Metrology methods and related metrology devices

Abstract

Disclosed is a method for determining at least one parameter of interest associated with a structure formed in at least one respective layer on a substrate, the method comprising: obtaining measured metrology data associated with measurement of the structure; obtaining a model, the model describing the structure with a plurality of model parameters, the model parameters including estimated values; and sequentially performing a plurality of optimization steps based on the measured metrology data to determine the plurality of model parameters, each of the plurality of optimization steps determining a subset of the plurality of model parameters.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to European Patent Application No. 22194304.6 filed September 7, 2022 and European Patent Application No. 22203557.8 filed October 25, 2022, which are incorporated herein by reference in their entireties.

[0002] The present invention relates to metrology methods and devices that can be used, for example, to determine the properties of structures on a substrate. [Background technology]

[0003] A lithographic apparatus is a machine constructed to apply a desired pattern onto a substrate. Lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus can, for example, project a pattern (often called a "design layout" or "design") in a patterning device (e.g., mask) onto a layer of radiation-sensitive material (resist) provided on the substrate (e.g., wafer).

[0004]

[0004] Lithographic apparatus may use electromagnetic radiation to project a pattern onto a substrate. The wavelength of this radiation determines the minimum size of features that can be formed on the substrate. Typical wavelengths currently in use are 365 nm (i-line), 248 nm, 193 nm, and 13.5 nm. Lithographic apparatus using extreme ultraviolet (EUV) radiation with wavelengths in the range 4-100 nm, for example 6.7 nm or 13.5 nm, can form smaller features on a substrate than lithographic apparatus using radiation with a wavelength of, for example, 193 nm.

[0005]

[0005] Low k1 lithography can be used to process features with dimensions smaller than the classical resolution limit of a lithographic apparatus. In such processes, the resolution equation can be expressed as CD = k1 × λ / NA, where λ is the wavelength of the radiation used, NA is the numerical aperture of the projection optics of the lithographic apparatus, CD is the "critical dimension" (generally the smallest feature size to be printed, in this case the half pitch), and k1 is an empirical resolution factor. In general, the smaller k1 is, the more difficult it is to reproduce on a substrate a pattern that resembles the shape and dimensions planned by a circuit designer to achieve a particular electrical functionality and performance. To overcome such difficulties, advanced fine-tuning steps can be applied to the lithographic projection apparatus and / or the design layout. Such steps include, but are not limited to, optimization of the NA, customization of the illumination scheme, use of phase-shift patterning devices, various optimizations of the design layout, such as optical proximity correction (OPC, sometimes also called "optical and process correction") in the design layout or other methods commonly defined as "resolution enhancement techniques" (RET). Alternatively, a strict control loop can be used to manage the stability of the lithographic apparatus to improve pattern replication at low k1.

[0006]

[0006] In lithography and other manufacturing processes, it is desirable to frequently measure the structures created (e.g., for process control and verification). Various tools are known for making such measurements, including scanning electron microscopes, which are often used to measure critical dimensions (CD), and dedicated tools to measure overlay, which is the accuracy of the alignment of two layers in a device. Recently, various forms of scatterometers have been developed for use in the lithography field.

[0007]

[0007] The manufacturing process may be, for example, lithography, etching, deposition, chemical mechanical planarization, oxidation, ion implantation, diffusion, or a combination of two or more thereof.

[0008]

[0008] Examples of known scatterometers often rely on the provision of a dedicated metrology target. For example, the method may require a target in the form of a simple grating that is large enough that the measurement beam produces a spot smaller than the grating (i.e., the grating is underfilled). So-called reconstruction methods can calculate the properties of the grating by simulating the interaction of scattered radiation with a mathematical model of the target structure. The parameters of the model are adjusted until the simulated interaction produces a diffraction pattern similar to that observed from the real target.

[0009] In addition to measuring feature shapes through reconstruction, diffraction-based overlay can be measured using an apparatus such as that described in U.S. Patent Application Publication No. 2006066855A1. Diffraction-based overlay metrology, which uses dark-field imaging of diffraction orders, enables overlay measurement of smaller targets. These targets may be smaller than the illumination spot and may be surrounded by product structures on the wafer. Examples of dark-field imaging metrology can be found in many published patent applications, such as U.S. Patent Application Publication No. 2011102753A1 and U.S. Patent Application Publication No. 20120044470A. Multiple gratings can be measured in a single image using a composite grating target. Known scatterometers tend to use light in the visible or near-infrared (IR) wavelength range, which requires the grating pitch to be much coarser than the actual product structure whose characteristics are actually of interest. Such product features can be defined using deep ultraviolet (DUV), extreme ultraviolet (EUV), or X-ray radiation, which have much shorter wavelengths. Unfortunately, such wavelengths are not typically available or usable for metrology.

[0010]

[0010] On the other hand, the dimensions of modern product structures are too small to be imaged by optical metrology techniques. Small features include, for example, features formed by multiple patterning processes and / or pitch augmentation. Therefore, targets used for mass production metrology often use features much larger than the product whose overlay error or critical dimension is the characteristic of interest. Measurement results are only indirectly related to the dimensions of the actual product structures and can be inaccurate because metrology targets do not experience the same distortions under different processing conditions during optical projection in the lithography apparatus and / or other steps in the manufacturing process. While scanning electron microscopes (SEMs) can directly resolve such modern product structures, SEMs are much slower than optical measurements. Furthermore, electrons cannot penetrate thick process layers, making them unsuitable for metrology applications. Other techniques, such as measuring electrical properties using contact pads, are known, but they provide only indirect evidence of the true product structure.

[0011]

[0011] Reducing the wavelength of radiation used during metrology allows for the resolution of smaller features, increased sensitivity to structural variations in the structure, and / or deeper penetration into the product structure. One such method of generating suitable high frequency radiation (e.g., hard X-rays, soft X-rays, and / or EUV radiation) is to use pump radiation (e.g., infrared IR radiation) to excite a generating medium, which results in the generation of emission radiation, optionally harmonic generation, including high frequency radiation.

[0012]

[0012] Current reconstruction techniques for reconstructing the parameters of a measured structure are mathematically and computationally complex due to the large number of permutations of parameters that are varied. They also often require prior knowledge of many precise parameters that describe the measured sample, and detailed sample information may not be available. To address this, at least in the context of overlay metrology, other overlay measurement techniques have been developed that do not require reconstruction, such as techniques based on measuring target asymmetries, which are typically biased to separate overlay asymmetries from other asymmetries.

[0013] It would be desirable to improve such reconstruction and / or overlay metrology techniques. Summary of the Invention

[0014]

[0014] In a first aspect of the present invention, there is provided a method for determining at least one parameter of an object associated with a structure formed in at least one respective layer on a substrate, the method comprising: obtaining measured metrology data associated with measurement of the structure; obtaining a model, the model describing the structure with a plurality of model parameters, the model parameters including estimated values; and sequentially performing a plurality of optimization steps based on the measured metrology data to determine the plurality of model parameters, each of the plurality of optimization steps determining a subset of the plurality of model parameters.

[0015] According to a second aspect of the present invention there is provided a computer program product comprising one or more sequences of machine readable instructions for carrying out the computational steps of the method according to the first aspect of the present invention.

[0016] The present invention further provides a processing arrangement and metrology device comprising the computer program of the second aspect.

[0017]

[0017] These and other aspects and advantages of the apparatus and methods disclosed herein will be understood by consideration of the following description and drawings of exemplary embodiments.

[0018]

[0018] Embodiments will now be described, by way of example only, with reference to the accompanying schematic drawings, in which: [Brief explanation of the drawings]

[0019] [Figure 1] 1 depicts a schematic overview of a lithographic apparatus; [Figure 2] 1 shows a schematic overview of a lithography cell; [Figure 3]

[0018] A schematic representation of holistic lithography is shown, which represents the collaboration of three main technologies to optimize semiconductor manufacturing. [Figure 4] 1 illustrates a schematic representation of a scatterometry apparatus; [Figure 5] 1 illustrates schematically a transmission scatterometry apparatus; [Figure 6] 1 shows a schematic representation of a metrology apparatus in which EUV and / or SXR radiation is used. [Figure 7]

[0018] A simplified schematic diagram of an illumination source is shown. [Figure 8(a)]

[0018] A portion of an overlay target showing true dimensions is shown. [Figure 8(b)] 1 shows a model of the same overlay target, including estimated dimensions, as used in the initial setup of the method of the embodiment. [Figure 9(a)]

[0018] Figure 8(a) shows a portion of an overlay target showing true dimensions. [Figure 9(b)]

[0018] Figure 3 shows a model of the same overlay target with some estimated dimensions, which have been optimized in a first step using the method of the embodiment. [Figure 10(a)]

[0018] Figure 8(a) shows a portion of an overlay target showing true dimensions. [Figure 10(b)] 10 shows a model of the same overlay target after execution of an embodiment method for determining overlay. [Figure 11] 10 shows a portion of a target structure on a stack illustrating parameters that can be reconstructed using a method according to a further embodiment; [Figure 12(a)] 1 is a flowchart illustrating a method for determining an optimized sequence according to an embodiment. [Figure 12(b)] 1 is a flowchart illustrating a method for determining an optimized sequence according to an embodiment. [Figure 13(a)] 13 is a chart illustrating the diagonal of a covariance matrix of several exemplary parameters associated with a structure as determined by the method of FIG. 12. [Figure 13(b)] 13 is a chart illustrating a correlation matrix of several exemplary parameters related to structure as determined by the method of FIG. 12. [Figure 13(c)] FIG. 13 is a flow diagram illustrating an exemplary optimization sequence determined using the method of FIG. DETAILED DESCRIPTION OF THE INVENTION

[0020]

[0018] In this document, the terms "radiation" and "beam" are used to encompass all types of electromagnetic and particulate radiation, including ultraviolet radiation (e.g., having a wavelength of 365, 248, 193, 157, or 126 nm), EUV (e.g., extreme ultraviolet radiation, having a wavelength in the range of about 5 to 100 nm), X-ray radiation, electron beam radiation, and other particulate radiation.

[0021]

[0019] As used herein, the terms "reticle," "mask," or "patterning device" may be broadly interpreted to refer to a general patterning device that can be used to provide an incident radiation beam with a patterned cross-section that corresponds to the pattern to be created in a target portion of a substrate. The term "light valve" is also sometimes used in this context. In addition to classic masks (transmissive or reflective masks, binary masks, phase-shifting masks, hybrid masks, etc.), examples of other such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0022] 1 schematically depicts a lithographic apparatus LA. The lithographic apparatus LA includes an illumination system IL (also called an illuminator) configured to condition a radiation beam B (e.g. UV radiation, DUV radiation, EUV radiation or X-ray radiation), a mask support (e.g. a mask table) T constructed to support a patterning device (e.g. a mask) MA and connected to a first positioner PM configured to accurately position the patterning device MA according to certain parameters, a substrate support (e.g. a wafer table) WT constructed to hold a substrate (e.g. a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate support according to certain parameters, and a projection system (e.g. a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W.

[0023]

[0021] In operation, the illumination system IL receives a radiation beam from a radiation source SO (e.g. via a beam delivery system BD). The illumination system IL may include various types of optical components for directing, shaping and / or controlling the radiation, such as refractive, reflective, diffractive, magnetic, electromagnetic, electrostatic and / or other types of optical components or any combination thereof. The illuminator IL may be used to condition the radiation beam B so that it has a desired spatial and angular intensity distribution in its cross-section in the plane of the patterning device MA.

[0024]

[0022] As used herein, the term "projection system" PS should be interpreted broadly to encompass various types of projection systems. Such systems may include refractive, reflective, diffractive, catadioptric, anamorphic, magnetic, electromagnetic and / or electrostatic optical systems, or any combination thereof, as required by the exposure radiation being used and / or other factors (e.g., the use of an immersion liquid or a vacuum). Where the term "projection lens" is used herein, it may all be considered as synonymous with the more general term "projection system" PS.

[0025] Lithographic apparatus LA may be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index (e.g. water) so as to fill a space between the projection system PS and the substrate W, which is also known as immersion lithography. Further details about immersion techniques are provided in U.S. Patent No. 6,952,253, which is incorporated herein by reference in its entirety.

[0026] The lithographic apparatus LA may be of a type having two or more substrate supports WT (also known as "dual stage"). In such a "multiple stage" machine, the substrate supports WT may be used in parallel, and / or a substrate W on one of the substrate supports WT may be used to expose a pattern thereon, while a procedure is being performed on another substrate W on the other substrate support WT in preparation for a subsequent exposure of that other substrate W.

[0027] In addition to the substrate support WT, the lithographic apparatus LA may include a measurement stage. The measurement stage is configured to hold a sensor and / or a cleaning apparatus. The sensor may be configured to measure a property of the projection system PS or a property of the radiation beam B. The measurement stage may hold multiple sensors. The cleaning apparatus may be configured to clean part of the lithographic apparatus, for example part of the projection system PS or part of a system for supplying immersion liquid. The measurement stage may move below the projection system PS when the substrate support WT is spaced apart from the projection system PS.

[0028]

[0026] In operation, a radiation beam B is incident on a patterning device (e.g. a mask MA held on a mask support T) and is patterned according to a pattern (design layout) on the patterning device MA. After traversing the mask MA, the radiation beam B passes through the projection system PS, which focuses the beam onto a target portion C of the substrate W. With the aid of the second positioner PW and the position measurement system IF, the substrate support WT can be precisely moved, for example so that different target portions C are positioned at focused and aligned positions in the path of the radiation beam B. Similarly, the first positioner PM, and possibly another position sensor (which is not explicitly shown in Figure 1), may be used to precisely position the patterning device MA with respect to the path of the radiation beam B. The patterning device MA and substrate W may be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although substrate alignment marks P1, P2 occupy dedicated target portions as illustrated, they may be located in spaces between target portions. When located between target portions C, substrate alignment marks P1, P2 are referred to as scribe-lane alignment marks.

