System and method using x-rays for depth-resolving metrology and analysis

Abstract

This invention discloses a system and method for analyzing the three-dimensional structure of a sample, comprising: generating a first X-ray beam having a first energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and a first average X-ray energy in the range of 1 eV to 1 keV higher than the absorption edge energy of a first element of interest, and collimating it to have a collimation angle range of less than 7 mrad in at least one direction perpendicular to a propagation direction of the first X-ray beam; irradiating the sample with the first X-ray beam at a plurality of incident angles relative to a substantially flat surface of the sample, the incident angles being in the range of 3 mrad to 400 mrad; and simultaneously detecting a reflected portion of the first X-ray beam from the sample and detecting X-ray fluorescence and / or photoelectrons from the sample.

Description

[Technical Field]

[0001] This application generally relates to systems and methods for analyzing samples using X-ray reflectance measurement, X-ray fluorescence and / or X-ray photoelectric emission spectroscopy. [Previous Technology]

[0002] The limitations of scaled-down physical structures naturally drive the semiconductor industry toward 3D architectures, which typically comprise multiple stacked layers of nanometer-thickness containing a large amount of material. Examples include gate-all-around (GAA) field-effect transistors, 3D NAND memory devices, and magnetoresistive random access memory. Manufacturing these devices involves numerous processing steps, including thin film and film stack deposition, doping, etching, and chemical mechanical polishing.

[0003] The dimensions and / or material units of the manufactured device are used and verified during both the search and development phases (e.g., for process monitoring to ensure the manufactured device operates within acceptable parameters or program windows). Typical parameters of interest include film structure dimensions (e.g., film thickness), distribution of (a number of) elements or (a number of) specific materials, dopant concentration, elemental composition, chemical species formation, and other parameters. For 3D architectures, a depth resolution of 2 nm or better (e.g., spatial resolution normal to the surface of a wafer) is desirable.

[0004] An emerging example of a novel 3D semiconductor architecture is a gate-all-around (GAA) device comprising nanosheets and nanowires. Information expected for process monitoring and measurement during manufacturing includes: structural information of the initial superlattice (e.g., the thickness of the Si nanosheets and SiGe layers), residues after the removal of sacrificial nanosheet layers, silicon oxide formation, and parameters related to the gate dielectric layer. Parameters related to the gate dielectric layer include the depth-direction dielectric thickness around each nanosheet, variations in the difference between the dielectric thickness at the top and bottom of the nanosheet, variations in dopant at each layer of the dielectric (used for tuning the work function), and dopant diffusion.

[0005] 3D architectures pose a challenge to conventional methods used for measurement and inspection. Characterization techniques using incident X-rays offer unique advantages because they do not require destructive sample preparation and can provide penetration to detect structures beneath the surface. X-ray reflectivity (XRR) is a useful technique for characterizing surfaces and interfaces (including their roughness, the diffusion of buried layers, and the thickness of single and multilayer stacks) at sub-nano resolution.

[0006] XRR curves are primarily determined by the electron density distribution along the surface normal of the sample and lack elemental and material specificity. Determining XRR based on its structure is an ill-posed problem, as it is due to various factors (such as short data collection time limited by processing power requirements in some applications), especially for XRR with low signal-to-noise ratios. Different material compositions and mass densities can lead to the same XRR curve. [Summary of the Invention]

[0007] In one embodiment disclosed herein, a method for analyzing the three-dimensional structure of a sample is provided. The method includes generating a first X-ray beam having a first energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and a first average X-ray energy in a range of 1 eV to 1 keV (e.g., 1 eV to 5 eV) higher than a first absorption edge energy of a first element of interest. The first X-ray beam is collimated to have a first collimation angle range of less than 7 mrad in at least one direction perpendicular to a first propagation direction of the first X-ray beam. The method further includes irradiating the sample with the first X-ray beam at a plurality of incident angles relative to a substantially flat surface of the sample. The incident angles are in the range of 3 mrad to 400 mrad. The method further includes simultaneously detecting a reflected portion of the first X-ray beam from the sample and detecting X-ray fluorescence and / or photoelectrons from the sample.

[0008] In another embodiment disclosed herein, a method for analyzing a layered structure comprising substantially parallel interfaces is provided. The method includes irradiating the layered structure with an incident X-ray beam at one or more incident angles relative to the substantially parallel interfaces in the range of 3 mrad to 400 mrad. The incident X-ray beam has an energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and an average X-ray energy in the range of 1 eV to 1 keV (e.g., 1 eV to 5 eV) higher than the absorption edge energy of an element of interest. The incident X-ray beam has sufficient coherence to produce X-ray intensity modulation within the layered structure through constructive and destructive interference between the X-rays transmitted from the incident X-ray beam and those reflected by the substantially parallel interfaces of the layered structure. The method further includes simultaneously detecting at least some of the X-rays reflected by the substantially parallel interfaces and detecting X-ray fluorescence and / or photoelectrons from the layered structure.

[0009] In another embodiment disclosed herein, a system for analyzing a three-dimensional structure of a sample is provided. The system includes at least one X-ray source configured to generate at least one X-ray beam having an energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and an average X-ray energy in the range of 1 eV to 1 keV higher than the absorption edge energy of an element of interest. The at least one X-ray beam is collimated to have a collimation angle range of less than 7 mrad in at least one direction perpendicular to the propagation direction of the at least one X-ray beam. The at least one X-ray source is further configured to guide the at least one X-ray beam to irradiate the sample at a plurality of incident angles relative to a substantially flat surface of the sample. The incident angles are in the range of 3 mrad to 400 mrad. The system further includes at least one first detector configured to detect a reflected portion of the at least one X-ray beam from the sample. The system further includes at least one second detector configured to simultaneously detect X-ray fluorescence and / or photoelectrons from the sample, along with the at least one first detector detecting the reflected portion of the at least one X-ray beam.

Implementation Method

[0033] Priority Claim

[0034] This application claims priority to U.S. Provisional Application No. 63 / 079,940, filed on September 17, 2020, the entire contents of which are incorporated herein by reference.

[0035] It has been previously disclosed that, in order to add element specificity, an X-ray photoelectron spectroscopy (XPS) and an X-ray fluorescence signal (XRF) are collected together with XRR to obtain information on (a number of) elements and (a number of) materials (see, for example, U.S. Patent No. 10,151,713 to Wu et al.). However, such prior systems have various limitations that have not been adequately addressed. For example, the inelastic mean free path (IMFP) of XPS photoelectrons is generally independent of the analyzed material, varies according to the kinetic energy E of the photoelectrons (e.g., for E greater than 100 eV, it is empirically proportional to E 0.78), and is generally less than 10 nm. As the photoelectrons propagate from their production points to the surface of the object, the IMPF causes substantial attenuation of the photoelectrons and thus results in poor signals from photoelectrons of (a number of) elements of interest located at a depth of more than 10 nm from the surface. XRF can provide element-specificity without the substantial attenuation experienced by XPS, but prior art uses incident X-rays with energies too low to excite many important elements (e.g., Wu et al. used an Al X-ray source with 1.5 keV X-rays). Multiple energy excitations can be used to generate photoelectrons with different selected energies and different selected IMPFs and / or refractive indices in a sample to tune the photoelectron IMPF, photoelectron emission angle, and / or refractive index as needed.

[0036] Regarding another illustrative limitation, the XRF signal of the prior art is typically weak due to its small quantity (e.g., dopants, gate dielectrics (such as HfO2), single-nm thick layers, and etching residues) compared to many (some) elements in semiconductor front-end device fabrication. Furthermore, these small quantities are located in a small analytical region / volume, further reducing the signal. Due to the low XRF signal, an X-ray source with multiple X-ray generating materials, as described herein, is used. The incident X-ray energy can be selected and used to select the characteristic fluorescent X-rays of (some) elements of interest, because the XRF signal generation efficiency is highly dependent on the excitation X-ray energy and is maximized when the X-ray energy is slightly above the absorption edge of one of the elements (e.g., the characteristic X-ray generation efficiency decreases as the excitation X-ray energy minus the absorption edge energy is cubed). Furthermore, XRF signals from the substrate material can contribute significantly to the background, which can block XRF signals from elements with characteristic XRF energies lower than those from the substrate. For example, strong Si substrate signals can reduce the signal-to-noise ratio (SNR) of the M-lines of Hf and La, which are elements of interest. A modified SNR for these lines can be achieved by using an X-ray source with multiple X-ray generating materials, as described herein, to select incident X-ray energies lower than the Si K absorption edge energies (e.g., SiC).

[0037] In response to another illustrative limitation, standard XRR measurements (alone or in combination with other techniques such as XPS and / or XRF) can be performed by acquiring data in many small angular steps (e.g., over a reasonably wide angular range). These XRR measurements utilize long data acquisition times to obtain acceptable data quality and are therefore too slow to meet the process monitoring speeds required in semiconductor device manufacturing.

[0038] These limitations have not been adequately addressed by previous XRR techniques, which were performed at very low incident angles relative to the sample surface and therefore did not focus the incident X-ray beam onto a semiconductor test pattern (e.g., in the range of 40 μm x 40 μm to 40 μm x 300 μm). Furthermore, previous XRR techniques utilized a filter and / or monochromatic X-ray optics (e.g., multilayer or single crystal) to monochromate the incident X-rays during XRR, thus reducing the flux from the laboratory X-ray source.

[0039] Figure 1 schematically illustrates an exemplary system 10 for XRR, XRF, and / or XPS from a sample 20 to be analyzed, according to certain embodiments described herein. System 10 can be configured to perform metrological and / or detection methods for at least a portion of the sample 20 as described herein. For example, sample 20 may include a substrate 22 (e.g., a silicon wafer) and a plurality of layered material structures 24 (e.g., nanosheet transistors) on a substantially flat surface 26 of sample 20. In some embodiments, XRR divergence may be less than 10 mrad, less than 5 mrad, and / or less than 3 mrad, and depth-direction measurement sensitivity may be 0.1 nm or less for a given atomic element of interest (e.g., an atomic element to be detected within a portion of sample 20).

[0040] In some embodiments, exemplary system 10 includes an X-ray source 30 configured to generate a first X-ray beam 32. The first X-ray beam 32 has a first energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and a first average X-ray energy in a range of 1 eV to 1 keV (e.g., a range of 1 eV to 5 eV) higher than a first absorption edge energy of a first element of interest (e.g., an element to be detected within a portion of the analyzed sample 20). The first X-ray beam 32 is collimated to have a first collimation angle range of less than 7 mrad in at least one direction perpendicular to a first propagation direction of the first X-ray beam 32. The X-ray source 30 is configured to irradiate the layered material structure 24 with the first X-ray beam 32 at a plurality of incident angles 34 relative to the surface 26, the incident angles ranging from 3 mrad to 400 mrad. For example, at least a portion of the X-ray source 30 and / or sample 20 may be mounted on at least one stage (not shown), which is configured to precisely adjust and set the incident angle 34 of the first X-ray beam 32 relative to the surface 26. For example, at least one stage may include an electromechanical system configured to guide the X-ray beam onto a layered material structure on a planar surface at a predetermined grazing incident angle or within a predetermined angle range of the incident angle.

[0041] In some embodiments, the exemplary system 10 of FIG1 further includes at least one first X-ray detector 40 configured to detect (e.g., measure) a reflection portion 36 of a first X-ray beam 32 from sample 20, and at least one energy-analyzing second detector 50 configured to simultaneously detect (e.g., measure) X-ray fluorescence (XRF) X-rays 52 and / or photoelectrons 54 from sample 20 with the first X-ray detector 40 detecting the reflection portion 36 of the first X-ray beam 32.

