Sensitive particle detection using spatially varying polarization rotators and polarizers

Abstract

Embodiments of the present application relate to sensitive particle detection using a spatially varying polarization rotator and a polarizer. A dark field inspection system may include: an illumination source for generating an illumination beam; an illumination optical device configured to direct the illumination beam to a sample at an off-axis angle along an illumination direction; a focusing optical device for focusing scattered light from the sample in response to the illumination beam in a dark field mode; a polarization rotator located at a pupil plane of one or more focusing optical devices, wherein the polarization rotator provides a spatially varying polarization rotation angle selected to rotate light scattered from the surface of the sample to a selected polarization angle; a polarizer aligned to reject light polarized along the selected polarization angle to reject light scattered from the surface of the sample; and a detector for generating a dark field image of the sample based on scattered light from the sample transmitted by the polarizer.

Description

[0001] Information about divisional applications

[0002] This application is a divisional application of the invention patent application with the application date of February 10, 2020, application number "202080019246.7", and invention name "Sensitive Particle Detection Using Spatially Varying Polarization Rotors and Polarizers".

[0003] Related Applications Cross Reference

[0004] This application claims the benefit of U.S. Provisional Application No. 62 / 806,820, filed on February 17, 2019, entitled “METHOD AND SYSTEM OF SENSITIVITY ENHANCEMENT FOR PARTICLE DETECTION IN WAFER INSPECTION SYSTEM,” with Xuefeng Liu and Jenn-Kuen Leong as inventors, under 35 U.S.C. §119(e), which is incorporated herein by reference in its entirety. Technical Field

[0005] The present disclosure relates generally to particle inspection, and more particularly to particle inspection using dark field imaging based on scattered or diffracted light. Background Art

[0006] Particle detection systems are commonly used in semiconductor processing lines to identify defects or particles on wafers (such as, but not limited to, non-patterned wafers). As semiconductor devices continue to shrink, there is a need to correspondingly increase the sensitivity and resolution of particle detection systems. A significant source of noise that can limit measurement sensitivity is surface scattering (e.g., surface haze) on the wafer, which may still exist even on optically polished surfaces. Although various methods have been proposed to suppress surface scattering relative to particle scattering, such methods may not achieve the desired sensitivity level and / or may achieve sensitivity at the expense of reduced image quality. Therefore, there is a need to develop systems and methods that reduce the disadvantages described above. Summary of the invention

[0007] A system is disclosed according to one or more illustrative embodiments of the present disclosure. In one illustrative embodiment, the system includes an illumination source to generate an illumination beam. In another illustrative embodiment, the system includes one or more illumination optics to direct the illumination beam to a sample at an off-axis angle along an illumination direction. In another illustrative embodiment, the system includes one or more focusing optics to gather scattered light from the sample in response to the illumination beam in a dark field mode. In another illustrative embodiment, the system includes a polarization rotator located at a pupil plane of the one or more focusing optics, wherein the polarization rotator provides a spatially varying polarization rotation angle selected to rotate light scattered from a surface of the sample to a selected polarization angle. In another illustrative embodiment, the system includes a polarizer aligned to reject light polarized along the selected polarization angle to reject the light scattered from the surface of the sample. In another illustrative embodiment, the system includes a detector configured to generate a dark field image of the sample based on scattered light from the sample transmitted by the polarizer, wherein the scattered light from the sample transmitted by the polarizer includes at least a portion of light scattered by one or more particles on the surface of the sample.

[0008] According to one or more illustrative embodiments of the present disclosure, an apparatus is disclosed. In one illustrative embodiment, the apparatus includes a polarization rotator located at a pupil plane of a dark-field imaging system, wherein the dark-field imaging system includes one or more light-collecting optics to collect scattered light from a sample in response to off-axis illumination. In another illustrative embodiment, the polarization rotator provides a spatially varying polarization rotation angle selected to rotate light scattered from a surface of the sample to a selected polarization angle. In another illustrative embodiment, the polarization rotator is configured to couple with a polarizer aligned to reject light polarized along the selected polarization angle to reject the light scattered from the surface of the sample.

[0009] A method is disclosed according to one or more illustrative embodiments of the present disclosure. In one illustrative embodiment, the method includes receiving an electric field distribution of light scattered from a surface of a sample in response to an illumination beam of known polarization at a known angle of incidence. In another illustrative embodiment, the method includes designing a polarization rotator suitable for placement at a pupil plane of an imaging system to provide a spatially varying polarization rotation angle, the spatially varying polarization rotation angle being selected to rotate the polarization of light having the electric field distribution to a selected polarization angle. In another illustrative embodiment, the method includes generating a dark field image of a sample using the imaging system having the polarization rotator located in the pupil plane and a linear polarizer aligned to reject light polarized along the selected polarization angle, wherein the dark field image is based on light passed by the polarizer.

[0010] A system is disclosed according to one or more illustrative embodiments of the present disclosure. In one illustrative embodiment, the system includes an illumination source for generating an illumination beam. In another illustrative embodiment, the system includes one or more illumination optical devices for directing the illumination beam to a sample at an off-axis angle along an illumination direction. In another illustrative embodiment, the system includes a detector. In another illustrative embodiment, the system includes one or more focusing optical devices that generate a dark field image of the sample on the detector based on light gathered from the sample in response to the illumination beam. In one illustrative embodiment, the system includes a segmented polarizer, the segmented polarizer including a plurality of segments distributed in a pupil plane of the one or more focusing optical devices, wherein a rejection axis of each segment is oriented to reject light scattered from a surface of the sample within the segment.

[0011] It should be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and do not necessarily limit the invention as claimed. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the general description, serve to explain the principles of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Those skilled in the art may better understand the numerous advantages of the present disclosure by referring to the accompanying drawings, in which:

[0013] Figure 1 is a conceptual diagram of a particle detection system according to one or more embodiments of the present disclosure;

[0014] Figure 2A is a pupil plane scattering diagram of surface scattering in response to obliquely incident p-polarized light according to one or more embodiments of the present disclosure;

[0015] Figure 2B is a pupil plane scattering diagram of light scattered by a sub-resolution particle in response to oblique incident p-polarized light according to one or more embodiments of the present disclosure;

[0016] Figure 3A is a conceptual top view of a segmented polarizer having wedge-shaped segments radially distributed about an apex position according to one or more embodiments of the present disclosure;

[0017] Figure 3B is a conceptual top view of a segmented polarizer in which segments are linearly distributed along selected segment directions in a pupil plane according to one or more embodiments of the present disclosure;

[0018] Figure 4is a conceptual top view of a phase mask including two segments that divide a pupil into two segments according to one or more embodiments of the present disclosure.

[0019] Figure 5 is a conceptual top view of a polarization rotator formed as an angled segmented half-wave plate according to one or more embodiments of the present disclosure;

[0020] Fig. 6A and 6B is a graph of orthogonal polarization portions of collected sample light after propagating through an angled segmented polarization rotator and a polarization beam splitter according to one or more embodiments of the present disclosure;

[0021] Fig. 7A is a conceptual top view of a polarization rotator formed as a linear segmented half-wave plate according to one or more embodiments of the present disclosure;

[0022] Figure 7B According to one or more embodiments of the present disclosure Fig. 7A A calculated graph showing the orientation direction of the optical axis of the linear segmented polarization rotor shown in FIG. 1 as a function of the position along the segment direction in the pupil plane;

[0023] Figure 7C is a graph of the orientation direction of the optical axis of a linear segmented polarization rotor that rotates the polarization of surface haze to a selected polarization angle according to one or more embodiments of the present disclosure;

[0024] Fig. 8A and 8B is a graph of orthogonal polarization portions of collected sample light after propagating through an angled segmented polarization rotator and a polarization beam splitter according to one or more embodiments of the present disclosure;

[0025] Fig.9A is an image of a particle smaller than the resolution of an imaging system produced based on scattering of obliquely incident p-polarized light according to one or more embodiments of the present disclosure;

[0026] Fig. 9B A method comprising using one or more embodiments of the present disclosure having Figure 5 An imaging system with an angled segmented polarization rotor and a polarization beam splitter as illustrated in Fig. 8A Images of particles in the medium;

[0027] Fig. 9C Including using an imaging system according to one or more embodiments of the present disclosure Fig.9A The imaging system has the following features: Fig. 7A A linear segmented polarization rotor with 72 segments as illustrated in FIG. 1 and having a linear polarizer;

[0028] Fig.10 is a graph illustrating the performance and convergence behavior of an angled segmented polarization rotator and a linear segmented polarization rotator according to one or more embodiments of the present disclosure;

[0029] Fig.11A is a graph of SNR as a function of pixel size for a segmented polarizer and a segmented polarization rotator using an illumination beam having a wavelength of 266 nm according to one or more embodiments of the present disclosure;

[0030] Fig. 11B is a graph of SNR as a function of pixel size for a segmented polarizer and a segmented polarization rotator using an illumination beam having a wavelength of 213 nm according to one or more embodiments of the present disclosure;

