High-sensitivity particle detection using spatially variable polarizing rotors and polarizers

Abstract

As semiconductor devices continue to shrink, particle detection systems require corresponding improvements in sensitivity and resolution. [Solution] The dark-field inspection system includes an illumination source for generating an illumination beam, an illumination optical component configured to direct the illumination beam towards the sample at an off-axis angle along the illumination direction, a collection optical component for collecting scattered light from the sample in response to the illumination beam in dark-field mode, a polarization rotor positioned on the pupil plane of the collection optical component, which provides a spatially variable polarization rotation angle selected to rotate the light scattered from the surface of the sample to a selected polarization angle, a polarizer aligned to block light polarized along the selected polarization angle in order to block the light scattered from the surface of the sample, and a detector that generates a dark-field image of the sample based on the scattered light from the sample that has passed through the polarizer.

Description

Technical Field

[0001] The present disclosure generally relates to particle inspection, and more particularly to particle inspection using dark field imaging based on scattered light or diffracted light.

Background Art

[0002] This application claims the benefit under 35 U.S.C. § 119(e) of U.S. Provisional Patent Application No. 62 / 806,820, filed on Feb. 17, 2019, in the names of inventors Xuefeng Liu and Jenn-Kuen Leong, which is hereby incorporated by reference in its entirety.

[0003] Particle detection systems are generally utilized in semiconductor processing lines to identify defects or particles on wafers, such as unpatterned wafers. As semiconductor devices continue to shrink, particle detection systems require corresponding improvements in sensitivity and resolution. The main noise source that can limit the measurement sensitivity is surface scattering (e.g., surface haze) on the wafer, which can even exist for optically polished surfaces. With respect to scattering from particles, various methods have been proposed to suppress surface scattering, but such methods cannot achieve the desired sensitivity level and / or can achieve sensitivity at the expense of degraded image quality.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] Therefore, it is necessary to develop systems and methods to mitigate the shortcomings mentioned above. [Means for solving the problem]

[0006] A system according to one or more exemplary embodiments of the present disclosure is disclosed. In one exemplary embodiment, the system includes an illumination source for generating an illumination beam. In another exemplary embodiment, the system includes one or more illumination optics for directing the illumination beam onto a sample at an off-axis angle along the illumination direction. In another exemplary embodiment, the system includes one or more collection optics for collecting scattered light from a sample in response to the illumination beam in dark-field mode. In another exemplary embodiment, the system includes a polarizing rotor positioned on the pupil plane of one or more collection optics, the polarizing rotor resulting in a spatially variable polarization rotation angle selected to rotate the light scattered from the surface of the sample to a selected polarization angle. In another exemplary embodiment, the system includes a polarizer aligned to block light polarized along a selected polarization angle in order to block light scattered from the surface of the sample. In another exemplary embodiment, the system includes a detector configured to produce a dark-field image of a sample based on scattered light from the sample passed by the polarizer, the scattered light from the sample passed by the polarizer includes at least a portion of the light scattered by one or more particles on the surface of the sample.

[0007] Apparatuses according to one or more exemplary embodiments of the present disclosure are disclosed. In one exemplary embodiment, the apparatus includes a polarizing rotator positioned on the pupil plane of a dark-field imaging system, the dark-field imaging system including one or more collecting optical components for collecting scattered light from a sample in response to off-axis illumination. In another exemplary embodiment, the polarizing rotator provides a spatially variable polarization rotation angle selected to rotate the light scattered from the surface of the sample to a selected polarization angle. In another exemplary embodiment, the polarizing rotator is configured to be coupled to a polarizer aligned to block light polarized along a selected polarization angle in order to block the light scattered from the surface of the sample.

[0008] Methods according to one or more exemplary embodiments of the present disclosure are disclosed. In one exemplary embodiment, the method includes receiving the electric field distribution of light scattered from the surface of a sample in response to an illumination beam having a known polarization at a known incident angle. In another exemplary embodiment, the method includes designing a polarization rotor suitable for placement in the pupil plane of an imaging system to produce a selected spatially varying polarization rotation angle such that the polarization of the light having an electric field distribution is rotated to a selected polarization angle. In another exemplary embodiment, the method includes generating a dark-field image of a sample using an imaging system having a polarization rotor in the pupil plane and a linear polarizer aligned to block light polarized along a selected polarization angle, wherein the dark-field image is generated based on the light passed through the polarizer.

[0009] A system according to one or more exemplary embodiments of the present disclosure is disclosed. In one exemplary embodiment, the system includes an illumination source for generating an illumination beam. In another exemplary embodiment, the system includes one or more illumination optics for directing the illumination beam onto a sample at an off-axis angle along the illumination direction. In another exemplary embodiment, the system includes a detector. In another exemplary embodiment, the system includes one or more collecting optics for generating a dark-field image of a sample on the detector based on light collected from the sample in response to the illumination beam. In one exemplary embodiment, the system includes a segmented polarizer comprising a plurality of segments distributed within the pupil plane of one or more collecting optics, the stop axis of each segment being oriented to block light scattered from the surface of the sample within the segment.

[0010] It should be understood that both the above general description and the following detailed description are for illustrative and explanatory purposes only and do not necessarily limit the claimed invention. The accompanying drawings incorporated herein and constituting part thereof illustrate embodiments of the invention and, together with the general description, are useful in illustrating the principles of the invention.

[0011] Many of the advantages of this disclosure can be better understood by those skilled in the art by referring to the accompanying drawings. [Brief explanation of the drawing]

[0012] [Figure 1] This is a conceptual diagram of a particle detection system according to one or more embodiments of the present disclosure. [Figure 2A] This figure shows pupil scattering maps of surface scattering in response to obliquely incident p-polarized light, according to one or more embodiments of the present disclosure. [Figure 2B] This figure shows pupil-plane scattering maps of light scattered by sub-resolution particles in response to obliquely incident p-polarized light, according to one or more embodiments of the present disclosure. [Figure 3A]This is a conceptual top view of a segmented polarizer having wedge-shaped segments radially distributed around a vertex position, according to one or more embodiments of the present disclosure. [Figure 3B] This is a conceptual top view of a segmented polarizer according to one or more embodiments of the present disclosure, in which the segments are linearly distributed along a selected segmentation direction within the pupil plane. [Figure 4] This is a conceptual top view of a phase mask including two divisions for dividing the pupil into two sections, according to one or more embodiments of the present disclosure. [Figure 5] This is a conceptual top view of a polarizing rotor formed as an angularly segmented half-wave plate according to one or more embodiments of the present disclosure. [Figure 6A] This is a graph of the orthogonally polarized portion of the collected sample light after it has propagated through an angularly segmented polarizing rotor and a polarizing beam splitter according to one or more embodiments of the present disclosure. [Figure 6B] This is a graph of the orthogonally polarized portion of the collected sample light after it has propagated through an angularly segmented polarizing rotor and a polarizing beam splitter according to one or more embodiments of the present disclosure. [Figure 7A] This is a conceptual top view of a polarizing rotor formed as linearly segmented half-wave plates according to one or more embodiments of the present disclosure. [Figure 7B] Figure 7A shows a calculated graph of the azimuthal direction of the optical axis of a linearly segmented polarizing rotor as a function of the position in the pupil plane along the segmentation direction, according to one or more embodiments of the present disclosure. [Figure 7C] A graph of the orientation of a linearly segmented polarizer rotor with respect to the optical axis for rotating the polarization of surface haze to a selected polarization angle, according to one or more embodiments of the present disclosure. [Figure 8A] This is a graph of the orthogonally polarized portion of the collected sample light after it has propagated through an angularly segmented polarizing rotor and a polarizing beam splitter according to one or more embodiments of the present disclosure. [Figure 8B]A graph of the orthogonally polarized portion of the collected sample light after propagating through an angularly segmented polarizer rotator and a polarizing beam splitter, according to one or more embodiments of the present disclosure. [Figure 9A] A diagram showing an image of particles smaller than the resolution of an imaging system, generated based on the scattering of obliquely incident p-polarized light, according to one or more embodiments of the present disclosure. [Figure 9B] A diagram including an image of the particles of FIG. 8A, using an imaging system having an angularly segmented polarizer rotator and a polarizing beam splitter as shown in FIG. 5, according to one or more embodiments of the present disclosure. [Figure 9C] A diagram including an image of the particles of FIG. 9A, using an imaging system having a linearly segmented polarizer rotator as shown in FIG. 7A, which has 72 segments and linear polarizers, according to one or more embodiments of the present disclosure. [Figure 10] A graph showing the performance and convergence behavior of an angularly segmented polarizer rotator and a linearly segmented polarizer rotator, according to one or more embodiments of the present disclosure. [Figure 11A] A graph of SNR as a function of pixel size for segmented polarizers and segmented polarizer rotators, using an irradiation beam having a wavelength of 266 nm, according to one or more embodiments of the present disclosure. [Figure 11B] A graph of SNR as a function of pixel size for segmented polarizers and segmented polarizer rotators, using an irradiation beam having a wavelength of 213 nm, according to one or more embodiments of the present disclosure. [Figure 12] A conceptual top view of a polarizer rotator formed from an optically active material, according to one or more embodiments of the present disclosure. [Figure 13A] A graph of the thickness profile along the vertical direction of FIG. 12 of a polarizer rotator formed from an optically active material, designed to rotate the polarization of surface haze having wavelengths of 266 nm and 213 nm, respectively, in the horizontal direction of FIG. 12, according to one or more embodiments of the present disclosure. [Figure 13B]This is a cross-sectional view of a polarizing rotor having a thickness profile according to one or more embodiments of the present disclosure, as shown in Figure 13A. [Figure 14A] Figure 12 shows a graph of the thickness profile along the vertical direction of a polarization rotor formed from an optically active material designed to rotate the polarization of a surface haze having wavelengths of 266 nm and 213 nm, respectively, in the horizontal direction of Figure 12, according to one or more embodiments of the present disclosure. [Figure 14B] This is a cross-sectional view of a polarizing rotor having a thickness profile according to one or more embodiments of the present disclosure, as shown in Figure 14A. [Figure 15] This is a flowchart illustrating the steps taken in a method for particle detection according to one or more embodiments of the present disclosure. [Modes for carrying out the invention]

