Metrology systems and methods

Abstract

This invention discloses a method and system for calibrating the position of an X-ray beam incident on a sample in an X-ray scattering measurement system. The precise position of the illumination beam incident on the surface of a wafer is determined based on the obstruction of the illumination beam by two or more obstructing elements. The center of the illumination beam is determined based on a measurement of the transmitted flux and a model of the interaction between the beam and each obstructing element. A wafer is oriented such that its axis of rotation within an incident angle range is adjusted to align with the wafer surface and intersect the illumination beam at the measurement position. A precise offset between the normal incident angle of the illumination beam relative to the wafer surface and the zero incident angle measured by the sample positioning system is determined.

Description

[Technical Field]

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

[0002] Semiconductor devices (such as logic devices and memory devices) are typically manufactured by a series of processing steps applied to a sample. Various features and multiple structural layers of a semiconductor device are formed by these processing steps. For example, lithography (especially) is a semiconductor manufacturing process involving the formation of a pattern on a semiconductor wafer. Additional examples of semiconductor manufacturing processes include (but are not limited to) chemical mechanical polishing, etching, deposition, and ion implantation. Multiple semiconductor devices can be manufactured on a single semiconductor wafer and then divided into individual semiconductor devices.

[0003] Metrology procedures are used at various steps during a semiconductor manufacturing process to detect defects on a wafer to improve yield. 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] Typically, critical size measurements of scattering measurements are performed on targets composed of thin films and / or repeating periodic structures. During device fabrication, these thin films and periodic structures typically represent the actual device geometry and material structure or an intermediate design. Characterization becomes more difficult as devices (e.g., logic devices and memory devices) move toward smaller nanoscale dimensions. Devices incorporating complex three-dimensional geometries and materials with diverse physical properties contribute to the difficulty of characterization. For example, modern memory structures are often high aspect ratio three-dimensional structures that make it difficult for optical radiation to penetrate the underlying layers. Optical metrology tools using infrared to visible light can penetrate many layers of translucent materials, but the longer wavelengths that provide good penetration depth do not provide sufficient sensitivity to small anomalies. In addition, the increasing number of parameters required to characterize complex structures (e.g., FinFETs) leads to increased parameter dependence. Therefore, the parameters of a characterized target often cannot be reliably separated from available measurements.

[0005] In one instance, a longer wavelength (e.g., near-infrared) has been used in an attempt to overcome the penetration problem of 3D FLASH devices that utilize polycrystalline silicon as one of the alternating materials in the stack. However, the mirror-like structure of 3D FLASH inherently causes the light intensity to decrease as illumination propagates deeper into the thin film stack. This causes loss of sensitivity at depth and related problems. In this approach, SCD can only successfully extract a set of reduced metering dimensions with high sensitivity and low correlation.

[0006] In another example, opaque, high-dielectric-constant materials are increasingly 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 from reflected signals have been developed (e.g., measuring multiple Mueller matrix elements in addition to more familiar reflectivity or elliptic polarization signals). However, these methods have not yet reliably overcome the fundamental challenges associated with many advanced targets (e.g., complex 3D structures, structures smaller than 10 nm, structures using opaque materials) and metrology applications (e.g., line edge roughness measurement 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 require long scan times. Scanning electron microscopy (SEM) achieves intermediate resolution but cannot penetrate structures to sufficient depth. Therefore, high aspect ratio apertures are not well characterized. Additionally, the required charging of the sample negatively impacts 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.) and destructive sample preparation techniques (such as focused ion beam (FIB) processing, ion polishing, coating, or selective etching, etc.) are employed. For example, transmission electron microscopy (TEM) achieves high resolution and can probe arbitrary depths, but TEM requires destructive partitioning of the sample. Several repetitions of material removal and measurement typically provide the information needed to measure the critical metrological parameters of the entire three-dimensional structure. However, these techniques require sample destruction and lengthy processing time. The complexity and time required to complete these types of measurements are attributed to the significant bias introduced by the drift of the etching and metrological steps. In addition, these techniques require multiple repetitions, which introduce alignment errors.

[0010] Transmission, small-angle X-ray scattering (T-SAXS) systems have demonstrated their promise to solve challenging metrological applications. Current T-SAXS tools employ a beam-forming slit to form an illumination beam incident on the sample during measurement. A beam-diverging shaping slit is located in the beam path before or after the focusing optics define the beam divergence angle. A beam-shaping slit is located in the beam path after the beam-diverging shaping slit defines the size of the beam spot incident on the wafer. Furthermore, T-SAXS measurements are performed over a wide range of incident angles. Accurate alignment of the incident beam position on the metrological target is required to ensure reliable measurements over a wide range of incident angles.

[0011] To further improve device performance, the semiconductor industry continues to focus on vertical integration rather than lateral scaling. Therefore, accurate measurement of complex, fully three-dimensional structures is crucial for ensuring survivability and continued scaling improvements. Future metrology applications present metrological challenges due to increasingly smaller resolution requirements, multi-parameter correlations, increasingly complex geometries including high aspect ratio structures, and the increasing use of opaque materials. Therefore, methods and systems for improved T-SAXS measurement are desired. [Summary of the Invention]

[0012] This document describes a method and system for calibrating the position of an X-ray beam incident on a 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 range of incident angles and azimuths relative to the surface of a sample (e.g., a semiconductor wafer) having a small beam spot size (e.g., less than 50 micrometers over the entire effective illumination point). This document describes calibration to accurately position the illumination beam on a desired target area on the surface of a semiconductor wafer across the full range of incident angles and azimuths.

[0013] In one state, the precise incident position of the illumination beam in two dimensions of the plane of the wafer surface is determined based on the interaction between the illumination beam and two or more blocking elements. The center of the illumination beam is determined based on a model of the interaction between the transmitted flux and the material and geometry of the beam and the blocking elements.

[0014] In a further embodiment, the incident position of the illumination beam is determined at any location on the wafer based on an image measured by an alignment camera. The alignment camera aligns the relative position of the illumination beam with respect to a feature (e.g., an edge or reference) of an obstructing element and transfers this alignment to one or more locations on the surface of the wafer. Furthermore, the position of the wafer in the Z direction relative to the Z position of the obstructing element is measured by changing the focal position of the alignment camera until the lithography feature on the wafer surface is precisely focused. The change in focal position indicates the difference between the Z position between the obstructing elements and the imaging position on the wafer.

[0015] In some embodiments, a shielding element is a blade structure. A blade structure is typically a thin, sharpened, dense, high-Z material (such as tungsten carbide) having a straight edge oriented perpendicular to the position to be calibrated. Furthermore, the surface of the blade coincides with the surface of the wafer. This allows the alignment camera to focus on a plane identical to the wafer, thereby ensuring a good match between the measured beam position at the wafer and the reference beam position at the blade measured by the alignment camera.

[0016] In some embodiments, the blocking element is a precision cylinder having one of known diameters. In these embodiments, the beam blocking is offset in the Z direction by the radius of the cylinder. In these embodiments, an additional surface, coinciding with the central axis of the cylinder and marked with a reference mark, advantageously makes the camera frame reference the axis and radius of the cylindrical blocking element. In these embodiments, the central axis of the cylindrical blocking element coincides with the surface of the wafer and is oriented perpendicular to the position to be calibrated.

[0017] In another embodiment, the position of the rotation axis associated with orienting a wafer within an incident angle range is aligned to be coplanar with the surface of the wafer and intersect with the illumination beam at the measurement position to avoid drift of the illumination point within that incident angle range.

[0018] In some embodiments, the position of the rotation axis is calibrated by aligning the center of the illumination beam with a blocking element and measuring the transmitted flux at a plurality of different incident angles. The apparent motion of the blocking element is determined from the measured flux based on a selected blocking model. A geometric model maps the apparent motion of the blocking element to adjustments in the stage configuration to achieve the desired alignment.

[0019] In some other embodiments, the position calibration of the rotation axis is achieved by positioning a high-resolution X-ray camera having a focal plane aligned with the wafer plane of the wafer stage. The position of the illumination point at the wafer plane is measured by the high-resolution X-ray camera as the stage rotates over a large incident angle range. A mapping of the position of the illumination point at the wafer plane based on the measurement is generated.

[0020] In some other embodiments, the position of the rotation axis of the stage reference frame is calibrated by positioning a small target on a wafer with a high diffraction efficiency. The intensity of the diffraction class is measured as the stage rotates over a wide range of incident angles. The intensity of the diffraction class indicates the misalignment between the illumination point and the target based on an incident angle. A mapping based on the misalignment at an incident angle is generated based on the measurement.

[0021] In another state, one of the AOI offset values ​​between the normal angle of incidence of the illumination beam relative to the wafer surface and the zero angle of incidence measured by the sample positioning system is precisely measured.

[0022] In some embodiments, the AOI offset value is determined based on absorption measurements within an AOI range. In some embodiments, the AOI offset value is determined based on measurements of the diffraction order of scattering from one of two azimuth angles at which the calibration grating is separated by 180 degrees.