[0031] Fig.12 is a conceptual top view of a polarization rotator formed of optically active material according to one or more embodiments of the present disclosure;

[0032] Fig.13A A polarization rotator formed of an optically active material according to one or more embodiments of the present disclosure is formed along Fig.12 The polarization rotator is designed to rotate the polarization of the surface haze at wavelengths of 266 nm and 213 nm to Fig.12 Horizontal direction in

[0033] Fig. 13B According to one or more embodiments of the present disclosure, Fig.13A A cross-sectional view of a polarization rotor with a thickness profile;

[0034] Fig.14A A polarization rotator formed of an optically active material according to one or more embodiments of the present disclosure is formed along Fig.12 The polarization rotator is designed to rotate the polarization of the surface haze at wavelengths of 266 nm and 213 nm to Fig.12 Horizontal direction in

[0035] Fig. 14B According to one or more embodiments of the present disclosure, Fig.14A a cross-sectional view of the polarization rotor having a thickness profile of ; and

[0036] Fig.15 is a flow chart illustrating steps performed in a particle detection method according to one or more embodiments of the present disclosure. DETAILED DESCRIPTION

[0037] Reference will now be made in detail to the disclosed subject matter illustrated in the accompanying drawings. The present disclosure has been particularly shown and described with respect to specific embodiments and specific features of the present disclosure. The embodiments set forth herein should be considered illustrative and not restrictive. As used herein, directional terms (e.g., "left," "right," "top," "bottom," "above," "below," "upper," "upward," "lower," "downward," "downward") are intended to provide relative positions for descriptive purposes and are not intended to specify an absolute reference system. It should be readily apparent to those skilled in the art that various changes and modifications may be made in form and detail without departing from the spirit and scope of the present disclosure.

[0038] Embodiments of the present disclosure are directed 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 the surface (e.g., particle scattering). Additional embodiments of the present disclosure are directed to simultaneously generating separate images of a sample based on surface scattering and particle scattering.

[0039] Wafer inspection is generally described in U.S. Pat. No. 9,874,526, issued on Jan. 1, 2018, U.S. Pat. No. 9,291,575, issued on Mar. 22, 2016, U.S. Pat. No. 8,891,079, issued on Nov. 18, 2014, and U.S. Pat. No. 9,891,177, issued on Feb. 13, 2018, all of which are incorporated herein by reference in their entirety. Furthermore, for purposes of the present disclosure, a particle may include any surface defect on the sample of interest, including but not limited to foreign particles, scratches, pits, holes, protrusions, and the like.

[0040] It is recognized herein that light scattered from particles and light scattered from surfaces can exhibit different electric field distributions (e.g., polarization and electric field strength) as a function of scattering angle. Moreover, the difference in electric field distribution (e.g., scattering pattern) can be particularly pronounced for obliquely incident p-polarized light. For example, surface haze from obliquely incident p-polarized light can be approximately radially polarized relative to the specular reflection angle, while scattering from particles can be approximately radially polarized relative to the surface normal.

[0041] In some embodiments, a dark field imaging system includes: a polarization rotator located in a pupil plane to selectively rotate the polarization of surface haze to a selected polarization angle; and a linear polarizer to separate 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 provide varying polarization rotation angles across the pupil plane based on a known or expected polarization distribution of the surface haze, wherein the spatial distribution of the polarization rotation angles across the pupil is selected to rotate the surface haze distributed across the pupil to a common selected polarization angle. In this regard, a linear polarizer (e.g., a polarizing beam splitter) aligned to this selected polarization angle can effectively separate the surface haze from the particle scattering.

[0042] Additional embodiments of the present disclosure relate to polarization rotors for providing spatially varying amounts of polarization rotation suitable for use in a pupil plane of an imaging system. Various configurations of polarization rotors are contemplated herein. In some embodiments, the polarization rotor comprises a segmented half-wave plate comprising a plurality of half-wave plates having different optical axis orientations. For example, the polarization rotor may comprise a plurality of half-wave plates radially distributed around a vertex position (e.g., but not limited to, a point in the pupil plane corresponding to a specular reflection of an illumination beam). In this regard, each half-wave plate may cover a radial angle range across the specular reflection angle (e.g., to simulate a substantially radial polarization distribution of surface haze). By way of another example, the polarization rotor may comprise a series of half-wave plates linearly distributed along a single direction in the pupil plane. In some embodiments, the polarization rotor comprises an optically active material having a spatially varying thickness. In this regard, the thickness at a given point in the pupil plane may determine the polarization rotation angle.

[0043] Additional embodiments of the present disclosure relate to methods for designing a spatial distribution of polarization rotation angles suitable for rotating surface haze to a selected polarization angle for filtering using a polarization beam splitter. For example, a polarization rotator can be designed to selectively rotate light associated with any noise source to a common selected polarization angle for filtering using a polarization beam splitter. Thus, while the present disclosure is primarily concerned with surface haze based on oblique incident p-polarized light, the examples herein are provided for illustrative purposes only and should not be construed as limiting. Rather, it is contemplated herein that the systems and methods described herein may be applicable to light having any wavelength, polarization, or incident angle.

[0044] Additional embodiments of the present disclosure relate to a segmented polarizer suitable for use in a pupil plane of an imaging system to selectively filter (e.g., absorb by a segmented polarizer) surface haze based on a known polarization angle distribution of the surface haze in the pupil plane. For example, the segmented polarizer may include multiple polarizers distributed across the pupil plane, with each polarizer oriented to block light along a selected direction. Various configurations of segmented polarizers are contemplated herein. In some embodiments, the segmented polarizer includes multiple polarizers distributed radially around a vertex position (e.g., but not limited to, a point in the pupil plane corresponding to a specular reflection of an illumination beam). In some embodiments, the segmented polarizer includes multiple polarizers distributed linearly in the pupil plane.

[0045] Reference now Figures 1 to 13B , systems and methods for performing sensitive particle detection will be described in more detail.

[0046] Figure 1 1 is a conceptual diagram of a particle detection system 100 according to one or more embodiments of the present disclosure. In one embodiment, particle detection system 100 includes: an illumination source 102 to generate an illumination beam 104; an illumination pathway 106 including one or more illumination optics to direct illumination beam 104 to sample 108; and a focusing pathway 110 including one or more focusing optics to focus light emitted from sample 108 (e.g., sample light 112). For example, focusing pathway 110 may include an objective lens 114 to focus at least a portion of sample light 112. Sample light 112 may include any type of light emitted from sample 108 in response to illumination beam 104, including but not limited to scattered light, reflected light, diffracted light, or luminescent light.

[0047] The illumination beam 104 may include light of one or more selected wavelengths, including but not limited to ultraviolet (UV) radiation, visible radiation, or infrared (IR) radiation. For example, the illumination source 102 may provide, but need not provide, an illumination beam 104 having a wavelength shorter than about 350 nm. By way of another example, the illumination beam 104 may provide a wavelength of about 266 nm. By way of another example, the illumination beam 104 may provide a wavelength of about 213 nm. It is recognized herein that both imaging resolution and light scattered by small particles (e.g., relative to the wavelength of the illumination beam 104) are generally proportional to wavelength, such that reducing the wavelength of the illumination beam 104 may generally increase imaging resolution and the scattered signal from small particles. Thus, the illumination beam 104 may include short wavelength light, including but not limited to extreme ultraviolet (EUV) light, deep ultraviolet (DUV) light, or vacuum ultraviolet (VUV) light.

[0048] The illumination source 102 may include any type of light source known in the art. In addition, the illumination source 102 may provide an illumination beam 104 having any selected spatial or temporal coherence characteristics. In one embodiment, the illumination source 102 includes one or more laser sources, such as but not limited to one or more narrowband laser sources, one or more broadband laser sources, one or more supercontinuum laser sources, or one or more white light laser sources. In another embodiment, the illumination source 102 includes a laser driven light source (LDLS), such as but not limited to a laser sustained plasma (LSP) source. For example, the illumination source 102 may include but not limited to an LSP lamp, an LSP bulb, or an LSP chamber suitable for containing one or more elements that can emit broadband illumination when excited into a plasma state by a laser source. In another embodiment, the illumination source 102 includes a lamp source, such as but not limited to an arc lamp, a discharge lamp, or an electrodeless lamp.

[0049] In another embodiment, the illumination source 102 provides a tunable illumination beam 104. For example, the illumination source 102 may include a tunable illumination source (e.g., one or more tunable lasers, etc.). By way of another example, the illumination source 102 may include a broadband illumination source coupled to any combination of fixed filters or tunable filters.

[0050] The illumination source 102 can further provide an illumination beam 104 having any temporal profile. For example, the illumination beam 104 can have a continuous temporal profile, a modulated temporal profile, a pulsed temporal profile, and so on.

