Metrology system and method for metrology system

Abstract

Methods and systems for positioning a specimen and characterizing an x-ray beam incident onto the specimen in a Transmission, Small-Angle X-ray Scatterometry (T-SAXS) metrology system are described herein. A specimen positioning system locates a wafer vertically and actively positions the wafer in six degrees of freedom with respect to the x-ray illumination beam without attenuating the transmitted radiation. In some embodiments, a cylindrically shaped occlusion element is scanned across the illumination beam while the detected intensity of the transmitted flux is measured to precisely locate the beam center. In some other embodiments, a periodic calibration target is employed to precisely locate the beam center. The periodic calibration target includes one or more spatially defined zones having different periodic structures that diffract X-ray illumination light into distinct, measurable diffraction patterns.

Description

[Technical Field]

[0001] The described embodiments relate to X-ray metrology systems and methods, and more particularly to methods and systems for improving measurement accuracy. [Previous Technology]

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

[0003] Metrology procedures are used at various steps during a semiconductor manufacturing process to detect defects on the wafer to promote higher yields. Several metrology-based techniques (including scattering and reflection measurement implementations and associated analytical algorithms) are typically used to characterize the critical dimensions, film thickness, composition, and other parameters of nanoscale structures.

[0004] Traditionally, scattering measurements are performed on targets composed of thin films and / or repeating periodic structures to determine critical size. During device fabrication, these films and periodic structures typically represent the actual device geometry and material structure or an intermediate design. As devices (e.g., logic and memory devices) move towards smaller nanometer-scale dimensions, characterization becomes more difficult. Devices incorporating complex three-dimensional geometries and materials with diverse physical properties create characterization challenges. For example, modern memory structures are often high-aspect-ratio three-dimensional structures that make it difficult for optical radiation to penetrate to the underlying layers. Optical metrology tools using infrared to visible light can penetrate many translucent material layers, but the longer wavelengths that provide good penetration depth do not provide sufficient sensitivity to small anomalies. In addition, the increased number of parameters required to characterize complex structures (e.g., FinFETs) leads to increased parameter correlation. Therefore, the parameters of a characterized target are often not reliably decoupled from available measurements.

[0005] In one instance, an attempt has been made to use longer wavelengths (e.g., near-infrared) to overcome the penetration problem in 3D FLASH devices that utilize polycrystalline silicon as one of the alternating materials in the stack. However, as illumination propagates deeper into the film stack, the mirror-like structure of the 3D FLASH inherently leads to a reduction in light intensity. This results in sensitivity loss and correlation problems at deeper depths. In this case, the SCD was only able to successfully extract the metrological dimensions of a simplified group with high sensitivity and low correlation.

[0006] In another example, opaque high-k materials are increasingly being used in modern semiconductor structures. Optical radiation typically cannot penetrate layers constructed from such materials. Therefore, measurements using thin-film scattering measurement tools such as ellipsometers or reflectometers are becoming increasingly challenging.

[0007] In response to these challenges, more sophisticated optical metrology tools have been developed. For example, tools with multiple illumination angles, shorter illumination wavelengths, wider illumination wavelength ranges, and more complete information acquisition of self-reflection signals have been developed (e.g., measuring multiple Mueller matrix elements in addition to more familiar reflectivity or ellipsometric measurement signals). However, these approaches have not reliably overcome the fundamental challenges associated with the measurement and metrology applications of many advanced targets (e.g., complex 3D structures, structures smaller than 10 nm, structures using opaque materials) (e.g., line edge roughness and linewidth roughness measurement).

[0008] Atomic force microscopy (AFM) and scanning tunneling microscopy (STM) can achieve atomic resolution, but they can only probe the surface of the sample. Furthermore, AFM and STM microscopy require long scan times. Scanning electron microscopy (SEM) achieves intermediate resolution, but cannot penetrate structures to sufficient depth. Therefore, it does not effectively characterize high aspect ratio holes. Additionally, the charging required for the sample has a detrimental effect on imaging performance. X-ray reflectometers also suffer from penetration problems that limit their effectiveness when measuring high aspect ratio structures.

[0009] To overcome the penetration depth problem, traditional imaging techniques (such as TEM, SEM, etc.) are combined with destructive sample preparation techniques (such as focused ion beam (FIB) processing, ion milling, blanket etching, or selective etching). For example, transmission electron microscopy (TEM) achieves high-resolution alignment and can probe arbitrary depths, but TEM technology requires destructive segmentation of the sample. Several iterations of material removal and measurement typically provide the information needed for key metrological parameters across three-dimensional structures. However, these techniques require sample destruction and lengthy procedure times. The complexity and time required to complete these types of measurements are attributed to the inaccuracies introduced by the drift of etching and metrological steps. In addition, these techniques require several iterations to introduce alignment errors.

[0010] The transmission small-angle X-ray scattering (T-SAXS) system using photons at a hard X-ray energy level (>15 keV) has shown promise for solving challenging measurement applications. The following cases describe various applications of SAXS technology to critical dimension (CD-SAXS) and overlay (OVL-SAXS) measurements: 1) U.S. Patent No. 7,929,667, entitled "High-brightness X-ray metrology," by Zhuang and Fielden; 2) U.S. Patent Publication No. 2014 / 0019097, entitled "Model Building And Analysis Engine For Combined X-Ray And Optical Metrology," by Bakeman, Shchegrov, Zhao, and Tan; 3) U.S. Patent Publication No. 2015 / 0117610, entitled "Methods and Apparatus For Measuring Semiconductor Device Overlay Using X-Ray Metrology," by Veldman, Bakeman, Shchegrov, and Mieher; and 4) U.S. Patent Publication No. 2015 / 0117610, entitled "Measurement System Optimization For X-Ray Based," by Hench, Shchegrov, and Bakeman. The aforementioned patent documents are: 5) U.S. Patent Publication No. 2016 / 0202193 entitled "X-ray Metrology For High Aspect Ratio Structures" by Dziura, Gellineau, and Shchegrov; and 6) U.S. Patent Publication No. 2017 / 0167862 entitled "X-ray Metrology For High Aspect Ratio Structures" by Gellineau, Dziura, Hench, Veldman, and Zalubovsky; and 7) U.S. Patent Publication No. 2018 / 0106735 entitled "Full Beam Metrology for X-Ray Scatterometry Systems" by Gellineau, Dziura, Hench, Veldman, and Zalubovsky. These patent documents are assigned to KLA-Tencor Corporation of Milpitas, California, USA.

[0011] SAXS has also been applied to material characterization and other non-semiconductor related applications. Exemplary systems have been commercialized by several companies, including Xenocs SAS (www.xenocs.com), Bruker Corporation (www.bruker.com), and Rigaku Corporation (www.rigaku.com / en).

[0012] Studies on CD-SAXS metrology of semiconductor structures are also described in the scientific literature. Most research teams have used high-brightness X-ray synchrotron sources, which are unsuitable for use in a semiconductor manufacturing facility due to their enormous size, cost, etc. An example of such a system is described in the article entitled "Intercomparison between optical and x-ray scatterometry measurements of FinFET structures" by Lemaillet, Germer, Kline, et al., Proc. SPIE, Vol. 8681, p. 86810Q (2013). Recently, a team at the National Institute of Standards and Technology (NIST) has begun studies using a compact and bright X-ray source similar to that described in U.S. Patent No. 7,929,667. This study is described in an article titled "X-ray scattering critical dimensional metrology using a compact x-ray source for next generation semiconductor devices", J. Micro / Nanolith. MEMS MOEMS 16(1), 014001 (January–March 2017).

[0013] A metrology system must be used to calibrate and align the interaction between the X-ray beam and the target to ensure effective measurement. Exemplary characterization includes: precisely positioning the peak intensity of the X-ray beam on the target; measuring the X-ray beam intensity distribution; and identifying the boundaries of the X-ray beam such that a specific percentage of the beam flux lies outside the boundaries. Exemplary alignment includes the alignment of the X-ray beam with an optical vision system, and the alignment of the X-ray beam with specific mechanical features of an tool (e.g., a wafer rotation axis).

[0014] Generally speaking, the wafer is navigated in the path of an X-ray beam by means of optical measurement of alignment marks placed throughout the wafer using an optical microscope. In order to ensure accurate navigation of a specific target relative to the X-ray beam, the beam profile needs to be measured in the coordinates of the optical microscope used to measure the alignment marks.

[0015] In some instances, an optical microscope is aligned with a blade and the blade is aligned with an X-ray beam. The characteristic of an X-ray beam with a conventional blade is due to the complexity arising from the translucency of the blade material illuminated by X-ray radiation near the edge of the blade. For example, tungsten has a beam attenuation length of approximately 8.4 micrometers when illuminated by photons with an energy level of 20 keV. At this length, the transmittance decreases by ~1 / e (e=2.718). For a blade shaped at an angle of 30 degrees, the length of the wedge corresponding to a height of 8.4 micrometers is approximately 14.5 micrometers. This simple estimate of the uncertainty in the position of a blade during an X-ray beam scan illustrates that the translucency of the blade is limited when the required alignment accuracy is less than a few micrometers (e.g., less than 10 micrometers).

[0016] In some other examples, the X-ray beam profile is characterized by a high-resolution X-ray camera positioned relative to a point on the X-ray beam (e.g., a focal point of a focusing optics). In these examples, the beam profile is measured using the high-resolution X-ray camera, and the measured coordinates of the beam are transmitted to an optical microscope used to navigate the wafer in the path of the X-ray beam. Unfortunately, the error associated with transmitting the measured coordinates from the X-ray camera to the optical microscope is significant and exceeds the required navigation accuracy.

[0017] Furthermore, characterization of an X-ray beam by means of an X-ray camera or blade is essentially indirect and does not provide quantitative data on the photon flux incident on the target and the photon contamination in the adjacent area.

[0018] Future metrology applications face metrological challenges due to increasingly smaller resolution requirements, multi-parameter correlations, increasingly complex geometrologies (including high aspect ratio structures), and the growing use of opaque materials. Existing methods for X-ray tool alignment and target navigation are limited to an accuracy of approximately 10 to 20 micrometers. These methods cannot locate and measure metrological targets of small size (~50 micrometers) within an X-ray beam with sufficient accuracy for semiconductor metrology applications. Therefore, improved alignment and calibration methods and systems for X-ray beams in SAXS systems are desired to meet the placement requirements of advanced manufacturing nodes. [Summary of the Invention]

[0019] This document describes a method and system for positioning a sample and characterizing an X-ray beam incident on the sample in a transmission small-angle X-ray scattering (T-SAXS) metrology system. Practical T-SAXS measurements in a semiconductor manufacturing environment require measurements over a large angle of incidence and azimuth relative to the surface of a sample (e.g., a semiconductor wafer) having a small beam spot size (e.g., less than 50 micrometers across the effective illumination point). Accurate positioning of the wafer and characterization of the beam size and shape are required to achieve a small measurement cell size. Furthermore, this document presents calibration for accurately positioning the illumination beam on a desired target area on the surface of a semiconductor wafer across the entire range of angles of incidence and azimuth.

[0020] In one embodiment, a metrology tool includes a sample positioning system configured to vertically position a wafer (i.e., the plane of the wafer surface is substantially aligned with the gravity vector) and actively position the wafer relative to an illumination beam in six degrees of freedom. The sample positioning system supports the wafer at its edges, thereby allowing the illumination beam to penetrate the wafer at any location within the active region of the wafer without remounting. By vertically supporting the wafer at its edges, gravity-induced indentation of the wafer is effectively mitigated.

[0021] In a further state, a balancer statically balances the rotating mass of the sample positioning system such that the center of gravity of the rotating mass is approximately aligned with its axis of rotation.

[0022] In some embodiments, three sensors are mounted on the sample positioning system to measure the distance of the back side of the wafer relative to the sample positioning system. In this way, wafer warpage is measured and compensated by moving the wafer using a tip-tilt Z-stage.

[0023] In another embodiment, a SAXS metrology system employs at least one beam-blocking calibration target to position an X-ray illumination beam relative to a sample positioning system. The beam-blocking calibration target comprises at least one marker and a cylindrical blocking element. A alignment camera is used to position the marker in the coordinates of the sample positioning system. The position of the marker relative to the cylindrical blocking element is known in advance (e.g., with an accuracy of less than 200 nanometers). Therefore, the position of the cylindrical blocking element in the coordinates of the sample positioning system is easily determined by a direct coordinate transformation. The cylindrical blocking element is scanned across the illumination beam while measuring the detected intensity of the transmission flux. The center of the illumination beam is precisely positioned relative to the cylindrical blocking element based on the measured intensity. Since the position of the cylindrical blocking element in the coordinates of the sample positioning system is known, the center of the illumination beam in the coordinates of the sample positioning system is precisely positioned by a simple coordinate transformation.

[0024] In some instances, a beam-blocking calibration target is used to calibrate the incident position of the illumination beam relative to the sample positioning system. In other instances, a beam-blocking calibration target is used to align the rotation axis of the stage reference frame relative to the illumination beam at the incident point of the illumination beam and a wafer.

[0025] In another embodiment, a SAXS metrology system employs at least one periodic calibration target to position an X-ray illumination beam relative to the sample positioning system. Each periodic calibration target comprises one or more spatially defined regions having different periodic structures that diffract the X-ray illumination beam into dissimilar diffraction patterns measurable by one of the SAXS metrology systems described herein. Additionally, each periodic calibration target includes one or more markers that can be read by an optical microscope to position the periodic calibration target relative to the sample positioning system with high alignment accuracy (e.g., 0.5 micrometers or less). Each spatially defined region has spatially well-defined boundary lines. The positions of these boundary lines relative to the markers are known to have high accuracy (e.g., 0.2 micrometers or less) in one or more dimensions.

[0026] In another embodiment, the precise alignment of the illumination beam with the plane of the wafer surface is determined based on the interaction between the illumination beam and two or more beam-blocking calibration targets, such as those measured by an X-ray detector.

[0027] In another embodiment, the precise alignment of the rotation axis with a calibration target mark in the plane of the surface of the wafer is determined based on an image of a mark collected by an alignment camera mounted on a transverse alignment stage.