[0023] In another sample, an azimuth offset value between the zero azimuth angle of the wafer surface relative to the illumination beam and the zero azimuth angle measured by the sample positioning system is precisely measured. Additionally, an offset value between the center of the wafer surface and the rotation center of the rotating stage is precisely measured.

[0024] In another embodiment, the precise calibration of the azimuth offset between the wafer coordinates and the stage coordinates is based on the position of the diffraction order associated with a measurement of a calibration grating having known response characteristics for one or more azimuth angles.

[0025] In another configuration, multiple calibrated incident angles, along with well-known formulas for conical diffraction, are used to calibrate the detector relative to the stage, and simultaneously calibrate the azimuth relative to the stage.

[0026] In some embodiments, a beam shaping slit mechanism rotates about a beam axis aligned with the orientation of the sample to optimize the profile of the incident beam at various incident angles, azimuth angles, or both. In this way, the beam shape matches the shape of the metrological target. Unfortunately, defects in the rotary actuator cause the beam shaping slit mechanism to advance about the axis of the illumination beam. This causes the incident position of the illumination beam to drift with respect to different azimuth angles and corresponding beam slit angles.

[0027] In a further state, a calibration mapping of the XY stage offset is determined based on the measurement of the incident position of the illumination beam within a azimuth angle and the corresponding beam slit angle range.

[0028] In some embodiments, the measurement is performed by an X-ray camera having a focal plane at a location on the wafer surface. In some other embodiments, a calibration mapping of the XY stage offset is determined based on a small target measured by a detector with an azimuth angle and a corresponding beam slit angle range.

[0029] 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, or any other suitable proximity sensor.

[0030] In a further embodiment, the Z-actuator is controlled to adjust the wafer 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.

[0031] In another further embodiment, the Z-actuator is controlled to adjust the wafer Z-position, Rx orientation, Ry orientation, or any combination thereof so that the axis of rotation in the azimuth angle is aligned with the stage reference frame so that a specific target remains in the focus of the aligned camera within an azimuth angle range.

[0032] The foregoing is a [Summary of the Invention] and therefore necessarily contains simplifications, generalizations and omissions of details; thus, those skilled in the art should understand that the [Summary of the Invention] is merely illustrative and not in any way limiting. Other forms, features and advantages of the apparatus and / or procedures described herein will become apparent in the non-limiting [Description] set forth herein. [Simplified Explanation of the Diagram]

[0176] Figure 1 is a diagram illustrating a metrology system 100 configured to perform calibration of various system parameters according to the methods described herein.

[0177] Figure 2 depicts an end view of a beam shaping slit mechanism 120 in a set configuration.

[0178] Figure 3 depicts an end view of a beam shaping slit mechanism 120 in another configuration.

[0179] Figure 4 depicts an X-ray illumination beam 116 incident on a wafer 101 at a specific orientation described by angles φ and θ.

[0180] Figure 5 is a diagram illustrating a sample positioning system 140 of a wafer stage in which an illumination beam 116 is moved to a position on the wafer 101.

[0181] Figure 6A depicts a top view of an illumination beam 116 incident on wafer 101 as shown in Figure 5, wherein the rotation axis 153 intersects the illumination beam 116 and wafer 101 at the point of incidence of the illumination beam 116.

[0182] FIG6B 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.

[0183] FIG6C 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.

[0184] Figure 7 is a diagram illustrating a sample positioning system 140 of a wafer stage in which an illumination beam 116 is moved to a position where a cylindrical pin element 151 blocks one of the positions.

[0185] Figure 8 depicts a graph 170 illustrating the measurement of flux based on the relative position of a blocking element with respect to the illumination beam 116.

[0186] Figure 9A depicts a grating structure 171 measured by a T-SAXS system 100 at a zero azimuth angle.

[0187] Figure 9B depicts the same grating structure 171 measured by a T-SAXS system 100 at a 180-degree azimuth angle.

[0188] Figure 10 depicts a graph showing the measured intensity of a diffraction class detected by a detector 119, which is a measurement 172 performed at a zero azimuth angle and another measurement 173 performed at a 180-degree azimuth angle.

[0189] Figure 11 is a diagram illustrating one of the components of the metering system 100 contained in the vacuum environment separated from the sample 101.

[0190] Figure 12 is a diagram illustrating a model building and analysis engine 180 configured to analyze sample parameter values ​​based on T-SAXS data according to the method described herein.

[0191] Figure 13 depicts a flowchart illustrating an exemplary method 200 for calibrating an angle of incidence offset value based on T-SAXS measurements at multiple angles of incidence and azimuth as described herein.

Implementation Method

[0033] This patent application claims priority to U.S. Provisional Patent Application No. 62 / 411,152, filed October 21, 2016, pursuant to 35 USC §119, the entire contents of which are incorporated herein by reference.

[0034] Reference is now made in detail to the background examples and some embodiments of the present invention, examples of which are illustrated in the accompanying drawings.

[0035] This document describes a method and system for calibrating the position of an X-ray beam incident on a 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 range of incident angles and azimuths relative to the surface of a sample (e.g., a semiconductor wafer) having a small beam spot size (e.g., less than 50 micrometers over the entire effective illumination point). This document describes calibration to accurately position the illumination beam on a desired target area on the surface of a semiconductor wafer across the full range of incident angles and azimuths.

[0036] Figure 1 illustrates an embodiment of a T-SAXS metrology tool 100 used to measure the characteristics of a sample according to the exemplary method presented herein. As shown in Figure 1, the system 100 can be used to perform T-SAXS measurements on an inspection area 102 of a sample 101 illuminated by a point of illumination beam.

[0037] In the depicted embodiment, the metrology instrument 100 includes an x-ray illumination source 110 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.

[0038] 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 stationary solid anode source, a microjoule source, a microjoule rotating anode source, a plasma-based source, and an inverse Compton source may be used as the x-ray illumination source 110. In one example, an inverse Compton source available from Lyncean Technologies, Inc., Palo Alto, California (USA) is conceivable. An inverse Compton source has the additional advantage of being able to generate x-rays within a photon energy range, thereby enabling the x-ray source to deliver x-ray radiation at different selectable wavelengths.

[0039] An exemplary X-ray source includes an electron beam source configured to impinge on 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 April 19, 2011, by KLA-Tencor Corp., the entire contents of which are incorporated herein by reference.

[0040] The X-ray illumination source 110 generates X-ray emission in 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 located 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.

[0041] A beam divergence control slit 112 is located 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 during measurement. An additional intermediate slit 113 is located in the beam path between the beam divergence control slit 112 and the beam shaping slit mechanism 120. The intermediate slit 113 provides additional beam shaping. However, the intermediate slit 113 is typically optional.

[0042] The beam shaping slit mechanism 120 is located 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 amplification of the incident beam spot size due to beam divergence defined by the finite source size. In one example, the beam spot size expansion due to shadows generated by the finite source size is approximately 1 micrometer for a 10-micrometer X-ray source size and a 25-millimeter distance between the beam shaping slit and the sample 101.

[0043] In some embodiments, the beam shaping slit mechanism 120 includes a plurality of independently actuated beam shaping slits (i.e., blades). In one embodiment, the beam shaping slit mechanism 120 includes four independently actuated beam shaping slits. These four beam shaping slits effectively block a portion of the incident beam 115 and produce an illumination beam 116 having a box-shaped illumination cross-section.

[0044] Figures 2 and 3 depict end views of the beam shaping slit mechanism 120 depicted in Figure 1 in two different configurations. As shown in Figures 2 and 3, the beam axis is perpendicular to the page. As depicted in Figure 2, the incident beam 115 has a large cross-section. In some embodiments, the incident beam 115 has a diameter of approximately 1 mm. Furthermore, the position of the incident beam 115 within the beam shaping slits 126 to 129 has an uncertainty of approximately 3 mm due to beam pointing error. To accommodate the uncertainty of the size and position of the incident 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 located at a maximum distance from the beam axis (i.e., the slits are fully open and the slits do not restrict the light passing through the beam shaping slit mechanism 120).

[0045] Figure 3 depicts slits 126 to 129 of the beam shaping slit mechanism 120 at a position that blocks a portion of the incident beam 115, so that the outgoing beam 116 delivered to the sample under measurement has a reduced size and a clearly defined shape. As depicted in Figure 3, each of the slits 126 to 129 has been moved inward toward the beam axis to achieve the desired output beam shape.

[0046] Slits 126 to 129 are made of a material that minimizes scattering and effectively blocks incident radiation. Exemplary materials include single-crystal materials (such as germanium, gallium arsenide, indium phosphide, etc.). Typically, the slit material is split rather than cut along a crystallographic direction to minimize scattering across structural boundaries. Additionally, the slits are oriented relative to the incident beam so that the interaction between the incident radiation and the internal structure of the slit material produces a minimum amount of scattering. Crystals are attached to slit frames 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 having a width of about 0.5 mm and a height of about 1 mm to about 2 mm. As depicted in Figure 2, the length L of a slit is about 6 mm.

