Transmission X-ray Critical Dimension Characterization of High Aspect Ratio Structure Stacking Shift and Tilt

Abstract

This application relates to the characterization of critical dimensions of high aspect ratio structures in stacked layer shift and tilt by transmission X-rays. A method for X-ray measurement includes generating an X-ray beam and directing the X-ray beam to a sample that includes at least a first and a second layer stacked on top of each other, the X-ray beam being incident on a sample location where the first and second layers include respective first and second high aspect ratio (HAR) structures. Measuring an X-ray scattering profile emitted from the sample location in response to the X-ray beam according to an angle of tilt between the sample and the X-ray beam. Estimating a shift between the first and second layers and a characteristic tilt of the first and second layers based on the X-ray scattering profile measured according to the angle of tilt.

Description

Field of the Invention

[0001] The present invention generally relates to materials and process analysis, and more particularly to systems and methods for using X-rays for surface analysis of samples. Background of the Invention

[0002] A variety of techniques are known in the field of analyzing samples. Some techniques irradiate a sample with X-rays and measure the resulting scattered signal. For example, PCT International Publication WO 2020 / 008420 (the disclosure of which is incorporated herein by reference) describes a system capable of determining the orientation of an array of high aspect ratio (HAR) structures of a sample by: (i) obtaining different small angle X-ray scattering (SAXS) patterns for at least one of different angular relationships or planar spatial relationships between the sample and the X-ray beam irradiating the sample; where each SAXS pattern represents the angular intensity distribution of scattered X-rays detected by a position sensitive sensor; (ii) for at least some of the different SAXS patterns, calculating at least one sum of intensities within at least one angular range of the angular intensity distribution to provide a first plurality of sums; and (iii) determining the orientation of the array of HAR holes based at least on the first plurality of sums.

[0003] As another example, U.S. Patent 10,352,695 describes methods and systems for using transmission small angle X-ray scattering (T-SAXS) techniques to characterize the dimensions and material properties of vertically fabricated high aspect ratio devices. Exemplary structures include spin transfer torque random access memory (STT-RAM), vertical NAND memory (V-NAND), dynamic random access memory (DRAM), three-dimensional flash memory (3D-FLASH), resistive random access memory (Re-RAM), and PC-RAM. In one aspect, T-SAXS measurements are performed at a plurality of different orientations that are more densely concentrated near the normal incidence angle and less densely concentrated at orientations further from the normal incidence angle. In another aspect, T-SAXS measurement data is used to generate an image of the measured structure based on the measured intensity of the detected diffraction orders.

[0004] U.S. Patent 9,606,073 describes an apparatus including a sample holder that holds a sample in a plane having an axis, the plane defining first and second regions separated by the plane. A source base in the first region rotates about the axis, and an X-ray source on the source base directs first and second incident beams of X-rays to impinge on the sample at first and second angles along a beam axis orthogonal to the axis. A detector base in the second region moves within a plane orthogonal to the axis, and an X-ray detector on the detector base receives first and second diffracted beams of X-rays transmitted through the sample in response to the first and second incident beams, and outputs first and second signals respectively in response to the received first and second diffracted beams. A processor analyzes the first and second signals to determine a profile of the surface of the sample. SUMMARY OF THE INVENTION

[0005] Embodiments of the invention described hereinafter provide a method for X-ray measurement that includes generating an X-ray beam and directing the X-ray beam to a sample including at least first and second layers stacked on one another, the X-ray beam impinging on a sample location where the first and second layers include respective first and second high aspect ratio (HAR) structures. Measuring an X-ray scattering profile emitted from the sample location in response to the X-ray beam according to an angle of tilt between the sample and the X-ray beam. Estimating a shift between the first and second layers and a characteristic tilt of the first and second layers based on the X-ray scattering profile measured according to the angle of tilt.

[0006] In some embodiments, estimating the characteristic tilt of the first and second layers includes estimating one or more of the following: an average tilt of the first and second layers, an extreme tilt of the first and second layers, and a relative tilt between the first and second layers.

[0007] In some embodiments, estimating the shift and the characteristic tilt includes: defining a model of the X-ray scattering profile according to a relative shift and a characteristic tilt, calculating a fit between the measured X-ray scattering profile and the model, and extracting the estimated shift and characteristic tilt from the fit.

[0008] In one embodiment, calculating the fit includes applying a regression model to the measured X-ray scattering profile. In another embodiment, calculating the fit includes: fitting a function including a plurality of peaks to the X-ray scattering profile and solving a regression model to obtain (i) relative intensities of the peaks and (ii) angular positions of center peaks that best match the measured X-ray scattering profile.

