High signal-to-noise ratio scanning superposition metrology

Abstract

A superposition metrology system may include: illumination optics for splitting illumination from an illumination source into primary and secondary illumination and directing the primary illumination to a sample comprising a superposition target having gratings in two or more layers; and an objective lens for collecting positive and negative diffraction from the constituting gratings. The system may further include collection optics for overlapping auxiliary illumination with at least some of the collected diffraction lobes to generate a time-varying interference signal. The system may further include a controller for generating superposition measurements based on the time-varying interference signal.

Description

Technical Field

[0001] This disclosure generally relates to superposition metrology, and more specifically, to scanning superposition metrology based on scattering techniques. Background Technology

[0002] The growing demand for smaller semiconductor devices has led to a corresponding increase in the need for accurate and efficient metrology. One approach to improving the efficiency and throughput of metrology tools is to generate metrological data about the sample while it is moving within the measurement field of view, rather than in a static position. In this way, the time delay associated with a stable translation stage before measurement can be eliminated or reduced. However, improving the sensitivity and throughput of such measurements remains a core challenge for this type of scanning metrology method. Therefore, it is desirable to provide systems and methods to address these shortcomings. Summary of the Invention

[0003] According to one or more illustrative embodiments, a superposition metrology system is disclosed. In one illustrative embodiment, the system includes an illumination source. In another illustrative embodiment, the system includes a first beam splitter configured to split illumination from the illumination source into a main illumination and an auxiliary illumination. In another illustrative embodiment, the system includes one or more illumination optics configured to guide the main illumination onto a superposition target on a sample during metrology formulation application, wherein the superposition target according to the metrology formulation comprises gratings in two or more layers. In another illustrative embodiment, the system includes an objective lens for collecting at least one positive diffraction lobe and at least one negative diffraction lobe associated with diffraction of the main illumination from the gratings in each of the two or more layers during metrology formulation application. In another illustrative embodiment, the system includes one or more photodetectors in a collection pupil plane. In another illustrative embodiment, the system includes one or more collection optics configured to implement the metrology formula by: overlapping a first portion of the auxiliary illumination with at least one diffraction lobe of the main illumination through the superimposed target onto at least one of the one or more photodetectors to generate a first interference pattern; and overlapping a second portion of the auxiliary illumination with at least one additional diffraction lobe of the main illumination through the superimposed target onto at least one of the one or more photodetectors to generate a second interference pattern. In another illustrative embodiment, the system includes a scanning subsystem comprising a stage or at least one of one or more scanning optics to modulate the phase of the first and second interference patterns during scanning of the superimposed target when implementing the metrology formula. In another illustrative embodiment, the system includes a controller for receiving time-varying interference signals from the one or more photodetectors during scanning of the superimposed target and generating one or more superimposed measurements of the superimposed target based on the time-varying interference signals.

[0004] According to one or more illustrative embodiments, a superposition metrology method is disclosed. In one illustrative embodiment, the method includes generating illumination using an illumination source. In another illustrative embodiment, the method includes splitting the illumination from the illumination source into a main illumination and an auxiliary illumination. In another illustrative embodiment, the method includes guiding the main illumination to a superposition target on a sample, wherein the superposition target comprises gratings in two or more layers. In another illustrative embodiment, the method includes overlapping a first portion of the auxiliary illumination with at least one diffraction lobe associated with diffraction of the main illumination from the gratings in each of the two or more layers onto one or more first photodetectors in a collection pupil plane to generate a first interference pattern. In another illustrative embodiment, the method includes overlapping a second portion of the auxiliary illumination with at least one additional diffraction lobe associated with diffraction of the main illumination from the gratings in each of the two or more layers onto one or more second photodetectors in the collection pupil plane to generate a second interference pattern. In another illustrative embodiment, the method includes modulating the phases of the first and second interference patterns during scanning of the superimposed target with a scanning subsystem, wherein the scanning subsystem includes at least one of a translation stage for scanning the sample relative to the main illumination, a beam-scanning optics for scanning the main illumination relative to the sample, or a phase modulator for modulating the phase of the auxiliary illumination. In another illustrative embodiment, the method includes generating a time-varying interference signal using the one or more first photodetectors and the one or more second photodetectors based on the modulated phases of the first and second interference patterns. In another illustrative embodiment, the method includes generating one or more superimposed measurements of the superimposed target based on the time-varying interference signal.

[0005] According to one or more illustrative embodiments, a superposition metrology system is disclosed. In one illustrative embodiment, the system includes an illumination source configured to generate illumination. In another illustrative embodiment, the system includes one or more beam splitters configured to split the illumination from the illumination source into a main illumination and an auxiliary illumination. In another illustrative embodiment, the system includes one or more illumination optics configured to guide the main illumination onto a superposition target (the superposition target having gratings in two or more layers) on a sample during metrology formulation, wherein the superposition target according to the metrology formulation includes one or more units containing a first group of gratings having a first grating orientation and one or more units containing a second group of gratings having a second grating orientation, and wherein the main illumination has a rotated quadrupole distribution relative to the first and second grating orientations. In another illustrative embodiment, the system includes an objective lens for collecting at least one positive diffraction lobe and at least one negative diffraction lobe associated with the diffraction of the main illumination from the gratings in each of the two or more layers during metrology formulation. In another illustrative embodiment, the system includes a first collection channel having one or more photodetectors in a first group of one or more collection pupil planes. In another illustrative embodiment, the first collection channel is configured to implement the metrological formulation by: overlapping a first portion of the auxiliary illumination with at least one diffraction lobe of the main illumination along a first diagonal of the rotating quadrupole distribution through the superposition target onto at least one of the one or more photodetectors in the first group to produce a first interference pattern; and overlapping a second portion of the auxiliary illumination with at least one additional diffraction lobe of the main illumination along a first diagonal of the rotating quadrupole distribution through the superposition target onto at least one of the one or more photodetectors in the first group to produce a second interference pattern. In another illustrative embodiment, the system includes a second collection channel having one or more photodetectors in a second group of one or more collection pupil planes. In another illustrative embodiment, the second collection channel is configured to implement the metering formulation by: overlapping a first portion of the auxiliary illumination with at least one diffraction lobe of the main illumination along the second diagonal of the rotating quadrupole distribution through the superposition target onto at least one of one or more photodetectors in the second group to produce a third interference pattern; and overlapping a second portion of the auxiliary illumination with at least one additional diffraction lobe of the main illumination along the second diagonal of the rotating quadrupole distribution through the superposition target onto at least one of one or more photodetectors in the second group to produce a fourth interference pattern.In another illustrative embodiment, the system includes a scanning subsystem configured to modulate the phases of the first, second, third, and fourth interference patterns during scanning of the superimposed target when implementing the metrology formula. The scanning subsystem includes at least one of a translation stage for scanning the sample relative to the main illumination, a beam-scanning optics for scanning the main illumination relative to the sample, or a phase modulator for modulating the phase of the auxiliary illumination. In another illustrative embodiment, the system includes a controller configured to receive time-varying interference signals from the first and second collection channels during scanning of the superimposed target and to generate one or more superimposed measurements of the superimposed target based on the time-varying interference signals along the first and second grating directions.

[0006] It should be understood that the above general description and the following detailed description are for illustrative purposes only and do not necessarily limit the invention. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the general description, serve to explain the principles of the invention. Attached Figure Description

[0007] Those skilled in the art will better understand the many advantages of this disclosure by referring to the accompanying drawings.

[0008] Figure 1A This is a conceptual diagram of a superposition metrology system according to one or more embodiments of the present disclosure for performing scattering superposition metrology on a superposition target suitable for superposition measurement along any particular measurement direction.

[0009] Figure 1B This is a schematic diagram of a superimposed metering tool according to one or more embodiments of the present disclosure.

[0010] Figure 2A This is a top view of a unit of a superimposed target having a textured structure according to one or more embodiments of the present disclosure.

[0011] Figure 2B On a substrate according to one or more embodiments of this disclosure Figure 2A A side view of a single unit of the superimposed target.

[0012] Figure 2C This is a side view of a superimposed target according to one or more embodiments of the present disclosure, the superimposed target comprising two units having different configurations of a textured structure suitable for superimposed measurements along a particular measurement direction.

[0013] Figure 3A This is a top view of the illumination pupil plane of a superimposed measuring tool according to one or more embodiments of the present disclosure.

[0014] Figure 3BThis is a top view of the collection pupil boundary in the collection pupil plane of a superimposed metering tool according to one or more embodiments of the present disclosure, illustrating the interaction between auxiliary illumination and main illumination. Figures 2A to 2C The overlap between the + / -1st order diffraction lobes of the lattice structure.

[0015] Figure 4 This is a conceptual diagram of a metering tool for providing tilted main lighting and associated auxiliary lighting according to one or more embodiments of the present disclosure.

[0016] Figure 5 This is a conceptual diagram of a superposition metering tool that simultaneously characterizes superposition targets and multiple lighting conditions according to one or more embodiments of the present disclosure.

[0017] Figure 6 This is a flowchart illustrating the steps performed in a superposition metering method according to one or more embodiments of the present disclosure. Detailed Implementation

[0018] The objectives of this disclosure will now be explained in detail with reference to the accompanying drawings. This disclosure has been specifically shown and described with respect to particular embodiments and their specific features. The embodiments set forth herein should be considered illustrative rather than limiting. It will be readily apparent to those skilled in the art that various changes and modifications in form and detail may be made without departing from the spirit and scope of this disclosure.

[0019] Embodiments of this disclosure pertain to systems and methods for scanning scattering superposition based on time-varying interferometric signals generated by superimposing a target onto a grating using reference light (e.g., auxiliary illumination herein). It is anticipated that the systems and methods disclosed herein can facilitate rapid superposition measurements of moving samples with high signal-to-noise ratios.