[0047] Typically, X-ray optics shape and guide X-ray radiation onto sample 101. In some instances, the X-ray optics include an X-ray monochromator to monochromate the X-ray beam incident on sample 101. In some instances, the X-ray optics collimate the X-ray beam or focus the X-ray beam onto a measurement region 102 of sample 101 to a divergence of less than 1 milliradian using multilayer X-ray optics. In these instances, multilayer X-ray optics are also used as a beam monochromator. In some embodiments, the X-ray optics include 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 ellipsoidal mirrors), capillary optics (such as hollow capillary X-ray waveguides), multilayer optics or systems, or any combination thereof. Further details are described in U.S. Patent Publication No. 2015 / 0110249, the entire contents of which are incorporated herein by reference.

[0048] The X-ray detector 119 collects the X-ray radiation 114 scattered from the sample 101 and generates an output signal 135 indicating one of the properties of the sample 101 that is sensitive to the incident X-ray radiation, according to a T-SAXS measurement mode. In some embodiments, the scattered X-rays 114 are collected by the X-ray detector 119 when the sample positioning system 140 positions and orients the sample 101 to generate angularly resolved scattered X-rays.

[0049] 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.

[0050] In some embodiments, the x-ray detector analyzes one or more x-ray photon energies and generates signals for each x-ray energy component indicating the properties of the sample. In some embodiments, the x-ray detector 119 includes any of a CCD array, a microchannel plate, a photodiode array, a microstrip proportional counter, a gas proportional counter, a scintillator, or a fluorescent material.

[0051] In this manner, X-ray photon interactions within the detector are identified by energy other than pixel position and count. In some embodiments, X-ray photon interactions are identified by comparing the energy of interactions between X-ray photons and 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.

[0052] In a further state, a T-SAXS system is used to determine the properties (e.g., structural parameter values) of a sample based on one or more diffraction orders of the scattered light. As depicted in FIG1, the metrology tool 100 includes a computational system 130 for acquiring a signal 135 generated by the detector 119 and determining the properties of the sample based at least in part on the acquired signal.

[0053] In some instances, T-SAXS-based metrology involves determining the sample size by inverse kinematics of a predetermined measurement model with measured data. The measurement model contains several (approximately 10) adjustable parameters and represents the geometry and optical properties of the sample and the optical properties of the measurement system. Inverse kinematics methods include (but are not limited to) model-based regression, computed tomography, machine learning, or any combination thereof. In this manner, the parameters of the target quantitative curve are estimated by solving for a parameterized measurement model value that minimizes the error between the measured scattered X-ray intensity and the modeling result.

[0054] It is desirable to perform measurements over a wider range of incident and azimuth angles to increase the precision and accuracy of the measured parameter values. This method reduces the correlation in parameters by expanding the number and diversity of datasets available for analysis to include a variety of 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 wider range of incident and azimuth angles provide sufficient resolution and penetration depth to characterize high aspect ratio structures across their entire depth.

[0055] Measurements of the intensity of diffracted radiation are collected based on the X-ray incident angle relative to the wafer surface normal. Information contained in multiple diffraction levels is generally unique among the model parameters under consideration. Therefore, X-ray scattering produces estimates of the parameters of interest with small errors and reduced parameter correlation.

[0056] The orientation systems of the illuminating X-ray beam 116 relative to the surface normal of a semiconductor wafer 101 are described by any two angular rotations of the wafer 101 relative to the X-ray illumination beam 115, or vice versa. In one example, the orientation is described relative to a coordinate system fixed to the wafer. Figure 4 depicts the X-ray illumination beam 116 incident on the wafer 101 at 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 the wafer 101. The Y-axis is aligned with the surface of the wafer 101 in a plane. X and Z are not aligned with the surface of the wafer 101. Z' is aligned with an axis perpendicular to the surface of the wafer 101, and X' and Y' lie in a plane aligned with the surface of the 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. Together, θ and φ 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 perpendicular 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.

[0057] As illustrated in FIG. 1, the metrology tool 100 includes a sample positioning system 140 configured to align and orient the sample 101 within a large range of incident and azimuth angles relative to the illumination beam 116. In some embodiments, the sample positioning system 140 is configured to rotate the sample 101 within a large range of rotational angles (e.g., at least 60 degrees) aligned with the surface plane of the sample 101. In this manner, angular resolution 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 command signals (not shown) to the sample positioning system 140, which instructs the sample 101 to a desired position. In response, the sample positioning system 140 generates command signals to various actuators of the sample positioning system 140 to achieve the desired positioning of the sample 101.

[0058] FIG5 depicts a sample positioning system 140 in one embodiment. As depicted in FIG5, 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. For reference, 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. A wafer 101 is supported on the wafer stage 144 by a flip-tilt-Z-axis translation stage 156 including actuators 150A to 150C. A rotating stage 158, mounted to one of the flip-tilt-Z translation stages 156, orients the wafer 101 within an azimuth angle φ relative to an illumination beam 116. 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.

[0059] Actuator 145 translates the laterally aligned stage 142 relative to substrate frame 141 along the XBF axis. Rotation actuator 146 rotates stage reference frame 143 about a rotation axis 153 aligned with the YNF axis relative to the laterally aligned stage 142. Rotation actuator 146 orients wafer 101 within an incident angle θ relative to illumination beam 116. Wafer stage actuators 147 and 148 translate wafer stage 144 relative to stage reference frame 143 along the XRF and YRF axes, respectively. Actuators 150A to 150C operate in coordination to translate and rotate stage 158 and wafer 101 relative to wafer stage 144 in the ZSF direction and to flip and tilt the rotating stage 158 and wafer 101 relative to wafer stage 144 about an axis coplanar with the XSF-YSF plane. The rotating stage 158 causes the wafer 101 to rotate about an axis perpendicular to the surface of the wafer 101.

[0060] In summary, the wafer stage 144 is capable of moving the wafer 101 relative to the illumination beam 116 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 XRF and YRF directions). The rotary actuator 146 is capable of rotating 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 incident angle range (e.g., greater than 2 degrees). In one embodiment, the rotary actuator 146 is configured to rotate the stage reference frame 143 within a range of at least 60 degrees. The rotary stage 158 mounted to the wafer stage 144 is capable of rotating 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 within a large azimuth angle range (e.g., at least a 90-degree rotation range).

[0061] 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 rotary actuator 146. In these embodiments, the x-ray illumination system includes actuators that move one or more of the optics of the x-ray illumination system, causing the x-ray illumination beam 116 to move relative to the substrate frame 141 in, for example, the XBF direction. In these embodiments, the movement of the stage reference frame 143 for calibration as described herein is replaced by, for example, movement of the x-ray illumination beam to a desired position relative to the rotation axis 153 by one or more of the optics of the x-ray illumination system.

[0062] In some embodiments (such as the embodiment depicted in FIG. 5), a sample positioning system includes at least one beam blocking element and an alignment camera for calibrating the incident position of an illumination beam and aligning the axis of rotation of the stage reference frame with respect to the illumination beam at the incident point of the illumination beam and a wafer. The blocking element is mounted to a wafer stage coplanar with the surface of the wafer under measurement. The alignment camera is mounted to the stage reference frame and thus rotates with the stage reference frame.

[0063] In the embodiment depicted in FIG. 5, the blocking elements are cylindrical pin-shaped elements 151 and 152 mounted to the wafer stage 144 such that the central axes of the cylindrical pin-shaped elements 151 and 152 are approximately coplanar with the surface of the wafer 101. As depicted in FIG. 5, cylindrical pin element 151 includes a central axis approximately parallel to the YNF axis, and cylindrical pin element 152 includes a central axis approximately parallel to the XRF axis. Similar to a beam slit, the cylindrical pin blocks the beam by absorbing a large portion of any irradiating X-rays.

[0064] The sample positioning system 140 also includes an alignment camera 154 mounted to the stage reference frame 143. The alignment camera 154 is configured to generate a high-resolution image of an object (such as wafer 101) in its field of view. The alignment camera 154 also includes an autofocus mechanism that maintains a clear image focus by precisely moving the camera's focus to a measurement distance. In this way, 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 cylindrical pin elements 151 and 152 imaged by the camera by monitoring the z-displacement of the camera's focus.

[0065] In one state, the precise incident position of the illumination beam in two dimensions of the plane of the wafer surface is determined based on the interaction between the illumination beam and two or more blocking elements.

[0066] Figure 7 illustrates a sample positioning system 140 of a wafer stage having a position in which the illumination beam 116 is blocked by the cylindrical pin element 151. The precise incident position of the illumination beam relative to the cylindrical pin 151 is determined based on the X position of the cylindrical pin 151 relative to the illumination beam 116 (i.e., the substrate frame 141) and the flux transmitted, as measured by the detector 119. As depicted in Figure 7, when 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, when 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 based on 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.