[0029] 2, the lithography apparatus LA may be part of a lithography cell LC (sometimes called a litho-cell or (litho)-cluster), which often also includes apparatus for performing pre-exposure and post-exposure processes on the substrate W. Conventionally, such apparatus include a spin coater SC for depositing a resist layer, a developer DE for developing the exposed resist, a chill plate CH, and a bake plate BK (which, for example, adjust the temperature of the substrate W, e.g., to adjust the solvent in the resist layer). A substrate handler (i.e., robot) RO picks up substrates W from input / output ports I / O1, I / O2, moves them between various process tools, and delivers them to a loading bay LB of the lithography apparatus LA. The devices within a lithocell are often collectively referred to as a track and may be under the control of a track control unit TCU, which may itself be controlled by a supervisory control system SCS, which may also control the lithographic apparatus LA (e.g., via a lithography control unit LACU).

[0030]

[0028] In lithographic processes, it is desirable to frequently measure the structures created (e.g., for process control and verification). Tools that perform such measurements may be called metrology tools MT. Various types of metrology tools MT that perform such measurements are known, for example scanning electron microscopes or various forms of scatterometer metrology tools MT. A scatterometer is a multipurpose instrument that allows measurements of parameters of the lithographic process to be made by having a sensor at or near the pupil or a conjugate plane to the pupil of the scatterometer objective lens (usually referred to as pupil-based measurements), or by having a sensor at or near the image plane or a conjugate plane to the image plane (in which case measurements are usually referred to as image-based or field-based measurements). Such scatterometers and associated measurement techniques are described in detail in U.S. Patent Application Publication Nos. 20100328655, 2011102753A1, 20120044470A, 20110249244, 20110026032, or EP 1,628,164A, which are incorporated herein by reference in their entireties. Such scatterometers can measure gratings using light from hard X-ray (HXR), soft X-ray (SXR), extreme ultraviolet (EUV), visible to near-infrared (IR), and IR wavelength ranges. When the radiation is hard X-ray or soft X-ray, the scatterometer can optionally be a small-angle X-ray scattering metrology tool.

[0031] To ensure that substrates W are exposed accurately and consistently by lithographic apparatus LA, it is desirable to inspect the substrates to measure properties of the patterned structures, such as overlay error between successive layers, line thickness, critical dimension (CD), shape of the structures, etc. To that end, inspection tools and / or metrology tools (not shown) may be included in lithocell LC. If errors are detected, adjustments can be made, for example, to the exposure of subsequent substrates or other processing steps to be performed on substrate W, particularly if inspection is performed before other substrates W of the same batch or lot are subsequently exposed or processed.

[0032] Inspection apparatus, sometimes called metrology apparatus, are used to determine the properties of substrates W, and in particular to determine how the properties of different substrates W vary, or how properties associated with different layers of the same substrate W vary from layer to layer. Alternatively, the inspection apparatus can be constructed to identify defects on substrates W and can, for example, be part of a lithocell LC, integrated into a lithography apparatus LA, or even be a stand-alone apparatus. The inspection apparatus can measure properties of a latent image (an image in a resist layer after exposure), a semi-latent image (an image in a resist layer after a post-exposure bake step PEB), a developed resist image (from which exposed or unexposed portions of the resist have been removed), or even an etched image (an image after a pattern transfer step such as etching).

[0033] In a first embodiment, the scatterometer MT is an angle-resolved scatterometer. In such a scatterometer, a reconstruction method may be applied to the measurement signal to reconstruct or calculate the properties of the grating. Such a reconstruction may, for example, be the result of simulating the interaction of the scattered radiation with a mathematical model of the target structure and comparing the simulation results with the measurement results. Parameters of the mathematical model are adjusted until the simulated interaction produces a diffraction pattern similar to that observed from the real target.

[0034]

[0032] In a second embodiment, the scatterometer MT is a spectroscopic scatterometer MT. In such a spectroscopic scatterometer MT, radiation emitted by a radiation source is directed towards a target, and radiation reflected, transmitted or scattered from the target is directed towards a spectrometer detector, which measures the spectrum of the specularly reflected radiation (i.e., measures the intensity as a function of wavelength). From this data, it is possible to reconstruct the structure or profile of the target giving rise to the detected spectrum, for example by rigorous coupled wave theory and nonlinear regression, or by comparison with a library of simulated spectra.

[0035] In a third embodiment, the scatterometer MT is an ellipsometric scatterometer. An ellipsometric scatterometer makes it possible to determine parameters of a lithographic process by measuring scattered or transmitted radiation for each polarization state. Such a metrology apparatus emits polarized light (e.g., linearly, circularly, or elliptically polarized light), for example using appropriate polarizing filters in the illumination section of the metrology apparatus. A source suitable for the metrology apparatus can provide polarized radiation as well. Various embodiments of existing ellipsometric scatterometers are described in U.S. Patent Application Publication Nos. 11 / 451,599, 11 / 708,678, 12 / 256,780, 12 / 486,449, 12 / 920,968, 12 / 922,587, 13 / 000,229, 13 / 033,135, 13 / 533,110, and 13 / 891,410, which are incorporated by reference herein in their entireties.

[0036] In one embodiment of the scatterometer MT, the scatterometer MT is adapted to measure the overlay of two misaligned grating or periodic structures by measuring the asymmetry of the reflectance spectra and / or the detection configuration, where the asymmetry is related to the degree of overlay. The two (possibly overlapping) grating structures can be applied in two different (not necessarily consecutive) layers and formed at substantially the same location on the wafer. The scatterometer can have a symmetric detection configuration, for example, as described in co-owned European Patent Application Publication No. 1628164A, so that any asymmetry can be clearly distinguished. This provides a straightforward method for measuring grating misalignment. Further examples of overlay errors between two layers containing periodic structures when a target is measured through the asymmetry of the periodic structures can be obtained from PCT Patent Application Publication No. WO 2011 / 012624 or U.S. Patent Application No. 20160161863, which are incorporated herein by reference in their entirety.

[0037]

[0035] Other parameters of interest can be focus and dose. Focus and dose can be determined simultaneously by scatterometry (or alternatively by scanning electron microscopy), as described in U.S. Patent Application No. 2011-0249244, which is incorporated herein by reference in its entirety. A single structure can be used that has a unique combination of critical dimension and sidewall angle measurements for each point of the focus-energy matrix (FEM, also called focus-exposure matrix). If these unique combinations of critical dimension and sidewall angle are available, focus and dose values ​​can be uniquely determined from these measurements.

[0038]

[0036] A metrology target can be a collection of composite gratings, mostly formed by a lithography process in resist, but also formed after other manufacturing processes, such as etching processes. The pitch and linewidth of the grating structures can be strongly dependent on the measurement optics (specifically, the NA of the optics) to capture the diffraction orders obtained from the metrology target. As previously shown, the diffraction signal can be used to determine the shift between two layers (also called "overlay") or to reconstruct at least a portion of the original grating as produced by the lithography process. This reconstruction can be used to provide guidance on the quality of the lithography process and can be used to control at least a portion of the lithography process. The target can have smaller subsegments configured to mimic the dimensions of the features of the design layout in the target. This subsegmentation allows the target to behave more similarly to the features of the design layout, so that all process parameter measurements closely resemble the features of the design layout. The target can be measured in underfill mode or overfill mode. In underfill mode, the measurement beam generates a spot that is smaller than the entire target. In overfill mode, the measurement beam generates a spot that is larger than the entire target. In such an overfill mode, it may be possible to simultaneously measure different targets, and therefore determine different process parameters therefrom.

[0039] The overall measurement quality of a lithography parameter using a particular target depends, at least in part, on the measurement recipe used to measure that lithography parameter. The term “substrate measurement recipe” can include one or more parameters of the measurement itself, one or more parameters of the measured pattern(s), or both. For example, if the measurement used in the substrate measurement recipe is a diffraction-based optical measurement, one or more of the parameters of the measurement can include the wavelength of the radiation, the polarization of the radiation, the angle of incidence of the radiation to the substrate, the orientation of the radiation relative to the pattern on the substrate, etc. One of the criteria for selecting a measurement recipe can be, for example, the sensitivity of one of the measurement parameters to process variations. Further examples are described in U.S. Patent Application No. 2016-0161863 and published U.S. Patent Application No. 2016 / 0370717A1, which are incorporated herein by reference in their entireties.

[0040] The patterning process in a lithography apparatus LA may be one of the most critical steps in processing, requiring high accuracy in the dimensioning and placement of structures on a substrate W. To ensure this high accuracy, three systems can be combined in a so-called "holistic" control environment, as shown schematically in FIG. 3. One of these systems is a lithography apparatus LA, which is (virtually) connected to a metrology tool MT (a second system) and a computer system CL (a third system). The key to such a "holistic" environment is optimizing the coordination between these three systems to enforce the overall process window and provide a tight control loop to ensure that the patterning performed by the lithography apparatus LA stays within the process window. The process window defines the range of process parameters (e.g., dose, focus, overlay) within which a particular manufacturing process will produce a specified result (e.g., a functioning semiconductor device) and within which the process parameters of the lithography or patterning process can vary.

[0041] The computer system CL can use (part of) the design layout to be patterned to predict which resolution enhancement techniques should be used, and can perform computational lithography simulations and calculations to determine mask layouts and lithography apparatus settings that maximize the overall process window of the patterning process (indicated in FIG. 3 by the double-headed arrow at the first scale SC1). The resolution enhancement techniques can be configured to match the patterning capabilities of the lithography apparatus LA. The computer system CL can also be used to detect where in the process window the lithography apparatus LA is currently operating (e.g., using input from the metrology tool MET) to predict whether defects are likely to be present, for example due to suboptimal processing (indicated in FIG. 3 by the arrow pointing to "0" at the second scale SC2).

[0042]

[0040] The metrology tool MT can provide input to the computer system CL to enable accurate simulation and prediction, for example providing feedback to the lithographic apparatus LA to identify possible drifts in the calibration status of the lithographic apparatus LA (indicated in Figure 3 by multiple arrows at the third scale SC3).

[0043]

[0041] Many different forms of metrology tools MT for measuring structures produced using lithographic patterning apparatus can be provided. The metrology tools MT can use electromagnetic radiation to interrogate the structures. The radiation characteristics (e.g., wavelength, bandwidth, power) can affect different measurement characteristics of the tool, and generally, shorter wavelengths can increase resolution. The radiation wavelength affects the resolution that the metrology tool can achieve. Therefore, to be able to measure structures with features having small dimensions, metrology tools MT with short wavelength radiation sources are preferred.

[0044] Another way in which the radiation wavelength can affect the measurement properties is the penetration depth and transparency / opacity of the material to be inspected at the radiation wavelength. Depending on the opacity and / or penetration depth, the radiation can be used for measurements in transmission or reflection. The type of measurement can affect whether information about the surface and / or inside the bulk of the structure / substrate can be obtained. Therefore, penetration depth and opacity are other factors to consider when selecting a radiation wavelength for a metrology tool.

[0045] To achieve higher resolution for measuring lithographically patterned structures, short-wavelength metrology tools MT are preferred. This can include wavelengths shorter than visible wavelengths, such as the UV, EUV, and X-ray portions of the electromagnetic spectrum. Hard X-ray methods, such as transmission small-angle X-ray scattering (TSAXS), take advantage of the high resolution and penetration depth of hard X-rays and can therefore operate in a transmission mode. On the other hand, soft X-rays and EUV do not penetrate deeply into the target but can induce rich optical responses in the materials to be probed. This can be a legitimate optical property of many semiconductor materials and can be due to structures of comparable size to the probe wavelength. As a result, EUV and / or soft X-ray metrology tools MT can operate in a reflection mode, for example, by imaging lithographically patterned structures or analyzing diffraction patterns from the same.

[0046]

[0044] In the case of hard X-rays, soft X-rays, and EUV radiation, applications in high-volume manufacturing (HVM) applications can be limited due to a lack of available high-brightness radiation sources at the required wavelengths. In the case of hard X-rays, radiation sources commonly used in industrial applications include X-ray tubes. X-ray tubes (including advanced X-ray tubes based on liquid metal anodes or rotating anodes, for example) are relatively accessible and compact, but may lack the brightness required for HVM applications. While high-brightness X-ray sources such as synchrotron light sources (SLS) and X-ray free electron lasers (XFEL) currently exist, their size (>100 m) and high cost (hundreds of millions of euros) make them prohibitively large and expensive for metrology applications. Similarly, there is a lack of availability of sufficiently bright EUV and soft X-ray radiation sources.

[0047] An example of a metrology apparatus, such as a scatterometer, is shown in FIG. 4. It may include a broadband (e.g., white light) radiation projector 2 that projects radiation 5 onto a substrate W. Reflected or scattered radiation 10 is sent to a spectrometer detector 4, which measures the spectrum 6 of the specularly reflected radiation (i.e., a measurement of the intensity I as a function of wavelength λ). From this data, the structure or profile 8 giving rise to the detected spectrum may be reconstructed by a processing unit (PU), for example by rigorous coupled-wave analysis and nonlinear regression, or by comparison with a library of simulated spectra as shown at the bottom of FIG. 4. Typically, for reconstruction, the general form of the structure is known and some parameters are assumed from knowledge of the process by which the structure was created, thereby leaving only a few parameters of the structure to be determined from the scatterometry data. Such a scatterometer may be configured as a normal-incidence scatterometer or an oblique-incidence scatterometer.