[0013] Next, we will refer in detail to the subject matter disclosed as shown in the accompanying drawings. This disclosure is specifically described with respect to several embodiments and their particular features. The embodiments described herein should be considered illustrative rather than restrictive. The directional terms used herein, such as “left,” “right,” “top,” “bottom,” “over,” “under,” “upper,” “upward,” “lower,” “down,” and “downward,” are intended to indicate relative positions for illustrative purposes and do not specify an absolute reference system. It should be readily apparent to those skilled in the art that various modifications and changes can be made in form and detail without departing from the spirit and scope of this disclosure.

[0014] Embodiments of this disclosure relate to systems and methods for particle detection based on dark-field imaging in which surface scattering (e.g., surface haze) is separated from light scattered by particles on a surface (e.g., particle scattering). Further embodiments of this disclosure relate to simultaneously generating separate images of a sample based on surface scattering and particle scattering.

[0015] Wafer inspection is generally described in U.S. Patent No. 9,874,526 issued on January 1, 2018, U.S. Patent No. 9,291,575 issued on March 22, 2016, U.S. Patent No. 8,891,079 issued on November 18, 2014, and U.S. Patent No. 9,891,177 issued on February 13, 2018, all of which are incorporated herein. Furthermore, for the purposes of this disclosure, particles may include, but are not limited to, any surface defects on the sample of interest, including foreign particles, scratches, small indentations, holes, protrusions, etc.

[0016] In this specification, it is recognized that light scattered from particles and light scattered from a surface may exhibit different electric field distributions (e.g., polarization and electric field strength) depending on the scattering angle. Furthermore, the difference in electric field distribution (e.g., scattering map) can be particularly pronounced for p-polarized light incident at an oblique angle. For example, surface haze from p-polarized light incident at an oblique angle may be approximately radially polarized with respect to the angle of specular reflection, while scattering from particles may be approximately radially polarized with respect to the surface normal.

[0017] In some embodiments, a dark-field imaging system includes an in-pupil polarization rotator for selectively rotating the polarization of surface haze to a selected polarization angle, and a linear polarizer for separating the surface haze polarized along the selected polarization angle from the remaining signal (e.g., particle scattering) into different imaging channels. For example, the polarization rotator can produce a varying polarization rotation angle across the pupil based on a known or expected polarization distribution of the surface haze, and the spatial distribution of the polarization rotation angle across the pupil is selected to rotate the surface haze distributed across the pupil to a common selected polarization angle. In this context, a linear polarizer (e.g., a polarization beam splitter) aligned to this selected polarization angle can effectively separate the surface haze from particle scattering.

[0018] Further embodiments of this disclosure relate to polarizers for providing a spatially varied amount of polarization rotation suitable for use in the pupil plane of an imaging system. Multiple configurations of polarizers are contemplated herein. In some embodiments, a polarizer includes a segmented half-wave plate, comprising a plurality of half-wave plates having different orientations of the optical axis. For example, a polarizer may include a plurality of half-wave plates radially distributed around vertex positions, such as a point in the pupil plane corresponding to the specular reflection of the illumination beam. In this context, each half-wave plate may occupy a range of radial angles around the specular reflection angle (e.g., to mimic the approximate radial polarization distribution of surface haze). In other examples, a polarizer may include a series of half-wave plates linearly distributed along a single direction in the pupil plane. In some embodiments, a polarizer includes an optically active material having a spatially varied thickness. In this context, the thickness at a given point in the pupil plane may determine the angle of polarization rotation.

[0019] Further embodiments of this disclosure relate to a method for designing a spatial distribution of polarization rotation angles suitable for rotating surface haze to a selected polarization angle for filtering using a polarizing beam splitter. For example, a polarization rotator may be designed to selectively rotate light associated with any noise source to a common selected polarization angle for filtering using a polarizing beam splitter. Thus, while this disclosure primarily focuses on surface haze based on obliquely incident p-polarized light, the examples herein are provided for illustrative purposes only and should not be construed as limiting. Rather, it is intended that the systems and methods described herein may be applied to light having any wavelength, polarization, or incident angle.

[0020] Further embodiments of this disclosure relate to a segmented polarizer suitable for use in the pupil of an imaging system for selectively filtering surface haze (e.g., through absorption within the segmented polarizer) based on a known distribution of polarization angles of surface haze within the pupil. For example, a segmented polarizer may include a plurality of polarizers distributed across the pupil, each polarizer oriented to block light along a selected direction. Several configurations of a segmented polarizer are contemplated herein. In some embodiments, a segmented polarizer includes, but is not limited to, a plurality of polarizers radially distributed around vertex positions, such as points in the pupil corresponding to specular reflections of the illumination beam. In some embodiments, a segmented polarizer includes a plurality of polarizers linearly distributed within the pupil.

[0021] Next, referring to Figures 1 to 13B, the systems and methods for high-sensitivity particle detection will be described in more detail.

[0022] Figure 1 is a conceptual diagram of a particle detection system 100 according to one or more embodiments of the present disclosure. In one embodiment, the particle detection system 100 includes an illumination source 102 for generating an illumination beam 104, an illumination path 106 including one or more illumination optical components for directing the illumination beam 104 toward a sample 108, and a collection path 110 including one or more collection optical components for collecting light (e.g., sample light 112) emitted from the sample 108. For example, the collection path 110 may include an objective lens 114 for collecting at least a portion of the sample light 112. The sample light 112 may include any type of light emitted from the sample 108 in response to the illumination beam 104, including, but not limited to, scattered light, reflected light, diffracted light, or emitted light.

[0023] The irradiation beam 104 may, non-limitingly, include one or more selected wavelengths of light, including ultraviolet (UV) radiation, visible radiation, or infrared (IR) radiation. For example, the irradiation source 102 may, but is not required, produce an irradiation beam 104 with a wavelength shorter than approximately 350 nm. As another example, the irradiation beam 104 may have a wavelength of approximately 266 nm. As yet another example, the irradiation beam 104 may have a wavelength of approximately 213 nm. In this specification, it is recognized that imaging resolution and light scattering by small particles (e.g., compared to the wavelength of the irradiation beam 104) both generally correspond to wavelength, and consequently, reducing the wavelength of the irradiation beam 104 can generally increase imaging resolution and the scattering signal from small particles. Therefore, the irradiation beam 104 may, non-limitingly, include short-wavelength light, including extreme ultraviolet (EUV) light, deep ultraviolet (DUV) light, or vacuum ultraviolet (VUV) light.

[0024] The irradiation source 102 may include any type of light source known in the art. Furthermore, the irradiation source 102 may produce an irradiation beam 104 having any selected spatial or temporal coherence characteristics. In one embodiment, the irradiation source 102 includes, but is not limited to, one or more laser sources, such as one or more narrowband laser sources, one or more broadband laser sources, one or more supercontinium laser sources, one or more white light laser sources, etc. In other embodiments, the irradiation source 102 includes a laser-driven light source (LDLS), such as a laser-sustained plasma (LSP) light source, etc. For example, the irradiation source 102 may include, but is not limited to, an LSP lamp, an LSP bulb, or an LSP chamber suitable for containing one or more elements that can emit broadband irradiation when excited to a plasma state by a laser source. In other embodiments, the irradiation source 102 includes, but is not limited to, a lamp source, such as an arc lamp, a discharge lamp, or an electrodeless lamp.

[0025] In other embodiments, the irradiation source 102 provides a tunable irradiation beam 104. For example, the irradiation source 102 may include a tunable irradiation source (e.g., one or more tunable lasers). As another example, the irradiation source 102 may include a broadband irradiation source coupled to any combination of fixed and tunable filters.