[0009] In some embodiments, estimating the shift and the characteristic tilt includes deriving the shift and the characteristic tilt from relative intensities and angular positions that best match the measured X-ray scattering profile.

[0010] In other embodiments, calculating the fit includes applying a non-linear regression model to the measured X-ray scattering profile.

[0011] In some embodiments, estimating the shift and feature tilt includes applying a machine learning model to the measured X-ray scattering profile.

[0012] In one embodiment, measuring the X-ray scattering profile includes combining a plurality of X-ray scattering measurements from a plurality of different angular ranges into a combined measured X-ray scattering profile.

[0013] In some embodiments, the HAR structure is a hole.

[0014] Furthermore, according to another embodiment of the present invention, there is provided a system for X-ray measurement, the system including an X-ray source, an optical device, and a processor. The X-ray source is configured to generate an X-ray beam. The optical device is configured to direct the X-ray beam to a sample including at least a first layer and a second layer stacked on top of each other, the X-ray beam being incident on a sample position where the first and second layers include respective first and second high aspect ratio (HAR) structures. The processor is configured to (a) measure, using a detector, an X-ray scattering profile emitted from the sample position in response to the X-ray beam according to an angle of inclination between the sample and the X-ray beam, and (b) estimate a shift between the first and second layers and a feature tilt of the first and second layers based on the X-ray scattering profile measured according to the angle of inclination.

[0015] The present invention will be more fully understood from the following detailed description of embodiments of the present invention in conjunction with the accompanying drawings, in which: Brief Description of the Drawings

[0016] Figure 1 is a schematic isometric view of a transmission X-ray critical dimension (T-XCD) metrology system according to an embodiment of the present invention;

[0017] Figures 2A - 2D are schematic isometric views of a stack of two-tier high aspect ratio (HAR) structures and views of the shift and tilt of the two tiers according to an embodiment of the present invention;

[0018] Figures 3A - 3C is a simulated intensity distribution from two-tier HAR holes representative of advanced 3D and non-type memories for ω, χ = 0° in (a) the case of showing high and low intensity diffraction orders at a long acquisition time, (b) the case of a shorter acquisition showing only the higher intensity diffraction orders, and (c) the case of high intensity diffraction orders from an array and "parasitic" scattering from an underlying structure (e.g., CMOS logic) according to an embodiment of the present invention;

[0019] Figure 4Simulation 1D intensity profiles for a two - level HAR shifted hole with JSX = - 20 nm, JSY = 20 nm and tilts of TiltX1 = - 0.4°, TiltX2 = 0.4°, and the best fit with 7 peaks; and

[0020] Figure 5 is a flow chart schematically showing a method of X - ray T - XCD metrology for shift and average tilt of a HAR structure according to an embodiment of the present invention. Detailed description of embodiments

[0021] Overview

[0022] Embodiments of the present invention described herein provide systems and methods for using transmission small - angle X - ray scattering (T - SAXS) to measure an array of scattering objects (structures). This technique, also known as transmission critical dimension SAXS (CD - SAXS), refers to a geometry where an incident X - ray beam irradiates a first side of a sample, such as a semiconductor wafer, and then the beam transmits through the sample, after which the scattered intensity is measured by a detector on a second side of the sample. Thus, this technique can measure structures buried beneath the surface or optically opaque. Aspects of SAXS measurements are published, for example, in the above - cited PCT International Publication WO2020 / 008420.

[0023] In some embodiments, X - ray scattering from an array of structures is observed as a series of peaks in the intensity distribution on a position - sensitive X - ray detector. The spacing between adjacent peaks is inversely proportional to the period P, defined as the spacing between adjacent objects, in the case of a periodic array, and inversely proportional to the average spacing in an aperiodic array. The relative intensities of these peaks depend on the shape and size of the scattering structures and thus provide a means for determining their critical dimensions.

[0024] Embodiments of the present invention are applicable to various applications, such as but not limited to analyzing semiconductor wafers, and thus the terms "wafer" and "sample" may be used interchangeably in this patent application.

[0025] The above - mentioned CD - SAXS technique is also referred to as transmission X - ray critical dimension (T - XCD) metrology in this patent application. (XCD is a registered trademark of Bruker Corporation.) This technique is based on small - angle X - ray scattering of X - rays with a wavelength of ∼0.1 nm from an array of structures with a pitch of less than 1 micron. This technique can measure many parameters, including but not limited to average shape parameters of the scattering structures, such as the height, width, angle, thickness, and density of a film. T - XCD is sensitive to disorder parameters such as roughness and pitch variations.

[0026] The T-XCD technique can measure a range of materials and dimensions, such as from relatively thin ~1μm carbon hard masks used in patterning processes to very deep >10μm memory holes in complex multi-layers. The technique can be used on microstructures composed of amorphous, polycrystalline, and single-crystalline materials, and the intensity of X-ray scattering is proportional to the difference in electron density of the scattering structures relative to their surroundings.

