Metrology method and apparatus, computer program and lithography system

Abstract

A method, computer program, and related apparatus for metrology are disclosed. The method includes determining a reconstruction scheme that describes at least nominal values ​​for use in a reconstruction describing a parameterization of a target. The method includes acquiring first measurement data associated with a measurement of a plurality of targets on at least one substrate, the measurement data associated with one or more acquisition settings, and performing an optimization by minimizing a cost function that minimizes a difference between the first measurement data and simulated measurement data based on a reconstructed parameterization of each of the plurality of targets. Constraints on the cost function are imposed based on a hierarchical prior. A hybrid model for providing simulation data for reconstruction is also disclosed, including acquiring a coarse model operable to provide simulation coarse data; and training a data-driven model to correct the simulation coarse data to determine the simulation data.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to EP application 19162808.0 filed on March 14, 2019 and EP application 19178432.1 filed on June 5, 2019, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present invention relates to methods and apparatus useful for metrology of devices manufactured, for example, by photolithography. Background Art

[0004] A lithographic apparatus is a machine that applies a desired pattern to a substrate (usually to a target portion of the substrate). A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In this case, a patterning device (which is alternatively referred to as a mask or reticle) can be used to generate a circuit pattern to be formed on a single layer of the IC. The pattern can be transferred to a target portion (e.g., a portion including one or several dies) on a substrate (e.g., a silicon wafer). The transfer of the pattern is usually performed via imaging onto a layer of radiation-sensitive material (resist) disposed on the substrate. Typically, a single substrate will contain a network of adjacent target portions that are patterned continuously. In the lithographic process, it is often necessary to measure the created structure, for example, for process control and verification. Various tools for making such measurements are known, including scanning electron microscopes that are typically used to measure critical dimensions (CDs), and special tools for measuring overlap (measurement of the alignment accuracy of two layers in a device). Overlap can be described in terms of the degree of misalignment between two layers, for example, a reference to a measured overlap of 1 nm can describe a situation where the two layers are misaligned by 1 nm.

[0005] Recently, various forms of scatterometers have been developed for use in the field of lithography. These devices direct a radiation beam onto a target and measure one or more properties of the scattered radiation—for example, intensity at a single reflection angle as a function of wavelength; intensity at one or more wavelengths as a function of reflection angle; or polarization as a function of reflection angle—to obtain a diffraction image or pattern from which a property of interest of the target can be determined.

[0006] In order to cause the radiation impinging on the substrate to be diffracted, an object of a specific shape is printed onto the substrate and is often referred to as a scatterometry target or simply a target. As described above, the actual shape of the scatterometry object can be determined using a cross-sectional scanning electron microscope or the like. However, this involves a lot of time, effort and dedicated equipment and is not well suited for measurements in a production environment, as separate dedicated equipment is required that is consistent with the normal equipment in, for example, a lithography cell.

[0007] The determination of the characteristic of interest can be performed by various techniques: for example, reconstruction. Reconstruction (defined as inference of a given parameterization based on measured data) uses an iterative solver to find the solution to the inverse problem (e.g., intensity via reflectivity to parameterization). RCWA is a forward model (parameterization via reflectivity to intensity) that can simulate the response of the model to light; however, it cannot be used alone to infer the backward parameterization.

[0008] To perform such a reconstruction, a contour defining the shape of the measured structure in terms of multiple parameters may be used. To make the contour more robust, a reconstruction scheme describing good nominal values ​​of the parameters (representative of the whole data) should be chosen.

[0009] Hopefully this provides a method that can help define refactoring scenarios. Summary of the invention

[0010] In a first aspect, the present invention provides a method for determining a reconstruction scheme, which describes at least nominal values ​​used in a reconstruction describing a parameterization of a target; the method comprises: acquiring first measurement data related to measurements of multiple targets on at least one substrate, the measurement data being related to one or more acquisition settings; performing optimization by minimizing a cost function, the cost function minimizing the difference between the first measurement data and simulated measurement data based on the reconstructed parameterization of each of the multiple targets; wherein constraints on the cost function are imposed based on a hierarchical prior.

[0011] In a second aspect, the present invention provides a method for constructing a hybrid model for providing simulated data for use in parameter reconstruction of a structure, the method comprising: obtaining a coarse model operable to provide simulated coarse data; and training a data-driven model to correct the simulated coarse data to determine the simulated data.

[0012] The present invention provides in a third aspect a metrology apparatus operable to perform the method of the first and / or second aspect. The present invention provides in a fourth aspect a lithography system comprising the metrology apparatus of the third aspect.

[0013] The invention also provides a computer program comprising processor-readable instructions which, when run on a suitable processor-controlled device, cause the processor-controlled device to perform the method of the first and / or second aspects, and a computer program carrier comprising such a computer program. The processor-controlled device may comprise the metrology device of the third aspect or the lithography system of the fourth aspect.

[0014] The other features and advantages of the present invention, as well as the structure and operation of various embodiments of the present invention are described in detail below with reference to the accompanying drawings. Note that the present invention is not limited to the specific embodiments described herein. Such embodiments are presented herein for illustrative purposes only. Based on the teachings contained herein, other embodiments will be clear to those skilled in the relevant art. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0016] Figure 1 depicts the lithographic apparatus;

[0017] Figure 2 The lithographic unit is depicted;

[0018] Figure 3 The first scatterometer is depicted;

[0019] Figure 4 A second scatterometer is depicted;

[0020] Figure 5 is a flow chart depicting a first example process for reconstructing a structure from scatterometry measurements;

[0021] Figure 6 is a flow chart depicting a second example process for reconstructing a structure from scatterometry measurements;

[0022] Figure 7 depicts input data for a hierarchical solver according to an embodiment of the present invention;

[0023] Figure 8 is a flowchart depicting a method according to an embodiment of the present invention;

[0024] Fig. 9 is a flow chart depicting the matching of single-objective reconstruction with hierarchical solver;

[0025] Fig.10 is a flow chart depicting the training of a hybrid model according to an embodiment of the present invention;

[0026] Fig.11 Is Fig.10 Abstract visualization of the parameter space defined by the coarse model and the data-driven model of the hybrid model;

[0027] Fig.12 is a flow chart depicting the training of an alternative hybrid model according to an embodiment of the present invention;

[0028] Fig.13 is a schematic diagram of a method in which parameter reasoning is based on measurements of in-product and out-of-product objectives;

[0029] Fig.14 is a schematic diagram of a first example of a decorrelation library for metrological inference;

[0030] Fig.15 is a schematic diagram of a second example of a decorrelation library for metrology inference (including parameter bypassing);

[0031] Fig.16 is a schematic diagram of a third example of a decorrelation library for metrological inference (including direct inference of one or more parameters);

[0032] Fig.17 is a schematic diagram of a fourth example of a decorrelation library for metrological inference (including another example of direct inference of one or more parameters);

[0033] Fig.18 is a schematic diagram of a fifth example of a decorrelation library for metrological inference including parallel bottleneck layers for different classes of parameters; and

[0034] Fig.19 is a schematic diagram of a sixth example of a decorrelation library for metrological reasoning (including a remapping library);

[0035] Fig. 20 is a schematic diagram of a polynomial model and associated sigmoid of material properties as a function of wavelength according to one embodiment of the present invention. DETAILED DESCRIPTION

[0036] Before describing embodiments of the present invention in detail, it is helpful to present an example environment in which embodiments of the present invention may be implemented.

[0037] Figure 1 A lithographic apparatus LA is schematically depicted. The apparatus comprises an illumination optical system (illuminator) IL configured to condition a radiation beam B (e.g., UV radiation or DUV radiation), a patterning device support or support structure (e.g., mask stage) MT configured to support a patterning device (e.g., mask) MA and connected to a first positioner PM configured to accurately position the patterning device according to certain parameters, a substrate stage (e.g., wafer stage) WT configured to hold a substrate (e.g., a wafer coated with resist) W and connected to a second positioner PW configured to accurately position the substrate according to certain parameters, and a projection optical 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.

[0038] The illumination optics system may include various types of optical components for directing, shaping, or controlling radiation, such as refractive, reflective, magnetic, electromagnetic, electrostatic or other types of optical components, or any combination thereof.

[0039] The patterning device support holds the patterning device in a manner that depends on the orientation of the patterning device, the design of the lithographic apparatus, and other conditions (e.g., whether the patterning device is held in a vacuum environment). The patterning device support can hold the patterning device using mechanical, vacuum, electrostatic, or other clamping techniques. The patterning device support can be, for example, a frame or a workbench that can be fixed or movable as needed. The patterning device support can ensure that the patterning device is in a desired position, for example, relative to a projection system. Any use of the term "reticle" or "mask" herein can be considered synonymous with the more general term "patterning device".

[0040] The term "patterning device" as used herein should be broadly interpreted as referring to any device that can be used to impart a pattern to a cross-section of a radiation beam so as to produce a pattern in a target area of ​​the substrate. It should be noted that the pattern imparted to the radiation beam may not exactly correspond to the desired pattern in the target portion of the substrate, for example if the pattern includes phase-shifting features or so called assist features. Typically, the pattern imparted to the radiation beam will correspond to a specific functional layer in a device being produced in the target portion, such as an integrated circuit.

[0041] The patterning device may be transmissive or reflective. Examples of patterning devices include masks, programmable mirror arrays, and programmable LCD panels. Masks are well known in lithography and include mask types such as binary, alternating phase shift, and attenuated phase shift, as well as various hybrid mask types. An example of a programmable mirror array employs a matrix arrangement of small mirrors, each of which can be individually tilted to reflect an incoming radiation beam in different directions. The tilted mirrors impart a pattern in the radiation beam, which is reflected by the matrix of mirrors.

[0042] As depicted herein, the device is transmissive (eg, employing a transmissive mask). Alternatively, the device may be reflective (eg, employing a programmable mirror array of the type described above, or employing a reflective mask).

[0043] The lithographic apparatus may also be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index (e.g., water) to fill the space between the projection system and the substrate. Immersion liquid may also be applied to other spaces in the lithographic apparatus, such as between the mask and the projection system. Immersion techniques for increasing the numerical aperture of the projection system are well known in the art. The term "immersion" as used herein does not mean that structures such as the substrate must be submerged in the liquid, but only that the liquid is located between the projection system and the substrate during exposure.

[0044] refer to Figure 1 , the illuminator IL receives a radiation beam from a radiation source SO. The source and the lithographic apparatus may be separate entities, for example when the source is an excimer laser. In this case, the source is not considered to form part of the lithographic apparatus, and the radiation beam is transferred from the source SO to the illuminator IL with the aid of a beam delivery system BD comprising, for example, suitable directional mirrors and / or a beam expander. In other cases, for example when the source is a mercury lamp, the source may be an integral part of the lithographic apparatus. If desired, the source SO and the illuminator IL together with the beam delivery system BD may be referred to as a radiation system.

