System and method for overlay metrology using phase mask

Abstract

An overlay metrology system is disclosed. The overlay metrology system may include a controller having one or more processors. The processor may be configured to execute program instructions to cause the processor to receive a pupil image of collected light from an overlay target and to receive a known phase distribution of an illumination beam to be introduced to the overlay target. The processor may model an intensity function related to the pupil image, the known phase distribution, and one or more eccentricity shift parameters of a structure of the overlay target. The processor may fit the pupil image to the intensity function that depends on the known phase distribution and the eccentricity shift parameter. The processor may generate overlay measurements based on the fit.

Description

Technical Field

[0001] This disclosure generally relates to superposition metrology, and more specifically, to superposition metrology using samples of known phase distributions of illumination beams, for example, which may be introduced using a phase mask. Background Technology

[0002] Superposition metrology refers to the measurement of the relative alignment of layers on a sample (e.g., but not limited to semiconductor devices). Superposition measurement, or superposition error measurement, typically refers to the measurement of misalignment of manufactured features on two or more sample layers. Proper alignment of manufactured features on multiple sample layers is necessary for the proper operation of the device.

[0003] The need to reduce feature size and increase feature density correspondingly leads to an increased demand for accurate and efficient superposition metrology. Metrology systems typically generate metrological data associated with a sample by measuring or otherwise verifying a dedicated metrological target (i.e., a superposition target) across a sample distribution. Therefore, the sample is typically mounted on a translation stage, and the translation sequentially moves the metrological target into the measurement field of view.

[0004] Therefore, it is desirable to provide systems and methods for addressing the above-mentioned deficiencies. Summary of the Invention

[0005] According to one or more illustrative embodiments of this disclosure, a superposition metrology system is disclosed. In one illustrative embodiment, the superposition metrology system may include a controller having one or more processors. In another illustrative embodiment, the processor may be configured to execute program instructions to cause the processor to receive a pupil image of collected light from a superposition target and a known phase distribution of an illumination beam to be introduced toward the superposition target. In another illustrative embodiment, the processor may model an intensity function relating to the pupil image, the known phase distribution, and one or more eccentricity shift parameters of the structure of the superposition target. In another illustrative embodiment, the processor may fit the pupil image to the intensity function, which depends at least on the known phase distribution and the one or more eccentricity shift parameters. In another illustrative embodiment, the processor may generate superposition measurements based on the fitting.

[0006] In another aspect, the superposition target may be a single-cell superposition target. In another aspect, the fitting may include linear regression pattern fitting. In another aspect, the fitting may include a first pattern fitting and a second pattern fitting, wherein the first pattern fitting is based on the first-order diffraction overlap region of the pupil image, and the second pattern fitting is based on the second-order diffraction overlap region of the pupil image. In another aspect, the fitting may be based on calibrating a phase mask configured to induce the known phase distribution. In another aspect, the superposition target may include a moiréfringe superposition target. In another aspect, the system may further include performing defocus adjustment on the superposition target, wherein the fitting is based on the amount of the performed defocus adjustment, and the known phase distribution is based on the amount of the performed defocus adjustment. In another aspect, receiving the pupil image may include performing multiple defocus adjustments on the superposition target. In another aspect, receiving the pupil image may include receiving multiple pupil images of multiple spot positions of the cells of the superposition target, and the fitting may be based on the multiple pupil images. In another aspect, the known phase distribution may include an F1-type phase distribution, which is wavelength-independent and can be characterized in the form of at least one of the following: F_1(NA_x, NA_y) = NA_x NA_y + constant; or F_1(NA_x, NA_y) = NA_x|NA_y| + constant. In another aspect, the introduction of the known phase distribution into the illumination beam can be performed via a phase mask of the system having the F1-type phase distribution. In another aspect, the fitting of the pupil image to the intensity function can be performed simultaneously for both the +1 first-order diffraction intensity function and the -1 first-order diffraction intensity function of the F1-type phase distribution. In another aspect, the known phase distribution may include an F2-type phase distribution, which is wavelength-independent and can be characterized in the form of at least one of the following: F_2(NA_x, NA_y) = NA_x^2 + constant; or F_2(NA_x, NA_y) = NA_x^2 + NA_y^2 + constant. In another aspect, the introduction of the known phase distribution into the illumination beam can be performed via a phase mask of the system having the F2-type phase distribution. In another aspect, the fitting of the pupil image to the intensity function can be performed sequentially for the +1 first-order diffraction intensity function and the -1 first-order diffraction intensity function of the F2-type phase distribution. In another aspect, the phase mask having the F2-type phase distribution may include at least one of a toric lens, a plano-convex cylindrical lens, or a defocused pupil apodizer. In another aspect, the fitting of the pupil image may include multiple fittings configured to simultaneously solve for the effective mask height (nh), optical stack thickness (Δ), and superposition measurements, the multiple fittings scanning the parameter space of nh and Δ.

[0007] According to one or more illustrative embodiments of this disclosure, a superposition metrology system is disclosed. In one illustrative embodiment, the superposition metrology system may include an optical subsystem. In another illustrative embodiment, the optical subsystem may include an illumination source configured to generate an illumination beam. In another illustrative embodiment, the system may include an objective lens configured to guide the illumination beam, including a known phase distribution, to a superposition target of a sample. In another illustrative embodiment, the system may include a phase mask configured to induce the known phase distribution in a portion of the illumination beam. In another illustrative embodiment, the system may include a detector configured to receive a pupil image of collected light emitted from the superposition target. In another illustrative embodiment, the system may include a controller communicatively coupled to the detector. In another illustrative embodiment, the controller may include one or more processors configured to execute program instructions that cause the processors to receive the pupil image of the collected light emitted from the superposition target and to receive a known phase distribution of the illumination beam to be introduced toward the superposition target. In another illustrative embodiment, the processor can model an intensity function relating to one or more eccentricity shift parameters of the pupil image, the known phase distribution, and the structure of the superimposed target. In another illustrative embodiment, the processor can fit the pupil image to the intensity function, which depends at least on the known phase distribution and the eccentricity shift parameters of the superimposed target. In another illustrative embodiment, the processor can generate a superimposed measurement based on the fit.

[0008] According to one or more illustrative embodiments of this disclosure, a method for superposition metrology is disclosed. In one illustrative embodiment, the method may include guiding an illumination beam comprising a known phase distribution to illuminate a superposition target. In another illustrative embodiment, the method may include receiving a pupil image of collected light emitted from the superposition target. In another illustrative embodiment, the method may include modeling an intensity function relating to the pupil image, the known phase distribution, and one or more eccentricity shift parameters of the structure of the superposition target. In another illustrative embodiment, the method may include fitting the pupil image to the intensity function, which depends at least on the known phase distribution and the one or more eccentricity shift parameters of the structure of the superposition target. In another illustrative embodiment, the method may include generating a superposition measurement based on the fitting.