[0026] The irradiation source 102 can further produce an irradiation beam 104 having any arbitrary temporal profile. For example, the irradiation beam 104 may have a continuous temporal profile, a modulated temporal profile, a pulsed temporal profile, and so on.

[0027] In this specification, it is recognized that the intensity of surface haze may depend on several factors, including, but not limited to, the angle of incidence or polarization of the irradiation beam 104. For example, the intensity of surface haze may be relatively high for angles of incidence close to the normal and may decrease for higher angles of incidence. In one embodiment, the irradiation path 106 may include, but not limited to, one or more irradiation optical components, such as a lens 116 or a mirror, to direct the irradiation beam 104 onto the sample 108 at an oblique angle of incidence to reduce the generation of surface haze. The oblique angle of incidence may generally include any selected angle of incidence. For example, the angle of incidence may be greater than 60 degrees relative to the surface normal, but is not required.

[0028] In other embodiments, the irradiation path 106 includes one or more irradiation beam adjustment components 118 suitable for modifying and / or adjusting the irradiation beam 104. For example, one or more irradiation beam adjustment components 118 may include, but are not limited to, one or more polarizers, one or more waveplates, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, and one or more beam shapers. In one embodiment, one or more irradiation beam adjustment components 118 include polarizers or waveplates directed to bring a p-polarized irradiation beam 104 onto the sample 108.

[0029] In other embodiments, the particle detection system 100 includes at least one detector 120 configured to capture at least a portion of the sample light 112 collected by the collection path 110. The detector 120 may include any type of photodetector known in the art that is suitable for measuring the irradiation received from the sample 108. For example, the detector 120 may include, but is not limited to, a multi-pixel detector suitable for capturing an image of the sample 108, such as a charge-coupled device (CCD) detector, a complementary metal-oxide-semiconductor (CMOS) detector, a time-delay integral (TDI) detector, a photomultiplier tube (PMT) array, or an avalanche photodiode (APD) array. In other embodiments, the detector 120 may include a spectroscopic detector suitable for identifying the wavelength of the sample light 112.

[0030] The particle detection system 100 may include any number of detectors 120 to simultaneously image the sample 108. Furthermore, the collection path 110 may include a linear polarizer 122 configured to filter the sample light 112 so that it is imaged on the detectors 120 based on its polarization. In one embodiment, as shown in Figure 1, the linear polarizer 122 acts as a polarization beam splitter, resulting in the linear polarizer 122 splitting the sample light 112 into two orthogonally polarized beams. The particle detection system 100 may then include detectors 120 for generating an image of the sample 108 using each of the orthogonally polarized portions of the sample light 112.

[0031] The collection path 110 may include any number of beam adjustment elements 124 for guiding and / or modifying the sample light 112, including, but not limited to, one or more lenses, one or more filters, one or more apertures, one or more polarizers, or one or more phase plates.

[0032] In one embodiment, as shown in Figure 1, the collection path 110 includes one or more beam adjustment elements 124 located on or near the pupil plane 126. For example, as will be discussed in more detail below, the collection path 110 may include, but is not limited to, beam adjustment elements 124 such as a continuous polarizer or a phase mask on or near the pupil plane 126. In this context, the particle detection system 100 may, non-limitingly, control and / or adjust a selected aspect of the sample light 112 used to generate an image on the detector 120, including the luminance, phase, and polarization of the sample light 112 as a function of scattering angle and / or sample position.

[0033] Furthermore, the collection path 110 may have any number of pupil planes 126. For example, as shown in Figure 1, the collection path 110 may include one or more lenses 128 for generating an image of the pupil plane 126 on the detector 120 and one or more lenses 130 for generating an image of the surface of the sample 108. However, it is recognized herein that a limited number of beam adjustment elements 124 may be placed on or sufficiently close to a particular pupil plane 126 to produce a desired effect. Thus, for the purposes of this disclosure, reference to one or more elements on the pupil plane 126 may generally describe one or more elements on or sufficiently close to the pupil plane 126 to produce a desired effect. Not shown in the figures, in some embodiments, the collection path 110 may include additional lenses to generate one or more additional pupil planes 126 so that any number of beam adjustment elements 124 may be placed on or near the pupil plane 126.

[0034] In other embodiments, the particle detection system 100 includes a controller 132 which includes one or more processors 134 configured to execute program instructions held in a memory medium 136 (e.g., memory). Furthermore, the controller 132 may be communicatively coupled to any component of the particle detection system 100. In this context, one or more processors 134 of the controller 132 may perform any of the various process steps described throughout this disclosure. For example, the controller 132 may receive, analyze, and / or process data from the detector 120 (e.g., associated with an image of the sample 108). As another example, the controller 132 may control or otherwise instruct any component of the particle detection system 100 using control signals.

[0035] One or more processors 134 of controller 132 may include any processing elements known in the art. In this sense, one or more processors 134 may include any microprocessor type device configured to execute algorithms and / or instructions. In one embodiment, one or more processors 134 may consist of a desktop computer, a mainframe computer system, a workstation, an imaging computer, a parallel processor, or any other computer system (e.g., a networked computer) configured to execute a program configured to operate the particle detection system 100 as described throughout this disclosure. Furthermore, it is recognized that the term “processor” may be broadly defined to include any device having one or more processing elements that execute program instructions from a non-temporary memory medium 136. Furthermore, the steps described throughout this disclosure may be performed by a single controller 132, or alternatively, by multiple controllers. In addition, controller 132 may include one or more controllers housed in a common housing or in multiple housings. Thus, any controller or combination of controllers may be packaged separately as modules suitable for integration into the particle detection system 100.

[0036] The memory medium 136 may include any storage medium known in the art that is suitable for storing program instructions executable by one or more associated processors 134. For example, the memory medium 136 may include a non-temporary memory medium. Other examples of the memory medium 136 may include, but are not limited to, read-only memory (ROM), random-access memory (RAM), magnetic or optical memory devices (e.g., disks), magnetic tapes, solid drives, etc. It should be further noted that the memory medium 136 may be housed in a common controller housing together with one or more processors 134. In one embodiment, the memory medium 136 may be located remotely from the physical locations of one or more processors 134 and the controller 132. For example, one or more processors 134 of the controller 132 may have access to remote memory (e.g., a server) accessible over a network (e.g., the Internet, an intranet, etc.). Therefore, the above description should not be construed as a limitation on the invention, but merely illustrative.

[0037] In this specification, the particle detection system 100 is intended to be configured as any type of image-based particle detection system known in the art. In one embodiment, as shown in Figure 1, the particle detection system 100 is a dark-field imaging system for eliminating specular reflection. In this context, the particle detection system 100 can image a sample 108 primarily based on scattered light. Dark-field imaging can further be performed using any technique known in the art. In one embodiment, the orientation and / or numerical aperture (NA) of the objective lens 114 may be selected so that the objective lens 114 does not collect specular reflection. For example, as shown in Figure 1, the objective lens 114 is oriented approximately normal to the sample 108 and has an NA that does not include the specular reflection portion of the illumination beam 104. Furthermore, the objective lens 114 may have an NA of approximately 0.9 or greater, but is not required. In other embodiments, the particle detection system 100 may include one or more components for blocking specular reflection from reaching the detector 120.

[0038] Next, with reference to Figures 2A to 2B, the pupil plane polarization rotation of surface haze and the subsequent filtering are described in more detail.

[0039] In this specification, it is recognized that light scattered from the surface of a sample (e.g., surface haze, surface scattering, etc.) can be considered noise in particle detection applications. Therefore, it may be desirable to filter out the portion of the sample light 112 associated with surface haze from the portion associated with light scattered by the particle of interest.

[0040] Figure 2A is a pupil scattering map 202 of surface scattering (e.g., surface haze) in response to obliquely incident p-polarized light, according to one or more embodiments of the present disclosure. Figure 2B is a pupil scattering map 204 of light scattered by small particles (e.g., small compared to the imaging resolution of the particle detection system 100 or the wavelength of the illumination beam 104), in response to obliquely incident p-polarized light, according to one or more embodiments of the present disclosure.

[0041] Specifically, the scattering maps 202 and 204 include the electric field intensity, indicated by shading with white as the highest brightness and black as the lowest brightness. Furthermore, the scattering maps 202 and 204 include the polarization direction of the light as a function of the collection angle (e.g., scattering angle) within the pupil plane 126, indicated by superimposed ellipses. The scattering maps 202 and 204 are bounded by the collection area 206 within the pupil plane 126, which is related to the range of angles over which the sample light 112 is collected by the particle detection system 100. For example, the collection area 206 may correspond to the numerical aperture (NA) of the objective lens 114.

[0042] Scatter maps 202 and 204 are based on the configuration of the particle detection system 100 shown in Figure 1. In Figures 2A and 2B, the specular reflection angle 208 is located outside the collection area 206 along the illumination direction 210 (e.g., outside the collection area 206 to the right of the circular collection area 206 in Figure 2A), indicating that the objective lens 114 does not capture the specular reflection. However, alternative configurations are within the scope of this disclosure. For example, if the specular reflection angle 208 is located within the pupil plane 126, the specular reflection may be blocked in front of the detector 120 to produce a dark-field image.