[0042] In some embodiments, as schematically illustrated by FIG1, the X-ray source 30 includes at least one X-ray generator 60 configured to generate X-rays 62 and at least one X-ray optical subsystem 70 configured to receive at least some X-rays 62 and generate a first X-ray beam 32 including at least some of the received X-rays 62.

[0043] FIG2 schematically illustrates an exemplary X-ray generator 60 according to some embodiments described herein. The X-ray generator 60 may include at least one X-ray target 64 comprising a thermally conductive substrate 65 (e.g., copper; diamond) and at least one structure 66 on or embedded in at least a portion of a surface of the substrate 65, the at least one structure 66 including at least one thermally conductive material 67 (e.g., diamond) in thermal communication with the substrate 65 and at least one X-ray generating material 68 (e.g., in the form of a thin film deposited on the thermally conductive material 67) on the at least one thermally conductive material 67. The substrate 65 may be in thermal communication with at least one heat dissipation structure (e.g., heat pipe; liquid coolant; another material having high thermal conductivity). The at least one X-ray generating material 68 is configured to generate X-rays 62 in response to bombardment by at least one electron beam (not shown).

[0044] X-ray 62 may comprise X-rays having a characteristic X-ray energy of at least one X-ray generating material (e.g., a characteristic X-ray emission line) in a low energy range (e.g., below 5.4 keV; below 3 keV; in the range of 0.1 keV to 50 keV; in the range of 0.2 keV to 5.5 keV; in the range of 0.5 keV to 5.5 keV). For example, at least one X-ray generating material 68 may comprise at least one atomic element configured to generate X-ray 62 having a low-energy K characteristic line energy, a low-energy L characteristic line energy, and / or a low-energy M characteristic line energy. Examples of at least one atomic element include (but are not limited to) substantially pure, alloyed, or compound forms of silicon, magnesium, aluminum, carbon (e.g., in the form of silicon carbide or SiC), nitrogen (e.g., in the form of TiN), fluorine (e.g., in the form of MgF2), oxygen (e.g., in the form of Al2O3), calcium (e.g., in the form of CaF2), titanium (e.g., K characteristic line energy of about 0.5 keV), rhodium (e.g., L characteristic line energy of 2.7 keV), and tungsten (e.g., M characteristic line energy of 1.8 keV). Other examples of at least one atomic element include (but are not limited to): MgO, SrB6, CaB6, CaO, HfO2, LaB6, GeN, and other borides, nitrides, oxides, and fluoride compounds. In some embodiments, at least 50% (e.g., at least 70%; at least 85%) of the X-rays 62 generated by the X-ray generator 60 have energy at the characteristic X-ray emission line energy in a narrow energy band (e.g., having an irradiation line width of less than 4 eV).

[0045] In some embodiments, the X-ray generator 60 includes a plurality of structures 66, each structure including a different X-ray generating material 68 configured to generate X-rays 62 with different X-ray spectra and different characteristics of X-ray emission lines. For example, the different structures 66 may be separated from each other but thermally connected to a common substrate 65, such that an electron beam can bombard only one structure 66 at a time to generate a single X-ray spectrum at a time. In some embodiments, the structure 66 may include multiple X-ray generating materials 68 (e.g., a MgF layer on top of a SiC layer) and the layer thickness may be configured such that the incident electron beam can simultaneously generate multiple different X-ray spectra. The plurality of structures 66 may include X-ray generating materials 68, which may have predetermined thermal conductivity and melting temperature and may be configured to generate characteristic X-rays (e.g., Kα characteristic lines from BeO, C, B4C, TiB2, Ti3N4, MgO, SiC, Si, MgF, Mg, Al, Al2O3, Ti, V, Cr; Lα characteristic lines from Sr, Zr, Mo, Ru, Rh, Pd, Ag and other compounds having melting temperatures greater than 1000 degrees Celsius; Mα characteristic lines from Hf, Ta, W, Ir, Os, Pt, Au, W and other compounds having melting temperatures greater than 1000 degrees Celsius). In some embodiments, the X-ray generating materials 68 are selected to generate X-rays with energies greater than the absorption edge energy of one of the atomic elements of the analyzed sample 20. Since the X-ray fluorescence cross-section of an atomic element is largest when the excitation X-ray energy is slightly higher than the absorption edge energy of the atomic element, it is useful to select the average X-ray energy of the first X-ray beam 32 to optimize the production efficiency of XRF X-ray 52.

[0046] Table 1 lists some exemplary X-ray generating materials 68 and characteristic X-ray beams that are compatible with certain embodiments described herein. Table 1: X-ray generating materials Characteristic X-rays Be Be Kα has a linewidth of less than 0.5 eV at 108.5 eV. 1,2 graphite C Kα has a linewidth of less than 0.5 eV at 277 eV. 1,2 Al2O3 O Kα with a linewidth of less than 1 eV at 525 eV. Mg Mg Kα has a linewidth of 0.85 eV at 1253.3 eV. 1,2 Al or Al2O3 Al Kα with a linewidth of less than 1 eV at 1486.6 eV. 1,2 SiC Si Kα with a linewidth of approximately 1 eV at 1740 eV. 1,2 Mo Mo Lα1 with a linewidth of less than 1 eV at approximately 2293 eV. Rh Rh Lα has a linewidth greater than 1 eV at approximately 2697 eV. Ti Ti Kα1 with a linewidth greater than 1 eV at 4511 eV Cr Cr Kα1 with a linewidth greater than 1 eV at 5415 eV Cu Cu Kα1 with a linewidth greater than 1 eV at 8048 eV For certain X-ray generating materials 68 (e.g., SiC; Mo; Rh; Ti; Cr; Cu), the X-ray optical subsystem 70 may include a filter / monochromator.

[0047] In some embodiments where at least one X-ray generating material 68 includes a nominally electrically insulating material (e.g., MgF), the at least one X-ray generating material 68 has a sufficiently small thickness (e.g., less than 10 micrometers; less than 2 micrometers) such that the material conducts electrons to the underlying substrate. In some other embodiments where at least one X-ray generating material 68 includes a nominally electrically insulating material, at least one structure 66 further includes a conductive conduit configured to suppress charging of at least one X-ray generating material 68. For example, at least one structure 66 may include a layer of X-ray generating material 68 (e.g., 1 micrometer to 10 micrometers thick) on a conductive and thermally conductive material 67. Various X-ray generators 60 and X-ray targets 64 compatible with certain embodiments described herein are disclosed by way of U.S. Patent No. 10,658,145, the entire contents of which are incorporated herein by reference.

[0048] FIG. 3A schematically illustrates an exemplary X-ray optical subsystem 70 (e.g., an X-ray optical series) for receiving X-rays 62 generated by an exemplary X-ray generator 60 according to certain embodiments described herein. The X-ray optical subsystem 70 of FIG. 3A includes a plurality of X-ray optical elements 72 configured to receive at least some X-rays 62 and generate a first X-ray beam 32 including at least some of the received X-rays 62 (e.g., at least 85% of the X-ray flux of at least one of the characteristic X-ray rays from the X-ray generator 60). For example, the plurality of X-ray optical elements 72 may include at least one portion of an axially symmetric capillary, each portion having at least one quadratic (e.g., parabolic, ellipsoidal, hyperboloid) reflecting surface 74 configured to reflect at least some of the X-rays 62. In some other embodiments, at least one of the X-ray optical elements 72 is non-axially symmetric and / or includes a curved crystal or a multilayer mirror. The plurality of X-ray optical elements 72 may include X-ray reflective coatings configured to increase the X-ray reflectivity or critical angle of the X-ray optical elements 72. In some embodiments, the X-ray optical subsystem 70 further includes a controllably adjustable stage (e.g., a support) on which the components of the X-ray optical subsystem 70 are mounted, the stage being configured to align the components of the X-ray optical subsystem 70 with each other and with the X-ray generator 60.

[0049] In some embodiments, the plurality of X-ray optical elements 72 have more than one quadratic reflective surface 74 (e.g., Wolter-type optics). In some embodiments, the reflective surfaces of the plurality of X-ray optical elements 72 are coated with a thin layer (e.g., 1 nm to 10 nm thick) of at least one high atomic number element to increase the critical angle of the X-ray optical element 72 and provide a large stereo angle of acceptance. In some other embodiments, the reflective surfaces 74 of the plurality of X-ray optical elements 72 are coated with a multilayer coating for reducing the pleochroism of the incident X-ray 62 (e.g., reducing the energy bandwidth of the resulting first X-ray beam 32).

[0050] In the exemplary X-ray optical subsystem 70 of FIG3A, a plurality of X-ray optical elements 72 include: a first X-ray optical element 72a, which includes a collimating Wörther I mirror having reflective surfaces 74a, 74b; and a second X-ray optical element 72b, which includes a focusing Wörther I mirror having reflective surfaces 74c, 74d. In some other embodiments, the first X-ray optical element 72a includes a parabolic reflective surface 74 configured to collimate at least some X-rays 62 received from the X-ray generator 60, and the second X-ray optical element 72b includes a parabolic reflective surface 74 configured to focus at least some collimated X-rays 62 received from the first X-ray optical element 72a. In some embodiments, the X-ray optical subsystem 70 further includes a beam stop 76 configured to block X-rays 62 that would otherwise travel through the X-ray optical subsystem 70 without being reflected by the plurality of X-ray optical elements 72.

[0051] In some embodiments, the X-ray optical subsystem 70 further includes at least one aperture 77 (e.g., beam slit; pinhole) configured to collimate focused X-rays 62 from a plurality of X-ray optical elements 72 in at least one direction by limiting the divergence of a first X-ray beam 32 incident on the sample 20. Figure 3B schematically illustrates an exemplary aperture 77 at one exit end of a second X-ray optical element 72b of Figure 3A according to some embodiments described herein. In some embodiments, at least one aperture 77 provides angular collimation in at least one direction such that the first X-ray beam 32 appears as a plane wave in the reflection direction. The angular collimation of aperture 77 can be determined by the following formula: ∆θ<λ / (2d) / 5 where ∆θ is the angular collimation, λ is the wavelength of the X-ray 62 incident on aperture 77, and d is the period of the interference pattern generated by the incident and reflected X-ray waves. In some embodiments, the angular collimation of at least one aperture 77 is less than 5 mrad. In some embodiments, at least one aperture 77 is defined by at least two X-ray opaque elements 78 configured to block at least some X-rays 62 and (e.g., by a motor) adjustable relative to each other such that the size (e.g., width) of at least some X-rays 62 that can propagate through it to the sample 20 can be controllably adjusted. The size of at least one aperture 77 may vary depending on the size of the features of the sample 20 to be analyzed (e.g., along the reflection dimension).

[0052] At least one aperture 77 may be upstream or downstream of the X-ray optical element 70 or between a plurality of X-ray optical elements 72. For example, for a plurality of X-ray optical elements 72 including two parabolic reflective surfaces, at least one aperture 77 may be placed between the two parabolic reflective surfaces. For example, as schematically illustrated in FIG3A, at least one aperture 77 may be downstream of a plurality of X-ray optical elements 72. At least one aperture 77 may be used to limit the size and / or angular range of the first X-ray beam 32 on the surface of the layered structure of the sample 20 and apply a predetermined amount of spatial coherence to form a standing wave at the surface of the layered structure of the sample 20.