[0027] Most commonly with the T-XCD technique, a physical model is constructed that mimics the sample structure and materials as well as the significant features of the instrument and measurement. The expected intensity distribution in the model is generally calculated on a general-purpose high-performance computer.

[0028] Measuring the shift and tilt of high aspect ratio (HAR) structures is very challenging. HAR arrays are encountered in the semiconductor and related industries. Stacked HAR structures will be used in the latest generation of 3D NAND flash memory and other advanced memory technologies (such as phase change (PC) devices). In this document, the aspect ratio is defined as the ratio of the transverse (out-of-plane of the wafer) dimension to the lateral dimension. In this context, structures with an aspect ratio greater than 10:1 are considered HAR structures.

[0029] Embodiments of the present invention relate to X-ray scattering measurements (such as T-XCD) using the aforementioned transmission geometry and methods for simultaneously determining the shift between at least two HAR structures and the characteristic tilt of at least two HAR structures. These methods provide improvements in terms of the accuracy, precision, and throughput of the analysis. The results of the analysis can be used directly for process control or can be used to provide meaningful starting values and constraints for data fitting using more detailed physical models.

[0030] The disclosed embodiments show that T-XCD is particularly suitable for measuring the structural parameters of single-layer and stacked HAR structures. In particular, embodiments of the present invention relate to methods for SAXS characterization and metrology of the shift between at least two arrays of HAR structures stacked on top of each other and the tilt of the two arrays. The characterized tilt can be the average tilt and, in some cases, the relative tilt between the two arrays. In this context, the term "shift between arrays of structures" (also referred to as overlay) refers to the lateral translation in the plane of the wafer between arrays of structures. The term "tilt of an array of structures" refers to the characteristic angle of the plane of the array of structures, such as the average angle at which the structures are oriented relative to the normal of the sample plane.

[0031] In some embodiments of the present invention, a numerical goodness-of-fit (GOF) parameter is used to compare the calculated and measured intensities, and the model parameters are adjusted to minimize the difference between the calculated and measured data. The fitting data set may include one or more 1D data sets, such as the intensity distributions of diffraction peaks in different orientations of a sample or a series of 2D images of a scattering intensity pattern.

[0032] Optionally, the raw data from the measurement (which may include 1D intensity profiles and / or 2D images for one or more rotation angles) can be fed directly or after some preprocessing into a model-free regression engine, such as traditional multiple linear regression or machine learning algorithms, such as those provided in packages such as Scikit-Learn or TensorFlow. Then, the regression model can be used to make useful predictions of the structural parameters using the measured data. Generally, such methods require high sampling of the measured reference data in order to develop a reliable regression-based model, but optionally, forward simulations using approximate physical models can be used. In another embodiment, a non-linear regression model is used.

[0033] The disclosed techniques allow the parameters of the relative shift and tilt of the stacked HAR structures, as well as other parameters, to be measured both on two test structures in the scribe line and on the device itself within the body of the die. The ability to make measurements on the device rather than on a simplified test structure is advantageous because some parameters may be affected by other features that are not present in the test structure, such as tilt being affected by structures that introduce local stress.

[0034] In some embodiments, a method is provided that includes generating and directing an X-ray beam incident at a given angle at a sample location that at least includes a stack of a first and a second layer of a HAR structure having a respective shift and an average tilt between two or more layers with a structure, one on top of the other. During the measurement, the sample is variably rotated, and the X-ray scattering signal emitted from the sample location is measured as a function of the sample tilt angle. The shift between the first and second layers and the average tilt of the first and second layers are estimated based on the X-ray scattering signal measured as a function of the rotation angle of the sample.

[0035] In one embodiment, the estimation is accomplished by (i) defining a model of the X-ray scattering profile based on the relative shift and tilt between the first and second layers and (ii) fitting the measured X-ray scattering profile to the model and extracting the estimated shift and tilt from the fit.

[0036] In another embodiment, to reduce the measurement time, the method utilizes the symmetric nature of the diffraction signal from the location to combine X-ray scattering measurements from multiple regions of interest (ROIs) on a position-sensitive X-ray detector. Different ROIs on the detector correspond to different angular ranges of scattering from the sample; thus, the terms "ROI" and "angular range" may be used interchangeably.

[0037] System description

[0038] Figure 1 is a schematic isometric view of a transmission X-ray critical dimension (T-XCD) metrology system 100 according to an embodiment of the present invention. The system 100 is used to analyze the physical properties of a macroscopic planar sample 102 (e.g., a silicon wafer with lithographically patterned features). Assuming that the sample 102 defines a three-dimensional set of axes, the sample is located in the xy plane of the axes, and the z-axis is defined as perpendicular to the sample. Without loss of generality, the xy plane is considered to be horizontal, and so is the sample.

