Method for correcting measurements in the manufacture of integrated circuits and associated equipment

Abstract

A metrology method is disclosed. The method includes: irradiating radiation onto a substrate; obtaining measurement data associated with at least one measurement value of each of one or more structures on the substrate; transforming the measurement data into transformed measurement data using a Fourier correlation transform; and extracting a characteristic of the substrate or eliminating the influence of an interfering parameter from the transformed measurement data.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to EP application 19217327.6 filed on December 18, 2019, EP application 20151585.5 filed on January 14, 2020, EP application 20157947.1 filed on February 18, 2020, and EP application 20174105.5 filed on May 12, 2020, which are incorporated herein by reference in their entirety. Technical Field

[0003] The present invention relates to metrology applications in the manufacture of integrated circuits. Background Art

[0004] A lithographic apparatus is a machine configured to apply a desired pattern to a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus can project a pattern (often also referred to as a "design layout" or "design"), for example, at a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) disposed on a substrate (e.g., a wafer).

[0005] In order to project a pattern onto a substrate, a lithographic apparatus can use electromagnetic radiation. The wavelength of this radiation determines the minimum size of a feature that can be formed on the substrate. Typical wavelengths currently used are 365nm (i-line), 248nm, 193nm, and 13.5nm. Compared to lithographic apparatuses using, for example, radiation with a wavelength of 193nm, lithographic apparatuses using extreme ultraviolet (EUV) radiation with a wavelength in the range of 4 to 20nm (e.g., 6.7nm or 13.5nm) can be used to form smaller features on a substrate.

[0006] Low k1 lithography can be used to process features with dimensions smaller than the classical resolution limit of the lithographic apparatus. In such a process, the resolution formula can be expressed as CD=k1×λ / NA, where λ is the wavelength of the radiation employed, NA is the numerical aperture of the projection optics in the lithographic apparatus, CD is the “critical dimension” (usually the minimum feature size printed, but in this case it is half the pitch), and k1 is an empirical resolution factor. In general, the smaller k1 is, the more difficult it is to reproduce a pattern on the substrate that is similar in shape and size to that planned by the circuit designer in order to achieve specific electrical functionality and performance. To overcome these difficulties, complex fine-tuning steps can be applied to the lithographic projection apparatus and / or the design layout. For example, these include, but are not limited to, optimization of the NA, customized illumination schemes, use of phase-shifting patterning devices, various optimizations of the design layout such as optical proximity correction (OPC, sometimes also referred to as “optical process correction”) in the design layout, or other methods generally defined as “resolution enhancement techniques” (RET). Alternatively, a tight control loop for controlling the stability of the lithographic apparatus can be used to improve the reproduction of patterns at low k1.

[0007] During photolithography, it is desirable to frequently measure the structures being created, for example, for process control and verification. Various tools are known for making such measurements, including scanning electron microscopes (commonly used to measure critical dimensions (CDs)) and specialized tools for measuring the overlay, or alignment accuracy, of two layers in a device. More recently, various forms of scatterometers have been developed for use in the field of photolithography.

[0008] Examples of known scatterometers typically rely on providing a dedicated measurement target. For example, one approach might require a target in the form of a simple grating, large enough to generate a measurement beam with a spot size smaller than the grating (i.e., the grating is underfilled). In so-called reconstruction methods, the properties of the grating can be calculated by simulating the interaction of the 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 an actual target.

[0009] In addition to measuring feature shapes by reconstruction, diffraction-based overlay can also be measured using such equipment, as described in published patent application US2006066855A1. Diffraction-based overlay measurement using dark field imaging of diffraction orders allows overlay measurements to be made on smaller targets. These targets can be smaller than the illumination spot and can be surrounded by product structures on the wafer. Examples of dark field imaging measurements can be found in many published patent applications, such as, for example, US2011102753A1 and US20120044470A. Multiple gratings can be measured in one image using a composite grating target. Known scatterometers tend to use light in the visible or near IR wave range, which requires the pitch of the grating to be much coarser than the actual product structure whose properties are of actual interest. Such product features can be defined using deep ultraviolet (DUV), extreme ultraviolet (EUV) or X-ray radiation with shorter wavelengths. Unfortunately, such wavelengths are often not available or cannot be used for measurement.

[0010] On the other hand, the dimensions of modern product structures are so small that they cannot be imaged using optical metrology techniques. Small features include, for example, those formed by multiple patterning processes and / or pitch multiplication. Therefore, targets for high-volume metrology typically use features that are much larger than the product where overlay error or critical dimensions are the properties of interest. The measurements are only indirectly related to the dimensions of the actual product structure and may not be accurate because the measurement target does not suffer the same distortion under optical projection in lithography and / or different processing in other steps of the manufacturing process. Although scanning electron microscopes (SEMs) can directly resolve these modern product structures, SEMs are more time-consuming than optical measurements. Moreover, electrons cannot penetrate thicker process layers, which makes them less suitable for metrology applications. Other techniques (such as measuring electrical properties using contact pads) are also known, but they only provide indirect evidence of the actual product structure.

[0011] By reducing the wavelength of radiation used during metrology (i.e., shifting towards "soft X-ray (SXR)" wavelengths spectrum), smaller structures can be resolved to increase sensitivity to structural changes in the structure and / or to penetrate further into the product structure. One such method of generating suitable high-frequency radiation (e.g., soft X-rays and / or EUV radiation) can be to use pump radiation (e.g., infrared radiation) to excite the generating medium, thereby generating emitted radiation, optionally including the generation of higher-order harmonics of the high-frequency radiation.

[0012] It is desirable to eliminate or mitigate signal effects due to variations in drifting parameters, i.e., parameters that have drifted from assumed, nominal, and / or designed values. Such drifting parameters may include, for example, detector position, illumination polar angle (incident and azimuth angles), and layer thickness of one or more substrate layers. Summary of the Invention

[0013] In a first aspect of the present invention, a metrology method is provided, comprising: obtaining measurement data associated with at least one measurement value for each of one or more structures on a substrate; the measurement data being dependent on one or more drift parameters, the drift parameters including at least one interdependent drift parameter for each measurement value being dependent on a structure response metric, the structure response metric varying interdependently with an illumination setting and the at least one interdependent drift parameter; and correcting the measurement data based on an approximately invariant transformation of the structure response metric or a related metric.

[0014] In a second aspect of the invention, a method for inferring a value of a parameter of interest from measurement data is provided, comprising: obtaining the measurement data, the measurement data being associated with scattered radiation from a target captured on a detector; obtaining a trained forward model describing the measurement signal in terms of at least one parameter comprising a term of interest describing a periodic response of the parameter of interest of the target, one or more nuisance terms describing other variations between measured values ​​of the target, and a constant term representing a constant component of the measurement data; and inferring the value of the parameter of interest from the measurement data using the trained forward model.

[0015] Also disclosed are a computer program, a metrology apparatus and a lithographic apparatus operable to perform the method of the first aspect or the second aspect.

[0016] The above and other aspects of the invention will be understood by considering the following examples. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Embodiments will now be described, by way of example only, with reference to the accompanying schematic drawings, in which:

[0018] - Figure 1 depicts a schematic overview of a lithographic apparatus;

[0019] - Figure 2 A schematic overview of a lithography cell is depicted;

[0020] - Figure 3 Depicted is a schematic representation of overall lithography, showing the collaboration between three key technologies to optimize semiconductor manufacturing;

[0021] - Figure 4 schematically illustrates a scatterometry device;

[0022] - Figure 5 depicts a schematic representation of a metrology apparatus in which EUV and / or SXR radiation is used;

[0023] - Figure 6 Depicts a simplified schematic diagram of an illumination source that might be used for, e.g. Figure 5Irradiation source generated by high-order harmonics of the measurement equipment shown;

[0024] - Figure 7 including (a) a schematic diagram of a dark-field scatterometer for measuring a target according to an embodiment of the present invention using a first pair of illumination apertures, (b) details of a diffraction spectrum of a target grating given an illumination direction, (c) a second pair of illumination apertures providing a further illumination pattern when performing diffraction-based overlay measurements using the scatterometer, and (d) a third pair of illumination apertures combining the first and second pairs of apertures;

[0025] - Figure 8 depicts a schematic overview of a level sensor device, which may use a method according to an embodiment of the invention;

[0026] - Figure 9 depicts a schematic overview of an alignment sensor device, which may use a method according to an embodiment of the invention;

[0027] - Figure 10 is a flowchart describing a method according to an embodiment of the present invention;

[0028] - Figure 11 is a reflectivity graph showing the reflectivity metric from a target as a function of illumination angle θ (y-axis) and wavelength λ (x-axis);

[0029] - Figure 12 Shown are (a) intensity profiles in pupil space with and without displaced illumination (planar diffraction), and (b) the difference between the nominal signal and the displaced signal in terms of geometric contribution and target response contribution;

[0030] - Figure 13 is a flow chart describing a layer thickness inference method according to an embodiment;

[0031] - Figure 14 shows (a) a (partial) graph of the derivative signal |YΛ| in Fourier space over a time period; and (b) the estimated layer thickness as a function of time;

[0032] - Figure 15 are schematic cross-sectional views of targets having various asymmetries;

[0033] - Figure 16 Two grating configurations acting as effective point scatterers are shown; (a) a first target comprising two layers of gratings, and (b) a single tilted grating;

[0034] - Figure 17 Graphs of distance spectra in distance space for (a) top asymmetry, (b) bottom asymmetry, and (c) overlap are shown;

[0035] - Figure 18 is a flowchart describing a first method of overlap inference according to an embodiment of the present invention;

[0036] - Figure 19 is a schematic diagram of an overlaid target, illustrating the effect of the different refractive indices of the different layers and the surrounding vacuum on the diffraction from the target;

[0037] - Figure 20 is a flow chart describing a method for determining interlayer height for a given diffraction signal.

[0038] - Figure 21 It shows p x = 0.1 μm and normal incidence to (m,q z )’s mapping graph;

[0039] - Figure 22 Shown are (a) a plot of the unit cell of the overlapping targets in X, Z space, (b) a plot of the target diffraction efficiency, and (c) a plot of the target reconstructed signal.

[0040] - Figure 23 is a plot of the measured asymmetry versus wavelength, targeting variations in overlay and grating imbalance; and

[0041] - Figure 24 is a flowchart describing yet another method of overlap inference according to an embodiment of the present invention. DETAILED DESCRIPTION

[0042] In this document, the terms "radiation" and "beam" are used to cover all types of electromagnetic radiation and particle radiation, including ultraviolet radiation (e.g., wavelengths of 365, 248, 193, 157 or 126 nm), EUV (extreme ultraviolet radiation, e.g., wavelengths in the range of about 5 to 100 nm), X-ray radiation, electron beam radiation, and other particle radiation.

[0043] As used herein, the terms "reticle," "mask," or "patterning device" should be broadly interpreted as referring to a general patterning device that can be used to impart a patterned cross-section to an incoming radiation beam, corresponding to the pattern to be created in a target portion of the substrate. In this context, the term "light valve" may also be used. In addition to classical masks (transmissive or reflective, binary, phase-shifting, hybrid, etc.), other examples of such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0044] Figure 1A lithographic apparatus LA is schematically depicted. The lithographic apparatus LA comprises an illumination system (also called illuminator) IL configured to condition a radiation beam B (e.g., UV radiation, DUV radiation, EUV radiation, or X-ray radiation), a mask support (e.g., mask table) T configured to support a patterning device (e.g., 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., wafer stage) WT configured 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., 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.

[0045] 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, such as refractive, reflective, diffractive, magnetic, electromagnetic, electrostatic, and / or other types of optical components, or any combination thereof, for directing, shaping, and / or controlling the radiation. The illuminator IL may be used to condition the radiation beam B so as to have a desired spatial and angular intensity distribution in its cross-section at the plane of the patterning device MA.

[0046] The term "projection system" PS as used herein should be broadly understood to cover various types of projection systems, including refractive, reflective, diffractive, catadioptric, anamorphic, magnetic, electromagnetic and / or electrostatic optical systems, or any combination thereof, as appropriate with regard to the exposure radiation used and / or other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system" PS.

[0047] The 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, such as water, to fill the space between the projection system PS and the substrate W, which is also known as immersion lithography. More information on immersion technology is given in US6952253, which is incorporated herein by reference in its entirety.

[0048] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also referred to as a "dual stage"). In such a "multi-stage" machine, the substrate supports WT may be used in parallel, and / or steps for preparing a substrate W for subsequent exposure may be performed on a substrate W located on one of the substrate supports WT, while another substrate W on another substrate support WT is used to expose a pattern on the other substrate W.

[0049] In addition to the substrate support WT, the lithographic apparatus LA can include a measurement table. The measurement table is arranged to hold sensors and / or cleaning equipment. The sensors can be arranged to measure properties of the projection system PS or properties of the radiation beam B. The measurement table can hold multiple sensors. The cleaning equipment can be arranged to clean part of the lithographic apparatus, such as part of the projection system PS or part of the system for providing immersion liquid. The measurement table can be moved under the projection system PS when the substrate support WT is away from the projection system PS.

[0050] In operation, a radiation beam B is incident on a patterning device (e.g. a mask MA) which is held on a mask support T and which is patterned by a pattern (design layout) present on the patterning device MA. After traversing the mask MA, the radiation beam B passes through a projection system PS which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position measurement system IF, the substrate support WT can be accurately moved, for example in order to position different target portions C in the path of the radiation beam B at focused and aligned positions. Similarly, a first positioner PM and possibly a further position sensor (not shown) are provided. Figure 1 The patterning device MA (depicted explicitly in FIG) can be used to accurately position the patterning device MA relative to the path of the radiation beam B. The patterning device MA and substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the illustrated substrate alignment marks P1, P2 occupy dedicated target portions, they can be located in spaces between target portions. When the substrate alignment marks P1, P2 are located between target portions C, these are referred to as scribe lane alignment marks.

[0051] like Figure 2 As shown, the lithography apparatus LA may form part of a lithocell LC, sometimes also referred to as a lithocell or (lithocell) cluster, which typically also includes equipment for performing pre- and post-exposure processes on a substrate W. Conventionally, these 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, for example, for regulating the temperature of the substrate W (e.g., for regulating the solvent in the resist layer). A substrate handler or robot RO picks up substrates W from input / output ports I / O1, I / O2, moves them between the different process equipment, and delivers the substrates W to a feed station LB of the lithography apparatus LA. The devices in the lithocell (also often collectively referred to as a track) may be controlled by a track control unit TCU, which itself may be controlled by a supervisory control system SCS, which may also control the lithography apparatus LA, for example via a litho control unit LACU.

[0052] During the lithographic process, it is desirable to frequently measure the structures being created, for example, for process control and verification. The tool that performs such measurements may be referred to as a metrology tool MT. Different types of metrology tools MT for performing such measurements are known, including scanning electron microscopes or various forms of scatterometer metrology tools MT. Scatterometers are versatile instruments that allow for measurement of parameters of the lithographic process by placing a sensor in the pupil of the scatterometer objective, or in a plane conjugate to the pupil (such measurements are often referred to as pupil-based measurements), or by placing the sensor in the image plane, or in a plane conjugate to the image plane (in which case these measurements are often referred to as image-based or field-based measurements). Such scatterometers and associated measurement techniques are further described in patent applications US20100328655, US2011102753A1, US20120044470A, US20110249244, US20110026032, or EP1,628,164A, which are incorporated herein by reference in their entirety. The scatterometer can measure gratings using light from hard X-rays, soft X-rays, extreme ultraviolet, and visible to near IR wavelength ranges. Where the radiation is hard or soft X-rays, optionally with a wavelength range from 0.01 to 10 nm, the scatterometer can optionally be a small angle X-ray scattering measurement tool.

[0053] In order to ensure that the substrates W exposed by the lithographic apparatus LA are correctly and consistently exposed, it is desirable to inspect the substrates to measure properties of the patterned structures, such as overlay errors between subsequent layers, line thickness, critical dimensions (CD), structure shape, etc. For this purpose, inspection tools and / or metrology tools (not shown) may be included in the lithography cell LC. If errors are detected, for example, adjustments may be made to the exposure of subsequent substrates or other processing steps to be performed on the substrates W, particularly if the inspection is completed before other substrates W from the same batch or lot are yet to be exposed or processed.

[0054] Inspection equipment (which may also be referred to as metrology equipment) is used to determine properties of a substrate W, in particular how properties vary between different substrates W, or how properties associated with different layers of the same substrate W vary between layers. The inspection equipment may alternatively be configured to identify defects on the substrate W and may, for example, be part of the lithography cell LC, or may be integrated into the lithography apparatus LA, or may even be a standalone device. The inspection equipment may measure properties on a latent image (the image in the resist layer after exposure), a semi-latent image (the image in the resist layer after a post-exposure bake step (PEB), or a developed resist image (where exposed or unexposed portions of the resist have been removed), or even on an etched image (after a pattern transfer step such as etching).

[0055] In a first embodiment, the scatterometer MT is an angle-resolved scatterometer. In such a scatterometer, reconstruction methods can be applied to the measured signals to reconstruct or calculate the properties of the grating. For example, such reconstruction can be performed by simulating the interaction of the scattered radiation with a mathematical model of the target structure and comparing the simulation results with the measured values. The parameters of the mathematical model are adjusted until the simulated interaction produces a diffraction pattern similar to that observed from an actual target.

[0056] 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 onto a target, and reflected, transmitted, or scattered radiation from the target is directed to 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, the structure or profile of the target that produced the detected spectrum can be reconstructed, for example, by rigorous coupled wave analysis and nonlinear regression or by comparison with a library of simulated spectra.

[0057] In a third embodiment, the scatterometer MT is an ellipsometer. An ellipsometer allows parameters of a lithographic process to be determined by measuring scattered or transmitted radiation for each polarization state. Such a metrology device emits polarized light (such as linear, circular, or elliptical) by using, for example, appropriate polarization filters in the illumination section of the metrology device. A source suitable for the metrology device can also provide polarized radiation. Various embodiments of existing ellipsometers are described in U.S. patent applications Ser. 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 herein by reference in their entirety.

[0058] In one embodiment of the scatterometer MT, the scatterometer MT is adapted to measure the overlap of two misaligned gratings or periodic structures by measuring the reflection spectrum and / or an asymmetry in the detection configuration, the asymmetry being related to the degree of overlap. The two (possibly overlapping) grating structures may be applied in two different layers (not necessarily continuous layers) and may be formed at substantially the same location on the wafer. The scatterometer may have a symmetrical detection configuration, such as described in co-owned patent application EP1,628,164A, so that any asymmetry is clearly distinguishable. This provides a straightforward way to measure misalignment in the gratings. Further examples for measuring the overlay error between two layers containing periodic structures when the target passes through the asymmetry measurement of the periodic structure can be found in PCT patent application publication number WO 2011 / 012624 or U.S. patent application US 20160161863, which are incorporated herein by reference in their entirety.

[0059] Other parameters of interest may be focus and dose. Focus and dose may be determined simultaneously by scatterometry (or alternatively by scanning electron microscopy), as described in U.S. Patent Application US2011-0249244, which is incorporated herein by reference in its entirety. A single structure may be used that has a unique combination of critical dimension and sidewall angle measurements for each point in the focus energy matrix (FEM, also called focus exposure matrix). If these unique combinations of critical dimension and sidewall angle are available, then focus and dose values ​​may be uniquely determined from these measurements.

[0060] The metrology target can be the entirety of a composite grating, formed by a lithographic process, primarily in resist, but also after, for example, an etching process. The pitch and linewidth of the structures in the grating can be largely determined by the measurement optics (particularly the NA of the optics) to be able to capture the diffraction orders from the metrology target. As indicated earlier, the diffraction signal can be used to determine the shift between two layers (also known as 'overlay') or to reconstruct at least a portion of the original grating produced by the lithographic process. This reconstruction can be used to provide guidance on the quality of the lithographic process and to control at least a portion of the lithographic process. The target can have smaller subdivisions configured to mimic the dimensions of a functional portion of the design layout in the target. Due to this subdivision, the target's behavior will more closely resemble that of the functional portion of the design layout, allowing the overall process parameter measurement to better resemble that of the functional portion of the design layout. The target can be measured in either underfill mode or overfill mode. In underfill mode, the measurement beam generates a smaller spot than the overall target. In overfill mode, the measurement beam generates a larger spot than the overall target. In this overfill mode, it is also possible to measure different targets simultaneously, thereby determining different process parameters simultaneously.

[0061] The overall measurement quality of a lithographic parameter using a specific target is determined at least in part by the measurement scheme used to measure the lithographic parameter. The term "substrate measurement scheme" can include one or more parameters of the measurement itself, one or more parameters of the one or more patterns being measured, or both. For example, if the measurement used in the substrate measurement scheme is an optical measurement based on diffraction, the one or more parameters measured can include the wavelength of the radiation, the polarization of the radiation, the angle of incidence of the radiation relative to the substrate, the orientation of the radiation relative to the pattern on the substrate, etc. One of the criteria for selecting a measurement scheme can be, for example, the sensitivity of one of the measurement parameters to process variations. More examples are described in U.S. patent application US2016-0161863 and published U.S. patent application US 2016 / 0370717A1, which are incorporated herein by reference in their entirety.

[0062] The patterning process in the lithographic apparatus LA is one of the most critical steps in the process, requiring high accuracy in dimensioning and placement of structures on the substrate W. To ensure this high accuracy, the three systems can be combined into a so-called "holistic" control environment, such as Figure 3 Schematically depicted in FIG. One of these systems is the lithography apparatus LA, which is (in practice) connected to a metrology tool MT (a second system) and a computer system CL (a third system). The key to this "holistic" environment is to optimize the collaboration between these three systems to enhance 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 specific manufacturing process will produce a defined result (e.g., a functional semiconductor device), and within which process parameters of the lithography process or patterning process are allowed to vary.

[0063] The computer system CL may use (a portion of) the design layout to be patterned to predict the resolution enhancement technique to be used and perform computational lithography simulations and calculations to determine which mask layouts and lithographic equipment settings achieve the maximum overall process window for the patterning process (in Figure 3 The resolution enhancement technique is arranged to match the patterning possibilities of the lithographic apparatus LA. The computer system CL may also be used to detect where within the process window the lithographic apparatus LA is currently operating (e.g. using input from a metrology tool MET) to predict whether defects may be present due to, for example, suboptimal processing (e.g., in the process window). Figure 3 is depicted by an arrow pointing to “0” in the second scale SC2).

[0064] The metrology tool MT may provide input to the computer system CL to enable accurate simulations and predictions, and may provide feedback to the lithographic apparatus LA to identify possible drift, e.g. in the calibration condition of the lithographic apparatus LA (e.g., in the case of a lithographic apparatus LA). Figure 3 (depicted by multiple arrows in the third scale SC3).