[0045] The illuminator IL may include an adjuster AD for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent of the intensity distribution in a pupil plane of the illuminator (commonly referred to as outer σ and inner σ, respectively) may be adjusted. Furthermore, the illuminator IL may include various other components, such as an integrator IN and a condenser CO. The illuminator may be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0046] The radiation beam B is incident on a patterning device (e.g. a mask) MA held on a patterning device support (e.g. a mask table MT) and is patterned by the patterning device. After passing through the patterning device (e.g. a mask) MA, the radiation beam B passes through a projection optical system PS, which focuses the beam onto a target portion C of the substrate W, thereby projecting an image of the pattern onto the target portion C. With the aid of a second positioner PW and a positioning sensor IF (e.g. an interferometric measurement device, a linear encoder, a 2D encoder or a capacitive sensor), the substrate table WT can be accurately moved, for example, in order to position different target portions C in the path of the radiation beam B. Similarly, for example, after mechanical retrieval from a mask library or during scanning, the first positioner PM and the further positioning sensor (not in Figure 1 ) can be used to accurately position the patterning device (e.g., mask) MA relative to the path of the radiation beam B.

[0047] Mask alignment marks M1, M2 and substrate alignment marks P1, P2 can be used to align the patterning device (e.g., mask) MA and substrate W. Although the substrate alignment marks as shown occupy dedicated target portions, they can be located in the space between the target portions (these are referred to as scribe alignment marks). Similarly, in the case where more than one die is provided on the patterning device (e.g., mask) MA, the mask alignment marks can be located between the dies. Small alignment marks can also be included in the die, in the device features, in which case it is desired that the marks be as small as possible and do not require imaging or process conditions that are different from adjacent features. The alignment system for detecting alignment marks is further described below.

[0048] The lithographic apparatus LA in this example is of a so-called dual-stage type having two substrate tables WTa, WTb and two stations (exposure station and measurement station) between which the substrate table can be exchanged. While one substrate on one substrate table is being exposed at the exposure station, another substrate can be loaded onto the other substrate table at the measurement station and various preparation steps performed. The preparation steps may include mapping the surface control of the substrate using a level sensor LS and measuring the positioning of alignment marks on the substrate using an alignment sensor AS. This enables a significant increase in the throughput of the apparatus.

[0049] The depicted apparatus may be used in a variety of modes including, for example, step mode or scan mode.The construction and operation of lithographic apparatus are well known to those skilled in the art and require no further description for an understanding of the present invention.

[0050] like Figure 2 As shown, the lithographic apparatus LA forms part of a lithographic system, referred to as a lithographic cell LC or a lithocell. The lithographic cell LC may also include equipment for performing pre-exposure and post-exposure processes on a substrate. Typically these include a spin coater SC for depositing a resist layer, a developer DE for developing the exposed resist, a cooling plate CH and a baking plate BK. A substrate handler or robot (RO) picks up substrates from input / output ports I / O1, I / O2, moves them between different processing devices, and then transfers them to a loading station LB of the lithographic apparatus. These devices (generally referred to as tracks) are under the control of a track control unit TCU, which itself is controlled by a supervisory control system SCS, which also controls the lithographic apparatus via a lithographic control unit LACU. Therefore, different devices can be operated to maximize throughput and processing efficiency.

[0051] In order to correctly and consistently expose substrates exposed by a lithographic apparatus, it is necessary to inspect the exposed substrates to measure characteristics such as overlay errors between subsequent layers, line thickness, critical dimensions (CD), etc. If errors are detected, the exposure of subsequent substrates can be adjusted, especially if the inspection can be completed soon and quickly enough so that other substrates of the same batch are still to be exposed. In addition, already exposed substrates can be stripped and reworked (to improve yield) or discarded, thereby avoiding exposures performed on substrates that are known to be defective. In the case where only some target portions of the substrate are defective, further exposures can be performed only on the good target portions.

[0052] The inspection equipment is used to determine the characteristics of the substrate, in particular how the characteristics of different substrates or different layers of the same substrate vary between layers. The inspection equipment can be integrated into the lithographic equipment LA or the lithographic unit LC or can be a stand-alone device. In order to be able to make the fastest measurement, it is desirable that the inspection equipment measures the characteristics in the exposed resist layer immediately after exposure. However, the latent image in the resist has a very low contrast - the difference in refractive index between the part of the resist that has been exposed to radiation and the part that has not been exposed to radiation is small - and not all inspection equipment has sufficient sensitivity to make useful measurements of the latent image. Therefore, the measurement can be made after the post-exposure baking step (PEB), which is usually the first step performed on the exposed substrate and increases the contrast between the exposed and unexposed parts of the resist. At this stage, the image in the resist can be called semi-latent. It is also possible to measure the developed resist image - at this time, the exposed or unexposed parts of the resist have been removed - or after a pattern transfer step such as etching. The latter possibility limits the possibility of reworking defective substrates, but can still provide useful information.

[0053] Figure 3 A scatterometer that can be used in the present invention is depicted. It comprises a broadband (white light) radiation projector 2 that projects radiation onto a substrate W. The reflected radiation is passed to a spectrometer detector 4 which measures the spectrum 10 (intensity as a function of wavelength) of the specularly reflected radiation. From this data, for example by Rigorous Coupled Wave Analysis and nonlinear regression or by comparing Figure 3 The structure or profile of the detected spectrum produced by comparison with the simulated spectral library shown at the bottom can be reconstructed by the processing unit PU. In general, for the reconstruction, the general form of the structure is known and some parameters are assumed based on knowledge of the process by which the structure was manufactured, leaving only a few parameters of the structure to be determined from the scatterometry data. Such a scatterometer can be configured as a normal incidence scatterometer or an oblique incidence scatterometer.

[0054] Another scatterometer that can be used with the present invention is Figure 4 1 is shown in FIG. 1 . In this device, the radiation emitted by the radiation source 2 is collimated using a lens system 12 and transmitted through an interference filter 13 and a polarizer 17, partially reflected by a reflective surface 16, and focused onto a substrate W via a microscope objective 15, which has a high numerical aperture (NA), preferably at least 0.9, more preferably at least 0.95. An immersion scatterometer can even have a lens with a numerical aperture greater than 1. The reflected radiation is then transmitted through the partially reflective surface 16 into a detector 18 in order to detect the scatter spectrum. The detector can be located in a back-projected pupil plane 11, which is at the focal length of the lens system 15, however, the pupil plane can alternatively be re-imaged onto the detector using auxiliary optics (not shown). The pupil plane is a plane in which the radial positioning of the radiation defines the angle of incidence and the angular positioning defines the azimuth of the radiation. The detector is preferably a two-dimensional detector so that a two-dimensional angular scatter spectrum of a substrate target 30 can be measured. The detector 18 may be, for example, a CCD or CMOS sensor array, and may use an integration time of, for example, 40 milliseconds per frame.

[0055] The reference beam is often used, for example, to measure the intensity of the incident radiation. To this end, when the radiation beam is incident on the beam splitter 16, part of it is transmitted through the beam splitter as a reference beam towards the reference mirror 14. The reference beam is then projected onto a different part of the same detector 18 or alternatively onto a different detector (not shown).

[0056] A set of interference filters 13 may be used to select wavelengths of interest in the range of, for example, 405-790 nm or even lower, such as 200-300 nm. The interference filters may be tunable, rather than comprising a set of different filters. Gratings may be used instead of interference filters.

[0057] Detector 18 can measure the intensity of scattered light of a single wavelength (or narrow wavelength range), the intensity of a single plurality of wavelengths, or the intensity integrated over the wavelength range. In addition, the detector can measure the intensity of transverse magnetic polarized light and transverse electric polarized light and / or the phase difference between transverse magnetic polarized light and transverse electric polarized light, respectively.

[0058] A broadband light source (i.e., a light source with a wide range of optical frequencies or wavelengths - and therefore colors) can be used, which provides a large etendue, allowing the mixing of multiple wavelengths. The multiple wavelengths in the broadband preferably each have a bandwidth of Δλ and a spacing of at least 2Δλ (i.e., twice the bandwidth). The several radiation "sources" can be different parts of an extended radiation source, which have been separated using a fiber optic bundle. In this way, angle-resolved scatter spectra can be measured in parallel at multiple wavelengths. A 3D spectrum (wavelength and two different angles) can be measured, which contains more information than a 2D spectrum. This allows more information to be measured, thereby improving the robustness of the metrology process.

[0059] The target 30 on the substrate W may be a 1-D grating which is printed so that after development the bars are formed by solid resist lines. The target 30 may be a 2-D grating which is printed so that after development the grating is formed by solid resist columns or vias in the resist. The bars, columns or vias may alternatively be etched into the substrate. The pattern is sensitive to chromatic aberrations in the lithographic projection equipment (particularly the projection system PL) and the illumination symmetry and the presence of such aberrations will manifest themselves in variations in the printed grating. Therefore, scatterometry data of the printed grating are used to reconstruct the grating. Based on knowledge of the printing step and / or other scatterometry processes, parameters of the 1-D grating (such as line width and shape) or parameters of the 2-D grating (such as column or via width or length or shape) may be input to a reconstruction process performed by the processing unit PU.

[0060] As mentioned above, the target is on the surface of the substrate. The target is typically in the shape of a series of lines in a grating or a basic rectangular structure of a 2-D array. The purpose of rigorous optical diffraction theory in metrology is to efficiently calculate the diffraction spectrum reflected from the target. In other words, the target shape information is acquired for CD (critical dimension) uniformity and overlay or focus metrology. Overlay metrology is a measurement system in which the overlap of two targets is measured to determine whether two layers on a substrate are aligned. Focus metrology determines the focus (and / or dose) setting used when forming the target. CD uniformity is simply a measure of the uniformity of the grating over the spectrum to determine how the exposure system of the lithographic equipment works. Specifically, the CD or critical dimension is the width of the object "written" on the substrate and is the limit of what the lithographic equipment can physically write on the substrate.

[0061] Reconstruction-based scatterometry - Background

[0062] Using a scatterometer (such as described above in conjunction with modeling of a target structure such as target 30 and its diffraction properties), measurement of the shape and other parameters of the structure can be performed in a variety of ways. Figure 5In the first type of process, a diffraction pattern based on a first estimate of the target shape (a first candidate structure) is calculated and compared to the observed diffraction pattern. The parameters of the model are then systematically varied and the diffraction is recalculated in a series of iterations to generate new candidate structures to achieve the best fit. In the second type of process, as Figure 6 As shown, the diffraction spectra of many different candidate structures are pre-calculated to create a "library" of diffraction spectra. The observed diffraction pattern according to the measurement target is then compared to the calculated spectral library to find the best fit. These two methods can be used together: a rough fit can be obtained from the library, and then an iterative process is used to find the best fit.

[0063] exist Figure 5 and Figure 6 Throughout the description of Figure 3 or Figure 4 The term "diffraction image" is used on the assumption of a scatterometer. A diffraction image is an example of an inspection data element within the context of the present disclosure. One skilled in the art can easily adapt the teachings to different types of scatterometers, or even other types of measurement instruments.