[0039] A system similar to system 100 is described in the previously mentioned international patent application publication WO 2020 / 008420, the disclosure of which is incorporated herein by reference.

[0040] The sample 102 is mounted on a sample holder 103, also referred to as a "chuck", which allows X-rays to be transmitted through the sample. Generally, the chuck 103 includes an annular sample holder, but other designs are possible, such as a three-point kinematic mount for the sample. The chuck 103 is mounted on a workbench 105 (also referred to as a "motion stage" or "processor-controlled workbench"). The workbench 105 is controlled by a control unit (not shown) as indicated by a processor 108 to perform accurate adjustment of the positioning of the sample 102 along three directions (X, Y, and Z) and adjustment of the orientation of the sample 102 in two angles (the angle of incidence ω with respect to the Y-axis and the azimuth angle χ with respect to the X-axis). The stage is also configured to set the rotation of the sample 102 about the z-axis perpendicular to the surface of the sample

[0041] System 100 also includes an excitation source driven by a high-voltage power supply unit (PSU), such as a high-brightness X-ray source 107. In some embodiments, source 107 emits an X-ray beam 104 having suitable energy to penetrate sample 102, such as characteristic Kα radiation, flux, and angular divergence from molybdenum (17 keV), silver, or indium. The X-ray beam passes through X-ray optics 109, which may include apertures (e.g., slits), diffractive elements (e.g., crystals or multilayer mirrors), to adapt the properties of the beam in terms of intensity, spatial (spot size), angular (collimation) range, and energy (monochromaticity) range. The properties of the beam are adjusted based on the structure of the sample being measured. The adjusted X-ray beam is incident on a small area (area 110) of sample 102 (generally a spot with a diameter of approximately <100 μm), and is collimated in at least one direction (generally to an angular resolution of <1 milliradian (mrad)).

[0042] In some embodiments, detector assembly 106 (e.g., a pixelated detector) is configured to detect X-ray photons of beam 114 incident on detector assembly 106 at one or more regions 116 (hereinafter also referred to as, e.g., region of interest (ROI) 116). Each ROI 116 corresponds to a respective angular range of scattering from sample 102. In one embodiment, a beam blocker (not shown) made of an X-ray opaque or partially opaque material is located between sample 102 and detector 106, and is configured to block at least part of beam 116 from irradiating detector 106. In other embodiments, the beam blocker may be omitted.

[0043] The beam path may be in ambient air or in partial vacuum to reduce air-induced scattering, although this partial vacuum is generally not required for X-ray beam energies >10 keV.

[0044] A portion of the incident X-rays is scattered from the structures on the sample into multiple beams, and the intensity distribution (counts relative to pixels) is measured by 2D pixelated X-ray detector 106. Several X-ray detector technologies are suitable for making such measurements, including but not limited to CMOS detectors and hybrid photon counting (HPC) detectors with Si, CdTe, or other sensing materials.

[0045] In the illustrated embodiment, pixelated detector 106 measures the diffraction orders 114 in the direction normal to and around the surface of the sample (i.e., of the X-ray photons diffracted by region 110 of sample 102). The diffracted X-rays 114 indicate the geometric properties of the patterned structures within region 110. In the context of this description, X-ray diffraction is a specific form of X-ray scattering that preserves the aforementioned information about the macroscopic (e.g., rather than atomic) geometric properties of the target.

[0046] The intensity of peaks corresponding to characteristic X-ray scattering from structures in the sample is identified by software, after which the net intensity (intensity above the background) is determined. The difference between the measured and calculated angular spectra is minimized by a linear regression algorithm that automatically adjusts the fitting parameters, as described below in Figure 4 .

[0047] Generally, most measurement information (such as the angular resolution and size of the incident X-ray beam, the sample scan range and step size, and the counting time at each step) is specified by the engineer or operator before the measurement, but some parameters can be determined dynamically during the measurement based on calibration gauges and the X-ray intensity recorded on the pixelated detector 106. The typical range of angles scanned in the measurement of HAR structures is a few degrees.

[0048] Several gauges and their combinations can be used to determine the surface orientation of the sample 102 relative to a reference point (such as the direction of the incident X-ray beam 104), including but not limited to optical autocollimators and triangulation gauges, mechanical inclinometers, or X-ray diffraction when sample misalignment is properly interpreted.