[0028] In another embodiment, the shape of the wafer surface in the Z direction is mapped using an alignment camera, an optical proximity sensor, a capacitive proximity sensor, an interferometric sensor, or any other suitable proximity sensor. In some instances, the wafer surface is mapped onto the front side (i.e., the patterned side) of the wafer. In some other instances, if the wafer thickness is sufficiently uniform, well-modeled, or measured in situ or pre-measured, the wafer surface is mapped onto the back side (i.e., the unpatterned side) of the wafer.

[0029] The foregoing is the description of the invention and therefore must contain simplifications, generalizations and omissions of details; thus, those skilled in the art will understand that the description of the invention is merely illustrative and in no way limiting. Other forms of the apparatus and / or process described herein, as well as the inventive features and advantages, will become apparent from the non-limiting detailed description set forth herein.

Implementation Method

[0055] Cross-reference to related applications

[0056] This patent application claims priority to U.S. Provisional Patent Application No. 62 / 505,014, filed May 11, 2017, pursuant to 35 USC §119, the entire contents of which are incorporated herein by reference.

[0057] The background examples and some embodiments of the present invention will now be illustrated in detail with reference to the accompanying drawings.

[0058] This document describes a method and system for positioning a sample and characterizing an X-ray beam incident on the sample in a transmission small-angle X-ray scattering (T-SAXS) metrology system. Practical T-SAXS measurements in a semiconductor manufacturing environment require measurements over a large angle of incidence and azimuth relative to the surface of a sample (e.g., a semiconductor wafer) having a small beam spot size (e.g., less than 50 micrometers across the effective illumination point). Accurate wafer positioning and characteristic beam size and shape are required to achieve a small measurement cell size. Furthermore, this document presents calibration for accurately positioning the illumination beam on a desired target area on the surface of a semiconductor wafer across the entire range of angles of incidence and azimuth.

[0059] This paper presents a six-degree-of-freedom sample positioning system. Furthermore, the dedicated calibration target described herein enables highly accurate characterization of the X-ray beam profile and highly accurate alignment of the X-ray beam relative to the calibration target. This enables precise navigation of wafers required for metrology targets the size of a small measurement box (e.g., a metrology target positioned in a scribing track with a size of 100 micrometers or less).

[0060] Figure 1 illustrates an embodiment of a T-SAXS metrology tool 100 for measuring one of the characteristics of a sample in at least one novel sample. As shown in Figure 1, the system 100 can be used to perform T-SAXS measurements over a detection area 102 of a sample 101 illuminated by a point of illumination beam.

[0061] In the depicted embodiment, the metrology tool 100 includes an x-ray illumination subsystem 125, which includes an x-ray illumination source 110, focusing optics 111, a beam divergence control slit 112, an intermediate slit 113, and a beam shaping slit mechanism 120. The x-ray illumination source 110 is configured to generate x-ray radiation suitable for T-SAXS measurements. In some embodiments, the x-ray illumination source 110 is configured to generate wavelengths between 0.01 nanometers and 1 nanometer. Generally, any suitable high-brightness x-ray illumination source capable of generating high-brightness x-rays at flux levels sufficient to achieve high throughput, in-line metrology, is conceivable for supplying x-ray illumination for T-SAXS measurements. In some embodiments, an x-ray source includes a tunable monochromator that enables the x-ray source to deliver x-ray radiation at different selectable wavelengths.

[0062] In some embodiments, one or more x-ray sources emitting radiation with photon energies greater than 15 keV are employed to ensure that the x-ray sources supply light at wavelengths that allow sufficient transmission through the entire device and the wafer substrate. By way of non-limiting examples, any of a particle accelerator source, a liquid anode source, a rotating anode source, a fixed solid anode source, a microfocusing source, a microfocusing rotating anode source, a plasma-based source, and an inverse Compton source can be used as the x-ray illumination source 110. In one example, an inverse Compton source available from Lyncean Technologies, Inc., Palo Alto, California (United States) is conceivable. Inverse Compton sources have the additional advantage of being able to generate x-rays within a range of photon energies, thereby enabling the x-ray source to deliver x-ray radiation at different selectable wavelengths.

[0063] An exemplary X-ray source includes an electron beam source configured to bombard a solid or liquid target to stimulate X-ray radiation. A method and system for generating high-brightness, liquid metal X-ray illumination are described in U.S. Patent No. 7,929,667, issued to KLA-Tencor Corp. on April 19, 2011, the entire contents of which are incorporated herein by reference.

[0064] The X-ray illumination source 110 generates X-ray emission over a source region having a finite lateral dimension (i.e., a non-zero dimension orthogonal to the beam axis). A focusing optics 111 focuses the source radiation onto a metrological target positioned on the sample 101. The finite lateral source dimension results in a finite point size 102 on the target defined by rays 117 from the edge of the source. In some embodiments, the focusing optics 111 comprises an elliptical focusing optics element.

[0065] A beam divergence control slit 112 is positioned in the beam path between the focusing optics 111 and the beam shaping slit mechanism 120. The beam divergence control slit 112 limits the divergence of illumination provided to the sample to be measured. An additional intermediate slit 113 is positioned in the beam path between the beam divergence control slit 112 and the beam shaping slit mechanism 120. The intermediate slit 113 provides additional beam shaping. However, generally speaking, the intermediate slit 113 is optional.

[0066] The beam-shaping slit mechanism 120 is positioned in the beam path immediately preceding the sample 101. In one embodiment, the slit of the beam-shaping slit mechanism 120 is positioned close to the sample 101 to minimize the expansion of the incident beam size, defined by the finite source size, due to beam divergence. In one example, for a 10-micron X-ray source size and a distance of 25 millimeters between the beam-shaping slit and the sample 101, the expansion of the beam size due to shadowing caused by the finite source size is approximately 1 micron.

[0067] In some embodiments, the beam shaping slit mechanism 120 includes a plurality of independently actuated beam shaping slits. In one embodiment, the beam shaping slit mechanism 120 includes four independently actuated beam shaping slits. These four beam shaping slits effectively block a portion of the incoming beam 115 and produce an illumination beam 116 having a box-shaped illumination cross-section.

[0068] Figures 2 and 3 depict two different configurations of one end view of the beam-shaping slit mechanism 120 depicted in Figure 1. As shown in Figures 2 and 3, the beam axis is perpendicular to the drawing page. As depicted in Figure 2, the incoming beam 115 has a large cross-section. In some embodiments, the incoming beam 115 has a diameter of approximately 1 mm. Furthermore, the position of the incoming beam 115 within the beam-shaping slits 126 to 129 has an uncertainty of approximately 3 mm, attributable to beam pointing error. To accommodate the uncertainty of the size and position of the incoming beam, each slit has a length L of approximately 6 mm. As depicted in Figure 2, each slit can move in a direction perpendicular to the beam axis. In the illustration of Figure 2, slits 126 to 129 are positioned at a maximum distance from the beam axis (i.e., the slits are fully open and do not restrict light from passing through the beam-shaping slit mechanism 120).

[0069] FIG3 depicts slits 126 to 129 of a beam shaping slit mechanism 120 in a position that blocks a portion of the incoming beam 115 so that the outgoing beam 116 delivered to the sample to be measured has a reduced size and a well-defined shape. As depicted in FIG3, each of the slits 126 to 129 has been moved inward toward the beam axis to achieve the desired output beam shape.

[0070] Slits 126 to 129 are constructed of a material that minimizes scattering and effectively blocks incident radiation. Exemplary materials include single-crystal materials such as germanium, gallium arsenide, and indium phosphide. Typically, the slit material is split rather than sawn along a crystallographic direction to minimize scattering across structural boundaries. Additionally, the slits are oriented relative to the incoming beam so that the interaction between the incoming radiation and the internal structure of the slit material produces minimal scattering. Crystals are attached to slit holders made of a high-density material (e.g., tungsten) to completely block X-ray beams from one side of the slit. In some embodiments, each slit has a rectangular cross-section with a width of approximately 0.5 mm and a height of approximately 1 to 2 mm. As depicted in Figure 2, the length L of a slit is approximately 6 mm.

[0071] Generally speaking, an X-ray optics device shapes and directs X-ray radiation toward sample 101. In some instances, the X-ray optics device includes an X-ray monochromator to monochromate the X-ray beam incident on sample 101. In some instances, the X-ray optics device uses a multilayer X-ray optics device to collimate or focus the X-ray beam onto a measurement region 102 of sample 101 to a divergence of less than 1 milliradian. In these instances, the multilayer X-ray optics device also functions as a beam monochromator. In some embodiments, the X-ray optics device includes one or more X-ray collimators, X-ray apertures, X-ray beam stops, refractive X-ray optics, diffractive optics (such as zone plates), Montel optics, specular X-ray optics (such as grazing-incidence ellipsoidal mirrors), multicapillary optics (such as hollow capillary X-ray waveguides), multilayer optics devices or systems, or any combination thereof. Further details are described in U.S. Patent Publication No. 2015 / 0110249, the contents of which are incorporated herein by reference in their entirety.

[0072] The X-ray detector 119 collects the X-ray radiation 114 scattered from the sample 101 and generates an output signal 135 according to a T-SAXS measurement mode, indicating one of the properties of the sample 101 that are sensitive to the incident X-ray radiation. In some embodiments, the X-ray detector 119 collects the scattered X-rays 114, while the sample positioning system 140 positions and orients the sample 101 to generate angularly resolved scattered X-rays.

[0073] In some embodiments, a T-SAXS system includes one or more photon counting detectors having a high dynamic range (e.g., greater than 10⁵). In some embodiments, a single photon counting detector detects the position and number of detected photons.

[0074] In some embodiments, the x-ray detector analyzes one or more x-ray photon energies and generates signals indicating the properties of the sample for each x-ray energy component. In some embodiments, the x-ray detector 119 includes any one of a CCD array, a microchannel plate, a photodiode array, a microstrip proportional counter, a gas proportional counter, a scintillator, or a fluorescent material.

[0075] In this manner, in addition to pixel position and count, X-ray photon interactions within the detector are also identified by energy. In some embodiments, X-ray photon interactions are identified by comparing the energy of the X-ray photon interactions with a predetermined upper threshold and a predetermined lower threshold. In one embodiment, this information is transmitted to a computing system 130 via an output signal 135 for further processing and storage.

[0076] In a further state, a T-SAXS system is used to determine the properties of a sample (e.g., structural parameter values) based on one or more diffraction orders of scattered light. As depicted in FIG1, the metrology tool 100 includes a computational system 130 used to acquire a signal 135 generated by the detector 119 and to determine the properties of the sample at least in part based on the acquired signal.

[0077] In some instances, T-SAXS-based metrology involves determining the sample size by inversely solving a predetermined measurement model using measured data. The measurement model contains several (approximately ten) adjustable parameters and represents the geometry and optical properties of the sample, as well as the optical properties of the measurement system. Inverse methods include (but are not limited to) model-based regression, tomography, machine learning, or any combination thereof. In this way, target profile parameters are estimated by solving for the value of a parameterized measurement model that minimizes the error between the measured scattered X-ray intensity and the modeled result.

[0078] It is desirable to perform measurements over a wide range of incident and azimuth angles to increase the precision and accuracy of the measured parameter values. This method reduces the correlation between parameters by expanding the number and diversity of datasets available for analysis to include various large-angle, out-of-plane orientations. For example, in a normal orientation, T-SAXS can resolve the critical dimensions of a feature, but is largely insensitive to the sidewall angles and height of a feature. However, by collecting measurement data over a wide range of out-of-plane orientations, the sidewall angles and height of a feature can be resolved. In other instances, measurements performed over a wide range of incident and azimuth angles provide sufficient resolution and penetration depth to characterize high aspect ratio structures through their entire depth.

[0079] Measurements of the intensity of diffracted radiation, which varies with the X-ray incident angle relative to the wafer surface normal, are collected. The information contained in multiple diffraction levels is usually unique among the model parameters under consideration. Therefore, X-ray scattering produces estimates of the values ​​of the parameters of interest with small errors and reduced parameter correlation.

[0080] The orientation of the illumination x-ray beam 116 relative to the surface normal of the wafer 101 is described by rotating a semiconductor wafer 101 relative to any two angles of the x-ray illumination beam 115, or vice versa. In one example, the orientation can be described with respect to a coordinate system fixed to the wafer. Figure 4 depicts an x-ray illumination beam 116 incident on wafer 101 with a specific orientation described by an incident angle θ and an azimuth angle ϕ. The coordinate system XYZ is fixed to a metrology system (e.g., the illumination beam 116) and the coordinate system X'Y'Z' is fixed to wafer 101. The Y-axis is aligned with the surface of wafer 101 in a plane. X and Z are not aligned with the surface of wafer 101. Z' is aligned with an axis normal to the surface of wafer 101, and X' and Y' are in a plane aligned with the surface of wafer 101. As depicted in Figure 4, the x-ray illumination beam 116 is aligned with the Z-axis and therefore lies in the XZ plane. The incident angle θ describes the orientation of the x-ray illumination beam 116 relative to the surface normal of the wafer in the XZ plane. Furthermore, the azimuth angle ϕ describes the orientation of the XZ plane relative to the X'Z' plane. θ and ϕ together uniquely define the orientation of the x-ray illumination beam 116 relative to the surface of wafer 101. In this example, the orientation of the x-ray illumination beam relative to the surface of wafer 101 is described by rotation about an axis normal to the surface of wafer 101 (i.e., the Z' axis) and rotation about an axis aligned with the surface of wafer 101 (i.e., the Y axis). In some other examples, the orientation of the x-ray illumination beam relative to the surface of wafer 101 is described by rotation about a first axis aligned with the surface of wafer 101 and another axis aligned with the surface of wafer 101 and perpendicular to the first axis.

[0081] In one embodiment, the metrology tool 100 includes a sample positioning system 140 configured to vertically position a wafer (i.e., the plane of the wafer surface is substantially aligned with the gravity vector) and to actively position the sample 101 relative to the illumination beam 116 in six degrees of freedom. Additionally, the sample positioning system 140 is configured to align the sample 101 and orient it within a large angle of incidence (e.g., at least 70 degrees) and azimuth (e.g., at least 190 degrees) relative to the illumination beam 116. In some embodiments, the sample positioning system 140 is configured to rotate the sample 101 within a large rotational angle range (e.g., at least 70 degrees) aligned with the plane of the sample 101's surface. In this manner, angular resolving measurements of the sample 101 are collected by the metrology system 100 at any number of locations and orientations on the surface of the sample 101. In one example, the computing system 130 transmits a command signal (not shown) instructing the sample 101 to the sample positioning system 140. In response, the sample positioning system 140 generates command signals to its various actuators to achieve the desired positioning of the sample 101.