[0064] Figure 5 is a flow chart of the steps of a method of measuring a target shape and / or material property which is generally described. The steps are as follows and are then described in more detail:

[0065] 402- measuring the diffraction image;

[0066] 403-define model scheme;

[0067] 404-estimate shape parameter θ0;

[0068] 406-calculate model diffraction image;

[0069] 408 - Comparing the measured image with the calculated image;

[0070] 410-calculate merit function;

[0071] 412 - generating a modified shape parameter θ1;

[0072] 414 - Report final shape parameters

[0073] For this description it will be assumed that the target is periodic in only 1 direction (1-D structure). In practice it may be periodic in 2 directions (2D structure) and the processing will be adapted accordingly.

[0074] 402: The diffraction image of the actual target on the substrate is measured using a scatterometer (such as the scatterometer described above). The measured diffraction image is forwarded to a computing system such as a computer. The computing system may be the processing unit PU described above, or may be a separate device.

[0075] 403: Create a profile that defines a parameterized model of the target structure in terms of a number of parameters θ. For example, in a 1-D periodic structure, these parameters may represent the angle of a sidewall, the height or depth of a feature, the width of a feature. Properties of the target material and underlying layers are also represented by parameters such as the refractive index (at a specific wavelength present in the scattered measurement radiation beam). Specific examples are given below. Importantly, while the target structure may be defined by many parameters that describe its shape and material properties, the profile defines many of the parameters as having fixed values, while defining others as variable or "floating" parameters for purposes of the following process steps. Additionally, a manner in which parameters may be allowed to vary rather than being completely independent floating parameters will be described. To describe Figure 5 , considering only the variable parameters as parameters θ. The profile also defines the measurement radiation settings for a given target structure and how the parameter values ​​are estimated by fitting the inspection data to the model.

[0076] 404: Estimate the model target shape by setting initial values ​​θ0 for the floating parameters. Each floating parameter will be generated within a specific predetermined range, as defined in the scheme.

[0077] 406: The parameters representing the estimated shape are used together with the optical properties of the different elements of the model to calculate the scattering properties, for example using a rigorous optical diffraction method such as RCWA or any other solver of Maxwell's equations. This gives an estimated or modeled diffraction image of the estimated target shape.

[0078] 408, 410: The measured diffraction image and the model diffraction image are then compared and their similarities and differences are used to calculate a "merit function" for the model target shape.

[0079] 412: Assuming the merit function indicates that the model needs improvement before it accurately represents the actual target shape, new parameters θ1 are estimated, etc. and iteratively fed back to step 406. Steps 406-412 are repeated.

[0080] To assist the search, the calculation in step 406 may also generate partial derivatives of the merit function, indicating that increasing or decreasing the parameter in this particular region in the parameter space will increase or decrease the sensitivity of the merit function. The calculation of the merit function and the use of derivatives are well known in the art and will not be described in detail here.

[0081] 414: When the merit function indicates that the iterative process has converged on a solution with a desired accuracy, the current estimated parameters are reported as measurements of the actual target structure.

[0082] The computation time of this iterative process is mainly determined by the forward diffraction model used, i.e., the computation of the estimated model diffraction image using a rigorous optical diffraction theory from the estimated target structure. If more parameters are needed, there are more degrees of freedom. The estimated or model diffraction image calculated at 406 can be represented in various forms. If the calculated image is represented in the same form as the measurement image generated in step 402 (e.g., spectrum, pupil image), the comparison is simplified.

[0083] Figure 6 is a flow chart generally describing the steps of an alternative method for measuring target shape and / or material properties. In this method, multiple model diffraction images of different estimated target shapes (candidate structures) are pre-computed and stored in a library for comparison with actual measurements. Basic principles and terminology are similar to Figure 5 The steps are as follows and are then described in more detail:

[0084] 502-Generate library;

[0085] 503-Define model scheme;

[0086] 504-sample shape parameter θ0, ...;

[0087] 506-calculate and store the model diffraction image;

[0088] 508-new sample shape parameter θ1;

[0089] 510-measure the diffraction image;

[0090] 512- Comparing the measured image with the library image;

[0091] 514-report final shape parameters;

[0092] 516-Optimize shape parameters.

[0093] 502: The process of generating a library begins. A separate library may be generated for each type of target structure. The library may be generated on demand by the user of the measurement device or may be pre-generated by the supplier of the device.

[0094] 503: Build a profile that defines a parameterized model of the target structure in terms of a plurality of parameters θ. Considerations are similar to those in step 503 of the iterative process.

[0095] 504: Generate a first set of parameters θ0, etc., for example by generating random values ​​for all parameters, each value being within its expected value range.

[0096] 506: Calculate a model diffraction image and store it in a library, the model diffraction image representing the diffraction image expected according to the target shape represented by the parameters.

[0097] 508: Generate a new set of shape parameters θ1, etc. Steps 506 to 508 are repeated tens, hundreds, or even thousands of times until the library of all stored modeled diffraction images is judged to be sufficiently complete. Each stored image represents a sample point in the multidimensional parameter space. The samples in the library should fill the sample space with sufficient density so that any real diffraction image can be represented closely enough.

[0098] 510: After the library is generated (although it could be before), a real target 30 is placed in the scatterometer and its diffraction image is measured.

[0099] 512: Compare the measured image to the modeled image stored in the library to find the best matching image. The comparison can be performed for each sample in the library, or a more systematic search strategy can be adopted to reduce the computational burden.

[0100] 514: If a match is found, the estimated target shape used to generate the matching library image can be determined as the approximate object structure. The shape parameters corresponding to the matching sample are output as the measured shape parameters. The matching process can be performed directly on the model diffraction signal or on an alternative model optimized for fast evaluation.

[0101] 516: Optionally, use the closest matching sample as a starting point and use a refinement process to obtain the final parameters for reporting. For example, the refinement process may include something very similar to Figure 5 The iterative process is shown.

[0102] Whether the refinement step 516 is needed is a matter of choice for the implementer. If the library is very densely sampled, iterative refinement may not be needed because a good match will always be found. On the other hand, such a library may be too large to be practically used. Therefore, a practical solution is to use the library to search for a rough set of parameters, and then use the merit function to perform one or more iterations to determine a more accurate set of parameters, thereby reporting the parameters of the target substrate with the desired accuracy. In the case of performing additional iterations, the calculated diffraction image and the associated set of refined parameters can be selected as new entries to the library. In this way, a library based on a relatively small amount of computational work can be used initially, but it is built into a larger library using the computational work of the refinement step 516. Regardless of which scheme is used, further refinement of the values ​​of one or more of the reported variable parameters can also be obtained based on the goodness of the match of multiple candidate structures. For example, the parameter value finally reported can be generated by interpolating between the parameter values ​​of two or more candidate structures, assuming that two or all of these candidate structures have high matching scores.

[0103] The computation time of this iterative process is mainly determined by the forward diffraction model at steps 406 and 506, ie, the computation of the estimated model diffraction image according to the estimated target structure shape using a rigorous optical diffraction theory.

[0104] The creation of the profile involves multiple refinements of the profile, wherein the physical model is gradually adjusted to best represent the inspection data. The inspection data may include inspection data elements. The inspection data elements may be images, diffraction images (if a diffraction-based scatterometer is used), spectra, or pupil images; or may be reconstructed parameter values ​​obtained from such diffraction images, etc. For example, using a scatterometer such as described above, each of the inspection data elements may be obtained by inspecting the corresponding target structure. Each of these inspection data elements may be described by a plurality of intensity values. The adjustment is typically based on the results of the reconstruction. As described, the reconstruction fits the model to the inspection data, thereby converting the inspection data elements into parameter values. At the beginning of the process, the reconstruction may fail because the uncertainty may be large. Therefore, it may be more efficient to reconstruct only one or a few measurements rather than the complete data set.

[0105] To make the contour more robust, the nominal parameter values ​​of the contour should be well chosen. Ideally, many target structures should be reconstructed in order to correctly estimate these nominal parameter values.

[0106] According to the first measurement data; for example, the intensity of scattered light I m For measurements of , parameter inference is usually done in two different ways:

[0107] Inference based on inverse model: The stacked structure parameterized with stack parameters is modeled by electromagnetic (EM) simulation and its response is compared with the measured intensity data I m In this approach, only the transition from parameter θ to the measured intensity I m A direct mapping of is known. This solution can be found by solving an optimization task that includes the data terms and the prior knowledge encoded in the cost function. In a simplified view, the inference iteratively maps θ to an intensity I(θ) until I(θ) ≈ I m .

[0108] Typically, optimization tasks have the following general form:

[0109]

[0110] where f(θ) is a common prior (e.g., L2 norm) that encodes the prior information that the targets should belong to the same process / process window, for example: where θ * Describe the nominal parameterization. Here V and W are (eg, diagonal) scaling matrices. It should be understood that both diagonal matrices and full scaling matrices are possible.

[0111] Data-driven inference: An empirical, approximate direct mapping constructed using a priori assumptions and experimental data. A priori assumptions may include, for example, linearity about parameters, preprocessing to convert the measured intensities into a more usable form (e.g., such as using symmetry or antisymmetry). The mapping can then be used for direct predictions. In a simplified view, the inference starts from I m Mapped to θ.

[0112] A third hybrid approach combining data-driven and model-based solutions is additionally disclosed herein (below).

[0113] For hybrid or traditional model based reasoning approaches, the current way of working involves contour creation using stackup information and building solutions according to a solution creation process. The ultimate goal is to have a solution that meets the specification in terms of goodness of fit and match (between tools, using reference tools).

[0114] Hierarchical and data-driven scenario creation

[0115] Current approaches for creating and validating model-based reasoning solutions include a large number of steps that can be referred to as a solution creation flow (RCF). Solution creation involves using multiple tools in a feed-forward manner, without any feedback, to meet desired key performance indicators (KPIs); for example, in terms of fingerprint matching (FPM). Such a flow can be decomposed into three independent (non-communicating) blocks: material property optimization, profile verification, and profile optimization.

[0116] Plan creation can be very labor intensive due to lack of automation and the need for super user input throughout the process. User experience is required to arrive at a profile that meets accuracy / matching requirements. Typically, the plan creation process includes arbitrary adjustments of (e.g., fixed / floating, nominal) parameters, which makes it impossible to reproduce the creation process.

[0117] To improve the solution creation process as described above, an automated optimization-driven solution will now be described. This approach can generate effective solutions with minimal user interaction. The main concepts include performing a reconstruction that combines all or a large number of possible information channels (e.g., multiple targets and multiple wavelengths) and includes observations from other metrology tools to provide all the statistics (mean, variation, fixed / floating) needed to set up the solution.

[0118] The proposed method includes the use of hierarchical priors coupled with data-driven priors in the cost function, which ties together measurements from a large number of targets at multiple wavelengths. The data-driven prior information can be obtained based on any suitable available metrology data (e.g., CD-SEM data, ellipsometric data of material properties) and ensures that the solution matches the tool (i.e., the reference tool). It also adds more information to the reasoning and helps with parameter association. The resulting large-scale optimization task couples, automates, and improves the manual steps of current solution control flow methods.