[0009] In another aspect, the superposition target may be a unit cell superposition target. In another aspect, the fitting may include linear regression pattern fitting. In another aspect, the fitting may include a first pattern fitting and a second pattern fitting, wherein the first pattern fitting is based on the first-order diffraction overlap region of the pupil image, and the second pattern fitting is based on the second-order diffraction overlap region of the pupil image. In another aspect, a single fitting may be based on a combination of the first-order diffraction overlap region and the second-order diffraction overlap region. In another aspect, the fitting may be based on calibrating a phase mask configured to induce the known phase distribution. In another aspect, the superposition target may include a moiré pattern superposition target. In another aspect, the method may further include performing defocus adjustment on the superposition target, wherein the fitting is based on the amount of the performed defocus adjustment, and the known phase distribution is based on the amount of the performed defocus adjustment. In another aspect, receiving the pupil image may include performing multiple defocus adjustments on the superposition target. In another aspect, receiving the pupil image may include multiple pupil images that receive multiple spot positions of cells of the superimposed target, and the fitting may be based on the multiple pupil images. In another aspect, the known phase distribution may include an F1-type phase distribution, which is wavelength-independent and can be characterized in the form of at least one of the following: F_1(NA_x,NA_y) = NA_x NA_y + constant; or F_1(NA_x, NA_y) = NA_x|NA_y| + constant. In another aspect, the introduction of the known phase distribution into the illumination beam may be performed via a phase mask of the system having the F1-type phase distribution. In another aspect, the known phase distribution may include an F2-type phase distribution that is wavelength independent and can be characterized in the form of at least one of the following: F_2(NA_x, NA_y) = NA_x^2 + constant; or F_2(NA_x, NA_y) = NA_x^2 + NA_y^2 + constant.

[0010] It should be understood that the above general description and the following detailed description are for illustrative purposes only and do not necessarily limit the invention. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the general description, serve to explain the principles of the invention. Attached Figure Description

[0011] Those skilled in the art will be able to better understand the many advantages of this disclosure by referring to the accompanying drawings.

[0012] Figure 1A This is a conceptual diagram of a system for superimposed metering according to one or more embodiments of the present disclosure.

[0013] Figure 1BThis is a schematic diagram of an optical subsystem having a phase mask in the illumination pupil plane according to one or more embodiments of the present disclosure.

[0014] Figure 2 This is a side view of a single cell of a sample superimposed according to one or more embodiments of the present disclosure.

[0015] Figure 3 This is a conceptual diagram of the diffraction order pupil plane distribution according to one or more embodiments of the present disclosure.

[0016] Figure 4 This is a flowchart of a method for superimposed measurement according to one or more embodiments of the present disclosure. Detailed Implementation

[0017] This disclosure has specifically shown and described particular embodiments and their specific features. The embodiments set forth herein should be considered illustrative rather than restrictive. It will be readily apparent to those skilled in the art that various changes and modifications in form and detail may be made without departing from the spirit and scope of this disclosure. The disclosed subject matter will now be described in detail with reference to the accompanying drawings.

[0018] refer to Figures 1A to 3 According to one or more embodiments of this disclosure, a system and method for superposition measurement are disclosed, which includes fitting a pupil image to an intensity function.

[0019] Embodiments of this disclosure relate to inducing (known) phase modulation of an illumination beam directed at a target of a sample, and fitting a pupil image of the light emitted from the target to an intensity function to determine superposition. For example, a phase mask can be used to introduce a known phase distribution that allows a (measured) pupil image (e.g., a pupil plane image of the collected light emitted from the sample) to superimpose the target. For example, systems and methods can fit a pupil image to an intensity function that is a function of the known phase distribution and the grating structure of the target. In embodiments, the closer the fit, the closer the superposition will be to a given value. Phase modulation of a specific amount in the light directed at the sample can generate a specific pupil image based on a specific grating structure of the target, which can be used in a comparison / fitting operation to determine the amount of superposition.

[0020] This paper considers that various superimposed metrological target designs, measurement techniques, and corresponding optical subsystems can be used to implement phase masks (e.g., phase mask apodizers).

[0021] In one embodiment, the image-based optical subsystem includes a phase mask within the illumination pupil. For example, the image-based optical subsystem can illuminate a superimposed target (e.g., a grating-to-grating target, a box-to-box metering target, or the like) and capture a superimposed signal of a pupil image containing the superimposed target.

[0022] For other techniques for determining superposition (which are not necessarily applied here, but the differences can be illustrated), scanning-based scattering measurement techniques can be used in conjunction with a fast photodetector at a selected location in the focusing pupil to capture time-varying interference signals generated as the sample moves continuously and is scanned relative to the illumination beam. Various non-limiting scanning scattering measurement superposition metrology techniques are described in U.S. Patent Publication No. 2022 / 0034652, filed February 17, 2021, and U.S. Patent Application No. 17 / 119,536, filed December 11, 2020, the entire contents of which are incorporated herein by reference. For example, a fast photodetector can be positioned at an overlap location between selected diffraction orders to capture time-varying interference signals in these regions. On the other hand, in the embodiments described herein, it is considered that if the phase modulation is sufficiently expressive, a phase mask in the illumination pupil of a static (i.e., non-scanning) optical subsystem can be used to achieve fast and robust superposition measurements using a single cell.

[0023] Figure 1A This is a conceptual diagram of a system 100 for superimposed metering according to one or more embodiments of the present disclosure.

[0024] In one embodiment, system 100 includes an optical subsystem 102 for performing superposition measurements on sample 104.

[0025] In one embodiment, system 100 includes a controller 122 communicatively coupled to optical subsystem 102. Controller 122 may include one or more processors 124 and a memory device 126 or memory. For example, one or more processors 124 may be configured to execute a set of program instructions maintained in memory device 126.

[0026] Figure 1B This is a schematic diagram of an optical subsystem 102 having a phase mask 148 in an illumination pupil plane 120, according to one or more embodiments of the present disclosure. For example, Figure 1A The phase mask 148 can be the same as Figure 1B The phase mask 148 shown in the figure.

[0027] In an embodiment, system 100 includes detector 112. Unless otherwise mentioned, one or more detectors 112 may be used for static superposition metrology and are positioned within and / or outside (e.g., near) the light-collecting pupil plane 114 and the light-collecting field plane 150. Detector 112 may comprise any type of optical detector known in the art suitable for capturing light. For example, detector 112 may comprise a multi-pixel detector, such as a complementary metal-oxide-semiconductor (CMOS) detector, a charge-coupled device (CCD) detector, or the like.

[0028] In one embodiment, the optical subsystem 102 may include a translation stage 116 for moving the sample 104 through the measurement field of view of the optical subsystem 102.

[0029] In an embodiment, the optical subsystem 102 may perform scattering and superposition measurements on portions of the sample 104 that have superimposed targets (e.g., but not limited to grating-to-grating structures).

[0030] In this embodiment, the optical subsystem 102 includes an illumination subsystem 106 and a light-collecting subsystem 110. A phase mask 148 may be positioned at a first pupil plane (e.g., any illumination pupil plane 120 before and / or after objective lens 136, but before sample 104). One or more detectors 112 may be positioned at a second pupil plane (e.g., any light-collecting pupil plane 114 after sample 104).

[0031] In an embodiment, the superposition metering system 100 (or optical subsystem 102) includes an illumination subsystem 106 configured to generate illumination in the form of one or more illumination beams 108 to illuminate the sample 104, and a light-collecting subsystem 110 for collecting the collected light 138 from the illuminated sample 104. Furthermore, the one or more illumination beams 108 may be spatially confined such that they illuminate selected portions of the sample 104. For example, each of the one or more illumination beams 108 may be spatially confined to illuminate a specific superposition target 202.

[0032] System 100 can be configured according to a "dosing recipe" for a specific type of sample or the characteristics of sample 104. For example, system 100 can be programmed according to a dosing recipe (e.g., methodology, process, procedure instructions and / or the like) to calculate superimposed measurements of a specific type of characteristic.

[0033] Figure 2 This is a side view of a single cell 204 of a superimposed target 202 of sample 104 in the context of a scattering measurement superposition metrology according to one or more embodiments of the present disclosure.

[0034] In an embodiment, the grating structures of sample 104 on two layers (e.g., first layer 210 and second layer 214) in the superimposed target 202 have a common pitch (e.g., the periodic distance between elements 212).