[0065] During a lithographic process, it is desirable to frequently measure the structures being created, for example for process control and verification. Various tools are known for making such measurements, including scanning electron microscopes or various forms of metrology equipment, such as scatterometers. Examples of known scatterometers typically rely on the supply of dedicated metrology targets, such as underfilled targets (targets, in the form of simple gratings or overlapping gratings in different layers, that are large enough to allow the measurement beam to generate a spot smaller than the grating) or overfilled targets (where the illumination spot partially or completely encompasses the target). Further, the use of metrology tools (e.g., angle-resolved scatterometers that illuminate underfilled targets, such as gratings) allows the use of so-called reconstruction methods, where the properties of the grating can be calculated by simulating the interaction of the scattered radiation with a mathematical model of the target structure and comparing the simulation results with the measured values. The parameters of the model are adjusted until the simulated interaction produces a diffraction pattern similar to that observed from an actual target.

[0066] Scatterometers are versatile instruments that allow parameters of a lithographic process to be measured by placing a sensor in the pupil of the scatterometer objective or in a plane conjugate to the pupil (these measurements are often referred to as pupil-based measurements) or by placing the sensor in the image plane or in a plane conjugate to the image plane (in which case these measurements are often referred to as image-based or field-based measurements). Such scatterometers and associated measurement techniques are further described in patent applications US20100328655, US2011102753A1, US20120044470A, US20110249244, US20110026032, or EP1,628,164A, which are incorporated herein by reference in their entirety. Such scatterometers can measure multiple targets from multiple gratings in a single image using light from hard X-rays, soft X-rays, extreme ultraviolet, and visible to the near-IR wavelength range.

[0067] An example of a measurement device such as a scatterometer is Figure 4 It may comprise a broadband (e.g. white light) radiation projector 2 that projects radiation 5 onto a substrate W. The reflected or scattered radiation 10 is passed to a spectrometer detector 4 which measures the spectrum 6 of the specularly reflected radiation (i.e. the measured intensity I as a function of wavelength λ). From this data, for example by rigorous coupled wave analysis and nonlinear regression or by comparing Figure 4 The structure or profile 8 of the detected spectrum produced by comparison with the simulated spectral library shown at the bottom can be reconstructed by the processing unit PU. Typically, for reconstruction, the general form of the structure is known, and some parameters are assumed through knowledge of the process by which the structure was manufactured. Only a few parameters of the structure are to be determined from the scatterometry data. Such a scatterometer can be configured as a normal-incidence scatterometer or an oblique-incidence scatterometer.

[0068] As an alternative to optical metrology, the use of hard X-rays, soft X-rays, or EUV radiation is also contemplated, for example, radiation in the wavelength range between 0.1 nm and 100 nm, or alternatively between 0.01 nm and 50 nm, or alternatively between 1 nm and 50 nm, or alternatively between 10 nm and 20 nm. An example of a metrology tool that operates in one of the wavelength ranges mentioned above is transmission small-angle X-ray scattering (T-SAXS, as described in US 2007224518A, the contents of which are incorporated herein by reference in their entirety). The use of T-SAXS for profiling (CD) measurements is discussed by Lemaillet et al. in "Intercomparison of optical and X-ray scattering measurements of FinFET structures," SPIE Proceedings, 2013, p. 8681. It is noted that the use of a laser generated plasma (LPP) x-ray source is described in U.S. Patent Publication No. 2019 / 003988A1 and U.S. Patent Publication No. 2019 / 215940A1, which are incorporated herein by reference in their entirety. It is known that reflectometry techniques using X-rays (GI-XRS) and extreme ultraviolet (EUV) radiation at grazing incidence can be used to measure the properties of thin films and stacks on substrates. Within the general field of reflectometry, goniometric and / or spectroscopic techniques can be applied. In goniometric measurement, the change in the reflected beam with different angles of incidence is measured. On the other hand, spectroscopic reflectometers measure the spectrum of wavelengths reflected at a given angle (using broadband radiation). For example, EUV reflectometers have been used to check mask blanks before manufacturing reticles (patterning devices) for EUV lithography.

[0069] In a transmission version of an example measurement device such as a scatterometer, the transmitted radiation is passed to a spectrometer detector, which measures the spectrum discussed above. Such a scatterometer can be configured as a normal-incidence scatterometer or an oblique-incidence scatterometer. Optionally, the transmission version uses hard X-ray radiation with a wavelength of <1 nm, optionally <0.01 nm.

[0070] The range of applications may make the use of wavelengths in, for example, the soft X-ray or EUV domain insufficient. Therefore, published patent applications US 20130304424A1 and US 2014019097A1 (Bakeman et al. / KLA) describe hybrid metrology techniques in which measurements using X-rays and optical measurements at wavelengths between 120 nm and 2000 nm are combined to obtain measurements of parameters such as CD. The CD measurements are obtained by coupling and using one or more common points with an X-ray mathematical model and an optical mathematical model. The contents of the cited US patent applications are incorporated herein by reference in their entirety.

[0071] Figure 5A schematic representation of a metrology device 302 is depicted, wherein radiation having a wavelength in the range of 0.1 nm to 100 nm may be used to measure parameters of structures on a substrate. Figure 5 The metrology device 302 proposed in is suitable for the soft X-ray or EUV domain.

[0072] Figure 5 A schematic physical arrangement of a metrology apparatus 302 is illustrated by way of example only, comprising a spectroscopic scatterometer using EUV and / or SXR radiation at grazing incidence. An alternative form of inspection apparatus may be provided in the form of an angle-resolved scatterometer using radiation at normal or near-normal incidence, similar to conventional scatterometers operating at longer wavelengths.

[0073] The inspection apparatus 302 includes a radiation source or so-called illumination source 310 , an illumination system 312 , a substrate support 316 , detection systems 318 , 398 and a metrology processing unit (MPU) 320 .

[0074] In this example, the radiation source 310 is used to generate EUV or soft x-ray radiation, which can be based on high-order harmonic generation (HHG) technology. 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 or optical laser. The pump radiation source 330 can be, for example, a fiber-based laser with an optical amplifier, and the infrared radiation pulses produced can last, for example, less than 1 ns (1 nanosecond) per pulse, with a pulse repetition rate of up to several megahertz, as required. The wavelength of the infrared radiation can, for example, be in the region of 1 μm (1 micrometer). Optionally, laser pulses are delivered to the gas delivery system 332 as first pump radiation 340, where a portion of the radiation is converted to a higher frequency than the first radiation in the gas to become emitted radiation 342. A gas supply 334 delivers a suitable gas to the gas delivery system 332, where it is optionally ionized by a power supply 336. The gas delivery system 332 may be a cut tube.

[0075] The emitted radiation can contain multiple wavelengths. If the emitted radiation is monochromatic, then measurement calculations (e.g., reconstruction) can be simplified, but it is easier to generate radiation with multiple wavelengths. The emission divergence angle of the emitted radiation can be wavelength-dependent. The gas provided by the gas delivery system 332 defines a gas target, which can be a gas flow or a static volume. The gas can be, for example, an inert gas such as neon (Ne), helium (He), or argon (Ar). N2, O2, Ar, Kr, and Xe gases can all be considered. These can be optional options within the same device. For example, when imaging structures of different materials, different wavelengths will provide different levels of contrast. For example, for the inspection of metal structures or silicon structures, different wavelengths can be selected as wavelengths for imaging the features of (carbon-based) resists, or for detecting contamination of such different materials. One or more filtering devices 344 can be provided. For example, filters such as aluminum (Al) or zirconium (Zr) films can be used to cut the fundamental IR radiation to prevent further transmission into the inspection device. A grating (not shown) can be provided to select one or more specific harmonic wavelengths from those generated. Some or all of the beam path may be contained within a vacuum environment, keeping in mind that SXR radiation is absorbed when propagating in air. Various components of the radiation source 310 and illumination optics 312 may be adjustable to implement different measurement 'regimens' within the same device. For example, different wavelengths and / or polarizations may be selectable.

[0076] Depending on the material of the structure being inspected, different wavelengths may provide the desired level of penetration into lower layers. In order to resolve the smallest device features and defects in the smallest device features, then short wavelengths may be preferred. For example, one or more wavelengths in the range of 1 to 20 nm, or alternatively in the range of 1 to 10 nm, or alternatively in the range of 10 to 20 nm may be selected. When reflecting materials of interest in semiconductor manufacturing, wavelengths less than 5 nm may be affected by very low critical angles. Therefore, selecting a wavelength greater than 5 nm will provide a stronger signal at higher angles of incidence. On the other hand, if the detection task is to detect the presence of a certain material, for example to detect contamination, then wavelengths up to 50 nm may be useful.

[0077] From the radiation source 310, the filtered beam 342 enters the inspection chamber 350, where a substrate W including a structure of interest is held by a substrate support 316 for inspection at a measurement position. The structure of interest is labeled T. The atmosphere within the inspection chamber 350 is maintained at a near-vacuum by a vacuum pump 352, allowing the EUV radiation to pass through the atmosphere without excessive attenuation. The irradiation system 312 has the function of focusing the radiation into a focused beam 356 and may include, for example, a two-dimensional curved mirror or a series of one-dimensional curved mirrors, as described in published U.S. patent application US2017 / 0184981A1 (the contents of which are incorporated herein by reference in their entirety), as mentioned above. When projected onto the structure of interest, focusing is performed to achieve a circular or elliptical spot S with a diameter of less than 10 μm. The substrate support 316 includes, for example, an XY translation stage and a rotation stage, by which any portion of the substrate W can be brought to the focus of the beam to a desired orientation. Thus, a radiation spot S is formed on the structure of interest. Alternatively or additionally, the substrate support 316 includes, for example, a tilting stage, which can tilt the substrate W at a certain angle to control the angle of incidence of the focused beam on the structure T of interest.

[0078] Optionally, illumination system 312 provides a reference radiation beam to reference detector 314, which can be configured to measure the spectrum and / or intensity of different wavelengths in filtered beam 342. Reference detector 314 can be configured to generate signal 315, which is provided to processor 310 and the filter, which can include information about the spectrum of filtered beam 342 and / or the intensity of different wavelengths in the filtered beam.

[0079] The reflected radiation 360 is captured by the detector 318 and the spectrum is provided to the processor 320 for use in calculating the properties of the target structure T. The illumination system 312 and the detection system 318 thus form an inspection apparatus. The inspection apparatus may include a soft X-ray and / or EUV spectroscopic reflectometer of the type described in US2016282282A1, the contents of which are incorporated herein by reference in their entirety.

[0080] If the target T has a certain periodicity, the radiation of the focused beam 356 may also be partially diffracted. The diffracted radiation 397 follows another path at a well-defined angle relative to the angle of incidence, followed by the reflected radiation 360. Figure 5 In FIG, the plotted diffracted radiation 397 is plotted in a schematic manner, and the diffracted radiation 397 may follow many other paths than the plotted path. The inspection device 302 may also include a further detection system 398 that detects and / or images at least a portion of the diffracted radiation 397. Figure 5398 is depicted, but embodiments of the inspection apparatus 302 may also include more than one further detection system 398, which are arranged at different positions to detect and / or image the diffracted radiation 397 in a plurality of diffraction directions. In other words, the (higher) diffraction orders of the focused radiation beam impinging on the target T are detected and / or imaged by the one or more further detection systems 398. The one or more detection systems 398 generate a signal 399 that is provided to the metrology processor 320. The signal 399 may include information of the diffracted light 397 and / or may include an image obtained from the diffracted light 397.

[0081] To assist in aligning and focusing the spot S with the desired product structure, the inspection apparatus 302 may also use auxiliary radiation to provide auxiliary optics 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, rotation stage, and / or tilt stage. The processor 320 receives highly accurate 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 delivered to the metrology processing unit 320.

[0082] As mentioned, alternative forms of inspection equipment use soft X-rays and / or EUV radiation at normal incidence or near normal incidence, for example to perform diffraction-based asymmetry measurements. Both types of inspection equipment can be provided in a hybrid measurement system. The performance parameters to be measured may include overlay (OVL), critical dimension (CD), focus of the lithography apparatus as it prints a target structure, coherent diffraction imaging (CDI) and resolution overlay (ARO) measurements. The soft X-ray and / or EUV radiation may, for example, have a wavelength of less than 100 nm, for example using radiation in the range 5 to 30 nm, optionally 10 nm to 20 nm. The radiation may be narrowband or broadband in nature. The radiation may have discrete peaks in specific wavelength bands, or may have a more continuous nature.

[0083] Like optical scatterometers used in today's production facilities, inspection device 302 can be used to measure structures in resist materials processed in a lithography cell (after development inspection or ADI) and / or to measure structures in harder materials after they have been formed (after etch inspection or AEI). For example, a substrate can be inspected using inspection device 302 after it has been processed by a development device, an etching device, an annealing device, and / or other devices.

[0084] The measurement tool MT, including but not limited to the scatterometer mentioned above, can use radiation from a radiation source to perform measurements. The radiation used by the measurement tool MT can be electromagnetic radiation. The radiation can be optical radiation, such as radiation in the infrared, visible and / or ultraviolet parts of the electromagnetic spectrum. The measurement tool MT can use radiation to measure or inspect various properties and aspects of a substrate, such as a photolithographic exposure pattern on a semiconductor substrate. The type and quality of the measurement may depend on multiple properties of the radiation used by the measurement tool MT. For example, the resolution of the electromagnetic measurement may depend on the wavelength of the radiation, for example due to the diffraction limit, smaller wavelengths can measure smaller features. In order to measure features with small dimensions, it may be preferable to use radiation with a short wavelength, such as EUV and / or soft X-ray (SXR) radiation to perform the measurement. In order to perform measurements at a specific wavelength or wavelength range, the measurement tool MT needs access to a source that provides radiation of that / those wavelength(s). There are different types of sources for providing radiation of different wavelengths. Depending on the wavelength(s) provided by the source, different types of radiation generation methods can be used. For extreme ultraviolet (EUV) radiation (e.g., 1 nm to 100 nm) and / or soft X-ray (SXR) radiation (e.g., 0.1 nm to 10 nm), sources can use high-order harmonic generation (HHG) to obtain radiation of the desired wavelength(s). One of the challenges faced in the development of these sources is how to effectively couple the emitted radiation out of the generation setup and separate the emitted radiation from the radiation used to drive the process.

[0085] Figure 6 A simplified schematic diagram of an embodiment 600 of an illumination source 310 is shown, which may be an illumination source for high-order harmonic generation. Figure 5 One or more features of the illumination source in the described metrology tool may also be present in the illumination source 600. The illumination source 600 comprises a chamber 601. The illumination source 600 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. Figure 5As shown. Pump radiation 611 can be directed into the chamber 601 via a radiation input 605, which can be a viewport, which can be made of fused silica or a similar material. The pump radiation 611 can have a Gaussian or hollow (e.g., annular) cross-sectional profile and can be incident (optionally focused) on a gas flow 615 within the chamber 601, which has a flow direction indicated by a second arrow. The gas flow 615 includes a small volume (e.g., a few cubic millimeters) of a specific gas (e.g., an inert gas, optionally helium, argon or neon, nitrogen, oxygen or carbon dioxide), where the gas pressure is above a specific value. The gas flow 615 can be a steady gas flow. Other media can also be used, such as metal plasma (e.g., aluminum plasma).

[0086] The gas delivery system of the irradiation source 600 is configured to provide a gas flow 615. The irradiation source 600 is configured to provide pump radiation 611 in the gas flow 615 to drive the generation of emission radiation 613. The region where at least most of the emission radiation 613 is generated is called the interaction region. The interaction region can vary from tens of micrometers (for tightly focused pump radiation) to several millimeters or centimeters (for moderately focused pump radiation) or even up to several meters (for very loosely focused pump radiation). Optionally, the gas flow 615 is provided by the gas delivery system into an evacuated or nearly evacuated space. The gas delivery system includes a gas nozzle 609, such as Figure 6 As shown, it includes an opening 617 in the outlet plane of the gas nozzle 609. The gas flow 615 is provided from the opening 617. In almost all prior art, the gas nozzle has a cut-tube geometry, which is a uniform cylindrical internal geometry, and the shape of the opening in the outlet plane is circular. Elongated openings are also used, as described in patent application CN101515105B.

[0087] The sizes of the gas nozzle 609 may also be scaled up or down, from micrometer-scale nozzles to meter-scale nozzles. This wide range of sizes comes from the fact that the setup can be scaled so that the intensity of the pump radiation at the gas flow ends up in a specific range that may be beneficial for the emitted radiation, which requires different sizing for different pump radiation energies (which may be pulsed lasers), and the pulse energies can vary from tens of microjoules to joules.

[0088] 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 emission radiation 613, which can be Figure 5An example of emitted radiation 342 is shown. The central axis of the emitted radiation 613 can be collinear with the central axis of the incident pump radiation 611. The emitted radiation 613 can have a wavelength in the X-ray or EUV range, wherein the wavelength is in the range from 0.01 nm to 100 nm, optionally from 0.1 nm to 100 nm, optionally from 1 nm to 100 nm, optionally from 1 nm to 50 nm, or optionally from 10 nm to 20 nm.

[0089] In operation, a beam of emitted radiation 613 may pass through the radiation output 607 and may then be Figure 5 The illumination system 603 of the example illumination system 312 in FIG. 6 is manipulated and directed to a wafer to be inspected for metrology measurements. Emitted radiation 613 can be directed (optionally focused) to a target on the wafer.

[0090] Because air (and indeed any gas) strongly absorbs SXR or EUV radiation, the volume between the gas flow 615 and the wafer to be inspected may be evacuated or nearly evacuated. Since the central axis of the emitted radiation 613 may be collinear with the central axis of the incident pump radiation 611, the pump radiation 611 may need to be blocked to prevent it from passing through the radiation output 607 and entering the illumination system 603. This can be accomplished by placing Figure 5 The filter arrangement 344 shown is incorporated into the radiation output 607, which is placed in the emitted beam path and is opaque or nearly opaque to the drive 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 of zirconium. When the pump radiation 611 has a hollow (optionally annular) cross-sectional profile, the filter can be a hollow (optionally annular) block.

[0091] Methods, apparatus, and assemblies are described herein for obtaining radiation that is optionally emitted at higher harmonic frequencies of pump radiation. The radiation output by this process (optionally using nonlinear effects to generate HHG radiation at harmonic frequencies of the provided pump radiation) can be provided as radiation in a metrology tool MT for inspection and / or measurement of a substrate. The substrate can be a lithographically patterned substrate. The radiation obtained by this process can also be provided in a lithographic apparatus LA and / or a lithographic cell LC. The pump radiation can be pulsed radiation, which can provide high peak intensity for short bursts.

[0092] The pump radiation 611 may include radiation having one or more wavelengths higher than the wavelength or wavelengths of the emitted radiation. The pump radiation may include infrared radiation. The pump radiation may include radiation having a wavelength(s) in the range of 800 nm to 1500 nm. The pump radiation may include radiation having a wavelength(s) in the range of 900 nm to 1300 nm. The pump radiation may include radiation having a wavelength(s) in the range of 100 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.

[0093] For some embodiments, the emitted radiation (optionally higher order harmonic radiation) may include one or more harmonics of the pump radiation wavelength(s). The emitted radiation may include wavelengths in the extreme ultraviolet (EUV), soft X-ray (SXR), and / or hard X-ray (HXR) portions of the electromagnetic spectrum. The emitted radiation 613 may include wavelengths in the range of 0.01 nm to 100 nm. The emitted radiation 613 may include wavelengths in the range of 0.1 nm to 100 nm. The emitted radiation 613 may include wavelengths in the range of 0.1 nm to 50 nm. The emitted radiation 613 may include wavelengths in the range of 1 nm to 50 nm. The emitted radiation 613 may include wavelengths in the range of 10 nm to 20 nm.

[0094] exist Figure 7 A further metrology device suitable for use in embodiments of the present invention is shown in (a). Note that this is only one example of a suitable metrology device. Alternative suitable metrology devices may use EUV radiation, such as those disclosed in WO 2017 / 186483 A1, for example. The target structure T and the diffracted rays of the measurement radiation used to illuminate the target structure are Figure 7(b) is illustrated in more detail. The metrology apparatus illustrated is of a type known as a dark field metrology apparatus. The metrology apparatus may be a stand-alone device or incorporated into the lithography apparatus LA, for example at a measurement station, or incorporated into the lithography cell LC. The optical axis having multiple branches throughout the apparatus is represented by the dashed line O. In the apparatus, light emitted by a source 11 (e.g. a xenon lamp) is directed onto the substrate W via a beam splitter 15 by an optical system comprising lenses 12, 14 and an objective lens 16. These lenses are arranged in a double sequence of a 4F arrangement. Different lens arrangements may be used, provided that they still provide an image of the substrate to the detector while allowing access to the intermediate pupil plane for spatial frequency filtering. Thus, the angular range over which the radiation is incident on the substrate can be selected by defining a spatial intensity distribution in a plane representing the spatial spectrum of the substrate plane (here referred to as the (conjugate) pupil plane). Specifically, this can be accomplished by inserting an aperture plate 13 of suitable form between the lenses 12 and 14 in a plane that serves as a back-projected image of the objective lens pupil plane. In the illustrated example, aperture plate 13 has different forms, labeled 13N and 13S, allowing different illumination modes to be selected. The illumination system in this example forms an off-axis illumination mode. In the first illumination mode, aperture plate 13N provides off-axis illumination in a direction designated 'North' for illustration purposes only. In the second illumination mode, aperture plate 13S is used to provide similar illumination, but from the opposite direction, labeled 'South'. By using different apertures, other illumination modes are possible. The remainder of the pupil plane is preferably dark, as any unwanted light outside the desired illumination mode will interfere with the desired measurement signal.

[0095] like Figure 7 As shown in (b), the target structure T is positioned normal to the substrate W along the optical axis O of the objective lens 16. The substrate W may be supported by a support (not shown). A measurement radiation ray I (e.g., comprising an SXR wavelength) striking the target structure T at an angle off-axis O generates a zero-order ray (solid line 0) and two first-order rays (dashed-dotted line +1 and dashed-dotted line -1). It should be remembered that with a small, overpopulated target structure, these rays are only one of many parallel rays that cover the substrate area (including the measurement target structure T and other features). Because the aperture in the plate 13 has a finite width (must allow a significant amount of light to enter), the incident ray I actually occupies a certain angular range, and the diffracted rays 0 and +1 / -1 will be slightly spread out. Depending on the point spread function of the small target, each order +1 and -1 will be further spread out over a certain angular range, rather than the single ideal ray shown. Note that the grating pitch and illumination angle of the target structure can be designed or adjusted so that the first-order rays entering the objective are closely aligned with the central optical axis. Figure 7 The rays illustrated in (a) and 7(b) are shown slightly off-axis purely to make them easier to distinguish in the drawings.