[0020] Some scattering-based superposition techniques involve illuminating the superposition target with a periodic structure (e.g., a grating structure) associated with different photolithographic exposures and determining the superposition error associated with said exposure based on the asymmetry of diffraction orders (e.g., +1 and -1 diffraction lobes). For example, the phase difference between light associated with diffraction from different grating structures can cause intensity variations in the pupil plane, such as (but not limited to) interference fringes. In this way, the asymmetry of the periodic structure (e.g., superposition error) can lead to asymmetry in the interference fringes, which can serve as the basis for superposition measurements.

[0021] Furthermore, scanning-based scattering superposition measurements can be performed by scanning an illumination beam (or vice versa) relative to a superimposed target containing such grating structures, where the illumination beam is set to a size smaller than the superimposed target. In this configuration, the interference pattern associated with diffraction from the two grating structures can oscillate with a time-varying interference signal during the scan, which can be captured using a photodetector with sufficient bandwidth. For example, this technique can be implemented using a relatively fast photodetector (e.g., but not limited to, a photodiode, a burst photodiode, or the like) positioned in the plane of the collection pupil. Additionally, scanning the illumination beam relative to the superimposed target can generally be performed by movement of the superimposed target, the illumination beam, or both.

[0022] Various measurement methods have been developed based on these general principles. Generally, the position of the time-varying interferometric signal in the collecting pupil can depend on the layout and pitch of the grating structure of the superimposed target. Scanning-based scattering superposition techniques are broadly described in the following: U.S. Patent No. 11,300,405, published April 12, 2022; U.S. Patent No. 11,378,394, published July 5, 2022; U.S. Patent No. 10,197,389, published February 5, 2019; U.S. Patent Application No. 17 / 708,958, filed March 30, 2022; U.S. Patent Application No. 17 / 709,104, filed March 30, 2022; and U.S. Patent Application No. 18 / 099,798, all of which are incorporated herein by reference in their entirety.

[0023] It is anticipated that capturing such time-varying interference signals at the overlap of the 0th-order illumination with the diffraction lobes constituting the grating may be advantageous. In this way, the 0th-order illumination can be operated as a reference and can facilitate the determination of the asymmetry of the time-varying interference signals associated with the positive and negative diffractions, which can indicate superposition errors. However, the requirement for overlap between the 0th-order diffraction and this higher-order diffraction in the collection pupil can impose various constraints on the superposition target or the corresponding superposition metrology system, such as (but not limited to) the pitch of the grating structure on the superposition target, the wavelength of the illumination beam, or the shape of the illumination beam. Furthermore, such constraints may be inconsistent with other performance trade-offs. For example, it may be desirable to provide an extended illumination beam shape to mitigate the effects of target inhomogeneities. However, this extended illumination beam shape can limit the overlap region between the 0th-order diffraction and the higher-order diffraction lobes of interest and result in a relatively low signal-to-noise ratio of the time-varying signal of interest.

[0024] Embodiments of this disclosure are for generating time-varying interferometric signals indicating superposition based on the overlap of an auxiliary illumination beam (e.g., a reference beam) with diffraction lobes of interest. As an illustration, coherent illumination can be split into a main illumination and an auxiliary illumination, wherein the main illumination is directed to a superposition target in a scan-based scattering superposition metrology system. The diffraction orders of interest from the superposition target can then be collected and superimposed with the auxiliary illumination (e.g., at the collection pupil plane). In this way, the time-varying interferometric signals associated with positive and negative diffraction can share a common reference.

[0025] It is anticipated that the systems and methods disclosed herein can eliminate or alleviate the constraints of stacking targets and / or stacking metrology tools associated with the overlap of 0th-order diffraction with selected higher-order diffraction lobes. Therefore, the systems and methods disclosed herein can be substantially adapted to stacking targets and / or stacking metrology tools to provide measurements with high signal-to-noise ratio (SNR) and high throughput.

[0026] For example, using auxiliary illumination to generate a time-varying signal eliminates the requirement for overlap between the 0th-order illumination and the higher-order diffraction lobes of interest in the pupil plane. Therefore, the shape of the main illumination (and thus the associated shape of the diffraction lobes) can be adapted to facilitate efficient sampling of the superimposed target. For illustration, the main illumination can extend in a direction orthogonal to the scan to facilitate interaction with the extended portion of the superimposed target, which mitigates manufacturing inhomogeneities and eliminates the requirement for overlap between the 0th-order illumination and the higher-order diffraction lobes in the collection pupil. Conversely, the auxiliary illumination can be shaped into any suitable distribution to overlap with the selected diffraction order. Furthermore, the pitch of the grating structure and / or the illumination wavelength can be more flexibly selected to facilitate substantially smaller pitches and / or smaller targets.

[0027] To give another example, using auxiliary illumination to generate a time-varying signal allows the relative intensity of a portion of the auxiliary illumination to be tuned relative to the diffraction order of interest to promote high contrast in the time-varying interferometric signal. This technique generally improves the signal-to-noise ratio of the captured time-varying interferometric signal and thus increases the sensitivity of the corresponding superposition measurements. More generally, any property of the auxiliary illumination can be tuned according to the different diffraction lobes of interest, such as (but not limited to) intensity, wavelength, or polarization. This tuned auxiliary illumination is referred to herein as structured auxiliary illumination.

[0028] It is further anticipated here that the systems and methods disclosed herein can be extended to any scanning scattering superposition metrology technique, including (but not limited to) the techniques described below: U.S. Patent No. 11,300,405, published April 12, 2022; U.S. Patent No. 11,378,394, published July 5, 2022; U.S. Patent No. 10,197,389, published February 5, 2019; U.S. Patent Application No. 17 / 708,958, filed March 30, 2022; U.S. Patent Application No. 17 / 709,104, filed March 30, 2022; and U.S. Patent Application No. 18 / 099,798, filed March 30, 2022, all of which are cited above and are incorporated herein by reference in their entirety.

[0029] Additional embodiments of this disclosure are directed to providing a formulation for configuring a superposition metrology tool to facilitate superposition measurements based on selected diffraction orders. Superposition metrology tools are typically configured according to a formulation comprising a set of parameters for controlling various aspects of the superposition measurement, such as (but not limited to) illuminating the sample, collecting light from the sample, or the position of the sample during the measurement. In this way, the superposition metrology tool can be configured to provide selected types of measurements for one or more superposition targets of interest. For example, the metrology formulation may include illumination parameters, such as (but not limited to) illumination wavelength, illumination pupil distribution (e.g., the distribution of illumination angles and the associated intensity of illumination at said angle), polarization of incident illumination, or spatial distribution of illumination. As another example, the metrology formulation may include collection parameters, such as (but not limited to) collection pupil distribution (e.g., the desired distribution of angular light from the sample used for measurement and the associated filtered intensity of said angle), collection field aperture setting for selecting portions of the sample of interest, polarization of the collected light, wavelength filtering, or parameters for controlling one or more detectors. To give another example, a metrological formulation may include various parameters associated with the sample position during measurement, such as (but not limited to) sample height, sample orientation, whether the sample is static or in motion during measurement (and associated parameters describing speed, scanning pattern or the like).

[0030] Furthermore, for the purposes of this disclosure, the term "overlay target" is generally used to refer to a structure on a sample suitable for a particular overlay measurement. In some embodiments, the overlay target comprises a dedicated structure designed to facilitate overlay measurements according to a specific technique (e.g., based on a metrology formula). For example, a dedicated overlay target may comprise one or more cells having a grating structure with a pitch and orientation selected according to the metrology formula to provide a selected distribution of diffraction orders in a collection pupil plane. In some embodiments, the overlay target is formed from device features on a sample. For example, in some applications, the device features may be distributed in a manner that allows overlay measurements to be generated directly on these device features. In this way, potential systematic measurement errors associated with dedicated overlay targets can be avoided.

[0031] For reference Figures 1A to 6 The system and method for scanning scattering superposition metrology with high signal-to-noise ratio will be described in more detail according to one or more embodiments of the present disclosure.

[0032] Figure 1A This is a conceptual diagram of a superposition metrology system 100 for performing scattering superposition metrology on a superposition target 102 suitable for superposition measurement along any particular measurement direction, according to one or more embodiments of the present disclosure. In some embodiments, the superposition metrology system 100 includes an optical subsystem 104 for performing scattering superposition measurements on the superposition target 102 across a sample 106 distribution. Figure 1B This is a schematic diagram of an optical subsystem 104 according to one or more embodiments of the present disclosure.

[0033] For the purposes of this disclosure, the term "overlay" is generally used to describe the relative positions of features on a sample fabricated by two or more photolithographic patterning steps, while the term "overlay error" describes the deviation of a feature from its nominal arrangement. Within this context, overlay measurements can be expressed as measurements of relative positions or overlay errors associated with those relative positions. For example, a multilayer device may comprise features patterned on multiple sample layers using different photolithographic steps for each layer, where the alignment of features between layers must typically be tightly controlled to ensure proper performance of the resulting device. Therefore, overlay measurements characterize the relative positions of features on two or more sample layers. As another example, multiple photolithographic steps can be used to fabricate features on a single sample layer. Such techniques (often referred to as dual patterning or multiple patterning techniques) facilitate the fabrication of highly dense features at near-photolithographic system resolution. Overlay measurements within this context characterize the relative positions of features from different photolithographic steps on this single layer. It should be understood that the examples and descriptions in this disclosure relating to specific applications of overlay metrology are illustrative only and should not be construed as limiting the scope of this disclosure.

[0034] Furthermore, the term "scattering metrology" is used herein to broadly encompass both "scattering-based metrology" and "diffraction-based metrology," wherein a sample having periodic characteristics on one or more sample layers is illuminated with an illumination beam having a finite angular range, and one or more different diffraction orders are collected for measurement. Additionally, the term "scanning metrology" is used to describe metrological measurements that occur when the sample moves relative to the illumination used for measurement. Generally, scanning metrology can be implemented by moving the sample, the illumination, or both. Accordingly, the specific descriptions herein of particular techniques used to implement scanning metrology are illustrative only and should not be construed as limiting.