[0082] Figure 5 depicts a sample positioning system 140 in one embodiment. In one embodiment, the sample positioning system 140 provides active control over the position of wafer 101 relative to illumination beam 116 in all six degrees of freedom, while supporting wafer 101 perpendicularly relative to the gravity vector (i.e., the gravity vector is approximately in the same plane as the wafer surface). The sample positioning system 140 supports wafer 101 at its edges, thereby allowing illumination beam 116 to penetrate wafer 101 in any portion of the active region of wafer 101 without remounting wafer 101. By supporting wafer 101 perpendicularly at its edges, gravity-induced indentation of wafer 101 is effectively mitigated.

[0083] As depicted in Figure 5, the sample positioning system 140 includes a substrate frame 141, a lateral alignment stage 142, a stage reference frame 143, and a wafer stage 144 mounted to the stage reference frame 143. For reference purposes, the coordinates {XBF, YBF, ZBF} are attached to the substrate frame 141, the coordinates {XNF, YNF, ZNF} are attached to the lateral alignment stage 142, the coordinates {XRF, YRF, ZRF} are attached to the stage reference frame 143, and the coordinates {XSF, YSF, ZSF} are attached to the wafer stage 144. The wafer 101 is supported on the wafer stage 144 by a flip-tilt-Z stage 156 including actuators 150A to 150C. A rotating stage 158, mounted to one of the flip-tilt-Z stage 156, orients the wafer 101 relative to the illumination beam 116 within an azimuth angle ϕ. In the depicted embodiment, three linear actuators 150A to 150C are mounted to the wafer stage 144 and support the rotating stage 158, which in turn supports the wafer 101.

[0084] Actuator 145 translates the lateral alignment stage 142 relative to the substrate frame 141 along the XBF axis. Rotation actuator 146 rotates the stage reference frame 143 relative to the lateral alignment stage 142 about one of the rotation axes 153 aligned with the YNF axis. Rotation actuator 146 orients the wafer 101 relative to the illumination beam 116 within an incident angle θ. Wafer stage actuators 147 and 148 translate the wafer stage 144 relative to the stage reference frame 143 along the XRF and YRF axes, respectively.

[0085] In one configuration, the wafer stage 144 is an open-aperture, biaxial (XY) linearly stacked stage. The open aperture allows the measurement beam to pass through any portion of the entire wafer (e.g., a 300 mm wafer). The wafer stage 144 is configured such that the Y-axis stage extends in a direction substantially parallel to the rotation axis 153. Furthermore, the Y-axis stage extends in a direction substantially aligned with the gravity vector.

[0086] Actuators 150A to 150C operate in coordination to translate the rotary stage 158 and wafer 101 relative to the wafer stage 144 in the ZSF direction and to flip and tilt the rotary stage 158 and wafer 101 relative to the wafer stage 144 about an axis coplanar with the XSF-YSF plane. The rotary stage 158 rotates the wafer 101 about an axis normal to the surface of the wafer 101. In a further embodiment, a frame of the rotary stage 158 is coupled to the actuators 150A to 150C by a motion mounting system comprising motion mounting elements 157A to 157C respectively. In one example, each motion mounting element 157A to 157C includes a ball attached to a corresponding actuator and a V-slot attached to the rotary stage 158. Each ball and a corresponding V-slot form two-point contact. Each kinematic mounting element constrains the motion of the rotary stage 158 relative to the actuators 150A to 150C in two degrees of freedom, and three kinematic mounting elements 157A to 157C jointly constrain the motion of the rotary stage 158 relative to the actuators 150A to 150C in six degrees of freedom. Each kinematic coupling element is preloaded to ensure that the sphere always remains in contact with the corresponding V-slot. In some embodiments, this preload is provided by gravity, a mechanical spring mechanism, or a combination thereof.

[0087] In another further embodiment, the rotating stage 158 is an open-aperture rotating stage. The open aperture allows the measurement beam to pass through any portion of the entire wafer (e.g., a 300 mm wafer). The rotating stage 158 is configured such that its axis of rotation is substantially perpendicular to the axis of rotation 153. Furthermore, the axis of rotation of the rotating stage 158 is substantially perpendicular to the gravity vector. The wafer 101 is secured to the rotating stage 158 via an edge holder to provide complete wafer coverage with minimal edge exclusion.

[0088] In summary, the sample positioning system 140 can actively control the position of the wafer 101 relative to the illumination beam 116 in six degrees of freedom, such that the illumination beam 116 can be incident on any location on the surface of the wafer 101 (i.e., within a range of at least 300 mm in the XFR and YRF directions). The rotary actuator 146 can rotate the stage reference frame 143 relative to the illumination beam 116, such that the illumination beam 116 can be incident on the surface of the wafer 101 at any of a large angular range (e.g., greater than two degrees). In one embodiment, the rotary actuator 146 is configured to rotate the stage reference frame 143 within a range of at least one of sixty degrees. A rotary actuator 158 mounted to the wafer stage 144 can rotate the wafer 101 relative to the illumination beam 116, such that the illumination beam 116 can be incident on the surface of the wafer 101 at any of a large azimuth range (e.g., at least a ninety-degree rotation range). In some embodiments, the azimuth range is a rotation range of at least 190 degrees.

[0089] In some other embodiments, the lateral alignment stage 142 is removed and the stage reference frame 143 is rotated relative to the substrate frame 141 by a rotation actuator 146. In these embodiments, the x-ray illumination system includes one or more actuators that move one or more optical elements of the x-ray illumination system to cause the x-ray illumination beam 116 to move relative to the substrate frame 141, for example, in the XBF direction. In these embodiments, for example, movement of the stage reference frame 143 (replaced by movement of one or more optical elements of the x-ray illumination system for calibration purposes as described herein) moves the x-ray illumination beam relative to the rotation axis 153 to a desired position. In the embodiments depicted in Figures 1 and 21, the computing system 130 transmits a command signal 138 to the actuator subsystem 111' to reorient the x-ray emission relative to the substrate frame 141 by moving one or more elements of the x-ray illumination subsystem 125 to achieve a desired beam direction. In the depicted embodiment, the actuator subsystem 111' moves the focusing optics 111 to reguide the x-ray emission relative to the substrate frame 141, and thus repositions the x-ray emission relative to the rotation axis 153.

[0090] Figure 6 provides another detailed illustration of the sample positioning system 140. The same numbered elements depicted in Figure 6 are similar to those described with reference to Figure 5. As depicted in Figure 5, the rotary actuator 146 causes a bulk assembly comprising the stage reference frame 143, the wafer stage 144, the flip-tilt-Z stage 156, and the rotary stage 158 to rotate about the rotation axis 153. As depicted in Figure 6, the wafer stage 144, the flip-tilt-Z stage 156, and the rotary stage 158 are offset by a significant distance from the rotation axis 153.

[0091] In a further embodiment, the balancer 159 is mounted to the stage reference frame 143 to balance the wafer stage 144, the tilt-z stage 156, and the rotating stage 158, such that the center of gravity of the rotational mass of the stage reference frame 143 and all mounting components is substantially aligned with the rotation axis 153. In this way, the force applied by the actuator 146 generates a torque about the rotation axis 153 with a minimum parasitic linear force.

[0092] As depicted in Figure 6, an air bearing 172 is used to guide the movement of the lateral alignment stage 142 relative to the base frame 141. Similarly, an air bearing 171 is used to guide the movement of the stage reference frame 143 relative to the lateral alignment stage 142. The air bearings, operating on a precision granite surface, minimize static friction and provide axial stability. This improves positioning performance (i.e., high repeatability and short settling time) while supporting large loads.

[0093] To ensure that the intersection position of the illumination beam 116 and the surface of the wafer 101 does not change within a large incident angle range, the rotation axis 153 must have very small synchronization and asynchrony errors. Additionally, any Abbe error must be minimized. To minimize Abbe error, air bearings 171 are radially equidistant around the rotation axis 153. The bearing races are large enough to prevent large angular errors. The bearings are constrained perpendicularly by the surface of the lateral alignment stage 142. In some embodiments, the surface of the lateral alignment stage 142 is a precision-ground granite surface perpendicular to the rotation axis 153.

[0094] Generally speaking, the sample positioning system provides automated positioning of semiconductor wafers in six degrees of freedom. In addition, the sample positioning system includes edge gripping features and actuators on a rotating stage to efficiently load and unload wafers in a vertical position in coordination with a wafer handling robot.

[0095] In some embodiments, three sensors are mounted on a sample positioning system to measure the distance of the back side of the wafer relative to the sample positioning system. In this way, wafer warpage is measured and compensated by moving the wafer using a flip-tilt-Z stage.

[0096] In another embodiment, a SAXS metrology system employs at least one beam-blocking calibration target to position an X-ray illumination beam relative to a sample positioning system. The beam-blocking calibration target comprises at least one marker and a cylindrical blocking element. A alignment camera is used to position the marker in the coordinates of the sample positioning system. The position of the marker relative to the cylindrical blocking element is known in advance (e.g., with an accuracy of less than 200 nanometers). Therefore, the position of the cylindrical blocking element in the coordinates of the sample positioning system is easily determined by a direct coordinate transformation. The cylindrical blocking element is scanned across the illumination beam while measuring the detected intensity of the transmission flux. The center of the illumination beam is precisely positioned relative to the cylindrical blocking element based on the measured intensity. Since the position of the cylindrical blocking element in the coordinates of the sample positioning system is known, the center of the illumination beam in the coordinates of the sample positioning system is precisely positioned by a simple coordinate transformation.

[0097] In some instances, a beam-blocking calibration target is used to calibrate the incident position of the illumination beam relative to the sample positioning system. In other instances, a beam-blocking calibration target is used to align the rotation axis of the stage reference frame relative to the illumination beam at the incident point of the illumination beam and a wafer.

[0098] Figure 7 depicts one embodiment of a beam blocking calibration target 190. In the embodiment depicted in Figure 7, the beam blocking calibration target 190 includes a precisely shaped cylindrical pin 192 and a frame 191 supporting the cylindrical pin 192. The cylindrical pin 192 is manufactured with high surface quality and precise dimensions on the order of target uncertainty (e.g., tolerance less than 0.5 micrometers).

[0099] In some embodiments, the frame 191 may be a structure mounted to a sample positioning system (such as sample positioning system 140). In these embodiments, the beam-blocking calibration target 190 is mounted to the sample positioning system 140 instead of a calibration wafer. In some other embodiments, the frame 191 may be a dedicated calibration wafer comprising one or more cylindrical pins attached to the wafer itself. In these embodiments, the beam-blocking calibration target 190 is mounted to a calibration wafer. The beam-blocking calibration target 190 also includes an opening 193 on one or both sides of the cylindrical pin 192. The opening 193 is sized such that an illumination beam (e.g., illumination beam 197) can pass through the beam-blocking calibration target 190 without obstruction (e.g., at least 2 mm by 2 mm). The beam-blocking calibration target 190 also includes one or more markings (e.g., markings 195 and 196) that can be read by an optical microscope mounted to a sample positioning system. The positions of marks 195 and 196 relative to the edges 198 and 199 of the cylindrical pin are precisely known. In this way, the position of the edge of the cylindrical pin 192 can be determined from the position of either mark 195 or 196, or both, by a simple coordinate transformation.

[0100] A cylindrical pin-shaped shielding element largely eliminates the limited transparency problem that arises when using a blade as an aligned target. The beam path through the cylindrical pin is defined by the radius R of the cylinder and the irradiation depth S of the beam path relative to the edge of the cylindrical pin. When R is significantly greater than S, the length L of the beam path through the cylindrical pin is approximately calculated by equation (1).

[0101] When a tungsten carbide cylindrical pin with a diameter of approximately 2 mm is used, the edge position uncertainty attributable to the translucency of hard X-rays is less than one micrometer. Generally speaking, the cylindrical pin 192 can be made of any suitable dense, high atomic number material. By way of non-limiting examples, the cylindrical pin 192 can be constructed from tungsten carbide, tungsten, platinum, etc. The diameter of the cylindrical pin should be large enough that the induced uncertainty at the edge position attributable to the translucency of the material is entirely within the total alignment error budget. Typically, a diameter of 2 to 3 mm is sufficient to keep the induced uncertainty at the edge position attributable to the translucency of the material below one to two micrometers.

[0102] As depicted in FIG. 7, the beam blocking calibration target 190 includes one or more flat surfaces (e.g., flat surface 194) precisely aligned with the axis of the cylindrical pin 192. In some instances, surface 194 is a reference surface used to measure the target position in a direction collinear with the X-ray beam by means of a distance sensor (e.g., a capacitive probe, an inductive probe, etc.). Additionally, in some embodiments, one or more markers are positioned on the flat surface. For example, as depicted in FIG. 7, marker 195 is positioned on flat surface 194.

[0103] In the embodiment depicted in FIG5, beam-blocking calibration targets 151 and 152 are mounted to a frame of a rotating stage 158 such that the central axis of the cylindrical pins is substantially coplanar with the surface of wafer 101. As depicted in FIG5, cylindrical pin 151 includes a central axis substantially parallel to the YNF axis and cylindrical pin 152 includes a central axis substantially parallel to the XRF axis. Each cylindrical pin blocks the beam by absorbing a large portion of any irradiating X-rays.

[0104] The sample positioning system 140 also includes an alignment camera 154 mounted to the stage reference frame 143. In the depicted embodiment, the alignment camera is mounted to the stage reference frame and thus rotates with the stage reference frame. The alignment camera 154 is configured to produce a high-resolution image of an object (such as wafer 101) in its field of view. In some embodiments, the alignment camera 154 also includes an autofocus mechanism that maintains a clear image focus by precisely moving the camera's focus by a measured distance. In some of these embodiments, the alignment camera 154 can be used to measure the relative distance between the stage reference frame to which the camera body is mounted and the wafer 101 or markers 151A and 152A imaged by the camera by monitoring the z-displacement of the camera's focus.