[0035] In an embodiment, the grating structures of sample 104 on the two layers of the stacked target have different pitches, wherein the gratings form a mottled structure (e.g., ...) on the grating structures. Figure 2 (As shown in the image).

[0036] In an embodiment, cell 204 includes a first layer printed element 208 positioned on a first layer 210 of sample 104 and a second layer printed element 212 positioned on a second layer 214 of sample 104. The first layer printed element 208 and the second layer printed element 212 are oriented such that the regions containing the first layer printed element 208 and the second layer printed element 212 overlap to form a grating-to-grating structure. Furthermore, as... Figure 2 As explained, the first layer printed element 208 may (but is not required to) be designed to include a selected amount of expected offset (due to different pitches) from the second layer printed element 212 along the X direction.

[0037] Many scattering measurement superposition metrology techniques determine superposition by illuminating a superposition target having a grating structure in two layers (e.g., a grating-to-grating structure), where superposition measurement is based on the asymmetry between a positive (e.g., +1) diffraction order and a negative (e.g., -1) diffraction order. For example, various scattering measurement techniques are described in the following documents: U.S. Patent Application No. 17 / 068,328, filed October 12, 2020; U.S. Patent No. 10,824,079, published November 3, 2020; U.S. Patent No. 10,197,389, published February 9, 2019; and Adel et al., “Diffraction order control in overlay metrology: a view of the roadmap options,” Proc. SPIE. 6922, Metrology, Inspection and Process Control of Microlithography XXII, 692202. (2008); the entire contents of all the aforementioned applications are incorporated herein by reference. As considered herein, a phase mask positioned in the illumination pupil of the scattering measurement optical subsystem can achieve calibrated pattern matching of the phase pattern.

[0038] However, it should be understood that Figure 2 The superimposed target 202 (and related) Figure 3The elements in the description and related descriptions are for illustrative purposes only and should not be construed as limiting. Rather, the superposition target 202 may include any suitable design (e.g., grating-to-grating superposition target design, grating adjacent to grating, three-layer grating).

[0039] Figure 3 A conceptual diagram illustrating the light-gathering pupil plane distribution 302 according to one or more embodiments of the present disclosure.

[0040] Figure 3 Examples of overlapping diffraction orders 308a and 308b are shown. It should be recognized herein that the distribution of diffraction orders of the illumination beam 108 by a periodic structure (e.g., a grating-to-grating structure) can be influenced by a variety of parameters, such as, but not limited to, the wavelength of the illumination beam 108, the incident angle of the illumination beam 108 in both the height and azimuth directions, the period (i.e., pitch) of the periodic structure, or the numerical aperture (NA) of the focusing lens. Therefore, in embodiments, the illumination subsystem 106, the focusing subsystem 110, and the superposition target 202 can be configured to provide an overlapping distribution of zero-order and first-order diffraction in the focusing pupil plane 114 of the focusing subsystem 110. For example, the illumination subsystem 106 and / or the focusing subsystem 110 can be configured to generate measurements on a grating-to-grating structure having a selected periodic range that provides the overlapping distribution. Furthermore, various components of the illumination subsystem 106 and / or the light-collecting subsystem 110 (e.g., aperture, pupil, or the like) may be adjustable to provide an overlapping distribution for a given structure (e.g., grating-to-grating) with a given periodicity.

[0041] The photon-collecting system 110 can collect at least one of the 0th-order diffraction 306a (e.g., specular reflection) and + / -1 first-order diffractions 306b, 306c associated with the diffraction of the illumination beam 108 from the sample 104. Furthermore, the photon-collecting system 110 may include one or more detectors 112 configured to image the collecting pupil plane 114 at a location containing an overlapping region of 0th-order diffraction, + / -1 first-order diffraction, and / or + / -2nd-order diffraction. Phase changes induced by the phase mask 148 can cause patterns in the image, which can be compared to determine superposition.

[0042] In an embodiment, the optical subsystem 102 includes an objective lens 136 for focusing an illumination beam 108 onto a sample 104 (e.g., a superimposed target 202 having superimposed target elements positioned on two or more layers of the sample 104). For example, the objective lens 136 may be configured to collect measurement light emitted from the sample 104 in response to the illumination beam 108, according to a metrological formulation. For example, as... Figure 2As shown in the figure, sample 104 may include a stacked target 202 formed by cell 204, and cell 204 includes a grating pair grating structure formed by grating structures 212 and 208 on two layers 210 and 214 of sample 104.

[0043] In this embodiment, the illumination beam 108 of the system 100 is circular. Figure 3 This relates to the diffraction order corresponding to a circular illumination beam. In an embodiment, the illumination subsystem 106 illuminates the superimposed target 202 with one or more illumination beams 108 incident at normal (or near-normal) incidence. Furthermore, the one or more illumination beams 108 can be used as described above... Figure 3 The incident angle illumination superposition target 202 is defined by the finite size of the distribution 302 of the light-gathering pupil plane 114. In this respect, the superposition target 202 can cause one or more illumination beams 108 to diffract into discrete diffraction orders 306 (306a, 306b, 306c).

[0044] When the superimposed target 202 is illuminated by a circular illumination beam, such as Figure 3 As shown, the circular illumination beam forms a circular diffraction pattern in the light-gathering pupil plane 114 through a zero-order (0) circular diffraction pattern 306a, a first-order (+1) circular diffraction pattern 306c, and a first-order (-1) circular diffraction pattern 306b.

[0045] For the moiré pattern superimposed target 202 (e.g., different pitches of gratings 208, 212 in different layers), different pitches can produce slightly offset diffraction orders. Two diffraction orders 312a, 312b correspond to two different pitches of a first-order (-1) circular diffraction order 306b. Two diffraction orders 314a, 314b correspond to two different pitches of a first-order (+1) circular diffraction order 306c. However, the moiré pattern configuration is merely a non-limiting example for illustrative purposes, and at least some embodiments herein may use a common pitch of gratings 208, 212.

[0046] It also demonstrates the overlapping first-order diffraction 304a (e.g., +1 and -1 overlap at the center).

[0047] System 100 may include a phase mask 148. Phase mask 148 may be configured to modulate the phase distribution according to a function. It should be noted that the phase mask 148 and the equation forms described below are non-limiting and illustrative for purposes of reference, and any phase mask 148 and / or equation form with sufficient expressiveness may be used. Phase mask 148 provides a known phase function that can influence the pupil plane image in a known manner, which can be used to provide sensitive metrological measurements. For example, phase mask 148 may be configured to modulate the phase distribution according to a function varying across the pupil plane (e.g., F(x-coordinate, y-coordinate)). For example, phase mask 148 may be a glass sheet of variable thickness with a refractive index (n). In embodiments, phase mask 148 may include a toric lens, a plano-convex cylindrical lens, and / or the like. In this way, phase mask 148 may allow selective modulation of specific / selected portions of the phase distribution of the illumination beam in the illumination pupil plane. Phase mask 148 can also be implemented via a phase-shifting film or coating, wherein a phase shift is introduced by changing the optical path length through variations in the film or coating thickness. These films or coatings can be deposited on a substrate (e.g., transparent glass) to produce phase mask 148. It should be noted that these are non-limiting examples of phase mask 148, and a wide range of other optical components can be used as phase masks, such as, but not limited to, crystals, diffraction elements, Fresnel lenses, and / or the like. Phase mask 148 may comprise multiple components, each having one or more constant and / or variable refractive indices and / or adjustments to the optical path length, such that the combined effect is a change in the phase distribution of light.

[0048] Furthermore, the use of phase mask 148 is particularly useful in system 100 in which light source 128 is coherent or partially coherent.