[0048] A transmission version of an example metrology apparatus such as the scatterometer shown in Figure 4 is shown in Figure 5. The transmitted radiation 11 is passed to a spectrometer detector 4 which measures a spectrum 6 as discussed with respect to Figure 4. Such a scatterometer may be configured as a normal incidence scatterometer or an oblique incidence scatterometer. The transmission version optionally uses hard X-ray radiation having a wavelength of <1 nm, optionally <0.1 nm, optionally <0.01 nm.

[0049] As an alternative to optical metrology methods, the use of hard X-rays, soft X-rays, or EUV radiation, such as radiation having at least one of the following wavelength ranges, is also contemplated: <0.01 nm, <0.1 nm, <1 nm, 0.01 nm to 100 nm, 0.01 nm to 50 nm, 1 nm to 50 nm, 1 nm to 20 nm, 5 nm to 20 nm, and 10 nm to 20 nm. One example of a metrology tool operating in one of the wavelength ranges presented above is transmission small-angle X-ray scattering (T-SAXS, such as in U.S. Patent Application Publication No. 2007224518A, the contents of which are incorporated herein by reference in their entirety). Profile (CD) measurements using T-SAXS are discussed by Lemaillet et al., “Intercomparison between optical and X-ray scatterometry measurements of FinFET structures,” Proc. of SPIE, 2013, 8681. It should be noted that the use of laser-produced plasma (LPP) X-ray sources is described in U.S. Patent Application Publication Nos. 2019 / 003988 A1 and 2019 / 215940 A1, which are incorporated herein by reference in their entireties. Reflectometry techniques using X-rays at grazing incidence (GI-XRS) and extreme ultraviolet (EUV) radiation can be used to measure the properties of film and layer stacks on substrates. Within the general field of reflectometry, goniometric and / or spectroscopic techniques can be applied. Goniometric methods can measure the variation of the reflected beam at different angles of incidence. Spectroscopic reflectometry, on the other hand, measures the spectrum of wavelengths reflected at a given angle (using broadband radiation). For example, EUV reflectometry has been used for the inspection of mask blanks prior to the fabrication of reticles (patterning devices) for use in EUV lithography.

[0050] Depending on the application, for example, the use of wavelengths in the hard X-ray, soft X-ray, or EUV regions may be insufficient. U.S. Patent Application Publication Nos. 20130304424A1 and 2014019097A1 (Bakeman et al / KLA) describe hybrid metrology techniques that combine measurements made using X-rays at wavelengths in the 120 nm to 2000 nm range with optical measurements to obtain measurements of parameters such as CD. CD measurements are obtained by coupling one or more common channels and X-ray and optical mathematical models. The contents of the cited U.S. patent applications are incorporated herein by reference in their entirety.

[0051]

[0049] Figure 6 shows a schematic representation of a metrology tool 302 that can use the aforementioned radiation to measure parameters of structures on a substrate. The metrology tool 302 shown in Figure 6 can be suitable for hard x-ray, soft x-ray and / or EUV regions.

[0052]

[0050] Figure 6 shows, purely by way of example, a schematic physical layout of a metrology apparatus 302 including a spectroscopic scatterometer using hard X-ray, soft X-ray and / or EUV radiation, optionally at grazing incidence. An alternative form of inspection apparatus may be provided in the form of an angle-resolved scatterometer, which may use radiation at or near normal incidence similar to conventional scatterometers operating at longer wavelengths, and which may also use radiation oriented at more than 1° or 2° from parallel to the substrate. An alternative form of inspection apparatus may be provided in the form of a transmission scatterometer, to which the arrangement of Figure 5 is applied.

[0053] The inspection apparatus 302 includes what is referred to as a radiation source or illumination source 310, an illumination system 312, a substrate support 316, detection systems 318, 398, and a metrology processing unit (MPU) 320.

[0054]

[0052] The illumination source 310 in this example is for generating EUV, hard X-ray or soft X-ray radiation. The illumination source 310 may be based on high harmonic generation (HHG) techniques, as shown in Fig. 6, or may be other types of illumination sources, such as a liquid metal jet source, an inverse Compton scattering (ICS) source, a plasma channel source, a magnetic undulator source, a free electron laser (FEL) source, a compact storage ring source, a discharge-produced plasma source, a soft X-ray laser source, a rotating anode source, a solid anode source, a particle acceleration source, a microfocus source or a laser-produced plasma source.

[0055] The HHG source can be a gas jet / nozzle source, a capillary / fiber source, or a gas cell source.

[0056] As shown in FIG. 6 , in the example of an HHG source, the main components of the radiation source are a pump radiation source 330 operable to emit pump radiation and a gas delivery system 332. Optionally, the pump radiation source 330 is a laser, and optionally, the pump radiation source 330 is a pulsed high-power infrared laser or optical laser. The pump radiation source 330 may be, for example, a fiber-based laser with an optical amplifier, and generates pulses of infrared radiation, which may last, for example, less than 1 ns (1 nanosecond) per pulse, optionally at a pulse repetition rate up to several megahertz. The wavelength of the infrared radiation is in the range of 200 nm to 10 μm, for example, in the 1 μm (1 micron) region. Optionally, laser pulses are delivered to the gas delivery system 332 as first pump radiation 340, and a portion of the gas in the radiation is converted to a higher frequency than the first radiation to become emitted radiation 342. A gas supply 334 supplies a suitable gas to a gas delivery system 332, which gas is optionally ionized by an electrical source 336. The gas delivery system 332 may be a cutting tube.

[0057] The gas supplied by the gas delivery system 332 defines a gas target, which may be a gas flow or a static volume. The gas may be, for example, air, neon (Ne), helium (He), nitrogen (N2), oxygen (O2), argon (Ar), krypton (Kr), xenon (Xe), carbon dioxide, or a combination thereof. These may be selectable within the same device. The emitted radiation may include multiple wavelengths. While measurement calculations (e.g., reconstruction) may be simplified if the emitted radiation were monochromatic, it is easier to generate radiation having several wavelengths. The emission divergence angle of the emitted radiation may depend on the wavelength. Different wavelengths may provide different levels of contrast, for example, when imaging structures made of different materials. For example, for inspection of metal or silicon structures, different wavelengths may be selected than those used to image resist (carbon-based) features or to detect contamination in such materials. One or more filtering devices 344 may be provided. For example, a filter, such as a thin film of aluminum (Al) or zirconium (Zr), serves to prevent fundamental IR radiation from penetrating further into the inspection apparatus. A grating (not shown) can be provided to select one or more specific wavelengths from among the generated wavelengths. Optionally, the illumination source includes a space configured to be evacuated, and a gas delivery system is configured to supply a gas target within the space. Optionally, part or all of the beam path can be contained within a vacuum environment, bearing in mind that SXR and / or EUV radiation is absorbed as it travels through air. Various components of the radiation source 310 and the illumination optics 312 can be adjustable to implement different metrology "recipes" within the same apparatus. For example, different wavelengths and / or polarizations can be selectable.

[0058] Depending on the material of the structure under inspection, different wavelengths may enable a desired level of penetration into lower layers. Shorter wavelengths may then be preferred for resolving the smallest device features and defects between the smallest device features. For example, one or more wavelengths in the range of 0.01 to 20 nm, optionally in the range of 1 to 10 nm, or optionally in the range of 10 to 20 nm may be selected. Wavelengths shorter than 5 nm suffer from the problem that the critical angle can be very low when reflected from the target material in semiconductor manufacturing. Therefore, selecting a wavelength longer than 5 nm allows for a stronger signal at a higher angle of incidence. On the other hand, if the inspection task is to detect the presence of a specific material, for example, to detect contamination, wavelengths up to 50 nm may be useful.

[0059] From the radiation source 310, the filtered beam 342 enters the inspection chamber 350, where a substrate W containing a structure of interest is held in a measurement position by a substrate support 316 for inspection. The structure of interest is labeled T. Optionally, the atmosphere within the inspection chamber 350 is maintained at a near-vacuum state by a vacuum pump 352, so that the SXR and / or EUV radiation can pass through the atmosphere without undue attenuation. The illumination system 312 functions to focus the radiation into a focused beam 356, which may include, for example, a two-dimensional curved mirror or a series of one-dimensional curved mirrors, as described in the above-referenced U.S. Patent Application Publication No. 2017 / 0184981 A1 (the contents of which are incorporated herein by reference in their entirety). The focusing is performed to achieve a circular or elliptical spot S having a diameter of less than 10 μm when projected onto the structure of interest. The substrate support 316 may include, for example, an XY translation stage and a rotation stage, which allow any portion of the substrate W to be brought close to the focal point of the beam at a desired orientation, thereby forming a radiation spot S on the structure of interest. Alternatively or additionally, the substrate support 316 may include, for example, a tilt stage, which may tilt the substrate W at an angle to control the angle of incidence of the focused beam on the structure of interest T.

[0060] Optionally, the illumination system 312 provides a reference beam of radiation to a reference detector 314, which may be configured to measure the spectrum and / or intensity of different wavelengths of the filtered beam 342. The reference detector 314 may be configured to generate a signal 315 that is provided to the processor 320, and the filter may include information about the spectrum of the filtered beam 342 and / or the intensity of different wavelengths of the filtered beam.

[0061] The reflected radiation 360 is captured by detector 318, and the spectrum is provided to processor 320 for use in calculating properties of target structure T. Illumination system 312 and detection system 318 thus form an inspection apparatus that may include a hard x-ray, soft x-ray, and / or EUV spectroreflectometer of the type described in U.S. Patent Application Publication No. 2016282282 A1, the contents of which are incorporated herein by reference in their entirety.

[0062] If the target Ta has a certain periodicity, the radiation of the focused beam 356 may be partially diffracted. The diffracted radiation 397 follows another path at a well-defined angle relative to the angle of incidence, and then becomes reflected radiation 360. In FIG. 6, the diffracted radiation 397 shown is shown schematically, and the diffracted radiation 397 may follow many paths other than the one shown. The inspection apparatus 302 may also include an additional detection system 398 that detects and / or images at least a portion of the diffracted radiation 397. Although FIG. 6 shows a single additional detection system 398, embodiments of the inspection apparatus 302 may also include multiple additional detection systems 398 arranged at different positions to detect and / or image the diffracted radiation 397 in multiple diffraction directions. In other words, the (higher) diffraction orders of the focused radiation beam impinging on the target Ta are detected and / or imaged by one or more additional detection systems 398. One or more detection systems 398 generate signals 399 that are provided to metrology processor 320. Signals 399 may include information about diffracted light 397 and / or may include an image obtained from diffracted light 397.

[0063] To assist in the alignment and focus of the spot S with the desired product structure, the inspection apparatus 302 may also provide auxiliary optics that use auxiliary radiation under the control of the metrology processor 320. The metrology processor 320 may also communicate with a position controller 372 that operates the translation stage, the rotation stage, and / or the tilt stage. The processor 320 receives high-precision feedback regarding the position and orientation of the substrate via sensors. The sensors 374 may include, for example, interferometers that can provide accuracy in the picometer range. During operation of the inspection apparatus 302, spectral data 382 captured by the detection system 318 is sent to the metrology processing unit 320.

[0064] As mentioned, an alternative form of inspection apparatus optionally uses hard X-ray, soft X-ray, and / or EUV radiation at normal or near-normal incidence, for example, to perform diffraction-based asymmetry measurements. Another alternative form of inspection apparatus uses hard X-ray, soft X-ray, and / or EUV radiation at more than 1° or 2° from parallel to the substrate. Both types of inspection apparatus can be provided in a hybrid metrology system. Measured performance parameters include overlay (OVL), critical dimension (CD), focus of the lithography apparatus while it prints the target structure, coherent diffraction imaging (CDI), and at-resolution overlay (ARO) metrology. The hard X-ray, soft X-ray, and / or EUV radiation can have a wavelength of, for example, less than 100 nm; for example, radiation in the range of 5 to 30 nm, optionally 10 to 20 nm, can be used. The radiation can be narrowband or broadband in nature. The radiation may have discrete peaks in particular wavelength bands, or it may have a more continuous character.

[0065] Similar to optical scatterometers used in production facilities today, the inspection system 302 can be used to measure structures in resist materials processed in a lithocell (post-develop inspection or ADI) and / or to measure structures after they have been formed into a harder material (post-etch inspection or AEI). For example, substrates can be inspected using the inspection system 302 after being processed by a developer, etcher, annealer, and / or other tools.

[0066] Metrology tools MT, including but not limited to the scatterometers mentioned above, can use radiation from a radiation source to perform measurements. The radiation used by the metrology tool MT can be electromagnetic radiation. The radiation can be optical radiation, such as radiation in the infrared, visible, and / or ultraviolet portions of the electromagnetic spectrum. The metrology tool MT can use radiation to measure or inspect properties and aspects of a substrate, such as a lithography exposure pattern on a semiconductor substrate. The type and quality of the measurement can depend on several characteristics of the radiation used by the metrology tool MT. For example, the resolution of electromagnetic measurements can depend on the radiation wavelength; the smaller the wavelength, the smaller features can be measured, for example, due to the diffraction limit. To measure features with small dimensions, it may be preferable to perform the measurement using radiation with a shorter wavelength, such as EUV, hard X-ray (HXR), and / or soft X-ray (SXR) radiation. To perform metrology at a specific wavelength or range of wavelengths, the metrology tool MT requires access to a radiation source that provides radiation at that / those wavelengths. There are various types of radiation sources that provide radiation of various wavelengths. Depending on the wavelength provided by the radiation source, different types of radiation generation methods can be used. In the case of extreme ultraviolet (EUV) radiation (e.g., 1 nm to 100 nm) and / or soft X-ray (SXR) radiation (e.g., 0.1 nm to 20 nm, 1 nm to 20 nm, or 10 nm to 20 nm), the radiation source can use the above-mentioned high harmonic generation (HHG) or any other type of radiation source to obtain radiation of the desired wavelength.