[0119] Equation 2 is an example of a hierarchical and data-driven cost function that can form the basis of the proposed method. The proposed method can be viewed as a multi-layer reasoning task, called a large optimization task:

[0120]

[0121]

[0122] Equation 2 includes a data fidelity term that combines measurements of multiple targets t acquired at multiple wavelengths λ. The (e.g., diagonal or full) scaling matrix V scales the data fidelity term to encode statistical assumptions about the variance of the (e.g., Gaussian) noise affecting the measured data. Other noise distributions can be encoded if norms other than the L2 norm are used. It is assumed here that the machine is properly calibrated and that the remaining remaining processes are normally distributed. The goal of solving the cost function is to recover the parameterization θ for each target t ,θ t，λ , which is based on some parameterization θ for each target t t ,θ t，λ The measured intensity I t，λ Minimize the difference between the computational intensity and tis a wavelength (or more generally, acquisition settings and goals) independent parameter, θ t，λ is a wavelength and target related parameter.

[0123] The other term is the a priori term, which sets fixed floating and nominal parameterization (the λ subscript again distinguishes the wavelength-dependent parameters), where Set the regularization strength. The diagonal scaling matrices Q and S encode a priori information about the scale of the parameters, e.g. given a physical change in sidewall angle of 2 to 3 degrees and a change in height of 200 nm, the regularization should penalize both with the same relative strength.

[0124] Fixed floats are imposed relative to a data-driven nominal parameterization. This is performed to reduce the dimensionality of the problem for faster online evaluation and to stabilize the solution by structurally breaking parameter dependencies. The l1 norm promotes relative to the nominal value The solution sparsity.

[0125] Equation 2 provides automatic matching with respect to the reference tool by constraining the parameters available from experimental data to follow the same trends across targets. The slope term s (k) and the offset term c (k) Each parameter term parameterizes a specific profile of the target on the wafer Linked to the reference tool (i.e., from experimental prior data DAT exp ) Equivalent parameter item These terms can be used to ensure that cases where the reference tool "sees" a different target than the current tool are treated similarly (e.g. where the reference tool measures top-cd, while the current parameterization is about mid-cd).

[0126] The statistical errors affecting the measured data are taken into account by allowing for inexact matching, and the solution is restricted to be of size ∈ p l p sphere, where p is generated by the error distribution (e.g., the statistical distribution of the errors produced by the reference tool). Typically, the errors are assumed to be normally distributed, resulting in an l2 sphere. More complex error statistics can be incorporated if the constraints preserve the convex programming.

[0127] Apply min-max constraints to constrain the region of interest. The range of stack parameters is limited to valid physical parameterizations. (such as for material properties (as opposed to geometric properties)). In this way, multiple targets They may be grouped under the assumption that they have the same parameter values, for example, the silicon characteristics, although unknown, are constant across a particular wafer, and so the objectives may be grouped and constrained in this way for each wafer.

[0128] The solution of equation 2 involves an iterative algorithm solution and is (was chosen to be) a priori a convex program to ensure that the algorithm is tractable. One possible solution is to employ an approximate splitting algorithm, such as an appropriately variable metric preconditioned proximal splitting algorithm, which splits the data fidelity term from the residual term. A variable metric method (quasi-Newton step) is performed on the data fidelity term. The proximal step obtained with respect to the (albeit complex and non-trivial) residual term yields a convex program cost function, and its solution can be found by sub-iteration, such as by using a proximal splitting primal-dual solver.

[0129] Figure 7 Schematic diagram of data used for solution creation. Here is a set of measurement data I from N wafers (W1-Wn) t，λ-W1 ...I t，λ-Wn , relates to a plurality of targets t (six targets t1 to t6 are shown - for clarity only t1 and t2 are labeled) that have been captured using several acquisition setups or wavelengths (two wavelengths are shown as λ1, λ2). Different acquisition setups in addition to wavelength may include different polarization setups, wafer rotations, phase retarder rotations (varied alone or in different combinations). In most of the description wavelength is used as an example, it should be understood that it can always be generalized to acquisition setups.

[0130] The measured data together with the experimental prior data DAT exp The (reference tool data, such as CD-SEM data) is fed to a hierarchical optimization solver SOL that solves equation (2). The output of the optimization solver SOL includes each target solution θ t ,θ t，λ , nominal solution and the offset term c relative to the reference tool (k) and the slope difference s (k) This concept is applicable to any number of wafers / wavelengths, including only a single wavelength and / or a single wafer. Note that Equation 2 can be extended to any suitable additional convex programming terms.

[0131] Main information flow of scenario creation

[0132] Figure 8 The method flow for solution creation is shown. It is proposed to solve the hierarchical problem described by Equation 2, where the (first) regularization term The regularization strength of varies by 800 between each solution, so that for multiple regularization strengths Solve the hierarchical problem. The hierarchical solver SOL output is then used as a solution for a single objective reconstruction, such as a nonlinear least squares (NLSQ) single objective reconstruction. The regularization prior for the NLSQ reconstruction is iteratively configured so that the solution statistics (mean, variance and / or covariance) between the two solvers (hierarchical solver SOL and single objective reconstruction 805) are matched across the measurements used.

[0133] The layered solver SOL receives the measured intensity I t，λ , experimental prior data DAT exp and (e.g., to speed up computation time) library data Lib. The solution of the proposed optimization task described by Equation 2 will generate the following information for transmission as a solution REC for a single-objective reconstruction, e.g., a single / dual wavelength, nonlinear, least squares-based online inference framework:

[0134] Nominal value is the starting point for searching for the solution to the inverse problem and is also used as a regularization point. This defines the centroid of the lithography process window.

[0135] · Strategies for fixing insensitive or constant parameters in one or more solution creation training datasets. This fixed / floating strategy is dynamically generated according to the optimization task and is valid within the process window.

[0136] Multi-objective reconstructionθ t ,θ t，λ , comparing the parameter of interest to a third-party measurement (via an offset term c (k) and the slope difference s (k) ) match within the confidence region of these measurements. Based on this solution, a regularization strategy is defined for single-objective reconstruction so that reconstructions without hierarchical / data-driven priors produce the same inferred parameter distribution.

[0137] The solution REC output from the hierarchical solver SOL is then used, for example, by the NLSQ solver in a single objective reconstruction 805. The statistical properties of the outputs of the two solvers are compared 810, and if not (sufficiently) matched, the regularization strength is updated 820 and the two solvers are run again. When matched, the parameter values ​​of interest 830 are returned. The parameter values ​​of interest are checked 840 against the relevant KPI (e.g., FPM), and the solution with the best KPI is reported 850.

[0138] The parameter range can be reduced around the found nominal to the extent that they cover the solver path for single-objective reconstruction using NLSQ. The solver trajectory can be experimentally evaluated by performing reconstructions on multiple wafers.

[0139] The choice to fix some parameters to nominal values ​​and search for solutions on the resulting manifold is implicitly generated by the l1 norm prior according to Equation 2. The prior attempts to explain the data with the fewest number of parameters that vary relative to the nominal values. An accurate fixed-float strategy requires post-processing of the solution to identify parameters that have not varied significantly from nominal.

[0140] The meta-problem can be defined as matching the statistical properties (mean and / or variance) of the solutions from the two solvers (NLSQ and hierarchical solver). The choice of scaling of the regularization term in Equation 1 can be determined via iterative solution. Equation 1 can be rewritten as:

[0141]

[0142] therefore, can be viewed as the second regularization term, and H can be viewed as a direction-dependent scaling of the regularization. To match the solution distribution, we should find and appropriate values ​​of H. H can be diagonal or fully scaled. For example, one choice of H is the matrix square root of the inverse of the variance or covariance matrix of the hierarchical solution.

[0143] This results in a parameter distribution from the hierarchical solver The Kullback-Leibler divergence between the distribution of single-objective solutions obtained by solving Eq. 3 for multiple objectives is This can be formulated as a non-convex optimization problem:

[0144]

[0145] This involves solving multiple optimization subproblems defined by Equation 3 for all objectives to produce the statistics

[0146] A simpler heuristic method can be designed to solve it, such as Fig. 9 A first choice for H can be set as the matrix square root of the inverse of the variance or covariance matrix. To find At step 900, it is determined whether the combined parameter change (of the parameter value of interest 830 output from solver 810) is greater than the combined parameter change of the hierarchical optimization solution. If so, then is increased by 910; otherwise is reduced by 920. This cycle is repeated n times (where n is the total number of objectives). Setting a separate value for H may improve the solution, but it makes the heuristic solution more complicated.

[0147] Thus, a solution creation flow is disclosed that includes a hierarchical optimization task. The method includes multiple measurements across multiple targets on (optionally) multiple wafers. The solution creation flow further couples reference tool data directly into the solution creation flow. It provides data-driven search for fixed-float strategies, ranges, and nominals directly in the optimization problem. A solution conversion from a hierarchical solver to a single-objective NLSQ solver is also described, with statistical property matching between solutions. An alternative criterion (essentially minimizing the error with respect to the reference tool value) also produces good results.

[0148] The described approach thus automates the entire RCF process and removes extensive human interaction. It provides a constructive and repeatable approach to solution creation that is constrained to match a reference tool and allows for automatic solution transfer between the solution creation phase and reasoning on a single target / tool.

[0149] Hybrid Reasoning System

[0150] It has been described that reconstruction tends to fall into two categories: data-driven methods and model-based reasoning methods. However, both methods have inherent disadvantages. Data-driven methods lack robustness because they rely on limited training data, which is expensive to obtain and can produce significant systematic and random errors. Pure data-driven methods can only work reliably in the same process window as they were trained. If the process drifts or changes, the reasoning model (scheme) needs to be adapted. Experimental wafers generally need to be produced and measured. Current methods for model-based reasoning are complex and information-intensive, including very high computational requirements and complex EM simulations. They require the construction of libraries to create alternative models for the target EM response. The model needs to be accurate and therefore requires a large amount of customer (sensitive) information. Model errors will have a significant impact on reasoning.

[0151] To address this problem, a hybrid inference system is proposed that bridges the gap between model-based and data-driven inference. The proposed approach starts with a coarse model and then refines the model in a data-driven approach. It can rely on optional auxiliary information, such as measurements performed by other tools (e.g., CD-SEM data), which can be coupled with scatterometry measurements.

[0152] Fig.10 is a high-level diagram of the proposed method. The hybrid model HM consists of a fixed coarse model CM and a data-driven model DDM, the latter of which needs to be trained. θ denotes the stacked parameterization, where the estimated θ e Indicates the simulation intensity I s Fit the measured intensity I to a given degree in the training iteration m The value of the parameter. Crepresents the rough reflectivity generated by the rough model CM, and R represents the reflectivity generated by the data-driven model DDM. From the reflectivity space R to the simulation intensity I S The mapping (i.e., calibration model) is made using To express.