[0105] In some other embodiments, an alignment camera is mounted to a lateral alignment stage 142. In some of these embodiments, the alignment camera is used to measure the relative distance between the {XNF, YNF, ZNF} coordinate system to which the camera body is mounted and the wafer 101 or the marks 151A and 152A imaged by the camera by monitoring the position of the optical marks mounted on the wafer 101 or the marks 151A and 152A within the field of view of the alignment camera.

[0106] In a further example, the precise incident position of the illumination beam in two dimensions of the plane on the surface of the wafer is determined based on the interaction between the illumination beam and two or more beam-blocking calibration targets.

[0107] Figure 9 is a schematic diagram of a sample positioning system 140, in which a wafer stage is moved to a position where the illumination beam 116 is blocked by a cylindrical pin element 151. The precise incident position of the illumination beam relative to the cylindrical pin 151 is determined based on the transmission flux, measured by the detector 119, which varies according to the X position of the cylindrical pin 151 relative to the illumination beam 116 (e.g., the substrate frame 141). As depicted in Figure 9, as the cylindrical pin 151 moves in the positive X direction (in the XBF direction), more and more of the illumination beam 116 is blocked by the cylindrical pin 151. Therefore, fewer photons reach the detector 119. However, as the cylindrical pin 151 moves in the negative X direction (opposite to XBF), less and less of the illumination beam 116 is blocked by the cylindrical pin 151. The detector 119 generates a signal 155 indicating the measured flux that varies according to the X position, and the result is analyzed to identify the position of the cylindrical pin corresponding to the center of the illumination beam 116.

[0108] Figure 10 depicts a graph 170 illustrating the measured flux as a function of the relative position of a cylindrical pin with respect to the illumination beam 116. The measured flux 155 is plotted as an S-shaped function (e.g., depending on the logic or other error function of the beam profile).

[0109] In some instances, the beam center is determined as the relative position of the cylindrical pin with respect to the illumination beam, where the measured flux falls between the minimum flux value FMIN and the maximum flux value FMAX, or the maximum value of the derivative dF / dx. However, in other instances, the beam center can be determined at a flux value different from the median of the measured flux range. In some instances, a more precise relationship is determined by modeling the interaction between the material and geometry of the beam and the cylindrical pin. In these instances, the modeled interaction is compared with the measured transmission flux, and a fitting algorithm is used to determine the relative position of the cylindrical pin with respect to the illumination beam (its alignment with the beam center) based on the fitting of the measured results to the model.

[0110] In one instance, an estimated distance ΔX between a current position of the cylindrical pin 151 relative to the center of the illumination beam 116 and a position of the cylindrical pin 151 coinciding with the beam center is based on the measured flux FMEAS, the flux midpoint FMID, and the reciprocal of the derivative of the measured flux, which vary according to the position of the cylindrical pin, as described by equation (2) and FMID is described by equation (3).

[0111] The maximum and minimum values ​​of the measured flux can be measured by scanning the wafer stage while measuring the transmission flux. Furthermore, the slope at the midpoint can also be estimated. Based on these quantities, an estimate of the change in the center position of the cylindrical pin can be determined solely by measuring the flux at a location according to equation (2). The change in center position can be repeatedly determined as needed to converge to a single center position.

[0112] Since the beam has a centroidal component in two directions (e.g., the X and Y directions), two cylindrical pins oriented perpendicular to the centroidal component are measured. In the embodiment depicted in FIG9, cylindrical pin 151 is used to position the beam center relative to the stage reference frame in the X direction, and cylindrical pin 152 is used to position the beam center relative to the stage reference frame in the Y direction. Generally, more than two cylindrical pins can be used to create redundancy and increase the accuracy of beam position calibration.

[0113] As depicted in FIG9, the center of the illumination beam 116 is aligned with the edges of the vertically and horizontally oriented cylindrical pins 151 and 152 as described above. In the embodiment depicted in FIG9, a reference mark 151A is positioned coplanar with the central axis of the cylindrical pin 151. Similarly, a reference mark 152A is positioned coplanar with the central axis of the cylindrical pin 152. At the position where the beam center is aligned with the cylindrical pin 151, the position of the illumination beam 116 relative to the cylindrical pin 151 or the reference mark 151A at or near the cylindrical pin is recorded by the alignment camera 154. This registers the relative position of the illumination beam with respect to a precise position in the field of view of the alignment camera (assuming the focus position does not change). As depicted in FIG5, the wafer 101 moves within the field of view of the alignment camera 154. The wafer 101 is moved such that a desired position on the wafer (e.g., a reference mark) is imaged within the field of view of the alignment camera 154. The position of the illumination beam 116 relative to the desired location is determined by the alignment camera 154 based on prior registration. In this way, the position of the illumination beam 116 on the wafer 101 in the X and Y directions is rapidly estimated based on an image collected by the alignment camera 154. In some embodiments, the Z-position of the wafer relative to the cylindrical pin 151 in the Z direction is measured by changing the focus position of the alignment camera 154 until the lithography features on the surface of the wafer 101 are precisely focused. The change in focus position indicates the Z-position difference between the cylindrical pin and the imaging position on the wafer. In some other embodiments, the Z-position of the wafer relative to the cylindrical pin 151 in the Z direction is measured by one or more optical proximity sensors, capacitive proximity sensors, interferometric sensors, or other suitable proximity sensors. Actuators 150A to 150C can be used to reposition wafer 101 in the Z direction to reposition the imaging position in the same plane as the cylindrical pin (e.g., reference mark 151A).

[0114] In a further embodiment, the incident position of the illumination beam is determined at any location on the wafer based on the wafer stage coordinates. Once the center of the illumination beam is aligned with the vertical and horizontal cylindrical pins, and the position of the illumination beam relative to the cylindrical pins is recorded by an alignment camera as described above, the incident position of the illumination beam can be transmitted to the stage coordinates. As depicted in FIG5, the wafer 101 moves within the field of view of the alignment camera 154. The movement of the wafer 101 is measured by a position measurement system (e.g., a linear encoder) of the wafer stage 144. By moving the wafer 101 to three or more desired positions (e.g., a reference mark) on the wafer imaged within the field of view of the alignment camera 154, the position of the illumination beam relative to the desired position and the position of the wafer in the stage coordinates are determined at each desired position. Based on the known position of the illumination beam and the stage coordinates at three or more positions, a mapping is generated that relates the stage coordinates to the incident position of the illumination beam.

[0115] After positioning the cylindrical pin 151 at the center of the illumination beam 116 (in the X direction), the alignment camera 154 images the position of the cylindrical pin itself or a reference mark positioned on or near the cylindrical pin to establish a relationship between the beam position and the image position within the field of view of the alignment camera 154. Since the alignment camera 154 is positioned in a fixed or repeatable position relative to the stage reference frame 143, the image aligns the position of the illumination beam relative to the stage reference frame 143 and thus serves as a reference for the beam position in the X direction. Furthermore, the alignment camera 154 establishes a precise focus position for the reference mark to establish a precise Z position of the cylindrical pin relative to the stage reference frame 143. In embodiments where the alignment camera 154 rotates with the stage reference frame, the focus position of the alignment camera 154 serves as a reference for the Z position of the cylindrical pin relative to the stage reference frame.

[0116] Since the incident position of the beam is estimated using the obstructed flux, there is a risk that changes in the flux in the illumination beam will be interpreted as a positional shift. In some embodiments, the flux of the illumination beam is measured immediately before, after, or simultaneously with the obstruction measurement. Variations in the illumination flux are compensated for in the analysis of the measured flux 155 to eliminate their effects on the measurement.

[0117] In another state, the precise alignment of the illumination beam with the plane of the wafer surface is determined based on the interaction between the illumination beam and two or more beam-blocking calibration targets, such as those measured by the X-ray detector 119.

[0118] To ensure measurement integrity, the incident position of the illumination beam 116 on the surface of the wafer 101 should remain fixed within a large range of incident and azimuth angles during measurement. To achieve this, the rotation axis 153 of the stage reference frame 143 must be substantially coplanar with the surface of the wafer 101 at the measurement position. Furthermore, the rotation axis 153 must be aligned with the illumination beam 116 in the XBF direction such that the rotation axis 153 intersects the illumination beam 116 at the point of incident between the illumination beam 116 and the wafer 101 at the measurement position.

[0119] FIG8A depicts a top view of an illumination beam 116 incident on wafer 101 as depicted in FIG5. FIG8A also depicts an end view of a rotation axis 153 in an aligned state, wherein the rotation axis 153 intersects the illumination beam 116 at position 103 on wafer 101 at the point of incidence of the illumination beam 116 on wafer 101. As depicted in FIG8A, as wafer 101 rotates about rotation axis 153 within a large angle of incidence, the illumination beam 116 remains incident at position 103. Therefore, in this case, the incident position of the illumination beam 116 on the surface of wafer 101 remains fixed within a large angle of incidence during measurement.

[0120] FIG8B depicts a top view of the illumination beam 116 incident on wafer 101 as depicted in FIG5. FIG8B also depicts an end view of the rotation axis 153 in an aligned state, wherein the rotation axis 153 is misaligned from the surface of wafer 101 by a distance ∂z. As depicted in FIG8B, as wafer 101 rotates about rotation axis 153 over a large incident angle θ range, a portion of position 103 is no longer illuminated (i.e., another portion of wafer 101 is illuminated instead). Therefore, in this case, the incident position of illumination beam 116 on the surface of wafer 101 drifts over a large incident angle range during measurement, which is highly undesirable.

[0121] FIG8C depicts a top view of an illumination beam 116 incident on wafer 101 as depicted in FIG5. FIG8C also depicts an end view of a rotation axis 153 in an aligned state, wherein the rotation axis 153 is coplanar with the surface of wafer 101 but offset from the illumination beam 116 by a distance ∂x. As depicted in FIG8C, as wafer 101 rotates about rotation axis 153 within a large incident angle θ range, a portion of position 103 is no longer illuminated (i.e., another portion of wafer 101 is illuminated instead). Therefore, in this case, the incident position of illumination beam 116 on the surface of wafer 101 drifts within a large incident angle range during measurement, which is highly undesirable.

[0122] In some embodiments, the rotation axis of the stage reference frame is calibrated by aligning the center of the illumination beam with the cylindrical pin 151 in the X direction and measuring the flux at a plurality of different rotational positions θ of the stage reference frame. The apparent motion (∆X) of the cylindrical pin in the X direction is determined based on a selected occlusion model as described above (e.g., the S-shaped function depicted in FIG1 or another model). In addition, the apparent motion of the cylindrical pin in the X direction is a function of one of the following: 1) the distance ∂x of the cylindrical pin from the rotation axis in the x direction and the distance ∂z of the cylindrical pin from the rotation axis in the z direction; 2) the distance ∂n of the cylindrical pin from the beam center and the rotation axis 153 in the x direction; and 3) the rotation angle θ around the rotation axis 153 of the stage reference frame. The relationship is described in Equation (4).

[0123] In one instance, the transmitted flux is measured at three incident angles. One of the linear equations described by equation (5) is derived from equation (4).

[0124] Equation (6) is obtained by inverse calculation of equation (5). Equation (6) is used to solve for the values ​​of ∂n, ∂x and ∂z from the apparent motion of the cylindrical pin in the X direction.

[0125] Equations (6) and (3) are combined to solve for the values ​​of ∂n, ∂x, and ∂z from the apparent motion of the cylindrical pin in the X direction, determined by the measured flux. In some instances, the solutions for the values ​​of ∂n, ∂x, and ∂z are obtained iteratively, as described by equation (7). , where (7) where k is the iteration exponent and w is the vector [∂n, ∂x, and ∂z] of the displacement values ​​of the actuators of the sample positioning system 140 required to align the rotation axis 153 and the blade 151 in the X and Z directions. The displacement ∂n is achieved by moving the entire stage reference frame 143 relative to the illumination beam 116 in the X direction by actuator 145. The displacement ∂x is achieved by moving the cylindrical pin 151 back to alignment with the beam by actuator 147. The displacement ∂z is achieved by moving the cylindrical pin in the Z direction using actuators 150A to 150C so that the rotating shaft 153 is aligned with the central axis plane of the cylindrical pin in the Z direction. Starting with an initial estimate w0, the recursion of equation (7) will converge to a point where the rotating shaft 153 is aligned with the cylindrical pin 151.

[0126] Generally speaking, it is not necessary to apply equation (7) precisely. The values ​​of AΘ and ∂X / ∂F can be calculated numerically. In other instances, other matrices can be used, provided that the iteration is stable and converges to the correct value.

[0127] Generally speaking, the transmitted flux can be measured at any three or more different incident angles to determine the displacement values ​​required to align the rotation axis 153 and the cylindrical pin 151 in the X and Z directions. The choice of any three different incident angles results in a linear equation system that can be directly inversely calculated. The choice of four or more different incident angles results in an overdetermined linear equation system that can be solved using a pseudo-inverse algorithm to determine the displacement values ​​required to align the rotation axis 153 and the cylindrical pin 151 in the X and Z directions. The matrix terms shown in equations (5) and (6) depend on the selected incident angles. Therefore, in instances where different incident angles are selected, the terms will differ from those in equations (5) and (6).

[0128] In another embodiment, the precise alignment of the rotation axis 153 with a calibration target (e.g., a mark 151A of the beam-blocking calibration target 151, a mark positioned on the wafer 101, etc.) is determined based on the image of the mark collected by an alignment camera mounted on the lateral alignment stage 142.

[0129] The apparent motion (∆X) of the marker in the X direction within the field of view of the alignment camera is a function of the distance ∂x of the marker from the rotation axis in the x direction, the distance ∂z of the marker from the rotation axis in the z direction, and the rotation angle θ around the rotation axis 153 of the stage reference frame. For an alignment camera mounted to a transverse alignment stage 142, the relationship is described in equation (8).

[0130] In some instances, the X position of a mark (e.g., mark 151A) is measured at any three different incident angles to determine the displacement values ​​required to align the rotation axis 153 and the cylindrical pin 151 in the X and Z directions. The choice of any three different incident angles results in a system of linear equations that can be directly calculated to solve the distance ∂x of the mark from the rotation axis in the x direction and the distance ∂z of the mark from the rotation axis in the z direction.