[0043] In addition, scattering maps 202 and 204 may represent scattering from a wide variety of materials, including, but not limited to, silicon, epitaxial, and polysilicon wafers. However, it should be understood that scattering maps 202 and 204 are provided solely for illustrative purposes and should not be construed as limiting the present disclosure.

[0044] As shown in Figures 2A and 2B, the electric field distribution (e.g., electric field strength and polarization direction) of light scattered by particles can differ significantly from that of light scattered by a surface, especially when the illumination beam 104 is p-polarized. For example, sample light 112 associated with surface haze generally exhibits an approximately radial polarization distribution with respect to the specular reflection angle 208 within the collection area 206, as shown in Figure 2A. In contrast, sample light 112 associated with particle scattering generally exhibits a radial polarization distribution with respect to the surface normal, as shown in Figure 2B. Furthermore, the polarization of scattered sample light 112 is generally elliptical. As can be seen from Figures 2A and 2B, at most positions within the pupil plane 126, the ellipse is very elongated, meaning that one linearly polarized component is much stronger than the other. For sample light 112 scattered from small particles (e.g., Figure 2B), the polarization can be more elliptical near the center of the pupil, meaning that the two linearly polarized components can be approximately equal in magnitude. However, the brightness of light in this region of the pupil is relatively low, and its contribution to the total scattering signal from small particles is small.

[0045] In one embodiment, the particle detection system 100 includes a polarizer positioned on or near the pupil plane 126 to preferentially block surface haze. In a general sense, the polarizer positioned on or near the pupil plane 126 may be designed to provide spatially varying polarization filtering corresponding to any known, measured, simulated, or other expected polarization of light. In connection with the present disclosure, the polarizer positioned on or near the pupil plane 126 may preferentially filter surface haze based on a known electric field distribution within the pupil plane 126. Thus, in some embodiments, the particle detection system 100 includes a radial haze blocking polarizer positioned on or near the pupil plane 126 to preferentially block approximately radially polarized surface haze as shown in Figure 2A.

[0046] Next, with reference to Figures 3A and 3B, a segmented haze-blocking polarizer 302 suitable for preferentially filtering surface haze from particle scattering is described according to one or more embodiments of the present disclosure. In a general sense, the haze-blocking polarizer 302 may be designed to provide spatially varying polarization filtering corresponding to any known, measured, simulated, or other expected polarization of light. In connection with the present disclosure, the haze-blocking polarizer 302 may preferentially filter surface haze based on a known electric field distribution within the pupil plane 126 (e.g., the electric field distribution of surface haze shown in Figure 2A). Figures 3A and 3B include a polarization ellipse 304 representing the polarization of surface haze within the pupil plane 126 based on Figure 2A.

[0047] The haze-blocking polarizer 302 may include any number of segments 306 distributed across the pupil plane 126, each segment 306 may include a linear polarizer oriented to transmit light polarized along a selected path polarization direction 308. In this context, the haze-blocking polarizer 302 may result in a spatially varying distribution of the polarization angles transmitted.

[0048] In one embodiment, the path polarization direction 308 of each section 306 of the haze-blocking polarizer 302 is directed to preferentially block surface haze. For example, the path polarization direction 308 for each section 306 may be directed to be perpendicular to the expected polarization ellipse 304 in the corresponding portion of the pupil surface 126.

[0049] Figure 3A is a conceptual top view of a haze-blocking polarizer 302 (e.g., an angularly segmented polarizer) having wedge-shaped segments 306 radially distributed around a vertex position 310, according to one or more embodiments of the present disclosure. In one embodiment, the vertex position 310 of the haze-blocking polarizer 302 is oriented to coincide with a point in the pupil plane 126 associated with the specular reflection angle of the illumination beam 104 from the sample 108. In this context, each segment 306 may occupy a range of radial angles in the pupil plane 126 with respect to the specular reflection angle 208, such that the surface haze within each segment 306 can be substantially uniform based on the scattering map 202 in Figure 2A. Furthermore, each pass polarization direction 308 for each segment 306 may be oriented to block light having radial polarization with respect to the vertex position 310 in order to preferentially block surface haze.

[0050] The specular reflection angle 208 can be located inside or outside the collection area 206, as previously described herein. Furthermore, the vertex positions 310 do not necessarily have to be located within the physical structure of the haze-blocking polarizer 302. For example, if the specular reflection angle 208 is located outside the collection area 206, the sections 306 can be oriented such that they converge to the vertex positions 310 outside the boundary defining the size of the haze-blocking polarizer 302.

[0051] Figure 3B is a conceptual top view of a haze-blocking polarizer 302 (e.g., a linearly segmented polarizer) according to one or more embodiments of the present disclosure, in which segments 306 are linearly distributed along a selected segmentation direction 312 within the pupil plane 126. For example, the segmentation direction 312 in Figure 3B is selected to be orthogonal to the illumination direction 210 as represented within the pupil plane 126. In this context, the path polarization direction 308 for each segment 306 may be selected to substantially reduce the transmission of surface scattered light through that segment 306.

[0052] It is recognized herein that the accuracy with which the haze-blocking polarizer 302 can preferentially filter surface haze may vary based on the number and layout of the sections 306 relative to the expected scattering map of the surface haze. It is also recognized herein that the manufacturing cost of the haze-blocking polarizer 302 may also correspond to its complexity. Therefore, the number and layout of the sections 306 may be selected to balance various requirements, including performance and manufacturing cost.

[0053] Furthermore, if the polarization ellipses 304 are not uniformly oriented within a particular section 306, the path polarization directions 308 within that particular section 306 may be selected to suppress surface haze according to an optimization function. For example, the path polarization directions 308 for each section 306 may be selected based on an expected polarization distribution (e.g., as shown in Figure 2A) such that they are orthogonal to the weighted average of the expected directions of the major axes of the polarization ellipses 304 within each section 306, with weights proportional to the expected electric field strength or luminance across the section 306. As another example, the path polarization directions 308 for each section 306 may be selected to maximize the ratio of transmitted sample light 112 associated with particle scattering to transmitted surface haze.

[0054] Referring next to Figure 4, in some embodiments, the particle detection system 100 includes one or more components positioned on or near the pupil plane 126 to reconstruct the point spreading function (PSF) of p-polarized light scattered by sub-resolution particles. It is recognized herein that images of particles smaller than the system's imaging resolution are generally limited by the system PSF, which is typically an Airy function when the image is formed from specularly reflected light. However, the actual PSF associated with a particle (e.g., particle PSF) and thus the actual image of the particle produced by the system may have a different size or shape than the system PSF, particularly when the image is formed from scattered light, due to the specific electric field distribution of light from the particle within the pupil plane 126.

[0055] Specifically, when illuminated by obliquely p-polarized light, dark-field images of particles smaller than the imaging resolution (e.g., images of particles formed by scattered or diffracted light) may appear as annular bands extending over an area larger than the system PSF, which negatively impacts particle detection sensitivity. This annular shape, and the increase in the size of the PSF or the imaged spot of the particle, may be related to destructive interference of the collected light at the center of the imaged spot of the particle on the detector 120.

[0056] Therefore, in some embodiments, the particle detection system 100 includes one or more components for correcting the phase of the sample light 112 across the pupil plane 126, such as one or more phase plates or one or more phase compensators, not limited to promoting constructive interference of light at the center of the imaged spot of the particle on the detector 120.

[0057] For example, a phase mask can have various configurations suitable for reconstructing the PSF of an imaged particle. A phase mask for reconstructing the PSF of an imaged particle based on scattered light is generally described in U.S. Patent Application No. 16 / 577,089, filed September 20, 2019, entitled “Radial Polarizer for Particle Detection,” which is incorporated herein by reference in its entirety. In some embodiments, the phase mask may include one or more half-wave plates occupying a selected portion of the pupil plane 126. In this context, the phase mask may be formed as a segmented optical component in which at least one of the segments includes a half-wave plate.

[0058] Figure 4 is a conceptual top view of a phase mask 402 comprising two divisions (e.g., half each) for dividing the pupil into two parts, according to one or more embodiments of the present disclosure. For example, as shown in Figure 4, the phase mask 402 comprises orthogonal polarization (e iπ E y The phase mask 402 may include a section 404 formed from a half-wave plate having an optical axis aligned with the X direction, so as to introduce a phase shift of π for light polarized along the Y direction (represented as ). Furthermore, the phase mask 402 may include a section 406 that does not rotate the polarization of the light. For example, section 406 may include a compensating plate formed from an optically homogeneous material along the direction of propagation so that light passing through section 406 propagates along the same (or substantially the same) optical path length as the light in section 404. In one embodiment, the compensating plate is formed from a material having approximately the same thickness and refractive index as the half-wave plate in section 404, but without birefringence along the direction of propagation. In another embodiment, the compensating plate is formed from the same material as the half-wave plate in section 404, but is cut along a different axis so that light propagating through the compensating plate does not undergo birefringence. For example, light propagating along the optical axis of a uniaxial crystal may not undergo birefringence so that the crystal can be optically homogeneous with respect to light propagating along the optical axis. As another example, section 406 may include an aperture.