[0053] In some embodiments, the size (e.g., area occupied) F of the first X-ray beam 32 on sample 20 can be expressed as: F = s / sin(α) where s is the beam size along the tangential (e.g., reflection) direction and α is the angle of incidence 34 of the first X-ray beam 32 relative to surface 26. In some embodiments, the size L of aperture 77 (e.g., near the exit end of the plurality of X-ray optics 72) is defined such that: s / sin(α) < L. For example, for an angle of incidence of L = 300 micrometers and α = 41 mrad (e.g., 1.74 keV on Pt-coated glass), the aperture 77 defining the size of the first X-ray beam 32 in one dimension can be equal to 12.3 micrometers. Using aperture 77 and the plurality of X-ray optics 72 (which produce a 20-micrometer diameter spot), approximately 60% of the X-ray flux incident on aperture 77 that would otherwise be delivered to sample 20 is transmitted (without reduction in the other dimension). It should be noted that for a standing wave at 8 keV, aperture 77 would be too small (or its characteristic value would be too large) to be practically useful, as shown in Table 2. Table 2: X-ray energy Critical angle Feature size Pore ​​width 1.74 keV 41 mrad 300 micrometers 12.3 micrometers 8 keV 8.9 mrad 300 micrometers 2.7 micrometers In some embodiments, the size of the pore 77 can be significantly increased to transmit sufficient X-ray flux to the sample 20. In some embodiments, the feature size is 500 micrometers in length instead of 300 micrometers as described above, and the width of the pore 77 can be further widened.

[0054] In some embodiments, the X-ray optical subsystem 70 further includes a filter and / or monochromator configured to monochromate one of the X-rays of the first X-ray beam 32. Any X-ray monochromator known to those skilled in the art can be used, examples of which include (but are not limited to) channel-cut crystals, planar crystals (e.g., Si(111)), and composite multilayers. In some embodiments, the monochromator is positioned between a first X-ray optical element 72a (e.g., a collimating first parabolic mirror) and a second X-ray optical element 72b (e.g., a focusing second parabolic mirror) such that the first X-ray optical element 72a collimates at least some of the X-rays 62 from the X-ray generator (e.g., X-rays 62 incident on a double or quadruple reflector crystal) and the second X-ray optical element 72b focuses at least some of the X-rays 62 from the first X-ray optical element 72a (e.g., to a spot size (FWHM) of less than 40 micrometers). In some embodiments, the monochromator includes at least one multilayer coating on at least one inner surface of the X-ray optical subsystem 70. In some embodiments where the X-rays 62 generated by the X-ray generator 60 are sufficiently monochromatic to form standing X-ray waves within a layered material structure (e.g., in some embodiments where the X-ray generating material includes Mg, Al and / or Si), the X-ray optical subsystem 70 may exclude having a multilayer or crystal monochromator.

[0055] In some embodiments, the average X-ray energy of the incident first X-ray beam 32 may be selected to reduce (e.g., suppress) the X-ray background contribution to the detected characteristic XRF X-ray 52 of the atomic elements of the analyzed sample 20, due to spectral interference and / or detector noise contributions (e.g., incomplete charge collection). An energy-dispersive detector (e.g., SDD) has a limited energy resolution (e.g., approximately 125 eV for detecting 5.9 keV X-rays), and spectral interference (e.g., overlap) between the characteristic X-rays of the atomic element of interest and the characteristic X-rays of one of the major atomic elements in the layered material structure 24 of sample 20 can make the detection and quantification of the atomic element of interest difficult, resulting in long data acquisition times. For example, for a stack of three Si nanosheet transistors, Si is a major atomic element, and the energy of the characteristic Si K-line is approximately 1.74 keV. HfO2 is a widely used gate dielectric material, and the characteristic M-line energy of Hf is approximately 1.64 keV, which differs from the characteristic Si Kα line energy by approximately 100 eV. In some embodiments, Si Kα X-rays are used as the first X-ray beam 32, thus preventing the generation of the characteristic Si Kα XRF X-ray 52 in sample 20.

[0056] In some embodiments, at least one first X-ray detector 40 is selected from the group consisting of: a proportional counter, a silicon drift detector, a direct-detection X-ray charge-coupled device (CCD), and a pixel array photon counting detector. In some embodiments, at least one energy-resolution second detector 50 includes an X-ray detector selected from the group consisting of: a silicon drift detector (SDD), a proportional detector, an ionization chamber, a wavelength dispersion detection system, or any other energy-resolution X-ray detector compatible with XRF measurement.

[0057] In some embodiments, at least one energy-resolution second detector 50 includes an energy-resolution photoelectron detector. For example, the energy-resolution photoelectron detector may include an angle-resolution hemispherical XPS electron energy analyzer having an angular resolution of about one degree and utilizing an electron projection lens column to collect angular resolution data in parallel to accept an angular range of up to 60 to 80 degrees along the non-dispersive direction. Other exemplary energy-resolution photoelectron detectors compatible with some embodiments described herein include (but are not limited to) hindrance field analyzers, cylindrical mirror analyzers, and time-of-flight analyzers. In some embodiments, the angular resolution XPS measurement may be acquired from a large sample, such as a complete semiconductor wafer that may be too large to be positioned within an XPS spectrometer at the desired grazing angle of incidence. The position of the energy-resolution photoelectron detector relative to the sample may remain fixed throughout the angular range, and the portion of the sample irradiated by the incident X-rays may remain constant during irradiation. Although the area occupied by the X-ray spot size increases as the grazing angle of incidence decreases (e.g., after the sample has been rotated relative to the incident X-ray beam), in some implementations, the analysis area can be substantially independent of the grazing angle of incidence by using a combination of source-defined small-area analysis and parallel collection.

[0058] In some embodiments, at least one first X-ray detector 40 and / or at least one energy-analyzing second detector 50 includes one or more apertures (e.g., beam slits; pinholes) at the input of one of the detectors. Exemplary Methods

[0059] Figure 4A is a flowchart of an exemplary method 100 for analyzing a three-dimensional structure (e.g., a characteristic spatial structure and material composition; using monoenergetic X-ray units) of a sample 20 according to certain embodiments described herein. In one operation block 110, method 100 includes generating a first X-ray beam 32 having a first energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and a first average X-ray energy in a range of 1 eV to 1 keV (e.g., a range of 1 eV to 5 eV) higher than a first absorption edge energy of a first element of interest. The first X-ray beam 32 is collimated to have a first collimation angle range of less than 7 mrad (e.g., less than 4 mrad; less than 1 mrad) in at least one direction perpendicular to a first propagation direction of the first X-ray beam 32.

[0060] In some embodiments, the first absorption edge energy of the first element of interest (e.g., 0.1 keV to 5.4 keV) is less than the absorption edge energy of one of the major elements of a portion of the analyzed sample 20 (e.g., at least 20% of the atoms constituting a portion of sample 20). For example, for a sample 20 comprising a silicon substrate, the first absorption edge energy of the first element of interest is less than 1.84 keV. In some embodiments, at least 50% of the X-rays of the first X-ray beam 32 irradiating sample 20 have X-ray energies greater than 100 eV higher than the first absorption edge energy of the first element of interest. In some embodiments, obtaining the X-ray energy bandwidth and generating the first X-ray beam 32 using an X-ray optical subsystem including a monochromator and / or a filter includes filtering the X-rays 62 to have the first energy bandwidth.

[0061] In some embodiments, the first X-ray beam 32 irradiates the sample 20 in a reflecting plane (e.g., a scattering plane) that includes a first propagation direction and a direction perpendicular to the surface 26, and the first X-ray beam 32 has a collimation angle (e.g., a collimation angle range) in the reflecting plane (e.g., containing the first X-ray beam 32 and the surface normal of the surface 26) and a convergence angle (e.g., a convergence angle range) in a convergence direction in a plane orthogonal to the reflecting plane (e.g., in a sagittal plane), the collimation angle being smaller than the convergence angle.

[0062] In one operation block 120, method 100 further includes irradiating sample 20 with a first X-ray beam 32 at a plurality of incident angles 34 in the range of 3 mrad to 400 mrad relative to one of the substantially flat surfaces 26 of sample 20. For example, the first X-ray beam 32 may irradiate one of the substantially flat regions of sample 20 at a grazing incident angle between 5 mrad and 25 mrad (e.g., an angle between the surface 26 of sample 20 and the first X-ray beam 32).

[0063] In one operation block 130, method 100 further includes simultaneously detecting a reflection portion 36 (e.g., XRR data) of a first X-ray beam 32 from sample 20 and detecting X-ray fluorescence X-rays 52 (e.g., XRF data) and / or photoelectrons 54 (e.g., XPS data) from sample 20. In some embodiments, method 100 further includes (e.g., in one operation block 132) analyzing the detected XRR data (e.g., first XRR data) and XRF data together to obtain information about the structure and materials of sample 20. For example, when sample 20 has undergone at least one processing procedure, and the sample 20 is irradiated with a first X-ray beam 32 while simultaneously detecting the reflection portion 36 of the first X-ray beam 32 and detecting XRF X-rays 52 and / or photoelectrons 54, method 100 may further include obtaining a first set of spatial and / or compositional information about sample 20 by at least analyzing the detected first reflection portion 36, the detected XRF X-rays 52, and / or the detected photoelectrons 54, and comparing the obtained first set of spatial and / or compositional information about sample 20 with a second set of spatial and / or compositional information about sample 20, before sample 20 undergoes at least one processing procedure. Figure 5A is a flowchart of another exemplary method 100 including the exemplary method 100 of Figure 4A (e.g., an example of operation blocks 110, 120, 130, and 132) according to certain embodiments described herein.

[0064] Figure 4B is a flowchart of another exemplary method 100 for analyzing a three-dimensional structure (e.g., characterizing spatial structures and material compositions; using dual-energy X-ray metric) of a sample 20 according to certain embodiments described herein. In addition to operation blocks 110, 120, and 130 of Figure 4A, method 100 of Figure 4B further includes, in operation block 140, generating a second X-ray beam having a second energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and a second average X-ray energy in a range of 1 eV to 1 keV (e.g., a range of 1 eV to 5 eV) lower than the first absorption edge energy of the first element of interest. The second X-ray beam is collimated to have a second collimation angle range of less than 7 mrad (e.g., less than 4 mrad; less than 1 mrad) in at least one direction perpendicular to a second propagation direction of the second X-ray beam. The method 100 of Figure 4B further includes irradiating the sample 20 with a second X-ray beam in an operation block 150 and detecting a second reflection portion (e.g., second XRR data) of the second X-ray beam from the sample 20 in an operation block 160. In some embodiments, the method 100 of Figure 4B further includes (e.g., in an operation block 162) obtaining spatial and compositional information about the sample 20 by analyzing the detected second reflection portion (e.g., second XRR data) and the detected first reflection portion (e.g., first XRR data), detected X-ray fluorescence X-rays (e.g., XRF data), and / or detected photoelectrons (e.g., XPS data). Figure 5B is a flowchart of another exemplary method 100 that includes a sample of the exemplary method 100 of Figure 4B (e.g., examples of operation blocks 110, 120, 130, 140, 150, 160, and 162) according to certain embodiments described herein.

[0065] Figure 4C is a flowchart of another exemplary method 100 for analyzing a three-dimensional structure (e.g., characterizing spatial structures and material compositions; using dual-energy X-ray metric) of a sample 20 according to certain embodiments described herein. In addition to operation blocks 110, 120, and 130 of Figure 4A, method 100 of Figure 4C further includes, in operation block 170, generating a second X-ray beam having a second energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and a second average X-ray energy in a range of 1 eV to 1 keV higher than a second absorption edge energy (e.g., a range of 1 eV to 5 eV). In some embodiments, the second absorption edge energy belongs to a first element of interest, and the first and second absorption edge energies are separated from each other by at least 1 keV. For example, the first absorption edge energy may be the L edge energy of one of the first elements of interest, and the second absorption edge energy may be the M edge energy of one of the first elements of interest. In some other embodiments, the second absorption edge energy belongs to a second element of interest that is different from the first element of interest. The second X-ray beam is collimated to have a second collimation angle range of less than 7 mrad (e.g., less than 4 mrad; less than 1 mrad) in at least one direction perpendicular to the second propagation direction of the second X-ray beam. The method 100 of FIG4C further includes irradiating the sample 20 with the second X-ray beam in an operation block 180 and detecting a second reflection portion (e.g., second XRR data) of the second X-ray beam from the sample 20 in an operation block 190. In some embodiments, the method 100 of FIG4C further includes obtaining spatial and compositional information about the sample 20 by analyzing the detected second reflection portion (e.g., second XRR data) and the detected first reflection portion (e.g., first XRR data), the detected X-ray fluorescence X-rays (e.g., XRF data), and / or the detected photoelectrons (e.g., XPS data).