[0051] It is recognized herein that the intensity of surface haze may depend on a number of factors, including, but not limited to, the angle of incidence or polarization of the illumination beam 104. For example, the intensity of the surface haze may be relatively high when the angle of incidence is close to normal, and may decrease when the angle of incidence is higher. In one embodiment, the illumination pathway 106 may include one or more illumination optics (such as, but not limited to, lenses 116, mirrors, etc.) to direct the illumination beam 104 to 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, but need not be, greater than 60 degrees relative to the surface normal.

[0052] In another embodiment, the illumination pathway 106 includes one or more illumination beam conditioning components 118 suitable for modifying and / or conditioning the illumination beam 104. For example, the one or more illumination beam conditioning components 118 may include, but are not limited to, one or more polarizers, one or more wave plates, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam formers. In one embodiment, the one or more illumination beam conditioning components 118 include a polarizer or wave plate oriented to provide a p-polarized illumination beam 104 onto the sample 108.

[0053] In another embodiment, the particle detection system 100 includes at least one detector 120 configured to capture at least a portion of the sample light 112 focused by the focusing pathway 110. The detector 120 may include any type of optical detector known in the art suitable for measuring the illumination received from the sample 108. For example, the detector 120 may include a multi-pixel detector suitable for capturing an image of the sample 108, such as, but not limited to, a charge coupled device (CCD) detector, a complementary metal oxide semiconductor (CMOS) detector, a time delayed integration (TDI) detector, a photomultiplier tube (PMT) array, an avalanche photodiode (APD) array, and the like. In another embodiment, the detector 120 includes a spectral detector suitable for identifying the wavelength of the sample light 112.

[0054] The particle detection system 100 may include any number of detectors 120 for simultaneously imaging the sample 108. In addition, the light collection path 110 may include a linear polarizer 122 configured to filter the sample light 112 to be imaged onto the detector 120 based on polarization. In one embodiment, Figure 1 , the linear polarizer 122 operates as a polarization beam splitter such that the linear polarizer 122 separates the sample light 112 into two orthogonally polarized beams. The particle detection system 100 may then include a detector 120 for generating an image of the sample 108 using each of the orthogonal polarization portions of the sample light 112.

[0055] The focusing pathway 110 may include any number of beam conditioning elements 124 to direct and / or modify 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.

[0056] In one embodiment, Figure 1 , the light focusing pathway 110 includes one or more beam conditioning elements 124 located at or near a pupil plane 126. For example, as will be discussed in greater detail below, the light focusing pathway 110 may include a beam conditioning element 124, such as, but not limited to, a continuous polarizer or phase mask at or near the pupil plane 126. In this regard, the particle detection system 100 may control and / or adjust selected aspects of the sample light 112 used to generate an image on the detector 120, including, but not limited to, intensity, phase, and polarization of the sample light 112 as a function of scattering angle and / or position on the sample.

[0057] Furthermore, the focusing path 110 may have any number of pupil planes 126. For example, Figure 1, the focusing pathway 110 may include: one or more lenses 128 to produce an image of a pupil plane 126 on the detector 120; and one or more lenses 130 to produce an image of the surface of the sample 108 on the detector 120. However, it is recognized herein that a limited number of beam conditioning elements 124 may be placed at or sufficiently close to a particular pupil plane 126 to provide a desired effect. Therefore, for purposes of this disclosure, reference to one or more elements at a pupil plane 126 may generally describe one or more elements at or sufficiently close to a pupil plane 126 to produce a desired effect. In some embodiments, although not shown, the focusing pathway 110 may include additional lenses to produce one or more additional pupil planes 126, such that any number of beam conditioning elements 124 may be placed at or near a pupil plane 126.

[0058] In another embodiment, the particle detection system 100 includes a controller 132 that includes one or more processors 134 configured to execute program instructions maintained on a storage medium 136 (e.g., a memory). In addition, the controller 132 can be communicatively coupled to any component of the particle detection system 100. In this regard, the one or more processors 134 of the controller 132 can perform any of the various process steps described throughout this disclosure. For example, the controller 132 can receive, analyze and / or process data from the detector 120 (e.g., associated with an image of the sample 108). By way of another example, the controller 132 can use control signals to control or otherwise direct any component of the particle detection system 100.

[0059] The one or more processors 134 of the controller 132 may include any processing element known in the art. In this sense, the one or more processors 134 may include any microprocessor type device configured to execute algorithms and / or instructions. In one embodiment, the one or more processors 134 may be composed of a desktop computer, a large computer system, a workstation, an image computer, a parallel processor, or any other computer system (e.g., a network connection computer) configured to execute a program, which is configured to operate the particle detection system 100 as described throughout this disclosure. It should be further recognized that the term "processor" can be broadly defined to encompass any device having one or more processing elements and executing program instructions from a non-transitory memory medium 136. In addition, the steps described throughout this disclosure may be performed by a single controller 132 or alternatively by multiple controllers. In addition, the controller 132 may include one or more controllers housed in a common housing or in multiple housings. In this way, any controller or combination of controllers can be individually packaged as a module suitable for integration into the particle detection system 100.

[0060] The memory medium 136 may include any storage medium known in the art that is suitable for storing program instructions that can be executed by the associated one or more processors 134. For example, the memory medium 136 may include a non-transitory memory medium. By way of another example, the memory medium 136 may include, but is not limited to, a read-only memory (ROM), a random access memory (RAM), a magnetic or optical storage device (e.g., a disk), a tape, a solid-state drive, and the like. It should be further noted that the memory medium 136 may be housed in a common controller housing with the one or more processors 134. In one embodiment, the memory medium 136 may be remotely located relative to the physical location of the one or more processors 134 and the controller 132. For example, the one or more processors 134 of the controller 132 may access a remote memory (e.g., a server) that may be accessed via a network (e.g., the Internet, an intranet, and the like). Therefore, the above description should not be construed as limiting the present invention, but is merely illustrative.

[0061] It is contemplated herein that particle detection system 100 may be configured as any type of image-based particle detection system known in the art. Figure 1 As illustrated in FIG. 1 , the particle detection system 100 is a dark field imaging system that excludes specular light. In this regard, the particle detection system 100 can image the sample 108 primarily based on scattered light. Dark field imaging can further be implemented using any technique known in the art. In one embodiment, the orientation and / or numerical aperture (NA) of the objective lens 114 can be selected so that the objective lens 114 does not focus specular light. For example, Figure 1 , objective lens 114 is oriented approximately normal to sample 108 and has a NA that does not include specularly reflected portions of illumination beam 104. Furthermore, objective lens 114 may have, but need not have, a NA of approximately 0.9 or greater. In another embodiment, particle detection system 100 may include one or more components to prevent specular reflections from reaching detector 120.

[0062] Reference now Figures 2A to 3B , pupil plane polarization rotation and subsequent filtering of surface haze are described in more detail.

[0063] It is recognized herein 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 a portion of the sample light 112 associated with the surface haze and a portion of the sample light 112 associated with light scattered by particles of interest.

[0064] Figure 2Ais a pupil surface scattering graph 202 of surface scattering (eg, 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 plane scatter plot 204 of light scattered by small particles (eg, small relative to the imaging resolution of particle detection system 100 or the wavelength of illumination beam 104) in response to obliquely incident p-polarized light in accordance with one or more embodiments of the present disclosure.

[0065] In particular, the scatter diagrams 202, 204 include electric field intensities indicated by shading, with white being the highest intensity and black being the lowest intensity. In addition, the scatter diagrams 202, 204 include polarization orientations of light that vary with a focusing angle (e.g., scattering angle) indicated by an overlaid ellipse in the pupil plane 126. The scatter diagrams 202, 204 are bounded by a focusing region 206 in the pupil plane 126 that is associated with an angular range over which the particle detection system 100 focuses the sample light 112. For example, the focusing region 206 may correspond to a numerical aperture (NA) of the objective lens 114.

[0066] Scatter diagrams 202 and 204 are based on Figure 1 The configuration of the particle detection system 100 illustrated in FIG. Figure 2A and 2B In the embodiment, the mirror reflection angle 208 is located outside the light focusing area 206 along the illumination direction 210 (for example, located at Figure 2A 126 ), which indicates that the objective lens 114 does not capture the specular reflection light. However, other configurations are within the scope of the present disclosure. For example, in the case where the specular reflection angle 208 is within the pupil plane 126, the specular reflection light can be blocked before the detector 120 to produce a dark field image.

[0067] Additionally, the scattering graphs 202, 204 may represent scattering from a variety of materials including, but not limited to, silicon, epitaxial, and polysilicon wafers. It should be understood, however, that the scattering graphs 202, 204 are provided for illustrative purposes only and should not be construed as limiting the present disclosure.