[0049] The following formulas relate to stacked targets with two or more layers, for example... Figure 2 As shown in the figure, the first (top) layer has a first pitch. And the second (lower) layer has a second pitch. In this embodiment, any first pitch can be used. and the second pitch For example, different pitches of the mottled overlay target 202, or common / equal pitches of the common pitch overlay target 202. For example, at least one of the mottled overlay target 202 or the common pitch overlay target 202 can be used.

[0050] Considering a periodic superposition target in the x-direction, the intensity (i.e., the +1 first-order diffraction intensity function) measured at the pupil plane 114 (e.g., where detector 112 is located) in the overlap between the zero-order diffraction and the +1 first-order diffraction is:

[0051] (Equation 1)

[0052] The intensity measured in the overlap between the zeroth-order diffraction and the -1 first-order diffraction (i.e., the intensity function of the -1 first-order diffraction) is:

[0053]

[0054]

[0055] (Equation 2)

[0056] in , , , These are the amplitudes associated with the zeroth and first orders of the top grating and the zeroth and first orders of the bottom grating, respectively. , is the NA pupil coordinate; and DC is a constant similar to non-interference (e.g., lack of intensity modulation). and These are the shifts from the centers of symmetry of the top and bottom grating structures of the stacked target, respectively, and can be referred to as eccentric shift parameters. They have the form... The function can be a known phase distribution inserted into the illumination beam 108 before reaching the sample.

[0057] and Let x and y represent the numerical aperture (NA) pupil coordinates, respectively. In an optical system, numerical aperture is a dimensionless number representing the angular range of light that the system can accept or emit. By incorporating these parameters into phase mask functions (e.g., F1 and F2 described below), how light scatters from the superimposed target to the detector can be accurately modeled. It should be noted that the equation forms (e.g., F1 and F2) are not restrictive, and any sufficiently expressive equation form can be used. The above process applies to any sufficiently expressive phase mask. Usually, although The phase difference is wavelength-dependent, but this needs to be considered during calibration.

[0058] The defocus adjustment optical path difference (OPD) phase factor is given as follows:

[0059] (Equation 3)

[0060] (Equation 4)

[0061] in It is the optical stacking thickness. It is the wavelength, and , These are the pitches of the top and bottom gratings, respectively.

[0062] The local phase on the illumination pupil induced by the phase mask is given by the following:

[0063] (Equation 5)

[0064] Local phase function It is true, and It is a characteristic of the mask, optical thickness ( It is the diffraction index of the mask material, and (Is the characteristic height), the parameter sought and These are shifts from the centers of symmetry of the top and bottom gratings, respectively, and the desired superposition is given below:

[0065] (Equation 6)

[0066] By decomposition Each of the cosine terms in the equation can be represented as a cosine term. , The coefficients of the dependency term as a function of the pupil coordinates are extracted. Then, the pupil coordinate function can be used as a feature in fitting the pupil image data. The fitting result varies depending on the fitting coefficients (e.g., typically, the fitting coefficients are multiplied by...). arctangent function) , (or a linear combination thereof).

[0067] For both types of phase masks 148, elimination is possible. The wavelength dependence of the phase difference in the ray provides a wavelength-independent phase mask. For gratings with x-periodity (strips or "y-gratings" along the y-direction), these two types of wavelength-independent phase masks (i.e., F1-type and F2-type phase distributions) can be characterized in the following form:

[0068] (Equation 7)

[0069] and

[0070] (Equation 8)

[0071] in It is any nontrivial (constant) function and It is any function. For y-periodicity (bars or "x-gratings" along the x-direction), then swap. .

[0072] In this embodiment, introducing a known phase distribution into the illumination beam is performed via a phase mask of the system having an F1-type phase distribution. Fitting the pupil image to the intensity function can be performed simultaneously for both the +1 first-order diffraction intensity function (e.g., Equation 1) and the -1 first-order diffraction intensity function (e.g., Equation 2) of the F1-type phase distribution.

[0073] In this embodiment, introducing a known phase distribution into the illumination beam is performed via a phase mask of the system having an F2-type phase distribution. A pupil image to intensity function fitting can be performed sequentially for the +1 first-order diffraction intensity function and the -1 first-order diffraction intensity function of the F2-type phase distribution. The phase mask of the F2-type phase distribution may include at least one of the following (e.g., any of them individually): a toric lens; a plano-cylindrical lens; or a defocused pupil plane apodizer (e.g., using defocus adjustment to introduce multiple known phase distributions to produce a superimposed measurement).

[0074] In these situations, The phase difference can be a linear function of the pupil coordinates, which is independent of the wavelength.

[0075] for A phase mask selection method can fit pupil image data (e.g., through linear regression) to a linear combination:

[0076]

[0077] (Equation 9)

[0078] The phase is:

[0079] (Equation 10)

[0080] (Equation 11)

[0081] (Equation 12)

[0082] (Equation 13)

[0083] (Equation 14)

[0084] in The regions 308a and 308b correspond to the overlapping regions of the 0+1 and 0-1 diffraction orders.

[0085] Spatial frequency is given by the following:

[0086] , , (Equations 15 to 17)

[0087] in It is a function of the pupil coordinates given below:

[0088] (Equation 18)

[0089] for The situation, at the same time and The image is fitted, and and The value is obtained from the fitting results using the following:

[0090] , , , , (Equations 19 to 23)

[0091] for In this case, the fit can be separated. and We obtained:

[0092] , , , , (Equations 24 to 28)

[0093] Then in and The results are averaged for each pair to remove the constant term.

[0094] for In some cases, the fitting features are degenerate, but otherwise, the analysis can follow a similar process.

[0095] It can be determined by the refractive index Examples of phase masks 148 (e.g., characteristicable forms of F1 and F2) made of materials (e.g., glass) include, but are not limited to, equations in the following characteristicable forms:

[0096] (Equation 29)

[0097] (Equation 30)

[0098] (Equation 31)

[0099] (Equation 32)

[0100] In an embodiment, The phase mask can be fabricated in a permanent configuration (e.g., a dedicated phase mask). For example, a dedicated phase mask may comprise a glass sheet having a predetermined phase modulation distribution, such as glass with a manufactured thickness. In embodiments, toric lenses, plano-cylindrical lenses, or the like may be used to achieve this. contour.

[0101] In this embodiment, we can use a defocused pupil planar apodizer to achieve this. Type mask. The defocusing phase effect can be understood as follows:

[0102] (Equation 33)

[0103] It is equivalent to having of Type mask.

[0104] By obtaining various defocus adjustment values From the pupil image, we can evaluate the superposition using multiple "effective" phase masks.

[0105] In one embodiment, system 100 is configured to receive pupil images at various / different spot locations (e.g., three or more) on the superimposed target. This step reduces dependence on spot locations.

[0106] Fitting the pupil image can involve multiple fittings configured to simultaneously solve for the effective mask height (nh), optical stack thickness (Δ), and superposition measurements. For example, the controller can be further configured to reduce tool-induced shift (TIS) errors (when the known phase distribution is of type F1 or F2) by performing a best-fit scan of the effective mask height (nh), optical stack thickness (Δ), and superposition measurements. Multiple fittings can scan the parameter space of nh and Δ. The two key input parameters of the intensity fitting function can include the effective mask height (nh) and optical stack thickness (Δ). The true values ​​of these quantities are subject to fluctuations from the referenced quantities due to process variations, erosion, and miscalibration. This reduces goodness of fit and can lead to inaccurate superposition estimates. To overcome this problem, multiple fittings can be performed. For example, system 100 can be configured to scan the (nh, Δ) parameter space. The best fit can occur at (or near) the true (nh, Δ) point, giving simultaneous results for (nh, Δ, superposition measurements). This can be useful in measuring stack thickness and in reducing metrological tool errors that may be caused by changes in nh (e.g., tool-induced shift (TIS)).