[0153] The training of the data-driven model DDM and the search for the inverse problem solution SOL together enable the measurement of strength I m With simulation intensity I s The goal is to jointly find the model correction and the solution parameterization θ (where θ is the universal parameterization, is the parameterization of a particular target i).

[0154] A coarse model CM of the stack can be constructed in a similar way to the current stack reconstruction, but with a high degree of inaccuracy allowed. This can include not using exact material properties, exact ranges or nominal values ​​of stack parameters when determining the coarse model. It is considered fixed during hybrid inference. In principle, small model errors (missing insensitive layers, inaccurate parameterization of insensitive areas of the stack) can also be tolerated. The coarse model can be accurately and quickly approximated using progressive library functions. For example, the library creates a proxy model that can map between parameterizations, WL and incident angle / pixel position to the reflectivity of the stack. It is built by evaluating the stack response in a large number of configurations for individual pixels (not the full pupil). A neural network model is trained to learn the mapping. The coarse model can be seen as a rough outline for which the library is built. A data-driven model DDM is attached on top of the coarse model to correct the coarse reflectivity R c , so that the measured intensities match, while also finding an appropriate parameterization θ.

[0155] The training of the hybrid model HM is an iterative process based on measurements of a large number (N) of targets. It can also use any available auxiliary information (e.g., CD-SEM data of a subset of targets) as a prior P. The data-driven model DDM consists of a neural network or other machine learning model definition. Initially, Represents the identity mapping, that is, R = R c .

[0156] We will now describe a training example, which consists of two steps that are repeated until convergence:

[0157] The first step consists in constructing the measured intensity data I m The inverse problem associated with model parameter inference is solved for all N available measurements for all wavelengths (if multiple wavelength measurements are used). Assume that a coarse EM model CM exists and a library is built for it.e ) to apply the prior information P by measuring some of the parameters defined by it (e.g., CD-SEM data).

[0158] In the second step, using the obtained solution θ e Update the Neural Network The model makes the measured intensity I m Better fit to model output (i.e., simulation intensity I s The function g(W, b) represents the general regularization. The training should be well regularized to avoid overfitting. At this point, it can be assumed that the rough reflectivity R c is quite accurate, so the exact reflectivity R can be forced to remain fairly close to the rough reflectivity R c . This can be done, for example, by is applied, where κ represents the strength of this assumption.

[0159] Iterations according to the scheme (i.e., according to Algorithm 1 below) produce estimates and the model correction defined by the neural network weights and biases W,b Convergent solution.

[0160] Algorithm 1:

[0161] For t = 1, iterate

[0162] Among them, for a certain i,

[0163]

[0164] Finish

[0165] where (·) denotes the parameters of the function, which in principle can be or Depending on the modeling choice ( Fig.10 and Fig.12 The mixed model HM in . They should be consistent between the two equations.

[0166] In general, to produce a robust solution, one should extrapolate beyond the training data. This ensures that the time between required solution updates is maximized. In the proposed hybrid approach, the coarse model can be considered to represent an extended coarse manifold θ of parameter values ​​where the signal / model lies c The observed measurements quantize only a subset θ of this coarse parameter space e , because the variation across the wafer is limited to a given process window (i.e., the process window defines a subset θ e ). Fig.11It should be understood that the training of data-driven models can only be guaranteed to be within θ e It is accurate within a small area.

[0167] To ensure generalization ability, the entire rough manifold θ c impose additional constraints. For any given small difference δ, such a constraint can be R c +δ≈R. Imposing a bound on the allowed δ ensures that the corrected reflectivity R does not diverge outside the observed process window. In this case, the data-driven model correction generalizes if possible; that is, if there is a correction function for the process window that is still general outside the process window. In the worst case, when the correction outside the observed process window is incorrect, the model is only slightly degraded from the coarse model. Additional constraints are imposed on δ over the entire coarse manifold to ensure consistency.

[0168] As mentioned above, external data (such as CD-SEM data or parameter values Some other estimates of ) can be used as prior information P to guide the solution towards the appropriate estimate For example, if CD parameter data is available, i.e., Known, you can add it to the item (e.g., in the first step of Algorithm 1).

[0169] Additionally, multiple priors P can be added to couple estimated parameters at, for example, wafer level and / or batch level. They can be data-linked (e.g., where measurement data for certain parameters are available), or they can be physically driven, i.e., enforcing that the height across the wafer cannot vary at high frequencies, so that drastic changes occur between adjacent targets, or assuming the same material properties for all targets of the wafer.

[0170] If a neural network model is used to generate a library for a coarse model, transfer learning techniques can be applied to augment the same library to build a data-driven model.

[0171] The above procedure assumes that the calibration model is correct, or at least more accurate than the target model. If this is not the case, the hybrid model will learn the calibration system and try to correct these as well. The resulting accurate model will not be independent of the machine, and the accuracy of other machines that need different calibrations will be reduced. Having measurements from multiple machines during training can improve the match. Currently, the Jones model is used, and calibration accuracy can cause errors. In particular, for small points / targets there are significant calibration and model errors. In this case, the proposed method builds an improved model that takes the calibration system into account.

[0172] Fig.12 Shows Fig.10 Variations of the hybrid model process are shown. Fig.10 In the example, the data driven model DDM is based on the input rough reflectivity R c Outputs a corrected / more accurate reflectance R. In contrast, in this variation, the data-driven model DDM estimates θ based on a parameterized e To output the rough reflectivity R c Additional (or otherwise combined) corrections.

[0173] Once trained, the hybrid model can be used to infer parameterizations of measured targets / structures in place of more conventional models; that is, to generate simulated intensities and minimize the difference between the simulated and measured intensities to infer structural parameterizations.

[0174] This section therefore discloses the coupling of an EM stack model (and its simplification so that less sensitive data is required) with data-driven techniques. The use of priors (data priors or physically motivated priors) is described to help learn the model and potential stack parameterization. Limited sensitive information is required, and inaccurate geometries can be tolerated if the stack response is not sensitive to them and material properties are not required. An accurate model is learned from the data, building on a coarse model and optionally other tool measurements (CD-SEM data, setpoints). The data-driven model can also correct the calibration if it is poor, but at the cost of becoming machine-specific. The model can be run in shadow mode to track calibration changes. The model can be used to model interference effects on small target measurements.

[0175] The above concepts (scenario creation and hybrid model) can be combined. Thus, the scenario creation method can be used to create scenarios to use as starting points in reconstructions performed using hybrid models constructed as described above. A tiered approach may be used.

[0176] Combined on-device and off-device reasoning

[0177] For model-based reasoning (including model-based reasoning using the layered solver disclosed herein) and / or hybrid reasoning disclosed herein, the current approach involves creating profiles based on user stackup information and / or third-party measurements (e.g., CD-SEM data.) In particular, in order to reconstruct material properties, special design of experiments (DoE) wafers obtained from the user (i.e., IC manufacturer) are required.

[0178] Often, users are reluctant to provide much information about their manufacturing process, and therefore, the details of the stack description available are limited and often do not include appropriate material properties. Furthermore, the generation of DoE wafers used to infer material properties is expensive, and the resulting wafers have no production value. If DoE wafers are not used, the optical material properties may have large uncertainties and may not match the properties derived from third-party experimental measurements. Furthermore, for some materials, the optical properties are a function of the processing applied to the wafer, and the default third-party measurements will be inaccurate or unavailable. Therefore, the profile information will be inaccurate, resulting in a wide range for parameterization. This is particularly troublesome for material parameters because they have a large impact on the stack response.

[0179] Since many existing metrology sensors can only measure low-order diffraction, the information content in each measurement is insufficient to infer a large number of parameters (i.e., to perform full-profile metrology). Also of interest is the possibility of measuring in-device structures that are designed for optimal performance in the end product, rather than optimal measurability.

[0180] Therefore, there is no way to control the signal strength and correlation with respect to optical metrology measurements. Typically, for a given feature, geometric and material parameters are observed by the sensor as their combined equivalent electrical quantities, which introduces significant correlation between the responses with respect to changes in the individual parameters. This significantly reduces the distinguishability of the signal.

[0181] In this section, combined reasoning of on-device and off-device structures is proposed. Such a proposal may use reasoning based on a hybrid or hierarchical framework as disclosed herein, or a combination of both. Furthermore, the use of libraries already described in the "Hybrid Reasoning System" section may also be utilized in such an embodiment. In one embodiment, modeling and solving for parameter values ​​from a large number of such on-device and off-device targets is also proposed.

[0182] In particular, it is proposed to perform combined reasoning based on measurements of one or more specially designed device-external targets and one or more measurements of device-internal structures (e.g., specially designed metrology targets and / or actual product structures within the device). The device-external targets may, for example, include scribe targets. The scribe targets may be optimized for measurability (generally, or in terms of one or more specific parameters or parameter categories, where, for example, a category of parameters may include material property parameters). Different scribe targets may be optimized for different parameters / parameter categories. This proposal enables more effective exploitation of physical correlations that exist across wafers (e.g., material optical parameters that tend to be stable across wafers; height or CD parameters that may vary smoothly across wafers).

[0183] Within the lanes, specialized targets only need to follow printability rules. Thus, for example, lane targets can be designed to provide signal enhancement. In this way, by combining off-device, high-signal targets with on-device measurements, additional parameters, especially material properties, can be inferred. Therefore, if certain parameters of interest are common between on-device and off-device targets, joint inference from these two types of targets will enrich the signal space, enabling more accurate measurements. It can be appreciated that material properties are a good example of such a common parameter.

[0184] Fig.13 The principle is schematically illustrated. It shows a portion of a substrate S comprising two fields F1, F2, each field having a device region DEV1, DEV2 and scribe lane regions SL1, SL2 (of course, scribe lanes may be shared between adjacent fields). The measurement data may include the device regions DEV1, DEV2 and scribe lane regions SL1, SL2. d，λ In-device measurements and off-device (or lane target) measurements are shown They are from the X fields (F1-Fx, two fields F1, F2 are shown) and at m acquisition setups or wavelengths λ (two wavelengths λ1, λ2 are shown). Different acquisition setups in addition to wavelength can include different polarization settings, wafer rotations, phase retarder rotations (varied alone or in different combinations). In a manner similar to the described hierarchical solver approach, various different combinations of in-device and out-of-device measurements for each field are possible. Therefore, the location and / or type of structure measured can vary for different fields. The wavelength / acquisition setup can also vary from target to target and / or field to field.

[0185] Including measurement data I d，λ On-device measurements MEAS DEV and including measurement data Device external (track) measurement MEAS SL Used by the solver SOL to perform multi-model hybrid / model-based optimization.

[0186] In one embodiment, it is assumed that for m wavelengths / acquisition settings indexed by λ, the in-device model / hybrid model is d，λ It is parameterized in . For example, it can be assumed that the geometric parameters are universal across wavelengths, while the material properties depend on the wavelength. It is suggested here to use an additional set of n targets (e.g., off-device or in-line targets), where the model is given by Parameterization to increase signal distinguishability between these scribe lane targets and shared / similar properties between intra-device(s) structures.

