Data estimation in metrology

Abstract

Methods and apparatus for estimating an unknown value of at least one data set of a plurality of data sets, each data set comprising a plurality of values indicative of radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate, wherein the plurality of data sets comprises at least one known value, and wherein at least one data set of the plurality of data sets comprises an unknown value, the apparatus comprising a processor that estimates the unknown value of the at least one data set based on: a plurality of known values of the plurality of data sets; a first condition between two or more values within a data set of the plurality of data sets; and a second condition between two or more values that are part of different data sets of the plurality of data sets.

Description

[0001] Cross-reference to related applications

[0002] This application claims priority to European application 17199539.2, filed on 1 November 2017, which is incorporated herein by reference in its entirety. Technical Field

[0003] This invention relates to the estimation of data in metrology. Specifically, the invention may relate to the estimation of data including values ​​of radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate, which may be a semiconductor substrate such as a wafer. Background Technology

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

[0005] To project a pattern onto a substrate, photolithography equipment can use electromagnetic radiation. The wavelength of this radiation determines the minimum size of the feature that can be formed on the substrate. Typical wavelengths currently used are 365 nm (i-line), 248 nm, 193 nm, and 13.5 nm. Photolithography equipment using soft X-rays or extreme ultraviolet (EUV) radiation (whose wavelengths range from 1 nm to 100 nm, for example, from 5 nm to 20 nm, such as 6.7 nm or 13.5 nm) can be used to form smaller features on the substrate than photolithography equipment using, for example, radiation with a wavelength of 193 nm.

[0006] Low-K1 lithography can be used to process features smaller than the classical resolution limit of lithography equipment. In this process, the resolution formula can be expressed as CD = k1 × λ / NA, where λ is the wavelength of the radiation used, NA is the numerical aperture of the projection optics in the lithography equipment, CD is the "critical size" (typically the smallest feature size printed, but in this case, half a pitch), and k1 is an empirical resolution factor. Generally, the smaller k1 is, the more difficult it becomes to reproduce patterns on the substrate that resemble the shape and size planned by the circuit designer to achieve specific electrical functions and performance. To overcome these difficulties, complex fine-tuning steps can be applied to the lithography projection equipment and / or design layout. These steps include, but are not limited to: NA optimization, custom illumination schemes, use of phase-shifting patterning apparatus, various optimizations in the design layout (such as optical proximity correction (OPC, sometimes also called "optical and process correction"), or other methods generally defined as "resolution enhancement techniques" (RET). Alternatively, the reproduction of patterns at low k1 can be improved using a tight control loop used to control the stability of the lithography equipment.

[0007] To ensure that the substrate W exposed by the lithography equipment LA is correctly and consistently exposed, it is desirable to inspect the substrate to measure properties of the patterned structure, such as overlap error between subsequent layers, line thickness, critical dimension (CD), etc. This process can be called metrology and can be performed by one or more inspection devices, such as metrology tools.

[0008] In some exemplary methods and apparatuses, metrology can be performed "on-product," meaning that metrology is performed using features fabricated in or on a substrate that function in the overall IC design and contribute to the operation of the IC. Such features are therefore not dedicated measurement targets. Techniques used in this type of metrology may require the development of databases that allow comparison of measured data with the database to determine one or more parameters of one or more features on or on the substrate. In some examples, these databases can identify multiple expected optical responses for features exhibiting specific parameters. By comparing the measured optical response with optical responses in the database, an estimate of the parameter can be determined.

[0009] The development of these libraries is a time-consuming process because they are typically generated by simulating or estimating optical responses exhibiting specific characteristics of specific parameters when irradiated by radiation from a particular optical system using Maxwell's equations. These libraries contribute to what can be termed metrological "matching schemes," increasing the "time to match" (T2R) through the time-consuming simulation process. Furthermore, the time-consuming simulation process also increases the simulation of the optical response during measurement. Therefore, more efficient methods and apparatus are desired for estimating data such as optical responses in metrology. Summary of the Invention

[0010] According to an aspect of the invention, an apparatus is provided for estimating unknown values ​​of at least one of a plurality of datasets, each dataset including a plurality of values ​​representing radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate. The plurality of datasets include at least one known value, and at least one of the plurality of datasets includes unknown values. The apparatus includes a processor configured to estimate the unknown values ​​of the at least one dataset based on: known values ​​of the plurality of datasets; a first condition between two or more values ​​within one dataset of the plurality of datasets; and a second condition between two or more values ​​representing portions of different datasets of the plurality of datasets.