[0068] like Figure 2A and 2B As illustrated in , particularly when the illumination beam 104 is p-polarized, the electric field distribution (e.g., electric field strength and polarization orientation) of light scattered by particles can be substantially different from the electric field distribution of light scattered by a surface. For example, sample light 112 associated with surface haze typically exhibits an approximately radial polarization distribution in the spotlight region 206 relative to the specular reflection angle 208, as shown in FIG. Figure 2A In contrast, sample light 112 associated with particle scattering typically exhibits a radial polarization distribution relative to the surface normal, as shown in FIG. Figure 2BIn addition, the polarization of the scattered sample light 112 is generally elliptical. Figure 2A and 2B It can be seen that at most locations in the pupil plane 126, the ellipse is extremely elongated, which means that one linear polarization component is much stronger than the other linear polarization component. Figure 2B ), the polarization may be more elliptical near the center of the pupil, which means that the magnitude of the two linear polarization components may be approximately equal. However, the intensity of the light in this pupil region is relatively low and has little effect on the total scattered signal from small particles.

[0069] In one embodiment, the particle detection system 100 includes a polarizer located at or near the pupil plane 126 to preferentially reject surface haze. In general, a polarizer located at or near the pupil plane 126 can be designed to provide spatially varying polarization filtering corresponding to any known, measured, simulated, or otherwise expected polarization of light. In the context of the present disclosure, a polarizer located at or near the pupil plane 126 can preferentially filter surface haze based on a known electric field distribution in the pupil plane 126. Thus, in some embodiments, the particle detection system 100 includes a radial haze rejecting polarizer located at or near the pupil plane 126 to preferentially reject surface haze. Figure 2A Approximate radially polarized surface haze illustrated in .

[0070] Reference now Figure 3A and 3B , a segmented haze rejection polarizer 302 suitable for preferentially filtering surface haze from particle scattering is described according to one or more embodiments of the present disclosure. In general, the haze rejection polarizer 302 can be designed to provide spatially varying polarization filtering corresponding to any known, measured, simulated, or otherwise expected polarization of light. In the context of the present disclosure, the haze rejection polarizer 302 can be based on a known electric field distribution in the pupil plane 126 (e.g., Figure 2A The surface haze is preferentially filtered based on the electric field distribution of the surface haze illustrated in FIG. Figure 3A and 3B A polarization ellipse 304 is included, wherein the polarization ellipse represents Figure 2A The polarization of the surface haze in the pupil plane 126 is determined.

[0071] The haze rejection polarizer 302 may include any number of segments 306 distributed across the pupil plane 126, wherein each segment 306 may include a linear polarizer oriented to pass light polarized along a selected pass polarization direction 308. In this regard, the haze rejection polarizer 302 may provide a spatially varying distribution of passed polarization angles.

[0072] In one embodiment, the pass polarization direction 308 of each segment 306 of the haze rejecting polarizer 302 is oriented to preferentially reject surface haze. For example, the pass polarization direction 308 of each segment 306 can be oriented orthogonal to the expected polarization ellipse 304 within the corresponding portion of the pupil plane 126.

[0073] Figure 3A 3 is a conceptual top view of a haze rejection polarizer 302 (e.g., an angled segmented polarizer) having wedge-shaped segments 306 radially distributed about a vertex position 310, according to one or more embodiments of the present disclosure. In one embodiment, the vertex position 310 of the haze rejection polarizer 302 is oriented to coincide with a point in the pupil plane 126 associated with a specular reflection angle of the illumination beam 104 from the sample 108. In this regard, each segment 306 may cover a radial angle range in the pupil plane 126 relative to the specular reflection angle 208, such that the surface haze within each segment 306 may be based on Figure 2A 2. Furthermore, each of the transmitted polarization directions 308 of each segment 306 can be oriented to reject light having a radial polarization relative to the vertex position 310 to preferentially reject surface haze.

[0074] The specular reflection angle 208 may be located within the light collecting region 206 or outside of the light collecting region, as previously described herein. Furthermore, the vertex position 310 need not be located within the physical structure of the haze rejection polarizer 302. For example, in the case where the specular reflection angle 208 is located outside of the light collecting region 206, the segments 306 may be oriented so that they will converge on the vertex position 310 outside of the boundaries defining the size of the haze rejection polarizer 302.

[0075] Figure 3B 3 is a conceptual top view of a haze rejection polarizer 302 (e.g., a linear segmented polarizer) in which segments 306 are linearly distributed along selected segment directions 312 in pupil plane 126 according to one or more embodiments of the present disclosure. Figure 3B The segment direction 312 in is selected to be orthogonal to the illumination direction 210, as represented in the pupil plane 126. In this regard, the transmission polarization direction 308 of each segment 306 can be selected to substantially reduce surface scattered light transmission through the segment 306.

[0076] It is recognized herein that the accuracy with which the haze rejecting polarizer 302 can preferentially filter out surface haze can vary based on the number and layout of the segments 306 relative to the expected scattering pattern of the surface haze. It is further recognized herein that the manufacturing cost of the haze rejecting polarizer 302 can also be proportional to the complexity. Thus, the number and layout of the segments 306 can be selected to balance various requirements including performance, manufacturing cost, etc.

[0077] Furthermore, in the case where the polarization ellipse 304 is not uniformly oriented in a particular segment 306, the transmitted polarization direction 308 in the particular segment 306 may be selected to reject surface haze according to an optimization function. Figure 2A , etc.), the transmitted polarization direction 308 of each segment 306 is selected to be orthogonal to a weighted average of the expected directions of the major axes of the polarization ellipses 304 within each segment 306, where the weights are proportional to the expected field strength or intensity across the segments 306. By way of another example, the transmitted polarization direction 308 of each segment 306 can be selected to maximize the ratio of transmitted sample light 112 associated with particle scattering to transmitted surface haze.

[0078] Reference now Figure 4 In some embodiments, the particle detection system 100 includes one or more components located at or near the pupil plane 126 to reshape the point spread function (PSF) of p-polarized light scattered by sub-resolution particles. It is recognized herein that images of particles smaller than the imaging resolution of the system are generally limited by the system PSF, which is typically an Airy function when the image is formed by specularly reflected light. However, the actual PSF associated with the particle (e.g., the particle PSF) and therefore the actual image of the particle produced by the system is related to the specific electric field distribution of the light from the particle in the pupil plane 126, and may have a different size or shape than the system PSF, particularly when the image is formed by scattered light.

[0079] In particular, a dark field image of a particle that is smaller than the imaging resolution when illuminated with oblique p-polarized light (e.g., an image of a particle formed using scattered or diffracted light) may be annular in shape extending to an area larger than the system PSF, which may negatively affect particle detection sensitivity. This annular shape and the increase in the size of the PSF or imaging spot of the particle may be associated with destructive interference of the collected light at the center of the imaging spot of the particle on the detector 120.

[0080] Therefore, in some embodiments, the particle detection system 100 includes one or more components to modify the phase of the sample light 112 across the pupil plane 126 to promote constructive interference of light at the center of the imaging spot of the particle on the detector 120, and the one or more components are such as but not limited to one or more phase plates or one or more phase compensators.

[0081] For example, the phase mask may have various configurations suitable for reshaping the PSF of the imaged particles. Phase masks for reshaping the PSF of particles imaged based on scattered light are generally described in U.S. Patent Application No. 16 / 577,089, entitled "RADIAL POLARIZER FOR PARTICLE DETECTION" and filed on September 20, 2019, which is incorporated herein by reference in its entirety. In some embodiments, the phase mask may include one or more half-wave plates covering selected portions of the pupil plane 126. In this regard, the phase mask may be formed as a segmented optical device in which at least one of the segments includes a half-wave plate.

[0082] Figure 4 4 is a conceptual top view of a phase mask 402 including two segments to divide a pupil into two segments (eg, halves) according to one or more embodiments of the present disclosure. Figure 4 As illustrated in FIG. 4 , the phase mask 402 may include segments 404 formed of half-wave plates having an optical axis along the X direction to introduce a phase shift π (denoted as e) for light polarized along the Y direction relative to the orthogonal polarization. iπ E y ). In addition, the phase mask 402 may include a segment 406 that does not rotate the polarization of light. For example, the segment 406 may include a compensation plate formed of an optically homogeneous material along the propagation direction, so that light passing through the segment 406 propagates along the same (or substantially the same) optical path length as the light in the segment 404. In one embodiment, the compensation plate is formed of a material having approximately the same thickness and refractive index as the half-wave plate in the segment 404, but does not undergo birefringence along the propagation direction. In another embodiment, the compensation plate is formed of the same material as the half-wave plate in the segment 404, but is cut along a different axis, so that light propagating through the compensation plate does not experience birefringence. For example, light propagating along the optical axis of a uniaxial crystal may not experience birefringence, so that the crystal may be optically homogeneous for light propagating along the optical axis. By way of another example, the segment 406 may include an aperture.

[0083] Furthermore, in some embodiments, the phase mask 402 may be skewed outward from the pupil plane 126 to at least partially compensate for the optical path length difference across the pupil plane 126 .

[0084] Segmented phase mask 402 may be formed using any technique known in the art. In one embodiment, the various segments (e.g., Figure 4 The segments 404 to 406) are formed as a single component, wherein the various segments are placed in a single plane.