[0096] At least the 0th and +1st orders diffracted by the target structure T on the substrate W are collected by the objective lens 16 and directed back through the beam splitter 15. Figure 7 (a) , both the first and second illumination modes are illustrated by designating diametrically opposed apertures labeled North (N) and South (S). When incident ray I of the measurement radiation comes from the north side of the optical axis, that is, when the first illumination mode is applied using aperture plate 13N, a +1 diffracted ray labeled +1 (N) enters objective lens 16. In contrast, when the second illumination mode is applied using aperture plate 13S, a -1 diffracted ray (labeled 1 (S)) enters lens 16.

[0097] A second beam splitter 17 splits the diffracted beam into two measurement branches. In the first measurement branch, an optical system 18 uses the zeroth-order and first-order diffracted beams to form a diffraction spectrum (pupil plane image) of the target structure on a first sensor 19 (e.g., a CCD or CMOS sensor). Each diffraction order hits a different point on the sensor, allowing image processing to compare and contrast the orders. The pupil plane image captured by sensor 19 can be used to focus a metrology device and / or normalize the intensity measurement of the first-order beam. The pupil plane image can also be used for many measurement purposes, such as reconstruction.

[0098] In the second measurement branch, the optical systems 20, 22 form an image of the target structure T on a sensor 23 (e.g., a CCD or CMOS sensor). In the second measurement branch, an aperture stop 21 is arranged in a plane conjugate to the pupil plane. The aperture stop 21 acts to block the zero-order diffraction beam so that the target image formed on the sensor 23 is formed only by the -1 or +1 order beam. The images captured by the sensors 19 and 23 are output to a processor PU that processes the image, the function of which will depend on the specific type of measurement being performed. Note that the term 'image' is used here in a broad sense. If only one of the -1 and +1 orders is present, such a raster line image will not be formed.

[0099] Figure 5 The particular forms of aperture plate 13 and field stop 21 shown are examples only. In another embodiment of the invention, on-axis illumination of the target is used, and an aperture stop with an off-axis aperture is used to pass substantially only one first order diffracted light to the sensor. In other embodiments, 2nd, 3rd and higher order beams ( Figure 5 ) can be used for measurement instead of or in addition to the first-order beam.

[0100] In order to adapt the measurement radiation to these different types of measurements, the aperture plate 13 may include a plurality of aperture patterns formed around a disk that rotates to place the desired pattern in the appropriate position. Note that aperture plates 13N or 13S can only be used to measure gratings oriented in one direction (X or Y, depending on the setup). For measurements of orthogonal gratings, target rotations of 90° and 270° can be implemented. Different aperture plates such as Figure 7 The use of these devices and many other variations and applications of the devices are described in the previously published applications mentioned above.

[0101] Another type of measurement tool used in IC manufacturing is a topography measurement system, a level sensor or a height sensor. This tool can be integrated into a lithographic apparatus to measure the topography of a substrate (or wafer). A map of the topography of the substrate (also referred to as a height map) can be generated from these measurements, which indicates the height of the substrate according to its position on the substrate. The height map can then be used to correct the position of the substrate during the pattern transfer onto the substrate so as to provide an aerial image of the pattern forming device in a properly focused position on the substrate. It is to be understood that in this context, "height" refers to a dimension (also referred to as the Z-axis) that is clearly outside the plane for the substrate. Typically, the level or height sensor performs measurement at a fixed position (relative to its own optical system), and the relative movement between the substrate and the optical system of the level or height sensor results in height measurement at positions across the substrate.

[0102] Examples of level or height sensors LS known in the art are Figure 8 As schematically shown in Figure 8 Only the operating principle is illustrated. In this example, the level sensor comprises an optical system comprising a projection unit LSP and a detection unit LSD. The projection unit LSP comprises a radiation source LSO, which provides a radiation beam LSB imparted by a projection grating PGR of the projection unit LSP. The radiation source LSO can be, for example, a narrowband or broadband radiation source (such as a supercontinuum light source), polarized or unpolarized, pulsed or continuous, such as a polarized or unpolarized laser beam. The radiation source LSO can comprise a plurality of radiation sources with different colors or wavelength ranges, such as a plurality of LEDs. The radiation source LSO of the level sensor LS is not limited to visible radiation, but can additionally or alternatively cover SXR wavelengths, UV and / or IR radiation and any wavelength range suitable for reflection from the substrate surface.

[0103] Projection grating PGR is a periodic grating comprising a periodic structure that causes radiation beam BE1 to have a periodically varying intensity. The radiation beam BE1, with its periodically varying intensity, is directed toward a measurement position MLO on a substrate W at an angle of incidence ANG between 0 and 90 degrees, typically between 70 and 80 degrees, relative to an axis perpendicular to the substrate surface (the Z-axis). At measurement position MLO, the patterned radiation beam BE1 is reflected by the substrate W (indicated by arrow BE2) and directed toward a detection unit LSD.

[0104] To determine the height level at the measurement location MLO, the level sensor further comprises a detection system comprising a detection grating DGR, a detector DET, and a processing unit (not shown) for processing an output signal of the detector DET. The detection grating DGR may be identical to the projection grating PGR. The detector DET generates a detector output signal that is indicative of the received light (e.g., the intensity of the received light), such as a photodetector, or represents a spatial distribution of the received intensity, such as a camera. The detector DET may comprise any combination of one or more detector types.

[0105] By means of triangulation techniques the height level at the measurement position MLO can be determined.The detected height level is typically related to the signal intensity measured by the detector DET, which has a periodicity that depends inter alia on the design of the projection grating PGR and the (oblique) angle of incidence ANG.

[0106] The projection unit LSP and / or the detection unit LSD may comprise further optical elements, such as lenses and / or mirrors, along the path of the patterned radiation beam between the projection grating PGR and the detection grating DGR (not shown).

[0107] In an embodiment, the detection grating DGR can be omitted and the detector DET can be placed where the detection grating DGR is located. This configuration provides a more direct detection of the image of the projection grating PGR.

[0108] In order to effectively cover the surface of the substrate W, the level sensor LS may be configured to project an array of measurement beams BE1 onto the surface of the substrate W, thereby generating a measurement area MLO or an array of spots covering a larger measurement range.

[0109] For example, various height sensors of the general type are disclosed in US7265364 and US7646471, both of which are incorporated herein by reference. A height sensor that uses UV radiation rather than visible or infrared radiation is disclosed in US2010233600A1, which is incorporated herein by reference. In WO2016102127A1 (which is incorporated herein by reference), a compact height sensor is described that uses a multi-element detector to detect and identify the position of a grating image without requiring a detection grating.

[0110] Another type of metrology tool used in IC manufacturing is an alignment sensor. Therefore, a key aspect of the performance of a lithographic apparatus is the ability to correctly and accurately place the applied pattern relative to features laid down in a previous layer (either by the same apparatus or a different lithographic apparatus). For this purpose, the substrate is provided with one or more sets of marks or targets. Each mark is a structure whose position can be measured at a later time using a position sensor (usually an optical position sensor). The position sensor may be referred to as an "alignment sensor," and the mark may be referred to as an "alignment mark."

[0111] The lithographic apparatus may include one or more (e.g., multiple) alignment sensors, by which the positions of alignment marks provided on the substrate can be accurately measured. The alignment (or position) sensor may use optical phenomena, such as diffraction and interference, to obtain position information from alignment marks formed on the substrate. An example of an alignment sensor currently used in a lithographic apparatus is based on a self-referencing interferometer described in US6961116. For example, as disclosed in US2015261097A1, various enhancements and modifications of position sensors have been developed. The contents of all of these publications are incorporated herein by reference.

[0112] Figure 9 FIG. 1 is a schematic block diagram of an embodiment of a known alignment sensor AS, such as that described in, for example, US Pat. No. 6,961,116 (incorporated herein by reference). A radiation source RSO provides a radiation beam RB of one or more wavelengths (e.g., including an SXR wavelength), which is directed by steering optics onto a mark (e.g., a mark AM located on a substrate W) as an illumination spot SP. In this example, the steering optics include a spot mirror SM and an objective lens OL. The diameter of the illumination spot SP, with which the mark AM is illuminated, can be slightly smaller than the width of the mark itself.

[0113] Radiation diffracted by the alignment mark AM is collimated (in this example, via the objective lens OL) into an information-bearing beam IB. The term "diffraction" is intended to include zero-order diffraction from the mark (which may be referred to as reflection). A self-referencing interferometer SRI (for example of the type disclosed in US6961116 mentioned above) causes the beam IB to interfere with itself, after which the beam is received by a photodetector PD. In the event that more than one wavelength is created by the radiation source RSO, additional optics (not shown) may be included to provide separate beams. If desired, the photodetector may be a single element, or it may comprise several pixels. The photodetector may comprise an array of sensors.

[0114] The steering optics, which in this example comprise a spot mirror SM, may also be used to block zeroth order radiation reflected from the mark so that the information-bearing beam IB comprises only higher order diffracted radiation from the mark AM (which is not essential for the measurement but improves the signal-to-noise ratio).

[0115] The intensity signal SI is supplied to the processing unit PU. Through a combination of optical processing in block SRI and computational processing in unit PU, values ​​of the X and Y position on the substrate relative to the reference frame are output.

[0116] A single measurement of the type shown only fixes the position of the mark within a specific range corresponding to one pitch of the mark. A coarse measurement technique is used in conjunction with this measurement to identify which period of the sine wave contains the marked position. The same process can be repeated at different wavelengths, at coarser and / or finer levels, to improve accuracy and / or robustly detect the mark, regardless of the material the mark is made of or the material above and / or below where the mark is placed. Wavelengths can be optically multiplexed and demultiplexed so they can be processed simultaneously, and / or they can be multiplexed by time or frequency division.

[0117] In this example, the alignment sensor and the light spot SP remain stationary while the substrate W is moving. The alignment sensor can therefore be rigidly and accurately mounted to the reference frame while effectively scanning the mark AM in a direction opposite to the direction of movement of the substrate W. The substrate W is controlled during this movement by being mounted on a substrate support and a substrate positioning system (controlling the movement of the substrate support). A substrate support position sensor (e.g., an interferometer) measures the position of a substrate support (not shown). In an embodiment, one or more (alignment) marks are provided on the substrate support. Measuring the position of the mark provided on the substrate support allows the position of the substrate support determined by the position sensor to be calibrated (e.g., relative to the frame to which the alignment system is connected). Measurement of the position of the alignment mark provided on the substrate allows the position of the substrate relative to the substrate support to be determined.

[0118] Different coordinate systems are mentioned in the following contexts. A "dual space" is defined, which is a pair (real space, reciprocal space), and there may be no phase in the reciprocal space data. The transformation between the two has scaling properties. For example, twice smaller in one space coordinate is equal to twice larger in the other space coordinate. Data represented in one space can be transformed into the other space using Fourier-related transforms, and vice versa. We broadly define Fourier-related transforms to include transforms such as Fourier transforms, Laplace transforms, and wavelet transforms.

[0119] The three coordinate systems mentioned below are (1) the diffraction angle coordinate system, which can also be described as pupil space or detector pixel coordinate system, which is a reciprocal space; (2) the wave number or wave vector space, which can be described as an inverse space, which is also a reciprocal space; and (3) the real space, which can also be referred to as the target coordinate system. One method of transforming measurement data into real space is the Fourier transform. More specifically, the following spaces are discussed:

[0120] Pupil space: as the diffraction angle, polar coordinates of the diffracted radiation, dimensionless pupil coordinates (components of the unit vector along the diffracted radiation (K x , K y )) or a function of the (x,y) coordinates of a pixel on an image sensor. Conversion between related pupil space representations is straightforward.

[0121] Reciprocal space: as wave numbers or wave vector A function of (wave number with direction vector; sometimes with factor 2π). Also called "inverse space". Note that "pupil space" can also be considered a reciprocal space.

[0122] Real space: as a function of the X, Y, and Z coordinates within the target (unit cell). The real space representation can be obtained by Fourier transforming the signal in reciprocal space. If the complex phase in real reciprocal space is not available, the real space representation is the autocorrelation function of the target characteristics.

[0123] To prevent confusion, spaces may also be referred to by symbolic names, such as (X, Z) space for real space, and -space or q-space is used for reciprocal space.

[0124] In SXR or HXR metrology, a target (or more generally, a structure, such as a periodic pattern on a wafer) is illuminated by a soft X-ray beam (which can have a divergence of 2 mrad and a bandwidth of 9 nm to 20 nm, for example) or a hard X-ray beam. The diffraction pattern is captured by one or more image sensors; for example, in some arrangements, there may be three separate sensors, one each for positive, zeroth (specular), and negative diffraction orders. Each wavelength component in the SXR or HXR beam creates a diffraction spot at a different location on the corresponding sensor.

[0125] The diffraction pattern (intensity as a function of detector position) is the combined effect of three types of parameters:

[0126] 1) Target parameters; these include (a) parameters of interest, such as overlay (OVL) and critical dimension (CD)—the targets are designed to measure and monitor these parameters; and (b) nuisance parameters that affect the measurement but are not necessarily of interest. Examples include the refractive index of the material (e.g., SiO2); the sidewall angle of buried structures created in earlier etch steps; and (in some cases) the thickness h of a layer or combination of layers at or near the top of the stack.

[0127] 2) Properties of the incident SXR beam: e.g., power, spectrum, divergence, and polarization;

[0128] 3) Metrology tool alignment: incident beam angle θ and azimuth relative to the wafer As well as the detector position and orientation relative to the target (the point where the chief ray of the incident beam impinges on the wafer) (e.g., in 6 degrees of freedom). In total, there are potentially 8 degrees of freedom for tool alignment. Note that errors in the position or orientation of the target itself also affect these 8 DoFs. This assumes that, in the case of multiple image sensors, they do not move relative to each other; otherwise, there would be additional degrees of freedom.

[0129] In SXR metrology tools, the goal is to estimate target parameters of interest from the measured diffraction pattern (category 1(a)). It is often necessary, or at least desirable, to eliminate or mitigate the effects of signal variations due to drifting parameters—i.e., parameters in categories 1(b), 2, and 3 that drift from their expected, assumed, nominal, and / or designed values ​​(where drift can be defined as the difference between the actual value of a parameter and its expected, assumed, nominal, and / or designed value). One approach is to design a metrology tool with sufficient stability and reproducibility so that the variation (from minute to minute or month to month) of some of these parameters is negligible. This approach is not feasible in practice; meeting the stability requirements would be prohibitively expensive, and it would not in any way help address the drifting parameters in category 1(b). Another approach is to measure the tool parameters and account for them in the analysis. This may be feasible for beam parameters (category 2), as most beam properties will be measured simultaneously with the on-target measurements. However, monitoring other drifting parameters is impossible or impractical given the constraints imposed by high-volume IC manufacturing processes.

[0130] It would be desirable to provide a method that can eliminate or mitigate the effects of one or more such drift parameter errors from measurements of a target without requiring a priori knowledge of how the specific target responds to changes in alignment parameters.

[0131] Tool alignment correction

[0132] In particular, it is desirable to provide a method that can eliminate or mitigate the effects of "entangled" or interdependent drift parameters, such as target response and tool alignment, which are interdependent drift parameters; for example, there is crosstalk between these parameters. Examples of two such interdependent drift parameters include the angle of incidence θ and the wafer / stack thickness h. For example, the result of a change in the angle of incidence θ is not only a shift in the diffraction pattern on the detector, but also a change in the target response metric (or structure response metric), such as (multiple) target diffraction coefficients; for example, the fraction of incident power that is diffracted into a given diffraction order for a given wavelength and / or polarization. This is illustrated by a specific numerical example: for a particular target, a 14.00 nm wavelength component of the incident beam may be diffracted to the first order at θ = 35.00 degrees, but not diffracted at θ = 35.01 degrees, and vice versa.

[0133] An embodiment includes performing data processing steps on a set of measurements associated with the same type of target. The differences between these measurements may arise from a variety of factors, including, for example, tool drift, tool-to-tool variations, and minor differences in target parameters (e.g., OVL, CD). These measurements can be described by a 3D array I[i, j, k], where i refers to a single measurement in the set and j and k refer to detector pixel rows and columns, respectively. These measurements may optionally undergo minor preprocessing, such as for noise removal.

[0134] Figure 10 is a flow chart describing such a method according to an embodiment. Note that the following paragraphs describe only one possible embodiment. It describes an example of a specific implementation that exploits the interdependence between specific drift parameters (e.g., incident angle θ, stack thickness h, and wavelength λ). Furthermore, for the sake of illustration, the mathematical details are described only for a specific example geometric arrangement.

[0135] In step 1000, the difference ΔI[i,j,k] between each measured image I[i,j,k] and the reference image I0[j,k] is calculated; for example, ΔI[i,j,k] = I[i,j,k] - I0[j,k]. The reference image I0[j,k] can be a single image and can include the average of the set of measurements I[i,j,k] or a DC signal. Thus, the DC signal I0[j,k] describes the invariant component of the measured image I[i,j,k], and the difference intensity measure ΔI[i,j,k] describes the varying component of the measured image I[i,j,k].

[0136] In step 1010, the partial derivatives J[i, j, k, m] with respect to the drift parameters are estimated for each data set (each value of i). Here, m refers to the drift parameter number. For example, m can range from 1 to 9 to cover the 8 DoFs of tool alignment as well as additional wafer parameters such as stack thickness. It can also include other tool parameters such as (e.g., SXR) illumination source power and / or beam divergence. For each drift parameter, the partial derivative describes how the measured image (intensity distribution) changes as the drift parameter drifts.

[0137] In step 1020, the coefficients c[i,m] are determined from minimization of a suitable cost function (e.g., least squares). Specific examples may include, for example:

[0138]

[0139] In this way, one or more components of the difference intensity measurement ΔI[i,j,k] attributable to drift in one or more drift parameters are subtracted from the intensity measurement ΔI[i,j,k] to obtain a corrected measurement or a drift-independent change image. Thus, the drift-independent variation image is minimized in terms of a linear combination of the difference between the difference signal images and the partial derivatives. Least squares minimization can optionally take into account the estimated noise level in the pixels. Other quality factors besides the 'sum of squared deviations' can also be used to find the coefficients. For example, Bayesian analysis that considers a known or estimated probability distribution of the coefficients c or methods that can handle non-Gaussian noise in the signal can be used.

[0140] In an alternative embodiment, the parameter of interest may be fitted together with the drift parameter, rather than first pre-processing the data by removing the signal contribution due to the drift parameter and then interpreting the pre-processed data to infer information about the parameter of interest.

[0141] In step 1030, the drift-independent change image can be used as a corrected measurement signal from which parameters of interest (e.g. overlay, CD, focus) can be determined. Alternatively or additionally, drift-independent variation images can be used for further analysis. For example, it can be used for error correction (i.e., to eliminate the influence of detrimental parameters on lithography process parameters such as overlay); for example, the original signal set can include multiple reference measurements from targets with known overlay and from targets with unknown overlay.

[0142] The above data is described in terms of pixel rows and columns included within the image sensor signal; however, it may alternatively be based on combined signals from multiple image sensors or mapped into pupil space (K x ,K y ) signals (see below).

[0143] More details of how step 1010 may be performed will now be described. This describes estimating partial derivatives J[i,j,k,m] of tool alignment / wafer drift parameters with no other information than the measurements I[i,j,k] and approximate estimates of the drift parameters; e.g., nominal (design) values ​​of those tool parameters and / or wafer parameters. Specifically, the method describes a method for estimating these partial derivatives of interdependent drift parameters where the target response varies interdependently with illumination setting (e.g., where the illumination setting may describe one or both of the wavelength and / or polarization of the illumination radiation) and drift parameter(s). In the following processing, the index i will be dropped from the equation.

[0144] Estimating the partial derivatives of two specific such interdependent parameters will be explicitly described, namely, the angle of incidence θ of the illumination beam on the substrate and the layer or stack thickness h. While these are nominally set to a value (e.g., the angle of incidence θ can be set to any nominal value between 10° and 70°, and the set value for thickness h will vary depending on the application), control of these parameters cannot be perfect, and therefore, the actual values ​​may have some deviation from the set or expected values. The fact that the target response metric (e.g., such as the target reflectivity as a function of wavelength and diffraction order), and therefore the measured intensity distribution, depends on each of these parameters being interdependent with wavelength, means that determining the partial derivatives of these interdependent parameters is not straightforward. In addition, methods that are superior to determining the partial derivatives of other tool alignment parameters will be described; these include other illumination polar angles, azimuthal angle φ, and detector position and orientation (6DoF).

[0145] In the following description, the transition from a signal represented as a detector image I[j,k] to the same signal represented in pupil space is A mapping will be available, parameterized by one or more tool alignment / wafer parameters; for example up to 9 degrees of freedom (8 tool alignment DoF and stack thickness h), parameterized by (p1, . . . p9). The parameter k represents the (K x ,K y ) vector, that is, the direction unit vector of the target ray in the xy plane (K x ,K y ,K y ) components of the pupil space. The representation in pupil space may be continuous rather than discrete pixels; this can be achieved using suitable interpolation methods. The inverse mapping will also be available, i.e., from To I.

[0146] As already stated, the derivative of the illumination angle θ is subject to geometric effects and target response effects, since the diffraction efficiency or reflectivity R(λ,θ) depends on the wavelength and the angle of incidence. However, the inventors have learned that upon careful inspection, the reflectivity R(λ,θ) appears to be approximately invariant under the transformation:

[0147]

[0148] therefore:

[0149]

[0150] This is for θ, θ' between 20 and 70 degrees, where θ, θ' are two different values ​​of the angle of incidence. Therefore, it is proposed to determine the partial derivative of the drift parameter θ based on this transformation.

[0151] Figure 11This is illustrated by the graph of reflectivity or diffraction efficiency as a function of illumination angle θ and wavelength λ. low (dark) to high reflectivity R high The graph is depicted by (bright) shading. The graph illustrates that for each diffraction coefficient value R, there is a predictable set of (λ, θ) pairs, forming the visible lines or ridges seen in the shading in the graph. Therefore, for each (λ, θ) pair with a specific diffraction coefficient value R, other (λ, θ) pairs with the same diffraction coefficient value can be reconstructed in a predictable manner.

[0152] More specifically, this invariance can be understood as the interference between the different layers of the target; with an interlayer distance h, the phase difference between the reflections from the upper and lower layers is 4πh cos(θ) / λ, which can be seen to be invariant under the above transformation. This is at least valid at SXR wavelengths, where the refractive index is always close to 1.0.