[0066] In some embodiments, prior knowledge of a space and material of sample 20 is known. For example, the space and material of the sample may be previously characterized before performing one or more new procedural steps (e.g., adding or removing material, such as adding a dielectric layer to a silicon nanosheet using atomic layer deposition). Measurement of sample 20 after one or more procedural steps may include selecting one atomic element of the material added in one or more new procedural steps as the atomic element of interest or selecting one atomic element of the material removed (e.g., residue) as the atomic element of interest and performing one of the methods described herein. In some embodiments, known space and material information may be used when analyzing XRR and XRF data obtained using an X-ray beam (e.g., a first X-ray beam 32) having an average X-ray energy in the range of 1 eV to 1 keV higher than the absorption edge energy of one of the elements of interest (e.g., in the range of 1 eV to 5 eV; in the range of 5 eV to 1 keV). In some other embodiments, XRR data may be collected by a second X-ray beam (e.g., having an average X-ray energy in the range of 1 eV to 1 keV or 1 eV to 5 eV) that employs an absorption edge energy lower than that of the element of interest and beam characteristics substantially similar to those of the first X-ray beam 32.

[0067] In some embodiments, XRR and XRF data obtained over a small grazing angle range or with a small number of discrete grazing angles are measured and analyzed to obtain spatial and material information about one or more added or removed materials. The grazing angle and / or small range of discrete grazing angles can be selected based on the sensitivity (e.g., variation) of the XRR and XRF data in response to spatial and material information about one or more added or removed materials. Sensitivity can be predetermined by analysis (e.g., simulation) or measurement. Some benefits of these embodiments include increased measurement processing power.

[0068] Figure 6 is a flowchart of an exemplary method 200 for detection (e.g., procedural monitoring) according to certain embodiments described herein. The exemplary method 200 can be used to measure one or more pre-selected spatial and material parameters of a 3D structure on a planar substrate by measuring XRR and / or XRF data at a finite number of grazing angles selected with high sensitivity to pre-selected specific parameters. In operation block 210, method 200 includes selecting (e.g., predetermined) at least one element of interest (EOI) in the pre-selected material. In operation block 220, method 200 further includes generating an X-ray beam for XRR and XRF measurements. The X-ray beam has an energy bandwidth (e.g., full width at half maximum) of less than 20 eV and an average X-ray energy in a range of 1 eV to 1 keV higher than the absorption edge energy of one of the elements of interest (EOI) (e.g., in the range of 1 eV to 5 eV; in the range of 5 eV to 1 keV), and is collimated in at least one direction with a collimation angle of less than 7 mrad (e.g., less than 4 mrad; less than 1 mrad). In some embodiments, the absorption edge energy of the element of interest is selected to be between 0.1 keV and 5.4 keV. In some embodiments, the average X-ray energy is less than the absorption edge energy of one of the main elements of the substrate (e.g., 1.84 keV for a silicon substrate).

[0069] In one operation block 230, method 200 further includes selecting (e.g., predetermined) a limited number of specific grazing incidence angles (e.g., less than 20, 50, or 100, wherein at least 20% of the grazing incidence angles are well separated from each other) for XRR and XRF signal collection. Specific grazing incidence angles can be selected for high sensitivity to one or more pre-selected specific parameters. In some embodiments, the specific grazing incidence angle corresponds to a peak value in the expected XRR signal and / or XRF signal. In some embodiments, data is also collected at specific grazing incidence angles corresponding to expected valleys and / or peak values ​​in the XRR curve and / or XRF spectrum. In some of these embodiments, the peak value in the XRR signal of the EOI corresponds to the positive interference of the excitation X-ray beam (e.g., the first X-ray beam 32) in the layer containing the EOI in sample 20. In one operation block 240, method 200 further includes collimating the X-ray beam to less than 3 mrad in at least one direction (e.g., in the reflecting plane).

[0070] In operation block 250, method 200 further includes guiding an X-ray beam at a predetermined grazing incidence angle on a region of a flat substrate of sample 20, and in operation block 260, simultaneously collecting XRR and XRF data at a predetermined grazing incidence angle. In operation block 270, method 200 further includes analyzing the XRR and XRF data together to obtain structural and material information of the sample.

[0071] In some embodiments, method 200 includes collecting a first XRR curve with a first average X-ray energy having an absorption edge energy higher than the EOI and collecting a second XRR curve with a second average X-ray energy having an absorption edge energy lower than the EOI. The first and second XRR curves can be collected sequentially or simultaneously, and the data from the first and second XRR curves can be analyzed together to obtain structural and material information of the sample. In some embodiments, a first XRR dataset and XRF data are collected using a first average X-ray energy having an absorption edge energy higher than the EOI, and a second XRR dataset is collected using a second average X-ray energy having an absorption edge energy lower than the EOI. The first and second XRR datasets can be collected sequentially or simultaneously, and the first and second XRR datasets can be analyzed together with the XRF data to obtain structural and material information of the sample.

[0072] In some embodiments, the analysis of measured data (e.g., in operation blocks 132, 162, 270) includes one or more of the following: comparing at least some of the measured data with expected values ​​from one or more simulated models of the sample; comparing at least some of the measured data with prior information (e.g., prior to the procedure) to determine a change; comparing at least some of the measured data with measurements from a known reference sample. In some embodiments, the analysis can determine deviations in the physical dimensions of sample 20 from expected values ​​(e.g., from prior information, expected simulated values, and / or known reference values). These deviation measurements can be used to provide process monitoring (e.g., rapid feedback on the device during the manufacturing process) by generating an automated alarm when a measured deviation falls outside a predetermined range of expected values. In some embodiments, the methods described herein can be used to measure 3D spatial information of a finite number of material layers containing one or more atomic elements of interest. Illustrative Applications

[0073] Applications of certain embodiments described herein include, for example, the measurement and / or detection of semiconductor processes for gate-all-around (GAA) devices during or after dielectric deposition (e.g., determining the uniformity of deposition) on silicon nanosheets, during / after dummy gate removal, etc. In some embodiments, the sample being analyzed is a semiconductor sample (e.g., a semiconductor wafer). In some embodiments, the region of interest on the sample is a test pattern or scribe line of a semiconductor sample, while in some other embodiments, the region of interest is an active region of a semiconductor sample. In some embodiments, the area occupied by an X-ray beam on the sample surface is less than 100 micrometers in at least two dimensions parallel to the surface. Depth-resolution HfO2 thickness in a nanosheet stack.

[0074] Certain embodiments described herein can provide depth-resolved thickness characterization of HfO2 in a semiconductor nanosheet stack. For example, X-ray generator 60 may utilize an X-ray generating material 68 (e.g., SiC) comprising Si configured to generate Si Kα X-rays 62. The Si Kα X-rays 62 have an average X-ray energy (1.74 keV) below the Si absorption edge but above the two M absorption edges (M4 at 1.7164 keV and M5 at 1.6617 keV) of Hf. X-ray optical subsystem 70 may include one or more focusing X-ray optical elements used in combination with a collimating beam blocker (e.g., aperture; slit; pinhole) and may be configured to collimate the X-ray beam 32 to have a collimation angle range of 3 mrad in a scattering plane containing the incident X-ray beam and the surface normal. The first X-ray beam 32 can be focused and collimated to be incident on the sample 20 with a spot size of less than or equal to 50 x 500 micrometers (e.g., 50 x 300 micrometers, 40 x 500 micrometers, 40 x 300 micrometers or smaller), and the XRR and XRF signals can be collected within a grazing incident angle range (e.g., between 3 mrad and 300 mrad).

[0075] Figure 7A schematically illustrates three exemplary simulation models of a semiconductor nanosheet stack structure according to some embodiments described herein. Each exemplary simulation model has a Si nanosheet having a thickness of 10 nm along the depth direction, and the lateral dimension perpendicular to the depth direction can be any size (e.g., in the range of 1 nm to 10 nm, in the range of 10 nm to 50 nm, or 50 nm or greater). The Si nanosheet is surrounded by HfO2 (dielectric material) having a thickness of (i) 2 nm, (ii) 1.5 nm or (iii) 1 nm, and is separated from each other by air gaps having a thickness of (i) 6 nm, (ii) 7 nm or (iii) 8 nm in the depth direction. The thickness of the air gap is equal to 10 nm minus the thickness of the adjacent HfO2 dielectric layer (e.g., for an HfO2 dielectric layer having a thickness of 2 nm, the air gap thickness is 10 nm - (2.2 nm) = 6 nm).

[0076] Figure 7B shows graphs of simulated XRR data (e.g., curves) corresponding to the three exemplary simulation models in Figure 7A, collected using three X-ray energies according to certain embodiments described herein. The graphs in Figure 7B represent simulated XRR intensities collected from the Si nanosheet structure in Figure 7A with (i) 2 nm, (ii) 1.5 nm, and (iii) 1 nm HfO2 layers, varying with the incident angle at different X-ray energies. The leftmost graph has an X-ray energy of 1.49 keV (e.g., Al characteristic emission X-rays); the center graph has an X-ray energy of 1.74 keV (e.g., Si characteristic emission X-rays from SiC); and the rightmost graph has an X-ray energy of 9.7 keV.

[0077] Figure 7C shows a graph of the simulated difference between the three XRR curves of Figure 7B at three X-ray energies, according to certain embodiments described herein. Figure 7C illustrates that the difference in XRR intensity increases with increasing X-ray energy, and that at high X-ray energies, most XRR information is at very low incident angles (e.g., below 1 degree). XRR measurements at such low incident angles can extend the X-ray beam area over a region greater than expected. In some embodiments, XRR measurements are performed using an X-ray energy of 1.74 keV, where the XRR curves show substantial differences varying with HfO2 layer thickness over a wider range of incident angles (e.g., between 1.5 degrees and 7 degrees).

[0078] Figure 7D shows a graph of a simulated signal of a characteristic XRF line of Hf M5N7 varying with the incident angle at an excitation X-ray energy of 1.74 keV according to certain embodiments described herein. It should be noted that the value on the vertical axis represents the expected XRF photon of an incident photon. Since the incident X-ray energy is slightly higher than the M absorption edge of Hf, the incident X-ray is effective in exciting the Hf M-ray fluorescence signal. Furthermore, the Si characteristic emission line X-rays at 1.74 keV do not excite X-ray fluorescence from the bulk Si substrate, thereby increasing the signal-to-noise ratio of the measured Hf XRF signal. Figures 7A to 7D demonstrate the advantage of using an X-ray generating material 68 according to certain embodiments described herein that produces characteristic X-ray energies (e.g., 1.74 keV) higher than the absorption edge energy of an atomic element in the analyzed bulk sample.

[0079] Figure 7E shows a graph of the simulated XRR signal difference at three different X-ray energies according to certain embodiments described herein, illustrating the sensitivity to interface and surface roughness. The simulated XRR signal difference in Figure 7E falls between a first model assuming zero roughness on all surfaces and interfaces of a Si nanosheet structure and a second model assuming 1 nm roughness on the top surface and 0.5 nm roughness at the interface. Figure 7E confirms that the effect of roughness on the XRR signal decreases as the X-ray energy decreases (i.e., as the X-ray wavelength increases). This information can be used to normalize data. Figure 7E also confirms the advantages of using a dual-energy methodology according to certain embodiments described herein.