[0085] It should be understood, however, that this is provided for illustrative purposes only. Figure 4 For example, the phase mask 402 having two segments may include a half-wave plate placed in the bottom portion of the light-concentrating region 206 instead of in the top portion, such as Figure 4 . In addition, the phase mask 402 may include any number of segments formed of any combination of materials, distributed in any pattern across the pupil plane 126, so as to reshape the PSF of light scattered from the particles. For example, given a known electric field distribution of light associated with an object of interest in the pupil plane 126 (e.g., measured, simulated, etc.), the segmented phase mask 402 described herein may be formed to selectively adjust the phases of various light regions in the pupil plane 126 to reshape the PSF of the image of the object of interest. In particular, the various segments of the phase mask 402 may be selected to promote constructive interference at the detector 120 to provide a tight PSF that is close to the system PSF (e.g., within a selected tolerance).

[0086] It is further recognized herein that the design of the phase mask 402 may represent a method based on a known electric field distribution associated with the particles of interest (e.g., Figure 2A , etc.) and practical design and / or manufacturing considerations. For example, there may be situations where an ideal or otherwise desired phase mask 402 is unreasonably expensive or difficult to manufacture. However, there may be situations where a particular design of phase mask 402 can meet both manufacturing and performance specifications (e.g., a particle PSF with a selected shape, etc.). Therefore, Figure 4 The design of the phase mask 402 illustrated in may represent a non-limiting example that provides a particular tradeoff between performance and manufacturability.

[0087] In another embodiment, as will be described in more detail below, the particle detection system 100 may include a phase compensator formed of an optically homogeneous material having a spatially varying thickness across the pupil plane 126 to promote constructive interference of sample light 112 associated with particle scattering at the center of the particle image on the detector 120.

[0088] As previously described herein, it is contemplated herein that various optical component combinations may be used to selectively filter surface haze from sample light 112 scattered by particles on the sample 108. Referring now to Figures 5 to 14BIn some embodiments, the particle detection system 100 includes a polarization rotator 502 to rotate the surface haze to a selected common polarization angle across the pupil plane 126 followed by a linear polarizer 122 oriented to reject light along a selected polarization direction. For example, the polarization rotator 502 in the pupil plane 126 can provide a spatially varying amount of polarization rotation (e.g., a spatially varying polarization rotation angle) across the pupil plane 126. The expected electric field distribution of the surface haze (e.g., Figure 2A This spatial distribution of polarization rotation angles is selected based on the scattering pattern 202 in FIG. 1 to selectively rotate the polarization of the surface haze to a selected polarization angle across the pupil plane 126. The particle detection system 100 may further include a linear polarizer (e.g., linear polarizer 122) aligned to reject light polarized along the selected polarization angle.

[0089] Furthermore, the selected polarization angle contemplated herein for rejecting surface haze may be any suitable angle. For example, the selected polarization angle may be selected based on the expected distribution of particle scattered sample light 112 (e.g., Figure 2B The selected polarization angle is chosen to minimize the intensity with which the sample light 112 is scattered by the rejection particles (illustrated in FIG. 1 ).

[0090] The linear polarizer 122 may reject sample light 112 polarized along a selected polarization direction via any process including transmission, reflection, or absorption. Figure 1 , the linear polarizer 122 includes a polarizing beam splitter so that sample light 112 polarized along a selected polarization direction (primarily surface haze) is directed along one optical path (e.g., via transmission or reflection), and orthogonally polarized sample light 112 (primarily particle scattered sample light 112) is directed along another 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 corresponding portions of the sample light 112.

[0091] It is recognized herein that in many applications it may be desirable to retain the portion of the sample light 112 associated with surface haze. For example, it may be desirable to monitor the relative signal strength associated with surface haze and particle scattering. By way of another example, it may be desirable to generate an image associated with surface haze. In some instances, a sample imaged with surface haze may provide additional relevant metrology data associated with the sample surface. Furthermore, there may be situations where the combination of the polarization rotator 502 and the linear polarizer 122 may not be able to completely separate the surface haze from the particle scattered sample light 112. Therefore, a multi-channel imaging system in which a first channel primarily includes light scattered from particles and a second channel primarily includes light scattered from a surface may facilitate verification of system performance suitable for improving the design of the polarization rotator 502.

[0092] Polarization rotator 502 may be formed from a variety of optical components. Figures 5 to 8B As illustrated in FIG. 1 , the polarization rotor 502 is formed by a segmented half-wave plate. In this regard, the polarization rotor 502 may include two or more half-wave plates distributed across the pupil plane 126, each half-wave plate having an optical axis oriented in a selected direction to provide a selected spatial distribution of polarization rotation angles. In some embodiments, as Figures 12 to 14B As illustrated in , the polarization rotator 502 includes an optically active material having a spatially varying thickness to provide a selected spatial distribution of polarization rotation angles. It should be understood, however, that the examples provided herein are merely illustrative and should not be construed as limiting.

[0093] Reference now Figures 5 to 8B , a polarization rotator 502 formed by a segmented half-wave plate is described according to one or more embodiments of the present disclosure.

[0094] In one embodiment, the polarization rotor 502 includes a plurality of segments 504 distributed across the pupil plane 126, wherein each segment 504 of the polarization rotor 502 includes a half-wave plate formed from a uniaxial crystal cut having an optical axis 506 oriented perpendicular to the direction of propagation through the crystal and a thickness selected to provide a π phase shift between orthogonal polarizations, which can have the effect of rotating the polarization of the light. Specifically, light polarized at an angle θ relative to the optical axis 506 can be rotated by 2θ. In another embodiment, the optical axis 506 of the half-wave plate in each segment 504 is oriented to rotate the polarization of the surface haze within the segment 504 to a selected polarization angle.

[0095] Figures 5 to 6B Illustrated is a polarization rotator 502 formed as an angled segmented half-wave plate in accordance with one or more embodiments of the present disclosure.

[0096] Figure 5 is a conceptual top view of a polarization rotor 502 formed as an angled segmented half-wave plate according to one or more embodiments of the present disclosure. For example, Figure 5 The angled segmented half-wave plate illustrated in FIG. 1 may be similar to Figure 3A 0048] The haze rejecting polarizer 302 illustrated in , but with an angled segmented half-wave plate comprising a half-wave plate instead of a polarizer.

[0097] In one embodiment, the polarization rotor 502 includes wedge-shaped segments 504 radially distributed around a vertex position 508. In another embodiment, the vertex position 508 corresponds to a specular reflection angle of the illumination beam 104 from the sample 108, which may be within or outside the spotlight region 206. In this regard, each segment 504 may cover a radial angle range in the pupil plane 126 relative to the specular reflection angle 208, such that the surface haze within each segment 504 may be based on Figure 2A The scatter diagram 202 in FIG. 2 is substantially uniform.

[0098] Fig. 6A and 6B The collected sample light 112 according to one or more embodiments of the present disclosure propagates through the angled segmented polarization rotor 502 (eg, Figure 4 ) and polarization linear polarizer 122 after the occurrence of orthogonal polarization portions. For example, graph 602 may include primarily surface haze, and graph 604 may include primarily particle scattering.

[0099] Fig. 7A is a conceptual top view of a polarization rotator 502 formed as a linear segmented half-wave plate according to one or more embodiments of the present disclosure. For example, Fig. 7A The linear segmented half-wave plate illustrated in FIG. Figure 3B , but the linear segmented half-wave plate includes a half-wave plate instead of a polarizer.

[0100] In one embodiment, the polarization rotor 502 includes segments 504 distributed linearly along the segment direction 702. For example, Fig. 7A The segmentation direction 702 in is selected to be orthogonal to the illumination direction 210, as represented in the pupil plane 126. However, it should be understood that the polarization rotor 502 can be designed to have the segmentation direction 702 in the pupil plane 126 along any direction.

[0101] Figure 7B According to one or more embodiments of the present disclosure Fig. 7A FIG. 7 is a calculated graph 704 showing the orientation direction of the optical axis 506 of the linear segmented polarization rotor 502 as a function of position along the segment direction 702 in the pupil plane 126. Specifically, Figure 7BThe diagram illustrates the orientation of the optical axis 506 relative to the illumination direction 210 of the illumination beam 104 having wavelengths of 266 nm and 213 nm, respectively. In addition, the graph 704 is calculated for a configuration in which the particle detection system 100 includes a phase mask (e.g., phase mask 402, etc.) located at or near the pupil plane 126 before the polarization rotator 502 to reshape the PSF of the particle scattered light to provide constructive interference at the central portion of the imaged particle.

[0102] For example, the linear segmented polarization rotor 502 may be designed to include a selected number of segments 504, each segment occupying a range of positions along the X-axis of the graph 704. Furthermore, the orientation angle of the optical axis 506 in each segment 504 may be selected based on the graph 704 using any selection technique known in the art. For example, the orientation angle of the optical axis 506 in each segment 504 may be selected as the midpoint of the corresponding range of angles in the corresponding position in the pupil plane 126, the average, or any other selection metric.