[0067] Figure 8 depicts a graph 170 illustrating the relative position of the measured flux 155 to the illumination beam 116 based on the position of a cylindrical pin (or, alternatively, a blade). The relationship depicted between the measured flux 155 and the relative position is an S-shaped function.

[0068] 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 lies between the minimum flux value FMIN and the maximum flux value FMAX. However, in other instances, the beam center can be determined at a flux value other than the middle of the range of measured flux. In some instances, a more precise relationship is determined by modeling the interaction between the beam and the material and geometry of the cylindrical pin or blade. In these instances, the modeled interaction is compared with the measured transmitted flux, and a fitting algorithm is used to determine the relative position of the cylindrical pin or blade with respect to the illumination beam aligned with the beam center based on the fitting of the measurement results to the model.

[0069] In one example, an estimate ΔX of the distance between a current position of the cylinder 151 relative to the center of the illumination beam 116 and a position of the cylindrical pin 151 coinciding with the center of the beam is based on the measured flux FMEAS, the midpoint of the flux FMID, and the reciprocal of the derivative of the measured flux as a function of the position of the cylindrical pin described by equation (1).

[0070] And FMID is described by equation (2).

[0071]

[0072] The maximum and minimum values ​​of the measured throughput can be measured by scanning the wafer stage while measuring the transmitted throughput. In addition, 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 according to equation (1) by measuring the throughput at only one position. If necessary, the change in the center position can be repeatedly determined to converge to a center position.

[0073] Since the beam has a centroid component in two directions (e.g., the X and Y directions), two cylindrical pins are used to measure directions perpendicular to the centroid component. In the embodiment depicted in Figure 7, 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. Typically, two or more cylindrical pins can be used to create redundancy and increase the accuracy of beam position calibration.

[0074] In a further embodiment, the incident position of the illumination beam is determined at any location on the wafer based on an image measured by an alignment camera. As depicted in FIG7, the center of the illumination beam 116 is aligned with the vertically and horizontally oriented cylindrical pins 151 and 152 as described above. In the embodiment depicted in FIG7, a reference mark 157 is positioned coplanar with the central axis of the cylindrical pin 151. Similarly, a reference mark is positioned coplanar with the central axis of the cylindrical pin 152. At the position of the beam center aligned with the cylindrical pin 151, the position of the illumination beam 116 relative to the cylindrical pin 151 or the reference 157 at or near the cylindrical pin is aligned by the alignment camera 154. This aligned illumination beam is positioned relative to a precise position in the field of view of the alignment camera (assuming no change in the focal position). As depicted in FIG5, the wafer 101 moves within the field of view of the alignment camera 154. The wafer 101 is moved so that a desired location (e.g., a reference mark) on the wafer 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 previous alignment. In this way, the position of the illumination beam 116 on the wafer 101 in the X and Y directions is quickly estimated based on an image collected by the alignment camera 154. Similarly, 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 difference in Z position between the cylindrical pin and the imaged location on the wafer. Actuators 150A to 150C can be used to reposition the wafer 101 in the Z direction to reposition the imaged location so that it is in the same plane as the cylindrical pin (e.g., reference 157).

[0075] 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 a reference mark at or near the cylindrical pins or blade is aligned by an alignment camera as described above, the incident position of the illumination beam can be transferred 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, etc.) of the wafer stage 144. By moving the wafer 101 to three or more desired locations (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 location, together with the position of the wafer in the stage coordinates, is determined at each desired location. Based on the known positions of the illumination beam and the stage coordinates at three or more locations, a mapping is generated that relates the stage coordinates to the incident position of the illumination beam.

[0076] After positioning the cylindrical pin 151 at the center of the illumination beam 116 (in the X direction), the alignment camera 154 images the cylindrical pin itself or a reference mark located 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 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 Z position of the cylindrical pin relative to the stage reference frame 143 by focusing on the cylindrical pin itself or a reference mark. Since the alignment camera 154 rotates together with the stage reference frame, the focal position of the alignment camera 154 serves as a reference for the Z position of the cylindrical pin relative to the stage reference frame.

[0077] In some embodiments, a shielding element is a blade structure. A blade structure is typically a thin, sharpened, dense, high-Z material (such as tungsten carbide) having a straight edge oriented perpendicular to the position to be calibrated. Furthermore, the edge of the blade coincides with the surface of the wafer. This allows the alignment camera 154 to focus on a plane identical to the wafer, thereby ensuring a good match between the measured beam position at the wafer and the reference beam position at the blade measured by the alignment camera.

[0078] In some embodiments, the blocking element is a precision cylinder having one of the known diameters described above. In these embodiments, the beam blocking is offset in the Z direction by the radius of the cylinder. In these embodiments, an additional surface coinciding with the central axis of the cylinder and marked with a reference mark (e.g., reference 157) advantageously makes the camera frame reference the axis and radius of the cylindrical blocking element. In these embodiments, the central axis of the cylindrical blocking element coincides with the surface of the wafer and is oriented perpendicular to the position to be calibrated, as described above.

[0079] Typically, a blocking element may be a linearly extending shape. In some instances, a blocking element has a polygonal cross-section extending along the central axis of one of the polygons. In some instances, a blocking element comprises one or more planar surfaces extending in a direction parallel to one of the central axes of the blocking element.

[0080] Since the obstruction flux is used to estimate the incident position of the beam, there is a risk that changes in the flux in the illumination beam will be interpreted as a displacement of position. In some embodiments, the flux of the illumination beam is measured before, immediately after, or simultaneously with the blade measurement. Variations in the illumination flux are compensated for in the analysis of the measured flux 155 to estimate the effect of these variations on the measurement.

[0081] To ensure measurement integrity, the incident position of the illumination beam 116 on the surface of the wafer 101 should remain stationary during measurement within a large range of incident and azimuth angles. To achieve this, the rotation axis 153 of the stage reference frame 143 must be approximately 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 incident point of the illumination beam 116, where the wafer 101 is located at the measurement position.

[0082] FIG. 6A depicts a top view of the illumination beam 116 incident on wafer 101 as depicted in FIG. 5. FIG. 6A depicts an end view of the axis of rotation 153 in alignment with wafer 101, where the incident point of the illumination beam 116 at position 103 on wafer 101 intersects with the illumination beam 116. As depicted in FIG. 6A, when wafer 101 rotates about the axis of rotation 153 within a large incident angle θ, the illumination beam 116 remains incident at position 103. Therefore, in this configuration, the incident position of the illumination beam 116 on the surface of wafer 101 remains stationary during measurement within a large incident angle range.

[0083] FIG6B depicts a top view of the illumination beam 116 incident on wafer 101 as depicted in FIG5. FIG6B also depicts an end view of the rotation axis 153 in an alignment state in which the rotation axis 153 is misaligned with the surface of wafer 101 by a distance z. As depicted in FIG6B, when wafer 101 rotates about the rotation axis 153 within a large incident angle θ, it no longer illuminates a portion of position 103 (i.e., instead, illuminates some other portions of wafer 101). Therefore, in this configuration, the incident position of the illumination beam 116 on the surface of wafer 101 remains stationary during measurement within a large incident angle range, which is highly undesirable.

[0084] FIG6C depicts a top view of an illumination beam 116 incident on wafer 101 as depicted in FIG5. FIG6C also depicts an end view of an aligned state in which the axis of rotation 153 is coplanar with the surface of wafer 101 but offset from the illumination beam 116 by a distance x. As depicted in FIG6C, when wafer 101 rotates about the axis of rotation 153 within a large incident angle θ, it is no longer illuminating a portion of position 103 (i.e., instead illuminating some other portions of wafer 101). Therefore, in this configuration, the incident position of the illumination beam 116 on the surface of wafer 101 drifts during measurement within a large incident angle range, which is highly undesirable.

[0085] In another embodiment, a sample positioning system is calibrated to align the rotation axis of a stage reference frame that is coplanar with the surface of the wafer, blade, or other shielding element, and also to align the rotation axis of the stage reference frame with an illumination beam in a direction approximately parallel to the surface of the wafer (e.g., the XBF direction) such that the rotation axis intersects the illumination beam at the point of incidence on the surface of the wafer, blade, or other shielding element.

[0086] In some embodiments, the rotation axis of the stage reference frame is calibrated by aligning the center of the illumination beam with an X-direction blocking element (e.g., cylindrical pin 151) and measuring the flux at a plurality of different rotational positions θ of the stage reference frame. The apparent motion (ΔX) of the cylindrical pin in the X direction is determined based on a selected blocking model as described above (e.g., the S-shaped function described in FIG8, or other models). Furthermore, 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 axis of rotation in the x direction and the distance z of the axis of rotation in the z direction; 2) the distance n 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. This relationship is described in Equation (3).