[0080] Figures 8A to 8E confirm another case similar to that of Figures 7A to 7E, but with modifications to the layer thickness. Furthermore, the cases in Figures 8A to 8E represent a dual-energy method in which the X-ray energies are selected to be higher than one of the absorption edges of the atom of interest: 1.74 keV (e.g., generated from a Si-based source), which is higher than the Hf M absorption edge; and 9.713 keV (e.g., generated from an Au-based source), which is higher than the Hf L absorption edge.

[0081] Figure 8A schematically illustrates two exemplary simulation models of a semiconductor nanosheet stack structure according to some embodiments described herein. Each exemplary simulation model has a Si nanosheet with a thickness of 10 nm along the depth direction, and the lateral dimension perpendicular to the depth direction can be any size (e.g., in the range of 1 nm to 10 nm, in the range of 10 nm to 50 nm, or 50 nm or greater). The Si nanosheet is surrounded by HfO2 (dielectric material), wherein (i) the first model has a top HfO2 layer with a thickness of 2 nm above each Si nanosheet and a bottom HfO2 layer with a thickness of 1.5 nm below each Si nanosheet, and (ii) the second model has a top HfO2 layer with a thickness of 1.5 nm above each Si nanosheet and a bottom HfO2 layer with a thickness of 2 nm below each Si nanosheet. In both models, the Si nanosheets are separated from each other by an air gap of 6.5 nm in thickness along the depth direction. Figure 8A confirms a challenging case in which the overall HfO2 signal remains the same despite the different structures.

[0082] Figure 8B shows a graph of simulated XRF signals from two models in Figure 8A at two different excitation X-ray energies according to certain embodiments described herein. For excitation X-rays with an X-ray energy of 9.713 keV (e.g., from an Au-based source), the simulated XRF signals from the two models, collected according to the incident angle, for the Hf L3M5 XRF line, show some distinguishing information, even though both models contain the same amount of HfO2. For excitation X-rays with an X-ray energy of 1.74 keV (e.g., from a SiC-based source), the simulated XRF signals from the two models, collected according to the incident angle, for the Hf M5N7 XRF line, also show some distinguishing information. The distinguishing information is provided by the interference pattern caused by reflection from the Si nanosheet in the constructive interference region at the HfO2 layer of interest, where the signal is stronger. In some implementations, the XRF signal is collected at 3 to 5 peaks and troughs before the XRF signal because a smaller incident angle provides greater sensitivity to the top layer. Additionally, Figure 8B shows that as the incident angle increases, the XRF signal "flips" between a first model with a signal strength greater than that of the second model and a second model with a signal strength less than that of the second model.

[0083] Figure 8C shows a graph of the simulated difference between the two Hf XRF curves of Figure 8B at two excitation X-ray energies according to certain embodiments described herein. As shown by Figure 8C, using an excitation X-ray energy of 9.713 keV provides a larger difference in the XRF signal but at a smaller incident angle.

[0084] Figure 8D shows a graph of simulated XRR signals (e.g., curves) collected from the Si nanosheet structure of Figure 8A using three X-ray energies according to certain embodiments described herein, corresponding to two exemplary simulation models of Figure 8A. The leftmost graph has an X-ray energy of 1.49 keV (e.g., Al characteristic emission line X-rays below the Hf M absorption edge); the center graph has an X-ray energy of 1.74 keV (e.g., Si characteristic emission line X-rays from SiC above the Hf M absorption edge); and the rightmost graph has an X-ray energy of 2.23 keV (e.g., above the Si K absorption edge). For each excitation X-ray energy, the XRR signals from the two models show the differences between them as a function of the incident angle.

[0085] Figure 8E shows a graph of the difference between the simulated XRR signals of Figure 8D according to certain embodiments described herein. Figure 8E confirms the advantage of selecting an excitation X-ray energy below one of the main absorption edges of the substrate and / or capping layer (e.g., silicon). The rightmost graph in Figure 8E confirms the difference between the XRR signals detectable by the absorption attenuation of the substrate and capping layer.

[0086] Figure 9 shows a graph illustrating the results of a dual-energy method for collecting XRF signals for two different atomic elements of interest according to certain embodiments described herein. In addition to the XRF signal of a first atomic element of interest, an XRF signal of a second atomic element of interest can also be collected. The second atomic element of interest may be another component of the analyzed material / layer / sample. For example, for HfO2, as shown in Figure 9, the second atomic element of interest is oxygen and the first atomic element of interest is Hf. In the XRF signals of Figure 9, the dual-energy method uses a first excitation X-ray energy above one absorption edge of the first atomic element of interest (e.g., Hf) and a second excitation X-ray energy below one absorption edge of the first atomic element of interest, while also using both excitation X-ray energies of the second atomic element of interest (e.g., oxygen) to generate the XRF signal. This additional information can be used to characterize the HfO2 layer thickness in a metrological extraction method or a detection extraction method, as described herein. Characterization related to certain elements

[0087] Certain embodiments described herein can be used to distinguish Si layers from SiGe layers in procedures commonly used for the development of silicon nanosheets. For Ge and any other element of interest having an absorption edge between 0.8 keV and 1.5 keV (examples of which include atomic elements having atomic numbers from 4 (B) to 11 (Na), from 19 (K) to 31 (Ge), and from 40 (Zr) to 64 (Gd), a Mg K line (1.254 keV) produced in an electron-bombarded X-ray source with a target including Mg or a Mg compound (e.g., MgCl) can be used to produce X-rays with X-ray energies in the range of 1 eV to 1 keV higher than the absorption edge of the element of interest (e.g., a range of 1 eV to 5 eV).

[0088] Certain embodiments described herein can be used to detect other atomic elements of interest. For example, for an atomic element of interest (including atomic elements having atomic numbers from 8 (O) to 12 (Mg), from 22 (Ti) to 34 (Se) and from 49 (In) to 68 (Er)) with an absorption edge between 0.8 keV and 1.5 keV, an Al K line (1.486 keV) generated in an electron-bombarded X-ray source having a target including Al or Al compounds can be used. For another example, for an atomic element of interest (including atomic elements having atomic numbers from 9 (F) to 13 (Al), from 24 (Cr) to 35 (Br) and from 56 (Ba) to 73 (Ta) with an absorption edge between 0.8 keV and 1.74 keV), a Si K line (1.74 keV) generated in an electron-bombarded X-ray source having a target including Si or Si compounds can be used. Alternatively, a W Mα line (1.8 keV) generated in an electron-bombarded X-ray source having a target including W or a W compound can be used. Further exemplary embodiments

[0089] In some embodiments, XRR can be measured across a Q value range (e.g., from 0 to 0.15), where Q is defined as: Q = (4π sinθ) / λ, where θ is the incident angle and λ is the wavelength of the incident X-ray. In some embodiments, XRR is performed at low X-ray energies close to (e.g., within 10%; within 20%) but below the absorption edge of one of the atomic elements of the substrate and / or non-atom elements of interest. In some of these embodiments, XRR measurements can be performed for X-ray energies close to (e.g., within 10%; within 20%) and below the absorption edge of the atomic element of interest.

[0090] Certain embodiments described herein use two or more X-ray energies to provide a metric (e.g., a finite number of XRR measurements obtained using two or more X-ray energies at a finite number of incident angles). For example, such X-ray energies may have a refractive index difference greater than 10% in the real and / or imaginary parts of the material including the element of interest. In some of these embodiments, one X-ray energy may be below one absorption edge of the element of interest and another X-ray energy may be above the absorption edge. The incident X-ray beam may have a small energy bandwidth and a small collimation angle range. The sample structure (e.g., the thickness of the Si nanosheet; the distance between the Si nanosheet and the substrate) may be known in a first stage of fabrication (e.g., before the deposition of the element of interest (e.g., HfO2)) and the metric may be available for analysis of the sample structure in a second stage of fabrication (e.g., after the deposition of the element of interest).

[0091] Certain embodiments include simulating XRR curves for various structures and X-ray energies, examples of which include: an HfO2 layer on a Si nanosheet using X-ray energies with Mg K-lines or Al K-lines and Si K-lines; a Ge layer in a Si / SiGe nanosheet stack using X-ray energies with K-lines of Mg, Al, or Si; and a Si layer on a Si nanosheet using X-ray energies with K-lines of Si or Al (which are below the Si K-edge absorption edge) and L-lines of Mo, Rh, or Pd. Certain embodiments include using XRR data with at least two X-ray energies to determine structural information of the atomic elements of interest in a layered material structure on a planar substrate. As described in this paper, simulations show that, partly due to the fact that the Si Kα line has an energy higher than the Hf M absorption edge but lower than the Si K absorption edge, and the Al Kα line has an energy lower than the Hf M absorption edge, the HfO2 film thickness variation can be measured using XRR with both the Si Kα line (1.74 keV energy) and the Al Kα line (1.5 keV) X-rays to provide complementary data.

[0092] In some embodiments, the metrology may additionally include collecting characteristic fluorescence X-rays of the element of interest during at least one XRR measurement using an X-ray excitation energy greater than the absorption edge energy of one of the atomic elements of interest but less than 3 keV for the effective generation of characteristic fluorescence X-rays of the element of interest to provide supplementary information. Some embodiments use XRR data and XRF data to determine structural information of the element of interest in a layered material structure on a planar substrate.

[0093] To monitor a manufacturing process in which a layered material structure contains an element of interest, certain embodiments may include: selecting a finite number of X-ray measurements having a strong correlation (e.g., response) with at least one element of interest in the structure; collecting a dataset of at least one element of interest on a reference standard using the selected number of X-ray measurements; collecting a dataset of at least one element of interest on a test object using the same selected number of X-ray measurements; calculating the deviation (e.g., difference) between the two datasets; and determining whether the deviation is within a procedure window for the structural parameters of the element of interest. A particular example of selecting a finite number of X-ray measurements may include using a finite number of measurements with an X-ray energy higher than the absorption edge of one of the elements of interest but less than 1 keV. The incident X-ray beam may have a small energy bandwidth and a small collimation range.

[0094] In some embodiments, the thickness of the HfO2 layer on three Si nanosheets (e.g., each Si nanosheet has a thickness of 10 nm and a spacing of 20 nm between adjacent nanosheets) is monitored at a finite number of incident angles using Si Kα X-rays and / or Al Kα X-rays. In one example, the three-Si nanosheet structure can be simulated using at least two models, each of which has corresponding HfO2 layer thicknesses equal to each other on both sides of all three Si nanosheets (e.g., the HfO2 layer thicknesses of the models differ from each other by 0.5 nm; a first model has an HfO2 layer thickness equal to 1.5 nm and a second model has an HfO2 layer thickness equal to 2.0 nm). In another example, the three-Si nanosheet structure can be simulated using at least two models, each having a top HfO2 layer thickness (e.g., 2.0 nm) and a bottom HfO2 layer thickness (e.g., 1.5 nm), but with different thicknesses at the top and bottom. In yet another example, the three-Si nanosheet structure can be simulated using at least two models, each having the same HfO2 thickness on both the top and bottom sides of the top and bottom Si nanosheets (e.g., 2.0 nm on both sides for the top Si nanosheet; 1.5 nm on both sides for the bottom Si nanosheet), and the HfO2 layer thickness on the top and bottom sides of the middle Si nanosheet equal to the average of the HfO2 layer thicknesses on the top and bottom Si nanosheets (e.g., 1.75 nm on both sides). For each instance, data can be obtained at one or two incident angles (e.g., selected because it is expected that the differences between its pairs of models will be sufficiently sensitive).