[0035] In some embodiments, the optical subsystem 104 includes an illumination source 108 for generating illumination 110-1. Illumination source 108 may include any type of illumination source suitable for providing illumination 110-1 with superposition metrology as disclosed herein. In some embodiments, illumination source 108 is a laser source. For example, illumination source 108 may include (but is not limited to) one or more narrowband laser sources, broadband laser sources, supercontinuum laser sources, white light laser sources, or the like. In this respect, illumination source 108 can provide illumination with high coherence (e.g., high spatial coherence and / or temporal coherence). In some embodiments, illumination source 108 includes a laser sustained plasma (LSP) source. For example, illumination source 108 may include (but is not limited to) an LSP lamp, LSP bulb, or LSP chamber adapted to house one or more elements capable of emitting broadband illumination when excited into a plasma state by a laser source.

[0036] In addition, the lighting 110-1 may include one or more selected wavelengths of light, including (but not limited to) ultraviolet (UV) radiation, visible light radiation, or infrared (IR) radiation.

[0037] The optical subsystem 104 may then include an interferometer 112 for splitting illumination 110-1 into two parts (referred herein to as main illumination 110-2 and auxiliary illumination 110-3). In this configuration, the illumination subsystem 1124 may direct the main illumination 110-2 to the superposition target 102 (e.g., in the form of one or more illumination beams) and collect at least a portion of the main illumination 110-2 emitted from the sample 106 (e.g., one or more diffraction orders of the main illumination 110-2). The light collected from the sample 106 (which may contain diffraction orders of the main illumination 110-2) is referred herein to as measurement light 114. The interferometer 112 may then combine the auxiliary illumination 110-3 with one or more selected diffraction orders of the main illumination 110-2, which may generate a time-varying signal indicating the superposition of the sample 106. The optical subsystem 104 may then include one or more photodetectors 116 for capturing time-varying signals indicating superposition and a controller 118 having one or more processors 120 and a memory 122 (e.g., a memory device). The one or more processors 120 may be configured to execute a set of program instructions maintained in the memory 122. In this manner, the controller 118 may implement any of the various process steps described in this disclosure, such as (but not limited to) receiving time-varying interference signals from the photodetectors 116, processing or filtering the time-varying interference signals, or generating superposition measurements associated with the sample 106 based on the time-varying interference signals.

[0038] For reference Figures 2A to 2C Various aspects of the overlay target 102 suitable for scanning overlay metrology will be described in more detail according to one or more embodiments of this disclosure. Specifically, Figures 2A to 2C This describes an overlay target 102 comprising at least one textured structure according to one or more embodiments of the present disclosure. This overlay target 102 may be adapted for (but is not limited to) measurement by an optical subsystem 104.

[0039] Figure 2A This is a top view of a unit 202 of a superimposed target 102 having a textured structure 204 according to one or more embodiments of the present disclosure. Figure 2B On substrate 206 according to one or more embodiments of this disclosure Figure 2A A side view of a single unit 202 of the superimposed target 102. In some embodiments, the overlay structure 204 includes a first grating 208 (e.g., a top grating) positioned on a first layer 210 of the sample 106 and a second grating 212 (e.g., a bottom grating) positioned on a second layer 214 of the sample 106, oriented such that the regions containing the first grating 208 and the second grating 212 overlap to form a grating-on-grating structure. Furthermore, the first grating 208 and the second grating 212 have different pitches. For example, Figure 2B The pitches of the first grating 208 and the second grating 212 are respectively defined as P and Q.

[0040] The superimposed target 102 can generally be formed by any number of units 202, and any particular unit 202 can include a textured structure 204 with periodicity along any direction. Furthermore, in some embodiments, the superimposed target 102 includes a plurality of units 202 containing a textured structure 204 with periodicity along a common direction, wherein different units 202 have different arrangements of periodicity of associated gratings.

[0041] Figure 2C This is a side view of a superimposed target 102 according to one or more embodiments of the present disclosure, comprising two units 202a, 202b having different configurations of a textured structure 204 suitable for superimposed measurements along a particular measurement direction (e.g., the X direction here). Specifically, Figure 2C The diagram illustrates a reverse overlay structure pair, wherein the first unit 202a comprises a first layer grating 208 having a first pitch (P) and a second layer grating 212 having a second pitch (Q), and the second unit 202b comprises a first layer grating 208 having a second pitch (Q) and a second layer grating 212 having a first pitch (P). It is anticipated that this reverse overlay structure pair can facilitate the determination of superposition based on the time-varying interference signals generated when scanning the two units 202 relative to the illumination beam during measurement.

[0042] It can be anticipated that the different units 202a, 202b of the inverted overlay structure pair can be oriented in various configurations within the stacking target 102. In some embodiments, units 202a, 202b are aligned along a periodic direction (e.g., Figure 2C (in the X direction) side by side orientation. Furthermore, such as Figure 2C As explained, element 202 can be arranged to provide a continuous structure, such that the phase transitions associated with time-varying interferometric signals are well-known and can be considered. This arrangement of the inverted overlay structure pair can (but does not necessarily) refer to vertically stacked targets. Specifically, Figure 2C This indicates a specific, unrestricted configuration where the central target features 216 overlap on the first layer 210 and the second layer 214. In this way, the center of the combined inverted overlay structure pair can provide a reference point for the phase transition (e.g., φ). 0 (This will be described in more detail below.)

[0043] However, it should be understood that Figures 2A to 2CThe superposition target 102 and its associated description are for illustrative purposes only and should not be construed as limiting. Specifically, the superposition target 102 may comprise any design suitable for superposition targets. For example, the superposition target 102 may comprise a grating-on-grating structure in which the first grating 208 and the second grating 212 have the same period (e.g., P). As another example, the superposition target 102 may comprise any number of cells 202 suitable for measurement along two directions. Furthermore, the cells 202 may be distributed in any pattern or arrangement. For example, a metrological target design suitable for scanning metrology is generally described in U.S. Patent Application No. 16 / 598,146, filed October 10, 2019, the entire contents of which are incorporated herein by reference. In some embodiments, the superposition target 102 comprises one or more groups of cells distributed along a scanning direction (e.g., the direction of movement of sample 106), wherein the cells 202 within each particular group of cells are oriented to have a periodic textured structure along a common direction. For example, a first unit group may contain one or more units 202 having periodicity along the X direction, and a second unit group may contain one or more units 202 having periodicity along the Y direction. In this way, all units 202 within a particular unit group can be imaged simultaneously while the sample 106 is scanned through the measurement field of view of the collection subsystem 136. As another example, a diagonal target suitable for metrological measurements in orthogonal directions in a single scan is generally described in U.S. Patent Application No. 16 / 964,734, filed July 24, 2020, the entire contents of which are incorporated herein by reference.

[0044] Refer again Figure 1A and 1B Various aspects of the optical subsystem 104 will now be described in more detail according to one or more embodiments of the present disclosure.

[0045] In some embodiments, the optical subsystem 104 includes an illumination subsystem 124 for manipulating light to guide to the sample 106 and may include any suitable combination of one or more components (e.g., optical elements or the like). For example, the illumination subsystem 124 may include one or more components for manipulating illumination 110-1 prior to interferometer 112. As another example, the illumination subsystem 124 may include one or more components for manipulating main illumination 110-2 and / or guiding this main illumination 110-2 to the sample 106.

[0046] refer to Figure 1BIn some embodiments, the illumination subsystem 124 may include one or more illumination lenses 126 (e.g., for collimating the main illumination 110-2, for relay illumination pupil plane 128, and / or illumination field plane 130, or the like). In some embodiments, the illumination subsystem 124 includes one or more illumination control optics 132 for shaping or otherwise controlling the main illumination 110-2. For example, the illumination control optics 132 may include (but are not limited to) one or more field stops, one or more pupil stops, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, one or more beam shapers, or one or more mirrors (e.g., static mirrors, translational mirrors, scanning mirrors, or the like).

[0047] In some embodiments, the optical subsystem 104 includes an objective lens 134 for focusing the main illumination 110-2 onto a sample 106 (e.g., a superimposed target 102 on the sample 106).

[0048] The main lighting 110-2 can be directed to the superimposed target 102 in any suitable spatial or angular distribution according to the specific metering formula implemented.

[0049] In some embodiments, the illumination subsystem 124 illuminates the superimposed target 102 with a single illumination beam from the main illumination 110-2 during scanning. For example, the superimposed target 102 may be designed according to a metrological formulation to include one or more units distributed along the scanning direction, which may be sequentially illuminated by a single illumination beam.

[0050] In some embodiments, the illumination subsystem 124 illuminates the superimposed target 102 with two or more illumination beams illuminated by the main illumination 110-2, wherein the two or more illumination beams may be incident on the same or different portions of the superimposed target 102. For example, the illumination subsystem 124 may illuminate different cells of the superimposed target 102 with different illumination beams. For example, simultaneous illumination of multiple cells 202 of the superimposed target 102 may facilitate simultaneous measurement along multiple measurement directions and / or measurement of multiple cells 202 required to complete a single measurement along a specific measurement direction. As another example, the illumination subsystem 124 may illuminate specific cells of the superimposed target 102 with illumination beams having different incident angles, which may be used (but not limited to) to control the distribution of diffraction lobes in the collection pupil plane.

[0051] The main illumination 110-2 can be provided as two or more illumination beams using any technique known in the art. In some embodiments, the optical subsystem 104 includes various optical elements (e.g., apertures, beam splitters, diffractive elements, or the like) for splitting illumination 110-1 into two or more beams prior to interferometer 112. In this way, the main illumination 110-2 and the auxiliary illumination 110-3 may have the same number of beams. For example, the optical subsystem 104 may include two or more apertures at the illumination pupil plane 128 to define two or more illumination beams based on azimuth and / or height incident angles. As another example, the optical subsystem 104 may include one or more beam splitters or diffractive elements for splitting illumination 110-1 into two or more illumination beams. As another example, the illumination source 108 directly generates illumination 110-1 in the form of two or more illumination beams. In some embodiments, the optical subsystem 104 includes various optical elements in the paths of the main illumination 110-2 and / or the auxiliary illumination 110-3 to individually modify the number and / or distribution of the associated illumination beams.