[0067] FIG. 7 shows a simplified schematic diagram of an embodiment 600 of an illumination source 310, which may be an illumination source for high harmonic generation (HHG). The illumination source 600 may also optionally include one or more of the features of the illumination source in the metrology tool described with respect to FIG. 6 . The illumination source 600 includes a chamber 601 and is configured to receive pump radiation 611 having a propagation direction indicated by an arrow. The pump radiation 611 shown here is an example of pump radiation 340 from the pump radiation source 330 as shown in FIG. 6 . The pump radiation 611 may be directed into the chamber 601 through a radiation input 605, which may optionally be a viewport made of fused silica or an equivalent material. The pump radiation 611 may have a Gaussian or hollow (e.g., annular) cross-sectional profile and may be incident on and optionally focused by a gas flow 615 within the chamber 601, the flow direction of which is indicated by a second arrow. The gas flow 615 contains a small volume (e.g., a few cubic mm) of a particular gas (e.g., air, neon (Ne), helium (He), nitrogen (N), oxygen (O), argon (Ar), krypton (Kr), xenon (Xe), carbon dioxide, and combinations thereof) so-called gas volume or gas target whose gas pressure exceeds a certain value. The gas flow 615 can be a steady flow. Other media, such as a metal plasma (e.g., aluminum plasma), can also be used.

[0068] The gas delivery system of the illumination source 600 is configured to provide a gas flow 615. The illumination source 600 is configured to provide pump radiation 611 into the gas flow 615 to drive the generation of emission radiation 613. The region where at least a majority of the emission radiation 613 is generated is called the interaction region. The interaction region can vary from tens of micrometers (for strongly focused pump radiation) to several millimeters or centimeters (for moderately focused pump radiation) or up to several meters (for very weakly focused pump radiation). The gas delivery system is configured to provide a gas target for generating emission radiation in the interaction region of the gas target, and optionally, the illumination source is configured to receive the pump radiation and provide the pump radiation in the interaction region. Optionally, the gas flow 615 is provided by the gas delivery system into an evacuated or nearly evacuated space. 6, the gas delivery system may include a gas nozzle 609, which includes an opening 617 on its outlet face. A gas flow 615 is supplied through the opening 617. The gas catcher confines the gas flow 615 to a certain volume by extracting residual gas flow, thereby maintaining a vacuum or near-vacuum atmosphere within the chamber 601. Optionally, the gas nozzle 609 may be made of a thick-walled tube and / or a highly thermally conductive material to avoid thermal deformation due to high-power pump radiation 611.

[0069]

[0067] It is also contemplated that the dimensions of the gas nozzle 609 may be used in scaled-up or scaled-down versions ranging from a micrometer-sized nozzle to a meter-sized nozzle. This wide range of dimensions stems from the fact that the setup can be scaled so that the intensity of the pump radiation in the gas flow is in a certain range that may be beneficial for the emitted radiation; different dimensions must be determined for different pump radiation energies, which may be pulsed lasers, and the pulse energy may vary from tens of microjoules to tens of joules. Optionally, the gas nozzle 609 has thick walls to reduce nozzle deformation caused by thermal expansion effects, which may be detected, for example, by a camera. A gas nozzle with thick walls can produce a stable gas volume with reduced fluctuations. Optionally, the illumination source includes a gas catcher in close proximity to the gas nozzle to maintain the pressure in the chamber 601.

[0070]

[0068] Due to the interaction of the pump radiation 611 with the gas atoms of the gas flow 615, the gas flow 615 converts a portion of the pump radiation 611 into emitted radiation 613, which may be an example of the emitted radiation 342 shown in Figure 6. The central axis of the emitted radiation 613 may be parallel to the central axis of the incident pump radiation 611. The emitted radiation 613 may have a wavelength in the X-ray or EUV range, hereinafter referred to as SXR radiation, with a wavelength in the range of 0.01 nm to 100 nm, optionally 0.1 nm to 100 nm, optionally 1 nm to 100 nm, optionally 1 nm to 50 nm, optionally 2 nm to 50 nm, optionally 2 nm to 20 nm, or optionally 10 nm to 20 nm.

[0071] In operation, the emitted radiation 613 beam passes through the radiation output 607 and may then be manipulated by the illumination system 603, which may be one example of the illumination system 312 of Figure 6, and directed to a substrate to be inspected for metrology measurements. The emitted radiation 613 may be directed and optionally focused to structures on the substrate.

[0072] Because air (and indeed any gas) significantly absorbs SXR or EUV radiation, the volume between the gas flow 615 and the wafer to be inspected may be evacuated or nearly evacuated. Because the central axis of the emitted radiation 613 may be parallel to the central axis of the incident pump radiation 611, it may be necessary to shield the pump radiation 611 to prevent it from passing through the radiation output 607 and entering the illumination system 603. This can be done by incorporating a filtering device 344, shown in FIG. 6, at the radiation output 607, which is positioned in the radiation beam path and is opaque or nearly opaque to the pump radiation (e.g., opaque or nearly opaque to infrared or visible light) but at least partially transparent to the emitted radiation beam. The filter can be made using zirconium or multiple materials combined in multiple layers. The filter can be a hollow block, optionally an annular block, if the pump radiation 611 has a hollow, optionally annular, cross-sectional profile. Optionally, the filter is neither perpendicular nor parallel to the propagation direction of the emitted radiation beam, so that pump radiation filtering is efficient. Optionally, filtering device 344 includes a hollow block and a thin film filter, such as an aluminum (Al) or zirconium (Zr) film filter. Optionally, filtering device 344 can include a mirror that efficiently reflects the emitted radiation but poorly reflects the pump radiation, or a wire mesh that efficiently transmits the emitted radiation but poorly transmits the pump radiation.

[0073]

[0071] Methods, apparatus, and assemblies are described herein for obtaining emitted radiation, optionally at harmonic frequencies of the pump radiation. The radiation generated through the process, optionally HHG using nonlinear effects to generate radiation, optionally at harmonic frequencies of the provided pump radiation, can be provided as radiation in a metrology tool MT for inspection and / or measurement of substrates. If the pump radiation comprises short pulses (i.e., a few cycles), the generated radiation does not necessarily exactly match the harmonic of the pump radiation frequency. The substrate can be a lithographically patterned substrate. The radiation obtained through the process can also be provided to a lithography apparatus LA and / or a lithography cell LC. The pump radiation can be pulsed radiation, providing a high peak intensity for a short period of time.

[0074] The pump radiation 611 may include radiation having one or more wavelengths higher than one or more wavelengths of the emitted radiation. The pump radiation may include infrared radiation. The pump radiation may include radiation having a wavelength in the range of 500 nm to 1500 nm. The pump radiation may include radiation having a wavelength in the range of 800 nm to 1300 nm. The pump radiation may include radiation having a wavelength in the range of 900 nm to 1300 nm. The pump radiation may be pulsed radiation. The pulsed pump radiation may include pulses having a duration in the femtosecond range.

[0075] In some embodiments, the emitted radiation, optionally harmonic radiation, may include one or more harmonics of the pump radiation wavelength. The emitted radiation may include wavelengths in the extreme ultraviolet, soft x-ray, and / or hard x-ray portions of the electromagnetic spectrum. The emitted radiation 613 may include one or more wavelengths in the ranges of less than 1 nm, less than 0.1 nm, less than 0.01 nm, 0.01 nm to 100 nm, 0.1 nm to 100 nm, 0.1 nm to 50 nm, 1 nm to 50 nm, and 10 nm to 20 nm.

[0076]

[0074] Radiation, such as the harmonic radiation described above, can be provided as source radiation in the metrology tool MT. The metrology tool MT can use the source radiation to perform measurements on a substrate exposed by the lithographic apparatus. The measurements can be to determine one or more parameters of a structure on the substrate. By using shorter wavelength radiation (e.g., radiation with EUV, SXR, and / or HXR wavelengths, such as those included in the wavelength ranges described above), the metrology tool can resolve smaller features of the structure compared to using longer wavelengths (e.g., visible radiation, infrared radiation). Shorter wavelength radiation, such as EUV, SXR, and / or HXR radiation, can also penetrate deeper into materials, such as a patterned substrate, meaning that metrology of deeper layers on the substrate is possible. Such deep layers may be inaccessible with longer wavelength radiation.

[0077] In the metrology tool MT, source radiation can be emitted from a radiation source and directed onto a target structure (or other structure) on a substrate. The source radiation can include EUV, SXR, and / or HXR radiation. The target structure can reflect, transmit, and / or diffract the source radiation incident on the target structure. The metrology tool MT can include one or more sensors for detecting diffracted radiation. For example, the metrology tool MT can include detectors for detecting positive first (+1) diffraction order and negative first (-1) diffraction order. The metrology tool MT can also measure specularly reflected or transmitted radiation (zeroth order diffracted radiation). Additional sensors for metrology can be present in the metrology tool MT, for example, to measure additional diffraction orders (e.g., higher diffraction orders).

[0078] In an exemplary lithography metrology application, the HHG-generated radiation may be focused onto a target on a substrate using an optical column, which may be called an illuminator, to transmit the radiation from the HHG source to the target. The HHG radiation is then reflected from the target and detected and processed, e.g., to measure and / or infer properties of the target.

[0079] Gas target HHG configurations can be broadly divided into three distinct categories: gas jet, gas cell, and gas capillary. FIG. 7 shows an example of a gas jet configuration in which a gas volume is introduced into the drive radiation laser beam. In a gas jet configuration, the interaction of the drive radiation with solid parts is minimized. The gas volume can, for example, comprise a gas stream perpendicular to the drive radiation beam, and the gas volume is enclosed within a gas cell. In a gas capillary setup, the dimensions of the capillary structure holding the gas are small laterally so as to significantly affect the propagation of the drive radiation laser beam. The capillary structure can, for example, be a hollow-core fiber, with the hollow core configured to hold the gas.

[0080]

[0078] The gas jet HHG configuration can offer relative freedom for shaping the spatial profile of the drive radiation beam in the far field because it is not subject to the constraints imposed by the gas capillary structure. Also, the gas jet configuration can have less stringent alignment tolerances. On the other hand, the gas capillary enlarges the interaction zone of the drive radiation and the gaseous medium, thereby optimizing the HHG process.

[0081] For example, to use HHG radiation in metrology applications, the HHG radiation is separated from the drive radiation downstream of the gas target. The separation of HHG radiation and drive radiation may differ between gas jet and gas capillary configurations. In either case, the drive radiation removal scheme may include a metal-permeable filter to filter out drive radiation remaining from the short-wavelength radiation. However, before using such a filter, the intensity of the drive radiation must be significantly reduced from the intensity at the gas target to avoid damaging the filter. The methods that can be used for this intensity reduction differ between gas jet and gas capillary configurations. In the case of gas jet HHG, the relative freedom of the shape and spatial profile (sometimes referred to as spatial distribution and / or spatial frequency) of the drive radiation beam focused on the gas target allows the far field to be designed so that the short-wavelength radiation has a low intensity along its propagation direction. This spatial separation in the far field means that an aperture can be used to block the drive radiation and reduce its intensity.

[0082]

[0080] In contrast, in a gas capillary structure, the spatial profile of the beam as it passes through the gaseous medium can be largely determined by the capillary. The spatial profile of the drive radiation can be determined by the shape and material of the capillary structure. For example, when using a hollow-core fiber as the capillary structure, the shape and material of the fiber structure determine the mode of the drive radiation supported for propagation in the fiber. For most standard fibers, the supported propagation mode leads to a spatial profile in which the high-intensity drive radiation overlaps with the high-intensity HHG radiation. For example, the drive radiation intensity can be centered in a Gaussian or near-Gaussian profile distribution in the far field.

[0083] In one embodiment of overlay metrology, an overlay target includes two or more diffraction gratings (substructures) printed in different layers so as to overlap. Some known overlay metrology methods infer overlay based on measurements of overlay targets programmed with biases (intentional position offsets between substructures / gratings). Overlay metrology methods using such biased targets can eliminate the need to perform model-based reconstruction, thus reducing the need to know the (geometric) stack parameters (also called stack information) between two or more gratings. The stack information is required for known model-based reconstruction methods. However, the stack information is often confidential and therefore not always available.

[0084]

[0075] Some known metrology methods use measurement illumination in the visible wavelength band and biased targets to set up recipes for overlay metrology. Similar approaches can be used at soft X-ray (SXR) wavelengths, and biased target-based methods for training models are an option for metrology inference, and optionally for overlay and / or profilometry inference.

[0085] The use of targets with multiple biases impacts yield, and such methods are still subject to grating asymmetry, stack imbalance, and the like. In addition, some metrology targets are printed in scribe lanes, which limits accuracy and requires additional steps to infer overlay of product structures. Other metrology methods address this latter issue, but at the cost of increased complexity in inferring overlay from structures with product-scale pitch. In addition, some metrology methods require a maximum layer separation between gratings of approximately 50 nm, which further limits their applicability. One or more of the problems mentioned above can be solved by embodiments of the present invention.