[0107] Figure 4A flowchart illustrating a method 400 for superimposed measurement according to one or more embodiments of this disclosure is provided. It should be noted that the embodiments and implementation techniques previously described herein in the context of system 100 should be interpreted as extending to method 400. It should further be noted herein that the steps of method 400 may be implemented in whole or in part by system 100. However, it should be further appreciated that method 400 is not limited to system 100, as additional or alternative system-level embodiments may implement all or part of the steps of method 400.

[0108] In step 402, an illumination beam 108 having a known phase distribution is guided (e.g., aimed, generated) to illuminate the superimposed target 202. For example, a phase mask 148 in the pupil plane 120 can be used to induce a known phase distribution in the illumination beam 108. For example, the phase mask 148 can induce a known phase distribution based on prior knowledge of the phase mask 148 (e.g., previous calibration, previous light wave simulation, and / or the like). For example, the phase mask 148 can have an F1 or F2 type, and / or any other phase function. For example, the phase mask 148 can be expected to produce a pattern in the received pupil image that indicates a given amount of superposition (e.g., zero superposition).

[0109] In a step (e.g., additional step 402), a known phase distribution configured to be introduced into the illumination beam is received. For example, controller 122 may receive values ​​indicating the type of the known phase distribution (e.g., type F1) and / or any other parameters of the known phase distribution (e.g., the thickness profile of the phase mask 148 used in system 100, the number and amount / value of defocus adjustments to be performed, and / or the like), or be used to calculate / receive the known phase distribution. For example, the known phase distribution may be fixed (e.g., built into system 100 and stored in memory 126). The known phase distribution may be dynamic (e.g., the system is configured to receive, in the illumination path, for example, a removably coupled phase mask having a known / measured / simulated known phase distribution; dynamically programmable defocus adjustments; both; and / or the like). For example, system 100 may be configured to sense (and / or user-inputable) values ​​to controller 122 indicating the known phase distribution (or phase mask 148) in use. For example, system 100 can be configured to calculate a known phase distribution based on system parameters of system 100 (e.g., defocus amount and / or the profile of phase mask 148).

[0110] In the step (e.g., an additional step), a pupil image of the collected light 138 emitted from the superimposed target 202 is received. For example, detector 112 may receive the pupil image, and / or controller 122 may receive data indicating the pupil image. Detector 112 may be positioned at pupil plane 114. Detector 112 may be positioned near pupil plane 114 (e.g., between pupil plane 114 and field plane 150; having 90% or more of the pupil plane condition for collecting light 138; and / or similar). For example, controller 122 may receive the pupil image and / or controller 122 may receive data indicating the pupil image.

[0111] In step 404, an intensity function is modeled in relation to one or more eccentricity shift parameters of the pupil image, the known phase distribution, and the structure of the superimposed target 202. For example, the intensity function can be modeled using Equations 1 and / or 2 from this disclosure (e.g., equal to Equations 1 and / or 2, mathematically derived from Equations 1 and / or 2, simulated using Equations 1 and / or 2, and / or the like).

[0112] In step 406, the pupil image is fitted to an intensity function (e.g., one or more functions of this disclosure, such as Equations 1 and 2, and others herein), said intensity function depending at least on a known phase distribution and one or more eccentric shift parameters (e.g., gratings 208, 212) of the structure of the superimposed target 202. and Fitting may involve calculating the difference or ratio, inputting known values, and / or calculating the correlation coefficient or similarity measure between the pupil image and the pupil image predicted using an intensity function for a given superposition value. For example, one or more eccentricity shift parameters can be two or more eccentricity shift parameters.

[0113] In step 408, a superposition measurement is determined based on the fitting from step 406. The superposition measurement can be (and / or based on) a quantitative measure of the difference or similarity between the pupil image and a pupil image predicted using an intensity function for a given superposition value. This can be obtained through various methods, such as direct computation, statistical modeling, machine learning, or other computational methods. It provides a measure of the accuracy with which the controlled process has produced the desired device features (e.g., gratings 208, 212).

[0114] Superposition measurements can be given in various units of measurement. They can represent physical distances, such as the displacement between an actual pattern or shape and a desired pattern or shape. Alternatively, they can be dimensionless measures, such as correlation coefficients, similarity indices, probability, or confidence levels.

[0115] In another step (not shown), one or more processes for manufacturing sample 104 are controlled based on superimposed measurements. This may involve adjusting process parameters (e.g., temperature, pressure, time, flow rate, concentration, intensity, or frequency) to minimize superposition. Adjustments may be made manually by an operator or automatically by the control system in response to the superimposed measurements.

[0116] For example, if the superimposed measurement value is greater than a predetermined threshold, the process parameters can be adjusted to reduce the superposition. Conversely, if the superimposed measurement value is less than the threshold, the process parameters can remain unchanged or be adjusted to slightly reduce the superposition while keeping it within an optimal range.

[0117] Such processes can include semiconductor manufacturing, photolithography, and many other processes.

[0118] In this embodiment, the fitting is based on linear regression pattern fitting. Linear regression pattern fitting may involve fitting a straight line to data points representing the pupil image. This can be done using the minimum flattening method or any other suitable fitting method. The slope, intercept, and other parameters of the fitted line provide numerical values ​​that can be used as parameters in the intensity function. This method allows for a more accurate and detailed description of the pupil image, which improves the accuracy of superimposed measurements.

[0119] In this embodiment, the fitting is based on calibration of the phase mask 148. The calibration process may involve adjusting the phase mask 148 to match a known standard or reference, and / or calibrating the system 100 to perform fitting for a given phase mask (i.e., such that the pupil image can be correlated with the corresponding superposition value). This can be accomplished using various techniques, such as using a calibration pupil image that includes a calibration target with a known superposition as a reference and comparing the pupil image with the calibration pupil image, and determining the superposition measurement based on the difference in the comparison.

[0120] For example, phase mask calibration may involve receiving a calibration pupil image including a known superimposed calibration target and determining the calibration associated with phase mask 148. This can be used to calibrate system 100 to know that a particular pupil image matches / corresponds to a particular superimposed measurement.

[0121] In an embodiment, the overlay metrology system 100 further includes performing defocus adjustment of the overlay target before / simultaneously with receiving the pupil image, wherein the fitting is based on the amount of defocus adjustment performed. Defocus adjustment may cause the pupil image to blur, shift, or otherwise change so that it can be quantified and used as a parameter during the fitting of the intensity function. In an embodiment (but not necessarily required), receiving the pupil image may include receiving multiple pupil images of multiple spot locations of cells of the overlay target 202, wherein the fitting is based on the multiple pupil images. This can further improve accuracy.

[0122] In an embodiment, the fitting includes first pattern fitting and second pattern fitting. For example, refer to Figure 3 The first pattern can be based on the first-order diffraction overlap region 308a of the pupil image, while the second pattern fitting is based on the second-order diffraction overlap region 308b of the pupil image. For example, the first-order diffraction overlap region 308a, the first pattern fitting, and one of the (+1 first-order diffraction intensity function or -1 first-order diffraction intensity function) can correspond to each other. A similar correspondence can exist between the second-order diffraction overlap region 308b and the remaining (+1 first-order diffraction intensity function or -1 first-order diffraction intensity function).

[0123] Refer again Figures 1A to 3 The present disclosure provides a more detailed description of various components according to one or more embodiments.