[0087]

[0088] In one instance, the transmitted flux is measured at three incident angles {-Θ, 0, +Θ}. One of the linear systems described by equation (4) is derived from equation (3).

[0089]

[0090] Equation (5) is obtained by reversing equation (4). Equation (5) is the solution to the values ​​of n, x and z from the apparent motion of the cylindrical pin in the X direction.

[0091]

[0092] Equation (5), combined with Equation (2), determines the values ​​of n, x, and z of the apparent motion of the cylindrical pin in the X direction for the self-measured flux. In some instances, the values ​​of n, x, and z are obtained repeatedly, as described in Equation (6).

[0093] , of which

[0094] where k is the recurrence 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 with the blade 151 in the X and Z directions. Displacement n is achieved by the actuator 145 moving the entire stage reference frame 143 relative to the illumination beam 116 in the X direction. Displacement x is achieved by the actuator 147 moving the cylindrical pin 151 back to be aligned with the beam. Displacement z is achieved by the actuators 150A to 150C moving the cylindrical pin in the Z direction to align the rotation axis 153 in the plane with the central axis of the cylindrical pin in the Z direction. Starting from an initial estimate w0, the recursion of equation (6) will converge to a point where the rotation axis 153 is aligned with the cylindrical pin 151.

[0095] Generally, it is not necessary to apply equation (6) precisely. The values ​​of AΘ and X / F can be approximated. In other instances, other matrices can be used if the iterations are more stable and converge to the correct values.

[0096] Typically, the transmitted flux can be measured at three or more different incident angles to determine the displacement values ​​required to align the rotation axis 153 with the cutting edge 151 in the X and Z directions. The selection of any three different incident angles results in a linear system of equations that can be directly reversed. The selection of four or more different incident angles results in an overdetermined linear system of equations that can be solved using a quasi-inverse algorithm to determine the displacement values ​​required to align the rotation axis 153 with the cutting edge 151 in the X and Z directions. The matrix terms shown in equations (4) and (5) depend on the selected incident angles. Therefore, in instances where different incident angles are selected, the terms will differ from those in equations (4) and (5).

[0097] For alignment of the rotation axis 153, a blade having a vertical edge in the Y direction can be considered infinitely thin in the Z direction. However, in reality, a blade has a finite thickness. The additional absorption at the longer path length due to larger incident angles can be modeled to compensate for this effect. In other embodiments where a cylindrical blocking element is employed, the recursion described in Equation (6) is applied; however, after convergence, the child offset from the X direction is subtracted from the radius ρ of the cylindrical blocking element to achieve correct alignment.

[0098] For an idealized beam-blocking element and rotation axis, using only one beam-blocking element for beam calibration is sufficient. However, depending on the system requirements, multiple beam blocking may be necessary. By aligning the edges of multiple blocking elements, any deviation of the rotation axis from the nominal YNF axis can be derived. In addition, multiple identical blocking elements allow for calibration of an edge from right and left or from top and bottom, thereby helping to eliminate systematic errors in the imaging edges (i.e., those derived from the imaging by the camera 154) and obvious edges derived from variations in the blocking flux.

[0099] In some other embodiments, the rotation axis of the stage reference frame is calibrated by positioning a high-resolution X-ray camera having a focal plane aligned with the wafer plane of the wafer stage. The position of the illumination point at the wafer plane is measured by the high-resolution X-ray camera as the stage reference frame rotates over a large incident angle range. Based on the measurement, a mapping of the position of the illumination point at the wafer plane according to the incident angle is generated. During the measurement, the wafer stage is commanded to move according to this mapping to maintain the same position of the illumination point for all incident angles.

[0100] In some other embodiments, the rotation axis of the stage reference frame is aligned by positioning a small target (approximately the size of the illumination point) on a wafer having a high diffraction efficiency. The intensity of the diffraction level is measured by detector 119 as the stage reference frame rotates over a large incident angle range. The intensity of the diffraction level indicates the misalignment between the illumination point and the target based on the incident angle. A mapping based on the misalignment based on the measurement is generated. During the measurement, the wafer stage is commanded to move according to this mapping to maintain the same position of the illumination point for all incident angles.

[0101] In another state, one of the AOI offset values ​​between the normal (i.e., zero) angle of incidence of the illumination beam relative to the wafer surface and the zero angle of incidence measured by the sample positioning system (i.e., stage coordinates) is precisely measured.

[0102] In some embodiments, the AOI offset value is determined based on absorption measurements within an AOI range. In one embodiment, an unpatterned region on wafer 101 is subjected to scattering measurements by system 100 within an incident angle range. The relative absorption of the wafer is determined based on the measured intensity of any or all diffraction orders according to the incident angle. The absorption follows Beer's exponential law α = e^(-2βk0L), where L is the absorption length, β is the extinction index of the material, and k0 is the wavenumber. Furthermore, the absorption length is a geometric function of the incident angle L = Tcosθ, where T is the measured wafer thickness. In some instances, a model of the expected response (e.g., Beer's law) is fitted to the measured flux data to determine the offset between the AOI measured by stage metrology (e.g., a rotary encoder corresponding to actuator 146) and the measured AOI at detector 119. The offset is applied by the stage positioning system 140 to the correctly positioned wafer 101 at the AOI to be measured based on one of the stage metrologies.

[0103] In some embodiments, the AOI offset value is determined based on the measurement of the diffraction order of the calibrated grating scattering at one of the two azimuth angles separated by 180 degrees. Figure 9A depicts a grating structure 171 measured by a T-SAXS system 100 at a zero azimuth angle. Figure 9B depicts the same grating structure 171 measured by a T-SAXS system 100 at a 180-degree azimuth angle. As illustrated in Figures 9A and 9B, the grating structure itself is tilted relative to the wafer surface at an angle α. Although the illumination beam 116 is incident on the wafer surface at the same AOI at both azimuth angles, the illumination beam is incident on the tilted grating structure at different angles. Therefore, by measuring the target at the covariant angle (i.e., the azimuth angle separated by 180 degrees), the AOI offset induced by the sample positioning system is maintained, while the AOI offset attributed to the tilt of the grating structure is reversed.

[0104] Figure 10 depicts a graph indicating the measurement intensity of a diffraction level detected by detector 119 for a measurement 172 performed at a zero azimuth angle and another measurement 173 performed at a 180-degree azimuth angle. As depicted in Figure 10, the symmetry point of measurements 172 and 173 indicates the AOI offset of the stage positioning system 140. This offset is applied by the stage positioning system 140 to the correctly positioned wafer 101 at the AOI to be measured based on stage metrology.

[0105] In addition, the difference between the peak value and the symmetry point of each scattering curve indicates the tilt angle α associated with the measured structure. In this way, by measuring one or more diffraction levels of a sample at an incident angle and within two azimuth angles separated by 180 degrees, the calibration of an AOI offset is separated from an angular offset of the target structure itself.

[0106] Typically, any combination of scattering levels can be used to separate the angular offset associated with the tilt of the measured structure from the angular offset associated with the sample positioning system. Utilizing more levels increases measurement accuracy and robustness.

[0107] This set of measurements provides an estimate of one value of a critical metrological parameter (e.g., etched hole tilt) without requiring prior knowledge of the specific structure and is robust to system variations due to the differential nature of the measurements. Additional examples of measurements based on robust and accurate X-rays are described in Andrei Veldman’s U.S. Patent Publication No. 2015 / 0117610, the entire contents of which are incorporated herein by reference.

[0108] In another state, one of the azimuth offset values ​​between the zero azimuth angle of the wafer surface relative to the illumination beam and the zero azimuth angle measured by the sample positioning system (i.e., stage coordinates) is precisely measured. In addition, one of the offset values ​​between the center of the wafer surface and the rotation center of the rotating stage 158 is precisely measured.

[0109] In some embodiments, the alignment camera 154 captures images of known points (e.g., references) located at different positions on the wafer 101. The wafer 101 is moved to different positions of the known points by the X actuator 147, Y actuator 148, and rotary actuator 149. A simple rigid body model of the rotation center point in the wafer coordinates is calculated from the images of the known points and the stage metrology coordinates associated with each of the images. In addition, an azimuth offset, a misalignment between the zero azimuth angle in the characteristic wafer coordinates and the zero azimuth angle in the stage coordinates, is also determined based on the rigid body model. The azimuth offset is applied to the rotary actuator 149 by the stage positioning system 140 to accurately position the wafer 101 at a desired azimuth angle based on stage metrology.

[0110] In some other embodiments, a low-resolution camera estimates the rotation center of an image that has been rotated and translated by a known amount using well-known image alignment techniques.

[0111] In another embodiment, one precise calibration of the azimuth offset between the wafer coordinates and the stage coordinates is based on the position of the diffraction order associated with a measurement of a calibration grating at one or more azimuth angles. The calibration grating has a known grating orientation. In one example, diffraction patterns at different azimuth angles are measured by detector 119. The azimuth angle is adjusted until the desired diffraction pattern is measured at detector 119. The azimuth angle associated with this measurement is the azimuth offset. If the detector is aligned with the stage, an angle of incidence is sufficient to calibrate the azimuth angle of the wafer relative to the stage.