[0095] In some embodiments, the relative thickness of the Si layer and SiGe layer of a three-layer Si / SiGe nanoparticle stack on at least one test sample is monitored using Si Kα line X-rays and reference data obtained from at least one reference sample (e.g., each Si / SiGe nanosheet of the at least one reference sample has a thickness of 10 nm and a spacing of 20 nm between adjacent Si / SiGe nanosheets). In one example, a reference sample has a Si / SiGe thickness ratio of 1.05 for each of the Si / SiGe nanosheets, and reference data from the reference sample and test data from at least one test sample can be obtained at one or two incident angles (e.g., selected because their pair is expected to be sufficiently sensitive to the thickness ratio of reference data from the reference sample). In another example, reference data is obtained from a reference sample in which the top, middle, and bottom Si / SiGe nanosheets have different Si / SiGe thickness ratios (e.g., top nanosheet: 1.0; middle nanosheet: 0.98; bottom nanosheet: 0.95). Reference and test data can be obtained at a limited number of XRR measurement points (e.g., selected because they are expected to be sufficiently sensitive to the thickness ratio of reference data from a reference sample).

[0096] In some embodiments, constructive and destructive interference between incident X-rays and X-rays reflected from the interface of the layered material structure can be used to provide additional sensitivity to structural parameters. In some embodiments, a limited number of characteristic XRF measurements can be obtained using an incident X-ray energy higher than the absorption edge of one of the atomic elements of interest but less than 1 keV. The incident X-ray beam can have sufficient coherence to produce X-ray intensity modulation within the layered material structure through constructive and destructive interference between the incident X-rays and X-rays reflected from the interface of the layered material structure. The X-ray energy can be selected to effectively generate characteristic fluorescent X-rays and / or provide a sufficiently high signal-to-background ratio (e.g., using incident Si K-line X-rays to effectively generate Hf M-line fluorescent X-rays and using incident Al K-line X-rays to effectively generate Ge L-line fluorescent X-rays).

[0097] For example, the layered material structure may include three Si nanosheets (e.g., each 10 nm thick) separated from each other by an air / vacuum region and a thin (e.g., less than 3 nm thick) HfO2 layer surrounding the Si nanosheet (e.g., see Figures 7A and 8A). The X-ray transmission of characteristic oxygen K-line fluorescent X-rays and characteristic Hf L-line fluorescent X-rays through 20 nm of Si can be greater than 90%, and even sufficient for characteristic fluorescent X-rays generated at the bottom side of the bottom Si nanosheet. To generate O characteristic K-line fluorescent X-rays, the excitation X-rays can have an X-ray energy greater than 532 eV (which is the oxygen K absorption edge energy). To efficiently generate O characteristic K-line fluorescent X-rays, and to have a sufficiently high X-ray flux within a sufficiently narrow spectral bandwidth to produce X-ray intensity modulation within the layered material structure, an X-ray source having a target material including Mg, Al and / or Si and related compounds (e.g., SiC) can be used. To generate Hf-characteristic L-line fluorescent X-rays, the excitation X-rays can have an X-ray energy greater than the Hf M3 absorption edge energy of 1.662 keV. To efficiently generate Hf-characteristic L-line fluorescent X-rays and to achieve a sufficiently high X-ray flux within a sufficiently narrow spectral bandwidth to produce X-ray intensity modulation within layered material structures, an X-ray source with a target material including Si, Mo, Ru, Rh, Pd, W, Ir, Pt, Au, Ti and / or Cr and related compounds can be used to generate at least one characteristic X-ray line with an X-ray energy in the range of 1.662 keV to 5.5 keV.

[0098] Figure 10 schematically illustrates a layered material structure 320 irradiated by an incident X-ray beam 332 according to certain embodiments described herein. The incident X-ray beam 332 is incident on a layered material structure 324 on a substantially flat substrate 322 (e.g., a Si wafer) (e.g., in an air / vacuum environment), the layered material structure 324 comprising two Si layers 325 on the substrate 322 and an air / vacuum gap region 326 below them. When the incident angle 334 is greater than the critical angle for total internal reflection, X-ray reflection 336 occurs at the entire interface between the Si layers 325 and the gap region 326 (e.g., between the Si layers 325 and the gap region 326) having a difference in X-ray refractive index. As shown in Figure 10, the reflected X-ray beam 336 includes a first reflected X-ray beam 336a reflected from the top interface of the two Si layers 325 and from the Si substrate 322 (long dashed line), and a second reflected X-ray beam 336b from a portion of the first reflected X-ray beam 336a reflected from various interfaces of the layered material structure 324. Figure 10 only shows some of these second reflected X-ray beams 336b.

[0099] When the incident X-ray beam 332 has sufficient longitudinal (e.g., temporal) coherence, the first reflected X-ray beam 336a and the second reflected X-ray beam 336b interfere with each other and with the incident X-ray beam 332. For example, the temporal coherence length of an X-ray beam is approximately equal to the X-ray wavelength λ multiplied by λ / Δλ, where Δλ is the spectral bandwidth. For a given spectral resolution λ / Δλ, the temporal coherence length is proportional to the X-ray wavelength. The interference results in X-ray intensity modulation within the layered material structure 320. X-ray intensity modulation can be maintained when the incident X-ray beam 332 has sufficient transverse (e.g., spatial) coherence. X-ray intensity modulation can be used to detect spatial information of at least one element of interest in the layered material structure 324. When the incident X-ray beam 332 has sufficient longitudinal (e.g., temporal) coherence and sufficient transverse (e.g., spatial) coherence, the X-ray intensity of the interference from the incident X-ray beam 332 and a reflected X-ray beam 336 can be expressed as: Ii=A12+A22+ 2·A1·A2·cos(φ), where A1 and A2 are the amplitudes of the incident X-ray beam 332 and the reflected X-ray beam 336, respectively, and φ is the relative phase difference between the incident X-ray beam 332 and the reflected X-ray beam 336.

[0100] Regarding the layered material structure 322 shown in Figure 10, the X-ray intensity modulation within the layered material structure 322 originates from the interference between the incident X-ray beam 332 and the first and second reflected X-ray beams 336a and 336b. The first reflected X-ray beam 336a originates from the incident X-ray beam 332 reflected by one of the interfaces of the two regions of the layered material structure 322 (e.g., the Si layer 325 and the gap 326), while the second reflected X-ray beam 336b originates from the first reflected X-ray beam 336a further reflected by one of the interfaces of the two regions of the layered material structure 322. The amplitude of the second reflected X-ray beam 336b is typically weaker than the amplitude of the first reflected X-ray beam 336a. For example, assuming that the attenuation of the incident X-ray beam 332 from the layered material structure 324 and the reduction in amplitude of reflection are negligible, the X-ray intensity I1 at the bottom surface of the bottom Si layer 325 (e.g., the Si layer closest to the substrate 322) can be approximately calculated and expressed as: I1 = (A0 + A1 + A2)·(A0 + A1 + A2)* = A0² + A1² + A2² + 2·A0·A1·cos(φ) + 2·A0·A2 + 2·A1·A2·cos(φ), Wherein A0 is the amplitude of the incident X-ray beam 332, A1 and A2 are the amplitudes of the first reflected X-ray beam 336a reflected from the substrate 322 and the bottom surface of the bottom Si layer 325, respectively, and φ is the relative phase difference between the incident X-ray beam 332 at the bottom surface of the bottom Si layer 325 and the first reflected X-ray beam 336a reflected from the substrate 322, which is approximately equal to the X-ray beam path length of the incident X-ray beam 332 from the bottom surface of the bottom Si layer 325 to the substrate 322 plus the X-ray beam path length of the first reflected X-ray beam 336a reflected from the substrate 322 to the bottom surface of the bottom Si layer 325.

[0101] When A0 is much larger than A1 and A2, the X-ray intensity I1 at the bottom surface of the bottom Si layer 325 can be approximately calculated and expressed as: I1 = A0² + 2·A0·A2 + 2·A0·A1·cos(φ). By varying the incident angle of the incident X-ray beam 332, the X-ray intensity I1 at the bottom surface of the bottom Si layer 325 can vary by 4·A0·A1, thereby providing information about the atomic elemental composition at the bottom surface of the bottom Si layer 325. Similarly, (assuming the distance between the bottom surface of the bottom Si layer 325 and the substrate 322 is the same as the thickness of the bottom Si layer 325), the approximate X-ray intensity at the top surface of the bottom Si layer 325 can be expressed as: I1=A02+ 2·A0·A3+ 2·A0·A1·cos(φ) + 2·A0·A2·cos(φ), where A3 is the amplitude of the first reflected X-ray beam 326a reflected from the top surface of the bottom Si layer 325.

[0102] Therefore, at the same incident angle of 334°, when the X-ray intensity on the top surface of the bottom Si layer 325 is modulated by 2·A0·A1·cos(φ) + 2·A0·A2·cos(φ), the X-ray intensity on the bottom surface of the bottom Si layer 325 is also modulated by 2·A0·A1·cos(φ). Table 3 below shows the values ​​of B = 2·A0·A1·cos(φ) and C = 2·A0·A1·cos(φ) + 2·A0·A2·cos(φ) for several selected values ​​of φ. Table 3: φ B C π / 4 1.4·A0·A1 1.4·A0·A2 π / 2 0 -2·A0·A1 3π / 4 -1.4·A0·A1 -1.4·A0·A2 π -2·A0·A1 2·A0·A1- 2·A0·A2 5π / 4 -1.4·A0·A1 -1.4·A0·A1 3π / 2 0 -2·A0·A1 2π 2·A0·A1 2·A0·A1+ 2·A0·A2 3π -2·A0·A1 2·A0·A1- 2·A0·A2 4π 2·A0·A1 2·A0·A1+ 2·A0·A2

[0103] For A1=A2 (which can be a good approximation when the energy of the incident X-ray beam 332 is greater than 1 keV), Table 2 can be simplified to have values ​​based on the factor A0·A1, as shown in Table 4. Table 4: φ B C π / 4 1.4·A0·A1 1.4·A0·A2 π / 2 0 -2·A0·A1 3π / 4 -1.4·A0·A1 -1.4·A0·A2 π -2·A0·A1 0 5π / 4 -1.4·A0·A1 -1.4·A0·A1 3π / 2 0 -2·A0·A1 2π 2·A0·A1 4·A0·A1 3π -2·A0·A1 0 4π 2·A0·A1 4·A0·A1

[0104] As shown in Tables 2 and 3, in some embodiments, the relative X-ray intensity at the top and bottom surfaces of the bottom Si layer can be changed by altering the relative phase difference, which can be used to obtain relative information about the materials on the two surfaces (e.g., relative Ge residue on the two surfaces after SiGe etching during a nanochip transistor manufacturing process; HfO2 layer thickness on both surfaces). In some embodiments, by selecting an appropriate value, a maximum or minimum X-ray intensity at one of the two surfaces can be obtained, thereby achieving the selection of optimal conditions for process monitoring during semiconductor device manufacturing.

[0105] The above discussion focuses on the calculation of X-ray intensity modulation at the interface of the bottom Si layer 325 and at the top and bottom surfaces of the bottom Si layer 325 in a bilayer material structure 324 consisting only of Si layers / interstitial regions. However, in some embodiments, the method of using X-ray interferometry to generate X-ray intensity modulation using an incident X-ray beam 332 with sufficient coherence conditions can be generalized to any layered material structure 324 having a finite number of layers. Some of these embodiments can be used for metrology and procedural monitoring, wherein reference is made to a small number of measurements optimized for a particular material and / or structural parameters under the same measurement conditions as a reference standard.

[0106] In some embodiments, X-ray intensity modulation within a sample can be revealed by X-ray reflectivity, which is proportional to the sum of all reflected X-rays emitted from the sample's surface and can be expressed as a fraction of the incident X-ray beam. X-ray reflectivity measures only the X-ray intensity of the reflected beam and not the phase of the reflected X-ray beam. Therefore, X-ray reflectivity measurement does not provide information about the X-ray intensity distribution within the sample.