[0059] Furthermore, in some embodiments, the phase mask 402 may be tilted from the pupil plane 126 to at least partially compensate for the optical path length difference across the pupil plane 126.

[0060] The segmented phase mask 402 can be formed using any technique known in the art. In one embodiment, the various segments (e.g., segments 404-406 in Figure 4) are formed as a single component in which the various segments are arranged in a single plane.

[0061] However, it should be understood that Figure 4 and the related description are provided solely for illustrative purposes and should not be construed as limiting. For example, a phase mask 402 having two divisions may include a half-wave plate positioned in the lower portion rather than the upper portion of the collection area 206, as shown in Figure 4. Furthermore, the phase mask 402 may include any number of divisions distributed in any pattern across the pupil plane 126, formed from any combination of materials, to reconstruct the PSF of light scattered from the particles. For example, given a known (e.g., measured, simulated, etc.) electric field distribution of light in the pupil plane 126 associated with an object of interest, a divisional phase mask 402 as described herein may be formed to selectively adjust the phase of different regions of light in the pupil plane 126 to reconstruct the PSF of an image of the object of interest. Specifically, the different divisions of the phase mask 402 may be selected to promote constructive interference in the detector 120 to result in a tight PSF (e.g., within a selected tolerance) approaching the system PSF.

[0062] It is further recognized herein that the design of the phase mask 402 may represent a trade-off between an "ideal" phase mask based on a known electric field distribution associated with the particle of interest (e.g., as shown in Figure 2A) and practical design and / or manufacturing considerations. For example, an ideal or otherwise desirable phase mask 402 may be unreasonably costly and difficult to manufacture. However, some phase mask 402 designs may satisfy both manufacturing and performance specifications (e.g., particle PSF with a selected shape). Thus, the phase mask 402 design shown in Figure 4 may represent a non-limiting example that results in a particular trade-off between performance and manufacturability.

[0063] In other embodiments, as will be described in more detail below, the particle detection system 100 may include a phase compensator formed from an optically homogeneous material having a spatially varying thickness across the pupil plane 126 to facilitate constructive interference of sample light 112 associated with particle scattering at the center of the image of the particles on the detector 120.

[0064] As previously stated herein, various combinations of optical components may be used to selectively filter surface haze from sample light 112 scattered by particles on sample 108. Referring now to Figures 5 to 14B, in some embodiments, the particle detection system 100 includes a polarizing rotator 502 for rotating the surface haze across the pupil plane 126 to a selected common polarization angle, followed by a linear polarizer 122 oriented to block light along the selected polarization direction. For example, the polarizing rotator 502 in the pupil plane 126 may result in a spatially varying amount of polarization rotation across the pupil plane 126 (e.g., a spatially varying polarization rotation angle). The spatial distribution of this polarization rotation angle may be selected based on the expected electric field distribution of the surface haze (e.g., the scattering map 202 in Figure 2A) to selectively rotate the polarization of the surface haze across the pupil plane 126 to a selected polarization angle. The particle detection system 100 may additionally include a linear polarizer (e.g., linear polarizer 122) aligned to block light polarized along a selected polarization angle.

[0065] Furthermore, in this specification, the selected polarization angle for suppressing surface haze can be any suitable angle. For example, the selected polarization angle may be chosen based on the expected distribution of the sample light 112 scattered by the particles (e.g., as shown in Figure 2B) so as to minimize the brightness of the sample light 112 scattered by the suppressed particles.

[0066] The linear polarizer 122 can block sample light 112 polarized along a selected polarization direction through any process including transmission, reflection, or absorption. In one embodiment, as shown in Figure 1, the linear polarizer 122 includes a polarization beam splitter, so that sample light 112 polarized along a selected polarization direction (primarily surface haze) is directed along one optical path (e.g., through transmission or reflection), and orthogonally polarized sample light 112 (primarily sample light 112 scattered by particles) is directed along the other optical path. Thus, the particle detection system 100 may include a detector 120 in either or both optical paths to generate an image of the sample 108 based on the corresponding portion of the sample light 112.

[0067] In this specification, it is recognized that retaining portions of the sample light 112 associated with surface haze may be desirable in many applications. For example, it may be desirable to monitor the relative signal intensity associated with surface haze and particle scattering. Another example is the desire to generate images associated with surface haze. In some cases, an imaged sample with surface haze may yield additional relevant metrological data associated with the sample surface. Furthermore, the combination of the polarizing rotor 502 and the linear polarizer 122 may not be able to completely separate the surface haze from the sample light 112 scattered by particles. Therefore, a multi-channel imaging system in which the first channel mainly contains light scattered from particles and the second channel mainly contains light scattered from the surface may facilitate verification of system performance, which is suitable for refining the design of the polarizing rotor 502.

[0068] The polarizing rotor 502 can be formed from a variety of optical components. In some embodiments, as shown in Figures 5 to 8B, the polarizing rotor 502 is formed from segmented half-wave plates. In this context, the polarizing rotor 502 may include two or more half-wave plates distributed across the pupil plane 126, each having an optical axis oriented in a selected direction to result in a selected spatial distribution of polarization rotation angles. In some embodiments, as shown in Figures 12 to 14B, the polarizing rotor 502 includes an optically active material having a spatially varying thickness to result in a selected spatial distribution of polarization rotation angles. However, it should be understood that the examples shown herein are merely illustrative and should not be construed as limiting.

[0069] Next, with reference to Figures 5 to 8B, a polarizing rotor 502 formed from a segmented half-wave plate according to one or more embodiments of the present disclosure is described.

[0070] In one embodiment, the polarizing rotor 502 includes a plurality of sections 504 distributed across the entire pupil surface 126, and each section 504 of the polarizing rotor 502 includes a half-wave plate formed from a uniaxial crystal, cut to a thickness selected to produce a π phase shift between orthogonal polarizations, which can have the effect of rotating the polarization of light on an optical axis 506 oriented perpendicular to the propagation direction through the crystal. Specifically, light polarized at an angle θ with respect to the optical axis 506 can be rotated by 2θ. In another embodiment, the optical axis 506 of the half-wave plate in each section 504 is oriented to rotate the polarization of the surface haze in the section 504 to a selected polarization angle.

[0071] Figures 5 to 6B show a polarizing rotor 502 formed as an angularly segmented half-wave plate according to one or more embodiments of the present disclosure.

[0072] Figure 5 is a conceptual top view of a polarizing rotor 502 formed as an angularly segmented half-wave plate according to one or more embodiments of the present disclosure. For example, the angularly segmented half-wave plate shown in Figure 5 may be similar to the haze-blocking polarizer 302 shown in Figure 3A, which includes a half-wave plate instead of a polarizer.

[0073] In one embodiment, the polarizing rotor 502 includes wedge-shaped sections 504 distributed radially around a vertex position 508. In another embodiment, the vertex position 508 corresponds to the specular reflection angle of the illumination beam 104 from the sample 108, which may be located inside or outside the collection area 206. In this context, each section 504 may occupy a range of radial angles within the pupil plane 126 with respect to the specular reflection angle 208, and as a result, the surface haze within each section 504 may be substantially uniform based on the scattering map 202 in Figure 2A.

[0074] Figures 6A and 6B are graphs 602 and 604 of the orthogonally polarized portions of the collected sample light 112 after it has propagated through an angularly segmented polarizing rotor 502 (e.g., shown in Figure 4) and a linear polarizing polarizer 122, according to one or more embodiments of the present disclosure. For example, graph 602 may mainly include surface haze, and graph 604 may mainly include particle scattering.

[0075] Figure 7A is a conceptual top view of a polarizing rotor 502 formed as a linearly segmented half-wave plate according to one or more embodiments of the present disclosure. For example, the linearly segmented half-wave plate shown in Figure 7A may be similar to the haze-blocking polarizer 302 shown in Figure 3B, which includes a half-wave plate instead of a polarizer.

[0076] In one embodiment, the polarizing rotor 502 includes sections 504 distributed linearly along a sectioning direction 702. For example, the sectioning direction 702 in Figure 7A is selected to be perpendicular to the illumination direction 210, as represented within the pupil plane 126. However, it should be understood that the polarizing rotor 502 may be designed to have a sectioning direction 702 along any direction within the pupil plane 126.