[0086]

[0077] In addition to overlay, the reconstruction of critical dimensions (CDs) and other geometric parameters of printed structures is becoming increasingly important for the control of lithography scanners. The CD is the dimension of a structure, and in one embodiment, it should be noted that the structure is a space from which material has been removed (e.g., etched away by an etching process).

[0087]

[0078] Profile control of photoresist can be achieved using a scanning electron microscope (SEM) or a transmission electron microscope (TEM), but such techniques are time-consuming and may destroy the structure being measured. As the structures being printed become more complex (e.g., gate all around, nanosheet, fork sheet), it is increasingly desired to perform such geometric parameter metrology without the need for information about the actual stack of the target or device (which is typically not available). Embodiments of the present invention provide a fast and non-destructive method for measuring geometric parameters, particularly for complex structures. [[ID=*]]

[0088] [[ID=*]]

[0079] Accordingly, it is proposed to perform a metrology method based on N-dimensional reconstruction by decomposing an N-dimensional reconstruction (or optimization) problem into a sequence of M (optionally M < N, optionally M > N, optionally M = N) reconstruction (or optimization) problems, where each sequence has a lower dimensionality L M having. Optionally Σ M L M It seems there are some tags with asterisks in the original text which might be incorrect or incomplete in terms of the provided rules. If you can clarify those, it would be possible to provide a more accurate translation.≧N. This simplifies the optimization problem behind the reconstruction procedure and also relaxes the constraints on the prior knowledge about the target required to start the reconstruction. As will be explained in more detail, this is possible due to the specific properties inherent in electromagnetic scattering at SXR wavelengths, particularly at wavelengths between 2 nm and 50 nm, and optionally between 2 nm and 20 nm. Additionally, since solving a complex structure all at once using an optimizer is an infeasible problem in terms of computational time, decomposing the reconstruction has an advantage in the total computational time of the reconstruction.

[0089] In one embodiment, it is proposed to perform such metrology in at least two main optimization steps. During the first optimization step, at least one vertical (or first direction) position parameter, e.g., a layer thickness-related parameter or an effective layer thickness-related parameter taking into account the optical properties of the layer, is determined or optimized while other parameters are fixed to estimated values. It should be noted that the determination process in this context can be an optimization process. That is, the determined value after a specific step or steps, optionally one or more optimization steps, may still differ from the actual value (being the ground truth), but is closer to the actual value compared to the value before the specific step or steps. The estimated value may differ from the actual value. The difference may deviate from the actual value by up to 10-20%. In one embodiment, the estimated CD values ​​may deviate by up to 5 nm and 8 nm from the actual CD values ​​of 40 nm and 50 nm, respectively. The vertical (or first direction) in this context refers to the direction perpendicular to the substrate plane, hereinafter labeled Z direction. This step can be achieved with high accuracy with limited prior knowledge about the target / structure. Once at least one vertical position parameter has been optimized, one or more second optimization steps can be used to optimize one or more further / other parameters, such as geometric parameters of interest (e.g., position parameters in at least one direction perpendicular to the vertical direction, e.g., in one or both directions (X and / or Y) in the substrate plane). The one or more other parameters determined in the one or more second optimization steps include one or more substrate plane position parameters of the model parameters. The one or more substrate plane position parameters are related to one or both directions in the substrate plane. The at least one vertical parameter may describe the position and / or thickness of at least one layer or structure. One or both of the first and second steps can include multiple substeps for separately optimizing individual parameters or different subsets of parameters in the Z direction and in each of the X and / or Y directions. In one embodiment, the vertical position parameter includes an optical property of a material that affects the effective optical path in the vertical direction.In one embodiment, the one or more additional parameters of interest include one or more of a sidewall angle, a hole or via angle, a tilt angle, a floor slope, or other slope.

[0090]

[0081] Thus, the method may include determining (and / or optimizing) at least one parameter of interest associated with a structure formed in at least one of the respective layers on the substrate. The method includes obtaining measured metrology data associated with measurements of the structure. The method further includes obtaining a model, the model describing the structure with a plurality of model parameters. The model parameters include estimated values. The method further includes performing (optionally sequentially) a plurality of optimization steps based on the measured metrology data to determine (and / or optimize) the plurality of model parameters. Optionally, each of the plurality of optimization steps determines a subset of the plurality of model parameters.

[0091] In one embodiment, the step of sequentially performing the plurality of optimization steps includes performing one or more first optimization steps using measured metrology data to determine one or more vertical position parameters of the model parameters. Optionally, the step of sequentially performing the plurality of optimization steps further includes, following the performance of the one or more first optimization steps, performing one or more second optimization steps using the measured metrology data and a model having the one or more vertical position parameters determined in the one or more first optimization steps to determine one or more other model parameters of the plurality of model parameters. Optionally, the one or more other model parameters are different from the one or more vertical position parameters. The one or more first optimization steps may optimize at least one vertical position parameter (e.g., optimizing only the at least one vertical position parameter such that other model parameters except the at least one vertical position parameter are fixed during this step). The one or more second optimization steps may optimize at least one other parameter of the model parameters, such as, for example, a substrate surface position parameter of the model parameters (at least one substrate surface position parameter related to one or both directions of the substrate surface). Optionally, the optimization sequence may be determined in the initial optimization sequence determination step, for example based on calculation of a covariance matrix and a correlation matrix of the model parameters.

[0092] The methods described herein may use a simulation model, such as a forward model, to simulate the electromagnetic interaction between the incident field, the target / structure, and the sensor configuration (e.g., based on the physical sensor configuration or optical configuration used to capture scattered radiation from the measurement structure or target). The forward model may, for example, be based on the Born approximation. Optionally, the simulation model is a model that describes the structure with multiple model parameters. Optionally, the simulation model is part of a model that describes the structure with multiple model parameters. Optionally, the simulation model is different from the model that describes the structure with multiple model parameters.

[0093] The method may include comparing the measured sensor output (e.g., diffraction pattern) with the forward model output (modeled diffraction pattern) for different model parameter values ​​until the two outputs match (e.g., according to a matching metric). In this manner, an optimization scheme can be used in which one or more parameters of the model are varied until an extremum of a suitable cost or merit function is found. One example of such a merit function is the cross-correlation of a calculated signal with a measured signal (e.g., the signal is the diffraction intensity of at least one diffraction order). Forward models are described in more detail below.

[0094] Soft X-ray (SXR) metrology uses simultaneous multi-wavelength measurement illumination at wavelengths below 100 nm, 70 nm, 50 nm, 30 nm, or 20 nm, e.g., in the 10-20 nm range (or any of the ranges disclosed elsewhere herein). This inherently provides higher spatial resolution compared to visible light. At such SXR wavelengths (e.g., at least below 100 nm, particularly wavelengths between 2 nm and 50 nm, and optionally between 2 nm and 20 nm), most materials have refractive indices close to that of vacuum. Therefore, the impact of multiple scattering effects, while still present, is less pronounced than at visible wavelengths. This allows the parameter inference problem to be decomposed into a set of simplified, independent subproblems. Thus, while the described approach is a model-based overlay retrieval, the requirements on the model are very relaxed, so we are dealing with quasi-model-based reconstruction. Essentially, the only prior knowledge required is very basic knowledge about the type of structure being measured (e.g., in the first example below, the only initial knowledge requirement is that an overlay target containing a grating within two or more patterned layers is being measured). The actual values ​​of other geometric and physical parameters of the stack (CD, dielectric constant) can be ignored because they do not significantly affect the accuracy of determining the Z-interface (the location in the Z direction of the interface of the patterned layer containing the overlay target). In other words, the actual locations of the interfaces of the patterned layers dominate the measurement signal at the SXR wavelength; as a result, these interfaces can be optimized or determined through a very simple representation of the stack, with all other parameters initially set to estimated (or nominal) values ​​that can vary significantly (e.g., 0%-20%, optionally 0%-10%) from their actual values.

[0095] At SXR wavelengths, in contrast to metrology in the visible spectrum, the parameter space can be considered to be factored into subspaces (e.g., Z-interface subspace, overlay subspace, CD subspace, etc.) that can be considered to be mutually independent of each other. A direct consequence of this is that the optimum can be found for each subspace sequentially. This leads to a significant simplification of the optimization process. Indeed, instead of having to optimize all parameters simultaneously (i.e., searching for the maximum in an N-dimensional optimization problem), the problem can be broken down into a series of lower-dimensional problems, each of which can be solved (sequentially) in a stepwise approach. In a further embodiment, each of the series of lower-dimensional problems can be solved in parallel.

[0096]

[0087] The disclosed concepts are first described in the context of overlay inference. Methods for inferring other geometric parameters are then described using the same basic concepts. The overlay embodiment method is described with reference to Figures 8-10.

[0097]

[0088] In one embodiment, since the overlay target comprises two patterned layers (these are two layers containing diffraction gratings and the other layers are not patterned), it is proposed to recover the overlay via two main successive steps: a first step of optimizing the position of the Z interfaces of the patterned layers of the stack, i.e., the position of the layer interfaces of the patterned layers in the stack in a direction perpendicular to the substrate surface, and a second step of determining or optimizing the overlay.

[0098] Determining the Z-interfaces of the patterned layer may involve using a forward model to find the similarity of global extrema or maxima by varying the location of the desired layer interfaces in the Z direction while keeping everything else fixed (e.g., keeping all other modeled target parameters at their estimated values). These interfaces may be parametrized by three undefined Z positions (i.e., undefined interface positions including the bottom Z-interface of the top lattice and the top and bottom Z-interfaces of the bottom lattice). The top Z-interface of the top lattice may be located at Z=0 by definition, and the other three interfaces are determined relative to this top-most interface. Of course, while this simplifies this step, the method can actively find all four Z-interfaces (e.g., when incorporating another interface as a reference). The Z-interfaces can be found, for example, by employing an exhaustive search or through a local or global optimizer, depending on how much prior information about the target is available. When such prior knowledge is limited, a global optimizer is preferred. Exhaustive search is a brute force approach that sweeps through the values ​​of the interface of the forward model within a given reasonable range until it finds the best match between the simulated and measured diffraction patterns.

[0099]

[0090] Figure 8 shows the initial position at the start of the overlay determination. Figure 8(a) shows the ground truth (actual target geometry, overlay, CD), and Figure 8(b) shows the first guess with estimated values. It can be seen that the initial guess is not accurate and all parameters (i.e., CD, overlay, Z interface) are significantly off. More specifically, in this illustrative example, the true CD value is 38 nm for both the top and bottom gratings, compared to the estimated value of 32 nm. The true overlay (offset between the two gratings) is 5 nm, compared to the estimated target of 0 nm. The target is 1D periodic along the x-direction, with a pitch of 90 nm. Only one period is shown in Figure 8.

[0100] Assume there are two patterned layers (1D periodic along the x-direction) that form the overlay target. The first step may involve sweeping over a large range of values ​​for each of the three interfaces of the putative target (the bottom interface of the top grating, the top and bottom interfaces of the bottom grating). For each combination of these interfaces, a simulated far-field signal is generated using a forward model and then compared to the true signal. This may be a computationally expensive exhaustive search (sweeping 3D space). However, it can be done quickly (e.g., less than a minute using current common hardware), for example, by using the Born approximation. For exact solvers, faster methods can be used.

[0101] FIG. 9(a) again shows the ground truth for comparison and is therefore identical to FIG. 8(a), while FIG. 9(b) shows the situation after determining the Z-interfaces of the patterned layers in the first step. A forward model is used to optimize these Z-interfaces, with all other parameters (including CD and overlay) fixed during this optimization. As can be seen in FIG. 9(b), the positions of the Z-interfaces in the stack are accurately retrieved. Of course, CD and overlay remain inaccurate and unchanged from their fixed initial estimates. Therefore, despite the incorrect CD and overlay values ​​of the modeled target, the Z-interfaces are determined to be in the correct positions. This demonstrates that the model / target parameters can be treated as independent parameter subspaces.

[0102] Once the Z interface values ​​for the patterned layer have been determined, the overlay can be determined in a second step by performing a further optimization using the forward model. In this optimization step, the currently known Z interface can be fixed at a determined position. Optionally, all other parameters can also be fixed, and only the overlay can be varied during the optimization. Alternatively, the optimization can jointly optimize the overlay and one or more other parameters (e.g., one or both CDs).

[0103]

[0094] Overlay optimization can be achieved by laterally shifting the position of either grating (or the positions of both gratings by different amounts) in the forward model so that different overlay values ​​(position offsets that are the top and bottom gratings) are modeled. Again, overlay values ​​can be determined by matching diffraction patterns from the model with actual measured diffraction patterns over a range of overlay values.

[0104]

[0095] Figure 10(a) again shows the ground truth for comparison and is therefore the same as Figures 8(a) and 9(a), while Figure 10(b) shows the situation after the overlay OV has been determined in this second step: even though the CD value is not yet known exactly, the overlay OV has been accurately determined using the disclosed method.

[0105] This approach is convenient and practical because, at SXR wavelengths, determining the Z-interface of a patterned layer is essentially independent of the actual grating geometry (OVL, CD, etc.) and the thicknesses of other layers in the stack. This is a result of the smaller impact of multiple scattering effects at SXR wavelengths, as mentioned above. More specifically, when an SXR probe beam interacts with a structure or target (e.g., an overlay target), the interaction between the light and the target consists of several scattering events. That is, every point on the target is excited by the incident field, which in turn creates new fields that add to the original incident field. This new field also propagates through other parts of the target, exposing the target not only to the original field but also to fields created by previous scattering events within the target. This process can continue, essentially forming a multiple scattering process in which each small region of the target contributes to modifying the total field at every other location within the target. The importance of such higher-order scattering phenomena depends on the refractive index of the materials involved, the wavelength of the light, and the size of the target. SXR wavelengths, particularly those between 2 nm and 50 nm, and optionally between 2 nm and 20 nm, have non-negligible but lower intensities than visible wavelengths. Thus, accurate values ​​for Z-direction parameters (e.g., patterned layer thickness) can be determined for patterned layer thicknesses regardless of the starting values ​​of other parameters.