[0103] However, it should be understood that Fig. 7A and 7B The illustration of polarization rotator 502 in is provided for illustrative purposes only and should not be construed as limiting. Rather, polarization rotator 502 may include any number and size of segments 504 with optical axis 506 having any selected orientation to rotate the polarization of surface haze to a selected polarization angle for rejection using linear polarizer 122. Figure 7C is a graph 706 of the orientation direction of the optical axis 506 of the linear segmented polarization rotator 502 to rotate the polarization of the surface haze to a selected polarization angle in accordance with one or more embodiments of the present disclosure.

[0104] Fig. 8A and 8B The collected sample light 112 according to one or more embodiments of the present disclosure propagates through the angled segmented polarization rotor 502 (eg, Figure 5 ) and polarization linear polarizer 122 after the occurrence of orthogonal polarization portion of the graph 802, 804. In this regard, the graph 802 may mainly include surface haze, and the graph 804 may mainly include particle scattering.

[0105] As previously described herein with respect to the haze rejecting polarizer 302, it is recognized herein that the optical axis 506 may be predicted based on an expected electric field distribution (e.g., Figure 2AThe accuracy with which the polarization of the surface haze across the pupil plane 126 is preferentially aligned to a selected polarization angle based on the scattering pattern 202 of the polarization rotator 502 can vary based on the number and layout of the segments 504. It is further recognized herein that the manufacturing cost of the polarization rotator 502 can also be proportional to the complexity. Thus, the number and layout of the segments 504 can be selected to balance various requirements including performance, manufacturing cost, etc.

[0106] Furthermore, in the case where the polarization ellipse 304 is not uniformly oriented in a particular segment 504, the orientation of the optical axis 506 in each segment 504 may be selected to achieve rejection of surface haze according to an optimization function. For example, the optical axis 506 of each segment 504 may be selected to maximize the power of surface haze that is rotated by that segment to a selected polarization based on an expected intensity distribution and / or polarization (e.g., within a selected tolerance) within the segment 504. By way of another example, the orientation of the optical axis 506 of each segment 504 may be selected to trade off the power of particle scattering passed by a polarizer placed downstream of the polarization rotator 502 (e.g., the linear polarizer 122) and the power of surface haze rejected by the polarizer.

[0107] Reference now Figures 9A to 9C , the use of a phase mask to reshape a point spread function (PSF) associated with a particle image that is smaller than the imaging resolution will be described in more detail according to one or more embodiments of the present disclosure. In particular, Fig. 9B and 9C Is to use Figure 4 1 and 12. The phase mask 402 illustrated in FIG. 4 is generated by being located at or near the pupil plane 126 before the corresponding polarization rotor 502.

[0108] Fig.9A 902 is an image of a particle that is smaller than the resolution of an imaging system (eg, particle detection system 100) and is generated based on scattering of obliquely incident p-polarized light according to one or more embodiments of the present disclosure. Fig.9A As illustrated in , the PSF of the particle based on p-polarized scattered light is a toroidal rather than an Airy function, due at least in part to the interference pattern associated with the particular polarization distribution of light in pupil plane 126 and the use of scattered light to form image 902. In particular, Fig.9A The destructive interference associated with the center point 904 in the image 902 causes the intensity at the center point 904 in the image 902 to decrease and the intensity to shift radially outward from the center point 904. Thus, the signal intensity and therefore the signal-to-noise ratio associated with the image of the particle is negatively impacted.

[0109] Fig. 9B A method comprising using one or more embodiments of the present disclosure having the following characteristics: Figure 5The imaging system (e.g., particle detection system 100) with an angled segmented polarization rotor 502 and a linear polarizer 122 illustrated in FIG. Fig.9A 906. Specifically, the angled segmented polarization rotor 502 includes segments 504 having an angular width of 5°. Fig. 9C A method comprising using one or more embodiments of the present disclosure having the following characteristics: Fig. 7A The linear segmented polarization rotor 502 (having 72 segments 504) illustrated in FIG. 5 and an imaging system (e.g., particle detection system 100) having a linear polarizer 122 obtains Fig.9A The image of the particles in 908. Figures 9A to 9C , an image of a particle produced without a phase mask as described herein has a donut-shaped shape with intensity dropping off in a 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 intensity distribution around the center point 904.

[0110] Fig.10 1 is a graph 1002 illustrating the performance and convergence behavior of an angled segmented polarization rotor 502 and a linear segmented polarization rotor 502 according to one or more embodiments of the present disclosure. In particular, Fig.10 The signal-to-noise ratio (SNR) of the sample light 112 associated with an image of a particle relative to background noise (including but not limited to surface haze) is illustrated.

[0111] Specifically, Fig.10 Corresponds to Figure 8B , where the illumination beam 104 is p-polarized and incident on a bare silicon wafer at an angle of 70° and the objective lens 114 has a NA of 0.97. Fig.10 The SNR in is defined by the following formula:

[0112]

[0113] where signal is the peak signal intensity associated with the image of the particle (e.g., the signal intensity at center point 904 in the case of using a phase plate to reshape the PSF), σ wafer is the chip background noise, σ laser is the laser noise, σ shot is the shot noise, and σ detector is the read noise of detector 120. Fig.10 As shown in , increasing the number of segments 504 generally improves the particle detection SNR, where the SNR reaches an asymptotic limit with increasing segments 504.

[0114] Reference now Fig.11A and11B , the performance of various configurations of the haze rejecting polarizer 302 and the segmented polarization rotator 502 are compared. Fig.11A is a graph 1102 of SNR as a function of pixel size (eg, pixel size of the detector 120 ) for various configurations of the haze rejecting polarizer 302 and the segmented polarization rotator 502 using an illumination beam 104 having a wavelength of 266 nm in accordance with one or more embodiments of the present disclosure. Fig. 11B is a graph 1104 of SNR as a function of pixel size (eg, pixel size of the detector 120 ) for various configurations of the haze rejecting polarizer 302 and the segmented polarization rotator 502 using an illumination beam 104 having a wavelength of 213 nm in accordance with one or more embodiments of the present disclosure.

[0115] Specifically, Fig.11A and 11B 302 (e.g., as shown in FIG. Figure 3A ) 1106, a linear haze rejecting polarizer 302 (e.g., as illustrated in Figure 3B ) ), an SNR 1108 having an angle segmented polarization rotor 502 (e.g., as illustrated in Figure 4 ) plus the SNR 1110 of the polarization linear polarizer 122 and the SNR 1112 of the linear segmented polarization rotator 502 (eg, as illustrated in FIG. 6 ) plus the polarization linear polarizer 122. In addition, Fig.11A and 11B The signals in are based on a particle detection system 100 incorporating a phase plate to reshape the PSF of the p-polarized illumination beam 104 by the particles, as previously described herein.

[0116] exist Fig.11A and 11B , similar performance can be achieved with either an angled segmented element or a linear segmented element. For example, the SNR 1106 of the angled haze rejection polarizer 302 can be comparable to the SNR 1110 of the angled segmented polarization rotator 502 plus the polarization linear polarizer 122. Similarly, the SNR 1108 of the linear haze rejection polarizer 302 can be comparable to the SNR 1112 of the linear segmented polarization rotator 502 plus the polarization linear polarizer 122.

[0117] Note that Figures 10 to 11B, the performance of the linear segmented element (e.g., the linear haze rejection polarizer 302 and the polarization rotator 502) is better than the angled haze rejection polarizer 302 element (e.g., the angled segmented haze rejection polarizer 302 and the polarization rotator 502), but it should be understood that this specific result should not be interpreted as limiting. In general, the performance of a particular polarization rotator 502 may depend on a variety of factors, including but not limited to the number and layout of the segments 504, the specific orientation of the corresponding optical axis 506, the manufacturing precision, the material and surface roughness of the sample 108, the power of the illumination beam 104, and the noise of the detector 120.

[0118] Reference now Figures 12 to 14B , a polarization rotator 502 formed of optically active materials having different thicknesses is described in more detail.

[0119] Fig.12 is a conceptual top view of a polarization rotator 502 formed of an optically active material according to one or more embodiments of the present disclosure. In one embodiment, the polarization rotator 502 is formed of an optically active material such as, but not limited to, quartz. The amount by which the optically active material rotates the polarization of light propagating through the optically active material depends on the thickness of the material. Thus, the polarization rotator 502 rotates along the direction of propagation (e.g., normal to Fig.12 The thickness of polarization rotor 502 (in the direction of the plane of pupil plane 126) may vary based on the position in pupil plane 126. In this regard, light propagating through polarization rotor 502 may exhibit different amounts of polarization rotation depending on the position of the light in pupil plane 126 (e.g., depending on the scattering angle).

[0120] In another embodiment, the spatial distribution of polarization rotation across the pupil plane 126 can be selected to preferentially rotate the polarization of the surface haze to a selected polarization angle 1202. Thus, the polarizing linear polarizer 122 can separate the surface haze polarized along this selected polarization angle from the rest of the light (e.g., particle scattering) at least within a selected tolerance. For example, in FIG11 , the polarization ellipse 304 (open ellipse) of the surface haze from the sample 108 before the polarization rotor 502 is radially oriented 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).