[0153] Based on this and substituting c = 2cosθ, the reflection coefficient of diffraction order n can be written as R n (λ,c), and has a partial derivative with respect to c (hence the illumination angle θ), which can be expressed as:

[0154]

[0155]

[0156]

[0157] It is more convenient to define the reflection coefficient in pupil space. To make the mathematics clearer and more manageable, the following example will describe the case of a 1D periodic target with planar (non-conical) diffraction. The more general case of diffraction from a 2D periodic target can be calculated along the same lines, as will be apparent to those skilled in the art. Thus:

[0158]

[0159] where p is the target pitch, and K = nλ / p is the diffraction distance between the pupil position of the diffracted ray k and the pupil position of the specularly reflected ray k0 in pupil space, K = k-k0.

[0160] Assuming a flat illumination spectrum, the diffraction pattern in pupil space is:

[0161]

[0162] based on Where S is the ratio of the irradiation (SXR) power. Here, is a function of two parameters. From this, we can derive an expression by applying the chain rule; note that n is eliminated. It can be seen that the measurement provides for a range of k values ​​(pupil space) and a single k0 value And the nominal value is known: k0 = sinθ. Partial derivatives It can be estimated from numerical differentiation:

[0163]

[0164] Examples can be found at Figure 12 It shows (a) the intensity profile in pupil space (plane diffraction) with and without displaced illumination (k0), and (b) the intensity profile in pupil space due to geometric effects CONT G The difference between the nominal signal and the displacement signal is shown in terms of the contribution due to the geometric effect and the contribution due to the target response to changes in the angle of incidence. Comparing this latter plot with equation (7), it can be seen that the first term in the brackets is the contribution due to geometric effects and the second term is the contribution due to changes in the target response to changes in the angle of incidence.

[0165] It can be understood that c = 2cosθ can be expressed as c = cosθ0 + cosθ d Instead, where θ0 is the angle of the mirror normal, and θ d is the angle of the diffracted ray normal.

[0166] Derivatives in pupil space can be mapped back to derivatives in detector pixel space.

[0167] The above treatment assumes a smooth SXR illumination spectrum. In many cases, this may be correct, but even if it is not, for example if the target's SXR reflectance spectrum is more 'sharp' than the illumination spectrum, it may still be a reasonable approximation. Otherwise, the second term in brackets may include some data about the source spectrum to account for particularly sharp or non-smooth SXR illumination spectra.

[0168] A further consequence of the fundamental physics of the reflectance spectrum, which is primarily a function of the expression 4πh cos(θ) / λ, is that most of the treatment described above in terms of the angle of incidence θ can be applied to the layer thickness h. This means that the reflectance spectrum as a function of layer thickness and wavelength is also invariant under the transformation:

[0169]

[0170] therefore

[0171]

[0172] This can be used to construct the derivative of the target reflectance spectrum R(λ,h) with respect to the layer thickness:

[0173]

[0174] Substituting K = nλ / p, for diffraction order n and target pitch p, the following can be defined: R'(K,h) = R(pK / n,h) and using some calculus:

[0175]

[0176] In pupil space, k = k0 + K, which can be written as And the derivative with respect to the layer thickness becomes:

[0177]

[0178] The factor 1 / h above can be interpreted as referring to the thickness of the topmost layer, or to the combined effect of multiple layers, i.e., 1 / h = a1 / h1 + a2 / h2 + ... with appropriate coefficients a1, a2, ... If the second layer from the top is very thick (e.g. > 50 nm), the lower layers may have a much smaller influence on the diffraction pattern due to absorption losses.

[0179] It should be noted that Equation (12) is expressed in terms of reflectance (R), while the equivalent equation for θ (7) is expressed in terms of the detector signal (I). The choice is entirely arbitrary. Equation (12) can be rewritten in terms of the detector signal, or the detector signal can be converted to reflectance before applying the correction.

[0180] Along the same lines as steps 1020 and 1030 above, The expression for can be used to remove any contribution to the signal caused by layer thickness variations. In this case, the value of h does not need to be known at all. Further analysis can optionally be performed to estimate the actual deviation of h from its nominal value.

[0181] As mentioned earlier, Figure 10 The method can be applied to other drift parameters; in each case, the step of determining the partial derivatives is more straightforward.

[0182] Regarding the dependence on the azimuth angle φ; typically, the plane of incidence is chosen to be the symmetry plane of the target. Due to this symmetry, the derivative of the target response with respect to the angle φ is zero. Even if the target is slightly asymmetric (e.g. due to a small overlay error), the target response derivative will be very small. Therefore, assuming the target reflectivity remains constant, a change in the azimuth angle φ will appear as a φ-dependent shift on the detector. The partial derivative in pupil space can be:

[0183]

[0184] If necessary, the derivative can be transformed into detector space.

[0185] The partial derivatives of the detector position and orientation (for example, to correct for changes in sensor position by calculating how a moving sensor affects the image) are also relatively simple. They can be estimated from a single detector image (a single value of i) and therefore may have different values ​​for different images. They can also be estimated from a reference image (I0[j,k]).

[0186] The partial derivatives can be determined separately for the detector x-position and the detector y-position; for example:

[0187]

[0188]

[0189] where δx and δy are the pixel sizes in the corresponding dimensions.

[0190] Other detector derivatives can be estimated by mapping the signal into pupil space I'(k), assuming best estimates of the tool parameter values ​​(e.g. nominal values), and then transforming back to detector space with one parameter perturbed by a small amount δp, producing a perturbed signal I"[j,k]. The corresponding derivative would then be (I"[j,k] - I[j,k]) / δp. Optionally, if the signal is noisy, a smoothing filter can be applied to the data in detector space.

[0191] Other drift parameters may include one or more parameters of the illumination supply. For example, the derivative of the signal with respect to the illumination (e.g., SXR) power may be useful and can be estimated from the measured signal alone; it is equal to the signal I[i,j,k] divided by the nominal source power in arbitrary units (which can be taken to be an arbitrary unit equal to the nominal source power).

[0192] The derivative of the signal with respect to the divergence of the illumination (e.g., SXR) beam can be estimated by convolving the signal in pupil space with a convolution kernel and subtracting the original signal from it. For example, if the nominal SXR beam has a Gaussian profile with divergence D (in pupil space), then the effect of a divergence change ΔD is equivalent to having a divergence in pupil space of Convolution with the Gaussian convolution kernel G. Then the derivative can be estimated as:

[0193]

[0194] This is not a true derivative; it depends on the actual chosen ΔD value, or multiple derivatives for multiple ΔD values ​​may be taken.

[0195] In the above description, it is assumed that the tool has been pre-aligned to a certain accuracy so that the position of the wavelength component on the detector deviates from the expected position by a significant amount less than the spot size on the detector. With a typical beam divergence D = 2 mrad and a typical target-detector distance L = 20 mm, this means that the position error is much less than 40 μm (= L * D) and the angular error is much less than 2 mrad (= D).

[0196] In the above description, an example value of the nominal angle or angle of incidence θ is described as 30 degrees. This is exemplary only, and any practical angle of incidence may be used, such as between 10 and 90 degrees or between 20 and 90 degrees. For example, a method using SXR radiation may use an angle of incidence between 10 and 70 degrees, or between 20 and 50 degrees, or between 20 and 40 degrees. For example, a method using hard x-ray wavelengths may use an angle of incidence between 85 and 90 degrees.

[0197] Pupil transform for compact representation of data

[0198] In a second main embodiment, the inference problem (i.e. how to convert the detector signal into a parameter of interest) is solved in a different way. Note that this embodiment may be complementary (e.g. in particular with respect to the angle of incidence transformation implementation) or an alternative to the embodiments described above. In particular, this embodiment describes a second method for removing nuisance parameters from the measurement data, e.g. removing grating height variations. Additionally, in addition to removing nuisance parameters, the method also describes a method for inferring profile parameters (e.g. grating height) from the measurement data. The extraction of the profile information will enable the use of unbalanced targets (e.g. targets with varying heights) in overlay measurements and will therefore improve the accuracy of the overlay measurements. This principle is applicable to profile measurements and solves the profile parameter extraction problem (e.g. inferring layer thickness from SXR measurements) without requiring large amounts of data from targets with known layer thickness (or other known profile values), for which no method currently exists.

[0199] The exact thickness of such a layer may not be critical for the performance of the final semiconductor product, but any variation in the layer thickness (e.g. between different targets on the same wafer) will affect the diffraction pattern, such as the SXR diffraction pattern, and may affect the inference of other parameters of interest such as overlay, unless the layer thickness contribution in the diffraction pattern can be separated from the contribution of the parameter of interest. For example, a diffraction-based overlay (DBO) measurement using two offset targets (e.g. overlay offset +b and -b) may be affected by layer thickness differences between the +b and -b targets, since the layer thickness difference will result in an additional A contribution above the overlay. + -A - Contribution. Here, A + and A -refers to the intensity asymmetry of the diffraction orders from +b and -b bias targets, respectively (e.g., the intensity difference between the +1st and -1st orders).

[0200] The oscillatory behavior as a function of wavelength is caused by multilayer interference. For the angle of incidence θ and the layer thickness h, the reflection coefficient R as a function of the wavelength λ can be expressed as follows:

[0201]

[0202] where a and b are positive coefficients, and φ is the phase angle. In reality, this is only an approximation, as the expression doesn't account for diffraction and wavelength-dependent absorption. It explains why the oscillation period is short for small wavelengths and long for large wavelengths. For some radiation, such as hard X-rays (HXR) and SXR, the signal may behave like this because the refractive index of all materials is very close to unity. For other radiation, such as visible light, the mathematical relationship is more complex.

[0203] In this embodiment, it is suggested to apply the following sequence of transformations to the measurement signal in order to transform the raw data into the inverse pupil space:

[0204] Transform the rectangular image into pupil space, i.e., signal Y k (k x ,k y ). This is straightforward for those skilled in the art and only requires knowing the positions of the detector pixels in 3D space using the techniques already described herein.

[0205] Transform pupil space into inverse coordinates q x ,q y , to obtain inverse coordinate measurement data in the inverse space or related data such as wave number data in the wave number space. This will be described in more detail below.

[0206] A method of transforming data into the frequency domain, such as Fourier transform, is applied to the signal in the inverse space. Fourier transform will be mentioned in the following embodiments only as an example, but any method of transforming data into the frequency domain may be applicable.

[0207] Points on the unit disk in pupil space can be represented by coordinate pairs (k x ,k y ) to describe, The zero-order diffraction can be For the diffraction at wavelength λ, the diffraction 2D order (m x ,m y ) results in diffraction at the pupil coordinates:

[0208]

[0209] Where p is the pitch of the target. The step of transforming the pupil space into inverse coordinates may comprise performing the following mapping:

[0210]

[0211] Can be defined: Y q (0,0)≡0 to prevent division errors.

[0212] In terms of k, the new signal Y q In q than Y k This periodicity is reflected in its spectrum, optionally in Fourier spectroscopy, where only a few narrow peaks can be observed, the peak positions of which are related to the layer thickness. Some peaks are associated with SXR spectra, which are approximately periodic in 1 / λ.

[0213] By the way, it can be noted that in the transformation Y k →Y q , scaling can be applied to preserve the integral flux, i.e.,

[0214] ∫Y κ dκ=∫Y q dq.

[0215] This scaling involves basic calculus and will not be described in further detail since its implementation is simple for the skilled person.

[0216] Two potential issues with SXR metrology are that the resist may shrink during SXR exposure (in a 'post-etch inspection' scenario) and that carbon may be deposited on the target during SXR exposure (carbon growth). As a result, the layer thickness may vary over time depending on the measurement.

[0217] Figure 13 A proposed method for inferring layer thickness based on the above principle is described. The specific example described involves the measurement of a 1D periodic grating pattern in a resist. During a time period t, many diffraction patterns are measured from the same target (i exposures), allowing for the prediction of resist shrinkage during this time period.

[0218] In step 1300, the diffraction signal Y d (x,y,t i ) is obtained from an image sensor (a single detector in this case; it could be a dual detector), where x, y are the coordinates on the sensor(s) and t i is the time of time exposure number i. In step 1310, the data can be smoothed in time, resulting in a continuous time This step is optional; depending on the signal-to-noise ratio, it may not provide added value. In step 1320, the signal is transformed into pupil space to obtain Yk (k x ,t). Note that since the target in this example is 1D periodic, k y The coordinates are redundant.

[0219] In step 1330, the derivative is determined. Since it can be assumed that all changes in the signal are due to thickness changes, such as resist shrinkage (since the same target is measured under the same conditions), the signal encodes changes in resist thickness. Step 1340 may include performing the above-described q (q x , t) (here only with respect to the diffraction order +1).

[0220] In step 1350, the signal is Fourier transformed. In this process, only q x > 0 is considered. The Fourier transform can take the following forms:

[0221]

[0222] And it can be approximated using the Fast Fourier Transform (FFT) method.

[0223] In step 1360, the distance Λ value of the highest peak (the position of the highest peak in the Fourier domain) is determined by Fourier transform:

[0224] Λ0(t)=argmax Λ |Y′ Λ (Λ,t)|

[0225] In step 1370, the distance Λ value can be converted to layer thickness:

[0226]

[0227] where θ is the angle of incidence and θ* is the average angle of the diffracted radiation relative to the normal.

[0228] Figure 14 Examples of partial Fourier spectra obtained using this method and the inferred layer thicknesses are shown. Figure 14 (a) shows the derivative signal |Y in Λ space or distance space at one (example) value of t (i.e., from one image corresponding to a single time) Λ |. Figure 14 (b) shows the estimated layer thickness h (corresponding to the position of the spectral peak) for each image (i.e., the resist shrinks over time).

[0229] It will be appreciated that various modifications can be made to the above examples; for example:

[0230] • The source spectrum can be considered, ideally resulting in Y(q) representing the target reflection spectrum in q-space, rather than the diffracted power.

[0231] • The fact that the diffraction angle θ* varies (predictably) across the spectrum (eg using the method disclosed in the first embodiment or otherwise) can be taken into account.

[0232] A window function can be applied to the Fourier transformed input to reduce artifacts from spectral edges.

[0233] Negative and positive diffraction orders can be used.

[0234] • Additional higher diffraction orders may be used (eg one or more of the +2, -2, +3, -3 orders may be used in addition to the +1st and / or -1st orders).

[0235] In metrology applications, such an embodiment can, for example, be applied to directly infer the thickness of a (resist) grating (e.g. over time) and correct the ADI measurements for parameters of interest (e.g. ADI overlay or ADI focus metrology). Alternatively or additionally, this embodiment enables profilometry by being able to infer the thickness of, for example, small spacers deposited in the grating or trenches.

[0236] Another application can include inferring grating heights or layer thicknesses in a collection of multiple overlapping gratings (e.g., DBO-type grating pairs). Height differences (uncorrected) can lead to overlay errors due to so-called grating imbalance. By directly measuring the height, grating imbalance can be detected and (possibly) corrected. This will improve the accuracy of DBO.

[0237] Possible methods for achieving this include, for example, providing a third bias target on the die (with a layer thickness difference) in addition to the first target (e.g., a +b bias target) and the second target (e.g., a -b bias target). This third bias target can, for example, be identical to the first or second bias targets, including having the same bias except for profile parameters (e.g., it has a slightly different layer thickness). In this way, it can be assumed that the signal difference between the two measurements is solely or primarily due to the layer thickness difference. The different layer thicknesses can be imposed intentionally or otherwise. The difference between the first +b target and the third target can be handled using the methods disclosed above. The inferred layer thickness can then be used to correct the overlay (or other parameters of interest) measurement. Note that only the difference in the bias between the first and second targets is meaningful; the bias does not need to be +b, -b. With overlay targets, the +b and -b targets are typically very close to each other, and the overlay is assumed to be the same. However, small differences in layer thickness still exist. Therefore, a third overlay target (e.g., with a +b bias) placed next to the other two may see similar layer thickness differences. It is assumed here that the thickness does not depend on the exposure time, i.e., it can be related to the post-etch inspection data without resist.

[0238] The dependence of the phase on wavelength (which may be referred to as the rocking curve) and the thickness of the spacer layer (including the optical properties of this layer) can be used to correct the measurement of the parameter of interest.

[0239] Optionally, instead of using the entire measured diffraction pattern, one of the asymmetric portion and the symmetric portion of the measured diffraction pattern is used.

[0240] The underlying concept of this embodiment can be further applied to infer overlap or other target parameters from target measurements, in particular asymmetric components of the measurement signal (although symmetric parts of the signal can be used for some target parameters).

[0241] Overlap inference method with reduced sensitivity to grating asymmetry

[0242] In diffraction-based overlay (DBO), two diffraction patterns from a target pair with positive and negative overlay bias (+b and -b, e.g. b = 5 nm) are typically acquired. For each pattern, the asymmetry (difference between +1 and -1 diffraction orders) is obtained, i.e., A + and A - , where the + and - signs refer to the signs of the biases. The overlap OV (profile parameter) is then obtained as:

[0243]

[0244] Variations are possible, for example A ±The signal is measured as a function of wavelength λ and the data at different wavelengths are combined to form an effective asymmetry value

[0245]

[0246] where f(λ) is a suitable weighting function; the overlap is then calculated using the effective asymmetry value. The weighting function can be created from a set of targets with known overlap and can be optimized to be insensitive to noise and variability in non-overlapping targets. For example, methods using singular value decomposition often yield results that are mathematically equivalent to finding a suitable function f.

[0247] Figure 15 is a schematic diagram of an asymmetry target cross section, illustrating why in practice it can be difficult to obtain accurate data from a target with known overlay values. The substrate surface plane is defined in the x / y directions, and the substrate thickness is defined in the z direction. Only the bias can be easily controlled, other (profile parameter) asymmetries cannot be controlled. The target consists of a bottom grating of height H3 and a top grating of height H1, separated by a gap H2 (grating spacing). In addition to the desired overlap OV (including any bias), the measured asymmetry signal A obtained from such a target is + and A - There will be additional contributions from non-overlapping target asymmetries, such as top asymmetry TA and bottom asymmetry BA (ie, grating asymmetry).

[0248] Especially if the top and / or bottom asymmetries do not average to zero on the measured target (e.g. two for A + / A - If hundreds of targets are measured or used to optimize the weighting function f), it is essentially impossible to eliminate its contribution to the overlap estimate. If measurements are made at a sufficient number of wavelengths, one can simply assume that the contribution averages to zero, but this is not necessarily the case. Moreover, requiring hundreds of measured targets to optimize the weighting function is undesirable, and any averaging assumption is unlikely to be valid across target pairs (i.e., an average based on only two measurements is unlikely to remove the unwanted contribution). Therefore, it is desirable to be able to obtain high accuracy overlap from target pairs with both positive and negative biases.

[0249] Another source of measurement error is the aforementioned profile parameter known as raster imbalance: If two adjacent targets (with positive and negative bias) have different layer thickness values ​​or raster tilt asymmetry, they are said to experience raster imbalance. This raster imbalance makes overlay inference more difficult. This raster imbalance is known to be caused by the different environments of the targets, which depend on the product being exposed and cannot therefore be changed.

[0250] At SXR wavelengths, for various materials, the refractive index will lie within the narrow range of 0.9 < n < 1.0. Because of this, diffraction from the grating can be interpreted as if the grating were a weak scatterer that has little effect on the phase of the incident wave. Figure 16 Two grating configurations are shown as point scatterers. Again, the substrate surface plane is defined in the x / y direction and the substrate thickness is defined in the z direction.

[0251] Figure 16 (a) Shows two gratings separated by a distance H. The diffraction efficiency (for the +1 or -1 order) can be evaluated as a function of the wave number as follows:

[0252]

[0253] where p is the grating pitch, is the phase angle that depends on the exact material properties and shape of the scatterer, and ΔL is the optical path length difference between the light diffracted from the top grating and the light diffracted from the bottom grating. For the geometry shown here, ΔL = (1 + cosθ)nH, where θ is the diffraction angle. For non-normal illumination configurations, throughout the description, the factor 1 + cosθ must be replaced by cosθ1 + cosθ2, where θ1 is the angle of incidence and θ2 is the angle of the diffracted radiation with respect to the target normal. If the refractive index n of the layer with height H is not equal to

[0254] 1, then cosθ can be replaced by:

[0255]

[0256] The diffraction efficiency can be Fourier-transformed from the wave number space to the distance space (Λ) as before, resulting in a distance spectrum. Note that the wave number space is closely related to the reciprocal space because where m is the diffraction order and p is the pitch. Therefore, any reference to the reciprocal space, the reciprocal pupil space, or the reciprocal domain should be understood to include the reciprocal coordinate space, the wave number space, or the wavelength space. In this example, a peak can be expected to occur at Λ = ΔL = (1 + cosθ)H.

[0257] Figure 16 (b) Shows a single tilted grating with a tilt angle α. In this case, can be derived as:

[0258]

[0259] where sinc(x) = sin(x) / x. Since in practical use cases Hα / p << 1 and so the function at is approximately periodic, with a distance "frequency" of (1+cosθ)H (assuming n≈1).

[0260] Therefore, the proposed method flow may include: obtaining a diffraction pattern from a target structure comprising at least two different bias targets; deriving a corresponding asymmetry pattern; Fourier transforming this asymmetry pattern into a depth spectrum; shifting the spectrum from one or two bias targets so that their corresponding main peaks overlap; transforming back and performing A+ / A- analysis to obtain the overlap (for example, the overlap can be described by the slope of an A+ / A- curve graph or similar analysis).

[0261] In this method, the measured signal can be initially split into a symmetric component and an asymmetric component. If only the layer thickness is desired, the asymmetric part does not need to be known. To determine the overlap, the asymmetric component is then used. The signal is then inverted (e.g. into wavenumber space). This step can include taking a pair of diffraction orders (e.g. +1 and -1 order, although higher order pairs can be used) and recombining the pair into symmetric and asymmetric components. Thus, if the diffraction pattern has an intensity distribution of positive diffraction order m, then the asymmetric component is used. and its complement Then the symmetric part can be defined as And the asymmetric part is defined as These quantities and is Fourier transformed into S' m (Λ) and A' m (Λ). Note that in the following it is assumed that the first order is used (m=1, -1), and thus it will not be mentioned explicitly further.

[0262] against Figure 15 For overlapping gratings in , one can expect the diffraction asymmetry spectrum (in wavenumber space) to have distance "frequency" components associated with H1, H2, H3, H1+H2, H2+H3, etc., all with a prefactor of 1+cosθ.