[0052] Additionally, the main illumination 110-2 may be angularly confined to the sample 106, allowing the grating structure in one or more units of the superimposed target 102 to produce discrete diffraction orders. Furthermore, the main illumination 110-2 may be spatially confined (e.g., as one or more illumination beams or lobes) to illuminate selected portions of the superimposed target 102. For example, the main illumination 110-2, split into two or more illumination beams, may each be spatially confined to illuminate specific units of the superimposed target 102. In some embodiments, the main illumination 110-2 is positioned below specific units of the superimposed target 102.

[0053] In some embodiments, the optical subsystem 104 includes a collection subsystem 136 for collecting measurement light 114 from the sample 106. For example, the measurement light 114 may include a main illumination 110-2 superimposed on a selected diffraction order of the target 102, as determined by the metrological formulation.

[0054] In some embodiments, the illumination subsystem 124 and the collection subsystem 136 may utilize or include the objective lens 134. For example, Figure 1B The beam splitter 138 is described, which is used to guide the illumination beam to the objective lens 134 to illuminate the sample 106 and also to guide the measurement light 114 from the objective lens 134 to the photodetector 116.

[0055] The collection subsystem 136 may further include one or more collection optics adapted to modify and / or adjust the measurement light 114 from the sample 106. In some embodiments, the collection subsystem 136 includes one or more collection lenses 140 (e.g., for collimating the illumination beam, for relaying the collection pupil plane 142 and / or the collection field plane 144, or the like). Furthermore, the collection lens 140 may include (but does not necessarily include) an objective lens 134. In some embodiments, the collection subsystem 136 includes one or more collection control optics 146 for shaping or otherwise controlling the measurement light 114. For example, the collection control optics 146 may include (but are not limited to) one or more field stops, one or more pupil stops, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, one or more beam shapers, or one or more mirrors 148 (e.g., static mirrors, translational mirrors, scanning mirrors, or the like).

[0056] Interferometer 112 can then combine selected diffraction orders (e.g., selected portions of measurement light 114) of auxiliary illumination 110-3 and main illumination 110-2 for detection. The main illumination 110-2 and auxiliary illumination 110-3 passing through interferometer 112 can generally have any optical path length, as long as coherence is maintained for the generation of time-varying interference signals. In some embodiments, the optical path lengths of the main illumination 110-2 and auxiliary illumination 110-3 passing through interferometer 112 are designed to be approximately equal.

[0057] Interferometer 112 may include any component or combination of components suitable for combining a portion of the main illumination 110-2 (e.g., a selected portion of the measurement light 114) from sample 106 with auxiliary illumination 110-3 to produce interference.

[0058] Interferometer 112 may generally contain any combination of optical elements suitable for causing auxiliary illumination 110-3 to interfere with selected diffraction orders of main illumination 110-2. For example, such as Figure 1B As described herein, interferometer 112 may include one or more beam splitters 150 for splitting illumination 110-1 from illumination source 108 into main illumination 110-2 and auxiliary illumination 110-3. Interferometer 112 may further include one or more beam combiners 152 (e.g., beam splitters or other combining elements) for combining auxiliary illumination 110-3 and main illumination 110-2 by means of selected diffraction lobes of superimposed target 102.

[0059] The collection subsystem 136 may further include at least two photodetectors 116a, 116b, positioned in at least one collection pupil plane 142 at a location associated with the indicated superimposed time-varying interference signal (e.g., a location corresponding to the overlapping collection pupil plane 142 between the auxiliary illumination 110-3 and the main illumination 110-2 through selected diffraction orders of the superimposed target 102). For example, as will be described in more detail below, the location suitable for photodetector 116 may include (but is not limited to) a location in the collection pupil plane 142 containing selected diffraction orders of the main illumination 110-2 through the superimposed target 102.

[0060] The photodetector 116 (e.g., photodetectors 116a, 116b) may generally comprise any type of optical detector known in the art suitable for capturing interference signals generated when the sample 106 is translated by the translation stage 154 and / or when one or more illumination beams are scanned by the beam scanning subsystem 156. In some embodiments, photodetectors 116a, 116b comprise single-pixel photodiodes, such as (but not limited to) photodiodes (e.g., fast photodiodes), light multipliers, or burst photodiodes (APDs). Such single-pixel photodetectors 116 may be individually placed at selected locations in the collection pupil plane 142 according to a selected metrological formulation, such as locations associated with diffraction orders (e.g., measurement light 114) from features of the superimposed target 102. In some embodiments, photodetectors 116a, 116b are part of a multi-pixel sensor, such as (but not limited to) a line sensor, a complementary metal-oxide-semiconductor (CMOS) sensor, or a charge-coupled device (CCD). In this way, photodetectors 116a, 116b may correspond to pixels or groups of pixels of this multi-pixel sensor.

[0061] Generally, the bandwidth or response time of the photodetector 116 should be sufficient to resolve the time frequency of the interference fringes, which is related to the pitch of the grating structure and the scanning speed along the scan. For example, with a scanning speed of 10 cm / s and a target pitch of 1 micrometer, the interference signal will oscillate at a rate of approximately 100 kHz. In some embodiments, the photodetector 116 comprises a photodetector with a bandwidth of at least 1 GHz. However, it should be understood that this value is not required. Specifically, the bandwidth of the photodetector 116, the translation speed along the measurement direction, and the pitch of the grating structure can be selected together to provide the desired sampling rate of the interference signal.

[0062] In some embodiments, the optical subsystem 104 includes a translation stage 154 for scanning the sample 106 through the measurement field of view of the optical subsystem 104 during a measurement for performing scanning metrology.

[0063] In some embodiments, the optical subsystem 104 includes a beam scanning subsystem 156 configured to modify or otherwise control the position of the main illumination 110-2 (e.g., in the form of at least one illumination beam) on the sample 106. For example, the beam scanning subsystem 156 may scan the main illumination 110-2 in a direction orthogonal to the scanning direction (e.g., the direction in which the translation stage 154 scans the sample 106) during measurement. In this way, scanning measurements can be performed by any relative movement of the sample 106 and the main illumination 110-2.

[0064] The translation stage 154 and / or the beam scanning subsystem 156 can be synchronized with the photodetector 116 during scanning using any suitable technique, such that the signal generated by the photodetector 116 can be correlated with the position of the main illumination 110-2 on the superimposed target 102 and / or the relative velocity of the superimposed target 102 with respect to the main illumination 110-2 during scanning. This information facilitates the correlation of the signal generated by the photodetector 116 with the characteristics of the superimposed target 102 for determining superimposed measurements.

[0065] In some embodiments, the optical subsystem 104 includes a phase modulator (not shown) for modulating the phase of the auxiliary illumination 110-3. In this way, both the main illumination 110-2 and the sample 106 can remain stationary during scanning.

[0066] The optical subsystem 104 may include one or more collection channels 158. For example, Figure 1B This describes the configuration of an optical subsystem 104 having two collection channels 158. It is conceivable that the photodetectors 116 can be distributed among one or more collection channels 158 as desired. In some embodiments, multiple photodetectors 116 are positioned in at least one collection channel 158. In this configuration, multiple collection channels 158 can facilitate simultaneous measurements of different units (e.g., associated with different measurement orientations, different units required for a particular measurement based on a specific metrological formulation, or the like). In some embodiments, each collection channel 158 contains a single photodetector 116 (e.g., photodetector 116a or photodetector 116b). In this way, each photodetector 116 can be placed anywhere in the collection pupil plane 142, regardless of its physical size or any associated components.

[0067] Optical subsystem 104 may include one or more channel beam splitters 160 arranged to split light in collection subsystem 136 into different collection channels 158. In some embodiments, such as Figure 1B As explained herein, channel beam splitter 160 is positioned after interferometer 112. In this manner, the light collected in channel 158 contains a time-varying interference pattern indicating superposition, as described herein.

[0068] The channel beamsplitter 160 may include any component suitable for splitting light using any technique and may include (but is not limited to) a polarizing beamsplitter or a dichroic beamsplitter (e.g., a dichroic mirror). In some embodiments, the channel beamsplitter 160 splits light into different collection channels 158 based on the properties of the light (e.g., (but not limited to) polarization or wavelength). In this way, the channel beamsplitter 160 can separate light from different beams from the main illumination 110-2 and / or from different units 202 of the superimposed target 102 into different collection channels 158. As an illustration, the optical subsystem 104 can guide different beams from the main illumination 110-2 to different units 202 of the superimposed target 102, wherein the different beams from the main illumination 110-2 have different properties (e.g., polarization, wavelength, or the like). One or more channel beams 160 can then separate the measurement light 114 associated with the different beams from the main illumination 110-2 and / or the different units 202 of the superimposed target 102 into different collection channels 158 to provide simultaneous measurement.

[0069] For reference Figures 3A to 5 Various configurations for overlapping selected diffraction lobes of the auxiliary illumination 110-3 with the main illumination 110-2 will be described in more detail according to one or more embodiments of this disclosure. Specifically, Figures 3A to 5 supply Figures 2A to 2C The non-limiting illustration of a specific case of superposition measurement on superposition target 102 depicted herein describes that superposition target 102 comprises at least one ribbed structure formed by gratings in specific cells having different pitches (e.g., pitches P and Q). Scan-based scattering superposition metrology based on ribbed structures is generally described in U.S. Patent Application No. 17 / 708,958, filed March 30, 2022, the entire contents of which are incorporated herein by reference. However, it should be understood that... Figures 3A to 5 This is for illustrative purposes only and should not be construed as limiting. Specifically, the systems and methods disclosed herein are extendable to use with any suitable design of the superposition target 102. In other words, the systems and methods disclosed herein are extendable to providing overlap between auxiliary illumination 110-3 and any selected diffraction lobes from any selected superposition target 102 target design suitable for superposition metrology based on any selected metrology formulation. For example, the systems and methods disclosed herein are extendable to (but not limited to) the superposition target 102 and / or associated metrology formulations described below: U.S. Patent No. 11,300,405, published April 12, 2022; U.S. Patent No. 11,378,394, published July 5, 2022; and U.S. Patent Application No. 17 / 709,104, filed March 30, 2022, all of which are incorporated herein by reference in their entirety.