[0106] There have been studies identifying a quantity (Γ) that can monitor the relevance of such higher-order scattering events (TA van der Sijs, O. El Gawhary, HP Urbach, Phys. Rev. Research 2, 013308, 2020, incorporated herein by reference). Such a quantity essentially depends on the dielectric constant contrast (Δε) of the medium, its size (d) and the wavelength of light (λ), according to the following formula:

number

[0107] When Γ≫1 (strong scattering regime), multiple scattering is very important and, in fact, contributes comparable to the original input field. When Γ≪1 (weak scattering regime), multiple scattering effects are negligible, but when Γ≈1 or slightly greater than 1, multiple scattering effects are not negligible but still represent a second-order correction to the original input field. For typical device sizes (e.g., in the range of 40 nm to several micrometers), it can be shown that scattering at visible wavelengths exhibits values ​​of Γ of the order of 10 or more (i.e., essentially always in the strong scattering regime). On the other hand, at SXR wavelengths, e.g., wavelengths between 2 nm and 50 nm, optionally between 2 nm and 20 nm, Γ is about 1 or slightly higher (e.g., less than 2, less than 1.8, less than 1.5, or less than 1.5, with the lower limit in each case being 0.1, 0.5, 0.8, 0.9, or 1). This is the main difference between the scattering process at SXR wavelengths and at longer wavelengths.

[0108] Additionally, if the target contains layers with a periodic pattern, the target's periodicity in those layers also imposes periodicity on the final field scattered by the target. Because the scattered field is periodic, when it propagates away from the target and reaches the detector, it splits into discrete parts (diffraction orders) propagating along different directions in space. In an SXR metrology tool, it is possible to detect some of these diffraction orders separately (so that, for example, the +1 order is separated from the −1 and / or 2 orders). The combination of multiple scattering and periodic targets leads to the fact that the signal of a particular diffraction order (e.g., 1st order) measured at the detector comes not only from the layer containing the periodic structure, but also from other layers in the stack. How strongly these different layers perturb the main signal coming from the periodic layer depends on whether the multiple scattering is really strong (e.g., from wavelengths in the visible range) or simply strong (e.g., from wavelengths in the SXR range). When using SXR radiation, particularly radiation with wavelengths between 2 nm and 50 nm, optionally between 2 nm and 20 nm, the effect of multiple scattering is present but not so strong that signals received from different parts of the target become too entangled.

[0109] For example, when attempting to retrieve the height of a diffraction grating, these considerations make it possible to ignore the effect of inaccuracies in the thickness of unpatterned layers below the grating (because unpatterned layers below or above the patterned layer can only contribute to the generation of signals in diffraction orders due to multiple scattering). This physical property, in combination with the correct choice of the merit function described below, makes it possible to perform a step-by-step reconstruction of the target, for example starting from the height of the patterned layer (as this is the parameter that determines the largest part of the measured signal).

[0110] As a result of this, when attempting to retrieve the height of a diffraction grating (or a layer containing a diffraction grating), it is possible to first ignore the effects of inaccuracies in other parameters such as CD and / or thickness of other unpatterned layers. This physical property makes it possible to decompose the reconstruction problem as described, for example, to perform a step-by-step reconstruction of the target height / Z position and overlay.

[0111] Another, more general method for reconstructing or determining other parameters of a structure or target object according to the concepts described herein is described. The specific case described in this embodiment is merely an example, and this method can be extended to other use cases. In this embodiment, it is assumed that the structure or target includes a 1D periodic grating on top of a multi-layer stack. In the first step of the reconstruction, at least one vertical position parameter determined is the height of the grating (e.g., the height of one grating feature). This step can be achieved with high accuracy with limited prior knowledge about the target, its underlying stack, and / or its underlying stack. After the height is determined, one or more other parameters can be reconstructed, such as the thickness of the layer below the target and / or the grating CD, depending on the type of target and / or the required accuracy.

[0112] FIG. 11 is a schematic diagram of an exemplary target feature (in resist) on a number of layers. The main parameters of interest describe the shape of the target feature, namely, the feature height hfea, top CD TCD, and bottom CD BCD. Any other geometries present (e.g., layer heights hL1-hL4 and silicon height hSi) can also be determined. The method may include recovering the shape of the target feature by first determining the grating height and then (optionally) determining one or more of the heights hL1-hL4 of layers L1-L4 (e.g., the height hL4 of at least the top layer L4 immediately below the patterned layer). In a further embodiment, layer L4 is immediately above the patterned layer, and the methods described herein are still applicable. This step may be followed by a step of determining the CD TCD, CD BCD of the feature.

[0113] As mentioned above, a simulation model or a forward model can be used (e.g., based on an exact electromagnetic solver). Measured sensor outputs (e.g., diffraction patterns) can be used to set up an optimization scheme that varies only the model grid height hfea until an extremum of a suitable cost function is found. At this stage, no precise prior knowledge of the target is required. All other geometries labeled in FIG. 11 can be roughly estimated. Because the optimization in this step is performed only for a single parameter value, an exhaustive search (e.g., a brute-force approach that sweeps through height values ​​within a given reasonable range until the best match between the simulated and measured diffraction patterns is found) can be used. If no prior knowledge is available, a global optimizer is preferred for height retrieval. Note that the height of a feature actually depends on the location of the top and bottom surfaces of the feature. However, as in the overlay example, the location of the top surface of the feature can be zero by definition.

[0114] Once the grating height value h has been determined, the next parameter to retrieve may be the thickness / height of at least one layer (e.g., the height of the top layer h). In this example, the height of layer L4 (e.g., the bottom anti-reflective coating BARC) layer may be determined in this step.

[0115] Optionally, after performing this step to determine the thickness of layer L4 (and / or other layers), the first step can be repeated to improve the reconstruction of the target height hfea based on the new knowledge of the layer heights. Because the measurement signal is dominated by the target feature parameters, it may be desirable to improve the determination of the target height hfea before moving on to another parameter.

[0116] Once the target height has been determined, at least one other parameter can be determined, such as a substrate surface position parameter, such as at least one dimension of the structure in one or both directions of the substrate surface (e.g., at least one CD). Specifically, in this example, the top CD TCD and bottom CD BCD can then be determined. This is only possible after the height of the grating has been determined with good accuracy. In this step, a forward model as already described can be used, and the height of the feature is fixed to the determined value. Additional other parameters can include one or more of the angle or slope of the structure or part thereof, for example, a sidewall angle, a hole or via angle, a slope angle, a floor slope, or any parameter related to other slopes.

[0117]

[0108] If desired, in a further optimization step, optimization for one or more other layer thicknesses and / or one or more other parameters can be performed. In one embodiment, the further optimization step is to determine one or more model parameters that were not determined in the first optimization step(s) and / or the second optimization step(s).

[0118] The physical reason why this method allows good reconstruction of heights in an initial step is that the shape of the merit function (which is highly nonlinear) is mostly determined by the height value hfea. In other words, the actual locations of the interfaces of the patterned layers dominate the measured signal at the SXR wavelength, and as a result, these interfaces can be determined through a very simple representation of the stack, with all other parameters initialized to estimates that can deviate significantly from the actual values ​​(up to 10% deviation).

[0119]

[0110] The above embodiment can be generalized to a method for reconstructing or optimizing a complex target (or other structure), including the following steps. a) Determine the height of the patterned layer. In this phase, the exact values ​​of CD, the layer thickness of the unpatterned layer, can be set to estimates that do not need to be exact. Height retrieval can be performed quickly because it is a search in 1D space. It can be performed through a wide-area search, a global optimizer using a forward solver based on the first-order Born approximation, or a global optimizer using an exact electromagnetic solver. b) If an anti-reflection coating layer is present, the thickness of the layer is collected. c) Recover the thickness of the other (e.g., thicker) layer. At SXR wavelengths, materials do not exhibit large differences in refractive index. For example, the maximum difference (absolute value) between the dielectric constants of silicon and resist is 0.07, while the maximum absolute value of the dielectric constant of silicon is 1.034. This means that

number

[0120]

[0111] Multiple iterations of these steps a)-d) can be performed, either by iterating the complete method and / or by iterating a subset of these steps, until a desired accuracy is reached.

[0121] Some targets have special characteristics, and are called, for example, pitch-walk or overlay targets. Both overlay and pitch-walk impose strong signatures on the measurement signal, since they break the general symmetry of the system. Therefore, the method for such targets may include an additional step between steps a) and b) of determining the overlay or pitch-walk (if necessary). Of course, as explained for overlay targets, steps c) and d) may also be omitted, since the overlay / pitch-walk are parameters of interest.

[0122] For complex targets (e.g., nanosheets) where substructures exist within the grating height, the target can be reconstructed by first ignoring the presence of substructures and retrieving only the full height of the feature (e.g., fin). After retrieving the height (e.g., step a)) and other layers below it, retrieval of the nanosheet thickness and CD can be performed.

[0123] Regarding optimization steps, these can be based on the use of an appropriate merit function. When using a first-order Born approximation or exact solver for electromagnetic scattering at SXR wavelengths (e.g., based on an integral equation that directly solves the so-called Lippmann-Schwinger equation), it has been observed that the effect of height changes on the measured signal is structurally different from the changes caused by CD changes. Height changes cause a shift in the dominant frequency of the observed signal, with a subsequent shift in the observed signal, in most cases leaving the scale (amplitude) virtually unchanged. In contrast, CD changes cause a shift in the scale (amplitude) of the measured signal in most cases, with a negligible change or subsequent shift in the dominant frequency of the signal. This observation allows the recovery of height values, but not CD, using a merit function that is only sensitive to dominant frequency and lateral shifts. An appropriate merit function with this property can be based, for example, on the degree of correlation between two signals, such as the measured signal / diffraction pattern and the simulated signal / diffraction pattern, which can be determined as the normalized dot product between the two signals. When determining the CD, a different merit function can be used that is sensitive to the CD (i.e., sensitive to scale / amplitude) and has little sensitivity to height (i.e., low or negligible sensitivity to dominant frequencies and their shifts).

[0124]

[0115] In this way, a merit function for a particular step of the method can be selected based on the parameters determined at that particular step of the method. In this way, different merit functions can be selected for different parameters, ideally such that the merit function selected is only sensitive to changes in the particular parameter being optimized (at that particular step), and less sensitive to other parameters.

[0125] A merit function that is primarily sensitive to shift or frequency changes but insensitive to scaling will primarily favor height changes (changes in the z-direction or vertical position parameter). This choice of merit function can potentially reduce the number of iterations the optimizer needs to achieve a successful reconstruction.

[0126]

[0117] Thus, the merit function used for each optimization in one or more first optimization steps may include high and / or maximized sensitivity to the dominant frequencies and lateral shifts of the measured metrology data and / or simulated metrology data, and low and / or minimized sensitivity to the scale of the measured metrology data and / or simulated metrology data.

[0127]

[0118] Similarly, the merit function used for each optimization in one or more second optimization steps may include high and / or maximized sensitivity to the scale of the measured metrology data and / or simulated metrology data and low and / or minimized sensitivity to the dominant frequencies and lateral shifts of the measured metrology data and / or simulated metrology data.

[0128] In one embodiment, one or more of the optimization steps can be regularized, for example, by adding a regularization term to one or more of the merit functions used. By adding a regularization term to the merit function, an N-dimensional problem can be automatically decomposed into multiple subproblems, and layers can be swept from top to bottom as the number of iterations increases. The purpose of this regularization is to automate the recovery strategy described above. For example, the regularization term R can be defined as

number

number

[0129]

[0120] While this regularization represents a particular case, any regularization added to the value of the parameter p as a parameter space constraint, a penalty term, or a physical constraint is within the scope of this disclosure. Also, any method of estimating such regularization hyperparameters by preprocessing or iterative methods is within the scope of this disclosure.

[0130] It has been proposed to reconstruct complex geometries by comparing measurements with simulations. This requires a rough model of the target (which in the proposed approach is defined initially and improved at each optimization step of the reconstruction process) and an electromagnetic solver. Exact electromagnetic solvers can be time-consuming. On the other hand, models based on a simpler description of the physical interaction between the probe and the target are less accurate but can be faster.

[0131]

[0122] The forward model has been described primarily in terms of approximating a solver based on the Born approximation, in which multiple scattering effects are ignored. As explained above, single scattering events contribute most of the time to the signal coming from the height of the patterned layer. This means that for this height parameter (which contributes to the strongest component of the measured signal), the rigorous and time-consuming Maxwell solver can be replaced with a simpler Born approximation solver. Since the shape of the merit function is expected to be approximately defined by the height of the patterned layer, and that height is approximately encoded in the first scattering event, it can be expected that a good estimate of the height can be obtained using such a simple solver. More generally, the accuracy (and complexity) of the Maxwell solver can be adapted to the current parameters of interest.

[0132]

[0123] Thus, any suitable electromagnetic solver (also called an exact solver) can be used. Electromagnetic solvers differ in the way they solve Maxwell's equations and the use cases for which they are suitable. For example, rigorous coupled wave analysis (RCWA) can be used to solve Maxwell's equations for periodic structures, and uses the expansion of fields and permittivity in Fourier series. Other solvers use numerical methods such as the finite element method (FEM) or modal methods (e.g., finite-domain time-domain FDTD).