[0049] Rotating the sample 102 about the y-axis (ω) allows features in the xz plane to be probed, and rotating the sample 102 about the x-axis (χ) allows features in the yz plane to be probed. The sample can be translated independently or together at a certain ratio along the x-axis or y-axis. The range of angles scanned, the type of motion (stepped or continuous), the step size, and the acquisition time per step, as well as other measurement information, are included in a "recipe" automatically run by the processor 108 of the system 100.

[0050] For example, the in-die structures with dimensions of a few millimeters can be measured with a larger spot size in the range of hundreds of micrometers, while the small test pads in the narrow scribe regions between the dies will require a beam FWHM of <50μm in diameter. Additionally, the collimation will be specified by the pitch of the array to be measured, where a higher degree of collimation is required for larger pitch structures, while a lower degree of collimation and thus higher intensity is more optimized for the measurement of smaller pitch structures. Representative values for the pitch and divergence for the measurement of stacked HAR structures are 150nm and 0.5mrad, respectively.

[0051] As can be seen, the beam 104 is collimated or focused onto the region 110. The X-ray beam 104 is capable of penetrating the full thickness of the sample, which is generally a 300mm silicon wafer or a coupon with a thickness of approximately 750μm. Several source technologies can generate X-rays of such energy, including but not limited to sealed and rotating anode sources, liquid metal jet sources, and also compact accelerator-based sources.

[0052] As mentioned above, beam 102 is diffracted by features of surface 112 of sample 102 to form diffracted beam 114. For clarity, it is assumed that surface 112 includes the top surface of sample 102, but it will be understood that surface 112 can be the top or bottom surface of the sample. Another surface of sample 112 is generally planar. Diffraction from surface 112 in the HAR structure is explained by the shift and tilt model of the diffracted beams described below.

[0053] System 100 is operated by processor 108, which uses software stored in the processor's memory to operate system 100. The software can be downloaded to processor 108 electronically, for example, via a network, or it can alternatively or additionally be provided and / or stored on a non-transitory tangible medium (such as magnetic, optical, or electronic memory). Processor 108 generally uses a graphical user interface (GUI) and input devices (both not shown), such as a keyboard or pointing device or a touchscreen of the processor. A user of system 100 can provide inputs (such as values of operating parameters of the system) to the system and receive results from the system via the GUI and input devices.

[0054] In various embodiments, suitable hardware (such as using one or more discrete components, one or more application specific integrated circuits (ASICs), and / or one or more field programmable gate arrays (FPGAs)) can be used to implement Figure 1 the different electronic components of the system shown. For example, some of the readout circuitry of detector assembly 106 can be implemented in this manner.

[0055] As Figure 1 The configuration of system 100 shown is an example configuration chosen purely for conceptual clarity. In alternative embodiments, any other suitable configuration can be used. For example, a configuration where the source and detector rotate coaxially and the chuck translates as needed but does not rotate.

[0056] Shift and tilt between stacks of high aspect ratio structures

[0057] Figures 2A - 2D are schematic isometric views of a stack of two layers of a HAR structure and views of the shift and tilt of the two layers according to an embodiment of the present invention. In this description, the terms "layer" and "tier" can be used interchangeably. Figure 2A shows the bottom tier 202 and top tier 204 of the HAR structure, which is a patterned hole in Figure 2A.

[0058] Figures 2B and 2C are top-down views of the lithography shift 214 (top of level 2 to top of level 1) and the combined shift 212 (bottom of level 2 to top of level 1) in the xy plane, respectively. Figure 2D is a side view showing the xz plane and different tilts 222 and 224 about the y axis for the two levels.

[0059] As seen in Figures 2B and 2C, both the shift and the average tilt parameters are vectors (respectively and ), which have components in the x and y directions: (JSX, JSY, TiltX1, TiltY1, TiltX2, and TiltY2).

[0060] Two common definitions of shift used in describing stacked structures: the shift due to lithography (LS or overlay), which is defined as the vector offset between the tops of two levels of a hole; and the combined shift (JS), which refers to the vector offset at the interface between the top of the lower level and the bottom of the upper level of a hole. The average tilt and the relative tilt are determined from the tilts of the individual levels. The shift and the average tilt are thus given by:

[0061]

[0062]

[0063] In some embodiments of the disclosed invention, the aim of the disclosed technique is to determine four parameters JSX, JSY, TiltX, TiltY.

[0064] The diagrams shown in Figures 2A - 2D were chosen for clarity of a purely future concept. Figures 2A - 2D show only one embodiment of the present invention. For example, as would be appreciated by those skilled in the art, other patterns, such as bars, can be analyzed. Other definitions of shift and tilt can be used. Additionally, while Figures 2A - 2D show a two-layer HAR structure, generally the disclosed technique can describe and analyze HAR structures where more than two HAR structures are stacked on top of one another and there is more than one corresponding shift between two or more layers. In such a structure, the average tilt is of two or more layers.