[0112] In another configuration, multiple calibrated incident angles, along with well-known formulas for conical diffraction, are used to calibrate the detector relative to the stage and simultaneously calibrate the azimuth relative to the stage. When the AOI is changed for a given azimuth at the stage, the detected diffracting stage moves along a designated manifold. However, the rotational offset of the detector will be a constant offset.

[0113] In the depicted embodiment, the beam shaping slit mechanism 120 is configured to rotate about a beam axis aligned with the orientation of the sample to optimize the profile of the incident beam at each incident angle, azimuth angle, or both. In this way, the beam shape matches the shape of the metrological target. As depicted in FIG5, the rotary actuator 122 rotates the frame 120 and all attachment mechanisms, actuators, sensors, and slits about the axis of the illumination beam 116. Unfortunately, a defect in the rotary actuator 120 causes the beam shaping slit mechanism 120 to precess about the axis of the illumination beam when it rotates relative to the flight tube 118. This causes the incident position of the illumination beam 116 to drift with respect to different azimuth angles and corresponding beam slit angles.

[0114] In a further state, a calibration mapping of the XY stage offset is determined based on the measurement of the incident position of the illumination beam 116 within the azimuth angle and the corresponding beam slit angle range.

[0115] In some embodiments, the measurement is performed by an X-ray camera having a focal plane at a location on the wafer surface. The incident position of the illumination beam 116 is recorded as the azimuth angle and the corresponding beam slit angle change. Based on the functional relationship between the azimuth angle and the incident position, a calibration mapping is generated that provides an XY stage offset that maintains the same incident position for any azimuth angle.

[0116] In some other embodiments, a calibration map for the XY stage offset is determined based on a small target (approximately the size of the illumination point) measured by a detector 119 within an azimuth angle and a corresponding beam slit angle range. This target has high diffraction efficiency. The measured intensity of the diffraction level indicates the misalignment between the target and the incident position of the illumination beam 116 at each azimuth angle and corresponding beam slit angle. Based on the functional relationship between the azimuth angle and the measured misalignment, a calibration map for the XY stage offset is generated that provides the same incident position for any azimuth angle.

[0117] In another example, the shape of the wafer surface in the Z direction is mapped using a aligned camera, an optical proximity sensor, a capacitive proximity sensor, or any other suitable proximity sensor. In some instances, the wafer surface is mapped to the front side (i.e., the patterned side) of the wafer. In some other instances, if the wafer thickness is sufficiently uniform or well-modeled, the wafer surface is mapped to the back side of the wafer. In some instances, the wafer pattern is modeled using several standard interpolators (e.g., polynomial basis functions, rational functions, neural networks, etc.). Furthermore, an analytical or numerical bending model of the wafer may be used to couple lateral and height displacements.

[0118] In a further embodiment, Z-actuators 150A to 150C are controlled to adjust 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 calibrated by Z-actuators 150A to 150C. Tilt calibration may be based on a mapping of wafer tilt or a locally measured tilt value.

[0119] In another further embodiment, Z-actuators 150A to 150C are controlled to adjust the wafer's Z-position, Rx orientation, Ry orientation, or any combination thereof to align the axis of rotation 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 remains in the 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.

[0120] Typically, 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 stage mapping that explains the non-ideal conditions in the wafer and stage.

[0121] In addition, changes in temperature and air pressure or any other ambient conditions may affect the positioning of the illumination beam. In some embodiments, beam movement and beam position are related to these variables based on measured temperature and pressure and related models.

[0122] Typically, the sample positioning system 140 may include any suitable combination of material elements for achieving the desired linear and angular positioning performance, including (but not limited to) a goniometer stage, a hexapod stage, an angular stage, and a linear stage.

[0123] Typically, the focal plane of the illumination optics system is optimized for each measurement application. In this way, system 100 is configured to position the focal plane at various depths within the sample depending on the measurement application. In one example, sample positioning system 140 is configured to move sample 101 in the z-direction to position the wafer within the focal plane of the optical system at the desired depth within sample 101.

[0124] In some embodiments, the x-ray illumination source 110, focusing optics 111, slits 112 and 113, or any combination thereof, are maintained in an atmospheric environment (e.g., a gas-purified environment) identical to that of sample 101. However, in some embodiments, the optical path lengths between and within any of these elements are relatively long, and X-ray scattering in the air contributes noise to the image on the detector. Therefore, in some embodiments, the x-ray illumination source 110, focusing optics 111, and any of 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 a vacuum window.

[0125] Similarly, in some embodiments, the x-ray detector 119 is maintained in an atmospheric environment (e.g., a gas-purified environment) identical to that of the sample 101. However, in some embodiments, the distance between the sample 101 and the x-ray detector 119 is very long, and X-ray scattering in the air contributes noise to the detected signal. Therefore, in some embodiments, one or more x-ray detectors are maintained in a localized vacuum environment separated from the sample (e.g., sample 101) by a vacuum window.

[0126] Figure 11 illustrates a vacuum chamber 160 containing an X-ray illumination source 110, a vacuum chamber 162 containing a focusing optics device 111, and a vacuum chamber 163 containing 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 made of any suitable material that is substantially transparent to X-ray radiation (e.g., Kapton, Beryllium, etc.). A suitable vacuum environment is maintained within each vacuum chamber to minimize the scattering of the illumination beam. A suitable vacuum environment can include any suitable vacuum level, any suitable cleanroom containing a gas with a small atomic number (e.g., helium), or any combination thereof. In this way, as many beam paths as possible are located in vacuum to minimize flux and minimize scattering.

[0127] In some embodiments, the entire optical system (including sample 101) is maintained in a vacuum. However, the cost associated with maintaining sample 101 in a vacuum is generally high due to the complexity associated with the construction of sample positioning system 140.

[0128] 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. Typically, it is desirable to encapsulate as much of the beam as possible in a vacuum before incident with 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. A vacuum window 164 is located at the output of the vacuum chamber 163 within the beam shaping slit mechanism 120 such that the incident beam 115 is retained in a vacuum within a portion of the beam shaping slit mechanism 120 before passing through the vacuum window 164 before interacting with any of the slits 126 to 129 and the sample 101.

[0129] In the embodiment depicted in FIG1, the focusing optics 111, slits 112 and 113 and the beam shaping slit mechanism 120 are maintained in a controlled environment (e.g., vacuum) within a flight tube 118.

[0130] 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 containing at least one geometric parameter from the structural model, and resolve at least one sample parameter value by performing a fitting analysis of the T-SAXS measurement data and the T-SAXS response model. An analysis engine is used to compare the simulated T-SAXS signal with the measured data, thereby allowing the determination of geometric and material properties (such as the electron density of the sample). In the embodiment depicted in Figure 1, the computing system 130 is configured as a model building and analysis engine to implement model building and analysis functionality, as described herein.

[0131] Figure 12 is a diagram illustrating an exemplary model building and analysis engine 180 implemented by the computing system 130. As depicted in Figure 12, 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 receives input as input to a 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 an x-ray form factor.

[0132] where F is the form factor, q is the scattering vector, and ρ(r) is the electron density of the sample in spherical coordinates. Next, the X-ray scattering intensity is given by the following equation.

[0133] 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 measurement data to determine the geometry and material properties of the sample.

[0134] In some instances, minimizing the chi-square value is used to achieve a fit between the modeled data and the experimental data. For example, in the case of T-SAXS measurement, the chi-square value can be defined as...

[0135] 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.). (v1,...vL) is the modeled T-SAXS signal Sj of "channel" j estimated for a set of structural (target) parameters v1,...vL, where these parameters describe geometry (CD, sidewall angles, overlap, etc.) and material (electron density, etc.). σSAXS,j is the uncertainty associated with the j-th channel. NSAXS is the total number of channels in the X-ray metrology. L is the number of parameters characterizing the metrological target.

[0136] Equation (9) assumes that the uncertainties associated with different channels are uncorrelated. In instances where the uncertainties associated with different channels are correlated, a covariance between the uncertainties can be calculated. In such instances, a chi-square value of the T-SAXS measurement can be expressed as

[0137] Where VSAXS is the covariance matrix of the uncertainty of the SAXS channel, and T indicates the transpose.

[0138] 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.

[0139] As described above, the fit of T-SAXS data is achieved by minimizing the chi-square value. However, the fit of T-SAXS data can usually be achieved by other functions.

[0140] Fitting T-SAXS metrological data is advantageous for any type of T-SAXS technique that provides sensitivity to the geometry 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., RMS height of sidewall roughness, roughness correlation length, etc.).