[0133] In one embodiment, it is proposed to use a solver that solves Maxwell's equations in integral form (essentially what are called vector Lippmann-Schwinger equations), but in principle any solver can be used, as it does not affect the results of the method disclosed herein, only the speed of the reconstruction and its numerical accuracy.

[0134] Another aspect that can be configured is the optimizer to use. Depending on the goal of a particular optimization step, a different optimizer can be selected to improve that step in terms of speed and / or accuracy. The optimizer can be a local optimizer or a global optimizer. An example of a global optimizer is a Bayesian optimizer.

[0135] A common choice is an optimizer based on the Levenberg-Marquardt algorithm. Depending on the stepwise reconstruction strategy, particularly the objective of the step, the choice of optimizer can improve the reconstruction. For example, during one of the first reconstruction steps, if there is uncertainty about the initial estimates or intervals of certain parameters of interest, the landscape is likely not a convex landscape. This part of the reconstruction strategy narrows the landscape to an interval that contains a convex region. Therefore, a global optimizer, such as a Bayesian optimizer (see below), can be used to explore the landscape. Global optimization in a limited 1D space is still a relatively fast operation. In later phases of the reconstruction strategy, if the parameters of interest are bounded and a convex problem is defined, local optimizers can be used to accurately reconstruct the parameters of interest.

[0136]

[0127] As mentioned above, to reduce the computation time, it is optionally proposed to replace the exhaustive search for the optimum with an adaptive sampling of the merit function based on Bayesian optimization. An important prerequisite for the convergence of both methods is the existence of a unique global extremum (i.e., the absence of swing curve behavior), which has been observed to be true for all models when the sweep range is below the pitch size of the structure. Bayesian optimization uses a global optimizer (Bayesian optimizer) to find the global optimum (minimum or maximum) of the merit function. The optimizer can operate as follows: 1) First, the merit function is computed for a small number of values ​​of the parameters collected in that step (e.g., initial guesses), so that the merit function has a global minimum sampled at the selected parameters. 2) The merit function is modeled as a Gaussian process, and the few values ​​measured in step 1) are used to determine the next point in parameter space where it is most convenient to observe the value of the merit function. This is determined by choosing values ​​that increase the level of information about the shape of the function. 3) Based on step 2), the merit function is updated with the new observed values. Steps 2) and 3) are repeated until a global minimum is found.

[0137] In many of the above embodiments, the optimization sequence, which describes which parameter subsets or subspaces to optimize in each optimization step and in what order, is determined using physical intuition. This means that the method is user-dependent and requires the experience of the metrology engineers involved. While generally applicable guidance is described above, e.g., optimizing height / vertical model parameters first in one or more optimization steps, followed by other model parameters, the optimal order is not always obvious. For example, for complex geometries, determining the appropriate optimization sequence can be difficult. Even for relatively simple geometries, better performance can be obtained by optimizing certain “other model parameters,” such as CD, in one of the first optimizations (e.g., co-optimizing with vertical model parameters or otherwise) and / or optimizing the vertical model parameters in a specific order.

[0138] To address this, we consider the N-dimensional reconstruction problem as M L M dimension (where Σ M L M A method for determining the optimal sequence is proposed that automatically decomposes the reconstruction problem into a sequence of N (N or more).

[0139] 12(a) is a flowchart illustrating a method for determining an optimization sequence according to an embodiment, which may determine the optimization sequence based on computation of covariance and correlation matrices of model parameters (e.g., based on initial values ​​of these model parameters) and determined derivatives with respect to these model parameters (e.g., in the case of a linear approximation).

[0140] Step 1200 may include determining the covariance and correlation matrices. This step can be decomposed into substeps as shown in FIG. 12(b). In step 1201, the derivatives can be determined, for example, using a simulation model or a forward model as described above. For example, to calculate the derivatives with respect to selected model parameters ("or parameters of interest (POI)"), one simulates a signal signal(POI) obtained with a structure defined by the initial values ​​of the model parameters, and a signal signal(POI+Δε) after introducing a small variation Δε of the selected model parameters (for example, in the range of less than 100 pm or 50 pm). The derivative J with respect to the parameter of interest POI is POI can be obtained using forward numerical differentiation.

number

number

[0141] Another alternative is to use automatic differentiation or any kernel-based method in the computational model to calculate the derivatives (e.g., J=h * signal) can be used.

[0142] In step 1202, these derivatives can be determined for each model parameter and then stacked into a matrix J (Jacobian), for example, with dimensions defined by the number of model parameters times the number of pixels.

[0143]

[0134] Then, for example,

number

[0144] In step 1204, the correlation matrix C is converted from the covariance matrix by rescaling, for example, according to the following equation: cor,ij can be obtained.

number

[0145] Once the correlation and covariance matrices have been computed, they can be used to divide the model parameters into subsets (subspaces), for example, by performing steps 1210-1280.

[0146] Step 1210 may include determining measurement repeatability metric data for the model parameters, taking into account noise introduced into the model. For example, this measurement repeatability metric data may be determined from the diagonal elements of a covariance matrix, where these diagonal elements correspond to measurement repeatability.

[0147] In step 1220, the repeatability of each model parameter can be scaled using a characteristic quantity for that model parameter. Good candidates for the characteristic quantity are variations due to the manufacturing process and / or specific target values ​​for the manufacturing process. Both the unscaled repeatability determined in step 1210 and the rescaled repeatability determined in this step are examples of measurement repeatability metrics.

[0148] In step 1230, the model parameters may be ordered or ranked according to the rescaled repeatability determined in step 1220 to obtain ranked model parameters. Model parameters with low rescaled repeatability tend to have low associated noise and high variability. These model parameters may tend to be vertical model parameters, such as the height of a structure.

[0149]

[0140] In step 1240, a regularization technique can be applied to deal with model parameters with high rescaled reproducibility, since the problem becomes ill-conditioned when the rescaled reproducibility is high. Different regularization techniques can also mitigate or solve this problem. A proposed regularization technique may involve filtering out all model parameters with high rescaled reproducibility. This is a specific example of a regularization technique (space restriction), but any suitable modern regularization technique can be used. For example, an appropriate rescaled reproducibility threshold or reproducibility metric threshold can be used to split the model parameters into high rescaled reproducibility and low rescaled reproducibility parts of the model.

[0150] In step 1250, among the remaining model parameters (e.g., those with a reproducibility metric value below the reproducibility metric threshold), the model parameter with the lowest associated reproducibility metric (e.g., rescaled reproducibility) can be selected, and correlations between this selected model parameter and the other model parameters can be considered, e.g., using the correlation matrix determined in step 1200. The correlation threshold C trheshold Any other model parameters having a correlation value or correlation coefficient higher than can be grouped together with the selected model parameter. In this way, a first group (i.e., the model parameter with the lowest reproducibility metric value and any correlated parameters grouped with it) can be defined and used as a first optimized subset of model parameters (i.e., the first subset of model parameters to be optimized).

[0151] In step 1260, it is determined whether there are any more model parameters that have not yet been assigned a group. If so, the model parameter with the next lowest associated reproducibility metric is selected, and step 1250 is repeated to determine the next optimized subset of model parameters. This is repeated until all model parameters (e.g., excluding those excluded in step 1240) have been grouped.

[0152]

[0143] In step 1270, the structure may be reconstructed according to the determined optimization sequence.

[0153] The above method can be interpreted in a more rigorous way in a Bayesian framework (e.g., as already described) using prior and posterior distributions. In such an embodiment, the characteristic quantities used in step 1220 can be interpreted as prior uncertainties, and the reproducibility metric may account for the variance of the likelihood distribution. This formalism allows for a rigorous analytical interpretation of the regularization described in step 1240.

[0154]

[0145] The covariance and correlation matrices can optionally be recomputed to a space more suitable for reconstruction, for example, new subspaces can be determined via diagonalization of the covariance and correlation matrices. These new subspaces may contain linear combinations of model parameters that are less correlated with each other.

[0155]

[0146] Step 1250 describes a particular algorithm for determining the connectivity of a graph. This is just an example of a method, and any suitable method for determining the connectivity of a matrix can be used, including graph-based methods.

[0156]

[0147] Although the above method only considers the problem model parameters, other quantities can be added to the problem if they are important for reconstruction. For example, if a parameter of the sensor model is important for target reconstruction, but its calibration is not accurate enough, this parameter can be designated as a model parameter and included in the procedure, thereby relaxing the specification of the parameter calibration.

[0157] This embodiment deals with crosstalk between model parameters using a linear approximation. This can be extended to consider nonlinear crosstalk, which can be quantified and used in the method in any suitable way (e.g., computing a Hessian or sampling the entire parameter space to recover crosstalk between model parameters).

[0158]

[0149] A specific example thereof will be described with reference to Figure 13. A structure can be described by ten model parameters, including four vertical model parameters or heights H1, H2, H3, H4, an over-etch model parameter OE, and five CD model parameters CD1, CD2, CD3, CD4, CD5. Figure 13(a) shows the reproducibility value REP for each of these model parameters, e.g., as described by the diagonal of the covariance matrix. Figure 13(b) shows the correlation matrix for these model parameters. An exemplary correlation threshold C trheshold Assuming that is 0.3, the model parameters can be grouped and ordered into the optimization sequence shown in Fig. 13(c), where each box contains one or more model parameters to be optimized at each optimization step.

[0159]

[0150] Naturally, the model parameters that should be optimized first include height. However, this method also informs us that parameter CD1 should be optimized early (i.e., in combination with parameter H2), capturing the importance of the correlation between these two parameters. Reconstructing these parameters separately would result in a reconstruction error on the order of the (relatively high) sensitivity of CD1 to H2, so taking this correlation into account is believed to be fundamental to successful reconstruction. Similarly, this method also informs us that parameter CD4 should be optimized together with parameter H4.

[0160]

[0151] Embodiments may include a computer program including one or more sequences of machine-readable instructions describing a method of optical metrology and / or a method of analyzing measurements to obtain information about a lithography process. Embodiments may include computer code including one or more sequences of machine-readable instructions or data describing a method. This computer program or code may be executed, for example, in unit MPU of the apparatus of FIG. 6 and / or in control unit CL of FIG. 3. A data storage medium (e.g., semiconductor memory, magnetic disk, optical disk, etc.) having such a computer program or code stored therein may also be provided. For example, where an existing metrology apparatus of the type shown in FIG. 6 is already in production and / or in use, embodiments of the present invention may be implemented by providing an updated computer program product for causing a processor to perform one or more of the methods described herein. The computer program or code may optionally be arranged to control optics, a substrate support, and the like to perform a method of measuring parameters of a lithography process on a suitable plurality of targets. The computer program or code may update the lithography and / or metrology recipe for measurements of additional substrates. The computer program or code can be arranged to control (directly or indirectly) a lithographic apparatus to pattern and process further substrates.

[0161]

[0152] The above embodiments have one or more advantages over currently existing model-based methods, including: The first step of determining parameters related to the Z direction, e.g., stack thickness, can be performed with high accuracy and limited prior knowledge. Instead of having to optimize all parameters simultaneously, the optimization process can be greatly simplified by breaking the problem down into a series of lower-dimensional problems, each of which can be solved independently. Can be implemented directly on the device, e.g. for OVL measurements.

[0162]

[0153] The illumination source may be provided to, for example, a metrology apparatus MT, an inspection apparatus, a lithography apparatus LA, and / or a lithography cell LC.

[0163]

[0154] The characteristics of the emitted radiation used to perform a measurement can affect the quality of the measurement obtained. For example, the shape and size of the transverse beam profile (cross-section) of the radiation beam, the intensity of the radiation, the power spectral density of the radiation, etc. can affect the measurement performed by the radiation. Therefore, it is beneficial to have a radiation source that provides radiation with characteristics that result in high quality measurements.