[0187] Formally, this can be expressed as an optimization task of Equation 5, for example, where the first term is the in-device data fidelity term (m wavelengths), the second term is the out-of-device data fidelity term (m wavelengths, n targets), and the third term is the regularization cost term. Here, θ c denotes the common part of the parameterization and f(·) denotes a general function encoding an additional prior / regularization, e.g., in a manner similar to Equation 2 above. It may be noted that, depending on the design and structure, not all targets necessarily share the same common properties, e.g., scribe lane targets may be designed to share similar geometric properties between them that are not shared with the intra-device structures, whereas overall material properties may be shared across the entire wafer.

[0188]

[0189] The cost function of Equation 5 allows for solutions similar to hybrid / hierarchical model-based inference schemes. In addition, it also supports combining multiple on-device objectives (e.g. Fig.13 as shown in domain F2).

[0190] In this manner, a multi-model metrology inference scheme is described that couples in-device and out-of-device measurements while enabling out-of-device targets to be designed to optimize signal strength and distinguishability with respect to common parameters (i.e., parameters shared between (multiple) in-device and out-of-device structures). This eliminates the need to fabricate expensive and time-consuming experimental wafers, and also allows the use of (multiple) custom target designs, which can optimize measurability for parameters that are insensitive and / or highly correlated with in-device structures (e.g., material properties).

[0191] In additional embodiments, a low-complexity machine learning model that links material properties (refractive and extinction coefficients) across wavelengths can be added to the intra-device and extra-device inference described in this paragraph, but it can also work independently within a hybrid inference system or work with an inverse problem inference scheme (e.g., RCWA). Such a low-complexity machine learning model can be considered if process-dependent materials such as amorphous carbon or amorphous silicon are present in or on the substrate within or outside the device. The optical properties of process-dependent materials may change during wafer processing and need to be characterized under the same conditions. Using a low-complexity machine learning model that links material properties across wavelengths can reduce the need for experimental wafers and / or customer information.

[0192] A low-complexity machine learning model can be defined by expressing the parameter k to be modeled as i Where To relate the parameterization across all wavelengths λ The model can be represented by a sigmoid-like activation function σ λiComposition, which is a generalized logic function, is used in low-complexity models across wavelengths For example, a small neural network takes wavelength as input and outputs a polynomial in wavelength. This will produce a model of the material parameters During solution creation, the model θ k The parameterization of is determined by fitting the data via an inverse problem, for example, as performed in in-device and out-of-device inference. The shape of the sigmoid σ can be wavelength-dependent and dependent on the parameter k.

[0193] Preferably, the generalized logistic function can be defined to be linear for a wide range of physical values ​​of p and to rapidly approach the asymptotic value c as p approaches a region that is not considered physical. m and c M Saturation. It is preferred to extend the linear range to a longer range to tune or reduce the effect of saturation at the asymptote.

[0194] The function is advantageously designed to be continuous. Continuity is advantageous because discontinuous functions may cause problems for learning the model. It can be scaled so that it covers the appropriate physical range. This range can be wavelength-dependent, in which case the scaling is different for each wavelength, e.g. Fig. 20 As shown. Fig. 20 In Figure 1, the polynomial model for the material property M and the physical range P, as well as the associated sigmoid, is plotted as a function of the wavelength λ.

[0195] Libraries can be constructed to estimate material properties p within the assumed physical range. k and the varying geometric parameters g k The metafunction is then applied during inverse problem reasoning The new inference problem is based on the parameterization of the geometric parameters and the applied material model θ k .

[0196] Nonlinear parameter decorrelation

[0197] As already mentioned, data-driven, hybrid and model-based solutions are all negatively affected by the correlation between the parameters of interest, for example, due to the physical coupling of the parameters. Most of the intensity signals mainly carry information about the electrical quantities that describe the different features of the stack, rather than a specific height, CD or sidewall angle. For data-driven solutions, this limits the distinguishability of the effective signal, for example, if the same experimental response can be generated by changing the height, CD or a combination of the two, the solution becomes ill-posed and difficult to generate experimental data. This places a fundamental limit on sensor capabilities. For hybrid and model-based solutions, this correlation introduces instability in the solution because the number of conditions of the problem becomes large. This slows down convergence and even triggers unstable behavior. Part of the reason for this correlation is due to the fundamental limitations of sensor capabilities. However, since the complete / rough model of the stack can only be expressed in terms of geometric description rather than in terms of the electrical quantities of the various features, the poor parameterization of the hybrid / complete model introduces additional correlations.

[0198] In this section, a method is proposed for mitigating the problems caused by the correlation of hybrid and model-based solutions caused by incorrect parameterization of the model. The proposal uses a surrogate model to create a reparameterization of the stack towards a minimum sufficient statistics representation. In addition, the alternative model can be used to speed up the solution by providing an approximation of the electromagnetic simulation via a library (the library can be disclosed in the "Hybrid Inference System" section).

[0199] In most current use cases, the stackup to be measured is very complex and inferring full-profile metrology of all parameters θ is neither practical nor necessary; only one or more specific stackup parameters of interest need to be estimated. Therefore, a data-driven machine learning reparameterization of the stackup is proposed, which attempts to construct a minimum sufficient statistic for all combinations of parameters while ensuring that the parameters of interest remain distinguishable within the minimum sufficient statistic.

[0200] In one embodiment, it is proposed to use a neural network to model the stack reflectivity response R up to a given level of accuracy, while also learning a mapping to a low dimensional space, which eliminates any redundancy in the parameterization (which represents correlations). The main feature is the introduction of a bottleneck in the architecture, which restricts the flow of information in order to learn a mapping to a low dimensional subspace. Note that similar uses of bottleneck structures are found in the very different context of building autoencoders. The training of the library is standard and represents minimizing the mean squared error cost, e.g. in represents an estimate / approximation. This can be achieved by using a stochastic solver to train a mapping from θ to R.

[0201] Fig.14is a schematic diagram of the concept according to a first example, and shows a decorrelation library or decorrelation network comprising a plurality of layers, the plurality of layers comprising one or more decorrelation layers DL, one or more bottleneck layers BL and one or more modeling layers ML. The input parameters θ are mapped to a lower dimensional nonlinear subspace parameterized by p, where p represents a reparameterization to a lower dimensional or restricted parameter space. Note that the restricted parameter space p is not just a proper subset of the input parameterization θ containing some of the same parameters, but a completely new smaller parameterization in terms of completely different parameters. The mapping is achieved via at least one decorrelation layer DL and a bottleneck layer BL, where these layers may comprise neural network layers or similar artificial intelligence network layers. The height of a layer in the schematic indicates the number of neurons (nodes) in the layer; i.e., a bottleneck layer BL has fewer neurons than a decorrelation layer DL. In the example shown here, there are two decorrelation layers DL, although this is purely exemplary and the number of decorrelation layers DL (and bottleneck layers BL) may be different than shown.

[0202] Then, a reflectance modeling library RML or a reflectance model including one or more modeling layers ML (e.g., a reparameterized stacked model layer or a reparameterized library layer) is used to learn how to model the reflectance according to the restricted parameter space p Modeling is performed. Once again, these layers may include layers of neural networks or similar artificial intelligence networks. In the example shown here, there are four modeling layers ML, although this is purely exemplary and the number of modeling layers ML may be different than shown.

[0203] The size of the bottleneck layer BL (i.e., the number of neurons) determines the information content available for the modeling layer ML. The training error and implicit accuracy on the modeled reflectivity can be determined and evaluated for several sizes of the bottleneck layer BL. The size of the bottleneck layer BL affects the predictability of the modeled reflectivity. It can be shown that the size of the bottleneck is problem-dependent and can typically be increased from 1 to an upper limit n p The rationale behind this is that if you keep the original parameterization θ, i.e. p=θ, then the mapping will be completely accurate (one-to-one). If the response has no correlation with respect to the parameterization θ, then you can have a smaller restricted parameterization p only if you lose some information. If there is a correlation, then there should be a restricted parameterization p that can model the same response with a smaller size.

[0204] As described in the previous section, current working methods include mapping θ to R and using an optical model to map the reflectivity R to the intensity I (eg, using the Jones model) to solve Equation 1. Such an approach does not eliminate possible correlations between the various parameters.

[0205] In this approach, it is proposed to solve the problem in an equivalent low-dimensional space parameterized by p; for example, by solving the following equation:

[0206]

[0207] where g similarly represents the prior information term.

[0208] In the following, the following will describe Fig.14 Several embodiments of the main concept are shown. Note that two or more of these embodiments can generally be combined into more complex structures. As with the previous examples, the number of layers (regardless of which type of layer) is purely exemplary and can vary.

[0209] Fig.15 Shows Fig.14 A variation of the arrangement incorporating a parameter θ for bypassing one or more bypassed b The bottleneck bypass (where the bypassed parameter θ b , including subsets of the full stack parameterization). One or more stack response parameters (e.g., wavelength and / or angle of incidence of the illumination) are usually known with high confidence. In this case, the bypassed parameters θ b These known parameters can be included and can be considered fixed during reconstruction / parameter inference, e.g., fixed to values ​​determined at measurement time. However, the known parameters should still be used for training the reflectance model library RML, since the actual values ​​are determined during measurement (e.g., to obtain a cross-wavelength model / library). Therefore, it is recommended to use these known parameters as bypass parameters θ b The θ values ​​are forwarded so that they bypass the bottleneck layer BL (and the decorrelation layer DL) and are used directly as input when building the reflectivity model library RML.

[0210] Another reason to bypass a parameter of the bottleneck layer is if it belongs to the class of "parameter of interest" for a given stack (e.g., if it is a parameter that is measured such that the value of the parameter is actively sought). For example, if CD is a parameter of interest, then it is recommended not to re-parameterize the CD parameter through the bottleneck layer. Instead, one or more of these parameters of interest can be used as bypass parameters θ b is forwarded, for example as an independent parameter outside the bottleneck layer BL. In this case, the bypassed parameter will be the parameter to be optimized. Therefore, the bypass parameter θ b One or more such parameters of interest may be included as an alternative to or in addition to the known parameters.

[0211] Fig.16 and Fig.17 An example of another embodiment is shown, in which in addition to modeling reflectivity In addition, the decorrelation library directly provides forward parameter predictions (For example, for a particular parameter of interest θ p ). For these parameters of interest θp , one way to ensure that inference is possible is to train the library or model to directly infer these parameters. This makes these parameters θ p can be passed through the bottleneck layer BL. In this way, the model can maximally decorrelate these parameters from the remaining stack parameters θ. For example, this approach can be an alternative to bottleneck bypassing. The requirement to match parameters at the output ensures that there can be a way from the restricted parameter space p to the actual parameters of interest θ p The mapping, such as Fig.16 Here, the parameters of interest are inferred via direct prediction. Fig.17 A method is shown where a restricted parameterization p allows reasoning about the parameters of interest via solving an inverse problem rather than via a modeling layer ML.