[0263] Figure 17Example distance Λ spectra of (a) top asymmetry, (b) bottom asymmetry and (c) overlap are shown, where only the asymmetry component trajectory is shown. Arrows L1, L2, L3 indicate the expected position (assuming n=1) of the peak amplitude A based on three heights H1, H2, H3, respectively. This data is based on smoothed SXR spectra. The contributions of the top and bottom asymmetries are clearly identifiable. The contribution of the overlap is more complex, but still visible. Note that these are example distance spectra from simulations where one of the asymmetry parameters is set to a non-zero value. Moreover, it can be seen that the peak of the bottom asymmetry is far away from its expected position L3. This is a result of some assumptions made in this treatment; namely, the refractive index n is 1 and the angle of incidence θ1 is equal to the angle of the diffracted radiation with the target normal θ2. To remove or mitigate this mismatch, a correction can be applied to the refractive index in wavenumber space (described in more detail below) and the values ​​of θ1, θ2 can be calculated for the layer(s) of interest.

[0264] Figure 18 is a flow chart describing a method for determining target parameters such as overlap. In step 1800, the diffraction pattern I + (x) and I - (x) is measured from the target with offsets +b, -b, where x is the position on the image sensor. This step can be performed in a conventional manner using existing overlay metrology techniques (e.g., DBO).

[0265] In step 1810, using the known target pitch, angle of incidence, and position of the image sensor, the diffraction pattern is converted to an asymmetry in an inverse space, such as wavenumber space: Targeting This can be done using the same basic approach as already described, based on and asymmetric components The determination of transforms the measured value into the inverse space. In the following, the notation A ± It is "A + and A - ", where A + Asymmetric with the +b bias target, and A - Asymmetric with the -b bias target. In this embodiment, the vector nature of q is not taken into account, ie, only the x-order is taken into account; furthermore, only m=1 is considered in this treatment.

[0266] In step 1820, the asymmetry is Fourier transformed into a complex-valued spectrum in range space, A' ± (Λ).

[0267] In step 1830, the path length difference associated with the overlap is calculated, e.g. in is the average refractive index over the wavenumber range.

[0268] In step 1840, the scalar complex asymmetry is calculated: a + =A + (Λ o ):a - =A - (Λ o ). There may be a phase difference of approximately π between the negative bias data and the positive bias data; if the two bias values ​​correspond to the same overlapping sign, the phase difference will be approximately zero. In an embodiment, the evaluation of scalar asymmetry can be achieved by integrating the peaks in the distance spectrum (optionally using a window function with 'soft edges'). For example, the integration can be performed using the following method:

[0269] a ± =∫W(Λ)A ± (Λ)dΛW(Λ) is the complex window function (Λ o Non-zero around, zero elsewhere).

[0270] use The fixed phase difference in the equation Estimates (see Figure 16 (a), the complex magnitude in step 1840 can be converted to a real value using the following equation

[0271]

[0272] If the contribution of the nuisance parameter in the distance spectrum is out of phase with the overlap contribution, this will suppress the contribution of the nuisance parameter. An estimate of φ can be obtained by computer simulation or by examining a large amount of experimental data.

[0273] Finally, in step 1850, the overlap may be evaluated as:

[0274]

[0275] where b is the amplitude of the target bias.

[0276] For example, one or more of the following steps can be performed in the wavenumber domain (e.g., after step 1810); or alternatively, in the transformation from the detector position domain (x) to the wavenumber domain Before:

[0277] ·Can Apply corrections to account for the illumination spectrum and / or the detector response spectrum, both in wavenumbers Approximate known functions of .

[0278] A correction can be applied to the refractive index in wavenumber space, i.e., substituting

[0279]

[0280] in It is the medium of H2 layer (interlayer medium- Figure 15 The real part of the refractive index of the reference) can be vertically averaged in the case of a layered medium. Then in step 1830, set In this way, errors caused by refractive index changes are reduced.

[0281] Some signals can be filtered out by substituting:

[0282]

[0283] in is a suitable window function that is non-zero only within a certain wavenumber range. By way of specific example, at the low end, there may be overlap with the second order diffraction, and at There may be a discontinuity in the refractive index of silicon near (blocking the second order), the window function can be set to zero for (blocking anything above the discontinuity) or only in a narrow band nearby.

[0284] In an embodiment, instead of steps 1840 and 1850, a bandpass filter (approximately Λ=Λ o ) can be applied, and then transformed back to wavenumber space (and optionally then back to pupil space). Any (e.g., already available) feature extraction tools can be used in one of these spaces, such as singular value decomposition and machine learning. (These methods may be easier to apply to real-valued data than complex-valued data).

[0285] Although specific embodiments have been described above and below, it is to be understood that the description of "feature extraction" is intended to be illustrative and not limiting. Feature extraction includes inferring lithographic process parameters such as overlay, focus, critical dimension, grating height, target asymmetry, measurement radiation incidence angle, layer thickness, and / or any lithography-related detrimental parameters, non-lithographic process parameters (such as optical properties of the substrate and / or any non-lithography-related detrimental parameters), and / or determining or other values ​​that can be used to calculate measured substrate properties and / or detrimental parameters.

[0286] The biases in step 1800 may be selected to be unequal in amplitude, for example, bias b - = -4nm and b + = 6 nm. This will result in a slight modification to the formula in step 1850:

[0287]

[0288] Although this embodiment has been described in terms of determining overlap and layer thickness, other target parameters can be extracted using the method of this embodiment (e.g., from the spectrum S' m (Λ) and A' m (Λ) either or both). In some cases, this may be possible without using a biased target pair (e.g., a single target).

[0289] As has been stipulated, the above treatment is based on an approximation of the refractive index that is independent of wavelength, which is incorrect and leads to inaccuracies. A generalization of the above just-disclosed embodiment that does not rely on such an approximation will now be described. This method can also be used to obtain layer thickness from measurements, rather than just eliminating the effects of layer thickness variations. These principles will be further extended to describe additional embodiments for obtaining detailed lateral information (such as critical dimension (CD) or top and bottom edge placement) from measurements.

[0290] Correct the refractive index and obtain the layer thickness

[0291] The contribution of the m-th order diffraction efficiency R m can be derived from the diffraction efficiency equation provided above and takes the following form:

[0292]

[0293] where H is the layer thickness, n is the refractive index, and θ 1,2 is the angle of the incident and diffracted radiation with respect to the normal of the target surface.

[0294] One problem here is that n, θ1, and θ2 are all functions of the wave number . Moreover, θ 1,2 should be interpreted as the angle within the layer, rather than the angle in vacuum outside the target, which means the refractive index should be taken into account. This is illustrated in Figure 19 which shows a target including four layers L0, L1, L2, L3. In this example, layers L0 and L3 each include a periodic structure, G1 and G2 respectively, and H is the spacing distance, spanning layers L1 and L2; H is the vertical distance of interest. In the figure, refers to the angles of the incident radiation IR and the diffracted radiation DR in each layer or in vacuum (vacuum is above the top layer L0). The parameter 0 < a < 1 describes the degree of contribution of layers L1 and L2 to the total distance H respectively.

[0295] In this case, the above expression can be rewritten as:

[0296]

[0297] in:

[0298]

[0299] and where both the angle and the refractive index are functions of the wave number. This is described here for two layers with refractive indices n1 and n2, but it can be generalized for any number of layers.

[0300] Figure 20 is a flow chart describing the and The recommended procedure for determining the distance H for the symmetric and asymmetric parts of the diffracted intensity (as already defined) is:

[0301] Step 2000: Estimate a, and The refractive index at the SXR wavelength can be obtained from general knowledge (e.g., public databases). For layers containing different material structures, an effective refractive index is assumed. The effective refractive index can be an average refractive index (e.g., weighted by the volume fraction of the corresponding material, or another averaging scheme). For a given target, the a parameter is usually approximately known.

[0302] Step 2010: Use these estimates to determine the function based on the above equation And use the following relationship:

[0303]

[0304] Step 220: Modify (e.g., smooth) the refractive index function. Often, these functions have (near) discontinuities and / or local maxima that would otherwise complicate the following steps (e.g., preventing them from being inverted over the entire wavenumber range). Smoothing can make the quantity The phase can be inverted in the wavenumber range of interest to where f is the appropriate function, and q' z describes a position in reciprocal space. This modification may include smoothing the refractive index function. Smoothing should be interpreted broadly; for example, it may mean that the refractive index function By low-pass filtering, approximating by a low-order polynomial (such as first or second order), or replacing by a constant value. These are just non-limiting examples of smoothing methods.

[0305] Step 2030: Transform function:

[0306]

[0307] And, similarly, for:

[0308]

[0309] In the remaining steps, only the asymmetric component function will be described explicitly; similar steps also apply to the symmetric component.

[0310] Step 2040: Optionally, maintain A and Integral of a function:

[0311]

[0312] And similarly for S and function.

[0313] Step 2050: and Fourier transform (in reciprocal space) to real space, we get and For one or more diffraction orders m, the layer thickness H will now appear as a peak centered around Z=H in the symmetric and / or asymmetric distance spectrum. This step therefore yields a value for the layer thickness H. It has been observed that the grating spacing distance tends to be The peak appears in the grating height, and the symmetrical spectrum The peak value in .

[0314] It can be shown that this approach provides good results in simulations using real SXR spectra (including many peaks) and is clearly superior to alternatives such as averaging n or averaging the angle θ over the spectrum.

[0315] It is also observed that layers comprising neither gratings nor a single spacer layer between two adjacent gratings (such as Figure 19 Layer L1 in the depth spectrum also generates significant peaks in the depth (distance) spectrum. These peaks do not always appear at Z values ​​equal to the layer thickness, but their thickness can be inferred from the depth spectrum using the techniques disclosed herein.

[0316] Instead of transforming the intensity signal before Fourier transforming the components or diffraction efficiency Splitting into symmetric and asymmetric components, a pair of (m,-m) diffraction orders can be combined as:

[0317]

[0318] After the Fourier transform, the signal can be split into symmetric and asymmetric components using the well-known properties of the Fourier transform; the Fourier transform of the symmetric part is the real part And the Fourier transform of the asymmetric part is the imaginary part

[0319] Extract features related to CD, layer thickness, overlay, and / or sidewall angle asymmetry.

[0320] Many of the concepts described (or to be described) can be generalized into methods for determining various profile parameters such as dimensional features (placement and size values), including CD and edge placement values, overlap, and SWA asymmetry. This method enables determination and monitoring of edge placement errors (EPE) and / or complete reconstruction of features (in 3D or fewer dimensions).

[0321] In 3D reciprocal space (the target is in the xy plane and along the period p x x is periodic and has a period of p y is periodic in y) or in momentum transfer space, the momentum transfer vector can be defined as:

[0322]

[0323] where m, m' are the diffraction orders in x and y respectively. This can be written more compactly as:

[0324]

[0325] in is the incident wave vector, whose z component has a different sign from The z component of q' is the same as that of q' described in the embodiment just described above. z consistent.

[0326] For diffraction from a target that is periodic in x and y, the Cartesian component of q has the following properties:

[0327]

[0328] Or alternatively:

[0329]

[0330] in is the directional unit vector of the zeroth-order reflected radiation (as defined previously).

[0331] By way of a specific example, if in Cartesian coordinates (wavelength is 10nm at normal incidence) And 1 / p x =10μm -1 ,So And q' 2,0 =(20,0,198)μm -1 .

[0332] Measured diffraction efficiency or Any of Equations E2.1 to E2.3 can be used to map to momentum transfer space as Or, equivalently, as Figure 21 is a graph illustrating an example of such a mapping, more specifically, for p x = 0.1 μm and normal incidence, from to (m,q' z ); the meaning of the dotted rectangle will be explained below. Note that Figure 21 Discrete wave numbers are shown; in reality, the wave numbers will span a continuous range, while the diffraction orders (m) are discrete as shown.

[0333] So remapped A portion of can now be Fourier transformed as:

[0334]

[0335] The integral limit q' z,a and q' z,b Can be chosen to cover all available data or a subset thereof.

[0336] Note that the factor 2π in this Fourier transform can also be replaced by -2π; in this case, most of the other factors 2π in the equations in the following description will also need to be replaced by -2π.

[0337] The proposed method comprises determining one or more contour parameters (e.g., position and / or size parameters) from one or more sizes and / or positions and / or configurations (e.g., shapes) corresponding to regions of higher amplitude in a reconstructed signal represented in real space (e.g., R'(X,Y,Z) in three dimensions, but the reconstructed signal may include fewer dimensions).

[0338] The regions of higher amplitude may correspond to different ones of the one or more position and / or size parameters. For example, the position in the real space corresponding to the region of higher amplitude in a first direction (i.e., a region of Z value having a higher amplitude, where Z corresponds to a direction perpendicular to the plane of the substrate) may indicate one or more of the position and / or size parameters in the first direction. One or more of the position and / or size parameters in the first direction may include the height of one or more structures; and / or the distance between one or more structures and / or features thereof. For example, different regions of higher amplitude may respectively correspond to different distance measurements associated with the same two structures; i.e., the distance between different features on these structures. By way of specific example, the first region may correspond to the distance between the top of a first feature and the top of a second feature, and the second region may correspond to the distance between the bottom of the first feature and the top of the second feature.

[0339] The size and / or position and / or configuration of the higher amplitude regions (i.e., regions having higher amplitude X and / or Y values) corresponding to the second and / or third directions parallel to the substrate plane can indicate one or more of the position and / or size parameters in the second and / or third directions. Such position and / or size parameters can include, for example, the width, critical dimension, or any other dimension of a structure; the difference in width, critical dimension, or any other dimension between any two structures or structural features (e.g., between the top and bottom of a structure); overlap or offset between two structures; and / or structural asymmetry in a structure. The size and / or position and / or configuration of the regions in the second and / or third directions can include one or more of the following: one or more offsets of the regions relative to an origin; the width of one or more of the regions; and / or the size of a flat region of the outline or contour of one or more of the regions.

[0340] Figure 22 An example 2D data set is shown illustrating this embodiment based on simplified calculations, with approximations for small refractive index variations. Figure 22 (a) is a 2D real-space plot of density as a function of X and Z (i.e., in X, Z space), representing the unit cell of an overlay target being measured. The target consists of a top grating with a height of 100 nm and a bottom grating with a height of 30 nm, separated by 50 nm. The top grating tapers from a critical dimension (width) of CD = 25 nm to CD = 35 nm; the bottom grating has a CD of 50 nm. Figure 22 (b) is the diffraction efficiency The graph shows the change of m, where the width of each black area represents the logarithm of the diffraction intensity. Figure 22(c) is the (2D) reconstructed signal R'(X,Z), including the autocorrelations of the magnitudes in the X,Z space. Each black region on the graph represents an area where the correlation magnitude is greater than 5% of the maximum magnitude appearing in the graph (i.e., an area of ​​higher magnitude). Note that this is only an example threshold, and other thresholds or criteria can be used to determine these black regions or areas of higher magnitude. Figure 22 (d) is the true value The graph shows Figure 22 Several slices of the R' values ​​for the data represented in , with all curves scaled to a maximum value of 1. Figure 22 (c) It can be seen that the Fourier transform data R'(X,Z) has point symmetry around the origin; the following description will only describe the part of Z≤0 in this figure:

[0341] The feature at Z = -100 nm corresponds to the top grating height. The X offset of -5 nm corresponds to the top grating tilt asymmetry. The full width at half maximum (FWHM) of 35 nm (see Figure 22 (d)) is equal to the width of the bottom of the top grating (CD).

[0342] The feature at Z = -50 nm corresponds to the grating spacing distance, i.e., the distance from the bottom of the top grating to the top of the bottom grating. The X offset of 10 nm corresponds to the overlap (center of the bottom of the top grating to the center of the top of the bottom grating). The FWHM is 51 nm, very close to the width (CD) of the bottom grating (50 nm).

[0343] The feature at Z = -150 nm corresponds to the distance from the top of the top grating to the top of the bottom grating; the 5 nm X offset corresponds to the center offset of the corresponding feature. The FWHM is 52 nm, very close to the width (CD) of the bottom grating (50 nm). The curve has a flat-top feature; its width is close to the difference between CD = 30 nm (top grating) and CD = 50 nm (bottom grating).

[0344] The feature at Z = -180 nm corresponds to the distance from the top of the top grating to the bottom of the bottom grating. The X offset of 8 nm corresponds to the center offset. The flat top feature is the same as the feature at Z = -150 nm.

[0345] ·Weak feature at Z = -80nm (only Figure 22 (c) visible on; not on Figure 22 (d) corresponds to the distance between the bottom of the top grating and the bottom of the bottom grating.

[0346] • The height of the bottom grating is not visible at Z = -30 nm because it is buried in the bright features near Z = 0. However, it does show up as the distance between the features at Z = -150 and Z = -180 nm.

[0347] In general, if two features of width a and b are correlated, such as Figure 22 (d), then the FWHM will be:

[0348] If a+b≤p, then FWHM≈max(a,b), and

[0349] If a+b≥p, then FWHM≈p-min(a,b)

[0350] The FWHM is defined as the midpoint between the highest and lowest values ​​of the cross-correlation curve. Related; R' is a complex-valued function that may have zero crossings. FWHM is only defined for real-valued functions; therefore, the formula allows real-valued curves to have both negative and positive values. Any suitable transformation from complex R' to real R' (allowing both positive and negative values) can be used.

[0351] From each of these features, a complete overlapping target geometric picture including 3D EPE aspects can be reconstructed.

[0352] In the following, references to R'(X,Z) may be interpreted as a 2D example that can be generalized to the 3D case with R'(X,Y,Z). Similarly, R' m,m’ (Z) is used for 3D cases, but can also be used for 2D cases R' m Thus, this embodiment can be used with data in 1, 2 or 3 dimensions and equivalent representations.

[0353] To extract CD-related information directly from R'(X,Z) space, it is generally necessary to use at least the {-1, 0, 1} or {-2, -1, 1, 2} orders. (This example is for |m| ≤ 3.) Exceptions may exist: for example, if the target includes layers with different pitches (e.g., half-pitch or double-pitch), these requirements may differ. It is possible to use only m = ±1 orders, but then CD will affect the amplitude of the R' signal. Therefore, calibration using simulated data or data from a target with known CD values ​​is required to convert the amplitude to CD values.

[0354] In mathematics, from The Fourier transform to R'(X,Z) (for the 2D case) is equivalent to computing the autocorrelation function of the unit cell. Not applicable to q' z ≈0, so it looks slightly different from the standard autocorrelation function. Figure 22 The curve in (d) can be interpreted as the cross-correlation function of the edges in the unit cell at different Z values.

[0355] In summary, this embodiment allows estimation of in-plane feature size (CD and CD-like parameters), overlay, relative top and bottom position of features (e.g., top grating bottom surface in an overlapping target), grating tilt (grating asymmetry), and vertical distance from a single measurement without the need for training data from measurement or simulation (however, machine learning can optionally be used to improve accuracy).

[0356] Variations of the Feature Extraction Embodiment

[0357] 1) Fourier transform can be performed on m,q' z It is performed on a rectangular area in space. Figure 21 As an example, assuming data is available for the wavelengths and orders shown, a Fourier transform can be performed to cover the area within the dashed rectangle, where m = {-5, ···, 5}, q' z,a =100μm -1 , and q' z,b =185μm -1 , so there is no missing data in this range. (m,q z ) The regions of different shapes in the space can also be selected so that for each q' z values, a continuous range of m values ​​is covered. For example, using Figure 21 The radiation source configuration in , spanning wave numbers Less than 100μm -1 q' z Values ​​can be excluded because is defined only for higher diffraction orders, while q' Z =197μm -1 may be included because it has a continuous range available -2≤m≤2. The selected region may be symmetric in m so that for a given q, z For every positive m value at the value, the corresponding -m order is available, and for every positive m' order, the corresponding -m' order is available. (This is particularly relevant for 2D periodic targets under non-normal illumination.)

[0358] 2) The window function can be used before Fourier transform Data application. Window functions can be 1D, 2D, or 3D. For example, Figure 22 The data in is obtained using the z Directions for Hann window treatments.

[0359] 3) A discrete range of steps can be selected; for example, step m = 0 can be omitted. By way of example, selecting only m = ± 1 will cover the A currently used in, for example, overlay measurements. + / A - Type inference.

[0360] 4) Given a broadband SXR source, (m,q' z ) space can be selected, covering combinations that can be explicitly extracted. For example, using Value of SXR source, spanning 50μm -1 to 100μm -1 (10nm to 20nm), normal incidence (with Figure 21 same) and target pitch 100nm, range 100μm -1 to 200μm -1 Can cover the order m=0, range 99μm -1 to 199μm -1 Can cover for order m=±1 and range 130μm -1 to 198μm -1 can be covered for orders m = ± 2. Therefore, The m=3 order sum The ambiguity between the m=2 orders can be avoided.

[0361] 5) The Fourier transform can be performed to cover only one or two dimensions instead of three dimensions (for the 3D case). For example, it is possible to only z Then select the order pair ±m, A + / A - Overlap inference can be similar to that about Figure 18 The overlap inference method described is performed. The asymmetry can be defined as:

[0362]

[0363] For a particular choice of m, for example m = 1. This asymmetry is usually complex valued. Using the asymmetry A with bias ±b, the measurement ± For two targets with unknown overlap OV, the overlap can be estimated as

[0364]

[0365] That is, this shows that this embodiment is Figure 18 Generalization of the described method.

[0366] 6) After Fourier transformation, phase gradient correction can be applied, i.e.,

[0367]

[0368] where μ and μ' are appropriately chosen numbers, and Q' zis a wave number that is appropriately chosen so that the phase of R' does not change too rapidly depending on X, Y or Z. This phase gradient can also be applied selectively to one or two of the three dimensions. In general, μ, μ', Q' z Can be selected by Weighted m, m', q' z The average value of .

[0369] 7) The X position of the feature in R'(X,Z) can be obtained from the complex value pair R' m (Z), R'- m (Z) is estimated, in particular from the case m = ± 1. For example, one of the following expressions can be used:

[0370]

[0371] as well as

[0372]

[0373] where the overline indicates the complex conjugate. This can also be expressed as:

[0374]

[0375] Both representations extract the phase difference between two complex values ​​(eg, of similar amplitude).

[0376] Therefore, the overlay or grating tilt asymmetry can be inferred from a single measurement. These expressions are only approximate. However, they are exact if a pair of positive and negative diffraction orders is related by:

[0377]

[0378] where c |m| is a complex value that does not depend on the sign of m.

[0379] 8) If it is desired to combine measurements from two or more offset targets for overlay, this can be done based on the R'(X,Z) representation; if a specific Z value Z is known o Associated with overlap (e.g. Figure 22 Z in (c) or (d) o =50nm), then the effective value can be evaluated for two bias values, namely, and For the corresponding Z o The measured value R' + (X,Z) and R' - The biases +b and -b of (X,Z). The inferred overlap is then given by:

[0380]

[0381] Effective value Examples of might include: function |R′ ± (X, Z o ), the mean, median or modulus of the above An expression in the expression of or other similar measures. R'(X,Z) can also be expressed in the expression of Z=Z o Integrate within the nearby Z range.