[0107] Figure 11 shows a calculated XRR curve for one of the layered material structures 324, including two pairs of Si / gap regions having 10 nm thick Si layers 325 spaced 10 nm apart (e.g., having a 20 nm period) on a silicon substrate 322 (e.g., see Figure 10). The XRR curve contains the minimum and maximum reflectivity of the interference from the incident X-ray beam 332 and all reflected X-ray beams 336 from the interface of the layered material structure 324. The minimum and maximum reflectivity are directly related to the X-ray intensity modulation within the layered material structure 324.

[0108] Figure 11 also schematically illustrates three relative phase differences at the indicated interfaces: for the top surfaces of the two Si layers 325 and the substrate 322 at four angles of incidence where the XRR curve is at a local minimum or a local maximum. The first minimum is the angle of incidence where the phase difference between the first reflected X-ray beam 336a from the top surface of the top Si layer 325 and the first reflected X-ray beam 336a reflected from the substrate 322 causes destructive interference. The first maximum reflectivity is the angle of incidence where the phase difference between the first reflected X-ray beam 336a from the top surface of the top Si layer 325 and the first reflected X-ray beam 336a reflected from the substrate 322 causes constructive interference.

[0109] Certain embodiments described herein can be used to characterize the depth distribution of one or more atomic elements of interest at various depths in a layered material structure on a flat substrate. For example, the relative amount of an atomic element (e.g., Ge) at or near the top and bottom surfaces of two Si layers 325 can be measured using four values ​​selected to provide a greater difference in incident angle in response to an incident X-ray beam 332 (e.g., detecting Ge characteristic X-rays). Certain embodiments described herein can be used to measure one or more atomic elements of interest at any depth (e.g., not limited to a specific interface) in a layered material structure. Certain embodiments described herein can be used to analyze layered material structures comprising a plurality of layers, with or without periodicity.

[0110] Some of the implementation schemes described herein include the specific selection of a limited number of X-ray measurement instances.

[0111] Some embodiments described herein utilize low-energy X-rays with long coherence lengths. For example, Cu Kα1 and Kα2 are 400X, 1.5 A results in a 600 A (60 nm) multilayer monochromator, requiring a single-crystal monochromator to achieve a resolution of 4000 (Kα1 only) to obtain a coherence length of 600 nm. For Si Kα, 1740 / 0.7 > 2000x x 0.6 nm = 1200 nm coherence length. Furthermore, lower-energy X-rays offer the advantage of using a small X-ray beam area on the sample for metrological and procedural monitoring because the angular collimation of the incident X-ray beam is proportional to the X-ray wavelength relative to the X-ray incident angle and critical angle on the objective surface, and for many low-Z elements of interest in semiconductor devices (such as O in HfO2), the fluorescence cross-section is larger. Assuming the ideal ratio remains the same or is known by other techniques or both, the thickness of HfO2 can be measured using one of the two elements.

[0112] In some embodiments in which the incident X-ray beam is focused in the sagittal direction onto a sample of a size less than 40 micrometers, multiple test pads may be used along the tangential direction, examples of which have one or more of the following: large convergence angle or high incident angle, high angle harmonics (e.g., high angle with shorter standing waves and therefore higher resolution), dual X-ray energies below and above the absorption edge of an atomic element of interest and / or an atomic element in a material of interest, and X-ray wavelengths shorter than half the standing wave spacing.

[0113] In some embodiments, the incident X-ray beam may be guided onto a sample comprising at least one layered material structure. For example, for a sample comprising a flat material structure, the angle of incidence may be less than 20 degrees and greater than the critical angle for total external reflection of a flat substrate or the critical angle for a layered material structure (whichever is greater). The variation in X-ray intensity within the layered material structure can be varied by changing the grazing angle of incidence at a fixed X-ray detection energy or by changing the X-ray energy at a fixed grazing angle of incidence.

[0114] In some embodiments, the X-ray energy of the incident X-ray beam is selected to produce secondary particles with short penetration lengths within the sample to obtain element-specific depth information. Using two or more secondary particles with short and varying penetration lengths allows for high depth measurement sensitivity and reasonably large detection depths. In some embodiments, multiple X-ray energies of the incident X-ray beam can be used and optimized for a range of atomic elements to produce secondary particles with desired penetration lengths. The depth detection capabilities of these techniques can be used individually or in combination.

[0115] Certain embodiments can be used to measure structures in depth and / or 3D at nanometer resolution. For example, an incident X-ray beam with certain properties can be guided at a grazing incidence angle relative to a flat surface of a substrate on one or more layered material structures to produce an X-ray intensity variation along the surface normal of the flat surface of the substrate. The X-ray intensity variation originates from the interference of the incident X-ray beam with X-rays reflected from the interface between the layered material structure and the substrate. By tuning the grazing incidence angle, the X-ray intensity distribution along the surface normal can be varied. Secondary particles (e.g., characteristic fluorescent X-rays, photoelectrons, and Auger electrons) can be generated due to the absorption (e.g., ionization) of X-rays by one or more atomic elements in the layered material structure. Characteristic fluorescent X-rays and Auger electrons are highly element-specific X-ray energies that are independent of the X-ray beam. When the incident X-rays are monochromatic, photoelectrons are also element-specific because their isoenergies are equal to the difference between the X-ray energy of the incident beam and the binding energy of the electrons within the element. For a given structure (e.g., a thin layer), the number of secondary particles generated by an atomic element is proportional to the X-ray intensity at the layer and the atomic number of the element. Therefore, the amount of one or more atomic elements in a layered material structure can be measured by measuring the number of specific secondary particles of an atomic element. Using a calibrated standard reference sample, this technique can be used to measure and monitor the amount of atomic elements in the material of interest during semiconductor manufacturing processes to ensure that the manufacturing process is within a predetermined process window. By tuning the grazing incidence angle, the distribution of one or more atomic elements along the surface normal of a flat surface can be measured, as the X-ray intensity distribution can vary between 1 nm and 20 nm depending on the X-ray energy and grazing incidence angle. Variations in X-ray intensity along the surface normal are particularly well-suited for studying the layered material structure of semiconductor devices and their manufacturing processes.

[0116] In some embodiments, the X-ray energy of the incident X-ray beam is selected to effectively generate a large number of at least two secondary particles having an effective linear decay length between 1 nm and 500 nm (e.g., equivalent to the inelastic mean free path of photoelectrons and Euger electrons) and a ratio greater than 50% of their equivalent effective linear decay lengths. A relatively short effective linear decay length can be useful for obtaining a relatively strong dependence of the secondary particles' transport from their equivalent origin to the surface of the layered material structure. A large difference between their equivalent effective linear decay lengths can be useful for balancing depth measurement sensitivity and sufficient depth measurement. For example, the photoelectron energy can be varied by selecting the X-ray energy of the incident beam. Furthermore, photoelectrons from two different electron shells in an atom have different energies and different corresponding effective linear decay lengths.

[0117] In some embodiments, the incident X-ray beam is monochromatic or quasi-monochromatic, wherein more than 50% of the X-rays are within an energy bandwidth of less than 1%. The incident X-ray energy can be selectively used to generate photoelectrons from an atomic element having an energy difference greater than 300 eV. The incident X-ray energy can be selectively used to generate photoelectrons with an energy difference greater than 300 eV from Ørsted electrons from the same or a different atomic element. The incident X-ray energy can be selectively used to generate X-rays with one or more characteristic X-ray energies from one or more atomic elements such that the linear decay length of the X-rays generated through the layered material structure is less than 200 nm. In some embodiments, two or more incident X-ray energies are used to generate secondary particles with a linear decay length of less than 500 nm and an inelastic mean free path of less than 30 nm for characteristic X-rays. Multiple secondary particles with linear decay lengths (X-rays) or inelastic mean free paths (electrons) can be detected and used to obtain structural information about the layered material structure. The efficiency of generating secondary particles can be achieved by varying one or more atomic elements in a layered material structure by altering the X-ray beam intensity and the grazing incidence angle for a given X-ray beam energy. For example, the grazing incidence angle can be scanned within a grazing incidence angle range while collecting secondary particles. X-ray reflectivity can be measured and used to calibrate or determine the value of the grazing incidence angle. In some embodiments, secondary particles are collected simultaneously with X-ray reflectivity measurements within a grazing incidence angle range. Data from both measurements can be used to obtain structural and material information about the layered material structure.

[0118] Certain embodiments described herein avoid one or more problems or controversies found in other analytical techniques. For example, optical scattering measurements are model-dependent (e.g., typically require imaging to provide a model), which can be complicated by the increasing complexity of layered material structures and the shrinking feature sizes of new semiconductor devices. Electron microscopy (EM) and atomic force microscopy (AFM) typically require destructive sample preparation to obtain depth information of layered material structures, which can be time-consuming and destructive, and therefore undesirable for a procedural monitoring technique. Electron microprobe-based techniques are limited in detection sensitivity due to large continuous bremsstrahlung X-ray backgrounds (e.g., for electron-induced X-ray fluorescence spectroscopy) and / or large electron backgrounds (e.g., in Ogee spectroscopy), and high depth resolution may require destructive sample preparation with thin cross-sections. Furthermore, electron beam-induced carbon deposition on the analytical region can lead to measurement errors associated with the amount of carbon deposited on the analytical region, and charging can be problematic, especially when detecting low-energy X-rays or Ogee electrons. Transmission small-angle X-ray scattering (tSAXS) systems with laboratory X-ray sources may not have the acceptable processing capability for measuring layered material structures with sufficient depth resolution.

[0119] While commonly used terminology is used for ease of understanding in describing systems and methods of certain embodiments, such terminology is used herein to have the broadest possible interpretation. Although various aspects of the invention are described with respect to illustrative examples and embodiments, the disclosed examples and embodiments should not be construed as limiting. Unless otherwise specifically stated or understood within the context of the context in which they are used, conditional language such as “may,” “can,” “may,” or “able” is generally intended to convey that certain embodiments include (while other embodiments do not include) certain features, elements, and / or steps. Therefore, such conditional language is generally not intended to imply that one or more embodiments require features, elements, and / or steps in any way. Specifically, the terms “comprise” and “comprising” should be interpreted as referring to an element, component, or step in a non-exclusive manner, thereby indicating that the referenced element, component, or step may be present or utilized or combined with other elements, components, or steps not expressly referenced.

[0120] Unless otherwise specifically stated, connective language such as the phrase "at least one of X, Y and Z" is understood in the context of ordinary use to convey that an item, term, etc., may be X, Y or Z. Therefore, this connective language is not generally intended to imply that some implementation requires the presence of at least one of X, at least one of Y and at least one of Z.

[0121] As used herein, degree terms (such as the terms "approximately," "about," "generally," and "substantially") refer to a value, quantity, or characteristic that is close to the stated value, quantity, or characteristic while still performing a desired function or achieving a desired result. For example, the terms "approximately," "about," "generally," and "substantially" may refer to a quantity within ±10%, ±5%, ±2%, ±1%, or ±0.1% of the stated quantity. As another example, the terms "generally parallel" and "substantially parallel" refer to a value, quantity, or characteristic that deviates from exact parallelism by ±10 degrees, ±5 degrees, ±2 degrees, ±1 degree, or ±0.1 degrees, and the terms "generally perpendicular" and "substantially perpendicular" refer to a value, quantity, or characteristic that deviates from exact perpendicularity by ±10 degrees, ±5 degrees, ±2 degrees, ±1 degree, or ±0.1 degrees. The scope disclosed herein also encompasses any and all overlaps, subscopes, and combinations thereof. Language such as “at most,” “at least,” “greater than,” “less than,” “between,” and the like includes the number stated. As used herein, “a,” “one,” and “the” have plural meanings unless the context clearly indicates otherwise. Although structure and / or method are discussed herein with respect to elements marked by ordinal adjectives, ordinal adjectives are used only as markers to distinguish one element from another, and are not used to indicate the order of such elements or their use.