[0070] Figure 3A and3B This describes a first non-limiting example of an illumination and collection pupil distribution for scanning superposition metrology based on normal incident main illumination 110-2, according to one or more embodiments of the present disclosure. Figure 4 This describes a second non-limiting example of an illumination and collection pupil distribution for scanning superimposed metrology based on an obliquely incident main illumination 110-2, according to one or more embodiments of the present disclosure. Figure 5 This describes a third non-limiting example of an illumination and collection pupil distribution for scanning superimposed metrology based on an obliquely incident main illumination 110-2, according to one or more embodiments of the present disclosure.

[0071] Figure 3A It is an optical subsystem 104 according to one or more embodiments of this disclosure (e.g., such as...). Figure 1B The image shows a top view of the illumination pupil plane 128. In some embodiments, the illumination subsystem 124 illuminates the superimposed target 102 with one or more illumination beams of the main illumination 110-2 in a normal incident (or near-normal) manner, such as... Figure 3A As explained in the text. For example... Figure 3A This describes a single illumination beam of the main illumination 110-2 at the center of the pupil boundary 302 of the illumination pupil plane 128. Furthermore, one or more illumination beams may illuminate the superimposed target 102 at finite angles of incidence (as illustrated by the finite size in the collecting pupil plane 142). In this respect, the superimposed target 102 can diffract the main illumination 110-2 into discrete diffraction orders.

[0072] It should be recognized that the distribution of diffraction orders through the periodic structure in the superposition target 102 can be affected by various parameters, such as (but not limited to) the wavelength of the illumination beam, the incident angle of the illumination beam along both the height and azimuth directions, the pitch of the grating of the superposition target 102, or the numerical aperture (NA) of the collecting lens. Therefore, in embodiments of this disclosure, the illumination subsystem 124, the collecting subsystem 136, and the superposition target 102 can be configured to provide a desired distribution of diffraction orders in a collecting pupil suitable for generating a time-varying interference pattern indicating the superposition. For example, the illumination subsystem 124 and / or the collecting subsystem 136 can be configured (e.g., using a measurement formula) to generate measurements with respect to the superposition target 102 having grating features with a selected pitch range to provide a desired collecting pupil distribution. Furthermore, various components of the illumination subsystem 124 and / or the collecting subsystem 136 (e.g., apertures, pupils, or the like) can be adjusted (e.g., using a measurement formula) to provide a desired collecting pupil distribution.

[0073] Furthermore, the size and shape of the diffraction orders in the collecting pupil plane 142 can generally be related to the size and shape of the illumination beam on the sample 106. For example, although not shown, if the illumination beam is elongated, then the associated diffraction orders can be similarly elongated.

[0074] For reference Figure 3B The adaptation overlap between the auxiliary illumination 110-3 and the selected diffraction lobe to facilitate a high signal-to-noise ratio will be described in more detail according to one or more embodiments of the present disclosure.

[0075] It is anticipated that the signal-to-noise ratio of the time-varying interference signal and thus the sensitivity of measurements based on the superposition of these signals can be affected by various factors, such as (but not limited to) the intensity and contrast of the time-varying interference signal generated by the photodetector 116. For example, it is generally desirable to increase the overlap region between the diffraction lobes of interest to increase the total number of photons contributing to the time-varying interference signal. It is also generally desirable to limit the collection of light from other portions of the collection pupil plane 142 (e.g., outside the overlap region of interest) to limit the constant (DC) bias signal captured by the photodetector 116 and the time-varying interference signal of interest. It is further generally desirable to match the relative intensities of the diffraction orders to contribute to a high-contrast interference pattern, resulting in highly visible interference fringes.

[0076] It can be further anticipated that using interferometer 112 to split illumination 110-1 from illumination source 108 into main illumination 110-2 and separate auxiliary illumination 110-3 incident on superimposed target 102 can adapt to various conditions to achieve a high signal-to-noise ratio.

[0077] For example, the amount of overlap between the diffraction lobes of the main illumination 110-2 by superimposing the target 102 (and thus the number of photons contributing to the time-varying interference signal) can be limited by parameters such as (but not limited to) the wavelength of the main illumination 110-2, the pitch of the grating in the target 102, and the beam shape of the incident main illumination 110-2 and thus the resulting diffraction lobes. In some cases, it is not possible or not possible to directly provide a distribution of diffraction lobes with a reasonable overlap region to provide a suitable signal-to-noise ratio. However, the use of a separate but coherent auxiliary illumination 110-3 eliminates or relaxes the requirement to directly generate overlapping diffraction lobes, because the auxiliary illumination 110-3 can be flexibly positioned in the collection pupil plane 142 as needed. More generally, various parameters of the auxiliary illumination 110-3 can be adjusted (e.g., using collection control optics 146 or the like), such as (but not limited to) the number of lobes, lobe size, lobe shape, lobe intensity, lobe polarization, or lobe position in the collection pupil plane 142.

[0078] As an explanation, Figure 3B This is a top view of the collection pupil boundary 304 in the collection pupil plane 142 of the optical subsystem 104 according to one or more embodiments of the present disclosure, illustrating that the auxiliary illumination 110-3 and the main illumination 110-2 are connected by... Figures 2A to 2B The overlap between the + / -1st order diffraction lobes of the 204-fold textured structure. Specifically, Figure 3B This describes the -1st order diffraction lobe 306 (-1) from the first layer grating 208.P ) and the -1st order diffraction lobe 308 (-1) from the second grating 212 Q The first lobe 110-3a of the overlapping auxiliary illumination and the +1st order diffraction lobe 310 (+1) from the first grating 208 P ) and the +1st order diffraction lobe 312 (+1) from the second grating 212 Q The second lobe of the overlapping auxiliary lighting 110-3b. Figure 3B Further explanation of the 0th order diffraction lobe 314 of the main illumination 110-2.

[0079] It can be expected that, Figure 3B The number or shape of the lobes of the auxiliary illumination 110-3 and / or the specific arrangement of the number or shape of the diffraction lobes associated with the diffraction of the main illumination 110-2 depicted herein are for illustrative purposes only and should not be construed as limiting. Specifically, any arrangement of such lobes providing the time-varying signal is within the spirit and scope of this disclosure. For illustration, the -1st order diffraction lobe 306 does not necessarily need to overlap with the -1st order diffraction lobe 308 and the +1st order diffraction lobe 310 does not necessarily need to overlap with the +1st order diffraction lobe 312. Specifically, the time-varying interference signal (which may have different frequencies) can be generated based on the overlap of these lobes with the auxiliary illumination 110-3. Furthermore, the auxiliary illumination 110-3 can be distributed as any number of lobes having any shape. For example, although... Figure 3B It is not specified, but the auxiliary illumination 110-3 can be split into four separate lobes arranged to overlap with the -1st order diffraction lobe 306, -1st order diffraction lobe 308, +1st order diffraction lobe 310 and +1st order diffraction lobe 312.

[0080] It can be further anticipated that the time-varying signal indicating the superposition can be generated by various configurations of one or more photodetectors 116 in the collection pupil plane 142. In some embodiments, the first photodetector 116 (not shown) can capture a first lobe 110-3a containing auxiliary illumination and a -1st order diffraction lobe 306 (-1) from the first grating 208. P ) and the -1st order diffraction lobe 308 (-1) from the second grating 212 Q The portion of the overlapping pupil plane between the first grating 208. Similarly, the second photodetector 116 (not shown) can capture the second lobe 110-3b containing auxiliary illumination, and the +1st order diffraction lobe 310 (+1) from the first grating 208. P ) and the +1st order diffraction lobe 312 (+1) from the second grating 212 Q The portion of the overlapping pupil plane between the first photodetector 116 (not shown) and the second photodetector 116 (not shown) may capture the first lobe 110-3a of the auxiliary illumination and the -1st order diffraction lobe 306 (-1) from the first grating 208. PThe overlap between the first lobe 110-3a of the auxiliary illumination and the -1st order diffraction lobe 308 from the second grating 212, and the second photodetector 116 (not shown) can capture the overlap between the second photodetector 110-3a and the -1st order diffraction lobe 308 from the second grating 212. Q The overlap between the second lobe 110-3b of the auxiliary illumination and the +1st order diffraction lobe 310 (+1) from the first grating 208, and the third photodetector 116 (not shown) can capture the overlap between the second lobe 110-3b of the auxiliary illumination and the +1st order diffraction lobe 310 from the first grating 208. P The overlap between the second lobe 110-3b of the auxiliary illumination and the +1st order diffraction lobe 312 (+1) from the second grating 212 is captured by the fourth photodetector 116 (not shown). Q The overlap between )

[0081] Therefore, in general, any number of photodetectors 116 can be used to capture time-varying interference signals associated with the overlap between various diffraction lobes. Furthermore, as previously described herein, the photodetectors 116 can be configured as single-pixel detectors or as pixel and / or multi-pixel sensors corresponding to a detector array.

[0082] Figure 3B The various aspects of the configuration described herein contribute to a high signal-to-noise ratio. (Regarding...) Figures 2A to 2B In the unrestricted unit 202, the time-varying interference signal can be generated by the overlap of diffraction lobes associated with both the first-layer grating 208 and the second-layer grating 212 with each other or another reference (e.g., 0th-order diffraction). If the separate auxiliary illumination 110-3 is not provided in the systems and methods disclosed herein, the time-varying interference signal can be generated at the location of the overlap between the + / -1 diffraction lobes constituting these gratings (e.g., the overlap between +1st-order diffraction lobes 310 and 312, the overlap between -1st-order diffraction lobes 306 and 308, or similar), at the location of the fringe diffraction lobes (e.g., associated with double diffraction from both the first-layer grating 208 and the second-layer grating 212), or at the overlap region between the fringe diffraction lobes and the 0th-order diffraction lobes 314. However, the amount of overlap between the diffraction lobes in each of these configurations depends on the difference between the pitches of these gratings and the beam shape of the incident illumination.

