties of high aspect ratio semiconductor structures, including, but not limited to, spin transfer torque random access memory (STT-RAM), three-dimensional NAND memory (3D-NAND) or vertical NAND memory (V-NAND), dynamic random access memory (DRAM), three-dimensional FLASH memory (3D-FLASH), resistive random access memory (Re-RAM), and phase change random access memory (PC-RAM), are performed by the T-SAXS measurement system described herein.

[0134] The term "critical dimension" as used herein includes any critical dimension of a structure (e.g., bottom critical dimension, middle critical dimension, top critical dimension, sidewall angle, grating height, etc.), the critical dimension between any 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 overlay grating structures, etc.). The structures may include three-dimensional structures, patterned structures, overlay structures, etc.

[0135] The terms "critical dimension application" or "critical dimension measurement application" as used herein include any critical dimension measurement.

[0136] The term "metrology system" as used herein includes any system used to at least partially characterize a specimen in any manner, including critical dimension applications, overlay metrology applications, etc. However, such terminology does not limit the scope of the term "metrology system" as used herein. Additionally, the metrology systems described herein may be configured for measurement of patterned and / or unpatterned wafers. The metrology systems may be configured as LED inspection tools, edge inspection tools, backside inspection tools, macro inspection tools, or multi-mode inspection tools (including simultaneous data from one or more platforms), as well as any other metrology or inspection tool that would benefit from the measurement techniques described herein.

[0137] Various embodiments are described herein with respect to semiconductor processing systems (e.g., inspection systems or lithography systems) that may be used to process specimens. The term "specimen" is used herein to refer to a wafer, a reticle, or any other sample that may be processed (e.g., printed or inspected for defects) by means known in the art.

[0138] As used herein, the term "wafer" generally 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 found and / or processed in semiconductor fabrication facilities. In some cases, a wafer may include only a substrate (i.e., a bare wafer). Alternatively, a wafer may include one or more layers of different materials formed on a substrate. The one or more layers formed on a wafer may be "patterned" or "unpatterned." For example, a wafer may include multiple dies having repeatable pattern features.

[0139] A "reticle" may be a reticle at any stage in the reticle fabrication process or a finished reticle that may or may not have been released for use in a semiconductor fabrication facility. A reticle or "mask" is generally defined as a substantially transparent substrate having substantially opaque regions formed thereon and configured in a pattern. The substrate may comprise, for example, a glass material such as amorphous SiO2. A reticle may be placed over a resist-coated wafer during the exposure step of a lithography process so that the pattern on the reticle can be transferred to the resist.

[0140] 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. The formation and processing of such layers of material may ultimately result in a completed device. Many different types of devices may be formed on a wafer, and the term wafer, as used herein, is intended to encompass a wafer on which any type of device known in the art may be fabricated.

[0141] In one or more exemplary embodiments, the functions described may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functions may be stored on or transferred as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media, including 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. By way of example, such computer-readable media may include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage devices, magnetic disk storage devices or other magnetic storage devices, or any other medium that can be used to carry or store required 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. Also, any connection is properly termed a computer-readable medium. For example, if 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, and microwave, the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technologies such as infrared, radio, and microwave are included within the definition of medium. Disk and disc, as used herein, include compact discs (CDs), laser discs, XRF discs, digital versatile discs (DVDs), floppy disks, and Blu-ray discs; disks typically reproduce data magnetically, while discs reproduce data optically with a laser. Combinations of the above are also intended to be included within the scope of computer-readable media.

[0142] Although certain specific embodiments are described above for illustrative purposes, the teachings of this patent specification have general applicability and are not limited to the specific embodiments described above. Accordingly, various modifications, adaptations, and combinations of the various features of the described embodiments may be made without departing from the scope of the invention as set forth in the claims.

Claims

1. 1. A measurement system comprising: an illumination source configured to generate a narrowband illumination light beam incident on the structure to be measured; a sample positioning system configured to orient the structure to be measured relative to the incident illumination beam at each of a plurality of angular orientations, each of the plurality of angular orientations being associated with a different measurement instance of a plurality of measurement instances; an imaging detector configured to detect, at each of the plurality of measurement instances, an image of light scattered from the structure to be measured in response to the incident illumination beam, wherein each detected image comprises multiple diffraction orders of scattered light; and 1. A computing system comprising: determining a plurality of discrete values ​​of a scalar function, each of the plurality of discrete values ​​being based on the detected image at each of the plurality of measurement instances; determining values ​​of a parameter that characterizes a continuous mathematical function that fits the plurality of discrete values ​​of the scalar function; and estimating a value of a parameter of interest characterizing the structure of the object based on one or more properties of the mathematical function. A measurement system comprising:

2. The metrology system of claim 1 , wherein the scalar function comprises an image filter, the image filter scaling the value of each pixel in each detected image.