[0077] Figure 7B is a calculated graph 704 of the orientation of the linearly segmented polarizing rotor 502 with respect to the optical axis 506, as a function of its position in the pupil plane 126 along the segmentation direction 702, according to one or more embodiments of the present disclosure. Specifically, Figure 7B shows the orientation of the optical axis 506 with respect to the irradiation direction 210 of the irradiation beam 104 for wavelengths of 266 nm and 213 nm, respectively. Furthermore, graph 704 is calculated for a configuration of the particle detection system 100 that includes a phase mask (e.g., phase mask 402) on or near the pupil plane 126 in front of the polarizing rotor 502 for reconstructing the PSF of light scattered by the particles so as to result in constructive interference in the central portion of the imaged particles.

[0078] For example, a linearly segmented polarizing rotor 502 may be designed to include a selected number of segments 504, each occupying a range of positions along the X-axis of the graph 704. Furthermore, the azimuth angle of the optical axis 506 within each segment 504 may be selected based on the graph 704 using any selection technique known in the art. For example, the azimuth angle of the optical axis 506 within each segment 504 may be selected as the midpoint, average, or any other selection metric of the range of corresponding angles at each position in the pupil plane 126.

[0079] However, it should be understood that the diagrams of the polarizing rotor 502 in Figures 7A and 7B are shown for illustrative purposes only and should not be interpreted as limiting. Rather, the polarizing rotor 502 may include any number and size of segments 504 having any selected orientation of the optical axis 506 to rotate the polarization of surface haze to a selected polarization angle for blocking using the linear polarizer 122. Figure 7C is a graph 706 of the orientations of linearly segmented polarizing rotors 502 with respect to the optical axis 506 for rotating the polarization of surface haze to a selected polarization angle according to one or more embodiments of the present disclosure.

[0080] Figures 8A and 8B are graphs 802 and 804 of the orthogonally polarized portions of the collected sample light 112 after it has propagated through an angularly segmented polarizing rotor 502 (e.g., shown in Figure 5) and a linear polarizing polarizer 122, according to one or more embodiments of the present disclosure. In this context, graph 802 may mainly include surface haze, and graph 804 may mainly include particle scattering.

[0081] As previously stated herein with respect to the haze-blocking polarizer 302, it is recognized herein that the accuracy with which the optical axis 506 can be mapped to a selected polarization angle based on the expected electric field distribution (e.g., the scattering map 202 in Figure 2A) so as to preferentially align the polarization of surface haze across the pupil plane 126 may vary depending on the number and layout of sections 504. It is further recognized herein that the manufacturing cost of the polarizer rotor 502 may also be commensurate with its complexity. Therefore, the number and layout of sections 504 may be selected to balance various requirements, including performance and manufacturing cost.

[0082] Furthermore, if the polarization ellipses 304 are not uniformly oriented within a particular section 504, the orientation of the optical axis 506 within each section 504 may be selected according to an optimization function to enable the blocking of surface haze. For example, the optical axis 506 for each section 504 may be selected to maximize the power of surface haze rotated to a selected polarization by the section (e.g., within a selected tolerance range) based on the expected distribution of luminance and / or polarization within the section 504. As another example, the orientation of the optical axis 506 for each section 504 may be selected to balance the power of particle scattering passed by a polarizer positioned downstream of the polarization rotor 502 (e.g., linear polarizer 122) with the power of surface haze blocked by the polarizer.

[0083] Next, with reference to Figures 9A to 9C, the use of a phase mask to reconstruct the point spread function (PSF) associated with an image of particles smaller than the imaging resolution is described in more detail according to one or more embodiments of the present disclosure. Specifically, Figures 9B and 9C were generated using a phase mask 402 configured as shown in Figure 4, positioned in or near the pupil plane 126 in front of each polarizing rotor 502.

[0084] Figure 9A shows an image 902 of a particle smaller than the resolution of an imaging system (e.g., particle detection system 100), generated based on the scattering of obliquely incident p-polarized light, according to one or more embodiments of the present disclosure. As shown in Figure 9A, the PSF of the particle based on p-polarized scattered light is annular rather than Airy, which is at least in part a result of interference patterns associated with a particular polarization distribution of light within the pupil plane 126 and the use of scattered light to form the image 902. Specifically, destructive interference associated with the center point 904 in Figure 9A results in reduced luminance at the center point 904 in the image 902 and a radial shift of luminance outward from the center point 904. As a result, the signal intensity and therefore the signal-to-noise ratio associated with the image of the particle are adversely affected.

[0085] Figure 9B includes an image 906 of the particle in Figure 9A, obtained using an imaging system (e.g., particle detection system 100) having an angularly segmented polarizing rotor 502 as shown in Figure 5 and a linear polarizer 122, according to one or more embodiments of the present disclosure. Specifically, the angularly segmented polarizing rotor 502 includes a segment 504 having an angular width of 5°. Figure 9C includes an image 908 of the particle in Figure 9A, obtained using an imaging system (e.g., particle detection system 100) having a linearly segmented polarizing rotor 502 as shown in Figure 7A, having 72 segments 504 and a linear polarizer 122, according to one or more embodiments of the present disclosure. As shown in Figures 9A to 9C, the image of the particle generated without using a phase mask as described herein has an annular shape with a brightness depression at the center point 904. However, incorporating a phase mask tightens the PSF so that the image of the particle has a central peak and a tighter brightness distribution around the center point 904.

[0086] Figure 10 is a graph 1002 showing the performance and focusing behavior of an angularly segmented polarizing rotor 502 and a linearly segmented polarizing rotor 502 according to one or more embodiments of the present disclosure. Specifically, Figure 10 shows the signal-to-noise ratio (SNR) of the sample light 112 associated with the particle image against background noise, including non-limiting surface haze.

[0087] Specifically, Figure 10 corresponds to the image generated by the light shown in Figure 8B, where the illumination beam 104 is p-polarized and incident on the bare silicon wafer at an angle of 70°, and the objective lens 114 has an NA of 0.97. The SNR in Figure 10 is defined by the following formula.

number

[0088] Next, the performance of various configurations of the haze-stopping polarizer 302 and the segmented polarizing rotor 502 is compared with reference to Figures 11A and 11B. Figure 11A is a graph 1102 of the SNR as a function of pixel size (e.g., of detector 120) for various configurations of the haze-stopping polarizer 302 and the segmented polarizing rotor 502 using an illumination beam 104 having a wavelength of 266 nm, according to one or more embodiments of the present disclosure. Figure 11B is a graph 1104 of the SNR as a function of pixel size (e.g., of detector 120) for various configurations of the haze-stopping polarizer 302 and the segmented polarizing rotor 502 using an illumination beam 104 having a wavelength of 213 nm, according to one or more embodiments of the present disclosure.

[0089] Specifically, Figures 11A and 11B show SNR 1106 of the angular haze-stopping polarizer 302 (e.g., as shown in Figure 3A), SNR 1108 of the linear haze-stopping polarizer 302 (e.g., as shown in Figure 3B), SNR 1110 of the linear polarizer 122 in addition to the angularly segmented polarizer rotator 502 (e.g., as shown in Figure 4), and SNR 1112 of the linear polarizer 122 in addition to the linearly segmented polarizer rotator 502 (e.g., as shown in Figure 6). Furthermore, the signals in Figures 10A and 10B are based on a particle detection system 100 that incorporates a phase plate to reconstruct the PSF of the p-polarized irradiation beam 104 by particles, as previously described herein.

[0090] In Figures 11A and 11B, similar performance can be achieved by angularly segmented or linearly segmented elements. For example, SNR 1106 of the angular haze-blocking polarizer 302 is equivalent to SNR 1110 of the linear polarizer 122 in addition to the angularly segmented polarizer rotor 502. Similarly, SNR 1108 of the linear haze-blocking polarizer 302 is equivalent to SNR 1112 of the linear polarizer 122 in addition to the linearly segmented polarizer rotor 502.

[0091] In Figures 10 to 11B, linearly segmented elements (e.g., linear haze-blocking polarizer 302 and polarizing rotor 502) perform better than angular haze-blocking polarizer 302 elements (e.g., angularly segmented haze-blocking polarizer 302 and polarizing rotor 502), but it should be noted that this particular result should not be interpreted as limiting. In a general sense, the performance of a particular polarizing rotor 502 may depend on a wide range of factors, including, but not limited to, the number and layout of segments 504, the specific orientation of the corresponding optical axis 506, manufacturing precision, the material and surface roughness of the sample 108, the power of the irradiation beam 104, and the noise of the detector 120.

[0092] Next, with reference to Figures 12 to 14B, the polarizing rotor 502, formed from an optically active material having a varying thickness, will be described in more detail.

[0093] Figure 12 is a conceptual top view of a polarizing rotor 502 formed from an optically active material according to one or more embodiments of the present disclosure. In one embodiment, the polarizing rotor 502 is formed from an optically active material, such as quartz, indefinitely. The amount by which the optically active material rotates the polarization of light propagating through it depends on the thickness of the material. Therefore, the thickness of the polarizing rotor 502 along the propagation direction (e.g., the direction normal to the plane in Figure 12) can vary based on its position in the pupil plane 126. In this context, light propagating through the polarizing rotor 502 may exhibit different amounts of polarization rotation depending on the position of the light in the pupil plane 126 (e.g., depending on the scattering angle).