[0131] For an idealized beam blocking calibration target and rotation axis, having only one beam blocking calibration target for beam calibration would be sufficient. However, depending on the system requirements, multiple beam blocking calibration targets may be needed. By aligning the edges of multiple blocking elements, any deviation of the rotation axis from the nominal YNF axis can be inferred. Moreover, multiple identical blocking elements allow for calibration of an edge from the right and left or top and bottom, thereby helping to eliminate systematic errors in the imaging edges (i.e., those imaged by the aligned camera 154) and inferred from the apparent edges due to changes in the blocked flux.

[0132] In another embodiment, a SAXS metrology system employs at least one periodic calibration target to position an X-ray illumination beam relative to a sample positioning system. Each periodic calibration target comprises one or more spatially defined regions having different periodic structures that diffract the X-ray illumination beam into dissimilar diffraction patterns measurable by one of the SAXS metrology systems described herein. Additionally, each periodic calibration target comprises one or more markers that can be read by an optical microscope to position the periodic calibration targets relative to the sample positioning system with high alignment accuracy (e.g., 0.5 micrometers or less). Each spatially defined region has spatially well-defined boundary lines. The positions of these boundary lines relative to these markers are known to have high accuracy (e.g., 0.2 micrometers or less) in one or more dimensions.

[0133] In some embodiments, the size of each periodic region is designed to be larger than the projection of the illumination beam onto the periodic calibration target. In this way, the beam profile can be characterized by scanning the illumination beam across an interface between two different periodic regions, each sized to be larger than the illumination beam. In some embodiments, the illumination beam 116 has a beam width of less than 200 micrometers. In some embodiments, the illumination beam 116 has a beam width of less than 100 micrometers. In some embodiments, the illumination beam 116 has a beam width of less than 50 micrometers. Additionally, in some instances, calibration measurements are performed at a large incident angle. In these instances, the projection of the illumination beam onto the periodic calibration target is elongated in one direction, and each periodic region is sized to be larger than the projected illumination area.

[0134] In some embodiments, the size of each periodic region depends on the direction relative to the illumination beam. For example, a periodic region may be larger in one direction perpendicular to the rotation axis 153 to accommodate a large incident angle. In another instance, the illumination beam may be larger in one direction than in another (e.g., a rectangular illumination beam shape) and a periodic region may be larger in the elongation direction.

[0135] In some embodiments, one or more of the periodic regions are sized to match the desired measurement box size. In one example, one of the periodic regions is sized to match the illumination beam size (e.g., 50 square micrometers or 100 square micrometers) or some other number used to calibrate the alignment of the rotation axis 153 relative to the illumination beam 116. In this example, perfect alignment is achieved when the illumination beam 116 does not move relative to the periodic calibration target within a large AOI range. In this example, if the illumination beam moves relative to the periodic calibration target as the AOI changes, the illumination beam will move from the periodic region sized to match the illumination beam size to an adjacent periodic region. This movement of the illumination beam across the boundary between regions is detected by detector 119.

[0136] Generally speaking, a set of periodic calibration targets or a group of regions of a periodic calibration target includes regions of different sizes used to characterize the beam profile and size. Generally speaking, one or more regions may be of a predetermined size that is larger than, smaller than or the same as the size of the illumination beam.

[0137] Generally speaking, the periodicity of a periodic calibration target is optimized to enhance X-ray scattering contrast. The spacing between each periodic structure is small enough to ensure sufficient spatial separation of the detected stages at the detector. The angle of each diffraction stage should be significantly greater than the beam divergence to ensure sufficient spatial separation, and the angle of each diffraction stage increases as the spacing decreases. In some embodiments, the spacing between each periodic structure should be about 0.1 micrometers (e.g., less than 200 nanometers) to ensure sufficient spatial separation and measurement accuracy.

[0138] Each periodic structure is made of a material with high contrast to hard X-rays and a large atomic number (e.g., tungsten, tungsten carbide, platinum, etc.).

[0139] In addition, each periodic structure is manufactured to a sufficient height to produce a measurable diffraction pattern within a reasonable exposure time. In some instances, a periodic structure with a height of 0.5 mm or greater is advantageous.

[0140] In some embodiments, any of the periodic calibration targets described herein are mounted to a sample positioning system (such as sample positioning system 140). In some other embodiments, any of the periodic calibration targets described herein are mounted to a calibration wafer or a production wafer to be measured.

[0141] FIG11 provides another illustration of the sample positioning system 140 in more detail. The same numbered elements depicted in FIG11 are similar to those described with reference to FIG5. In the embodiment depicted in FIG11, a periodic calibration target 171 is positioned on wafer 101.

[0142] The periodic calibration target 171 comprises at least one mark and multiple periodic structures (e.g., gratings). If the illumination beam 116 is incident on two or more different diffraction patterns, the ratio of the measured intensities of the levels associated with the different periodic structures provides information about the position of the illumination beam relative to the illuminated patterns. A alignment camera 154 is used to position the mark in the coordinates of the sample positioning system. The position of the mark relative to the periodic structures is known in advance. Therefore, the position of the periodic structures in the coordinates of the sample positioning system can be easily determined by a direct coordinate transformation. The periodic calibration target 171 is scanned across the illumination beam 116 while the detected intensity of the diffraction levels is measured by the detector 119. The center of the illumination beam 116 is precisely positioned relative to the periodic calibration target 171 based on the measured intensity. Since the position of the periodic calibration target 171 in the coordinates of the sample positioning system is known, the position of the center of the illumination beam in the coordinates of the sample positioning system can be precisely located by a simple coordinate transformation.

[0143] In some instances, a periodic calibration target is used to calibrate the incident position of the illumination beam relative to the sample positioning system. In other instances, a periodic calibration target is used to align the rotation axis of the stage reference frame relative to the illumination beam at the incident point of the illumination beam and a wafer. In still other instances, a periodic calibration target is scanned across the illumination beam at a number of azimuth angles. In this way, in addition to calibrating the position of the illumination beam relative to the target, the beam profile is also characterized.

[0144] In some embodiments, a periodic calibration target includes a central periodic region and one or more periodic regions surrounding the central periodic region. Each periodic region includes a different spacing, a different spacing orientation, or a combination thereof.

[0145] Figure 12 depicts one embodiment of a periodic calibration target 210. As depicted in Figure 12, the periodic calibration target 210 includes markers 211 and 212 readable by an optical microscope mounted to a sample positioning system, a small-pitch periodic structure 215 positioned in a central region 214, and a larger-pitch periodic structure 213 in a peripheral region surrounding the central region 214. Markers 211 and 212 are positioned in the same plane as the periodic structure of the periodic calibration target. Furthermore, the positions of markers 211 and 212 relative to the boundary of the central region 214 are precisely known. In this way, the position of the boundary is determined from the position of any one of markers 211 and 212 or both by a simple coordinate transformation.

[0146] Illumination of the central region 214 (i.e., periodic structure 215) by the illumination beam 116 results in multi-level diffraction across the detectors 119 with a relatively large spacing (e.g., 100 micrometers) in the horizontal direction. Illumination of the peripheral region (i.e., periodic structure 213) by the illumination beam 116 results in multi-level diffraction across the detectors 119 with a smaller spacing in the horizontal direction due to the larger spacing of the gratings 213. The intensity ratio between the measured levels of the gratings 215 and 213 indicates the position of the illumination beam 116 relative to the boundary line between the central region 214 and the peripheral region.

[0147] Figure 13 depicts one embodiment of a periodic calibration target 220. As depicted in Figure 13, the periodic calibration target 220 includes markers 221 and 222 readable by an optical microscope mounted to a sample positioning system, a vertically positioned periodic structure 225 located in a central region 224, and a horizontally positioned periodic structure 223 in a peripheral region surrounding the central region 224. Markers 221 and 222 are positioned in the same plane as the periodic structure of the periodic calibration target. Furthermore, the positions of markers 221 and 222 relative to the boundary of the central region 224 are precisely known. In this way, the position of the boundary is determined from the position of either marker 221 or 222, or both, by a simple coordinate transformation.

[0148] Illumination of the central region 224 (i.e., the periodic structure 225) by the illumination beam 116 results in multiple levels of diffraction across the detector 119 in a horizontal direction. Illumination of the peripheral region (i.e., the periodic structure 223) by the illumination beam 116 results in multiple levels of diffraction across the detector 119 in a vertical direction. The intensity ratio between the measured levels of gratings 225 and gratings 223 indicates the position of the illumination beam 116 relative to the boundary line between the central region 224 and the peripheral region.

[0149] Figure 14 depicts one embodiment of a periodic calibration target 230. As depicted in Figure 14, the periodic calibration target 230 includes markers 231 and 232 readable by an optical microscope mounted to a sample positioning system, and a horizontally arranged periodic structure 233 in a peripheral region surrounding a central region 234 that is completely devoid of periodic structure. Markers 231 and 232 are positioned in the same plane as the periodic structure of the periodic calibration target. Furthermore, the positions of markers 231 and 232 relative to the boundary of the central region 234 are precisely known. In this way, the position of the boundary is determined from the position of either marker 231 or 232, or both, by a simple coordinate transformation.

[0150] Illumination of the central region 234 by the illumination beam 116 does not cause diffraction; only the zero order is detected. Illumination of the peripheral region (i.e., the periodic structure 233) by the illumination beam 116 causes multi-order diffraction across the detector 119 in a vertical direction. The intensity ratio between the measured order and the zero order intensity of the grating 233 indicates the position of the illumination beam 116 relative to the boundary line between the central region 234 and the peripheral region.

[0151] In some embodiments, a periodic calibration target comprises any number of periodic regions intersecting at a common point. In this manner, the X-ray illumination beam is aligned with the common point shared by the various periodic regions. Each periodic region comprises a different spacing, a different spacing orientation, or a combination thereof.

[0152] Figure 15 depicts one embodiment of a periodic calibration target 240. As depicted in Figure 15, the periodic calibration target 240 includes markers 241 and 242 readable by an optical microscope mounted to a sample positioning system, and four periodic regions positioned in an orthogonal configuration. As depicted in Figure 15, a vertically positioned periodic structure 243 is positioned in a first quadrant, a horizontally positioned periodic structure 244 is positioned in a second quadrant, a vertically positioned periodic structure 245 is positioned in a third quadrant, and a horizontally positioned periodic structure 246 is positioned in a fourth quadrant. Markers 241 and 242 are positioned in the same plane as the periodic structures of the periodic calibration target. Furthermore, the position of the common point of markers 241 and 242 relative to the center of the orthogonal configuration is precisely known. In this way, the position of the common point is determined from the position of any of markers 241 and 242 or both by a simple coordinate transformation.

[0153] Illumination beam 116 illuminates structures 243 and 245, resulting in multiple levels of diffraction across detector 119 in a horizontal direction. Illumination beam 116 illuminates structures 244 and 246, resulting in multiple levels of diffraction across detector 119 in a vertical direction. The intensity ratio between the measurement levels indicates the position of illumination beam 116 relative to the common point shared by structures 243 to 246.

[0154] Figure 16 depicts one embodiment of a periodic calibration target 250. As depicted in Figure 16, the periodic calibration target 250 includes markers 251 and 252 readable by an optical microscope mounted to a sample positioning system, and four periodic regions positioned in an orthogonal configuration. As depicted in Figure 16, a periodic structure 253 oriented at -45 degrees to the vertical is positioned in a first quadrant, a periodic structure 254 oriented at 45 degrees to the vertical is positioned in a second quadrant, a horizontally positioned periodic structure 255 is positioned in a third quadrant, and a vertically positioned periodic structure 256 is positioned in a fourth quadrant. Markers 251 and 252 are positioned in the same plane as the periodic structures of the periodic calibration target. Furthermore, the position of the common point of markers 251 and 252 relative to the center of the orthogonal configuration is precisely known. In this way, the position of the common point is determined from the position of any of markers 251 and 252 or both by a simple coordinate transformation.

[0155] Illumination beam 116 illuminates structures 253 and 254, resulting in multi-level diffraction across detector 119 at +45 degrees and -45 degrees respectively. Illumination beam 116 illuminates structures 255 and 256, resulting in multi-level diffraction across detector 119 in a vertical and horizontal direction respectively. The intensity ratio between the measurement levels indicates the position of illumination beam 116 relative to the common point shared by structures 253 to 256.

[0156] Figure 17 depicts one embodiment of a periodic calibration target 260. As depicted in Figure 17, the periodic calibration target 260 includes markers 261 and 262 that can be read by an optical microscope mounted to a sample positioning system, and four periodic regions positioned in an orthogonal configuration. As depicted in Figure 17, a vertically positioned periodic structure 263 with relatively small spacing is positioned in a first quadrant, a horizontally positioned periodic structure 264 with relatively large spacing is positioned in a second quadrant, a vertically positioned periodic structure 265 with relatively large spacing is positioned in a third quadrant, and a horizontally positioned periodic structure 266 with relatively small spacing is positioned in a fourth quadrant. Markers 261 and 262 are positioned in the same plane as the periodic structures of the periodic calibration target. Furthermore, the positions of markers 261 and 262 relative to the common point at the center of the orthogonal configuration are precisely known. In this way, the position of the common point can be determined from the position of any of the markers 261 and 262 or both by a simple coordinate transformation.

[0157] Illumination beam 116 illuminates structures 263 and 265, resulting in multiple levels of diffraction across detector 119 in a horizontal direction. Illumination beam 116 illuminates structures 264 and 266, resulting in multiple levels of diffraction across detector 119 in a vertical direction. The levels associated with structures 263 and 266 and the levels associated with structures 264 and 265 are separately spaced. The intensity ratio between the levels indicates the position of illumination beam 116 relative to a common point shared by structures 263 to 266.