3. The measurement system of claim 2 , wherein the scalar function is a mathematical operator.

4. The measurement system of claim 2 , wherein the scalar function is a vector of coefficients that correspond one-to-one to each pixel of each detected image.

5. The metrology system of claim 1 , wherein the scalar function comprises a weighting function, the weighting function scaling the detected image at each of the plurality of measurement instances.

6. The measurement system of claim 1 , wherein the continuous mathematical function is a quadratic function.

7. The metrology system of claim 1 , wherein the one or more characteristics of the mathematical function include a value of the mathematical function at which a first derivative of the mathematical function is zero.

8. the computing system, The metrology system of claim 5 , further configured to optimize weight values ​​associated with the weighting function to fit the continuous mathematical function to the plurality of discrete values ​​of the scalar function.

9. 10. The metrology system of claim 1, wherein an exposure time of the structure to be measured to the incident illumination beam in one or more of the plurality of measurement instances is different from an exposure time associated with another of the plurality of measurement instances.

10. The metrology system of claim 1 , wherein the narrowband illumination incident on the structure to be measured is centered in the x-ray range of the electromagnetic spectrum, the optical range of the electromagnetic spectrum, or the infrared range of the electromagnetic spectrum.

11. 1. A measurement system comprising: an illumination source configured to generate a narrowband illumination light beam incident on the structure to be measured; a sample positioning system configured to orient the structure to be measured relative to the incident illumination beam at each of a first plurality of angular orientations and one or more of a second plurality of angular orientations, wherein each of the first plurality of angular orientations is associated with a different measurement instance of a first plurality of measurement instances and each of the one or more of the second plurality of angular orientations is associated with one or more different measurement instances of the second plurality of measurement instances; an imaging detector configured to detect an image of light scattered from the structure to be measured in response to the incident illumination beam at each of the first plurality of measurement instances and each of the one or more of the second plurality of measurement instances, wherein each detected image comprises multiple diffraction orders of scattered light; and 1. A computing system comprising: estimating a value of a tilt of the structure to be measured relative to the incident illumination beam based on the detected image at each of the first plurality of measurement instances; determining the one or more of the second plurality of orientations of the structure to be measured relative to the incident illumination beam based on the measured tilt; determining a value of a parameter of interest characterizing a structure of the measurement object based on the detected image at each of the one or more of the second plurality of measurement instances; and A measurement system comprising:

12. 12. The metrology system of claim 11, wherein the one or more of the second plurality of orientations more precisely aligns the incident illumination beam with the structure to be measured compared to the first plurality of orientations.

13. 13. The metrology system of claim 12, wherein determining the value of the parameter of interest characterizing the structure of the measured object comprises iteratively fitting a Bessel-squared function to the measured scattering pattern at the one or more of the second plurality of measurement instances.

14. The metrology system of claim 13 , wherein the parameter of interest is a critical dimension of a hole structure.

15. 13. The metrology system of claim 12, wherein determining the value of the parameter of interest characterizing the structure of the measured object comprises iteratively fitting a modified Bessel-squared function to the measured scattering pattern at the one or more of the second plurality of measurement instances.

16. The metrology system of claim 15 , wherein the parameter of interest is a parameter that characterizes a shape of an elliptical hole structure, an orientation of the elliptical hole structure, or both.

17. 12. The metrology system of claim 11, wherein the one or more of the second plurality of orientations more accurately aligns the incident illumination beam with the structure to be measured at a desired off-axis angle compared to the first plurality of orientations.

18. The metrology system of claim 11 , wherein the parameter of interest is one of a height of the structure to be measured or an overlay of the structure to be measured.

19. The measurement system of claim 11 , wherein the first plurality of measurement instances is smaller than the second plurality of measurement instances.

20. 1. A method comprising: generating a narrowband illumination light beam incident on a structure to be measured; orienting the structure to be measured relative to the incident illumination beam at each of a plurality of angular orientations, each of the plurality of angular orientations being associated with a different measurement instance of a plurality of measurement instances; detecting, at each of the plurality of measurement instances, an image of light scattered from the structure to be measured in response to the incident illumination beam, wherein each detected image comprises multiple diffraction orders of scattered light; determining a plurality of discrete values ​​of a scalar function, each of the plurality of discrete values ​​being based on the detected image at each of the plurality of measurement instances; determining values ​​of a parameter that characterizes a continuous mathematical function that fits the plurality of discrete values ​​of the scalar function; estimating values ​​of parameters of interest characterizing the structure of the object based on one or more properties of the mathematical function; A method comprising:

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