[0382] 9) If the above bias measurement pair is affected by grating imbalance, this may appear as overlapping features appearing at slightly different Z o Value, such as Z o+ =50nm and Z o- =51nm. and R′ + (X, Z o+ ) and R′ - (X, Z o- This is a generalization of the embodiment "Detection and correction of grating imbalance of DBO" described below.

[0383] 10) If one is only interested in overlay, CD, or other features in X space, and not in precise measurements of layer thickness (Z space), then measurement interpretation is insensitive to small errors in the angle of incidence. For example, if the angle of incidence is nominally 45 degrees, but the actual angle of incidence is 45.1 degrees, this will result in a small shift in the Z position of the feature in R'(X,Z). This is not a problem for inference of X-dependent features. This is a generalization of the "Tool Alignment Correction" embodiment described herein.

[0384] 11) The data can be corrected for the actual refractive index of the target or target layer (the above example is very close to the refractive index of n=1 for the entire target). This correction can be done from Convert to Corrections are specific to the material in layers spanning a given vertical distance; multiple corrections for different sets of layers may be applied to the same input data. Leading to multiple R'(X,Y,Z) or multiple R' m,m’ (Z) Datasets. These multiple data sets can be combined or interpreted individually.

[0385] 12) Similar to the previous embodiment, the signal can be (m,q' z ) space is divided into symmetrical and asymmetrical parts, where A m (q' z )=-A -m (q'z ) and S m (q' z )=S m (-q' z ) and its Fourier transform are considered separately. This split can also be performed after the Fourier transform.

[0386] 13) The user may wish to optimize the process parameters so that the critical dimension has a specific desired value. An example of a process parameter is the exposure dose on the resist. Figure 22 The cross-correlation curve (function) in (d) does not have a well-defined feature. This is a consequence of the optical diffraction limit. To determine the CD value of a feature from this curve, a criterion such as a threshold can be defined. This threshold can be calibrated by using the fact that diffraction of non-zero and even complementary diffraction orders (±2, ±4, ...) disappears in the specific case where the CD is equal to half the pitch. The user can achieve this by performing the following steps:

[0387] • Create a series of targets with varying process parameters so that the CD varies.

[0388] The cross-correlation curve related to CD is obtained using the method of this embodiment (for a specific value Z=Z o ).

[0389] ·Identification R'2(Z o ) and R' -2 (Z o ) is close to zero. A threshold is found such that the width of the portion of the cross-correlation curve above the threshold is equal to half the target pitch.

[0390] • Assign CD values ​​to the other cross-correlation curves using the threshold found in step c.

[0391] 14) CD can also be directly obtained from the R' m (Z) represents the estimate. Define a=CD / p (CD / pitch ratio) and know that CD corresponds to a specific value Z=Z o , then the following relationship may approximately hold:

[0392]

[0393] Thus, if, for example, R'0 and R'1 are known, or if R'1 and R'2 are known, one can solve for a and thus obtain CD.

[0394] If it is known that Z = Z o Correlating the cross-correlation of two features with two different CD values, i.e., CD1 and CD2, we can define a = CD1 / p and b = CD2 / p. The above equation then becomes

[0395]

[0396] If R' m (Z o ) If three values ​​of m are known, for example m = 0, 1, 2, then the values ​​of a and b can be solved. Alternatively, if a or b is known by other means, then the other can be solved from only two values ​​of m, R' m Value obtained.

[0397] 15) Although the mathematics are written starting from the diffraction efficiency R, the procedure can also be applied to the diffraction intensity I, that is, the product of the source spectral intensity and the target diffraction efficiency. An approximation can be made, that is, the pupil space (κ x , κ y ) can be converted to Space or zero-order accurate Pupil coordinates (m,m',q' z ) space, even if the illumination spans a (narrow) range of pupil coordinates, as defined by the numerical aperture of the illumination optics. The source can use high-order harmonic generation, resulting in a source spectrum with multiple peaks at wavenumbers The space is separated by a fixed interval, for example, from about 51 μm -1 to 99μm -1 25 peaks with a spacing of about 2 μm -1 This will result in a diffraction efficiency of Sampling is done at fixed intervals, and the diffraction efficiency is sampled at roughly fixed intervals. As is well known in signal processing, this leads to aliasing: when Fourier transforming the diffraction intensity I from reciprocal space to real space R' m (X) or R'(X, Z), after R' m A single layer thickness H will occur at multiple values ​​of Z in R'(X, Z). For example, at a first value Z = Z o (1) and the second value Z=Z o (2) and possibly more values, the overlap may appear as m The inference of individual structural parameters (such as overlap) can be used to determine the value of these Z o One or more of the values ​​are performed.

[0398] 16) To measure the diffraction efficiency over a wide range of wave numbers and diffraction orders The results from multiple measurements on the same target with different illumination spectra can be combined. Thus, for example, it is possible to distinguish between m=3 diffraction from a wavelength of 12 nm and m=2 diffraction from a wavelength of 18 nm. The spectrum can be modified by placing a spectral filter, such as a bandpass filter somewhere in the SXR beam path, downstream or upstream of the target. The filter can be a reflection filter or a transmission filter. Spectral selection can be achieved by multilayer coating or by using the absorption properties of a material (e.g. aluminum, zirconium, ruthenium, gold). The target can be designed with a built-in multilayer structure to enhance or suppress reflectivity in a dedicated wavelength range. The SXR radiation can pass through a tunable monochromator.

[0399] 17) As shown in Equations E2.3 and E2.4, from Space to (m,q' z ) space depends on the angle of incidence (θ1) or usually the specular reflection of the radiation vector, which is defined by θ1 and the illumination azimuth. The range of q covered can be extended by combining measurements at different angles of incidence and / or different azimuths with the same illumination spectrum. z Range. For example, the azimuth angle can be stepped in multiples of 90 degrees or multiples of 180 degrees.

[0400] 18) The R'(X,Z) representation can be used for feature extraction in machine learning methods. For example, R'(X,Z) itself or the locations of peaks in R'(X,Z) can be used as input to a regression model or neural network that is further trained on reference data, whether measured or simulated. This can be used to correct for assumptions used to derive R'(X,Z), such as the single scattering approximation (which is not strictly valid for these wavelengths), refractive indices significantly different from 1, more complex geometries, etc. This is a generalization of the "Pupil Transform for Compact Representation of Data" embodiment.

[0401] 19) In the case of overlapping diffraction orders, such as the third order at 12 nm and the second order at 18 nm, the ratio of the contributions usually depends on the angle of incidence or azimuth, since they have different effects on q. z In the case of a broadband SXR spectrum containing, for example, 12 nm and 18 nm, it is not possible to unambiguously map the entire diffraction pattern to m, Space. However, datasets at multiple incident angles can be transformed into inverse spaces (as in the example “Pupil Transform in SXR for Compact Data Representation”) and used for machine learning (ML). The combination of multiple incident angles will increase the diversity of the data, thereby contributing to better performance of the ML algorithm. During parameter inference, the trained ML algorithm can be reused with data collected at multiple incident angles.

[0402] 20) Another way to handle overlapping orders is through an iterative process. This iterative process may include the following steps:

[0403] ·generate A "first guess" estimate of the angle of incidence is obtained, for example by using Maxwell solver software according to the designed unit cell. (Multiple first guesses may be generated for different angles of incidence, azimuths, or polarizations. For example, two angles of incidence differ by 1, 2, 5, 10, 20, 30, 40, 45, 60, or 80 degrees. Larger step sizes are required for angles of incidence close to normal). Although angles of incidence less than 20 degrees may be more practical (or essentially enforced) due to current hardware limitations of some tools, other tool designs can be envisioned that allow larger angle variations without wafer contamination of mirrors and other hardware; for example, a broadband hard X-ray source for transmission diffraction (TSAXS).

[0404] Using knowledge of the SXR spectrum will estimate Transformed into the estimated diffraction pattern I e (K x , K y ). (Or multiple estimated diffraction patterns if the same target is measured with different angles of incidence, different source spectra, etc.)

[0405] Using the measured diffraction pattern(s) I(K x , K y ) to update the estimate Make (all) I e Consistent with (all) I. How to do this is generally known from ptychography and coherent diffraction imaging (CDI).

[0406] Updated estimates Transformed into R'(X,Y,Z) representation. (If the incident angle, etc., changes, there will be multiple R' representations.)

[0407] Update the R' representation based on constraints on physical possibility. For example, when the Z value does not correspond to the vertical distance between feature boundaries in the unit cell, R' must be zero. (If there are multiple R' representations corresponding to different angles of incidence, they must agree in the XYZ position of the feature, but not necessarily in magnitude.)

[0408] If R' is significantly updated: transform R'(X,Y,Z) to the updated estimate And return to the second step.

[0409] If R' has not been significantly updated: the iterative procedure has converged. Further data analysis can be performed on the R'(X,Y,Z) representation or R' m，m′(Z) is represented as described elsewhere in this disclosure.

[0410] 21) In the case of overlapping diffraction orders, such as the third order at wavelength 12 nm and the second order at 18 nm, the intensity measured in such ambiguous positions in the extended pattern can be assigned to Multiple m in For example, for a target with a pitch of 100 nm and a SXR spectral range of 10 to 20 nm, the pupil coordinate K in the range 0.2 to 0.4 x is assigned to m=2, and pupil coordinates 0.3 to 0.6 are assigned to m=3. Range 0.3≤K x ≤ 0.4 is assigned to m = 2 and m = 3. This can be seen as a hybrid approach between the embodiment "Pupil transformation for compact representation of data" on the one hand (the transformation does not take into account the diffraction order) and the complete disambiguation in the above variants (16), (19) and (20) on the other hand. The advantage of this hybrid approach is that it can be used to convert the measured diffraction pattern I(K x , K y ) is transferred to R'(X,Y,Z). This step can be performed losslessly (because the Fourier transform is bijective) and does not require any assumptions about overlap. Further processing (including disambiguation of overlap) can be done in R'(X,Y,Z) or R m,m’ (Z) indicates completion.

[0411] 22) Although all of the discussion of this embodiment is for SXR wavelengths of, for example, 10 nm to 20 nm, it is also applicable to other X-ray wavelengths; more generally, all wavelengths where the refractive index of the relevant material is close to 1. It is also applicable to hard X-ray transmission (small-angle diffraction). In transmission, Eq. E2.2 can be used to transform the wave vector into q space instead of Eq. 2.1. In Eq. E2.3, angle θ1 can be understood to have a value < 90 degrees, and θ2 can be understood to have a value > 90 degrees. Eq. E2.4 needs to be modified to:

[0412]

[0413] Detection and Correction of DBO Grating Imbalance

[0414] Another overlay extraction embodiment will now be described that addresses the problem of grating imbalance; for example, different grating spacing for targets with positive and negative biases, which can lead to overlay errors. This is a particular problem when the wavelength is very small (e.g., EUV, soft X-rays, and / or hard X-rays), because the error can be very large (e.g., up to 50% asymmetry errors may be observed). This asymmetry error can introduce significant errors into the measured overlay value. The method of this embodiment is related to the embodiment just described.

[0415] The method of this embodiment proposes modifying (e.g., shifting and / or scaling) an asymmetry rocking curve (i.e., a graph of asymmetry for a wavelength of a particular target). One embodiment may include modifying one or both of the corresponding rocking curves from targets with different offsets so that they have the same wavelength for a certain asymmetry (e.g., an asymmetry of zero).

[0416] This concept can be used to measure raster imbalance between different layers of an overlapping target.

[0417] One way to detect and correct grating imbalance is to consider the zero crossings in the asymmetry signal as a function of wavelength (rocking curve). Some measurement techniques (such as SXR measurement) are able to measure these asymmetries over wavelength in a single acquisition.

[0418] Figure 23 The asymmetry is plotted as a function of wavelength for two overlapping OV values, each with two different layer heights H. In this specific illustrative example, the grating pair has layer heights H = 95 nm and H = 96 nm, respectively, for example with a grating imbalance GI of 1 nm. Note that GI might more appropriately refer to the combined effect of all differences between the gratings of the grating pair, which are not directly related to the overlap. It can be seen that if the overlap varies but the spacing remains constant, the zero crossings overlap (e.g., the zero crossing overlap of the black trace (H = 95 nm) and the gray trace (H = 96 nm)). As the grating imbalance changes, the position of the zero crossing shifts in wavelength.

[0419] The zero crossings of each curve depend solely on the grating spacing divided by the wavelength. A zero crossing occurs when the wave from the bottom grating destructively interferes with the wave from the top grating. The interference depends on the phase difference between the top and bottom waves, and therefore on the optical path difference, which is proportional to the grating spacing relative to the wavelength.

[0420] Figure 24is a flow chart describing a method according to such an embodiment. In step 2400, measurements are performed on a target structure comprising at least two correspondingly different bias targets under a plurality of different illumination settings (e.g., different combinations of one or both of wavelength and polarization). In step 2410, for each bias target, an asymmetric component (asymmetry signal) is extracted from the diffraction pattern measured in step 2400 and plotted against wavelength (e.g., per polarization if more than one polarization is used) to obtain a corresponding asymmetric rocking curve. In step 2420, the zero-crossing position of the asymmetry signal is determined. It is then further determined whether the zero-crossing positions of the positive-bias target and the negative-bias target overlap (i.e., whether they have a common zero-crossing wavelength). If these rocking curves do not have a common zero-crossing position, the wavelength shift between the corresponding zero-crossing positions can be used as a measure of grating imbalance. In step 2430, if grating imbalance is detected, a correction for overlay error can be determined. This can be achieved by shifting one asymmetry signal (or both signals) so that the zero-crossings of the two asymmetry signals overlap. This will significantly reduce overlay errors.

[0421] An improved correction strategy may include transforming the asymmetry curve into wavenumber space or another inverse domain. Zero crossings are equidistant in wavenumber space, and their spacing depends on the grating spacing. Therefore, shifting cannot fully correct for the grating spacing. In this embodiment, wavenumber zero crossings can be linearly mapped from one measurement (associated with one bias target) to other measurements associated with other bias targets. This may include shifting and scaling the wavenumber axis to match all zero crossings. The transformation in wavenumber space is nonlinear.

[0422] In addition to shifting / scaling on the X-axis, there are many other mathematical methods that can be used to match zero crossings. For example, instead of a linear increasing function, a mapping ν'=f(ν) or λ'=f(λ) can be fitted. The function f can be any suitable function, or can be implemented by applying a neural network with multiple layers.

[0423] An example of a generalized process may include the following steps: (1) diffraction pattern measurement; (2) optionally, feature extraction for different wavelengths (typically symmetric or asymmetric components); (3) multi-wavelength transformation; (4) optionally, correction to combine multiple targets; and (5) mapping of the parameters of interest.

[0424] In all of the above embodiments involving inverse space / domain or wavenumber space / domain, transformation to any related space / domain (eg, inverse space, wavenumber space, wavelength space, etc.) may be included.

[0425] Overlap Inference Based on Fourier Signal Decomposition

[0426] In yet another main embodiment, the inference problem (i.e., how to convert the detector signal into a parameter of interest, such as overlap) is solved in a different way. Note that this embodiment can be complementary to or alternative to any of the above embodiments. When complementary, any of the above methods can be used initially, such as filtering the measurement signal for drift in the drift parameter, or inferring and correcting layer thickness before inferring the parameter of interest. It has been observed that some known inference methods, such as the asymmetry A+ / A- plot (i.e., a plot of the asymmetry of a positively biased target versus a negatively biased target), are ineffective for metrology devices based on SXR illumination.

[0427] The proposed method is a partially data-driven approach that can also incorporate known physical properties. The concept of a data-driven approach can be understood as meaning that some inference model is trained on a set of detector signals from targets with known parameter values ​​(e.g., known overlap), and then the trained model is used to infer the values ​​of the parameters during operation.

[0428] An inference model can be defined and applied to data from, for example, a single chip, field, or substrate that includes multiple targets (e.g., grating overlay targets) with different parameter values ​​(e.g., biases for overlay). The goal is to train a model on a subset of the data related to a subset of these targets (the training set), and then use the model to infer biases for the remaining data / targets (the test set). The method can do this by then minimizing a specified error or similar difference metric that describes the difference between the inferred biases and the actual programmed biases (e.g., a 3σ difference).

[0429] Where most inference methods rely solely on training an inverse model (e.g., from detector signal to parameter of interest), the method proposed here trains a forward model (parameter of interest to detector signal), which can then be inverted to perform the actual inference. Note that the forward model does not necessarily depend only on the parameter of interest, but may also depend on one or more other parameters (as is the case with the specific forward model referenced below). The advantage of this is that by defining a base form of this forward model, knowledge of the physical properties of the target response can be incorporated. A general disadvantage of purely data-driven methods is that they do not have a deep understanding of and cannot exploit the physical properties of the system.

[0430] The model can include three terms:

[0431] a constant term, which is the response resulting from the measurement of a target with a zero value for the parameter (e.g., zero overlap), with all other parameters varying by their mean values ​​across targets,

[0432] a parameter term of interest (e.g. an overlap term), which describes the (e.g. periodic) response of the detector signal to the parameter of interest (e.g. overlap or bias); and

[0433] One or more nuisance terms, which each describe any other variation between the target measurements.

[0434] In an embodiment, the one or more nuisance terms may be obtained via singular value decomposition (SVD), where each term comprises a single value or SVD component.

[0435] In an embodiment, the overlap term may be decomposed into harmonics, eg using Fourier decomposition. This is particularly relevant for periodic targets used, eg in overlay measurements, such that the parameter term of interest describes the periodic response of the detector signal.

[0436] The following equation describes an exemplary forward model according to an embodiment:

[0437]

[0438] in:

[0439] ·S ij (b,q) is the detector signal for object i, with the subscript j referring to the specific pixel on the camera. This is what the model aims to predict.

[0440] ·The first K j is a constant term representing the constant component of the camera signal;

[0441] The second term is the parameter term or overlap term of interest. This example is specific to a periodic response where the target is periodic, where p is the pitch of the target. In terms of overlap, b i is the overlap of the objective in question (more specifically, for training, the imposed bias or imposed overlap), and L kj and M kj describes the kth harmonic of the overlapping response. The model includes this harmonic #harm; observations show that #harm between 2 and 6, between 3 and 5, or #harm = 4 may be optimal. This terminology can be easily adapted by the skilled person to other parameters of interest, whether measured on a periodic target or otherwise.

[0442] The third term is a nuisance term that describes any other variation between target measurements, such as stack properties other than overlap or tool parameters (such as alignment). The model incorporates this variation #SVD, where each variation includes an SVD component; observations show that #SVD between 10 and 30, between 10 and 20, between 15 and 20, or #SVD = 17 may be optimal. The k-th variation is weighted by the detector signal P for each target i. kj With weight q ki to describe the changes.

[0443] Equations with an i subscript (target index) indicate the application of the equation to a specific target; the i subscript can be omitted from the general form of the equation.

[0444] To relate this to the previous embodiment, k is analogous to m in the previous embodiment, and j, which refers to a detector pixel, is analogous to the pupil coordinate k in the previous embodiment. x The matrices K, L, and M are the same as those in the previous embodiment. are closely related, because the combination m,q' z can be directly mapped to the number of pixels or pupil k x Coordinate; k j and Related. Here, can be interpreted as R'(X,Z o ) related Fourier components, where Z o is the Z value associated with the overlap. The sum P kj q ki Capture variations in other target characteristics, such as grating asymmetry.

[0445] To train the model, the detector signal term S ij With a known bias b i The training signal set is used to fit (e.g., in a least squares sense) the parameters K on the data. j , L kj 、M kj 、P kj and q ki This can be done, for example, by randomly partitioning the training data into multiple subsets and then training each subset on the other subsets in turn. This trains a forward model, such as j , L kj 、M kj 、P kj .

[0446] Note that, optionally, one or more processing operations may be performed on the training set S ij By way of example only (other pre-processing methods may be employed), processing may include one or more of the following steps:

[0447] Integrate the camera signal over the column (e.g., determine the column-wise integrated sum (CWIS));

[0448] • One order of concatenating (averaging) the nominal and rotational orientations, so there are four "orders" in total.

[0449] Note that no asymmetry is calculated;

[0450] Normalize the signal of each target based on the total intensity of the fourth order

[0451] Remove outliers (this can be based on SVD weights or final residual signatures, for example);

[0452] Smooth the signal using a Gaussian smoothing function. The convolution width σ can be, for example, between 0.5 and 2.5 pixels, between 0.75 and 1.75 pixels, between 1 and 1.5 pixels, or about σ = 1.2 pixels. Note that as an alternative to Gaussian smoothing, a Fourier domain low-pass filter can be used to reduce the (already low) effect of shot noise.

[0453] Note that one or more of the number of harmonics #harm, the number of SVD components #SVD, and the convolution width σ can be considered as hyperparameters that are fixed in hyperparameter optimization before the main training of the model.

[0454] Note that as an alternative to Gaussian smoothing, a Fourier domain low-pass filter can be used to reduce the (already low) effect of shot noise. Level errors in X can be corrected by shifting the signal. This can be implemented, for example, by adding a shift (or three shifts, one for each of the three measurements) to the inference model. This requires the possibility of applying a sub-pixel shift to the data, which would be trivial if the above low-pass filter were implemented.

[0455] For nuisance terms, an actual SVD can be performed on the data matrix of detector column index v·image i. Similarly, preprocessing can be applied, including one or more of the following: computing the column-wise integral sum of intensities for the nominal and rotated images; normalizing by the total intensity and subtracting the nominal CWIS from the rotated CWIS; for example, subtracting the left side from the right side for sensor correction due to asymmetry.

[0456] For inference, the detector signal term S ij is related to processing the image(s) to determine the parameter of interest, and the parameter K j 、L kj 、M kj 、P kj is fixed to the value learned during training. Then the parameter of interest (e.g. overlap) b i The value of (note that if the targets are intentionally biased, then this overlap value will be a combination of the overlap and the intentional bias) and the SVD weight q for each target ki is fitted (eg again in a least squares sense).

[0457] This approach allows for training a physics-based forward model, rather than directly training an inverse (inference) model. For example, regularization can be added to enforce physical constraints. By way of a specific example, it is understood that only low-frequency X content contains overlapping information (addressed above by the CWIS and smoothing steps). This can be better addressed by regularizing the actual inference model. Similarly, hard cutoffs on the number of harmonics and SVD components can be better enforced by regularization.

[0458] Another advantage of this approach is that it uses the complete signal rather than just the asymmetric portion (as is done in standard A+ / A- analysis).