[0158] Figure 18 depicts one embodiment of a periodic calibration target 270. As depicted in Figure 18, the periodic calibration target 270 includes markers 271 and 272 readable by an optical microscope mounted to a sample positioning system, and four periodic regions positioned in an orthogonal configuration. As depicted in Figure 18, a vertically positioned periodic structure 273 with relatively small spacing is positioned in a first quadrant, a horizontally positioned periodic structure 274 with relatively large spacing is positioned in a second quadrant, a vertically positioned periodic structure 275 with relatively small spacing is positioned in a third quadrant, and a horizontally positioned periodic structure 276 with relatively large spacing is positioned in a fourth quadrant. Markers 271 and 272 are positioned in the same plane as the periodic structures of the periodic calibration target. Furthermore, the positions of markers 271 and 272 relative to the common point at the center of the orthogonal configuration are precisely known. In this way, the position of the common point can be determined from the position of any of the markers 271 and 272 or both by a simple coordinate transformation.

[0159] Illumination beam 116 illuminates structures 273 and 275, resulting in multiple levels of diffraction across detector 119 in a horizontal direction. Illumination beam 116 illuminates structures 274 and 276, resulting in multiple levels of diffraction across detector 119 in a vertical direction. The levels associated with structures 273 and 275 and the levels associated with structures 274 and 276 are separately spaced. The intensity ratio between the diffraction levels is measured to indicate the position of illumination beam 116 relative to a common point shared by structures 273 to 276.

[0160] Figures 19A and 19B depict a set of periodic calibration targets 290 and 295, each adapted to position an illumination beam relative to the periodic calibration target in one direction. When both targets 290 and 295 are used to calibrate a SAXS metrology system, the position of the illumination beam relative to the sample positioning system is determined in two orthogonal dimensions. As depicted in Figure 19A, the periodic calibration target 290 includes markers 291 and 292 that can be read by an optical microscope mounted to the sample positioning system, and two periodic regions positioned adjacent to each other along a boundary line. As depicted in Figure 19A, a horizontally positioned periodic structure 293 is positioned alongside a vertically positioned periodic structure 294. Markers 291 and 292 are positioned in the same plane as the periodic structures of the periodic calibration targets. Furthermore, the positions of markers 291 and 292 relative to the boundary between structures 293 and 294 are precisely known. In this way, the position of the boundary line can be determined from the position of either or both of the marks 291 and 292 by a simple coordinate transformation.

[0161] The illumination beam 116 illuminates structures 293 and 294, resulting in multiple levels of diffraction across detector 119 in both a vertical and horizontal direction. The intensity ratio between the measurement levels indicates the position of the illumination beam 116 relative to the boundary line shared by structures 293 and 294.

[0162] Similarly, as depicted in FIG19B, the periodic calibration target 295 includes markers 296 and 297 that can be read by an optical microscope mounted to a sample positioning system, and two periodic regions positioned adjacent to each other along a boundary line. As depicted in FIG19B, the boundary line of target 295 is orthogonal to the boundary line of target 290. As depicted in FIG19B, a horizontally positioned periodic structure 298 is positioned alongside a vertically positioned periodic structure 299. Markers 296 and 297 are positioned in the same plane as the periodic structures of the periodic calibration target. Furthermore, the positions of markers 296 and 297 relative to the boundary between structures 298 and 299 are precisely known. In this way, the position of the boundary line is determined from the position of either marker 296 and 297 or both by a simple coordinate transformation.

[0163] The illumination beam 116 illuminates structures 298 and 299, resulting in multiple levels of diffraction across detector 119 in both a vertical and horizontal direction. The intensity ratio between the measurement levels indicates the position of the illumination beam 116 relative to the boundary line shared by structures 298 and 299.

[0164] Generally speaking, a periodic calibration target may comprise multiple different periodic regions in any suitable configuration. In some embodiments, the periodic regions are configured as a Cartesian pattern. However, other patterns of periodic regions are conceivable.

[0165] Figure 20 depicts a periodic calibration target 280 comprising markers 288 and 289 and one of seven different periodic regions 281 to 287 arranged in a hexagonal pattern. Each periodic region comprises a different spacing, a different spacing orientation, or a combination thereof.

[0166] In another embodiment, the shape of the wafer surface in the Z direction is mapped using a aligning camera, an optical proximity sensor, a capacitive proximity sensor, an interferometric sensor, or any other suitable proximity sensor. In some instances, the wafer surface is mapped onto the front side (i.e., the patterned side) of the wafer. In some other instances, if the wafer thickness is sufficiently uniform, well-modeled, or measured in situ or pre-measured, the wafer surface is mapped onto the back side (i.e., the unpatterned side) of the wafer. In some embodiments, a back-side sensor is used to measure wafer warpage because many sensor techniques are available for accurately measuring the location of the unpatterned surface. In some of these embodiments, only a back-side sensor is used to measure wafer warpage across the back side of the wafer and wafer warpage across the front side is estimated based on a thickness model or thickness mapping generated by a pre-performed thickness measurement. In some other embodiments, both a back-side sensor and a front-side sensor are used to measure wafer warpage. In some of these embodiments, a back-side sensor is used to measure wafer warpage across the back side of the wafer, and a thickness model or thickness mapping is used to estimate wafer warpage across the front side based on wafer thickness estimates derived at least partially from front and back-side measurements. In some instances, several standard interpolators (e.g., polynomial basis functions, rational functions, neural networks, etc.) are used to model the wafer map. Furthermore, an analytical or numerical bending model of the wafer can be used to couple lateral and height displacements.

[0167] In a further embodiment, Z-actuators 150A to 150C are controlled to adjust the Z-position, Rx orientation, Ry orientation, or any combination thereof in response to the shape of the wafer surface at the incident position of the illumination beam 116. In one example, wafer tilt is corrected by Z-actuators 150A to 150C. Tilt correction may be based on a wafer tilt map or a tilt value measured locally. This can also be achieved using an optically based tilt sensor that monitors Rx orientation and Ry orientation (i.e., flip and tilt) at the back surface of the wafer.

[0168] In another further embodiment, Z actuators 150A to 150C are controlled to adjust the Z position, Rx orientation, Ry orientation, or any combination thereof to align the rotation axis in the azimuth angle with the stage reference frame 143. In one example, Z actuators 150A to 150C are adjusted such that a specific target is held in focus of the alignment camera 154 within an azimuth angle range. To perform this calibration, the wafer stage translates the wafer 101 in the X and Y directions to maintain the target in the field of view of the alignment camera 154 for all azimuth angles.

[0169] Generally speaking, it is impossible to calibrate all offset effects. Usually, the calibration used to remove the largest deviation is selected and the remaining offsets are ignored or handled by the stage pattern that addresses the non-idealities in the wafer and stage.

[0170] In addition, changes in temperature and air pressure or any other ambient conditions can have an impact on the positioning of the illumination beam. In some embodiments, beam motion is correlated with these variables and the beam position is adjusted based on measured temperature and pressure and related models.

[0171] Generally speaking, the sample positioning system 140 may include any suitable combination of mechanical elements to achieve the desired linear and angular positioning performance, including (but not limited to) a goniometer stage, a hexagonal stage, an angular stage and a linear stage.

[0172] In some embodiments, the x-ray illumination source 110, focusing optics 111, slits 112 and 113, or any combination thereof, are maintained in the same atmospheric environment (e.g., a purged environment) as the sample 101. However, in some embodiments, the optical path lengths between and within any of these elements are long, and x-ray scattering in the air causes noise on the image on the detector. Therefore, in some embodiments, any one of the x-ray illumination source 110, focusing optics 111, and slits 112 and 113 is maintained in a localized vacuum environment. In the embodiment depicted in FIG1, focusing optics 111, slits 112 and 113, and beam-shaping slit mechanism 120 are maintained in a controlled environment (e.g., a vacuum) within a evacuated flight tube 118. The illumination beam 116 passes through a window 121 at the end of the flight tube 118 before incident on the sample 101.

[0173] In some embodiments, the x-ray illumination source 110, the focusing optics 111, and any of the slits 112 and 113 are maintained in a localized vacuum environment that is separated from each other and from the sample (e.g., sample 101) by vacuum windows. Figure 21 is a diagram illustrating a vacuum chamber 160 containing the x-ray illumination source 110, a vacuum chamber 162 containing the focusing optics 111, and a vacuum chamber 163 containing the slits 112 and 113. The openings of each vacuum chamber are covered by vacuum windows. For example, the opening of vacuum chamber 160 is covered by vacuum window 161. Similarly, the opening of vacuum chamber 163 is covered by vacuum window 164. The vacuum windows can be constructed of any suitable material that is substantially transparent to x-ray radiation (e.g., polyimide, beryllium, etc.). A suitable vacuum environment is maintained within each vacuum chamber to minimize scattering of the illumination beam. A suitable vacuum environment may include any suitable vacuum level, any suitable purging environment (containing a gas with a low atomic number (e.g., helium)), or any combination thereof. In this way, as many illumination beam paths as possible are positioned in a vacuum to maximize flux and minimize scattering.

[0174] Similarly, in some embodiments, the optical path (i.e., the beam-collecting path) between sample 101 and detector 119 is long, and X-ray scattering in the air causes noise on the image on the detector. Therefore, in a preferred embodiment, a significant portion of the beam-collecting path length between sample 101 and detector 119 is maintained in a localized vacuum environment separated from the sample (e.g., sample 101) by a vacuum window (e.g., vacuum window 124). In some embodiments, the X-ray detector 119 is maintained in a localized vacuum environment with the same beam path length as between sample 101 and detector 119. For example, as depicted in Figures 1 and 21, vacuum chamber 123 maintains a localized vacuum environment surrounding detector 119 and a significant portion of the beam path length between sample and detector 119.

[0175] In some other embodiments, the X-ray detector 119 is maintained in the same atmospheric environment (e.g., a gas-purged environment) as the sample 101. This can be advantageous for removing heat from the detector 119. However, in these embodiments, it may be preferable to maintain a significant portion of the beam path length between the sample 101 and the detector 119 in a localized vacuum environment within a vacuum chamber.

[0176] In some embodiments, the entire optical system (including sample 101) is maintained in a vacuum. However, generally speaking, the cost associated with maintaining sample 101 in a vacuum is high due to the complexity associated with the construction of sample positioning system 140.

[0177] In another further embodiment, the beam-shaping slit mechanism 120 is mechanically integrated with the vacuum chamber 163 to minimize the beam path length exposed to the atmospheric environment. Generally, it is desirable to encapsulate as much of the beam as possible in a vacuum before the beam is incident on the sample 101. In some embodiments, the vacuum beamline extends into a hollow, cylindrical cavity at the input of the beam-shaping slit mechanism 120. The vacuum window 164 is positioned at the output of the vacuum chamber 163 within the beam-shaping slit mechanism 120 such that the incoming beam 115 is held in a vacuum within a portion of the beam-shaping slit mechanism 120 and then passes through the vacuum window 164 before interacting with any of the slits 126 to 129 and the sample 101.

[0178] In another further embodiment, the computing system 130 is configured to: generate a structural model (e.g., a geometric model, a material model, or a combination of geometric and material models) of a measured structure of a sample; generate a T-SAXS response model from the structural model that includes at least one geometric parameter; and resolve at least one sample parameter value by performing a fitting analysis of the T-SAXS measurement data using the T-SAXS response model. An analysis engine is used to compare the simulated T-SAXS signal with the measured data, thereby allowing for the determination of the sample's geometry and material properties (such as electron density). In the embodiment depicted in Figure 1, the computing system 130 is configured as a model building and analysis engine, configured to implement model building and analysis functionality as described herein.

[0179] Figure 22 is a diagram illustrating an exemplary model building and analysis engine 180 implemented by the computing system 130. As depicted in Figure 22, the model building and analysis engine 180 includes a structural model building module 181 that generates a structural model 182 of a measured structure of a sample. In some embodiments, the structural model 182 also includes the material properties of the sample. The structural model 182 is received as input to the T-SAXS response function building module 183. The T-SAXS response function building module 183 generates a T-SAXS response function model 184 based at least in part on the structural model 182. In some instances, the T-SAXS response function model 184 is based on the x-ray shape factor, where F is the shape factor, q is the scattering vector, and ρ(r) is the electron density of the sample in spherical coordinates. The x-ray scattering intensity is then given by the following equation. The T-SAXS response function model 184 is received as input to the fitting analysis module 185. The fitting analysis module 185 compares the modeled T-SAXS response with the corresponding measured data to determine the geometry and material properties of the sample.

[0180] In some instances, the model data is fitted to the experimental data by minimizing the chi-square value. For example, for T-SAXS measurements, the chi-square value can be defined as:

[0181] wherein, is the measured T-SAXS signal 126 in "channel" j, where the exponent j describes a set of system parameters, such as diffraction level, energy, angular coordinates, etc. is the modeled T-SAXS signal Sj of "channel" j evaluated for a set of structural (target) parameters, where these parameters describe geometry (CD, sidewall angles, overlap, etc.) and material (electron density, etc.). is the uncertainty associated with the j-th channel. NSAXS is the total number of channels in X-ray metrology. L is the number of parameters characterizing the metrological target.

[0182] Equation (11) assumes that the uncertainties associated with different channels are uncorrelated. In instances where the uncertainties associated with different channels are correlated, the covariance between the uncertainties can be calculated. In such instances, one chi-square value used for T-SAXS measurement can be expressed as

[0183] where VSAXS is the covariance matrix of the uncertainty of the SAXS channel, and T represents the transpose.

[0184] In some instances, the fitting analysis module 185 resolves at least one sample parameter value by performing a fitting analysis on the T-SAXS measurement data 135 using the T-SAXS response model 184. In some instances, optimization is performed.

[0185] As described above, T-SAXS data fitting is achieved by minimizing the chi-square value. However, generally speaking, T-SAXS data fitting can be achieved using other functions.

[0186] Fitting T-SAXS metrological data is advantageous for any type of T-SAXS technique that provides sensitivity to the geometric and / or material parameters of interest. As long as an appropriate model describing the interaction between the T-SAXS beam and the sample is used, the sample parameters can be deterministic (e.g., CD, SWA, etc.) or statistical (e.g., root mean square height of sidewall roughness, roughness correlation length, etc.).

[0187] The computing system 130 is configured to access model parameters in real-time using Real-Time Critical Dimension (RTCD), or to access a pre-computed model library to determine one of the values ​​of at least one sample parameter associated with sample 101. Generally, some form of CD engine can be used to evaluate the difference between the assigned CD parameters of a sample and the CD parameters associated with the measured sample. An exemplary method and system for computing sample parameter values ​​is described in U.S. Patent No. 7,826,071, issued to KLA-Tencor Corp. on November 2, 2010, the entire contents of which are incorporated herein by reference.