[0094] In other embodiments, the spatial distribution of polarization rotation across the pupil plane 126 may be selected to preferentially rotate the polarization of the surface haze to a selected polarization angle 1202. Thus, the linear polarization polarizer 122 can separate the surface haze polarized along this selected polarization angle from the remaining light (e.g., particle scattering), at least within a selected tolerance range. For example, in Figure 11, the polarization ellipse 304 (open ellipse) of the surface haze from the sample 108 before the polarization rotor 502 is oriented radially with respect to the specular reflection angle 208, while the polarization ellipse 1204 (closed ellipse) of the surface haze after propagating through the polarization rotor 502 is aligned along the selected polarization angle 1202 (e.g., the X direction).

[0095] Next, with reference to Figures 13A to 14B, various designs of a polarizing rotor 502 formed from an optically active material according to one or more embodiments of the present disclosure will be described.

[0096] In this specification, it is recognized that the accuracy with which the optically active polarizing rotor 502 can preferentially rotate the polarization of the surface haze to a selected polarization angle 1202 may depend on how well the spatial distribution of the polarization rotation angle across the pupil plane 126 maps to the polarization distribution of the surface haze at the pupil plane 126. In this specification, it is intended that the polarizing rotor 502 may have any spatial distribution of the polarization rotation angle across the pupil plane 126. Furthermore, in this specification, it is intended that the manufacturing cost of the polarizing rotor 502 may also be able to accommodate the complexity. Therefore, the spatial distribution of the polarization rotation angle (e.g., spatial distribution of thickness) may be selected to balance various requirements, including performance and manufacturing cost.

[0097] In one embodiment, the polarization rotor 502 includes a two-dimensional spatial distribution of polarization rotation angles across the pupil plane 126. In another embodiment, the polarization rotor 502 includes a one-dimensional spatial distribution of polarization rotation angles across the pupil plane 126. In this context, the polarization rotation angle may vary along a single selected direction within the pupil plane 126 (e.g., the Y direction in Figures 12 to 14B).

[0098] Figure 13A is a graph 1302 of the thickness profile of a polarizing rotor 502 formed from an optically active material, along the vertical direction (e.g., Y direction) of Figure 12, designed to rotate the polarization of a surface haze having wavelengths of 266 nm and 213 nm, respectively, in the horizontal direction (e.g., X direction) of Figure 12, according to one or more embodiments of the present disclosure. Specifically, Figure 13A shows a symmetrical design of the polarizing rotor 502 around the Z axis (e.g., with respect to the 0 position in Figure 13A), which is intended to be used with a phase mask (e.g., a phase mask 402 shown in Figure 4) at or near the pupil plane 126 and in front of the polarizing rotor 502 to reverse the phase of Y polarization in one half of the pupil plane before the light arrives at the polarizing rotor 502.

[0099] In Figure 13A, the thickness is expressed in micrometers [(μm) / Δn], where Δn represents the difference in refractive index experienced by light with opposite circular polarization passing through the polarization rotor 502. Furthermore, a thickness of zero represents a reference thickness according to mλ / Δn, where λ is the wavelength of the irradiation beam 104 and m is any positive integer.

[0100] Figure 13B is a cross-sectional view 1304 of a polarizing rotor 502 having a thickness profile along the propagation direction (e.g., the Z direction) based on Figure 13A, according to one or more embodiments of the present disclosure. It is recognized herein that the thickness profile of Figure 13A includes a sharp thickness transition around the center point 1306, which can be difficult to manufacture using optically polished surfaces. Therefore, the cross-sectional view of Figure 13B represents a deviation from the thickness profile of Figure 13A to improve manufacturability.

[0101] In another embodiment, the particle detection system 100 includes a compensator 1308 for correcting different light rays to have approximately equal path lengths (e.g., equal across the pupil plane 126 within a selected tolerance, such as a non-limiting phase difference of π / 2). For example, the compensator 1308 may be formed from an optically homogeneous material along the propagation direction (e.g., the Z direction in Figure 12). As another example, the compensator 1308 may be formed from an optically active material having opposite rotational properties to the optically active material comprising the polarizing rotor 502. In one case, the polarizing rotor 502 may comprise a dextrorotatory quartz crystal, and the compensator 1308 may comprise a levorotatory quartz crystal, each having a thickness profile selected to achieve the desired polarization rotation and phase correction. Specifically, the compensator 1308 may facilitate constructive interference of light across the pupil plane 126 when imaged on the detector 120. In this context, the compensator 1308 may function similarly to the phase mask 402 previously described herein by causing the optical path length of one half of the Y-plane to differ by approximately π from that of the other half. In one embodiment, the compensator 1308 is formed from a material having a refractive index similar to that of the optically active material forming the polarizing rotor 502. For example, the polarizing rotor 502 may be formed from crystalline quartz oriented to its optical axis in the Z direction, and the compensator 1308 may be formed from quartz glass.

[0102] Figure 14A is a graph 1402 of the thickness profile along the vertical direction (e.g., Y direction) of Figure 12 for a polarizing rotor 502 formed from an optically active material designed to rotate the polarization of a surface haze having wavelengths of 266 nm and 213 nm, respectively, in the horizontal direction (e.g., X direction) of Figure 12, according to one or more embodiments of the present disclosure. As in Figure 13A, the thickness in Figure 14A is expressed in units of micrometers [(μm) / Δn], where a thickness of zero represents a reference thickness according to mλ / Δn. Furthermore, the thickness profile in Figure 14A does not include the abrupt thickness transitions seen in the thickness profile in Figure 13A.

[0103] Figure 14B is a cross-sectional view 1404 of a polarizing rotor 502, based on Figure 14A, according to one or more embodiments of the present disclosure, having a thickness profile along the propagation direction (e.g., the Z direction) and including a compensator 1308 for correcting different optical path lengths so that they are approximately equal (e.g., equal across the pupil plane 126).

[0104] In other embodiments, the particle detection system 100 may include a phase mask (e.g., a phase mask 402 shown in Figure 4) in front of both the polarizing rotor 502 and the compensator 1308 (e.g., as shown in Figures 13B and 14B) to further reconstruct the PSF of the image of particles generated by scattered light by promoting constructive interference in the central portion of the particle image on the detector 120. In this specification, several designs of the optically active polarizing rotor 502 are further intended to operate to produce constructive interference of light across the pupil plane 126 when imaged on the detector 120 such that the compensator 1308 does not necessarily yield the desired PSF for particle scattering.

[0105] Figure 15 is a flowchart illustrating the steps taken in Method 1500 for particle detection according to one or more embodiments of the present disclosure. The applicant notes that embodiments and enabling techniques previously described herein in relation to the particle detection system 100 should be interpreted as extensions of Method 1500. However, it should be noted that Method 1500 is not limited to the architecture of the particle detection system 100.

[0106] In one embodiment, method 1500 includes step 1502 of receiving a first electric field distribution of light scattered from the surface of a sample (e.g., surface haze) in response to an irradiation beam having a known polarization at a known incidence angle. In another embodiment, method 1500 includes step 1504 of receiving a second electric field distribution of light scattered from particles on the surface of a sample in response to an irradiation beam.

[0107] In another embodiment, method 1500 includes step 1506 of designing a polarization rotor suitable for placement on the pupil plane of an imaging system so as to rotate the polarization of light having a first electric field distribution to a selected polarization angle. For example, the polarization rotation angle of light passing through the polarization rotor may be selected to vary across the pupil plane according to a spatial distribution selected to rotate the polarization of light having a first electric field distribution to a selected polarization angle.

[0108] For example, surface haze may have a different electric field distribution within the pupil plane of the imaging system than light scattered by particles on the surface. Specifically, it is recognized herein that surface haze and particle scattering have substantially different electric field distributions when scattered by obliquely incident p-polarized light.

[0109] In this specification, the polarizing rotor designed in step 1506 is intended to be formed from a variety of materials. In one embodiment, the polarizing rotor includes a segmented half-wave plate formed from a plurality of half-wave plates distributed across the pupil plane, each having an optical axis selectively oriented to rotate the surface haze within each portion of the pupil plane to a first polarization angle. In other embodiments, the polarizing rotor includes, but is not limited to, an optically active material such as quartz having a spatially varying thickness profile. For example, the polarization rotation of light within an optically active material depends on the thickness of the optically active material. Thus, a polarizing rotor having a spatially varying thickness profile results in different polarization rotation angles for light across the pupil plane.

[0110] In another embodiment, method 1500 includes step 1508 of generating a dark-field image of a sample using an imaging system having a polarizing rotor in the pupil plane and polarizers aligned to block light polarized along a selected polarization angle, the dark-field image being based on light passed through the polarizers. For example, the light passed through the polarizers may correspond to light scattered by one or more particles on the surface of the sample within a selected tolerance range.