[0459] Each of the above embodiments can be applied to eliminate, remove, suppress, or correct the effects of one or more interfering parameters, such as angle of incidence or grating imbalance. Each of the above embodiments can also be applied to infer parameters of interest (such as overlap and layer thickness) or interfering parameters (such as grating height imbalance).

[0460] The effects of interfering parameters may need to be removed from the metrology measurement data in order to obtain accurate measurements of lithography process parameters such as overlay, feature size, structure optical properties, critical dimension, or focus. Interfering parameters may include one or more of incident angle variation, thickness drift or grating height drift (also referred to as separation variation or grating imbalance), and structural asymmetry.

[0461] Some embodiments provide not only a method for correcting measurement errors, but also a method for measuring the value of nuisance parameters.A plurality of embodiments may also be combined and implemented simultaneously or subsequently into one measurement data.

[0462] Optionally, the above embodiments are data driven methods or model training. Optionally, many of the above embodiments may include non-iterative methods, which are different from stacking and other forms of coherent diffraction imaging (CDI). The above embodiments are also different from crystallography, which is often used as a forward model.

[0463] The above embodiments may be "error correction" (i.e., eliminating the effects of nuisance parameters such as overlap) or "feature extraction," which may be different from "reconstruction," for example, it may include methods involving rigorous forward models such as rigorous coupled wave analysis (RCWA) and nonlinear regression. One advantage is that no rigorous forward model is required.

[0464] Further embodiments are disclosed in the subsequent numbered clauses:

[0465] 1. A measurement method comprising:

[0466] obtaining measurement data associated with at least one measurement value for each of one or more structures on the substrate; the measurement data being dependent on one or more drift parameters, the drift parameters including at least one interdependent drift parameter, each measurement value being dependent on a structural response metric that varies interdependently with an illumination setting and the at least one interdependent drift parameter; and

[0467] The measured data is corrected based on an approximately invariant transformation of the structural response metric or related metric.

[0468] 2. A method according to clause 1, wherein the illumination setting comprises one or more wavelengths of measurement illumination used to obtain the measurement data.

[0469] 3. A method according to clause 2, wherein the measuring radiation comprises one or more wavelengths in the range of 0.01 nm to 20 nm.

[0470] 4. A method according to clause 2 or 3, wherein at least one interdependent drift parameter comprises a measurement of the angle of incidence of light on the structure.

[0471] 5. A method according to clause 4, wherein the angle of incidence has a nominal value between 20 degrees and 90 degrees.

[0472] 6. A method according to any preceding clause, wherein at least one interdependent drift parameter comprises the total thickness of one or more layers on the substrate.

[0473] 7. A method according to any preceding clause, wherein the approximately invariant transformation of the structural response metric describes a set of pairs of at least one mutually dependent drift parameter and the illumination settings respectively having approximately common values ​​for the structural response metric.

[0474] 8. A method according to any of the preceding clauses, wherein the transformation comprises transforming a first value of the interdependent parameter into a second value of the interdependent parameter and scaling the first value of the illumination setting to obtain the second value of the illumination setting; the scaling comprises the ratio of the second value of the interdependent parameter or its trigonometric function to the first value of the interdependent parameter or its trigonometric function.

[0475] 9. A method according to any preceding clause, wherein the structure comprises a grating structure and the structural response metric comprises a diffraction efficiency metric of the structure.

[0476] 10. A method according to any preceding clause, wherein the step of correcting the measurement data comprises:

[0477] determining one or more partial derivatives of the measurement data, each partial derivative describing a change in a measurement value with respect to each of the one or more drift parameters, wherein determining the partial derivative of the at least one interdependent drift parameter comprises determining a partial derivative of an approximately invariant transformation of the structural response metric or related metric; and

[0478] The measurement data is corrected based on the one or more partial derivatives to obtain the corrected measurement data.

[0479] 11. A method according to clause 10, comprising an initial step of determining difference data describing the difference of each of the measurement values ​​relative to a reference measurement value; the measurement data comprising the difference data and the reference measurement value.

[0480] 12. A method according to clause 11, wherein the reference measurement value comprises an average of the measurement values.

[0481] 13. A method according to clause 11 or 12, comprising determining corrected measurement data by performing minimization of the difference data and the partial derivatives in terms of their coefficients, the corrected measurement data having subtracted a component, the minimization being estimated to be associated with the drift in the one or more drift parameters.

[0482] 14. A method according to any of clauses 10 to 13, wherein the measured values ​​each comprise an image captured by a detector at a detector plane.

[0483] 15. A method according to clause 14, wherein the method comprises mapping the measurement data from an image plane representation to a pupil plane representation.

[0484] 16. A method according to clause 14 or 15, wherein the drift parameters further comprise one or more parameters related to the position of the detector.

[0485] 17. The method of clause 16, wherein determining the partial derivatives of one or more parameters related to the detector position comprises: performing the following steps for each of the first direction and the second direction of the image plane:

[0486] For each pixel of each image, the difference between the measurements of the adjacent pixels in the corresponding direction on either side of this pixel is determined, divided by twice the pixel size in the corresponding direction.

[0487] 18. The method of clause 16 or 17, wherein determining partial derivatives of one or more parameters related to the detector position comprises:

[0488] mapping the measurement data from a raw image plane representation to a pupil plane representation;

[0489] Impose a perturbation on the pupil plane representation;

[0490] transforming the perturbed pupil plane representation back to the perturbed image plane representation; and

[0491] The partial derivative is determined as the difference between the perturbed image plane representation and the original image plane representation divided by the perturbation.

[0492] 19. A method according to any of clauses 10 to 18, wherein the drift parameter further comprises an azimuth angle.

[0493] 20. The method of any of clauses 10 to 19, wherein the drift parameter further comprises one or both of illumination power and illumination beam divergence.

[0494] 21. A method according to clause 20, wherein the partial derivative of the illumination beam divergence is estimated by convolving each measurement value in pupil space with a convolution kernel and subtracting the original measurement value from the convolution.

[0495] 22. A method according to clause 21, wherein the partial derivative of the illumination power is estimated by dividing the measured value by the nominal source power.

[0496] 23. A method according to any preceding clause, wherein the one or more structures comprises a plurality of similar structures.

[0497] 24. A method according to any preceding clause, wherein the drift parameter further comprises an azimuth angle.

[0498] 25. A method according to any preceding clause, further comprising:

[0499] obtaining a trained forward model describing the measurement signal in terms of at least one parameter of a term of interest describing a response of a parameter of interest of the target, one or more nuisance terms describing other variations between measured values ​​of the target, and a constant term representing a constant component of the corrected measurement data; and

[0500] Using the trained forward model, values ​​of parameters of interest are inferred from the corrected measurement data.

[0501] 26. A method according to clause 25, wherein the inferring step comprises fitting the parameters of interest and weights of each of the one or more nuisance terms to the corrected measurement data on the trained forward model.

[0502] 27. A method according to clause 25 or 26, wherein one or more nuisance terms are determined from a singular value decomposition.

[0503] 28. A method according to clause 27, comprising a plurality of nuisance terms, each associated with a separate singular value decomposition component.

[0504] 29. A method according to clause 28, comprising the step of optimizing the number of singular value decomposition components as a hyperparameter in the optimization phase.

[0505] 30. A method according to any of clauses 25 to 29, wherein the response of the parameter of interest of the target is described by a Fourier sequence.

[0506] 31. The method of clause 30, wherein the at least one parameter of the term of interest comprises a plurality of parameters of the term of interest, each associated with a separate harmonic as a result of the Fourier decomposition.

[0507] 32. A method according to clause 31, comprising the step of optimizing the number of harmonics as a hyperparameter during the training phase.

[0508] 33. A method according to any one of clauses 25 to 32, comprising training the model on training data using known values ​​of the parameters of interest in a training phase.

[0509] 34. A method according to any one of clauses 25 to 33, wherein the parameter of interest is overlap.

[0510] 35. A method according to any one of clauses 25 to 34, comprising applying regularization to the model to constrain the results based on known physical properties.

[0511] 36. A method of inferring a value of a parameter of interest from said measurement data, comprising:

[0512] obtaining the measurement data, the measurement data being related to scattered radiation from the target captured at the detector;

[0513] obtaining a trained forward model describing the measurement signal in terms of at least one parameter of a term of interest describing a response of a parameter of interest of the target, one or more nuisance terms describing other variations between measured values ​​of the target, and a constant term representing a constant component of the measurement data; and

[0514] Using the trained forward model, values ​​of parameters of interest are inferred from the measurement data.

[0515] 37. A method according to clause 36, wherein the inferring step includes: fitting the parameters of interest and weights of each of the one or more nuisance terms to the measured data on the trained forward model.

[0516] 38. A method according to clause 36 or 37, wherein one or more nuisance terms are determined from a singular value decomposition.

[0517] 39. A method according to clause 38, comprising a plurality of nuisance terms, each associated with a separate singular value decomposition component.

[0518] 40. A method according to clause 39, comprising the step of optimizing the number of singular value decomposition components as a hyperparameter during the optimization phase.

[0519] 41. A method according to any of clauses 36 to 40, wherein the at least one parameter of the term of interest comprises a plurality of parameters of the term of interest, each associated with a separate harmonic as a result of the Fourier decomposition.

[0520] 42. A method according to clause 41, comprising the step of optimizing the number of harmonics as a hyperparameter during the training phase.

[0521] 43. A method according to any one of clauses 36 to 42, comprising training the model on training data using known values ​​of the parameters of interest in a training phase.

[0522] 44. A method according to any one of clauses 36 to 43, wherein the parameter of interest is overlap.

[0523] 45. A method according to any one of clauses 36 to 44, comprising applying regularization to the model to constrain the results based on known physical properties.

[0524] 46. ​​A measurement method comprising:

[0525] obtaining measurement data associated with at least one measurement value for each of one or more structures on the substrate;

[0526] transforming the measurement data into a reciprocal space to obtain reciprocal measurement data;

[0527] further transforming the reciprocal measurement data to obtain transformed measurement data; and

[0528] Substrate-dependent profile parameter values ​​are inferred from the transformed measurement data.

[0529] 47. The metrology method of clause 46, wherein the further transforming step comprises a Fourier transform.

[0530] 48. A metrology method according to clause 46 or 47, wherein the step of inferring the value of the profile parameter comprises determining the position of a peak in the further transformed measurement data and inferring the value of the profile parameter from the position of the peak.

[0531] 49. The metrology method of any one of clauses 46 to 48, wherein the step of transforming the measurement data into a reciprocal space comprises one of the following:

[0532] transforming the measurement data so that the measurement data is represented by inverse coordinates in an inverse space;

[0533] transforming the measurement data so that the measurement data is represented by wavenumbers in a wavenumber space;

[0534] transforming the measurement data so that the measurement data is represented by wavelengths in a wavelength space; or

[0535] The measurement data is transformed so that the measurement data is represented by momentum transfer in a momentum transfer space.

[0536] 50. A metrology method according to any of clauses 46 to 49, wherein the measurement data comprises a data set associated with corresponding measurement values, wherein the only differences in the data set are assumed to be due to variations in profile parameters; and

[0537] The method comprises taking derivatives of the measurement data with respect to corresponding measurement values ​​prior to the transforming step.

[0538] 51. The metrology method of clause 50, wherein the measurement data relates to measurements of the same one or more structures, the measurements covering a time period over which profile parameter values ​​are expected to vary to obtain time-dependent measurement data; and the method comprises:

[0539] The transforming step is performed on the time-dependent measurement data.

[0540] 52. The metrology method of clause 51, comprising processing the time-dependent measurement data before the transforming step to obtain continuous time-dependent measurement data.

[0541] 53. A measurement method according to clause 52, wherein the method comprises determining the change in the value of the profile parameter over time.

[0542] 54. A metrology method according to any of clauses 51 to 52, wherein the measurement data relate to measurements of at least two identical structures, except for variations in the profile parameters between the structures.

[0543] 55. The metrology method of clause 54, wherein the profile parameter value relates to at least one of the at least two identical structures.

[0544] 56. The metrology method of clause 54 or 55, wherein the at least two identical structures include a first structure having a first bias, a second structure having a second bias, and a third structure, the third structure being substantially identical to the first structure except with respect to the profile parameter;

[0545] determining an overlap value from the measurement data from the first structure and the second structure;

[0546] performing at least the transforming and inferring steps on measurement data associated with the first structure and the third structure to determine profile parameter values ​​for the first structure and the second structure; and

[0547] The overlap value is corrected for differences in profile parameter values ​​between the first structure and the second structure.

[0548] 57. The metrology method of any of clauses 49 to 56, wherein the profile parameter relates to a layer thickness of a resist layer on the substrate.

[0549] 58. A metrology method according to any of clauses 49 to 57, comprising determining a value of a parameter of interest corrected for the profile parameter or any variation in the profile parameter.

[0550] 59. The metrology method of any one of clauses 49 to 58, wherein the method of clause 43 is performed in order to obtain measurement data and corresponding values ​​of the profile parameters; and using the measurement data as the training data.

[0551] 60. A measurement method according to any one of items 46 to 49, wherein the measurement data includes at least asymmetry component data describing the asymmetry in the one or more structures; and optionally, the step of further transformation is performed to obtain a complex-valued spectrum of each structure in the distance space.

[0552] 61. The metrology method of clause 60, wherein the structure comprises a target structure comprising at least a first grating in a first layer and a second grating in a second layer.

[0553] 62. The metrology method of clause 61, wherein the method further comprises determining a path length difference between first radiation scattered by the first layer and second radiation scattered by the second layer.

[0554] 63. The metrology method of clause 62, wherein the profile parameter is overlay, and the path length difference relates to overlay.

[0555] 64. The measurement method according to clause 62 or 63, comprising:

[0556] determining a scalar asymmetry value from the path length difference; and

[0557] The profile parameters are determined from the scalar asymmetry values.

[0558] 65. The metrology method of clause 64, comprising using an estimate of the fixed phase difference between the first and second radiation to convert the scalar asymmetry value to a true asymmetry value.

[0559] 66. A measurement method according to clause 64 or 65, wherein the determining of the scalar asymmetry value is performed by integrating the peaks in the corresponding distance spectrum.

[0560] 67. The measurement method of clause 62 or 63, comprising:

[0561] applying a bandpass filter around the path length differences in the corresponding range spectra; and

[0562] Transform back to the reciprocal space.

[0563] 68. The measurement method of any one of clauses 62 to 67, comprising performing one or more of the following:

[0564] applying a correction to the asymmetry component data or the scalar asymmetry value to account for an illumination spectrum and / or a response spectrum of a detector used to detect the first and second radiation;

[0565] applying a correction to the refractive index of one or more media between the first and second layers;

[0566] Use a window function to filter out unwanted parts of the asymmetry component data.

[0567] 69. A method according to clause 62, wherein the profile parameter value includes a distance between the first grating and the second grating.

[0568] 70. A method according to item 69, wherein the method takes into account the wavelength or wavenumber dependent refractive index function of the first layer, the second layer and (multiple) any intervening layers and the diffraction angle through the diffracting radiation layer, and the measurement data relates to obtaining the distance between the first grating and the second grating.

[0569] 71. A method according to clause 70, wherein the measurement data also includes symmetry component data describing symmetry in the one or more structures.

[0570] 72. The method of clause 69 or 70, wherein the transforming to reciprocal space comprises determining a wavelength or wavenumber dependent function describing diffraction through the layer; and

[0571] The refractive index function is modified so that the product of the refractive index function and a wavelength or wavenumber dependent function can be inverted to find the wavenumber in terms of a function of the product in the wavenumber range of interest.

[0572] 73. The metrology method of any of clauses 46 to 49, comprising determining a reconstructed signal in real space from the transformed measurement data; and

[0573] At least one of the profile parameters is determined from the reconstructed signal.

[0574] 74. A measurement method according to item 73, wherein at least one of the profile parameters comprises one or more position and / or size parameters of the one or more structures.

[0575] 75. A metrology method according to clause 73, wherein the one or more position and / or size parameters include one or both of overlap or critical dimension.

[0576] 76. A measurement method according to clause 73 or 75, wherein the one or more position and / or size parameters include edge placement and / or edge placement error.

[0577] 77. A metrology method according to any of clauses 73 to 76, wherein the reciprocal space is a momentum transfer space, so that the transformed measurement data are described in terms of momentum transfer.

[0578] 78. The measurement method of clause 77, comprising mapping the measurement data from another reciprocal space into the momentum transfer space.

[0579] 79. A measurement method according to item 78, wherein the other reciprocal space includes wave number or wavelength space.

[0580] 80. A metrology method according to any of clauses 73 to 79, wherein the measurement data comprises diffraction efficiency or diffraction intensity, or any amplitude measure involving multiple diffraction orders.

[0581] 81. A measurement method according to any one of clauses 73 to 80, wherein the reconstructed signal comprises an autocorrelation of the amplitude in the real space.

[0582] 82. The metrology method of any one of clauses 73 to 81, wherein the reconstructed signal comprises regions of higher amplitude; and

[0583] Said step of determining one or more position and / or size parameters comprises determining these parameters from the size and / or position and / or configuration of one or more corresponding ones of said regions of higher amplitude.

[0584] 83. A method of measurement according to clause 82, wherein at least some of the regions of higher amplitude correspond to a different one of the one or more position and / or size parameters.

[0585] 84. A measurement method according to item 82 or 83, wherein the position of the area of ​​higher amplitude corresponding to a first direction in the real space indicates one or more of the position and / or size parameters in the first direction, and the first direction corresponds to a direction perpendicular to the substrate plane.

[0586] 85. The metrology method of clause 84, wherein the one or more of the position and / or size parameters in the first direction comprises one or more of:

[0587] the height(s) of the one or more structures; and / or

[0588] One or more distances between the one or more structures and / or features thereof.

[0589] 86. A measurement method according to any one of items 82 to 85, wherein the size and / or position and / or configuration of the higher amplitude area corresponding to the second direction and / or third direction parallel to the substrate plane indicates one or more of the position and / or size parameters in the second direction and / or third direction.

[0590] 87. The measurement method of clause 86, wherein the one or more of the position and / or size parameters in the second direction and / or the third direction comprises one or more of the following:

[0591] a width, critical dimension, or any other dimension of one or more of the one or more structures;

[0592] a difference in width, critical dimension, or any other dimension of features of at least two of the one or more structures and / or of the same structure;

[0593] an overlap or offset between at least two of the one or more structures; and / or

[0594] Structural asymmetry in one or more of the one or more structures.

[0595] 88. The metrology method of clause 86 or 87, wherein the size and / or position and / or configuration of the region in the second and / or third directions parallel to the substrate plane that indicates one or more of the position and / or size parameters in the second and / or third directions comprises one or more of:

[0596] one or more offsets of said regions relative to an origin;

[0597] the width of one or more of the regions; and / or

[0598] The size of the flat area of ​​the profile of one or more of the regions.

[0599] 89. The metrology method of clause 87 or 88, wherein the one or more structures include two interrelated structures each having a first pitch, the method comprising determining a width or critical dimension of one or both of the two interrelated structures according to:

[0600] If the sum of the widths of two interrelated structures is less than or equal to the first pitch, the width or critical dimension of one or more of the regions corresponds to the width or critical dimension of the larger of the two interrelated structures; and

[0601] If the sum of the widths of two interrelated structures is greater than or equal to the first pitch, then the width or critical dimension of one or more of the regions will correspond to the difference between the first pitch and the width or critical dimension of the smaller of the two interrelated structures.

[0602] 90. A measurement method according to any one of items 87 to 89, wherein the width or critical dimension of one or more of the regions is determined as the half-maximum full width at the midpoint between the highest value and the lowest value of the region of corresponding higher amplitude and / or the corresponding real-valued cross-correlation function of the region.

[0603] 91. The metrology method of any of clauses 82 to 91, wherein the one or more structures comprise a combined target comprising two or more offset targets, and the method comprises:

[0604] determining at least one of the regions of higher magnitude as a region associated with an overlap associated with the combined object and an associated value in the real space;

[0605] determining, for each offset value, a corresponding position value in the real space based on the area associated with the overlap; and

[0606] An overlap value is determined from the corresponding position values.

[0607] 92. The metrology method of clause 91, wherein the combined target is subject to raster imbalance such that for at least two of the two or more offset targets there are respective different said regions in said real space associated with overlap and respective associated values; and

[0608] The method includes determining each respective position value from its respective associated value.

[0609] 93. The measurement method of any of clauses 82 to 92, comprising determining a calibration to calibrate the reconstructed signal; the calibration comprising:

[0610] Creating multiple targets with varying process parameters so that the critical dimension of each target also varies;

[0611] Determine the reconstructed signal and the corresponding cross-correlation function for each target;

[0612] identifying, for a pair of complementary even diffraction orders, a target where a region of the reconstructed signal associated with a critical dimension is zero or near zero;

[0613] determining a threshold value such that a portion of the cross-correlation function corresponding to the target and the region of the reconstructed signal above the threshold value has a width equal to half the target pitch; and

[0614] The threshold is used to assign a critical dimension value to one or more of the other cross-correlation functions.

[0615] 94. The measurement method of any one of clauses 82 to 93, comprising:

[0616] identifying at least one of the regions of higher magnitude in real space as a region associated with a critical dimension of the one or more structures; and

[0617] The critical dimension is determined from a ratio of a first value of the reconstructed signal corresponding to the region associated with the critical dimension corresponding to a first, higher diffraction order, and a second value of the reconstructed signal corresponding to the region associated with the critical dimension corresponding to a second, higher diffraction order, a different diffraction order.

[0618] 95. The metrology method of any one of clauses 73 to 94, wherein the step of further transforming is performed with respect to an optimized region in the reciprocal space; wherein the optimized region is optimized with respect to one or more of:

[0619] There is no missing data in the optimized region;

[0620] For each value in the reciprocal space, a continuous range of diffraction orders is covered by the optimized region; and

[0621] Only combinations that can be explicitly extracted are covered.

[0622] 96. A measurement method according to any one of clauses 73 to 95, comprising: constructing a complete reconstruction of the one or more structures in one, two or three dimensions using the reconstruction signal.

[0623] 97. A metrology method according to any of clauses 73 to 96, comprising applying a correction to the actual refractive index of one or more structures and / or associated layers.

[0624] 98. A metrology method according to any of clauses 73 to 97, wherein the reconstructed signal comprises a combination of results from a plurality of measurements using different illumination spectra on the same structure or structures.

[0625] 99. A metrology method according to any one of clauses 73 to 98, wherein the measurement data relates to at least three diffraction orders.

[0626] 100. A metrology method according to any of clauses 73 to 99, wherein the measurement data relates to at least one pair of complementary higher order and zero order; or

[0627] Two pairs of complementary higher order.