[0124] One or more processors 124 of controller 122 may comprise any processor or processing element known in the art. For the purposes of this disclosure, the terms “processor” or “processing element” may be broadly defined to encompass any device having one or more processing or logic elements (e.g., one or more microprocessor devices, one or more application-specific integrated circuit (ASIC) devices, one or more field-programmable gate arrays (FPGAs), or one or more digital signal processors (DSPs)). In this sense, one or more processors 124 may comprise any device configured to execute algorithms and / or instructions (e.g., program instructions stored in memory). In embodiments, one or more processors 124 may embody a desktop computer, mainframe computer system, workstation, graphics computer, parallel processor, networked computer, or any other computer system configured to execute a program configured to operate with or in conjunction with operating system 100, as described throughout this disclosure. Furthermore, different subsystems of system 100 may include processors or logic elements suitable for implementing at least a portion of the steps described in this disclosure. Therefore, the foregoing description should not be construed as limiting the embodiments of this disclosure, but is merely illustrative. Furthermore, the steps described throughout this disclosure can be implemented by a single controller or alternatively by multiple controllers. Additionally, controller 122 may comprise one or more controllers housed in a common enclosure or within multiple enclosures. In this manner, any controller or combination of controllers can be individually packaged as a module suitable for integration into system 100. Furthermore, controller 122 can analyze or otherwise process data received from one or more detectors 112, and feed the data to additional components within or outside system 100.

[0125] Furthermore, memory device 126 may include any storage medium known in the art suitable for storing program instructions executable by one or more associated processors 124. For example, memory device 126 may include non-transitory memory media. As additional examples, memory device 126 may include, but is not limited to, read-only memory, random access memory, magnetic or optical memory devices (e.g., magnetic disks), magnetic tape, solid-state drives, and the like. It should also be noted that memory device 126 may be housed together with one or more processors 124 in a common controller housing.

[0126] In this regard, controller 122 may perform any of the various processing steps associated with superposition measurement. For example, controller 122 may be configured to generate control signals to guide or otherwise control optical subsystem 102 or any of its components. For example, controller 122 may be configured to receive signals corresponding to pupil images from one or more detectors 112. By another example, controller 122 may generate correctable terms for one or more additional manufacturing tools as feedback and / or feedforward control of said one or more additional manufacturing tools based on superposition measurements from optical subsystem 102.

[0127] In an embodiment, controller 122 captures a pupil image detected by one or more detectors 112. Controller 122 may use any technique known in the art (e.g., but not limited to one or more phase-locked loops) to capture data (e.g., but not limited to the magnitude of the phase of the pupil image). Furthermore, controller 122 may use any combination of hardware (e.g., circuitry) or software techniques to capture a pupil image (e.g., a detection signal) or any data associated with the pupil image.

[0128] In an embodiment, controller 122 generates (or determines) superposition measurements between layers of superposition target 202 (e.g., first layer 210 and second layer 214).

[0129] In addition, the controller 122 can calibrate or otherwise modify the superimposed measurement based on known, assumed, or measured features of the sample that may also affect the pupil image (e.g., but not limited to, sidewall angles or other sample asymmetries).

[0130] Refer again Figure 1B The following describes in more detail the various components of the optical subsystem 102 according to one or more embodiments of the present disclosure.

[0131] In one embodiment, the lighting subsystem 106 includes a lighting source 128 configured to generate at least one lighting beam 108. The lighting from the lighting source 128 may include light of one or more selected wavelengths, including, but not limited to, ultraviolet (UV) radiation, visible light radiation, or infrared (IR) radiation.

[0132] The illumination source 128 may comprise any type of illumination source suitable for providing at least one illumination beam 108. In an embodiment, the illumination source 128 is a laser source. For example, the illumination source 128 may comprise, but is not limited to, one or more narrowband laser sources, broadband laser sources, supercontinuum laser sources, white light laser sources, or the like. In this respect, the illumination source 128 may provide an illumination beam 108 with high coherence (e.g., high spatial coherence and / or temporal coherence). In an embodiment, the illumination source 128 comprises a laser sustained plasma (LSP) source. For example, the illumination source 128 may comprise, but is not limited to, an LSP lamp, LSP bulb, or LSP chamber suitable for housing one or more elements capable of emitting broadband illumination when excited into a plasma state by a laser source.

[0133] In an embodiment, the illumination subsystem 106 includes one or more optical components adapted to modify and / or adjust the illumination beam 108 and guide the illumination beam 108 to the sample 104. For example, the illumination subsystem 106 may include one or more illumination lenses 130 (e.g., for collimating the illumination beam 108, for relaying the illumination pupil plane 120 and / or the illumination field plane 132, or the like). In an embodiment, the illumination subsystem 106 includes one or more illumination control optics 134 for shaping or otherwise controlling the illumination beam 108. For example, the illumination control optics 134 may include, but are not limited to, one or more field stops, one or more pupil stops, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, one or more beam shapers, or one or more mirrors (e.g., static mirrors, translation mirrors, scanning mirrors, or the like).

[0134] In an embodiment, the illumination subsystem 106 illuminates the sample 104 with two or more illumination beams 108. Furthermore, the two or more illumination beams 108 may (but are not required to) be incident on different portions of the sample 104 (e.g., different cells 204 of the superimposed target 202) within the measurement field of view (e.g., the field of view of objective lens 136). Various techniques can be used to generate the two or more illumination beams 108, as considered herein. In an embodiment, the illumination subsystem 106 includes two or more apertures at the illumination field plane 132. In an embodiment, the illumination subsystem 106 includes one or more beam splitters that split illumination from illumination source 128 into two or more illumination beams 108. In an embodiment, at least one illumination source 128 directly generates two or more illumination beams 108. In a sense, each illumination beam 108 can be considered as part of a different illumination channel, regardless of the technique used to generate the individual illumination beams 108.

[0135] The light-collecting subsystem 110 may include one or more optical elements adapted to modify and / or adjust the collected light 138 from the sample 104. In embodiments, the light-collecting subsystem 110 includes one or more light-collecting lenses 140 that may include (but are not required to include) an objective lens 136 (e.g., for collimating the illumination beam 108, for relaying the pupil and / or field plane, or the like). In embodiments, the light-collecting subsystem 110 includes one or more light-collecting control optics 142 for shaping or otherwise controlling the collected light 138. For example, the light-collecting control optics 142 may include, but are not limited to, one or more field stops, one or more pupil stops, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, one or more beam shapers, or one or more mirrors (e.g., static mirrors, translation mirrors, scanning mirrors, or the like). In another example, the photon-collecting subsystem 110 may include one or more photon-collecting field planes 150. It should be noted that the phase mask may be positioned before and / or after the photon-collecting control optics 142 and / or one or more photon-collecting lenses 140, and is unaffected by... Figure 1B Or the positional constraints shown in Figure 1C.

[0136] In an embodiment, the light-collecting subsystem 110 includes two or more light-collecting channels 144, each having a separate detector 112 (or multiple detectors 112). For example, the optical subsystem 102 may include one or more beam splitters 146 arranged to separate the collected light 138 into the light-collecting channels 144. Furthermore, the beam splitter 146 may be a polarized beam splitter, an unpolarized beam splitter, or a combination thereof.

[0137] In an embodiment, multiple light-collecting channels 144 are configured to collect light from multiple illumination beams 108 on the sample 104. For example, in the case where the superimposed target 202 has two or more cells, the optical subsystem 102 can simultaneously illuminate different cells 204 with different illumination beams 108 and simultaneously capture the detection signal associated with each illumination beam 108. Additionally, in an embodiment, the multiple illumination beams 108 directed to the sample 104 may have different polarizations. In this way, the diffraction order associated with each of the illumination beams 108 can be separated. For example, a polarizing beam splitter 146 can efficiently separate the diffraction orders associated with different illumination beams 108. By another example, a polarizer can be used in one or more light-collecting channels 144 to isolate the desired diffraction order for measurement.