[0141] Typically, the computing system 130 is configured to access model parameters in real-time using Real-Time Critical Dimensioning (RTCD), or a library of programs that can access a pre-computed model for determining one of the values ​​of at least one sample parameter associated with sample 101. Typically, some form of CD engine can be used to estimate 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 calculating sample parameter values ​​is described in U.S. Patent No. 7,826,071 to KLA-Tencor Corp., issued November 2, 2010, the entire contents of which are incorporated herein by reference.

[0142] In some instances, the model building and analysis engine 180 improves the accuracy of measurement parameters through any combination of side-feed analysis, feedforward analysis, and parallel analysis. Side-feed analysis refers to taking 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 taking datasets from different samples and using a progressively replicating accurate parameter feedforward method to forward transfer common parameters to subsequent analyses. Parallel analysis refers to the parallel or simultaneous application of a nonlinear fitting method to multiple datasets, where at least one common parameter is coupled during fitting.

[0143] Multiple tools and structure analysis refers to a method and system for multiple tools and structure analysis based on a regression-based feedforward, feedforward, or parallel analysis, a lookup table (i.e., "library" matching), or another fitting procedure for multiple datasets. U.S. Patent No. 7,478,019, issued January 13, 2009, by KLA-Tencor Corp., the entire contents of which are incorporated herein by reference.

[0144] In another further embodiment, an initial estimate of the value of one or more parameters of interest is determined based on a T-SAXS measurement performed at a single orientation of the incident X-ray beam relative to the measurement target. The initial estimate is implemented as the starting value for a regression of the parameter of interest using measurement data collected from T-SAXS measurements at multiple orientations. In this manner, an approximate estimate of the parameter of interest is determined with a relatively small computational workload, and a refined estimate of the parameter of interest is obtained with a relatively small overall computational workload by implementing this approximate estimate as the starting point for a regression on a much larger dataset.

[0145] In another embodiment, the measuring instrument 100 includes a computing system (e.g., computing system 130) configured to implement beam control functions 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, spot size, polarity, spectrum, and positioning of the incident illumination beam 116.

[0146] 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 one of the measurement responses of the sample (i.e., the intensity of the diffraction order). Based on the distribution of the measurement responses on the surface of the detector 119, the position and area of ​​the illumination beam 116 incident on the sample 101 are determined by the computing system 130. In one example, pattern recognition technology is applied by the computing system 130 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 or redirect x-ray emission. 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 so that the incident illumination beam 116 reaches the sample 101 with 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 relative to one of the samples 101 for a desired orientation. 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 angular orientation relative to the sample 101.

[0147] In a further embodiment, 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 coexisting electron density grid. This model is matched to the measurement signal while constraining the modeled electron density in the grid to enforce continuity and sparse edges, providing a three-dimensional image of the sample.

[0148] Although geometric, model-based parametric inversion systems are better for critical size (CD) measurements based on T-SAXS measurements, a mapping of samples from the same T-SAXS measurement data is useful for identifying and calibrating model error systems when the measured sample deviates from the assumptions of the geometric model.

[0149] In some instances, the image is compared with the structural characteristics estimated by a model-based parametric inversion from one of the measurement data obtained from the same scattering measurements. The discrepancy is used to update the geometric model of the measurement structure and improve measurement performance. The ability to converge to an accurate parametric measurement model is particularly important when measuring integrated circuits for control, monitoring, and troubleshooting of the manufacturing process of integrated circuits.

[0150] In some instances, a two-dimensional (2-D) plot of the electron density, absorbance, complex refractive index, or a combination of such material properties is generated. In some instances, a three-dimensional (3-D) plot of the electron density, absorbance, complex refractive index, or a combination of such material properties is generated. This plot is generated using relatively few solid constraints. In some instances, one or more parameters of interest (such as critical dimension (CD), sidewall angle (SWA), overlap, edge placement error, spacing displacement, etc.) are estimated directly from the resulting plot. In some other instances, the plot is useful for eliminating wafer process faults when the sample geometry or material deviates from the expected values ​​predicted by a parametric structure model used for model-based CD measurements. In one instance, the difference between the plot and a transposition of the structure predicted by a parametric structure model based on its measurement parameters is used to update the parametric structure model and improve its measurement performance. Further details are described in U.S. Patent Publication No. 2015 / 0300965, the entire contents of which are incorporated herein by reference. Additional details are described in U.S. Patent Publication No. 2015 / 0117610, the entire contents of which are incorporated herein by reference.

[0151] In a further example, a model building and analysis engine 180 is used to generate a model combining 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 equations are solved to calculate optical signals (such as reflectivity to different polarities, ellipsometer parameters, phase transitions, etc.).

[0152] The values ​​of one or more parameters of interest are determined by a combination fitting analysis based on the detected intensities of X-ray diffraction orders at a plurality of different incident angles and the detected optical intensities using a combined geometrically parameterized response model. The optical intensities are 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 entire contents of which are incorporated herein by reference.

[0153] Typically, a metrology target is characterized by an aspect ratio defined as a maximum height dimension (i.e., the dimension perpendicular to the wafer surface) divided by a maximum lateral extension dimension (i.e., the dimension aligned with the wafer surface). In some embodiments, the metrology target under measurement has an aspect ratio of at least 20. In some embodiments, the metrology target has an aspect ratio of at least 40.

[0154] It should be understood that the various steps described in this invention can be implemented 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 implementing 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, the one or more computing systems 130 can be configured to perform any of any other steps of any of the method embodiments described herein.

[0155] 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, the one or more computing systems 130 can be coupled to computing systems respectively associated with the x-ray illumination source 110, the beam shaping slit mechanism 120, the sample positioning system 140, and the detector 119. In another example, any 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.

[0156] 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, and 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.

[0157] The computer system 130 of the metrology system 100 can be configured to receive and / or acquire data or information (e.g., measurement results, modeling input, modeling results, etc.) from other systems via a transmission medium that may include wired and / or wireless components. In this manner, the transmission medium can act as a data link between the computer system 130 and other systems (e.g., on-board metrology system 100, external memory, or external systems). 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 190) 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 190). Accordingly, measurement results can be input from on-board memory or from an external memory system. Furthermore, the computer system 130 can transmit 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 190). Accordingly, the measurement result can be output to another system.

[0158] 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, the term "computing system" may be broadly defined to cover any device having one or more processors that execute instructions from a memory medium.

[0159] The program instructions 134 of the implementation method (such as the program instructions described herein) may 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. The 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.

[0160] Figure 13 illustrates one method 200 suitable for an embodiment of the metrology system 100 of the present invention. In one example, it is recognized that the data processing block of method 200 can be implemented via a pre-programmed algorithm executed by one or more processors of computing system 130. Although the metrology system 100 is presented in the text below, it should be understood herein that the particular structural example of metrology system 100 is not intended to be limiting and should be construed as illustrative only.

[0161] In block 201, a diffraction grating disposed on a semiconductor wafer is positioned in the path of an X-ray illumination beam at a plurality of incident angles at a first azimuth angle and at the same plurality of incident angles at a second azimuth angle. The first azimuth angle and the second azimuth angle are separated by 180 degrees.

[0162] In block 202, a diffraction level response signal is detected based on both the first azimuth angle and the second azimuth angle and is associated with a measurement of the diffraction grating at the plurality of incident angles.

[0163] In block 203, an angle of incidence (AOI) offset value is determined. This AOI offset is the angle between a normal angle of incidence of the X-ray illumination beam relative to the wafer surface and a zero angle of incidence measured by a wafer positioning system that positions the diffraction grating within the path of the X-ray illumination beam. The AOI offset value is the angle of incidence measured by the wafer positioning system at a symmetrical point associated with an intersection of detected diffraction level response signals related to the first azimuth and the second azimuth.

[0164] In some embodiments, the scattering measurement as described herein is incorporated into a manufacturing process tool. Examples of manufacturing process tools include (but are not limited to) lithography tools, thin film deposition tools, implantation tools, and etching tools. In this manner, the results of a T-SAXS analysis are used to control a manufacturing process. In one example, T-SAXS measurement data collected from one or more targets are sent to a manufacturing process tool. The T-SAXS measurement data is analyzed as described herein, and the results are used to adjust the operation of the manufacturing process tool.

[0165] The scattering measurement method described herein can be used to determine the characteristics of a variety of semiconductor structures. Exemplary structures include (but are not limited to) FinFETs, low-size structures (such as nanowires or graphene), sub-10nm structures, lithography structures, through-substrate vias (TSVs), memory structures (such as DRAM, DRAM 4F2, FLASH, MRAM), and high aspect ratio memory structures. Exemplary structural characteristics include (but are not limited to) geometric parameters (such as line edge roughness measurement, linewidth roughness, aperture size, aperture density, sidewall angles, profile, critical size, spacing, thickness, overlap) 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 aperiodic.

[0166] In some instances, the T-SAXS measurement system as described herein is used to perform measurements of critical dimensions, thickness, overlap, 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).