[0628] 101. A metrology method according to any of clauses 73 to 98, wherein the measurement data relates to only one pair of complementary higher orders, and the method comprises:

[0629] determining a pair of complex values ​​of the reconstructed signal in a first direction perpendicular to the substrate plane, each of the pair of complex values ​​being associated with a respective higher order of a pair of complementary higher orders; and

[0630] Positions of the one or more structures in a second direction or a third direction parallel to the substrate plane are estimated by the complex value pair.

[0631] 102. The measurement method of clause 101, wherein the estimating step is based on extracting a phase difference between a first reconstructed signal of the complex-valued pair and a second reconstructed signal of the complex-valued pair.

[0632] 103. A measurement method according to any one of clauses 73 to 102, comprising applying a phase gradient correction to the reconstructed signal.

[0633] 104. A metrology method according to any of clauses 73 to 103, comprising splitting the measurement data into symmetric and asymmetric components and processing each component separately.

[0634] 105. A measurement method according to any one of items 73 to 104, comprising: using the reconstructed signal represented in real space; and / or its characteristics as input to a model, and training the model on reference data so that the trained model is able to correct any assumptions used in generating the reconstructed signal.

[0635] 106. The measurement method of clause 105, comprising using the trained model to correct any assumptions used in generating the reconstructed signal.

[0636] 107. A measurement method comprising:

[0637] obtaining, using a plurality of measurement setups, first measurement data associated with measurement values ​​of a first structure on the substrate and second measurement data associated with measurement values ​​of a second structure on the substrate, the first structure and the second structure having a difference in an imposed bias therebetween;

[0638] determining a first relationship between the first measurement data and the measurement setup and a second relationship between the second measurement data and the measurement setup;

[0639] Correcting the first measurement data and / or the second measurement data to modify the first relationship relative to the second relationship so that they have a common measurement setting for a particular measurement value; and

[0640] A profile parameter value is inferred based on the corrected first measurement data and / or second measurement data.

[0641] 108. The metrology method of clause 107, wherein the correction step comprises applying a mapping function or model which modifies the first relationship with respect to the second relationship so that they have a common measurement setting for the specific measurement value.

[0642] 109. The measurement method of clause 108, comprising transforming the first measurement data and the second measurement data into wave number or wavelength space to obtain inverted first measurement data and inverted second measurement data; and

[0643] Wherein said applying a mapping function or model is performed on said inverted first measurement data and said inverted second measurement data in said wave number or wavelength space.

[0644] 110. The metrology method of clause 107, 108 or 109, wherein the measurement data comprises a measured asymmetry, and the particular measurement value is zero asymmetry.

[0645] 111. A measurement method according to any one of clauses 107 to 110, wherein the correction step comprises shifting and / or scaling one of the first relations relative to the other relations.

[0646] 112. A measurement method according to any one of items 107 to 111, wherein the profile parameter is overlap.

[0647] 113. The metrology method of any one of clauses 107 to 112, wherein the measurement setup is to measure the wavelength of the illumination.

[0648] 114. A measurement method according to any one of clauses 107 to 113, comprising, before the correction step, determining a measure of any grating imbalance between the first structure and the second structure according to the amplitude of the difference in the measurement setup for the specific measurement value.

[0649] 115. A metrology method according to any of clauses 46 to 114, comprising irradiating the target with EUV, soft X-rays or hard X-rays.

[0650] 116. A method according to any preceding clause, comprising performing said measurements to obtain said measurement data.

[0651] 117. A computer program comprising computer-readable instructions operable to perform at least the processing and determining position steps of the method of any one of clauses 1 to 106.

[0652] 118. A processor and associated storage medium, the storage medium comprising the computer program of clause 117, rendering the processor operable to perform the method of any one of clauses 1 to 106.

[0653] 119. A measurement device comprising the processor of clause 118 and associated storage medium so as to be operable to perform the method of any one of clauses 1 to 116.

[0654] 120. The metrology device of clause 119, operable to determine a parameter of interest from the corrected measurement data.

[0655] 121. The metrology apparatus of clause 120, wherein the parameters of interest include one or more of overlay, critical dimension, focus, edge placement error on a substrate that has undergone a lithography process.

[0656] 122. The measurement device of clause 120, wherein the parameter of interest comprises the position of the structure.

[0657] 123. A lithographic apparatus arrangement comprising the metrology apparatus of any one of clauses 119 to 122.

[0658] 124. A lithography cell operable to perform the method of any one of clauses 1 to 116.

[0659] 125. A measurement device operable to perform the method of any one of clauses 1 to 116.

[0660] Further embodiments are disclosed in the subsequent numbered clauses:

[0661] 1. A metrology method, comprising: irradiating radiation onto a substrate; obtaining measurement data associated with at least one measurement value of each of one or more structures on the substrate; transforming the measurement data into transformed measurement data using a Fourier-related transform; and extracting characteristics of the substrate or eliminating the influence of an interfering parameter from the transformed measurement data.

[0662] 2. The metrology method of clause 1, wherein the one or more structures are projected onto the substrate by a lithographic apparatus.

[0663] 3. The metrology method according to clause 1 or 2, wherein transforming the measurement data into transformed measurement data using a Fourier-related transform comprises transforming the measurement data from reciprocal space to real space.

[0664] 4. The measurement method according to any one of the preceding clauses, wherein transforming the measurement data into the frequency domain comprises a Fourier transform.

[0665] 5. A measurement method according to any of the preceding clauses, wherein the method comprises a data-driven step or a training model.

[0666] 6. The measurement method according to any one of clauses 1 to 4, wherein the method is a non-iterative method.

[0667] 7. A measurement method according to any preceding clause, wherein the method does not include a strict forward model.

[0668] 8. A metrology method according to any preceding clause, wherein the step of extracting a characteristic of the substrate from the transformed measurement data comprises: determining the position of a peak in the transformed measurement data, and extracting the characteristic of the substrate from the position of the peak.

[0669] 9. A metrology method according to any preceding clause, wherein the measurement data relates to measurements of the same one or more structures, said measurements covering a time period over which characteristic changes are expected to be obtained to obtain time-dependent measurement data; and the method comprises:

[0670] A Fourier correlation transformation step is performed on the time-dependent measurement data, wherein, optionally, the method includes determining a change in a characteristic over time.

[0671] 10. The measurement method according to any one of the preceding clauses, wherein the Fourier correlation transform step is performed multiple times.

[0672] 11. A metrology method according to any preceding clause, wherein the measurement data comprises at least: an asymmetry component of the measurement data describing an asymmetry in one or more structures.

[0673] 12. A measurement method according to any preceding clause, wherein a Fourier correlation transform is performed to obtain a complex-valued spectrum of one or more structures in range space.

[0674] 13. A metrology method according to any preceding clause, wherein the one or more structures comprises a target structure comprising at least a first grating in the first layer and a second grating in the second layer.

[0675] 14. The metrology method of clause 13, wherein the characteristic of the substrate comprises a distance between the first grating and the second grating.

[0676] 15. A metrology method according to any preceding clause, wherein the measurement data further comprises: symmetry component data describing symmetry in one or more structures.

[0677] 16. A measurement method according to any preceding clause, comprising: determining a reconstructed signal in real space from the transformed measurement data; and

[0678] One or more position and / or size parameters of the one or more structures are determined from the reconstructed signal.

[0679] 17. The metrology method of clause 16, wherein the one or more position and / or size parameters include one or both of overlay or critical dimension.

[0680] 18. The metrology method according to clause 16 or 17, wherein the one or more position and / or size parameters include edge placement and / or edge placement error.

[0681] 19. The measurement method according to any of clauses 16 to 18, wherein the reconstructed signal comprises: an autocorrelation of the amplitude in real space.

[0682] 20. The measurement method according to any one of clauses 16 to 19, wherein the reconstructed signal comprises regions of higher amplitude; and

[0683] The step of determining one or more position and / or size parameters comprises determining these parameters from the size and / or position and / or configuration of one or more corresponding ones of the regions of higher amplitude.

[0684] 21. The metrology method of clause 20, wherein at least some of the regions of higher amplitude correspond to a different one of the one or more position and / or size parameters.

[0685] 22. A measurement method according to item 20 or 21, wherein the position of the area of ​​higher amplitude corresponding to the first direction in real space indicates one or more of the position and / or size parameters in the first direction, wherein the first direction corresponds to the direction perpendicular to the substrate plane.

[0686] 23. The measurement method according to clause 22, wherein the one or more position and / or size parameters in the first direction include one or more of the following:

[0687] the height or heights of one or more structures; and / or

[0688] One or more distances between one or more structures and / or features thereof.

[0689] 24. A measurement method according to any one of items 20 to 23, wherein the size and / or position and / or configuration of the higher amplitude area corresponding to the second and / or third directions parallel to the substrate plane indicates one or more of the position and / or size parameters in the second and / or third directions.

[0690] 25. The measurement method according to clause 24, wherein one or more of the position and / or size parameters in the second and / or third directions comprises one or more of the following:

[0691] the width, critical dimension, or any other dimension of one or more of the one or more structures;

[0692] a difference in width, critical dimension, or any other dimension of features of at least two of one or more structures and / or of the same structure;

[0693] an overlap or offset between at least two of the one or more structures; and / or

[0694] Structural asymmetry in one or more of the one or more structures.

[0695] 26. The metrology method according to clause 24 or 25, wherein the size and / or position and / or configuration of the area in the second and / or third directions parallel to the substrate plane that is indicative of one or more of the position and / or size parameters in the second and / or third directions comprises one or more of the following:

[0696] One or more offsets in the region relative to the origin;

[0697] the width of one or more of the regions; and / or

[0698] The size of the flat area of ​​one or more of the contours in the region.

[0699] 27. The metrology method of clause 25 or 26, wherein the one or more structures include two interrelated structures each having a first pitch, the method comprising determining a width or critical dimension of one or both of the two interrelated structures according to:

[0700] If the sum of the widths of the two interrelated structures is less than or equal to the first pitch, then the width or critical dimension of one or more of the regions corresponds to the width or critical dimension of the larger of the two interrelated structures; and

[0701] If the sum of the widths of the two interrelated structures is greater than or equal to the first pitch, then the width or critical dimension of one or more of the regions will correspond to the difference between the first pitch and the width or critical dimension of the smaller of the two interrelated structures.

[0702] 28. A measurement method according to any one of clauses 25 to 27, wherein the width or critical dimension of one or more of the regions is determined as the full width at half maximum at the midpoint between the highest value and the lowest value of the corresponding region of higher amplitude and / or the corresponding real-valued cross-correlation function of said region.

[0703] 29. A metrology method according to any of clauses 20 to 28, wherein one or more structures comprises a combined target comprising two or more offset targets, and the method comprises:

[0704] determining at least one of the regions of higher magnitude as a region associated with an overlap and a correlation value in real space associated with the combined target;

[0705] determining, for each offset value, a corresponding position value in real space based on the area associated with the overlap; and

[0706] The overlap value is determined from the corresponding position values.

[0707] 30. The metrology method of clause 29, wherein the combined target is subject to raster imbalance such that for at least two of the two or more offset targets there are respective different regions in real space associated with overlap and respective associated values; and

[0708] The method includes determining each respective position value from its respective associated value.

[0709] 31. The measurement method according to any one of clauses 20 to 30, comprising determining a calibration to calibrate the reconstructed signal; said calibration comprising:

[0710] Creating multiple targets with varying process parameters so that the critical dimension of each target also varies;

[0711] Determine the reconstructed signal and the corresponding cross-correlation function for each target;

[0712] identifying a region of the target where the reconstructed signal associated with the critical dimension is zero or near zero for a pair of complementary even diffraction orders;

[0713] determining a threshold value such that a portion of the cross-correlation function corresponding to an area of ​​the target and the reconstructed signal above the threshold value has a width equal to half the target pitch; and

[0714] A threshold is used to assign a critical dimension value to one or more of the other cross-correlation functions.

[0715] 32. The measurement method according to any one of clauses 20 to 31, comprising:

[0716] identifying at least one of the regions of higher magnitude in real space as a region associated with a critical dimension of the one or more structures; and

[0717] The critical dimension is determined from a ratio of a first value of the reconstructed signal corresponding to an area associated with the critical dimension (corresponding to a first, higher diffraction order) and a second value of the reconstructed signal corresponding to an area associated with the critical dimension (corresponding to a second, higher diffraction order, a different diffraction order).

[0718] 33. The metrology method of any one of clauses 16 to 32, wherein the step of further transforming is performed on an optimized region in reciprocal space; wherein the optimized region is optimized for one or more of:

[0719] There is no missing data in the optimized region;

[0720] For each value of in reciprocal space, the continuous range of diffraction orders is covered by the optimization region; and

[0721] Only combinations that can be explicitly extracted are covered.

[0722] 34. The measurement method according to any of clauses 16 to 33, comprising constructing a complete reconstruction of the one or more structures in one, two or three dimensions by the reconstruction signal.

[0723] 35. The metrology method of any of clauses 16 to 34, comprising applying a correction to the actual refractive index of one or more structures and / or associated layers.

[0724] 36. The metrology method according to any of clauses 16 to 35, wherein the reconstructed signal comprises a combination of results from a plurality of measurements using different illumination spectra on the same structure or structures.

[0725] 37. The metrology method according to any of clauses 16 to 36, wherein the measurement data relate to at least three diffraction orders.

[0726] 38. The measurement method according to any one of clauses 16 to 37, wherein the measurement data relates to at least one pair of complementary higher order and zero order; or

[0727] Two pairs of complementary higher order.

[0728] 39. The metrology method of any one of clauses 16 to 36, wherein the measurement data relates to only one pair of complementary higher orders, and the method comprises:

[0729] determining a pair of complex values ​​of the reconstructed signal in a first direction perpendicular to the substrate plane, each associated with a corresponding higher order of a pair of complementary higher orders; and

[0730] The position of the one or more structures in a second or third direction parallel to the substrate plane is estimated by the complex value pair.

[0731] 40. The measurement method according to clause 39, wherein the estimating step is based on extracting a phase difference between a first reconstructed signal of the complex-valued pair and a second reconstructed signal of the complex-valued pair.

[0732] 41. The measurement method according to any of clauses 16 to 40, comprising applying a phase gradient correction to the reconstructed signal.

[0733] 42. A metrology method according to any of clauses 16 to 41, comprising splitting the measurement data into symmetric and asymmetric components and processing each component separately.

[0734] 43. A measurement method according to any one of clauses 16 to 42, comprising using a reconstructed signal represented in real space; and / or its characteristics as input to a model, and training the model on reference data so that the trained model is able to correct any assumptions used in generating the reconstructed signal.

[0735] 44. The measurement method of clause 43, comprising using the trained model to correct any assumptions used in generating the reconstructed signal.

[0736] 45. A measurement method according to any preceding clause, wherein the measurement data comprises diffraction efficiency or diffraction intensity, or any amplitude measure involving multiple diffraction orders.

[0737] 46. ​​A measurement method comprising:

[0738] obtaining, using a plurality of measurement setups, first measurement data associated with measurement values ​​of a first structure on the substrate and second measurement data associated with measurement values ​​of a second structure on the substrate, the first structure and the second structure having a difference in an imposed bias therebetween;

[0739] determining a first relationship between the first measurement data and the measurement setup and a second relationship between the second measurement data and the measurement setup;

[0740] Correcting the first and / or second measurement data to modify the first relationship relative to the second relationship so that they have a common measurement setting for the specific measurement value; and inferring a structural parameter value based on the corrected first and / or second measurement data.

[0741] 47. A method of inferring a value of a parameter of interest from measured data, comprising:

[0742] obtaining measurement data related to scattered radiation from the target captured at the detector;

[0743] obtaining a trained forward model describing the measurement signal in terms of at least one parameter of a term of interest describing a response of a parameter of interest of the target, one or more nuisance terms describing other variations between measured values ​​of the target, and a constant term representing a constant component of the measurement data; and

[0744] Using the trained forward model, the values ​​of the parameters of interest are inferred from the measured data.

[0745] 48. A computer program comprising computer-readable instructions operable to perform at least the steps of the method of any one of clauses 1 to 47, comprising:

[0746] transforming the measured data into the frequency domain, and

[0747] Extract substrate features or eliminate the influence of interfering parameters.

[0748] 49. A measurement device operable to perform the method of any one of clauses 1 to 47.

[0749] Although specific reference may be made herein to the use of lithographic apparatus in the manufacture of integrated circuits, it should be understood that the lithographic apparatus described herein may have other applications. Possible other applications include the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, and the like.

[0750] Although embodiments may be specifically referenced herein in the context of lithographic apparatus, embodiments may be used in other apparatus. Embodiments may form part of mask inspection equipment, metrology equipment, or any apparatus that measures or processes objects such as wafers (or other substrates) or masks (or other patterning devices). These apparatuses may generally be referred to as lithographic tools. Such lithographic tools may use vacuum conditions or ambient (non-vacuum) conditions.

[0751] Although embodiments may be specifically referenced herein in the context of inspection or metrology equipment, embodiments may be used in other equipment. Embodiments may form part of mask inspection equipment, lithography equipment, or any equipment that measures or processes objects such as wafers (or other substrates) or masks (or other pattern forming devices). The term "metrology equipment" (or "inspection equipment") may also refer to an inspection equipment or inspection system (e.g., a metrology equipment or a metrology system). For example, an inspection equipment including an embodiment may be used to detect defects in a substrate or defects in a structure on a substrate. In such embodiments, a characteristic of a structure of interest on a substrate may be associated with a defect in the structure, the absence of a specific portion of the structure, or the presence of an unwanted structure on the substrate.

[0752] Although specific reference may have been 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 imprint lithography, where the context permits.

[0753] While the targets or target structures (more generally, structures on a substrate) described above are metrology target structures that are specifically designed and formed for measurement purposes, in other embodiments, the property of interest may be measured on 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 provided specifically for the measurement being performed. Further, the pitch of the metrology target may be close to the resolution limit of the optical system of the scatterometer or may be smaller, but may be much larger than the size of typical non-target structures (optionally product structures) made by the lithographic process in the target portion C. In practice, the lines and / or spaces of the overlapping gratings within the target structure may be made to include smaller structures of similar size to the non-target structures.

[0754] Although specific embodiments have been described above, it will be appreciated that the present invention may be practiced in ways other than those described. The above description is intended to be illustrative, not restrictive. Therefore, it will be apparent to those skilled in the art that modifications may be made to the described invention without departing from the scope of the claims set forth below.

[0755] Although specific reference is made to a "metrology device / tool / system" or an "inspection device / tool / system," these terms may refer to the same or similar types of tools, devices, or systems. For example, an inspection or metrology device including embodiments of the present invention may be used to determine characteristics of structures on a substrate or wafer. For example, an inspection or metrology device including embodiments of the present invention may be used to detect defects in a substrate or defects in a structure on a substrate or wafer. In such embodiments, the characteristic of a structure of interest on a substrate may be related 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.

[0756] Although specific reference is made to SXR and EUV electromagnetic radiation, it is to be understood that the present invention can be practiced with all electromagnetic radiation, including radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays, where the context permits. As an alternative to optical metrology methods, it is also contemplated to use X-rays, optionally hard X-rays, for example radiation in the wavelength range between 0.01 nm and 10 nm, or alternatively between 0.01 nm and 0.2 nm, or alternatively between 0.1 nm and 0.2 nm, for metrology measurements.

Claims

1. A measurement method comprising: directing radiation onto the substrate; obtaining measurement data associated with at least one measurement value for each of one or more structures on the substrate; transforming the measurement data into transformed measurement data using a Fourier-related transform, wherein the transformed measurement data includes a depth spectrum; and Features of the substrate are extracted from the transformed measurement data or the influence of interfering parameters is eliminated.

2. The metrology method according to claim 1 , wherein the step of extracting the characteristics of the substrate from the transformed measurement data or eliminating the influence of the nuisance parameter comprises: determining a reconstructed signal from the transformed measurement data; as well as One or more position parameters and / or size parameters of the one or more structures are determined from the reconstructed signal.

3. The measurement method according to claim 2, wherein the reconstructed signal includes a region of higher amplitude; and The step of determining one or more position parameters and / or size parameters comprises: These parameters are determined by the size and / or position and / or configuration of the corresponding one or more of the regions of higher amplitude.

4. A measurement method according to claim 3, wherein the size and / or position and / or configuration of the higher amplitude area corresponding to the second direction and / or third direction parallel to the substrate plane indicates one or more of the position and / or size parameters in the second direction and / or third direction.

5. The measurement method according to any one of claims 2 to 4, wherein the reconstructed signal comprises: The results from multiple measurements using different illumination spectra on the same structure or structures are combined.

6. The metrology method according to claim 1 , wherein the step of extracting the characteristics of the substrate from the transformed measurement data or eliminating the influence of the nuisance parameter comprises: The location of the peak in the transformed measurement data is determined, and features of the substrate are extracted from the location of the peak.

7. The metrology method according to any one of the preceding claims, wherein said transforming the measurement data into transformed measurement data using a Fourier-related transform comprises: The measurement data are transformed from reciprocal space to real space.

8. The measurement method according to claim 7, wherein: The transforming of the measurement data into the frequency domain comprises a Fourier transform.

9. The measurement method according to claim 7 or 8, wherein: The method also includes converting the transformed measurement data back to the reciprocal space.

10. The metrology method according to any one of the preceding claims, wherein the step of extracting characteristics of the substrate from the transformed measurement data or eliminating the influence of nuisance parameters comprises: A bandpass filter is applied to the transformed measurement data.

11. The measurement method according to any one of the preceding claims, wherein the method further comprises: Weighting steps using a weighting function.

12. The metrology method according to any one of the preceding claims, wherein the step of obtaining measurement data relating to at least one measurement value for each of the one or more structures on the substrate comprises: A diffraction pattern is obtained from a target structure comprising at least two different offset targets.

13. The metrology method according to any one of the preceding claims, wherein the method is a non-iterative method.

14. The method according to any one of claims 1 to 12, wherein the method is an iterative method.

15. The metrology method according to any of the preceding claims, wherein the method comprises a data driven step or a training model.

16. The measurement method according to any one of the preceding claims, wherein the measurement data comprises at least: The asymmetry or symmetry component of the measurement data is used to describe the asymmetry in the one or more structures.

17. A metrology method according to any preceding claim, wherein the measurement data comprises diffraction efficiency or diffraction intensity, or any amplitude measure involving a plurality of diffraction orders.

18. The metrology method according to any of the preceding claims, wherein a Fourier correlation transform is performed to obtain a complex-valued spectrum of one or more structures in range space.

19. A non-transitory computer program product comprising machine-readable instructions configured to, when executed by a computer system, cause the computer system to at least perform the method of any one of claims 1 to 18.

20. A metrology device comprising a controller, wherein the controller is configured to cause performance of the method of any one of claims 1 to 18.

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