[0164]

[0155] Further embodiments are disclosed in the following numbered clauses. 1. A method for determining at least one parameter of interest associated with a structure formed in at least one respective layer on a substrate, comprising: obtaining metrology data relating to measurements of the structure; obtaining a model, the model describing the structure with a plurality of model parameters, the model parameters including estimates; performing a plurality of optimization steps in sequence based on the measured metrology data to determine a plurality of model parameters, each of the plurality of optimization steps determining a subset of the plurality of model parameters; A method comprising: 2. The step of executing multiple optimization steps in sequence is performing one or more first optimization steps using measured metrology data to determine one or more vertical position parameters of the model parameters; performing, following the performance of the one or more first optimization steps, one or more second optimization steps using the measured metrology data and a model having the one or more vertical position parameters determined in the one or more first optimization steps to determine one or more other model parameters of the plurality of model parameters, wherein the one or more other model parameters are different from the one or more vertical position parameters; 2. The method according to clause 1, comprising: 3. The method of clause 2, wherein the step of performing one or more first optimization steps optimizes only one or more vertical position parameters. 4. The method of clause 2 or 3, comprising performing one or more first optimization steps, respectively, with the model parameters fixed except for one or more vertical position parameters to be optimized. 5. A method according to any one of clauses 2 to 4, wherein the one or more other parameters determined in the one or more second optimization steps include one or more substrate surface position parameters of the model parameters, the one or more substrate surface position parameters being related to one or both directions of the substrate surface. 6. The method of any one of clauses 2 to 5, comprising performing one or more second optimization steps, respectively, with the model parameters fixed, except for one or more other parameters determined in the one or more second optimization steps, such that one or more vertical position parameters are fixed to values ​​determined in the one or more first optimization steps. 7. The method of any one of clauses 2 to 6, wherein each optimization step of the one or more first optimization steps and the one or more second optimization steps comprises comparing measured metrology data with simulated metrology data obtained by simulating measurements of a structure defined by the model. 8. The method of clause 7, wherein each optimization step includes maximizing the similarity between the measured metrology data and the simulated metrology data. 9. The method of clause 7 or 8, wherein the simulation uses a simulation model operable to simulate electromagnetic interactions between the incident field, the structure defined by the model and the sensor configuration. 10. The method of clause 9, wherein the sensor configuration is based on the physical sensor configuration used to obtain the measured metrology data. 11. The method of clause 9 or 10, wherein the simulation model comprises a forward model. 12. The method according to any one of clauses 9 to 11, wherein the simulation model is based on the Born approximation and / or an exact solver. 13. The method of any one of clauses 7 to 12, wherein each optimization step uses a respective merit function. 14. The method of clause 13, comprising selecting a merit function for each optimization step based on the model parameters optimized in that optimization step. 15. The method of clause 13 or 14, wherein the merit function used for each optimization in the one or more first optimization steps comprises high and / or maximized sensitivity to dominant frequencies and lateral shifts of the measured metrology data and / or simulated metrology data, and low and / or minimized sensitivity to scale of the measured metrology data and / or simulated metrology data. 16. The method of any one of clauses 13 to 15, wherein the merit function used for each optimization in the one or more first optimization steps is based on the degree of correlation between the measured metrology data and the simulated metrology data. 17. The method of any one of clauses 13 to 16, wherein the merit function used for each optimization in the one or more second optimization steps comprises a high and / or maximized sensitivity to scale of the measured metrology data and / or simulated metrology data, and a low and / or minimized sensitivity to dominant frequencies and lateral shifts of the measured metrology data and / or simulated metrology data. 18. A method according to any one of clauses 13 to 17, comprising selecting an optimizer for one or more of the optimization steps depending on the purpose of the optimization step. 19. The method of any one of clauses 13 to 18, wherein one or more of the optimization steps uses an optimizer based on the Levenberg-Marquardt algorithm. 20. The method of any one of clauses 13 to 19, wherein one or more of the optimization steps comprises adaptive sampling of the merit function based on Bayesian optimization. 21. The method of any one of clauses 13 to 20, comprising regularizing one or more of the optimization steps by applying at least one regularization term to one or more of the merit functions. 22. The method of clause 21, wherein at least one regularization term penalizes variations in model parameters being optimized outside a certain window in terms of number of iterations. 23. The method of any one of clauses 7-22, wherein the measured metrology data and the simulated metrology data each include diffraction pattern intensity or amplitude data. 24. The structure includes an overlay target including substructures in each of two or more patterned layers; the one or more vertical position parameters include at least a respective position of each undefined interface of the two patterned layers; 24. The method of any one of clauses 2 to 23, wherein the one or more other parameters determined in the one or more second optimization steps include overlay in one or both directions of the substrate surface. 25. The method of clause 24, wherein the undefined interfaces include all interfaces of two or more patterned layers other than the top interface, such that the undefined interfaces are determined relative to the top interface. 26. The one or more vertical position parameters include a height of the structure; 24. The method of any one of clauses 2 to 23, wherein the one or more other parameters determined in the one or more second optimization steps include at least one dimension of the structure in one or both directions in the plane of the substrate. 27. The method of clause 26, wherein the one or more other parameters determined in the one or more second optimization steps include at least one critical dimension of a feature of the structure. 28. The method of clause 26 or 27, wherein the one or more other parameters determined in the one or more second optimization steps include an upper critical dimension at an upper part of the feature and a lower critical dimension at a lower part of the feature. 29. The method of any one of clauses 26 to 28, wherein the one or more other parameters determined in the one or more second optimization steps include one or more of the sidewall angle of any wall of the structure, a measure of the slope of a floor of the structure and / or a measure of any other slope of the structure. 30. The method of any one of clauses 26-29, wherein the one or more vertical position parameters further include the height of one or more layers below or above the structure. 31. Performing one or more first optimization steps comprises: determining the height of the structure; determining the height of one or more stories immediately below or above the structure; repeating the step of determining a height of the structure using the determined heights of one or more layers immediately below or above the structure; 31. The method of clause 30, comprising: 32. The method of any one of clauses 2 to 31, comprising performing one or more further optimization steps to determine one or more model parameters not determined in the one or more first optimization steps and / or the one or more second optimization steps. 33. A method according to any one of the preceding clauses, including an initial step of determining an optimization sequence describing a sequence of a plurality of optimization steps. 34. Determining a measurement repeatability metric for each of the model parameters or a subset thereof in the presence of noise; Determining the optimized sequence from the measurement repeatability metric 34. The method of claim 33, comprising: 35. Determining a covariance matrix that describes the covariance of the model parameters in the presence of noise; determining a measurement repeatability metric for each of the model parameters from the diagonal of the covariance matrix; 35. The method of claim 34, comprising: 36. Determining the derivative with respect to each model parameter; Determining the covariance matrix from the derivatives and 36. The method of claim 35, comprising: 37. The method of any one of clauses 34 to 36, comprising ranking the model parameters according to a measurement repeatability metric to obtain ranked model parameters. 38. The method of clause 37, comprising applying regularization to model parameters with a high measurement repeatability metric. 39. The method of clause 38, wherein the regularization includes excluding from the ranking those model parameters that have a high measurement repeatability metric. 40. Selecting the model parameters with the lowest measurement repeatability metric; determining a correlation value between the selected model parameter and the other ranked model parameters; grouping the model parameters having a correlation value above a correlation threshold together with the selected model parameters to obtain a group of model parameters; repeating these steps until all ranked model parameters have been grouped, the optimization sequence including groups ordered according to the measurement repeatability metric of each selected model parameter in each group; 39. The method of any one of clauses 37 to 39, comprising: 41. The method of clause 40, comprising determining a correlation matrix from a covariance matrix. 42. The method of any one of the preceding clauses, wherein the measurement metrology data is obtained using measurement illumination having a wavelength less than 100 nm. 43. The method of any one of the preceding clauses, wherein the measurement metrology data is obtained using measurement illumination having a wavelength less than 50 nm. 44. The method of clause 43, wherein the measurement metrology data is obtained using measurement illumination including wavelengths between 2 nm and 50 nm. 45. The method of any one of clauses 1 to 43, wherein the measurement metrology data is obtained using measurement illumination having a wavelength less than 20 nm. 46. ​​The method of any one of the preceding clauses, wherein the measurement metrology data is obtained using measurement illumination including wavelengths between 2 nm and 20 nm. 47. The method of any one of the preceding clauses, wherein the number of optimization steps among the plurality of optimization steps comprises a number that is less than the number of model parameters among the plurality of model parameters. 48. A method according to any one of the preceding clauses, comprising performing measurements of the structure to obtain measured metrology data. 49. A computer program comprising program instructions operable to carry out the method according to any one of the preceding clauses when the computer program is run on a suitable device. 50. A non-transitory computer program carrier containing a computer program as referred to in clause 49. 51. A computer program carrier containing a computer program according to clause 50; a processor operable to execute a computer program; , including, a processing arrangement. 52. A metrology device comprising a processing arrangement according to clause 51. 53. A metrology device operable to perform the method described in clause 48. 54. A metrology device according to clause 52 or 53, comprising a scatterometer.

[0165]

[0156] Although specific reference is made in this specification to uses of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include the manufacture of integrated optics, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc.

[0166] Although embodiments may be specifically referenced herein in connection with a lithography apparatus, the embodiments may be used in other apparatus. The embodiments may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes objects such as wafers (or other substrates) or masks (or other patterning devices). These apparatus may collectively be referred to as lithography tools. Such lithography tools may use vacuum conditions or ambient (non-vacuum) conditions.

[0167] Although specific reference may be made in this specification to embodiments in the context of an inspection or metrology apparatus, the embodiments may be used in other apparatus. The embodiments may form part of a mask inspection apparatus, a lithography apparatus, or any apparatus that measures or processes objects, such as wafers (or other substrates) or masks (or other patterning devices). The term "metrology apparatus" (or "inspection apparatus") may also refer to an inspection apparatus or inspection system (or metrology apparatus or metrology system). For example, an inspection apparatus including embodiments may be used to detect defects in a substrate or in structures on a substrate. In such embodiments, the property of interest of a structure on a substrate may relate to a defect in the structure, the absence of a particular portion of the structure, or the presence of an unwanted structure on the substrate.

[0168]

[0159] Although specific reference may be made above to the use of embodiments in the context of optical lithography, it will be appreciated that the invention is not limited to optical lithography and may be used in other applications, such as, for example, imprint lithography, where the context permits.

[0169] While the targets or target structures (more generally, structures on a substrate) described above are metrology target structures specifically designed and formed for measurement purposes, in other embodiments, properties of interest may be measured in one or more structures that are functional parts of a device formed on a substrate. Many devices have regular, grating-like structures. The terms structure, target grating, and target structure, as used herein, do not require that the structure be specifically provided for the measurement being performed. Furthermore, the pitch of the metrology target may be near or smaller than the resolution limit of the scatterometer's optical system, but may be much larger than the dimensions of typical non-target structures (optionally, product structures) generated by a lithographic process in target portion C. In practice, the lines and / or spaces of the overlay grating in the target structure may be generated to include smaller features similar in dimension to the non-target structures.

[0170]

[0161] While specific embodiments have been described above, it will be understood that the invention can be practiced otherwise than as described. The above description is intended to be illustrative, not limiting. Accordingly, it will be apparent to those skilled in the art that modifications can be made to the invention as described without departing from the scope of the claims set forth below.

[0171] Although specific reference is made to a "metrology apparatus / tool / system" or an "inspection apparatus / tool / system," these terms may refer to the same or similar types of tools, apparatus, or systems. For example, an inspection or metrology apparatus incorporating embodiments of the present invention may be used to determine characteristics of structures on a substrate or wafer. For example, an inspection or metrology apparatus incorporating embodiments of the present invention may be used to detect defects in the substrate or in structures on the substrate or wafer. In such embodiments, the characteristic of interest in the structure on the substrate may relate to a defect in the structure, the absence of a particular portion of the structure, or the presence of an unwanted structure on the substrate or wafer.

[0172]

[0163] Although specific reference is made to SXR electromagnetic radiation, it will be understood that the invention can be practiced using all electromagnetic radiation, including radio waves, microwaves, infrared, (visible) light, ultraviolet, EUV, HXR, and gamma rays, where the context permits.

[0173]

[0164] Although specific embodiments have been described above, it will be understood that one or more features of one embodiment may also be present in a different embodiment, or that features of two or more different embodiments may be combined.

Claims

1. 1. A method for determining at least one parameter of interest associated with a structure formed in at least one respective layer on a substrate, the method comprising: obtaining metrology data relating to measurements of the structure; obtaining a model, the model describing the structure with a plurality of model parameters, the model parameters including estimates; performing a plurality of optimization steps in sequence based on the measured metrology data to determine the plurality of model parameters, each of the plurality of optimization steps determining a subset of the plurality of model parameters; A method comprising:

2. said step of sequentially performing a plurality of optimization steps comprising: performing one or more first optimization steps using the measured metrology data to determine one or more vertical position parameters of the model parameters; performing, following the performance of the one or more first optimization steps, one or more second optimization steps using the measured metrology data and the model having the one or more vertical position parameters determined in the one or more first optimization steps to determine one or more other model parameters of the plurality of model parameters, wherein the one or more other model parameters are different from the one or more vertical position parameters; The method of claim 1 , comprising:

3. 3. The method of claim 2, comprising performing each of the one or more first optimization steps with the model parameters fixed except for the one or more vertical position parameters that are optimized.

4. 4. The method of claim 2 or 3, wherein the one or more other parameters determined in the one or more second optimization steps comprise one or more substrate surface position parameters of the model parameters, the one or more substrate surface position parameters being related to one or both directions in the substrate surface.

5. 5. The method according to claim 2, comprising performing each of the one or more second optimization steps with the model parameters fixed, except for the one or more other parameters determined in the one or more second optimization steps.

6. 6. The method of claim 2, wherein each optimization step of the one or more first optimization steps and the one or more second optimization steps comprises comparing the measured metrology data with simulated metrology data obtained by simulating measurements of the structure defined by the model.

7. 7. The method of claim 6, wherein the simulation uses a simulation model operable to simulate electromagnetic interactions between an incident field, the structure defined by the model, and a sensor configuration, optionally based on a physical sensor configuration used to obtain the measured metrology data.

8. The method of claim 7 , wherein the simulation model comprises a forward model.

9. The method according to claim 7 or 8, wherein the simulation model is based on the Born approximation and / or an exact solver.

10. the one or more vertical position parameters include a height of the structure; 10. The method of claim 2, wherein the one or more other parameters determined in the one or more second optimization steps comprise at least one dimension of the structure in one or both directions in the substrate plane.

11. 11. The method according to any one of claims 2 to 10, comprising performing one or more further optimization steps to determine one or more of the model parameters that were not determined in the one or more first optimization steps and / or the one or more second optimization steps.

12. 12. The method of any one of claims 1 to 11, wherein the measured metrology data is obtained using measurement illumination comprising illumination at a wavelength between 2 nm and 50 nm, optionally between 2 nm and 20 nm.

13. The method according to any one of claims 1 to 12, wherein the number of optimization steps in the plurality of optimization steps comprises a number that is less than the number of model parameters in the plurality of model parameters.

14. A computer program comprising program instructions operable to perform the method of any one of claims 1 to 13 when said computer program is run on a suitable device.

15. A metrology device operable to perform the method according to any one of claims 1 to 13.

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