[0121] Reference now Figures 13A to 14B , various designs of polarization rotators 502 formed of optically active materials are described according to one or more embodiments of the present disclosure.

[0122] It is recognized herein that the accuracy with which the optically active polarization rotator 502 can preferentially rotate the polarization of the surface haze to the selected polarization angle 1202 can depend on how well the spatial distribution of polarization rotation angles across the pupil plane 126 maps to the polarization distribution of the surface haze at the pupil plane 126. It is contemplated herein that the polarization rotator 502 can provide a spatial distribution of any polarization rotation angle across the pupil plane 126. It is further contemplated herein that the manufacturing cost of the polarization rotator 502 can also be proportional to the complexity. Thus, the spatial distribution of polarization rotation angles (e.g., the spatial distribution of thickness) can be selected to balance various requirements including performance, manufacturing cost, etc.

[0123] In one embodiment, the polarization rotator 502 includes a two-dimensional spatial distribution of polarization rotation angles across the pupil plane 126. In another embodiment, the polarization rotator 502 includes a one-dimensional spatial distribution of polarization rotation angles across the pupil plane 126. In this regard, the polarization rotation angles may be distributed in the pupil plane 126 along a single selected direction (e.g., Figures 12 to 14B Y direction) changes.

[0124] Fig.13A The polarization rotator 502 is formed of an optically active material according to one or more embodiments of the present disclosure. Fig.12 1302 shows a graph of a thickness profile in a vertical direction (eg, Y direction) of a polarization rotator designed to rotate the polarization of the surface haze at wavelengths of 266 nm and 213 nm to Fig.12 Specifically, Fig.13A The diagram illustrates the polarization rotor 502 about the Z-axis (eg, relative to Fig.13A 0), which is intended to be symmetrical with a phase mask (e.g., Figure 4 ) is used in conjunction with the phase mask 402 illustrated in to reverse the phase of the Y polarization in half of the pupil plane before the light reaches the polarization rotator 502.

[0125] Fig.13A The thickness in is provided in units of micrometers [(μm) / Δn], where Δn represents the difference between the refractive indices experienced by light having relative circular polarization passing through the polarization rotator 502. Additionally, zero thickness represents a reference thickness according to mλ / Δn, where λ is the wavelength of the illumination beam 104 and m is any positive integer.

[0126] Fig. 13B According to one or more embodiments of the present disclosure, Fig.13A A cross-sectional view 1304 of the polarization rotor 502 having a thickness profile along the direction of propagation (eg, the Z direction). It is recognized herein that Fig.13AThe thickness profile in includes a sharp thickness transition around the center point 1306, which can make it difficult to produce an optically polished surface. Fig. 13B The cross-sectional view in Fig.13A Deviation of the thickness profile to improve manufacturability.

[0127] In another embodiment, the particle detection system 100 includes a compensator 1308 that corrects the optical path lengths of different rays so that the optical path lengths are approximately equal (e.g., equal within a selected tolerance across the pupil plane 126, such as but not limited to a phase difference of π / 2). For example, the compensator 1308 may be configured to correct the optical path lengths of different rays along the propagation direction (e.g., Fig.12 120 , the compensator 1308 may be formed of an optically homogeneous material in the Y plane (in the Z direction in the Y plane). By way of another example, the compensator 1308 may be formed of an optically active material having an opposite bias to the optically active material constituting the polarization rotator 502. In one example, the polarization rotator 502 may include right-biased quartz and the compensator 1308 may include left-biased quartz, each having a thickness profile selected so that the desired polarization rotation and phase correction are achieved. In particular, the compensator 1308 may promote constructive interference of light across the pupil plane 126 when imaging on the detector 120. In this regard, the compensator 1308 may function similarly to the phase mask 402 previously described herein by causing the path length in one half of the Y plane to differ from the path length in the other half by approximately π. In one embodiment, the compensator 1308 is formed of a material having a refractive index similar to the optically active material forming the polarization rotator 502. For example, polarization rotator 502 may be formed from crystalline quartz oriented with its optical axis in the Z direction, and compensator 1308 may be formed from fused silica.

[0128] Fig.14A The polarization rotator 502 is formed of an optically active material according to one or more embodiments of the present disclosure. Fig.12 1402 shows a graph of a thickness profile in a vertical direction (eg, Y direction) of a polarization rotator designed to rotate the polarization of the surface haze at wavelengths of 266 nm and 213 nm to Fig.12 The horizontal direction (e.g., X direction) in . Fig.13A Same, Fig.14A The thickness in is provided in micrometers [(μm) / Δn] and zero thickness represents a reference thickness according to mλ / Δn. In addition, Fig.14A The thickness profile does not include Fig.13A The sharp thickness transition seen in the thickness profile of .

[0129] Fig. 14B is a cross-sectional view 1404 of a polarization rotor 502 having a configuration based on a polarization rotor according to one or more embodiments of the present disclosure. Fig.14A The thickness profile along the propagation direction (e.g., Z direction) of FIG. 1304 and includes a compensator 1308 to correct the optical path lengths of different rays so that the optical path lengths are approximately equal (e.g., equal across the pupil plane 126).

[0130] In another embodiment, the particle detection system 100 may include a polarization rotator 502 and a compensator 1308 (e.g., Fig. 13B and 14B ) before the phase mask (e.g., Figure 4 120) to further reshape the PSF of the image of the particle produced using the scattered light by promoting constructive interference at the central portion of the particle image on detector 120. It is further contemplated herein that some designs of optically active polarization rotator 502 operate to provide constructive interference of light across pupil plane 126 when imaging on detector 120, such that compensator 1308 is not necessary to provide the desired PSF of particle scattering.

[0131] Fig.15 is a flow chart illustrating steps performed in a method 1500 for particle detection according to one or more embodiments of the present disclosure. Applicants note that the embodiments and enabling techniques previously described herein in the context of a particle detection system 100 should be interpreted as extending to the method 1500. However, it is further noted that the method 1500 is not limited to the architecture of the particle detection system 100.

[0132] In one embodiment, method 1500 includes a step 1502 of receiving a first electric field distribution of light scattered from a surface of a sample (e.g., surface haze) in response to an illumination beam of known polarization at a known angle of incidence. In another embodiment, method 1500 includes a step 1504 of receiving a second electric field distribution of light scattered from particles on the surface of the sample in response to the illumination beam.

[0133] In another embodiment, method 1500 includes a step 1506 of designing a polarization rotator suitable for placement at a pupil plane of an imaging system to rotate 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 rotator may be selected to vary across the pupil plane according to a selected spatial distribution to rotate polarization of light having the first electric field distribution to the selected polarization angle.

[0134] For example, there may be situations where surface haze may have a different electric field distribution in the pupil plane of an imaging system than light scattered by particles on the surface. In particular, it is recognized herein that surface haze and particle scattering have substantially different electric field distributions when scattered by oblique incident p-polarized light.

[0135] It is contemplated herein that the polarization rotator designed in step 1506 may be formed of a variety of materials. In one embodiment, the polarization rotator comprises a segmented half-wave plate formed of a plurality of half-wave plates distributed across a pupil plane, the plurality of half-wave plates having optical axes selectively oriented to rotate surface haze in corresponding portions of the pupil plane to a first polarization angle. In another embodiment, the polarization rotator comprises an optically active material, such as but not limited to quartz having a spatially varying thickness profile. For example, the polarization rotation of light in the optically active material depends on the thickness of the optically active material. Thus, the polarization rotator having a spatially varying thickness profile may provide different polarization rotation angles for light across the pupil plane.

[0136] In another embodiment, method 1500 includes the following step 1508: utilizing an imaging system having a polarization rotator located in a pupil plane and a polarizer aligned to reject light polarized along a selected polarization angle to generate a dark field image of the sample, wherein the dark field image is based on light passed by the polarizer. For example, the light passed by the polarizer may correspond to light scattered by one or more particles on a surface of the sample within a selected tolerance.

[0137] The subject matter described herein sometimes illustrates different components contained in or connected to other components. It should be understood that such depicted architectures are exemplary only, and in fact many other architectures that realize the same functionality can be implemented. In a conceptual sense, any component arrangement that realizes the same functionality is effectively "associated" so that the desired functionality is realized. Therefore, any two components combined to realize a specific functionality herein can be considered to be "associated" with each other so that the desired functionality is realized, regardless of the architecture or intermediate components. Similarly, any two components so associated can also be considered to be "connected" or "coupled" to each other to realize the desired functionality, and any two components that can be so associated can also be considered to be "coupleable" to each other to realize the desired functionality. Specific examples that can be coupled include, but are not limited to, components that can physically interact and / or physically interact and / or components that can wirelessly interact and / or wirelessly interact and / or components that can logically interact and / or logically interact.