[0065] Diffraction data acquisition

[0066] In some embodiments, during a metrology period, 2D diffraction intensity distributions are measured for various sample tilt angles ω and χ, respectively, and then these data are simultaneously fit to simulated intensity distributions based on a specific physical model of the structure in order to determine their shape in addition to the relative shift and tilt of the holes. However, this can be a relatively long process both in terms of measurement and analysis because the intensity distributions are measured over a wide range of intensities. To overcome this limitation, in some embodiments, the method can utilize the spatial symmetry properties of the scattering signal to combine X-ray scattering measurements from multiple ROIs (e.g., ROIs on the detection assembly 106) for any measured location on the sample. However, if sufficient signal can be acquired, the method can be readily used at a single location (i.e., at a single ROI).

[0067] Figures 3A - 3C are simulated intensity distributions from a two-level HAR hole representative of an advanced 3D AND-type memory for ω, χ = 0° in (a) the case of long acquisition times showing high and low intensity diffraction orders 302, (b) the case of shorter acquisitions showing only the higher intensity diffraction orders 304, and (c) the case of high intensity diffraction orders 306 from the array and "parasitic" scattering 338 from the underlying structure (e.g., CMOS logic).

[0068] Figure 3A Shows a simulated diffraction pattern 302 from a hexagonal arrangement of holes with a two-level HAR structure, each level having a nearest neighbor distance of 150 nm, a diameter of 100 nm, and a height of 4 μm. As can be seen, the scattering pattern has radial symmetry, along the angle There is 60° angular symmetry. During measurement, the detection assembly 106 acquires the intensity variation at each given scattering angle in the diffraction order 114.

[0069] In an embodiment of the method, as Figure 3B and Figure 3C shown, the detection assembly 106 simultaneously measures the intensity within one or more ROIs 334 and 336, respectively. Generally, the intensities within the various ROIs (after applying appropriate symmetry inversions or rotations) are combined by addition (e.g., by the multiplexing (mux) function of the processor 108 or the detector 106), but other operations (e.g., subtraction) can be used if they provide increased sensitivity to the parameter of interest of the structure.

[0070] The number, shape, size, and positioning of the ROIs (e.g., ROIs 334 and 336) can be optimized in software for the structure and generally include high intensity low order diffraction peaks and exclude the direct beam or any part thereof.

[0071] In some embodiments, different ROI measurements are combined to obtain a 1D intensity profile as a function of the rotation angle. This process can be repeated more than once using a stage 105 that performs sample rotation with scans about different rotation axes (e.g., the ω-axis (3B) with the χ-axis fixed, the χ-axis (3C) with the ω-axis fixed, or the ω-axis and χ-axis scanned together at some rate). Different scans are selected to allow the tilt and tilt components in the x and y directions to be determined.

[0072] If possible, the ROI is selected to minimize the effect of the shifted and tilted x-component on the y-component and vice versa. Additionally, the ROI can be established to avoid parasitic scattering from the instrument or from structures above or below the HAR structure of interest.

[0073] Figure 3B and Figure 3C illustrates exemplary ROIs of simulated intensity distributions from a 3D vs. non-type channel hole two-layer stack with reduced acquisition time compared to Figure 3A . ROI 334 is typical of an ω-scan of a sample without parasitic scattering. A possible ROI 336 is used for a χ-scan of a sample with a parasitic scattering pattern 338 (cross-shaped scattering 338) from an underlying metal structure in the CMOS circuitry below the HAR structure of interest. The intensities in the ROI are combined to produce a plot of 1D diffraction intensity vs. given tilt angle data.

[0074] Figure 4 is a simulated 1D diffraction intensity profile and best fit with 7 peaks for a two-layer HAR shifted hole with JSX = -20 nm, JSY = 20 nm and with tilts TiltX1 = -0.4°, TiltX2 = 0.4° according to an embodiment of the present invention. The particular shown intensity profile 402 is a 1D diffraction intensity profile given as a function of the sample tilt angle ω between -2.5° and +2.5° sample tilt. As mentioned above, profile 402 is obtained by combining measurements taken from several ROIs of detector 106.

[0075] In one embodiment, the 1D diffraction intensity profiles (e.g., profile 402) are each fit with a set of functions having one or more local maxima, e.g., a set of Gaussian functions of angle u including multiple peaks (i.e., having two or more local maxima), such as the function A,B,C,D,E,F>0, where the angle α j , the area, height, and / or width of the peaks are optimized using linear regression. For example, constraints on the equality of (some) peak widths and relative positioning can be used to make the peak fitting more stable and prevent the peak order from changing.