[0111] The subject matter described herein sometimes includes different components that are incorporated into or connected to other components. It should be understood that such presented architectures are merely illustrative, and in fact, many other architectures can be implemented to achieve the same function. In a conceptual sense, any configuration of components to achieve the same function is effectively “associated” in such a way that the desired function is achieved. Thus, any two components combined herein to achieve a particular function, whether in architecture or as intermediate components, can be seen as “associated” with one another in such a way that the desired function is achieved. Similarly, any two components thus associated can also be seen as “connected” or “combined” with one another in such a way that the desired function is achieved, and any two components having the ability to be associated in such a way can also be seen as “combinable” with one another in order to achieve the desired function. Specific examples of combinability include, but are not limited to, components that are physically interactable and / or interact with each other, and / or interact wirelessly and / or interact wirelessly, and / or interact logically and / or interact logically.

[0112] Many of the present disclosure and its associated advantages are understood from the above description and it is considered that various modifications can be made to the form, configuration, and arrangement of the components without departing from the disclosed subject matter or sacrificing all of its important advantages. The forms described are for illustrative purposes only, and the following claims are intended to encompass and include such modifications. Furthermore, it should be understood that the present invention is defined by the appended claims.

Claims

1. It is a system, An irradiation source that generates an irradiation beam, One or more irradiation optical components for directing the irradiation beam onto the sample at an off-axis angle along the irradiation direction, One or more collection optical components for collecting scattered light from the sample in response to the illumination beam in dark-field mode, A phase mask disposed on the first pupil surface of one or more collecting optical components, which causes different phase shifts for light within two or more pupil regions of the collection area to reconstruct the point spreading function (PSF) of light scattered from one or more particles on the surface of the sample, wherein the collection area corresponds to the numerical aperture of the one or more collecting components, A polarization rotor disposed on the second pupil of one or more collecting optical components, comprising an optically active material having an optical axis oriented perpendicular to the second pupil, which rotates the polarization of light in the second pupil based on optical activity, and which provides a spatially varying polarization rotation angle selected to rotate the light scattered from the surface of the sample to a selected polarization angle, wherein the optically active material has a spatially varying thickness across the second pupil based on the electric field distribution, and rotates the light scattered from the surface of the sample to a selected polarization angle, A linear polarizer having a blocking axis oriented to block light polarized along the selected polarization angle, A detector for generating a dark-field image of a sample based on light passed through the polarizer, wherein the light passed through the polarizer includes at least a portion of the light scattered by one or more particles on the surface of the sample; A system characterized by comprising the following features.

2. The system according to claim 1, characterized in that the phase mask is positioned in front of the polarization rotor.

3. The system according to claim 1, wherein the phase mask reconstructs the PSF of light scattered by one or more particles on the surface of the sample to produce a central peak in the PSF.

4. The system according to claim 1, characterized in that the first pupil surface and the second pupil surface are conjugate surfaces.

5. The system according to claim 1, characterized in that the first pupil surface and the second pupil surface are common surfaces.

6. The system according to claim 1, wherein the two or more pupil regions include a first semi-collection area and a second semi-collection area divided along the irradiation direction.

7. The system according to claim 6, wherein the first section of the phase mask includes a half-wave plate covering the first half-collection area.

8. The system according to claim 7, characterized in that the half-wave plate is oriented to produce a π phase shift along the direction in the first pupil plane, corresponding to an angle perpendicular to the incident plane of the irradiation beam on the sample.

9. The system according to claim 7, wherein the second section of the phase mask comprises a compensation plate made of an optically homogeneous material along the propagation direction that covers the second semi-collection area, The system is characterized in that the optical path of light that has passed through the compensation plate corresponds to the optical path of light that has passed through the half-wave plate within a selected tolerance value.

10. The system according to claim 7, wherein the second section of the phase mask includes an opening that covers the second half-collection area.

11. The system according to claim 10, wherein the half-wave plate is tilted to at least partially compensate for the optical path difference between the light passing through the first half-collection area and the second half-collection area.

12. It is a device, A polarization rotor, which, when placed on the pupil plane in an imaging system, provides a spatially variable polarization rotation angle selected to rotate light scattered from the surface of a sample to a selected polarization angle, wherein the light scattered from the surface of the sample propagates along the polarization rotor along the thickness direction, and comprises an optically active material having an optical axis oriented along the thickness direction and rotating polarization based on optical activity, wherein the optically active material has a spatially variable thickness over a transverse direction perpendicular to the thickness direction and rotates the light scattered from the surface of the sample to a selected polarization angle, A linear polarizer having a blocking axis oriented to block light polarized along the selected polarization angle, A device characterized by being equipped with the following features.

13. The apparatus according to claim 12, characterized in that the spatially varying thickness of the optically active material changes in a one-dimensional spatial distribution.

14. The apparatus according to claim 12, characterized in that the spatially varying thickness of the optically active material varies in a two-dimensional spatial distribution.

15. The apparatus according to claim 12, characterized in that the spatially varying thickness of the optically active material changes monotonically.

16. The apparatus according to claim 12, characterized in that the spatially varying thickness of the optically active material has a symmetrical distribution with respect to the center of the polarizing rotor.

17. The apparatus according to claim 12, characterized in that the optically active material includes an optically active crystal having an optical axis oriented perpendicular to the pupil surface.

18. It is a system, An irradiation source that generates an irradiation beam, One or more irradiation optical components for directing the irradiation beam onto the sample at an off-axis angle along the irradiation direction, One or more collection optical components for collecting scattered light from the sample in response to the illumination beam in dark-field mode, A phase mask disposed on the first pupil surface of one or more collecting optical components, which causes different phase shifts for light within two or more pupil regions of the collection area to reconstruct the point spreading function (PSF) of light scattered from one or more particles on the surface of the sample, wherein the collection area corresponds to the numerical aperture of the one or more collecting components, A polarization rotor positioned on the second pupil plane of one or more collecting optical components, comprising a plurality of segments of an annularly segmented half-wave plate having ends oriented to intersect at vertices in the second pupil plane, which provide a spatially variable polarization rotation angle selected to rotate light scattered from the surface of the sample to a selected polarization angle, the position of which is associated with the specular reflection of the illumination beam in the second pupil plane, and the polarization rotor, A linear polarizer having a blocking axis oriented to block light polarized along the selected polarization angle, A detector for generating a dark-field image of a sample based on light passed through the polarizer, wherein the light passed through the polarizer includes at least a portion of the light scattered by one or more particles on the surface of the sample; A system characterized by comprising the following features.

19. The system according to claim 18, characterized in that the phase mask is positioned in front of the polarization rotor.

20. The system according to claim 18, wherein the phase mask reconstructs the PSF of light scattered by one or more particles on the surface of the sample to produce a central peak in the PSF.

21. The system according to claim 18, characterized in that the first pupil surface and the second pupil surface are conjugate surfaces.

22. The system according to claim 18, characterized in that the first pupil surface and the second pupil surface are common surfaces.

23. The system according to claim 18, wherein the two or more pupil regions include a first semi-collection area and a second semi-collection area divided along the irradiation direction.

24. The system according to claim 23, wherein the first section of the phase mask includes a half-wave plate covering the first half-collection area.

25. The system according to claim 24, characterized in that the half-wave plate is oriented to produce a π phase shift along the direction in the first pupil plane, corresponding to an angle perpendicular to the incident plane of the irradiation beam on the sample.

26. The system according to claim 24, wherein the second section of the phase mask comprises a compensation plate made of an optically homogeneous material along the propagation direction that covers the second semi-collection area, The system is characterized in that the optical path of light that has passed through the compensation plate corresponds to the optical path of light that has passed through the half-wave plate within a selected tolerance value.

27. The system according to claim 24, wherein the second section of the phase mask includes an opening that covers the second half-collection area.

28. The system according to claim 27, wherein the half-wave plate is tilted to at least partially compensate for the optical path difference between the light passing through the first half-collection area and the second half-collection area.

29. The system according to claim 18, wherein one or more irradiation optical components are configured to direct the irradiation beam toward the sample by p-polarization.

30. The system according to claim 18, wherein the polarizer is The device includes a polarizing beam splitter, the polarizing beam splitter directs the scattered light from the sample that has passed through the polarizer along a first optical path, and the polarizing beam splitter directs the scattered light from the sample that has been blocked by the polarizer along a second optical path different from the first optical path. A system characterized by the following features.

31. The system according to claim 30, comprising an additional detector configured to generate a dark-field image of the sample based on the scattered light from the sample blocked by the polarizer along the second optical path, wherein the scattered light from the sample blocked by the polarizer includes light scattered by the surface of the sample within a selected blocking tolerance range. A system characterized by further comprising the features mentioned above.

32. The system according to claim 18, wherein the light scattered from the surface of the sample has a known electric field distribution, and the polarization rotor is configured to rotate the light polarized to the known electric field distribution to the selected polarization angle.

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