[0138] It is believed that the many advantages of the present disclosure and its attendant advantages will be appreciated from the foregoing description, and it will be apparent that various changes may be made in the form, construction, and arrangement of components without departing from the disclosed subject matter or sacrificing all of its important advantages. The forms described are merely illustrative, and the appended claims are intended to encompass and include such changes. Furthermore, it should be understood that the invention is defined by the appended claims.

Claims

1. A testing method, comprising: receiving an electric field distribution of light scattered from a surface of the sample in response to an illumination beam of known polarization at a known angle of incidence; a polarization rotator designed to be placed at a pupil plane of an imaging system to provide a spatially varying polarization rotation angle selected to rotate polarization of light having the electric field distribution to a selected polarization angle, wherein the polarization rotator comprises an optically active material having an optical axis oriented perpendicular to the pupil plane that rotates polarization of light within the pupil plane based on an optical rotation, wherein the optically active material has a spatially varying thickness across the pupil plane based on the electric field distribution to rotate the light scattered from the surface of the sample to the selected polarization angle; and A dark field image of a sample is produced using the imaging system having the polarization rotator located in the pupil plane and a linear polarizer aligned to reject light polarized along the selected polarization angle, wherein the dark field image is based on light passed by the polarizer. The inspection method according to claim 1 , wherein the known polarization is p-polarization.

3. The inspection method according to claim 1, further comprising: receiving an electric field distribution of light scattered from particles on the surface of the sample in response to the illumination beam, wherein designing the polarization rotator further comprises: The selected polarization angle is selected such that the linear polarizer passes at least a selected percentage of light having an electric field distribution.

4. The inspection method according to claim 1, further comprising: An additional dark field image of the sample is generated based on light polarized along the selected polarization angle that is rejected by the linear polarizer.

5. A testing system comprising: an illumination source configured to generate an illumination beam; one or more illumination optics for directing the illumination beam at an off-axis angle along an illumination direction to the sample; one or more focusing optics for focusing scattered light from the sample in response to the illumination beam in a dark field mode; a polarization rotator located at a pupil plane of the one or more light collecting optics, wherein the polarization rotator provides a spatially varying polarization rotation angle selected to rotate light scattered from a surface of the sample to a selected polarization angle, wherein the polarization rotator comprises an optically active material having an optical axis oriented perpendicular to the pupil plane that rotates polarization of light within the pupil plane based on an optical rotation, wherein the optically active material has a spatially varying thickness across the pupil plane to rotate the light scattered from the surface of the sample to the selected polarization angle; a polarizer aligned to reject light polarized along the selected polarization angle; and A detector is used to generate a dark field image of the sample based on light passed by the polarizer, wherein the light passed by the polarizer includes at least a portion of light scattered by one or more particles on the surface of the sample.

6. The inspection system of claim 5, wherein the optically active material comprises: An optically active crystal having an optical axis oriented perpendicular to the pupil plane.

7. The inspection system according to claim 5, further comprising: A phase compensator is positioned in the pupil plane before the polarization rotator to equalize the optical path length of the scattered light from the sample across the pupil plane.

8. The inspection system of claim 7, wherein the phase compensator is formed of an optically homogeneous material along a direction of propagation through the phase compensator.

9. The inspection system of claim 7, wherein the phase compensator is formed of an optically active material having a polarization opposite to that of the polarization rotator along a propagation direction through the phase compensator.

10. The inspection system of claim 7, wherein the light transmitted by the polarizer includes at least a portion of light scattered by one or more particles on the surface of the sample.

11. The inspection system of claim 7, wherein the light scattered from the surface of the sample has a known electric field distribution, wherein the polarization rotator is configured to rotate light polarized by the known electric field distribution to the selected polarization angle.

12. A testing device comprising: A polarization rotator located at a pupil plane of a darkfield imaging system, wherein the darkfield imaging system includes one or more focusing optics to focus scattered light from a sample in response to off-axis illumination, wherein the polarization rotator provides a spatially varying polarization rotation angle selected to rotate light scattered from a surface of the sample to a selected polarization angle, wherein the polarization rotator includes an optically active material having an optical axis oriented perpendicular to the pupil plane, the pupil plane rotating the polarization of light within the pupil plane based on an optical rotation, wherein the optically active material has a spatially varying thickness across the pupil plane to rotate the light scattered from the surface of the sample to the selected polarization angle.

13. The testing device of claim 12, wherein the optically active material comprises: An optically active crystal having an optical axis oriented perpendicular to the pupil plane.

14. The testing apparatus according to claim 12, further comprising: A phase compensator is positioned in the pupil plane before the polarization rotator to equalize the optical path length of the scattered light from the sample across the pupil plane.

15. The inspection apparatus of claim 14, wherein the phase compensator is formed of an optically homogeneous material along a direction of propagation through the phase compensator.

16. The inspection apparatus of claim 14, wherein the phase compensator is formed of an optically active material having a polarization opposite to that of the polarization rotator along a propagation direction through the phase compensator.

17. A testing system comprising: an illumination source for generating an illumination beam; one or more illumination optics for directing the illumination beam at an off-axis angle along an illumination direction to the sample; one or more focusing optics for focusing scattered light from the sample in response to the illumination beam in a dark field mode; a phase mask located at a first pupil plane of the one or more light collecting optics, wherein the phase mask is configured to provide different phase shifts to light in two or more pupil regions of a light collecting area to reshape a point spread function of light scattered from one or more particles on a surface of a sample, wherein the light collecting area corresponds to a numerical aperture of the one or more light collecting optics; a polarization rotator located at a second pupil plane of the one or more light collecting optics, wherein the polarization rotator provides a spatially varying polarization rotation angle selected to rotate light scattered from the surface of the sample to a selected polarization angle, wherein the polarization rotator comprises an optically active material having an optical axis oriented perpendicular to the second pupil plane that rotates polarization of light within the second pupil plane based on an optical rotation, wherein the optically active material has a spatially varying thickness across the second pupil plane to rotate the light scattered from the surface of the sample to the selected polarization angle; a polarizer aligned to reject light polarized along the selected polarization angle; and A detector is used to generate a dark field image of the sample based on the light passed by the polarizer, wherein the light passed by the polarizer includes at least a portion of the light scattered by one or more particles on the surface of the sample.

18. The inspection system of claim 17, wherein the phase mask is located before the polarization rotator.

19. The inspection system of claim 17, wherein the phase mask reshapes the point spread function of light scattered from one or more particles on the surface of the sample to provide a central peak in the point spread function.

20. The inspection system of claim 17, wherein the first pupil plane and the second pupil plane are conjugate planes.

21. The inspection system of claim 17, wherein the first pupil plane and the second pupil plane are a common pupil plane.

22. The inspection system of claim 17, wherein the two or more pupil regions include: A first half of the light-concentrating area and a second half of the light-concentrating area are divided along the irradiation direction.

23. The inspection system of claim 22, wherein the first segment of the phase mask comprises: A half-wave plate covers the first half of the focusing area.

24. The inspection system of claim 23, wherein the half-wave plate is positioned to provide a π phase shift along a direction in a first pupil plane, the direction corresponding to an angle normal to a plane of incidence of the illumination beam on the sample.

25. The inspection system of claim 23, wherein the second segment of the phase mask comprises: A compensator plate formed of an optically homogeneous material along a propagation direction covering the second half of the focusing area, wherein the optical path of light through the compensator corresponds to the optical path of light through the half-wave plate within a selected tolerance.

26. The inspection system of claim 23, wherein the second segment of the phase mask comprises: An aperture covering the second half of the spotlight area.

27. The inspection system of claim 26, wherein the half-wave plate is tilted to at least partially compensate for an optical path difference between light passing through the first and second halves of the light focusing region.

28. A testing device comprising: A polarization rotator that provides a spatially varying polarization rotation angle selected to rotate light scattered from a surface of a sample to a selected polarization angle when the polarization rotator is placed in a pupil plane of an imaging system, wherein the light scattered from the surface of the sample propagates through the polarization rotator along a thickness direction, wherein the polarization rotator includes an optically active material having an optical axis oriented along the thickness direction that rotates polarization of light based on an optical rotation, wherein the optically active material has a spatially varying thickness across a lateral direction orthogonal to the thickness direction to rotate the light scattered from the surface of the sample to the selected polarization angle.

29. The inspection apparatus of claim 28, wherein the spatially varying thickness of the optically active material varies with a one-dimensional spatial distribution.

30. The inspection apparatus of claim 28, wherein the spatially varying thickness of the optically active material varies with a two-dimensional spatial distribution.

31. The inspection apparatus of claim 28, wherein the spatially varying thickness of the optically active material varies monotonically.

32. The inspection apparatus of claim 28, wherein the spatially varying thickness of the optically active material has a symmetric distribution relative to a center of the polarization rotator.

33. The testing device of claim 28, wherein the optically active material comprises: An optically active crystal having the optical axis oriented perpendicular to the pupil plane.

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