[0167] 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.), a critical dimension between any two or more structures (e.g., the distance between two structures), and a displacement between two or more structures (e.g., the overlap displacement between overlapping grating structures, etc.). Structures may include three-dimensional structures, patterned structures, overlapping structures, etc.

[0168] As described herein, the terms “critical dimension application” or “critical dimension measurement application” include any critical dimension measurement.

[0169] As described herein, the term "metrology system" includes any system at least partially employed to characterize a sample in any state, including critical dimension applications and overlay 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 for the measurement of patterned and / or unpatterned wafers. A metrology system can be configured as an LED inspection tool, an edge inspection tool, a backside inspection tool, a giant 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.

[0170] This document describes various embodiments of 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 is processed in a manner known in the art (e.g., for printing or inspecting defects).

[0171] As described 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. Such substrates are typically found and / or processed in semiconductor manufacturing facilities. In some cases, a wafer may contain only a substrate (i.e., a bare wafer). Alternatively, a wafer may contain one or more different materials formed on a substrate. The one or more materials formed on a wafer may be "patterned" or "unpatterned." For example, a wafer may contain a plurality of grains having repeatable pattern features.

[0172] A "reduced photomask" may be a reduced photomask at any stage of a reduced photomask manufacturing process, or it may be a complete reduced photomask that may or may not be released for use in a semiconductor manufacturing facility. A reduced photomask or a "mask" is generally defined as a substantially transparent substrate having substantially opaque areas formed thereon and configured as a pattern. The substrate may comprise, for example, a glass material (such as amorphous SiO2). During an exposure step in a lithography process, a reduced photomask may be placed over a wafer covered with photoresist such that the pattern on the reduced photomask can be transferred to the photoresist.

[0173] One or more patterned or unpatterned layers formed on a wafer. For example, a wafer may contain a plurality of grains, each grain having repeatable pattern features. The formation and processing of these material layers can ultimately result in a complete device. Many different types of devices can be formed on a wafer, and the term wafer (as used herein) is intended to cover a wafer on which any type of device known in the art is manufactured.

[0174] 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 codes on a computer-readable medium or may be transmitted as one or more instructions or codes 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 media accessible by a general-purpose or special-purpose computer. For example (but not limited to), such computer-readable media may include RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other media 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 or special-purpose computer, or a general-purpose or special-purpose processor. Additionally, any connection is 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 that coaxial cable, fiber optic cable, twisted pair, DSL, or wireless technology (such as infrared, radio, and microwave) is 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 using laser optical copying. The combination of the above should also be included within the scope of computer-readable media.

[0175] Although certain specific embodiments have been described above for illustrative purposes, the teachings of this patent document are of general applicability and are not limited to the specific embodiments described above. Accordingly, various modifications, adaptations, and combinations of features of the described embodiments may be practiced without departing from the scope of the invention as set forth in the claims.

Claims

1. 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 periodic structure on a semiconductor wafer relative to an X-ray illumination beam, such that the X-ray illumination beam is incident on the periodic structure at each of a plurality of incident angles; an X-ray detector configured to detect at least one level of a diffraction level response signal associated with a scattering measurement of the periodic structure at each of the plurality of incident angles; and a computing system configured to determine a tilt angle between the periodic structure and the X-ray illumination beam incident on the semiconductor wafer based on a symmetry point of the diffraction level response signals.

2. As in request item 1, the computing system is further configured to: adjust a manufacturing process tool based on the determined tilt angle.

3. The system of claim 2, wherein the manufacturing process tool is any one of a photolithography tool, a thin film deposition tool, an implantation tool, and an etching tool.

4. The system of claim 1, wherein an angle of incidence associated with the symmetry point measured by the sample positioning system that positions the periodic structure in one path of the x-ray illumination beam is the angle of incidence at the point where the x-ray illumination beam is aligned with the normal to one surface of the semiconductor wafer.

5. The system of claim 1, wherein the determination of one of the tilt angle values ​​involves determining a difference between an angle of incidence associated with a peak of one of the detected diffraction level response signals and an angle of incidence associated with the symmetric point.

6. The system of claim 1, wherein the diffraction level response signal includes signal information associated with a plurality of diffraction levels.

7. A measurement method, comprising: according to An X-ray illumination beam at one of a plurality of incident angles illuminates a periodic structure disposed on a semiconductor wafer; at least one of a diffraction level response signals associated with a scattering measurement of the periodic structure at each of the plurality of incident angles is detected; and a tilt angle between the periodic structure and the X-ray illumination beam incident on the semiconductor wafer is determined based on a symmetry point of the diffraction level response signals.

8. The method of claim 7, further comprising: Based on the determined tilt angle adjustment, a manufacturing process tool is used.

9. The method of claim 8, wherein the manufacturing process tool is any one of a photolithography tool, a thin film deposition tool, an implantation tool, and an etching tool.

10. The method of claim 7, wherein an angle of incidence associated with the symmetry point measured by a wafer positioning system that positions the periodic structure in one path of the x-ray illumination beam is the angle of incidence at the point where the x-ray illumination beam is aligned with the normal of one surface of the semiconductor wafer.

11. The method of claim 7, wherein the determination of one value of the tilt angle involves determining a difference between an angle of incidence associated with a peak of one of the detected diffraction level response signals and an angle of incidence associated with the symmetric point.

12. The method of claim 7, wherein the diffraction level response signal includes signal information associated with a plurality of diffraction levels.

13. 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 periodic structure on a semiconductor wafer relative to an X-ray illumination beam, such that the X-ray illumination beam is incident on the periodic structure at each of a plurality of incident angles; an X-ray detector configured to detect at least one level of a diffraction level response signal associated with a scattering measurement of the periodic structure at each of the plurality of incident angles; and a computing system configured to determine, in the absence of a model of the detected diffraction level response signals, a tilt angle between the periodic structure and the X-ray illumination beam incident on the semiconductor wafer, wherein the determination of the tilt angle is based on the difference between the diffraction level response signals.

14. The system of request item 13, wherein the computing system is further configured to: adjust a manufacturing process tool based on the determined tilt angle.

15. The system of claim 14, wherein the manufacturing process tool is any one of a photolithography tool, a thin film deposition tool, an implantation tool, and an etching tool.

16. The system of claim 13, wherein an angle of incidence associated with a symmetrical point measured by the sample positioning system that positions the periodic structure in one path of the x-ray illumination beam is the angle of incidence at the point where the x-ray illumination beam is aligned with the normal to one surface of the semiconductor wafer.

17. The system of claim 16, wherein the computing system is further configured to: determine the symmetry point based on a difference between an angle of incidence associated with a peak of a detected diffraction level response signal associated with measurements at the plurality of angles of incidence and a first azimuth and an angle of incidence associated with a peak of a detected diffraction level response signal associated with measurements at the plurality of angles of incidence and a second azimuth.

18. The system of claim 17, wherein the calculation system is further configured to: determine a value of the tilt angle as a difference between the angle of incidence associated with the peak value of the detected diffraction level response signals associated with the measurements at the plurality of incident angles and the first azimuth angle and an angle of incidence associated with the symmetric point.

19. The system of claim 13, wherein the diffraction level response signal includes signal information associated with a plurality of diffraction levels.

20. A measurement method, comprising: according to An X-ray illumination beam at one of a plurality of incident angles illuminates a periodic structure disposed on a semiconductor wafer; at least one level of a diffraction level response signal associated with a scattering measurement of the periodic structure at each of the plurality of incident angles is detected; and, in the absence of a model of such detected diffraction level response signals, a tilt angle between the periodic structure and the X-ray illumination beam incident on the semiconductor wafer is determined, wherein the determination of the tilt angle is based on the difference between the diffraction level response signals.

21. The method of claim 20, further comprising: Based on the determined tilt angle adjustment, a manufacturing process tool is used.

22. The method of claim 21, wherein the manufacturing process tool is any one of a photolithography tool, a thin film deposition tool, an implantation tool, and an etching tool.

23. The method of claim 20, wherein an angle of incidence associated with a symmetrical point measured by a wafer positioning system that positions the periodic structure in one path of the x-ray illumination beam is the angle of incidence at the point where the x-ray illumination beam is aligned with the normal to one surface of the semiconductor wafer.

24. The method of claim 23, further comprising: The symmetry point is determined based on a difference between an angle of incidence associated with a peak value of the detected diffraction response signal associated with measurements at the plurality of angles of incidence and a first azimuth and an angle of incidence associated with a peak value of the detected diffraction response signal associated with measurements at the plurality of angles of incidence and a second azimuth.

25. The method of claim 24, further comprising: The tilt angle is determined as a difference between the angle of incidence associated with the peak value of the detected diffraction level response signal associated with the measurements at the plurality of incident angles and the first azimuth angle, and an angle of incidence associated with the symmetric point.

26. The method of claim 20, wherein the diffraction level response signal includes signal information associated with a plurality of diffraction levels.

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