[0083] In comparison, Figure 3B The configuration of the auxiliary illumination 110-3 overlapping with the + / -1 diffraction lobe is explained above. In this configuration, as... Figure 3B As explained, it is not required that the + / -1 diffraction lobes from the first grating 208 and the second grating 212 overlap with each other or the 0th order diffraction lobe 314. Specifically, the auxiliary illumination lobes 110-3a and 110-3b can be arranged and sized to overlap with the diffraction lobes from the first grating 208 and the second grating 212. In particular, Figure 3BThis describes a configuration where the diffraction lobes from the first grating 208 and the second grating 212 have minimal overlap (e.g., minimal overlap between the +1st order diffraction lobe 310 and +1st order diffraction lobe 312) and do not overlap with the reflected 0th order diffraction lobe 314. Therefore, the shape of the main illumination 110-2, the wavelength of the main illumination 110-2, and the pitch of the first grating 208 and the second grating 212 can all be flexibly selected. The size, position, shape, and intensity of the lobes of the auxiliary illumination 110-3 can then be selected to provide time-varying interference fringes with a high signal-to-noise ratio.

[0084] For reference Figure 4 , Figure 4 This is a conceptual diagram of an optical subsystem 104 providing a tilted main illumination 110-2 and associated auxiliary illumination 110-3 according to one or more embodiments of the present disclosure.

[0085] Figure 4 The concept illustrates the rotating dipole distribution of the illumination beam of the main illumination 110-2 (110-2a, 110-2b) guided by the beam splitter 138 and the objective lens 134 to the illumination pupil plane 128 of the superimposed target 102. Figure 4 Further explanation includes along Figures 2A to 2B The superimposed target 102 is illuminated by a main illumination 110-2 oriented in a periodic direction along the Y-axis, with a collection pupil plane 142 for the diffraction lobes. Specifically, Figure 4 This describes the -1st order diffraction lobes 306 and 308 from the first illumination lobe 110-2a, and the +1st order diffraction lobes 310 and 312 from the second illumination lobe 110-2b. Finally, Figure 4 The dipole distribution 402 of the auxiliary illumination 110-3 is explained. The auxiliary illumination 110-3 is rotated relative to the main illumination 110-2, such that the lobes 110-3a and 110-3b of the auxiliary illumination overlap with the first-order diffraction from the first grating 208 and the second grating 212. In this manner, Figure 4 It can provide something similar to Figure 3B The measurements depicted in the figure. However, the use of oblique illumination allows for the superimposed target 102 to have a smaller pitch and potentially a smaller overall size.

[0086] It should be noted that Figure 4 The beam splitter 138 is described as facilitating the illumination and collection by the objective lens 134, and simultaneously facilitating the combination of the diffraction lobes of the auxiliary illumination 110-3 and the main illumination 110-2 by the beam combiner 152 of the interferometer 112. However, it should be understood that this is for illustrative purposes only and the splitter assembly may be used.

[0087] For reference Figure 5 , Figure 5This is a conceptual diagram of an optical subsystem 104 that simultaneously characterizes a superimposed target 102 with multiple illumination conditions, according to one or more embodiments of the present disclosure.

[0088] In some embodiments, the optical subsystem 104 provides illumination 110-1 with two different illumination conditions having different properties (e.g., but not limited to, wavelength or polarization). In this way, the optical subsystem 104 can provide two distributions of main illumination 110-2 and associated auxiliary illumination 110-3 for different measurements in different collection channels 158.

[0089] For example, Figure 5 Illustrate the illumination pupil plane 128, which contains the first rotating dipole distribution of the illumination beam of the main illumination 110-2 (110-2a, 110-2b) (e.g., as shown in the image). Figure 4 (as described in the text) and the second rotating dipole distribution of the illumination beam of the main illumination 110-2 (110-2c, 110-2d) in the opposite quadrant of the illumination pupil plane 128. Figure 5 Further explanation is given of the corresponding rotating dipole distribution of the auxiliary illumination 110-3 containing lobes (110-3a, 110-3b) and the second rotating dipole distribution of the auxiliary illumination 110-3 containing lobes (110-3c, 110-3d).

[0090] Figure 5 Additionally, a channel beam splitter 160 is described for separating the diffraction lobes of the main illumination 110-2 and the corresponding auxiliary illumination 110-3 with different illumination distributions into different collection channels 158. For example, the channel beam splitter 160 may include a dichroic beam splitter, a polarizing beam splitter, or any other component suitable for separating the main illumination 110-2 and the auxiliary illumination 110-3 with different illumination conditions.

[0091] As an explanation, Figure 5 The first collection channel 158a is depicted, which may include auxiliary illumination lobes 110-3a and 110-3b that overlap with selected diffraction lobes 110-2a and 110-2b of the main illumination, while the second collection channel 158b may include auxiliary illumination lobes 110-3c and 110-3d that overlap with selected diffraction lobes 110-2c and 110-2d of the main illumination.

[0092] It can be expected that, Figure 5 The techniques described herein can be applied to various simultaneous measurement schemes. For example, such as... Figure 5As illustrated herein, two illumination conditions can be used to provide simultaneous measurements of the same cell 202 of the superimposed target 102 under different conditions. As another example, lobes of the main illumination 110-2 with different illumination conditions can be directed to different cells 202 of the superimposed target 102 to provide simultaneous measurements of the different cells 202. Furthermore, the different cells 202 may comprise grating structures having the same or different periodic orientations. In this manner, any of the systems and methods disclosed herein can be extended to (but is not limited to) any of the multi-cell illumination measurement techniques described below: U.S. Patent No. 11,300,405, published April 12, 2022, and U.S. Patent Application No. 17 / 708,958, filed March 30, 2022, the entire contents of which are incorporated herein by reference.

[0093] Refer again Figure 1A and 1B Further details of the optical subsystem 104 will be described in more detail according to one or more embodiments of this disclosure.

[0094] One or more processors 120 of controller 118 may generally comprise any processor or processing element known in the art. For the purposes of this disclosure, the terms “processor” or “processing element” may be broadly defined to encompass any means having one or more processing or logic elements (e.g., one or more microprocessor devices, one or more application-specific integrated circuit (ASIC) devices, one or more field-programmable gate arrays (FPGAs), or one or more digital signal processors (DSPs)). In this sense, one or more processors 120 may comprise any means configured to execute algorithms and / or instructions (e.g., program instructions stored in memory). In some embodiments, one or more processors 120 may embody a desktop computer, host computer system, workstation, graphics computer, parallel processor, network computer, or any other computer system configured to execute a program configured to operate or in conjunction with the operation of the overlay metering system 100, as described in this disclosure. Furthermore, different subsystems of the overlay metering system 100 may include processors or logic elements suitable for implementing at least a portion of the steps described in this disclosure. Therefore, the above description should not be construed as limiting the embodiments of this disclosure but is merely illustrative. Furthermore, the steps described in this disclosure can be implemented by a single controller or, alternatively, multiple controllers. Additionally, controller 118 may comprise one or more controllers housed within a common housing or multiple housings. In this manner, any controller or combination of controllers can be individually packaged as a module suitable for integration into the metering overlay metering system 100. Furthermore, controller 118 can analyze or otherwise process data received from photodetector 116 and feed the data to additional components within or outside the metering overlay metering system 100.

[0095] Furthermore, memory 122 may comprise any storage medium known in the art suitable for storing program instructions executable by one or more associated processors 120. For example, memory 122 may comprise a non-transitory memory medium. As additional examples, memory 122 may comprise (but is not limited to) read-only memory, random access memory, magnetic or optical storage devices (e.g., magnetic disks), magnetic tape, solid-state drives, or the like. It should be further noted that memory 122 may be housed in a common controller housing with one or more processors 120.

[0096] In this regard, controller 118 can perform any of the various processing steps associated with superposition metrology. For example, controller 118 can be configured to generate control signals to direct or otherwise control optical subsystem 104 or any of its components. For example, controller 118 can be configured to direct translation stage 154 to translate sample 106 along one or more measurement paths or tracks, scan one or more superposition targets through the measurement field of view of optical subsystem 104, and / or direct beam scanning subsystem 156 to position or scan one or more illumination beams on sample 106. As another example, controller 118 can be configured to receive signals corresponding to time-varying interference signals from photodetector 116. As yet another example, controller 118 can generate one or more correctable numbers of additional manufacturing tools as feedback and / or feedforward control of one or more additional manufacturing tools based on superposition measurements from optical subsystem 104.

[0097] In some embodiments, controller 118 captures the interference signal detected by photodetector 116. Controller 118 may generally use any technique known in the art to capture data, such as (but not limited to) the amplitude or phase (e.g., intensity and / or phase information) of the time-varying interference signal. For example, controller 118 may use phase-locked loop (PLL) techniques to capture data, such as (but not limited to) the amplitude or phase (e.g., intensity and / or phase information) of the time-varying interference signal. For example, controller 118 may use Fourier analysis techniques (or any other suitable spectral decomposition techniques) to capture data, such as (but not limited to) the amplitude or phase (e.g., intensity and / or phase information) of the time-varying interference signal. Generally, controller 118 may use any combination of hardware (e.g., circuitry) or software techniques to capture the interference signal or any data associated with the interference signal.