[0076] A representative example of such a model consisting of 7 Gaussian peaks (labeled 2 - 8) on top of a constant background is shown in Figure 4 and the highest peak is labeled "5". As can be seen, the triplets of peaks 2, 3, and 6 and the triplets of peaks 4, 7, and 8 are local maxima of three maximum Gaussian functions 404 and 406 (e.g., function f(u)).

[0077] Some embodiments of the disclosed technology use a regression model (e.g., multiple linear regression (described below)) to provide peak fitting to data in, for example, Figure 4 to extract the HAR shift and tilt. The best parameters from the peak fitting are selected based on their correlation with the input parameters for the simulation using, for example, R 2 and mean square error statistics (MSE) (i.e., the parameters with the highest R 2 (generally > 0.9) and the smallest MSE).

[0078] The parameters in the intensity profile and thus the peak fitting parameters are interdependent, and thus, for example, the positioning of peak 5 in Figure 4 depends on the combined shift component and the average shift, while the ratio of the intensities of the smaller (tail) peaks on the left (3, 4) and (6, 7) is mainly related to the combined shift. Therefore, to determine the shift and the average tilt, the positioning and intensity of the empirical peaks are combined and used together.

[0079] In this example, JS and tilt are the predictor variables for the positioning of the main peak (5), and the ratio of the intensities of the satellite peaks is

[0080] R37 = (Height 3 - Height 7) / (Height 3 + Height 7)

[0081] R46 = (Height 4 - Height 6) / (Height 4 + Height 6)

[0082] Therefore, as an example, an analysis Figure 4 of the multiple linear regression model can be applied to obtain the R 2 value and the regression equation. In this example, for the main peak positioning and the tail peak ratio of the ω scan and the χ scan are included as explanatory variables to determine the following four parameters: JSX, JSY, AverageTiltX, AverageTiltY.

[0083] Representative examples of the expressions for determining these parameters from the above - mentioned peak height ratios and the positioning of the main peak 5 (Pos5) are as follows:

[0084] Equation 1

[0085] JSX = 0.0934 - 106.527 * R37 - 13.228 * Pos5

[0086] JSY = 4.190 + 15.404 * R37 + 112.537 * Pos5

[0087] TiltX = -0.00376 + 1.125 * R37 - 0.866 * Pos5

[0088] TiltY = -0.0373 + 0.832 * R37 - 1.193 * Pos5

[0089] Given the ability to determine RelativeTiltX and RelativeTiltY, an additional set of regression equations can be constructed from the widths of the main peaks in the ω scan and the χ scan.

[0090] Note that other combinations of peak fitting parameters may be found to be optimal for other structures.

[0091] After obtaining the regression equation (e.g., Equation 1) based on simulation, the peak fitting model used above is applied to the measured data in order to determine the HAR shift and tilt components with high throughput.

[0092] Although simulation is used to construct the regression equations in the above scheme, measured data with external reference information can also be used in this method. In addition, the use of advanced machine learning and AI techniques can completely avoid the need for empirical peak fitting steps.

[0093] Figure 5 is a flowchart schematically showing a method of X-ray T-XCD metrology for shift and average tilt of a HAR structure according to an embodiment of the present invention. At the data acquisition step 502, a process is executed according to the algorithm of the proposed embodiment, which starts with the system 100 acquiring T-XCD signals from the region of the sample 102 including the HAR structure according to the tilt angles around the X-axis and the Y-axis.

[0094] Next, at the diffraction intensity profile extraction step 504, the processor 108 extracts a 1D diffraction intensity profile according to the tilt angles around the X-axis and the Y-axis, e.g., Figure 4 the profile 402 shown.

[0095] Next, at the best fit step 506, the processor 108 fits a set of functions (each function having one or more local maxima) to the 1D diffraction intensity profile to extract the intensity of the fitted peaks and the angular localization of the central highest intensity peak (e.g., Figure 4 the peak 5 in

[0096] Next, at the HAR shift and tilt estimation step 508, the processor 108 runs a linear regression model on the relative peak intensity and the angular localization of the central peak to estimate the shift and the average tilt of the HAR structure.

[0097] Finally, at the HAR shift and tilt output step 510, the processor 108 outputs the HAR relative shift and tilt to the high throughput process control system.

[0098] By way of example Figure 5 the process flow shown. Alternative steps may be performed, such as applying a machine learning model in place of the linear regression model.

[0099] It will be appreciated that the embodiments described above are cited by way of example, and the invention is not limited to what has been particularly shown and described above. Rather, the scope of the invention includes combinations and sub - combinations of the various features described above and variations and modifications thereof that will occur to those skilled in the art upon reading the foregoing description and that are not disclosed in the prior art. Documents incorporated by reference in this patent application shall be considered an integral part of this application, except to the extent that any term is defined in these incorporated documents in a manner that conflicts with the definitions expressly or implicitly made in this specification, in which case only the definitions in this specification shall be considered.