[0138] Refer again Figure 1AIt should be noted in this document that one or more components of system 100 may be communicatively coupled to various other components of system 100 in any manner known in the art. For example, one or more processors 124 may be communicatively coupled to each other and communicatively coupled to other components via wired (e.g., copper wire, fiber optic cable, and the like) or wireless connections (e.g., RF coupling, IR coupling, WiMax, Bluetooth, 3G, 4G, 4G LTE, 5G, and the like). By another example, controller 122 may be communicatively coupled to one or more components of optical subsystem 102 via any wired or wireless connection known in the art.

[0139] In embodiments, one or more processors 124 may comprise any one or more processing elements known in the art. In this sense, one or more processors 124 may comprise any microprocessor-type device configured to execute software algorithms and / or instructions. In embodiments, one or more processors 124 may comprise a desktop computer, mainframe computer system, workstation, graphics computer, parallel processor, or other computer system (e.g., a networked computer) configured to execute a program configured to operate system 100, as described throughout this disclosure. It should be understood that the steps described throughout this disclosure may be implemented by a single computer system or alternatively by multiple computer systems. Furthermore, it should be understood that the steps described throughout this disclosure may be implemented on any one or more of the one or more processors 124. Generally, the term "processor" may be broadly defined to encompass any device having one or more processing elements that execute program instructions from memory 126. Furthermore, different subsystems of system 100 may include processors or logic elements suitable for implementing at least a portion of the steps described throughout this disclosure. Therefore, the foregoing description should not be construed as a limitation of this disclosure, but is merely illustrative.

[0140] Those skilled in the art will recognize that, for clarity of concept, the components (e.g., operation), apparatus, objects, and accompanying discussions described herein are used as examples and are open to various configuration modifications. Therefore, as used herein, the specific examples illustrated and the accompanying discussions are intended to represent their more general categories. In general, the use of any particular example is intended to represent its category, and the omission of specific components (e.g., operation), apparatus, and objects should not be considered limiting.

[0141] Those skilled in the art will understand that various carriers (e.g., hardware, software, and / or firmware) exist that can implement the processes and / or systems and / or other technologies described herein, and the preferred carrier will vary depending on the context in which the processes and / or systems and / or other technologies are deployed. For example, if the implementer determines that speed and accuracy are of paramount importance, then the implementer may choose a primary hardware and / or firmware carrier; alternatively, if flexibility is of paramount importance, then the implementer may choose a primary software implementation; or again, alternatively, the implementer may choose a combination of hardware, software, and / or firmware. Thus, there are several possible carriers that can implement the processes and / or apparatus and / or other technologies described herein, none of which is inherently superior to another, because any carrier to be utilized is a choice dependent on the context in which the carrier will be deployed and the specific considerations of the implementer (e.g., speed, flexibility, or predictability), any of which can vary.

[0142] The foregoing description is presented to enable those skilled in the art to make and use the invention, as provided in the context of a particular application and its requirements. Those skilled in the art will appreciate various modifications to the described embodiments, and that the general principles defined herein may be applied to other embodiments. Therefore, the invention is not intended to be limited to the specific embodiments shown and described, but is to be accorded the broadest scope consistent with the principles and novel features disclosed herein.

[0143] Regarding the use of any plural and / or singular terms in this document, those skilled in the art can convert from plural to singular and / or from singular to plural based on the context and / or application. For clarity, various singular / plural substitutions are not explicitly described in this document.

[0144] All methods described herein may include storing the results of one or more steps of the method embodiments in memory. The results may include any of the results described herein and may be stored in any manner known in the art. The memory may include any memory described herein or any other suitable storage medium known in the art. After the results have been stored, they may be accessed in memory and used by any of the methods or system embodiments described herein, formatted for display to a user, used by another software module, method, or system, and the like. Furthermore, the results may be stored “permanently,” “semi-permanently,” “temporarily,” or for a period of time. For example, the memory may be random access memory (RAM), and the results may not necessarily remain in memory indefinitely.

[0145] Furthermore, upon further consideration, each of the embodiments of the methods described above may include any other step of any other method described herein. Additionally, each of the embodiments of the methods described above may be performed by any of the systems described herein.

[0146] The objects described herein sometimes refer to different components housed within or connected to other components. It should be understood that such depicted architectures are merely exemplary, and many other architectures can in fact be implemented to achieve the same functionality. Conceptually, any arrangement of components used to achieve the same functionality is effectively “associated” to achieve the desired functionality. Therefore, any two components combined herein to achieve a particular functionality can be considered “associated” with each other to achieve the desired functionality, regardless of the architecture or intermediate components. Similarly, any two such associated components can also be considered “connected” or “coupled” with each other to achieve the desired functionality, and any two components that can be suchly associated can also be considered “coupleable” with each other to achieve the desired functionality. Specific examples of coupleability include, but are not limited to, physically mating and / or physically interacting components, and / or wirelessly interacting and / or logically interacting components.

[0147] Furthermore, it should be understood that the invention is defined by the appended claims. Those skilled in the art will understand that, generally, the terms used herein and especially in the appended claims (e.g., the body of the appended claims) are intended to be “open-ended” terms (e.g., the term “including” should be interpreted as “including but not limited to,” the term “having” should be interpreted as “at least having,” the term “includes” should be interpreted as “including but not limited to,” etc.). Those skilled in the art will further understand that if a particular number of claims is anticipated to be introduced, this intention will be explicitly stated in the claims, and the absence of such a statement will not indicate this intention. For example, to aid understanding, the appended claims may contain the introductory phrases “at least one” and “one or more” to introduce the claims. However, the use of such phrases should not be construed as implying that the introduction of a claim statement by the indefinite article "a" limits any particular claim containing such an introduction to an invention containing only one such statement, even when the same claim contains the introductory phrase "a or more" or "at least one" and an indefinite article such as "a" (e.g., "a" should generally be interpreted as meaning "at least one" or "a or more"); the same applies to the use of definite articles used to introduce a claim statement. Furthermore, even if a specific number of introduced claim statements is explicitly stated, those skilled in the art will recognize that such a statement should generally be interpreted as meaning at least the number stated (e.g., a plain statement of "two statements" without other modifiers generally means at least two statements, or two or more statements). Furthermore, in examples using conventional expressions such as "at least one of A, B, and C, and similar ones," a person skilled in the art will generally understand that this construction is expected in the sense of the conventional expression (e.g., "a system having at least one of A, B, and C" includes, but is not limited to, systems having only A, only B, only C, having both A and B, having both A and C, having both B and C, and / or having both A, B, and C, and similar ones). In examples using conventional expressions such as "at least one of A, B, or C, and similar ones," a person skilled in the art will generally understand that this construction is expected in the sense of the conventional expression (e.g., "a system having at least one of A, B, or C" includes, but is not limited to, systems having only A, only B, only C, having both A and B, having both A and C, having both B and C, and / or having both A, B, and C, and similar ones). Those skilled in the art will further understand that any extractive words and / or phrases presenting two or more alternatives, whether in the description, claims, or drawings, should be understood to account for the possibility of including one, any, or both of the items.For example, the phrase “A or B” would be understood as including the possibility of “A” or “B” or “A and B”.

[0148] It is believed that this disclosure and its many accompanying advantages will be understood from the foregoing description, and it will be apparent that various changes can be made to the form, construction, and arrangement of the components without departing from the subject matter of the disclosure or sacrificing all its material advantages. The forms described are for illustrative purposes only, and the appended claims are intended to cover and encompass such changes. Furthermore, it should be understood that the invention is defined by the appended claims.