[0098] In some embodiments, controller 118 determines superposition measurements between layers of superimposed target 102 along the measurement direction based on comparison of interference signals. For example, controller 118 may compare the amplitude and / or phase of interference signals to generate superposition measurements. For example, the specific relationship between collecting the electric field of diffraction orders in the pupil and further providing superposition in the pupil plane and measured intensity is generally described in U.S. Patent No. 10,824,079, issued November 3, 2020, the entire contents of which are incorporated herein by reference. It is contemplated here that the systems and methods disclosed herein can extend the teachings of U.S. Patent No. 10,824,079 to time-varying interference signals captured by photodetector 116 placed in the overlapping region, as disclosed herein. Specifically, it is contemplated here that superposition on sample 106 may be proportional to asymmetry (e.g., (but not limited to) the relative phase shift between two time-varying interference signals). In another example, the relative intensity of diffraction orders in the pupil plane may be extracted from the time-varying interference signals. In this way, any superposition algorithm known in the field based on the relative intensity difference of diffraction order can be used to generate superposition measurements.

[0099] In addition, the controller 118 can calibrate or otherwise modify the superimposed measurement based on known, assumed, or measured characteristics of the samples that may also affect the time-varying interference signal (e.g., but not limited to, sidewall angles or other sample asymmetries).

[0100] In some embodiments, the optical subsystem 104 includes a beam scanning subsystem 156 for positioning, scanning, or modulating the position of one or more illumination beams on the sample 106 during measurement. Furthermore, the beam scanning subsystem 156 and the photodetector 116 may be synchronized to facilitate a link between the scanning speed and pitch of the superimposed features of the target 102.

[0101] The beam scanning subsystem 156 may include elements of any type or combination suitable for scanning the position of one or more illumination beams. In some embodiments, the beam scanning subsystem 156 includes one or more deflectors suitable for modifying the direction of the illumination beams. For example, the deflector may include (but is not limited to) a rotatable mirror (e.g., a mirror with adjustable tilt and / or tilt). Furthermore, the rotatable mirror may be actuated using any technique known in the art. For example, the deflector may include (but is not limited to) a galvanometer, a piezoelectric mirror, or a microelectromechanical system (MEMS) device. As another example, the beam scanning subsystem 156 may include an electro-optic modulator, an acousto-optic modulator, or the like.

[0102] The deflectors can be further positioned at any suitable location within the optical subsystem 104. In some embodiments, one or more deflectors are placed at one or more pupil planes shared by both the illumination subsystem 124 and the collection subsystem 136. In this regard, the beam scanning subsystem 156 can be a pupil-plane beam scanner, and the associated deflectors can modify the position of one or more illumination beams on the sample 106 without affecting the position of the diffraction order in the collection pupil plane 142. Furthermore, the distribution of one or more illumination beams in the illumination field plane 130 can be further stabilized when the beam scanning subsystem 156 modifies the position of one or more illumination beams on the sample 106. Pupil-plane beam scanning is generally described in U.S. Patent No. 11,300,524, issued April 12, 2022, the entire contents of which are incorporated herein by reference.

[0103] For reference Figure 6 , Figure 6 This is a flowchart illustrating the steps performed in a superimposed metering method 600 according to one or more embodiments of the present disclosure. The applicant notes that the embodiments and implementation techniques previously described herein within the text of the superimposed metering system 100 should be interpreted as extended to method 600. However, it should be further noted that method 600 is not limited to the architecture of the superimposed metering system 100.

[0104] In some embodiments, method 600 includes step 602: generating illumination using an illumination source. In some embodiments, method 600 includes step 604: splitting the illumination from the illumination source into a main illumination and an auxiliary illumination. In some embodiments, method 600 includes step 606: directing the main illumination to a stacking target on the sample, wherein the stacking target comprises gratings in two or more layers.

[0105] In some embodiments, method 600 includes step 608: overlapping a first portion of the auxiliary illumination with the main illumination through at least one diffraction lobe of the superimposed target onto a first photodetector in the collection pupil plane to generate a first interference pattern. In some embodiments, method 600 includes step 610: overlapping a second portion of the auxiliary illumination with the main illumination through at least one additional diffraction lobe of the superimposed target onto a second photodetector in the collection pupil plane to generate a second interference pattern. In some embodiments, method 600 includes step 612: modulating the phases of the first and second interference patterns during scanning of the superimposed target with a scanning subsystem. For example, the scanning subsystem may include at least one of a translation stage for scanning the sample relative to the main illumination, a beam scanning optics for scanning the main illumination relative to the sample, or a phase modulator for modulating the phase of the auxiliary illumination.

[0106] In some embodiments, method 600 includes step 614: generating a time-varying interference signal using first and second photodetectors based on the modulation phase of the first and second interference patterns. In some embodiments, method 600 includes step 616: generating one or more superimposed measurements of the superimposed target based on the time-varying interference signal.

[0107] It is anticipated that method 600 can be used to generate superimposed metrological measurements for any superimposed target design and associated metrological formulation suitable for scanning scattering superimposed metrology. For example, the superimposed target may comprise a grating with a common pitch. As another example, the superimposed target may comprise a grating with a different pitch (e.g., forming a ribbed structure). In this way, the specific diffraction lobe overlapping with the auxiliary illumination (e.g., in steps 608 and 610) can be varied based on the specific superimposed target design and associated metrological formulation.

[0108] Furthermore, it is anticipated that method 600 can be extended to provide simultaneous measurements. For example, the main illumination and auxiliary illumination can be split into multiple beams with different illumination conditions (e.g., varying wavelengths, polarization, or other suitable parameters), such that the diffraction lobes associated with each illumination condition can be isolated into different channels. In this way, method 600 can be extended to provide measurements of a single unit with different illumination conditions or measurements of different units with different illumination conditions. Regarding simultaneous measurements of different units, the different units may include grating structures with different periodic orientations (e.g., grating orientations) for simultaneous superposition of measurements along different directions, or may include grating structures with the same periodic orientation but different grating arrangements (e.g., offset between top and bottom gratings, different pitch configurations between top and bottom gratings, or the like) to facilitate multi-unit metrological formulations.

[0109] The objectives described herein sometimes refer to different components contained within or connected to other components. It should be understood that such depicted architectures are illustrative only, and in fact, many other architectures can be implemented to achieve the same functionality. Conceptually, any arrangement of components that achieve the same functionality is effectively “associated” to achieve the desired function. Therefore, regardless of the architecture or intermediate components, any two components combined herein to achieve a particular function can be considered “associated” with each other to achieve the desired function. Similarly, any two such associated components can also be considered “connected” or “coupled” with each other to achieve the desired function, and any two components that can be suchly associated can also be considered “coupleable” with each other to achieve the desired function. Specific examples of “coupleable” include (but are not limited to) physically interactive and / or physically interactive components and / or wirelessly interactive and / or logically interactive components.

[0110] It is believed that this disclosure and its many accompanying advantages will be understood from the above description, and it should be understood that various changes can be made to the form, construction, and arrangement of the components without departing from the disclosed objectives or sacrificing all their material advantages. The forms described are for illustrative purposes only, and the appended claims are intended to cover and encompass such changes. Furthermore, it should be understood that the invention is defined by the appended claims.

Claims

1. A superimposed metering system, comprising: Lighting source; A first beam splitter is configured to split the illumination from the illumination source into main illumination and auxiliary illumination; One or more illumination optics configured to direct the main illumination to a superimposed target on a sample during the implementation of a metrology formulation, wherein the superimposed target according to the metrology formulation comprises gratings in two or more layers; An objective lens for collecting at least one positive diffraction lobe and at least one negative diffraction lobe associated with the diffraction of the main illumination from the grating in each of the two or more layers when implementing the metrological formulation. One or more photodetectors, located in one or more collection pupil planes; One or more collecting optics configured to implement the metering formulation by: The first portion of the auxiliary illumination is overlapped with at least one diffraction lobe of the main illumination through the superimposed target onto at least one of the one or more photodetectors to produce a first interference pattern; and The second portion of the auxiliary illumination is overlapped with the main illumination through at least one additional diffraction lobe of the superimposed target onto at least one of the one or more photodetectors to produce a second interference pattern; A scanning subsystem comprising at least one of a translation stage for scanning the sample relative to the main illumination, a beam scanning optics for scanning the main illumination relative to the sample, or a phase modulator for modulating the phase of the auxiliary illumination during scanning of the superimposed target when implementing the metrology formulation; and A controller, communicatively coupled to the one or more photodetectors, the controller comprising one or more processors configured to execute program instructions to cause the one or more processors to implement the metering formula by: During the scanning of the superimposed target, a time-varying interference signal is received from one or more photodetectors; and One or more superimposed measurements of the superimposed target are generated based on the time-varying interferometric signal.

2. The superposition metrology system according to claim 1, wherein the at least one diffraction lobe comprises at least one positive diffraction lobe of a selected diffraction order, and wherein the at least one additional diffraction lobe comprises at least one negative diffraction lobe of the selected diffraction order.

3. The superposition metering system according to claim 1, wherein the main illumination has a rotating dipole distribution relative to the grating direction of the grating structure on the superposition target.

4. The superposition metering system according to claim 1, wherein the superposition target according to the metering formula comprises: The first unit comprises a grating with a pitch P on a first layer and a grating with a pitch Q on a second layer to form a first lattice structure; and The second unit comprises a grating having the pitch Q on the first layer and a grating having the pitch P on the second layer to form a second folded structure; The one or more collecting optics are configured to implement the metering formulation by: The first portion of the auxiliary illumination and the main illumination are overlapped by both the +1 diffraction lobe and the positive fringe diffraction lobe of the superimposed target onto at least one of the one or more photodetectors to produce the first interference pattern. and The second portion of the auxiliary illumination and the main illumination are overlapped by both the -1 diffraction lobe and the negative fringe diffraction lobe of the superimposed target onto at least one of the one or more photodetectors to produce the second interference pattern.