[0122] Various configurations have been described above. It should be understood that the embodiments disclosed herein are not mutually exclusive and can be combined with each other in various configurations. Although the invention has been described with reference to such specific configurations, the description is intended to illustrate the invention and is not intended to be restrictive. Various modifications and applications will be conceived by those skilled in the art without departing from the true spirit and scope of the invention. Thus, for example, in any method or procedure disclosed herein, the actions or operations constituting the method / procedure can be performed in any suitable sequence and are not required to be limited to any particular disclosed sequence. Features or elements from the various embodiments and examples discussed above can be combined with each other to produce alternative configurations compatible with the embodiments disclosed herein. Various forms and advantages of the embodiments have been described where appropriate. It should be understood that not all of these forms or advantages need to be achieved according to any particular embodiment. Thus, for example, it should be recognized that various embodiments can be implemented in a way that achieves or optimizes one advantage or group of advantages as taught herein without achieving other forms or advantages as may be taught or suggested herein. [Simplified Explanation of the Diagram]

[0010] Figure 1 schematically illustrates an exemplary system for XRR and XRF and / or XPS from a sample to be analyzed, according to certain embodiments described herein.

[0011] Figure 2 schematically illustrates an exemplary X-ray generator according to one of certain embodiments described herein.

[0012] Figure 3A schematically illustrates an exemplary X-ray optical subsystem for receiving X-rays generated by an exemplary X-ray generator according to certain embodiments described herein.

[0013] FIG3B schematically illustrates an exemplary aperture at the exit end of one of the second X-ray optical elements of FIG3A according to certain embodiments described herein.

[0014] Figure 4A is a flowchart of an exemplary method for analyzing a three-dimensional structure of a sample according to certain embodiments described herein.

[0015] Figure 4B is a flowchart of another exemplary method for analyzing the three-dimensional structure of a sample according to certain embodiments described herein.

[0016] Figure 4C is a flowchart of another exemplary method for analyzing the three-dimensional structure of a sample according to certain embodiments described herein.

[0017] Figure 5A is a flowchart of another exemplary method that includes the exemplary method of Figure 4A according to certain embodiments described herein.

[0018] Figure 5B is a flowchart of another exemplary method that includes the exemplary method of Figure 4B according to certain embodiments described herein.

[0019] Figure 6 is a flowchart of one of the exemplary methods for detection (e.g., process monitoring) according to certain embodiments described herein.

[0020] Figure 7A schematically illustrates three exemplary simulation models of a semiconductor nanosheet stack structure according to some embodiments described herein.

[0021] Figure 7B shows a graph of simulated XRR data (e.g., curves) for three exemplary simulation models corresponding to those in Figure 7A, based on certain embodiments described herein and using three X-ray energy harvesters.

[0022] Figure 7C shows a graph of the simulated difference between the three XRR curves of Figure 7B at three X-ray energies according to certain embodiments described herein.

[0023] Figure 7D shows a graph of an analog signal of a Hf M5N7 characteristic XRF line varying with the incident angle at an excitation X-ray energy of 1.74 keV according to certain embodiments described herein.

[0024] Figure 7E shows a graph of simulated XRR signal differences at three different X-ray energies according to certain embodiments described herein, which plots a sensitivity to the roughness of the interface and surface.

[0025] Figure 8A schematically illustrates two exemplary simulation models of a semiconductor nanosheet stack structure according to one of the embodiments described herein.

[0026] Figure 8B shows a graph of the simulated XRF signals of the two models in Figure 8A under two different excitation X-ray energies according to certain embodiments described herein.

[0027] Figure 8C shows a graph of the simulated difference between two Hf XRF curves of Figure 8B at two excitation X-ray energies according to certain embodiments described herein.

[0028] Figure 8D shows a graph of simulated XRR signals (e.g., curves) collected from the Si nanosheet structure of Figure 8A using three X-ray energies according to certain embodiments described herein, corresponding to two exemplary simulation models of Figure 8A.

[0029] Figure 8E shows a graph of the difference between the simulated XRR signals of Figure 8D according to some embodiments described herein.

[0030] Figure 9 shows a graph illustrating the results of a dual-energy method for collecting XRF signals for two different atomic elements of interest according to certain embodiments described herein.

[0031] Figure 10 schematically illustrates a layered material structure irradiated by an incident X-ray beam according to certain embodiments described herein.

[0032] Figure 11 shows the calculated XRR curve of one of the layered material structures according to certain embodiments described herein, and the relative phase difference at three indicated interfaces of the layered material structure.

Claims

1. A method for analyzing the three-dimensional structure of a sample, the method comprising: A first X-ray beam is generated having a first energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and a first average X-ray energy in the range of 1 eV to 1 keV higher than the first absorption edge energy of a first element of interest. The first X-ray beam is collimated to have a first collimation angle range of less than 7 mrad in at least one direction perpendicular to a first propagation direction of the first X-ray beam. The first X-ray beam is used to irradiate the sample at a plurality of incident angles relative to a substantially flat surface of the sample, the incident angles being in the range of 3 mrad to 400 mrad. Simultaneously, a reflected portion of the first X-ray beam from the sample is detected, and X-ray fluorescence and / or photoelectrons from the sample are detected, wherein the first average X-ray energy is less than the absorption edge energy of at least 20% of the major atomic elements constituting the analyzed portion of the sample.

2. The method of claim 1, wherein the first absorption edge energy of the first element of interest is in the range of 0.1 keV to 5.4 keV.

3. The method of claim 1, wherein the sample comprises a silicon substrate and the first average X-ray energy is less than the 1.84 keV absorption edge energy of silicon.

4. The method of request item 1, wherein the range of the first collimated angle is less than 4 mrad.

5. The method of claim 1, wherein the first average X-ray energy is in the range of 1 eV to 5 eV higher than the first absorption edge energy of the first element of interest.

6. The method of claim 1, wherein generating the first X-ray beam comprises irradiating at least one X-ray generating material with electrons and emitting X-rays from the at least one X-ray generating material having the characteristic of generating X-rays having an energy in the range of 100 eV to 5.5 keV.

7. The method of claim 6, wherein generating the first X-ray beam further includes filtering the X-rays to have the first energy bandwidth.

8. The method of claim 1, wherein the first X-ray beam irradiates the sample in a reflecting plane including the first propagation direction and a direction perpendicular to the surface, the first X-ray beam having a collimation angle in the reflecting plane that is smaller than a convergence angle of the first X-ray beam in a plane perpendicular to the reflecting plane.

9. The method of claim 1, wherein after the sample has undergone at least one processing procedure, the method of irradiating the sample with the first X-ray beam and simultaneously detecting the reflected portion of the first X-ray beam and detecting the X-ray fluorescence and / or the photoelectrons is performed, the method further comprising: A first set of spatial and / or compositional information about one of the samples is obtained by analyzing at least the detected first reflective portion, the detected X-ray fluorescence X-rays and / or the detected photoelectrons; and the obtained first set of spatial and / or compositional information about the sample is compared with a second set of spatial and / or compositional information about one of the samples before the sample undergoes the at least one processing procedure.

10. The method of claim 1, further comprising: A second X-ray beam is generated, the second X-ray beam having a second energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and a second average X-ray energy in the range of 1 eV to 1 keV lower than the first absorption edge energy of the first element of interest. The second X-ray beam is collimated to have a second collimation angle range of less than 7 mrad in at least one direction perpendicular to a second propagation direction of the second X-ray beam. The sample is irradiated with the second X-ray beam. A second reflection portion of the second X-ray beam from the sample is detected.

11. The method of claim 10, further comprising obtaining spatial and compositional information about the sample by analyzing the detected second reflective portion and the detected first reflective portion, the detected X-ray fluorescence X-rays and / or the detected photoelectrons.

12. The method of claim 1, further comprising: A second X-ray beam is generated having a second energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and a second average X-ray energy in a range of 1 eV to 1 keV higher than the second absorption edge energy of one of the first elements of interest. The first absorption edge energy and the second absorption edge energy are separated from each other by at least 1 keV. The second X-ray beam is collimated to have a second collimation angle range of less than 7 mrad in at least one direction perpendicular to one of the second propagation directions of the second X-ray beam. The sample is irradiated using the second X-ray beam, and a second reflection portion of the second X-ray beam from the sample is detected.

13. The method of claim 1, further comprising: A second X-ray beam is generated having a second energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and a second average X-ray energy in a range of 1 eV to 1 keV higher than the second absorption edge energy of a second element of interest that is different from the first element of interest. The second X-ray beam is collimated to have a second collimation angle range of less than 7 mrad in at least one direction perpendicular to the second propagation direction of the second X-ray beam. The sample is irradiated with the second X-ray beam, and a second reflection portion of the second X-ray beam from the sample is detected.

14. The method of claim 1, wherein the plurality of incident angles comprises less than 100 incident angles and at least 20% of such incident angles are separated from each other by at least 3 mrad.

15. The method of claim 14, further comprising selecting at least some of the plurality of incident angles to correspond to the expected extreme value in the detected reflection portion of the first X-ray beam from the sample and / or the expected extreme value in the detected X-ray fluorescence X-rays from the sample.

16. The method of claim 15, further comprising: Analyze the deviations between the expected values ​​and the detected first reflective portions and / or between the expected values ​​and the detected X-ray fluorescence X-rays; And in response to such deviations falling outside a predetermined range, an alarm is triggered.

17. A method for analyzing a layered structure comprising substantially parallel interfaces, the method comprising: The layered structure is irradiated with an incident X-ray beam at one or more incident angles in the range of 3 mrad to 400 mrad relative to the substantially parallel interfaces. The incident X-ray beam has an energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and an average X-ray energy in the range of 1 eV to 1 keV higher than the absorption edge energy of one of the atomic elements of interest. The incident X-ray beam is sufficiently coherent to produce X-ray intensity modulation within the layered structure through constructive and destructive interference between the incident X-ray beam and the X-rays of the incident X-ray beam reflected by the substantially parallel interfaces of the layered structure. Simultaneously, at least some of the X-rays reflected by the substantially parallel interfaces are detected, as well as X-ray fluorescence and / or photoelectrons from the layered structure are detected, wherein the average X-ray energy is less than the absorption edge energy of one of the major atomic elements constituting at least 20% of the atoms in the analyzed portion of the layered structure.

18. The method of claim 17, wherein the average X-ray energy is in the range of 1 eV to 5 eV higher than the absorption edge energy of the atomic element of interest.

19. A system for analyzing the three-dimensional structure of a sample, the system comprising: At least one X-ray source configured to generate at least one X-ray beam having an energy bandwidth of less than 20 eV at full width at half maximum (FWHM) and an average X-ray energy in the range of 1 eV to 1 keV higher than the absorption edge energy of one of the atomic elements of interest; the at least one X-ray beam being collimated to have a collimation angle range of less than 7 mrad in at least one direction perpendicular to one of the propagation directions of the at least one X-ray beam; the at least one X-ray source being further configured to guide the at least one X-ray beam to irradiate the sample at a plurality of incident angles relative to one of substantially flat surfaces of the sample, the incident angles being in the range of 3 mrad to 400 mrad; at least one first detector configured to detect a reflected portion of one of the at least one X-ray beams from the sample; and at least one second detector configured to simultaneously detect X-ray fluorescence and / or photoelectrons from the sample, in conjunction with the detection of the reflected portion of the at least one X-ray beam by the at least one first detector. The average X-ray energy is less than the absorption edge energy of at least 20% of the major atomic elements that constitute one of the analyzed portions of the sample.

20. The system of claim 19, wherein the average X-ray energy is in the range of 1 eV to 5 eV higher than the absorption edge energy of the element of interest.

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