Claims

1. A superimposed metering system, comprising: A controller comprising one or more processors configured to execute program instructions that cause the one or more processors to: Receives a pupil image of collected light emitted from the superimposed target and a known phase distribution of an illumination beam configured to be introduced toward the superimposed target; The intensity function is modeled in relation to one or more eccentric shift parameters of the pupil image, the known phase distribution, and the structure of the superimposed target. The pupil image is fitted to the intensity function, which depends at least on the known phase distribution and the structure of the superimposed target, by one or more eccentric shift parameters; and The superimposed measurement is generated based on the fitting.

2. The superposition metering system according to claim 1, wherein the superposition target is a unit cell superposition target.

3. The superimposed measurement system according to claim 1, wherein the fitting includes linear regression pattern fitting.

4. The superposition measurement system according to claim 1, wherein the fitting includes a first pattern fitting and a second pattern fitting, wherein the first pattern fitting is based on the first-order diffraction overlap region of the pupil image, and wherein the second pattern fitting is based on the second-order diffraction overlap region of the pupil image.

5. The superposition metrology system of claim 1, wherein the fitting is based on calibration of a phase mask configured to induce the known phase distribution.

6. The superposition metering system according to claim 1, wherein the superposition target includes at least one of the following: a mottled stripe superposition target or a common pitch superposition target.

7. The superposition metering system of claim 1, further comprising performing defocus adjustment on the superposition target, wherein the fitting is based on the amount of the defocus adjustment performed, wherein the known phase distribution is based on the amount of the defocus adjustment performed.

8. The overlay metering system of claim 7, wherein receiving the pupil image includes performing multiple defocus adjustments on the overlay target.

9. The superposition measurement system according to claim 1, wherein receiving the pupil image includes receiving multiple pupil images of multiple light spot positions of the cells of the superposition target; and wherein the fitting is based on the multiple pupil images.

10. The superposition metrology system of claim 1, wherein the known phase distribution includes an F1-type phase distribution, the F1-type phase distribution being wavelength-independent and characterizable in the form of at least one of the following: ;or 。 11. The superposition metering system of claim 10, wherein the introduction of the known phase distribution into the illumination beam is performed via a phase mask of the system having the F1-type phase distribution.

12. The superposition metrology system according to claim 10, wherein the fitting of the pupil image to the intensity function is performed simultaneously for the +1 first-order diffraction intensity function and the -1 first-order diffraction intensity function of the F1-type phase distribution.

13. The superposition metrology system of claim 1, wherein the known phase distribution includes an F2-type phase distribution, the F2-type phase distribution being wavelength-independent and characterizable in the form of at least one of the following: ;or 。 14. The superposition metering system of claim 13, wherein the introduction of the known phase distribution into the illumination beam is performed via a phase mask of the system having the F2-type phase distribution.

15. The superposition metrology system of claim 13, wherein the fitting of the pupil image to the intensity function is performed sequentially for the +1 first-order diffraction intensity function and the -1 first-order diffraction intensity function of the F2 type phase distribution.

16. The superimposed metering system of claim 15, wherein the phase mask having the F2-type phase distribution comprises at least one of the following: Complex toroidal lens; Cylindrical plano-convex lens; or Defocused pupil planar apodizer.

17. The overlay metrology system of claim 1, wherein the fitting of the pupil image comprises multiple fittings configured to simultaneously solve for the effective mask height (nh), the optical stack thickness (Δ), and the overlay measurement, the multiple fittings scanning the parameter space of nh and Δ.

18. A superimposed metering system, comprising: An optical subsystem, comprising: A light source configured to produce a beam of light; Objective lens, configured to direct the illumination beam toward the superimposed target of the sample; A phase mask configured to induce a known phase distribution in a portion of the illumination beam; A detector configured to receive a pupil image of the collected light emitted from the superimposed target; and A controller communicatively coupled to the detector, the controller comprising one or more processors configured to execute program instructions that cause the one or more processors to: The pupil image of the collected light emitted from the superimposed target is received, and the known phase distribution of the portion of the illumination beam configured to be introduced into the superimposed target is received; The intensity function is modeled in relation to one or more eccentric shift parameters of the pupil image, the known phase distribution, and the structure of the superimposed target. Fit the pupil image to the intensity function, which depends at least on the known phase distribution and the structure of the superimposed target, using one or more eccentric shift parameters; and The superimposed measurement is generated based on the fitting.

19. The superposition metering system according to claim 18, wherein the superposition target is a unit cell superposition target.

20. The superimposed measurement system of claim 18, wherein the fitting includes linear regression pattern fitting.

21. The superposition measurement system according to claim 18, wherein the fitting includes a first pattern fitting and a second pattern fitting, wherein the first pattern fitting is based on the first-order diffraction overlap region of the pupil image, and wherein the second pattern fitting is based on the second-order diffraction overlap region of the pupil image.

22. The superposition metrology system of claim 18, wherein the fitting is based on calibration of the phase mask configured to induce the known phase distribution.

23. The superposition metering system according to claim 18, wherein the superposition target includes at least one of the following: a mottled stripe superposition target or a common pitch superposition target.

24. The overlay metering system of claim 18, further comprising performing defocus adjustment on the overlay target, wherein the fitting is based on the amount of the defocus adjustment performed, wherein the known phase distribution is based on the amount of the defocus adjustment performed.

25. The overlay metering system of claim 24, wherein receiving the pupil image includes performing multiple defocus adjustments on the overlay target.

26. The superposition measurement system according to claim 18, wherein receiving the pupil image includes receiving multiple pupil images of multiple light spot positions of cells of the superposition target; and wherein the fitting is based on the multiple pupil images.

27. A method comprising: Guide an illumination beam, including one with a known phase distribution, to illuminate a superimposed target; Receive the pupil image of the collected light emitted from the superimposed target; The intensity function is modeled in relation to one or more eccentric shift parameters of the pupil image, the known phase distribution, and the structure of the superimposed target. The pupil image is fitted to the intensity function, which depends at least on the known phase distribution and the structure of the superimposed target, by one or more eccentric shift parameters; and The superimposed measurement is generated based on the fitting.

28. The method of claim 27, wherein the superposition target is a unit cell superposition target.

29. The method of claim 27, wherein the fitting comprises linear regression pattern fitting.

30. The method of claim 27, wherein the fitting includes a first pattern fitting and a second pattern fitting, wherein the first pattern fitting is based on the first-order diffraction overlap region of the pupil image, and wherein the second pattern fitting is based on the second-order diffraction overlap region of the pupil image.

31. The method of claim 27, wherein the fitting is based on calibration of a phase mask configured to induce the known phase distribution.

32. The method of claim 27, wherein the superimposed target includes at least one of the following: a mottled stripe superimposed target or a common pitch superimposed target.

33. The method of claim 27, further comprising performing a defocus adjustment on the superimposed target, wherein the fitting is based on the amount of the defocus adjustment performed, wherein the known phase distribution is based on the amount of the defocus adjustment performed.

34. The method of claim 33, wherein receiving the pupil image includes performing a plurality of defocus adjustments on the superimposed target.

35. The method of claim 27, wherein receiving the pupil image includes receiving a plurality of pupil images of a plurality of light spot positions of a cell of the superimposed target; and wherein the fitting is based on the plurality of pupil images.

36. The method of claim 27, wherein the known phase distribution comprises an F1-type phase distribution, the F1-type phase distribution being wavelength-independent and characterizable in the form of at least one of the following: ;or 。 37. The method of claim 36, wherein the introduction of the known phase distribution into the illumination beam is performed via a phase mask of the system having the F1-type phase distribution.

38. The method of claim 27, wherein the known phase distribution comprises an F2-type phase distribution, the F2-type phase distribution being wavelength-independent and characterizable in the form of at least one of the following: ;or 。

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