Claims

1. A method for X-ray measurement, the method comprising: generating an X-ray beam and directing the X-ray beam to a sample comprising at least a first layer and a second layer stacked on top of each other, the X-ray beam being incident at a sample location, the first layer and the second layer comprising respective first high aspect ratio (HAR) structures and second high aspect ratio (HAR) structures at the sample location; measuring an X-ray scattering profile emitted from the sample location in response to the X-ray beam according to an angle of inclination between the sample and the X-ray beam; and estimating a shift between the first layer and the second layer and a characteristic inclination of the first layer and the second layer based on the X-ray scattering profile measured according to the angle of inclination; wherein estimating the shift and the characteristic inclination comprises: defining a model of the X-ray scattering profile according to a relative shift and the characteristic inclination; and calculating a fit between the measured X-ray scattering profile and the model and extracting the estimated shift and the characteristic inclination from the fit.

2. The method according to claim 1, wherein Estimating the characteristic inclination of the first layer and the second layer comprises estimating one or more of the following: an average inclination of the first layer and the second layer, an extreme inclination of the first layer and the second layer, and a relative inclination between the first layer and the second layer.

3. The method according to claim 1, wherein, Calculating the fit comprises applying a regression model to the measured X-ray scattering profile.

4. The method according to claim 1, wherein, Calculating the fit comprises: fitting a function comprising a plurality of peaks to the X-ray scattering profile; and solving the regression model to obtain (i) a relative intensity of the peaks and (ii) an angular position of a central peak that best matches the measured X-ray scattering profile.

5. The method according to claim 4, wherein, Estimating the shift and the characteristic inclination comprises deriving the shift and the characteristic inclination from the relative intensity and the angular position that best match the measured X-ray scattering profile.

6. The method according to claim 1, wherein Calculating the fit comprises applying a non-linear regression model to the measured X-ray scattering profile.

7. The method according to claim 1 or 2, wherein Measuring the X-ray scattering profile comprises combining a plurality of X-ray scattering measurements from a plurality of different angular ranges into a combined measured X-ray scattering profile.

8. The method according to claim 1 or 2, wherein The first high aspect ratio (HAR) structure and the second high aspect ratio (HAR) structure are holes.

9. A system for X-ray measurement, the system comprising: an X-ray source configured to generate an X-ray beam; optics configured to direct the X-ray beam to a sample comprising at least a first layer and a second layer stacked on top of each other, the X-ray beam being incident at a sample location, the first layer and the second layer comprising respective first high aspect ratio (HAR) and second high aspect ratio (HAR) structures at the sample location; and a processor configured to: use a detector to measure an X-ray scattering profile emitted from the sample location in response to the X-ray beam according to an angle of inclination between the sample and the X-ray beam; and estimate a shift between the first layer and the second layer and a characteristic inclination of the first layer and the second layer based on the X-ray scattering profile measured according to the angle of inclination; wherein the processor is configured to estimate the shift and the characteristic inclination by: A model for defining an X-ray scattering profile based on relative shift and said characteristic tilt; and Calculating a fit between the measured X-ray scattering profile and said model, and extracting the estimated shift and said characteristic tilt from said fit.

10. The system according to claim 9, wherein, The processor is configured to estimate the characteristic tilt of the first and second layers by estimating one or more of the following: the average tilt of the first and second layers, the extreme tilt of the first and second layers, and the relative tilt between the first and second layers.

11. The system according to claim 9, wherein, The processor is configured to calculate the fit by applying a regression model to the measured X-ray scattering profile.

12. The system according to claim 9, wherein The processor is configured to calculate the fit by: Fitting a function including a plurality of peaks to the X-ray scattering profile; and Solving a regression model to obtain (i) the relative intensities of said peaks and (ii) the angular position of a central peak that best matches the measured X-ray scattering profile.

13. The system according to claim 12, wherein The processor is configured to derive the shift and said characteristic tilt from the relative intensities and the angular position that best match the measured X-ray scattering profile.

14. The system according to claim 9, wherein, The processor is configured to calculate the fit by applying a non-linear regression model to the measured X-ray scattering profile.

15. The system according to claim 9 or 10, wherein, The processor is configured to measure the X-ray scattering profile by combining a plurality of X-ray scattering measurements from a plurality of different angular ranges into a combined measured X-ray scattering profile.

16. The system according to claim 9 or 10, wherein The first high aspect ratio (HAR) and second high aspect ratio (HAR) structures are holes.

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