[0188] In some instances, the model building and analysis engine 180 improves the accuracy of measured parameters through any combination of feed sideways analysis, feedforward analysis, and parallel analysis. Feed sideways analysis refers to acquiring multiple datasets from different regions of the same sample and transferring common parameters determined from the first dataset to the second dataset for analysis. Feedforward analysis refers to acquiring datasets from different samples and using a progressively replicating accurate parameter feedforward method to forward common parameters to subsequent analyses. Parallel analysis refers to applying a nonlinear fitting method in parallel or simultaneously to multiple datasets, wherein at least one common parameter is coupled during fitting.

[0189] Multi-tool and structural analysis refers to one of the following: feedforward, side-feedback, or parallel analysis based on regression, a lookup table (i.e., "library" matching), or another fitting procedure for multiple datasets. An exemplary method and system for multi-tool and structural analysis is described in U.S. Patent No. 7,478,019, issued to KLA-Tencor Corp. on January 13, 2009, the entire contents of which are incorporated herein by reference.

[0190] In another further embodiment, an initial estimate of one or more parameters of interest is determined based on a T-SAXS measurement performed in a single orientation relative to an incident X-ray beam relative to the measurement target. This initial estimate is implemented as a starting value for the parameter of interest regressed using a measurement model based on measurement data collected from multiple orientation T-SAXS measurements. In this way, a close estimate of one parameter of interest is determined with a relatively small computational workload, and a refined estimate of the parameter of interest is obtained with a smaller overall computational workload by implementing this close estimate as a starting point for a regression within a much larger dataset.

[0191] In another embodiment, the measuring instrument 100 includes a computing system (e.g., computing system 130) configured to implement beam control functionality as described herein. In the embodiment depicted in FIG1, computing system 130 is configured as a beam controller operable to control any of the illumination properties, such as the intensity, divergence, dot size, polarization, spectrum, and positioning of the incident illumination beam 116.

[0192] As illustrated in Figure 1, the computing system 130 is communicatively coupled to the detector 119. The computing system 130 is configured to receive measurement data 135 from the detector 119. In one example, the measurement data 135 includes an indication of the measured response of the sample (i.e., the intensity of the diffraction order). Based on the distribution of the measured response on the surface of the detector 119, the computing system 130 determines the position and area of ​​the illumination beam 116 incident on the sample 101. In one example, the computing system 130 applies pattern recognition technology to determine the position and area of ​​the illumination beam 116 incident on the sample 101 based on the measurement data 135. In some examples, the computing system 130 transmits a command signal 137 to the X-ray illumination source 110 to select the desired illumination wavelength. In some instances, the computing system 130 transmits a command signal 138 to the actuator subsystem 111' to reorient the X-ray emission relative to the substrate frame 141 to achieve a desired beam direction. In some instances, the computing system 130 transmits a command signal 136 to the beam-shaping slit mechanism 120 to change the beam spot size, such that the incident illumination beam 116 reaches the sample 101 according to the desired beam spot size and orientation. In one instance, the command signal 136 causes the rotary actuator 122 depicted in FIG. 5 to rotate the beam-shaping slit mechanism 120 to one of the desired orientations relative to the sample 101. In another instance, the command signal 136 causes the actuators associated with each of the slits 126 to 129 to change position to reshape the incident beam 116 into a desired shape and size. In some other instances, the computing system 130 transmits a command signal to the wafer positioning system 140 to position and orient the sample 101 so that the incident illumination beam 116 reaches the desired position and angle relative to the sample 101.

[0193] In a further sample, T-SAXS measurement data is used to generate an image of a measured structure based on the measured intensity of the detected diffraction order. In some embodiments, a T-SAXS response function model is generalized to describe scattering from a generalized electron density grid. This model is matched to the measured signal, while constraining the modeled electron density in the grid to implement continuity and sparse edges to provide a three-dimensional image of the sample.

[0194] Although model-based geometric parameter inversion is better for critical size (CD) metrology based on T-SAXS measurements, a sample plot generated from T-SAXS measurement data can be used to identify and correct model errors when the measured sample deviates from the assumptions of the geometric model.

[0195] In some instances, structural characteristics are compared between images and geometric parameter inversion estimates based on a model derived from the same scattering measurement data. The differences are used to update the geometric model of the measured structure and improve measurement performance. The ability to converge to an accurate parametric measurement model is particularly important when measuring integrated circuits for processes such as control, monitoring, and fault finding.

[0196] In some instances, a two-dimensional (2-D) plot of electron density, absorptivity, complex refractive index, or a combination of such material properties is generated. In some instances, a three-dimensional (3-D) plot of electron density, absorptivity, complex refractive index, or a combination of such material properties is generated. The plot is generated using relatively few entity constraints. In some instances, one or more parameters of interest, such as critical size (CD), sidewall angle (SWA), overlap, edge placement error, pitch walk, etc., are directly estimated from the resulting plot. In some other instances, the plot can be used to debug wafer procedures when the sample geometry or material deviates from the expected values ​​envisioned by a parametric structural model used for model-based CD measurements. In one instance, the difference between the plot and the evolution of the structure predicted by the parametric structural model based on its measured parameters is used to update the parametric structural model and improve its measurement performance. Further details are described in U.S. Patent Publication No. 2015 / 0300965, the contents of which are incorporated herein by reference in their entirety. Additional details are described in U.S. Patent Publication No. 2015 / 0117610, the contents of which are incorporated herein by reference in their entirety.

[0197] In a further example, a model building and analysis engine 180 is used to generate a model that combines X-ray and optical measurement analysis. In some instances, the optical simulation is based on, for example, rigorous coupled-wave analysis (RCWA), in which Maxwell's equation is solved to calculate optical signals, such as reflectivity, ellipsoid parameters, and phase changes for different polarizations.

[0198] The values ​​of one or more parameters of interest are determined by a combination fitting analysis of the detected intensities and detected optical intensities of X-ray diffraction orders at multiple different incident angles using a combined geometrically parametric response model. The optical intensity is measured by an optical metrology instrument that may or may not be mechanically integrated with an X-ray metrology system (such as system 100 depicted in Figure 1). Further details are described in U.S. Patent Publication No. 2014 / 0019097 and U.S. Patent Publication No. 2013 / 0304424, the contents of which are incorporated herein by reference in their entirety.

[0199] Generally speaking, a metrology target is characterized by an aspect ratio defined as a maximum height dimension (i.e., the dimension normal to the wafer surface) divided by a maximum lateral dimension (i.e., the dimension aligned with the wafer surface). In some embodiments, the metrology target to be measured has an aspect ratio of at least 20. In some embodiments, the metrology target has an aspect ratio of at least 40.

[0200] It should be understood that the various steps described throughout this invention can be performed by a single computer system 130 or alternatively by multiple computer systems 130. Furthermore, different subsystems of system 100 (such as sample positioning system 140) may include computer systems suitable for performing at least a portion of the steps described herein. Therefore, the foregoing description should not be construed as a limitation of the invention, but merely as an illustration. Additionally, one or more computing systems 130 may be configured to perform any (or several) other steps of any method embodiment described herein.

[0201] Additionally, the computer system 130 can be communicatively coupled to the x-ray illumination source 110, the beam shaping slit mechanism 120, the sample positioning system 140, and the detector 119 in any manner known in the art. For example, one or more computing computers 130 can be coupled to computing systems associated with the x-ray illumination source 110, the beam shaping slit mechanism 120, the sample positioning system 140, and the detector 119, respectively. In another embodiment, any one of the x-ray illumination source 110, the beam shaping slit mechanism 120, the sample positioning system 140, and the detector 119 can be directly controlled by a single computer system coupled to the computer system 130.

[0202] The computer system 130 can be configured to receive and / or acquire data or information from subsystems of the system (e.g., X-ray illumination source 110, beam shaping slit mechanism 120, sample positioning system 140, detector 119, and the like) via a transmission medium that may include wired and / or wireless components. In this manner, the transmission medium can serve as a data link between the computer system 130 and other subsystems of the system 100.

[0203] The computer system 130 of the metrology system 100 can be configured to receive and / or retrieve data or information (e.g., measurement results, modeling inputs, modeling results, etc.) from other systems via a transmission medium that may include wired and / or wireless components. In this way, the transmission medium can act as a data link between the computer system 130 and other systems (e.g., the metrology system 100 on a memory board, external memory, or an external system). For example, the computing system 130 can be configured to receive measurement data (e.g., signal 135) from a storage medium (i.e., memory 132 or 187) via a data link. For example, spectral results obtained using detector 119 can be stored in a permanent or semi-permanent memory device (e.g., memory 132 or 187). In this regard, measurement results can be imported from on-board memory or from an external memory system. Furthermore, the computer system 130 can send data to other systems via a transmission medium. For example, the sample parameter value 186 determined by the computer system 130 can be stored in a permanent or semi-permanent memory device (e.g., memory 187). In this respect, the measurement results can be exported to another system.

[0204] The computing system 130 may include (but is not limited to) a personal computer system, a mainframe computer system, a workstation, a video computer, a parallel processor, or any other device known in the art. Generally speaking, the term "computing system" can be broadly defined to encompass any device having one or more processors that execute instructions from a memory medium.

[0205] Program instructions 134 implementing methods such as those described herein can be transmitted via a transmission medium such as a wire, cable, or wireless transmission link. For example, as illustrated in FIG1, program instructions stored in memory 132 are transmitted to processor 131 via bus 133. Program instructions 134 are stored in a computer-readable medium (e.g., memory 132). Exemplary computer-readable media include read-only memory, random access memory, a magnetic disk or optical disk, or a magnetic tape.

[0206] Figure 23 illustrates a method 300 suitable for implementation by the metrology system 100 of the present invention. In one embodiment, it should be understood that the data processing blocks of method 300 can be implemented via a pre-programmed algorithm executed by one or more processors of the computing system 130. Although the following description is presented in the background of metrology system 100, it should be understood herein that the specific structural embodiment of metrology system 100 is not intended to be limiting and should be interpreted only as illustrative.

[0207] In block 301, an X-ray illumination beam is generated by an X-ray illumination subsystem.

[0208] In block 302, a sample is positioned relative to the X-ray illumination beam such that the X-ray illumination beam is incident on the surface of the sample at any position on the surface of the sample.

[0209] In block 303, the sample is rotated about a rotation axis relative to the X-ray illumination beam, such that the X-ray illumination beam is incident on the surface of the sample at any position at a plurality of incident angles.

[0210] In block 304, the sample is rotated about an azimuth rotation axis so that the X-ray illumination beam is incident on the surface of the sample at any position according to a plurality of azimuth angles.

[0211] In block 305, an X-ray illumination beam is used to illuminate a calibration target. The calibration target contains one or more markings.

[0212] In block 306, a quantity of transmission flux is detected within a position range of one of the sample positioning systems, wherein at least a portion of the X-ray illumination beam is incident on the calibration target within the position range.

[0213] In block 307, the incident position of one of the X-ray illumination beams is determined relative to the sample positioning system based on the detected transmission flux.

[0214] In some embodiments, a scattering measurement as described herein is implemented as part of a process tool. Examples of process tools include (but are not limited to) lithography tools, film deposition tools, implantation tools, and etching tools. In this manner, the results of a T-SAXS analysis are used to control a process. In one example, T-SAXS measurement data collected from one or more targets are sent to a process tool. The T-SAXS measurement data are analyzed as described herein, and the results are used to adjust the operation of the process tool.

[0215] Scattering measurements as described herein can be used to determine the characteristics of various semiconductor structures. Exemplary structures include (but are not limited to) FinFETs, low-dimensional structures (such as nanowires or graphene), sub-10 nm structures, lithography structures, through-substrate vias (TSVs), and memory structures (such as DRAM, DRAM 4F2, FLASH, MRAM, and high aspect ratio memory structures). Exemplary structural characteristics include (but are not limited to) geometric parameters (such as line edge roughness, linewidth roughness, aperture size, aperture density, sidewall angles, profile, critical dimensions, spacing, thickness, and stacking) and material parameters (such as electron density, composition, grain structure, morphology, stress, strain, and element identification). In some embodiments, the metrological target is a periodic structure. In some other embodiments, the metrological target is non-periodic.

[0216] In some instances, the T-SAXS measurement system as described herein is used to perform measurements of critical dimensions, thickness, stack-up, and material properties of high aspect ratio semiconductor structures (including, but not limited to, spin-transfer torque random access memory (STTT-RAM), three-dimensional NAND memory (3D-NAND) or vertical NAND memory (V-NAND), dynamic random access memory (DRAM), three-dimensional FLASH memory (3D-FLASH), resistive random access memory (Re-RAM), and phase-change random access memory (PC-RAM)).

[0217] As described herein, the term "critical dimension" includes any critical dimension of a structure (e.g., bottom critical dimension, middle critical dimension, top critical dimension, sidewall angle, grating height, etc.), any critical dimension between any two or more structures (e.g., distance between two structures), and any displacement between two or more structures (e.g., overlap displacement between stacked grating structures, etc.). Structures may include three-dimensional structures, patterned structures, stacked structures, etc.

[0218] As described herein, the terms “critical size application” or “critical size measurement application” include any critical size measurement.

[0219] As described herein, the term "metrology system" includes at least a portion of any system employed to characterize a sample in any state, including critical size applications and stack-up metrology applications. However, these technical terms do not limit the scope of the term "metrology system" as described herein. Furthermore, the metrology systems described herein can be configured to measure patterned wafers and / or unpatterned wafers. A metrology system can be configured as an LED inspection tool, an edge inspection tool, a backside inspection tool, a macro inspection tool, or a multi-mode inspection tool (involving data from one or more platforms simultaneously), and any other metrology or inspection tool that benefits from the measurement techniques described herein.

[0220] Embodiments are described herein with respect to a semiconductor processing system (e.g., an inspection system or a lithography system) that can be used to process a sample. The term "sample" is used herein to refer to a wafer, a photomask, or any other sample that can be processed (e.g., printed or inspected for defects) by means of components known in this art.