[0212] Fig.18 An arrangement comprising multiple (parallel) parameter bottleneck layers BL1, BL2 is shown. When solving inverse problems, multiple priors are often placed on the solution (examples of which are described in the above layered priors and hybrid inference embodiments). In some cases, it may be useful to group specific parameters (e.g., according to the parameter θ 1 ,θ 2 θ ∈ ... 1 ,θ 2 There are two parallel paths (neural networks) for each class, each path includes a decorrelation layer DL1, DL2 and a bottleneck layer BL1, BL2. In this way, different corresponding priors can be placed on the parameters θ of the two classes. 1 ,θ 2 , and the two bottlenecks BL1, BL2 ensure that the two categories of parameterization (e.g., geometry and material) remain separable.

[0213] Fig.19 A method is shown in which a decorrelation library or model is used to determine a parameter distinguishability measure. A decorrelation library (e.g., a remapping library) can be used to infer the correlation between a parameter and another parameter or a set of other parameters, such as inferring a correlation measure between parameters that define a volume. Thus, the correlation measure can describe the degree of correlation between any two parameters. This can be achieved by attempting to invert / remap the low-dimensional mapping induced by the bottleneck layer. Such a task is generally ill-posed and the accuracy of the recovery can be viewed as an indicator of the correlation. Therefore, when training e.g. Fig.14Following a similar arrangement as shown, thereby creating a decorrelation library, an additional component or remapping library RemL can be trained, which attempts to invert this mapping. It should be noted that although Fig.19 Shown based on Fig.14 However, any previously described decorrelation structure may be used, for example, in this embodiment Figures 14 to 18 Any of the structures shown.

[0214] Training can make the remapping library RemL be trained to find an approximate solution where p is generated from a trained decorrelation library. The individual parameters are recovered from the reparameterized p The ability is With the remaining parameters The correlation level (correlation measure) can be reasoned about by varying the bottleneck size and evaluating the resulting error in predicting the reflectivity and the error in the parameterized remapping.

[0215] As a specific example, consider the case where the goal is to quantify the dependence of the response on three parameters that define the grating volume (e.g., height, width, and sidewall angle). This can be applied to any stack where all other parameters bypass the bottleneck layer BL. In this case, two libraries can be trained, each with a corresponding bottleneck layer. The error level of the two libraries (e.g., determined by ) provides a measure of modeling ability for each bottleneck layer stack. If the fit to the data reaches library accuracy, the error level of the remap library The distinguishability level for each of the parameters is defined.

[0216] Therefore, this section describes an automatic decorrelation / reparameterization technique that speeds up inference by reducing the number of conditions and lowering the number of effective parameters. This eliminates the need for expert user design of parameters to produce stable / consistent model behavior, and introduces a systematic approach to analyzing the information carried by the stack response. This approach can be used to improve the robustness of reasoning based on mixtures / models (including any model using layered priors), and to increase the convergence rate of inverse problem solvers. A correlation measure between different parameters can be defined by relating the achievable reflectivity accuracy to the size of the bottleneck layer.

[0217] The target and target structure in any of the above embodiments can be a metrology target structure specially designed and formed for measurement purposes, or a target structure as a functional part of a device formed on a substrate. The term target should not be limited to any specific structure or type of structure, but includes any measurable structure.

[0218] In association with a physical grating structure of a target structure as implemented on a substrate and a patterning device, an embodiment may include a computer program comprising one or more sequences of machine-readable instructions describing a method of measuring a target structure on a substrate and / or analyzing the measurements to obtain information about a lithography process. The computer program may be, for example, Figure 3 or Figure 4 The unit PU and / or Figure 2 A data storage medium (e.g. a semiconductor memory, a magnetic disk or an optical disk) in which such a computer program is stored may also be provided. Figure 3 or Figure 4 Where existing metering equipment of the type shown is already in production and / or in use, the present invention may be implemented by providing an updated computer program product to cause a processor to perform the methods as described above and in the claims.

[0219] Other embodiments according to the invention are described in the following numbered clauses:

[0220] 1. A method for determining a reconstruction scheme, the reconstruction scheme describing at least nominal values ​​for use in a parameterized reconstruction describing an object; comprising:

[0221] acquiring first measurement data associated with measurements of a plurality of targets on at least one substrate, the measurement data associated with one or more acquisition settings;

[0222] performing optimization by minimizing a cost function that minimizes a difference between the first measurement data and the simulated measurement data based on a reconstructed parameterization of each of the plurality of objectives;

[0223] The constraints on the cost function are imposed based on the layer-wise priors.

[0224] 2. A method according to clause 1, wherein the hierarchical prior encodes prior information about the scale of the parameters.

[0225] 3. A method according to clause 1 or 2, wherein a hierarchical prior imposes constraints on the difference between parameter values ​​in the reconstructed parameterization and corresponding experimentally measured parameter values ​​obtained by a reference tool.

[0226] 4. A method according to clause 3, wherein said constraints on the differences of parameter values ​​in said reconstructed parameterization and corresponding experimentally obtained parameter values ​​allow for an inexact match to account for statistical errors affecting the first measurement data.

[0227] 5. A method according to any of clauses 3 or 4, wherein the method further outputs tool matching data describing a relationship between the first measurement data relative to corresponding experimentally acquired measurement data from a reference tool.

[0228] 6. A method according to any of the preceding clauses, wherein a first regularization is applied on the layered prior.

[0229] 7. A method according to clause 6, wherein the first regularization determines the fixed-floating strategy by preferring the solution with the smallest number of changing parameters.

[0230] 8. A method according to clause 6 or 7, wherein the first regularization is an L1 norm regularization.

[0231] 9. A method according to clause 6, 7 or 8, comprising minimizing a cost function for different strengths of said first regularization.

[0232] 10. A method according to any of the preceding clauses, comprising matching the statistical properties of the solution to the cost function with the statistical properties of the solution to the single objective reconstruction, wherein the strength of the second regularization applied to the single objective reconstruction is iteratively determined.

[0233] 11. A method according to clause 10, wherein determining the strength of the second regularization comprises minimizing the difference between the parameter distribution of the solution of the single objective reconstruction over the plurality of objectives and the parameter distribution of the solution of the cost function.

[0234] 12. A method according to clause 10 or 11, wherein one or more performance indicators describing the performance of parameter values ​​from the matched single-objective reconstruction are evaluated and the reconstruction solution corresponding to the best performance indicator is selected as the determined reconstruction solution.

[0235] 13. A method according to any of the preceding clauses, wherein the hierarchical prior imposes constraints in favour of a region of interest that describes a valid physical parameterization.

[0236] 14. A method according to any of the preceding clauses, wherein the hierarchical prior imposes consistency constraints that favor consistency of highly correlated parameters across multiple objectives.

[0237] 15. The method according to clause 14, wherein the consistency constraint is related to at least a material property parameter, wherein it can be assumed that the material property will not vary significantly between targets.

[0238] 16. A method according to any of the preceding clauses, wherein the cost function includes at least one data fidelity term solved for the plurality of objectives.

[0239] 17. The method of clause 16, wherein for a plurality of acquisition settings, a data fidelity term is solved for each of the plurality of targets.

[0240] 18. A method according to clause 16 or 17, wherein at least one data fidelity item includes a first data fidelity item solved for a first subset of the multiple targets and a second data fidelity item solved for a second subset of the multiple targets, the first subset is located in a product area of ​​the substrate, and the second subset is located outside a device area of ​​the substrate.

[0241] 19. The method of clause 18, wherein a second subset of the plurality of targets is located within a scribe street region of the substrate.

[0242] 20. The method according to clause 18 or 19, wherein the second subset of the plurality of objectives is designed and / or optimized generally for measurability and / or in terms of one or more parameters.

[0243] 21. The method of clause 18, 19 or 20, wherein the first subset of the plurality of targets comprises one or more product structures.

[0244] 22. A method according to any one of clauses 18 to 21, wherein the first data fidelity item is parameterized with respect to a first parameter related to the first subset of the multiple targets, the second data fidelity item is parameterized with respect to a second parameter related to the second subset of the multiple targets, and each of the first data fidelity item and the second data fidelity item includes a common parameterization of separate processing related to both the first subset and the second subset of the multiple targets.

[0245] 23. A method of constructing a hybrid model for providing simulation data for use in parameter reconstruction of a structure, the method comprising:

[0246] obtaining a coarse model operable to provide coarse data for simulation; and

[0247] A data-driven model is trained to correct the simulated rough data in order to determine the simulated data.

[0248] 24. The method of clause 23, wherein simulating coarse data comprises simulating coarse reflectivity data.

[0249] 25. A method according to clause 23 or 24, wherein a data driven model is operable to determine a correction for combination with said simulated coarse data.

[0250] 26. A method according to clause 23 or 24, wherein a data driven model is operable to derive said simulation data from said simulation rough data.

[0251] 27. A method according to any one of clauses 23 to 26, wherein at least the data-driven model is a machine learning neural network model.

[0252] 28. A method according to clause 27, wherein the hybrid model is a machine learning neural network model and includes a bottleneck layer having fewer nodes than one or more preceding layers.

[0253] 29. A method according to clause 28, wherein the bottleneck layer and the one or more preceding layers together learn a mapping to a restricted parameter space parameterized with respect to the input.

[0254] 30. A method according to clause 29, wherein the hybrid model comprises one or more of the preceding layers, the preceding layers comprising a decorrelation layer.

[0255] 31. A method according to clause 29 or 30, wherein the restricted parameter space represents a minimum sufficient statistic for the combination of all parameters of the input parameterization.

[0256] 32. A method according to clause 29, 20 or 31, wherein the hybrid model comprises one or more modeling layers after the bottleneck layer, the one or more modeling layers modeling simulation data from the restricted parameter space.

[0257] 33. The method of clause 32, wherein the one or more modeling layers are operable to directly infer one or more parameter values ​​of one or more direct inference parameters.

[0258] 34. A method according to clause 33, wherein the one or more direct inference parameters include one or more parameters of interest.

[0259] 35. A method according to any one of clauses 29 to 34, wherein one or more parameters are bypassed at the bottleneck layer.

[0260] 36. The method of clause 35, wherein the one or more parameters that are bypassed include one or more known parameters whose values ​​are known and / or one or more parameters of interest.

[0261] 37. A method according to any of clauses 29 to 36, comprising at least two parallel bottleneck layers, each bottleneck layer being used for a respective subset of said input parameterizations.

[0262] 38. A method according to clause 37, wherein each of said parallel bottleneck layers enables imposition of a respective prior on each of said subsets of said input parameterizations.

[0263] 39. A method according to any of clauses 28 to 38, comprising training an additional model operable to invert and / or remap the mapping caused by the bottleneck layer; and

[0264] A correlation measure describing a correlation between the parameter and one or more other parameters is determined using the additional model.