5. The superposition metering system according to claim 1, wherein the superposition target according to the metering formula comprises: A unit comprising one or more gratings having a first and a second pitch on a first layer and a grating having a third pitch on a second layer; The one or more collecting optics are configured to implement the metering formulation by: The first portion of the auxiliary illumination is overlapped with the +1 diffraction order from the first, second, and third pitches onto at least one of the one or more photodetectors to produce the first interference pattern; and The second portion of the auxiliary illumination is overlapped with the -1 diffraction order from the first, second, and third pitches onto at least one of the one or more photodetectors to produce the second interference pattern.

6. The superposition metering system of claim 1, wherein the superposition target according to the metering formula comprises: The unit comprises a grating with a first pitch on a first layer and a grating with a second pitch on a second layer; and The one or more collecting optics are configured to implement the metering formulation by: The first portion of the auxiliary illumination is overlapped with the +1 and +2 diffraction orders from the first pitch and the +1 diffraction from the second pitch onto at least one of the one or more photodetectors to produce the first interference pattern; and The second portion of the auxiliary illumination is overlapped with at least one of the one or more photodetectors by the -1 and -2 diffraction orders from the first pitch and the -1 diffraction from the second pitch to produce the second interference pattern.

7. The superimposed metering system according to claim 1, wherein the one or more photodetectors comprise: One or more phase-locked optical detectors, locked to the frequency of the time-varying interferometric signal, wherein the one or more superposition measurements of the superposition target based on the time-varying interferometric signal include: Phase-locked loop (PLL) technology is used to extract at least one of the intensity or phase information associated with the time-varying interferometric signal; and The superposition error between the two or more layers of the sample is determined based on at least one of the intensity or the phase information.

8. The superposition measurement system according to claim 1, wherein generating the one or more superposition measurements of the superposition target based on the time-varying interferometric signal comprises: Fourier analysis is used to extract at least one of the intensity or phase information associated with the time-varying interference signal; and The superposition error between the two layers of the sample is determined based on at least one of the intensity or the phase information.

9. The superposition metering system according to claim 1, wherein the one or more illumination optics guide the main illumination to the superposition target according to the incident angle.

10. The superposition metering system of claim 1, wherein the illumination from the illumination source is spatially coherent.

11. A superposition measurement method, comprising: Light is generated using a light source; The illumination from the illumination source is split into main illumination and auxiliary illumination; The main illumination is directed onto a stacked target on the sample, wherein the stacked target comprises gratings in two or more layers; The first portion of the auxiliary illumination is overlapped with at least one diffraction lobe of the grating associated with the diffraction of the main illumination from each of the two or more layers onto one or more first photodetectors in the collecting pupil plane to produce a first interference pattern. The second portion of the auxiliary illumination is overlapped with at least one additional diffraction lobe of the grating associated with the diffraction of the main illumination from each of the two or more layers onto one or more second photodetectors in the collecting pupil plane to produce a second interference pattern; During scanning of the superimposed target with a scanning subsystem, the phases of the first and second interference patterns are modulated, wherein the scanning subsystem includes at least one of a translation stage for scanning the sample relative to the main illumination, a beam scanning optics for scanning the main illumination relative to the sample, or a phase modulator for modulating the phase of the auxiliary illumination. The modulated phase based on the first and second interference patterns is used to generate a time-varying interference signal using one or more first photodetectors and one or more second photodetectors; and One or more superimposed measurements of the superimposed target are generated based on the time-varying interferometric signal.

12. The superposition metrology method of claim 11, wherein overlapping the first portion of the auxiliary illumination with at least one diffraction lobe associated with the diffraction of the main illumination from each of the two or more layers onto the one or more first photodetectors in the collecting pupil plane to generate the first interference pattern comprises: The first portion of the auxiliary illumination is overlapped with at least one positive diffraction lobe of a selected diffraction order associated with the diffraction of the main illumination from each of the two or more layers onto one or more first photodetectors in the collecting pupil plane to produce the first interference pattern.

13. The superposition metrology method of claim 11, wherein overlapping the second portion of the auxiliary illumination with at least one additional diffraction lobe of the grating associated with the diffraction of the main illumination from each of the two or more layers onto the one or more second photodetectors in the collecting pupil plane to generate the second interference pattern comprises: The second portion of the auxiliary illumination is overlapped with at least one negative diffraction lobe of a selected diffraction order of the grating associated with the diffraction of the main illumination from each of the two or more layers onto one or more second photodetectors in the collecting pupil plane to produce the second interference pattern.

14. The superposition measurement method according to claim 11, wherein the superposition target comprises: The first unit comprises a grating with a pitch P on a first layer and a grating with a pitch Q on a second layer to form a first lattice structure; and The second unit comprises a grating having the pitch Q on the first layer and a grating having the pitch P on the second layer to form a second folded structure; One or more of the collecting optics are configured to implement the metering formulation by: The first portion of the auxiliary illumination and the main illumination are overlapped by both the +1 diffraction lobe and the positive fringe diffraction lobe of the superimposed target onto at least one of the one or more photodetectors to produce the first interference pattern. and The second portion of the auxiliary illumination and the main illumination are overlapped by both the -1 diffraction lobe and the negative fringe diffraction lobe of the superimposed target onto at least one of the one or more photodetectors to produce the second interference pattern.

15. The superposition measurement method according to claim 11, wherein the superposition target comprises: A unit comprising one or more gratings having a first and a second pitch on a first layer and a grating having a third pitch on a second layer; The one or more collecting optics are configured to implement the metrology formulation by: The first portion of the auxiliary illumination is overlapped with the +1 diffraction order from the first, second, and third pitches onto at least one of the one or more photodetectors to produce the first interference pattern; and The second portion of the auxiliary illumination is overlapped with the -1 diffraction order from the first, second, and third pitches onto at least one of the one or more photodetectors to produce the second interference pattern.

16. The superposition measurement method according to claim 11, wherein the superposition target comprises: The unit comprises a grating with a first pitch on a first layer and a grating with a second pitch on a second layer; and The one or more collecting optics are configured to implement the metrology formulation by: The first portion of the auxiliary illumination is overlapped with the +1 and +2 diffraction orders from the first pitch and the +1 diffraction from the second pitch onto at least one of the one or more photodetectors to produce the first interference pattern; and The second portion of the auxiliary illumination is overlapped with at least one of the one or more photodetectors by the -1 and -2 diffraction orders from the first pitch and the -1 diffraction from the second pitch to produce the second interference pattern.

17. A superimposed metering system, comprising: A light source, configured to produce illumination; One or more beam splitters configured to split the illumination from the illumination source into main illumination and auxiliary illumination; One or more illumination optics configured to guide the main illumination onto a stacking target on a sample during the implementation of a metrology formulation. The stacking target has gratings in two or more layers, wherein the stacking target according to the metrology formulation comprises one or more units containing a first group of gratings having a first grating orientation and one or more units containing a second group of gratings having a second grating orientation, wherein the main illumination has a rotating quadrupole distribution relative to the first and second grating orientations. An objective lens for collecting at least one positive diffraction lobe and at least one negative diffraction lobe associated with the diffraction of the main illumination from the grating in each of the two or more layers when implementing the metrological formulation. The first collection channel includes: The first group has one or more photodetectors in one or more collection pupil planes; One or more first collecting optics configured to implement the metering formulation by: The first portion of the auxiliary illumination and at least one diffraction lobe of the main illumination distributed along the first diagonal of the rotating quadrupole through the superimposed target are overlapped on at least one of the one or more photodetectors in the first group to produce a first interference pattern; and The second portion of the auxiliary illumination is overlapped with at least one additional diffraction lobe of the main illumination distributed along the first diagonal of the rotating quadrupole through the superposition target onto at least one of the one or more photodetectors in the first group to produce a second interference pattern. The second collection channel includes: The second group has one or more photodetectors in one or more collection pupil planes; One or more second collecting optics configured to implement the metering formulation by: The first portion of the auxiliary illumination and at least one diffraction lobe of the main illumination distributed along the second diagonal of the rotating quadrupole through the superimposed target are overlapped on at least one of the one or more photodetectors in the second group to produce a third interference pattern; and The second portion of the auxiliary illumination is overlapped with at least one additional diffraction lobe of the main illumination along the second diagonal of the rotating quadrupole distribution through the superposition target onto at least one of the one or more photodetectors in the second group to produce a fourth interference pattern. A scanning subsystem configured to modulate the phases of the first, second, third, and fourth interference patterns during scanning of the superimposed target when implementing the metrological formulation, wherein the scanning subsystem includes at least one of a translation stage for scanning the sample relative to the main illumination, a beam scanning optics for scanning the main illumination relative to the sample, or a phase modulator for modulating the phase of the auxiliary illumination; and A controller, communicatively coupled to the first and second photodetectors, includes one or more processors configured to execute program instructions to cause the processors to implement the metering formula by: Time-varying interference signals are received from the first and second collection channels during the scanning of the superimposed target; and One or more superimposed measurements of the superimposed target are generated based on the time-varying interference signal along the directions of the first and second gratings.

18. The superposition metrology system of claim 17, wherein the at least one diffraction lobe of the main illumination distributed along the first diagonal of the rotating quadrupole comprises at least one positive diffraction lobe of a selected diffraction order, wherein the at least one additional diffraction lobe of the main illumination distributed along the first diagonal of the rotating quadrupole comprises at least one negative diffraction lobe of the selected diffraction order, wherein the at least one diffraction lobe of the main illumination distributed along the second diagonal of the rotating quadrupole comprises at least one positive diffraction lobe of the selected diffraction order, and wherein the at least one additional diffraction lobe of the main illumination distributed along the second diagonal of the rotating quadrupole comprises at least one negative diffraction lobe of the selected diffraction order.

19. The superposition metering system of claim 17, wherein the illumination lobe of the first diagonal of the rotating quadrupole distribution is distinguished from the illumination lobe of the second diagonal of the rotating quadrupole distribution by at least one of wavelength or polarization.

20. The superposition metering system of claim 17, wherein the one or more illumination optics guide the main illumination to the superposition target at an oblique incident angle.

21. The superposition metering system of claim 17, wherein the illumination from the illumination source is spatially coherent.

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