[0221] As used herein, the term "wafer" generally refers to a substrate formed of a semiconductor or non-semiconductor material. Examples include (but are not limited to) single-crystal silicon, gallium arsenide, and indium phosphide. These substrates are typically found and / or processed in semiconductor manufacturing plants. In some cases, a wafer may consist only of a substrate (i.e., a bare wafer). Alternatively, a wafer may contain one or more different material layers formed on a substrate. The one or more layers formed on a wafer may be "patterned" or "unpatterned." For example, a wafer may contain a plurality of dies having repeatable pattern features.

[0222] A "reduced photomask" may be a reduced photomask at any stage of a reduced photomask manufacturing process, or a completed reduced photomask that may or may not be released for use in a semiconductor manufacturing plant. A reduced photomask or a "mask" is generally defined as a substantially transparent substrate having substantially opaque areas formed thereon in a pattern configuration. The substrate may comprise, for example, a glass material, such as amorphous SiO2. A reduced photomask may be placed over a photoresist-coated wafer during an exposure step in a lithography process, such that the pattern on the reduced photomask can be transferred to the photoresist.

[0223] One or more layers formed on a wafer may be patterned or unpatterned. For example, a wafer may contain a plurality of grains, each having repeatable pattern features. The formation and processing of these material layers can ultimately result in a completed device. Many different types of devices can be formed on a wafer, and the term wafer, as used herein, is intended to encompass a wafer on which any type of device known in this art is manufactured.

[0224] In one or more exemplary embodiments, the described functionality may be implemented in hardware, software, firmware, or any combination thereof. If implemented in software, the functionality may be stored as one or more instructions or program code on or transmitted via a computer-readable medium. A computer-readable medium includes both computer storage media and communication media, including any media that facilitates the transfer of a computer program from one location to another. A storage medium may be any available medium accessible by a general-purpose computer or a special-purpose computer. For example (and not limitingly), such a computer-readable medium may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to carry or store desired program code components in the form of instructions or data structures and is accessible by a general-purpose computer or a special-purpose computer or a general-purpose or special-purpose processor. Furthermore, any connection may be appropriately referred to as a computer-readable medium. For example, if software is transmitted from a website, server, or other remote source using a coaxial cable, fiber optic cable, twisted pair, digital subscriber line (DSL), or wireless technology (such as infrared, radio, and microwave), then the coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technology (such as infrared, radio, and microwave) are included in the definition of media. As used herein, magnetic disks and optical disks include optical discs (CDs), laser discs, XRF discs, digital versatile discs (DVDs), floppy disks, and Blu-ray discs, wherein magnetic disks typically reproduce data magnetically while optical discs reproduce data optically using lasers. The above combinations should also be included within the scope of computer-readable media.

[0225] Although certain specific embodiments have been described above for guiding purposes, the teachings of this patent document are generally applicable and not limited to the specific embodiments described above. Therefore, various modifications, adaptations, and combinations of the various features of the described embodiments can be practiced without departing from the scope of the invention as set forth in the claims. [Simplified Explanation of the Diagram]

[0030] Figure 1 is a diagram illustrating a metrology system 100 configured to perform calibration of various system parameters according to the methods described herein.

[0031] Figure 2 depicts an end view of a beam shaping slit mechanism 120 in a configuration.

[0032] Figure 3 depicts an end view of the beam shaping slit mechanism 120 in another configuration.

[0033] Figure 4 depicts an X-ray illumination beam 116 incident on wafer 101 in a specific orientation, described by angles ϕ and θ.

[0034] Figure 5 is a diagram of a sample positioning system 140, wherein the wafer stage is moved to a position where the illumination beam 116 is incident on the wafer 101.

[0035] Figure 6 is a diagram of a sample positioning system 140 with additional details.

[0036] Figure 7 depicts a beam blocking calibration target 190 in one embodiment.

[0037] FIG8A depicts a top view of an illumination beam 116 incident on wafer 101 as depicted in FIG5, wherein the rotation axis 153 intersects the illumination beam 116 at the point of incidence of the illumination beam 116 and wafer 101.

[0038] FIG8B depicts a top view of an illumination beam 116 incident on wafer 101 as depicted in FIG5, wherein the rotation axis 153 is misaligned with the surface of wafer 101 in the Z direction.

[0039] FIG8C depicts a top view of an illumination beam 116 incident on wafer 101 as depicted in FIG5, wherein the rotation axis 153 is offset from the illumination beam 116 in the X direction.

[0040] Figure 9 is a diagram of a sample positioning system 140, in which the wafer stage is moved to a position where the illumination beam 116 is blocked by a cylindrical pin element 151.

[0041] Figure 10 depicts a curve 170 showing the measured flux as a function of the relative position of a cylindrical pin with respect to the illumination beam 116.

[0042] Figure 11 depicts another illustration of a sample positioning system 140 including a periodic calibration target 171 positioned on wafer 101.

[0043] Figure 12 depicts one embodiment of a periodic calibration target 210.

[0044] Figure 13 depicts one embodiment of a periodic calibration target 220.

[0045] Figure 14 depicts one embodiment of a periodic calibration target 230.

[0046] Figure 15 depicts one embodiment of a periodic calibration target 240.

[0047] Figure 16 depicts one embodiment of a periodic calibration target 250.

[0048] Figure 17 depicts one embodiment of a periodic calibration target 260.

[0049] Figure 18 depicts one embodiment of a periodic calibration target 270.

[0050] Figures 19A to 19B depict a set of periodic calibration targets 290 and 295, each of which is adapted to position an illumination beam relative to the periodic calibration target in one direction.

[0051] Figure 20 depicts a periodic calibration target 280 containing markers 288 and 289 and one of seven different periodic regions 281 to 287 configured as a hexagonal pattern.

[0052] Figure 21 is a diagram showing one of the components of the metering system 100 contained in a vacuum environment separated from the sample 101.

[0053] Figure 22 is a diagram illustrating a model establishment and analysis engine 180 configured to analyze sample parameter values ​​based on T-SAXS data according to the method described herein.

[0054] Figure 23 depicts a flowchart illustrating an exemplary method 300 for calibrating an angle of incidence offset value based on T-SAXS measurements of multiple angles of incidence and azimuth as described herein.

Claims

1. A measurement system comprising: An X-ray illumination subsystem configured to generate an X-ray illumination beam; a sample positioning system configured to position a sample relative to the X-ray illumination beam such that the X-ray illumination beam is incident on the sample surface at any position on the sample surface and to rotate the sample about a rotation axis relative to the X-ray illumination beam such that the X-ray illumination beam is incident on the sample surface at any position according to a plurality of incident angles and to rotate the sample about an azimuth rotation axis such that the X-ray illumination beam is incident on the sample surface at any position according to a plurality of azimuth angles; a beam blocking calibration target comprising a cylindrical pin and one or more marks disposed in a plane aligned with a central axis of the cylindrical pin; An X-ray detector configured to detect a quantity of transmission flux within a location range of a sample positioning system, wherein at least a portion of the X-ray illumination beam is incident on the cylindrical pin within that location range; and a computing system configured to determine the incident position of the X-ray illumination beam relative to a location range of the sample positioning system based on the detected transmission flux.

2. The metrology system of claim 1, wherein the position range includes an incident angle range, and wherein the computing system is further configured to determine an adjustment of the rotation axis relative to one of the positions of the x-ray illumination beam to align the rotation axis with the x-ray illumination beam.

3. The metrology system of claim 2, wherein the determination of the adjustment of the position of the rotation axis relative to the X-ray illumination beam is based on the detected measurement of the transmission flux.

4. The metering system as described in claim 2, further comprising: A camera is aligned to generate a plurality of images of the one or more marks or at least a portion of the marks placed on the sample at a plurality of different incident angles, wherein a misalignment of the rotation axis relative to the position of the one or more marks or the marks placed on the sample is determined based on the displacement of the one or more marks or the marks placed on the sample measured in the plurality of images.

5. The metering system as described in claim 2, further comprising: One or more actuators are configured to adjust the position of one or more elements of the x-ray illumination subsystem to adjust the position of the rotation axis relative to the x-ray illumination beam.

6. The metering system of claim 2, further comprising: One or more actuators configured to adjust the position of the sample positioning system relative to the X-ray illumination beam to align the rotation axis with the X-ray illumination beam.

7. The metrology system of claim 1, wherein the determination of the incident position of the X-ray illumination beam relative to the sample positioning system is based on a transmission flux model that varies according to the position of the cylindrical pin relative to the X-ray illumination beam.

8. The metering system of claim 1, further comprising: A camera is aligned to generate an image of at least a portion of the mark, wherein the computing system is further configured to position the mark in the coordinate system of the sample positioning system based on the image and to estimate an incident position of the X-ray illumination beam in the coordinate system of the sample positioning system based on the position of the mark and a known distance between the mark and the cylindrical pin.

9. The metrology system of claim 8, wherein the alignment camera generates an image of at least one reference mark placed on the sample, and wherein the computing system is further configured to position the reference mark in the coordinate system of the sample positioning system based on the image.

10. The metrology system of claim 9, wherein the alignment camera rotates about the rotation axis relative to the sample.

11. The metering system of claim 1, further comprising: One or more sensors configured to measure the position of a back surface of the sample relative to a sample positioning system in a direction generally normal to one of the wafer surfaces; one or more sensors configured to measure the position of a front surface of the sample relative to a sample positioning system in a direction generally normal to one of the wafer surfaces; or a combination thereof.

12. The metrology system of claim 1, wherein the beam blocking calibration target is positioned on the sample positioning system or on the sample.

13. The metering system of claim 1, further comprising: A first vacuum chamber that encloses a significant portion of an illumination beam path between the X-ray illumination source and the sample.

14. The metering system of claim 1, further comprising: A first vacuum chamber that encloses a significant portion of a beam path between the sample and the X-ray detector.

15. A measurement system comprising: An X-ray illumination source configured to produce an X-ray illumination beam; A sample positioning system configured to position a sample relative to an X-ray illumination beam such that the X-ray illumination beam is incident on the surface of the sample at any position on the surface of the sample and to rotate the sample about a rotation axis relative to the X-ray illumination beam such that the X-ray illumination beam is incident on the surface of the sample at any position according to a plurality of incident angles and to rotate the sample about an azimuth rotation axis such that the X-ray illumination beam is incident on the surface of the sample at any position according to a plurality of azimuth angles; a periodic calibration target comprising one or more periodic structures having one or more known ranges on the periodic calibration target and one or more marks disposed in a plane aligned with one or more periodic structures, wherein the periodic calibration target includes a cylindrical pin, and wherein the one or more marks are disposed in a plane aligned with a central axis of the cylindrical pin; An X-ray detector configured to detect a quantity of transmission flux within a location range of a sample positioning system, wherein at least a portion of the X-ray illumination beam is incident on one or more periodic structures within that location range; and a computing system configured to determine the incident position of the X-ray illumination beam relative to a location range of the sample positioning system based on the detected transmission flux.

16. The metrology system of claim 15, wherein the position range includes an incident angle range, and wherein the computing system is further configured to determine, based on the detected transmission flux, an adjustment of the position of the rotation axis relative to one of the X-ray illumination beams.

17. The metrology system of claim 15, wherein the periodic calibration target is contained in a boundary line between two periodic structures that are different in periodicity, orientation, or both, and wherein the boundary line is known to have an accuracy of less than 200 nanometers relative to the location of one or more markers.

18. The metrology system of claim 15, wherein the periodic calibration target comprises an intersection of three periodsic structures that are periodic, oriented, or both, and wherein the intersection is known to have an accuracy of less than 200 nanometers relative to the location of one or more markers.

19. The metering system of claim 15, wherein the height of one or more of the periodic structures is at least 500 micrometers.

20. The metering system of claim 15, wherein the spacing of one or more periodic structures is less than 200 nanometers.

21. The metering system of claim 15, wherein the one or more periodic structures are made of tungsten, tungsten carbide or platinum.

22. The metrology system of claim 15, wherein the periodic calibration target is positioned on the sample positioning system or on the sample.

23. A method for a measurement system, comprising: An X-ray illumination beam is generated by an X-ray illumination subsystem; Positioning a sample relative to the X-ray illumination beam such that the X-ray illumination beam is incident on the surface of the sample at any position on the surface of the sample; rotating the sample relative to the X-ray illumination beam about a rotation axis such that the X-ray illumination beam is incident on the surface of the sample at any position according to a plurality of incident angles; rotating the sample about an azimuth rotation axis such that the X-ray illumination beam is incident on the surface of the sample at any position according to a plurality of azimuth angles; illuminating a calibration target with the X-ray illumination beam, the calibration target comprising one or more marks, wherein the calibration target includes a cylindrical pin, wherein the one or more marks are positioned in a plane aligned with a central axis of the cylindrical pin; detecting a quantity of transmission flux within a position range of the sample positioning system, wherein at least a portion of the X-ray illumination beam is incident on the calibration target within that position range; and determining the incident position of the X-ray illumination beam relative to the sample positioning system based on the detected transmission flux.

24. The method of claim 23, further comprising: The position of the rotation axis relative to one of the X-ray illumination beams is determined and adjusted to align the rotation axis with the X-ray illumination beam, wherein the position range includes an incident angle range.

25. The method of claim 24, wherein the determination of the adjustment of the position of the rotation axis relative to the x-ray illumination beam is based on the detected measurement of the transmission flux.

26. The method of claim 24, further comprising: Multiple images of the one or more marks or at least a portion of the marks placed on the sample are generated according to multiple different incident angles, wherein the rotation axis is misaligned relative to the position of the one or more marks or the marks placed on the sample based on the displacement of the one or more marks or the displacement of the marks or the displacement of the marks or the displacement of the marks placed on the sample measured in the multiple images.

27. The method of claim 24, further comprising: Adjust the position of one or more components of the X-ray illumination subsystem to adjust the position of the rotation axis relative to the X-ray illumination beam.

28. The method of claim 24, further comprising: Adjust the position of the sample positioning system relative to the X-ray illumination beam to align the rotation axis with the X-ray illumination beam.

29. The method of claim 23, wherein the calibration target comprises one or more periodic structures having a known range, and wherein the one or more marks are positioned in a plane aligned with the one or more periodic structures.

Images