[0265] 40. A method according to any one of clauses 23 to 39, wherein the training step comprises performing iterations of:

[0266] determining estimates of parameter values ​​for a coarse model based on the measured data and the simulated data; and

[0267] The determined parameter value estimates are used to update the data driven model so that the measured data and the simulated data are a better match.

[0268] 41. A method according to clause 40, wherein the measurement data comprises intensity data associated with a plurality of targets.

[0269] 42. The method of clause 41, wherein the plurality of targets comprises a first subset of targets and a second subset of targets, the first subset being located within a product region of the substrate and the second subset being located outside a device region of the substrate.

[0270] 43. The method of clause 42, wherein the second subset of targets is located within a scribe street region of the substrate.

[0271] 44. The method according to clause 42 or 43, wherein the second subset of objectives is optimized generally for scalability and / or in terms of one or more parameters.

[0272] 45. A method according to clause 42, 43 or 44, wherein the first target subset comprises one or more product structures.

[0273] 46. ​​A method according to any one of clauses 42 to 45, wherein the hybrid model is parameterized in terms of a first parameter relating to the first target subset, in terms of a second parameter relating to the second target subset, and in addition, a separately processed common parameterization relates to both the first target subset and the second target subset.

[0274] 47. A method according to any of clauses 40 to 46, wherein the measurement data comprises intensity data associated with a plurality of acquisition setups.

[0275] 48. A method according to any of clauses 40 to 47, wherein a priori information describing known parameter values ​​is used to constrain said determination of parameter value estimates.

[0276] 49. A method according to any one of clauses 40 to 48, wherein regularization is applied to the step of updating the data driven model based on an assumption that the simulated rough data and the simulated data are not too similar.

[0277] 50. A method according to any of clauses 23 to 49, comprising using the hybrid model in parameter reconstruction of a structure in a metrology operation.

[0278] 51. A method according to clause 50, further comprising an initial step of determining a reconstruction scheme for said parameter reconstruction using a method according to any one of clauses 1 to 22.

[0279] 52. A measurement method comprising:

[0280] Acquire first measurement data related to measurement of a plurality of targets on at least one substrate, wherein the plurality of targets include a first subset of targets and a second subset of targets, the first subset being located within a product region of the substrate and the second subset being located outside a device region of the substrate;

[0281] solving a cost function that minimizes a difference between the first measurement data and simulated measurement data based on the reconstructed parameterization of each of the plurality of objectives;

[0282] wherein the cost function is parameterized in terms of a first parameter relating to the first subset of targets, in terms of a second parameter relating to the second subset of targets, and additionally a separately processed common parameterization relates to both the first subset of targets and the second subset of targets.

[0283] 53. A metrology method according to clause 52, wherein the measurement data is associated with one or more acquisition settings.

[0284] 54. A metrology method according to clause 52 or 53, wherein the second target subset is located within a scribe street region of the substrate.

[0285] 55. A metrology method according to clause 52, 53 or 54, wherein the second subset of objectives is generally optimized for measurability and / or in terms of one or more parameters.

[0286] 56. A metrology method according to any one of clauses 52 to 55, wherein the first target subset comprises one or more product structures.

[0287] 57. A metrology method according to any one of clauses 52 to 56, wherein the cost function comprises a first data fidelity term parameterized in terms of the first parameter, a second data fidelity term parameterized in terms of the second parameter, each of the first data fidelity term and the second data fidelity term comprising a common parameterization of the separate processing.

[0288] 58. A method of constructing a decorrelation model for inferring one or more values ​​of one or more parameters describing a structure being measured, the method comprising:

[0289] training the decorrelation model to learn a mapping to a restricted parameter space parameterized with respect to an input;

[0290] 59. The method of clause 58, further comprising training the decorrelation model to simulate responses based on the restricted parameter space.

[0291] 60. A method according to clause 59, wherein the response comprises a reflectivity response.

[0292] 61. A method according to clause 58, 59 or 60, wherein the decorrelation model comprises a bottleneck layer having fewer nodes than one or more preceding layers.

[0293] 62. A method according to clause 61, wherein the bottleneck layer and the one or more preceding layers together learn a mapping to a restricted parameter space parameterized with respect to the input.

[0294] 63. A method according to clause 62, wherein the preceding layer comprises a decorrelation layer.

[0295] 64. A method according to clause 62 or 63, wherein the decorrelation model comprises one or more modeling layers after the bottleneck layer, the one or more modeling layers modeling the simulation data from the restricted parameter space.

[0296] 65. The method of clause 64, wherein the one or more modeling layers are operable to directly infer one or more parameter values ​​of one or more direct inference parameters.

[0297] 66. A method according to clause 65, wherein the one or more direct inference parameters include one or more parameters of interest.

[0298] 67. A method according to any of clauses 62 to 66, wherein one or more parameters are bypassed at the bottleneck layer.

[0299] 68. The method of clause 67, wherein the one or more parameters that are bypassed include one or more known parameters whose values ​​are known and / or one or more parameters of interest.

[0300] 69. A method according to any of clauses 62 to 68, comprising at least two parallel bottleneck layers, each bottleneck layer being used for a respective subset of said input parameterizations.

[0301] 70. The method of clause 69, wherein each of the parallel bottleneck layers enables imposition of a respective prior on each of the subsets of the input parameterizations.

[0302] 71. A method according to any of clauses 62 to 70, comprising training an additional model operable to invert and / or remap the mapping caused by the bottleneck layer; and

[0303] The additional model is used to determine a correlation measure for a correlation between the inference parameter and one or more other parameters.

[0304] 72. A method according to any of clauses 58 to 71, wherein the restricted parameter space represents a minimum sufficient statistic for the combination of all parameters of the input parameterization.

[0305] 73. A method according to any one of clauses 58 to 72, comprising using the decorrelation model in parameter reconstruction of a structure in a metrological operation.

[0306] 74. A metering apparatus operable to perform a method according to any one of clauses 1 to 73.

[0307] 75. Metering equipment according to clause 74, including:

[0308] a support for a substrate having a plurality of target structures thereon;

[0309] an optical system for measuring each target structure; and

[0310] A processor arranged to perform a method according to any of clauses 1 to 73.

[0311] 76. A lithography system comprising:

[0312] Lithographic equipment, including:

[0313] an illumination optical system arranged to illuminate the pattern;

[0314] a projection optical system arranged to project an inspection of said pattern onto a substrate; and

[0315] A metering device according to any of clauses 74 or 75.

[0316] 77. A computer program comprising processor-readable instructions which, when executed on a suitable processor-controlled device, cause the processor-controlled device to perform a method according to any of clauses 1 to 73.

[0317] 78. A computer program carrier comprising a computer program according to clause 77.

[0318] Although specific reference has been made above to the use of embodiments of the invention in the context of optical lithography, it will be appreciated that the invention may be used in other applications, such as imprint lithography, and is not limited to optical lithography where the context permits. In imprint lithography, the topography in the patterning device defines the pattern produced on the substrate. The topography of the patterning device may be pressed into a resist layer provided to the substrate, and the resist is then cured by applying electromagnetic radiation, heat, pressure, or a combination thereof. After the resist is cured, the patterning device is removed from the resist, leaving a pattern therein.

[0319] As used herein, the terms "radiation" and "beam" encompass all types of electromagnetic radiation, including ultraviolet (UV) radiation (e.g., having a wavelength of or about 365, 355, 248, 193, 157, or 126 nm) and extreme ultraviolet (EUV) radiation (e.g., having a wavelength in the range of 5-20 nm), as well as particle beams (such as ion beams or electron beams).

[0320] The term "lens," where the context permits, may refer to any one or combination of various types of optical components, including refractive, reflective, magnetic, electromagnetic, and electrostatic optical components.

[0321] The foregoing description of the specific embodiments will fully reveal the general characteristics of the present invention so that others can easily modify and / or adapt the various applications of these specific embodiments by applying the knowledge within the art without departing from the general concept of the present invention, without undue experimentation. Therefore, based on the teachings and guidance presented herein, such adaptations and modifications are intended to be within the meaning and scope of the equivalents of the disclosed embodiments. It should be understood that the wording or terminology herein is for the purpose of description by example, rather than restrictive, so that the terms or wording of this specification will be interpreted by those skilled in the art based on the teachings and guidance.

[0322] The breadth and scope of the present invention should not be limited by any of the above-described exemplary embodiments, but should be defined only in accordance with the following claims and their equivalents.

Claims

1. A method for determining a reconstruction scheme, the reconstruction scheme describing at least nominal values ​​for use in a parameterized reconstruction describing an object; the method comprising: acquiring first measurement data associated with measurements of a plurality of targets on at least one substrate, the measurement data associated with one or more acquisition settings; performing optimization by minimizing a cost function that minimizes a difference between the first measurement data and simulated measurement data based on a reconstructed parameterization of each of the plurality of objectives; The constraints on the cost function are imposed based on a layered prior. 2 . The method of claim 1 , wherein the hierarchical prior encodes prior information about the scale of the parameter. 3 . The method of claim 1 , wherein the hierarchical prior imposes constraints on differences in parameter values ​​in the reconstructed parameterization from corresponding experimentally measured parameter values ​​obtained from a reference tool.

4. The method of claim 3, wherein the constraints on differences in parameter values ​​in the reconstructed parameterization and corresponding experimentally obtained parameter values ​​allow for an inexact match to account for statistical errors affecting the first measurement data.

5. The method of claim 3, wherein the method further outputs tool matching data describing a relationship between the first measurement data relative to corresponding experimentally acquired measurement data from the reference tool.

6. A method according to any of the preceding claims, wherein a first regularization is applied to the layered prior.

7. The method of claim 6, wherein the first regularization determines a fixed-floating strategy by preferring a solution with a minimum number of varying parameters. The method of claim 6 , wherein the first regularization is L1 norm regularization.

9. The method of claim 6, comprising minimizing the cost function for different strengths of the first regularization.

10. The method according to any one of the preceding claims 1-5, 7-9 comprises matching the statistical characteristics of the solution of the cost function with the statistical characteristics of the solution of a single-objective reconstruction, wherein the strength of the second regularization applied to the single-objective reconstruction is iteratively determined.

11. The method of claim 10, wherein the determining the strength of the second regularization comprises minimizing a difference between a parameter distribution of a solution of the single-objective reconstruction over a plurality of objectives and a parameter distribution of a solution of the cost function.

12. The method of claim 10, wherein one or more performance indicators describing the performance of parameter values ​​from the matched single-objective reconstructions are evaluated, and the reconstruction solution corresponding to the best performance indicator is selected as the determined reconstruction solution.

13. A metering device operable to perform the method of any one of claims 1 to 12.

14. A photolithography system comprising: Lithographic equipment, including: an illumination optical system arranged to illuminate the pattern; a projection optical system arranged to project an inspection of said pattern onto a substrate; and A metering device according to claim 13.

15. A computer program product comprising processor readable instructions which, when executed on a suitable processor-controlled device, cause the processor-controlled device to perform the method of any one of claims 1 to 12.

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