[0011] The first and second conditions can be imposed conditions.

[0012] Optionally, the first condition includes a smoothness condition.

[0013] Optionally, the first condition includes data indicating the difference in magnitude between one or more values ​​within the plurality of datasets.

[0014] Optionally, the processor is configured to apply the first condition between two or more values, including adjacent values, within the plurality of datasets.

[0015] Optionally, the second condition may include a relevance condition.

[0016] Optionally, the second condition includes the correlation between corresponding values ​​in different datasets of the plurality of datasets.

[0017] Optionally, the correlation condition may also include the correlation between multiple values ​​in one of the multiple datasets.

[0018] Optionally, the first condition and / or the second condition indicate the information content of the plurality of datasets.

[0019] Optionally, the processor is configured to estimate the unknown values ​​of at least one dataset based on a matrix completion algorithm.

[0020] Optionally, the matrix completion algorithm is based on convex optimization techniques.

[0021] Alternatively, convex optimization techniques include one of proximity splitting and primal duality algorithms.

[0022] Optionally, the processor is configured to be based on

[0023] Estimate the unknown values ​​in at least one dataset.

[0024] Where, d i It is a dataset that forms a row of matrix D, D M There are multiple known values. It is a value that assigns a weight to the smoothness condition compared to the correlation condition. is the error term for estimating the known values ​​in D, M is the mask for identifying multiple known values, and TV is the total variation.

[0025] Optionally, the processor is configured to estimate unknown values ​​in one or more datasets for each of a plurality of optical parameters and / or characteristic parameters, and to generate a library of datasets that can be compared with a measured dataset obtained via measurements performed by a sensor.

[0026] Optionally, the processor is configured to match the measured dataset with at least one of a plurality of datasets in the library to determine at least one parameter of the photolithography process performed on the substrate.

[0027] Optionally, the processor is further configured to generate one or more of the plurality of known values ​​in the at least one dataset based on one or more of the following: at least one parameter of an optical system configured to direct radiation toward the one or more features fabricated in or on a substrate; at least one parameter of the radiation; and at least one parameter of the one or more features fabricated in or on a substrate.

[0028] Optionally, the processor is configured to generate one or more of the plurality of known values ​​at locations in the dataset where the information content is above a threshold.

[0029] Optionally, all values ​​in one or more of the plurality of datasets are known.

[0030] Optionally, all values ​​are known data sets associated with one or more additional features fabricated in or on the substrate or another substrate.

[0031] Optionally, one or more of the plurality of datasets represent pupil images, and one or more of the values ​​represent pixels of the pupil image.

[0032] Optionally, one or more of the pixels may include data indicating reflectivity or intensity.

[0033] Optionally, the device further includes a sensor configured to receive radiation diffracted and / or reflected and / or scattered by the one or more features.

[0034] According to an aspect of the present invention, an inspection apparatus is provided, comprising any of the apparatuses disclosed herein.

[0035] Alternatively, the inspection equipment is a measuring device.

[0036] According to an aspect of the present invention, a photolithography apparatus is provided, including any of the apparatuses disclosed herein.

[0037] According to an aspect of the present invention, a photolithography unit is provided, comprising any of the devices disclosed herein.

[0038] According to an aspect of the invention, a method is provided for estimating unknown values ​​in at least one of a plurality of datasets, each dataset including a plurality of values ​​representing radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate. The plurality of datasets includes at least one known value, and at least one of the plurality of datasets includes unknown values. The method includes estimating the unknown values ​​of the at least one dataset by a processor based on: the plurality of known values ​​of the plurality of datasets; a first condition between two or more values ​​within one dataset of the plurality of datasets; and a second condition between two or more values ​​that are parts of different datasets of the plurality of datasets.

[0039] Optionally, the first condition includes a smoothness condition.

[0040] Optionally, the first condition includes data indicating the difference in magnitude between one or more values ​​within the plurality of datasets.

[0041] Optionally, the method further includes applying the first condition between two or more values, including adjacent values, within the plurality of datasets.

[0042] Optionally, the second condition may include a relevance condition.

[0043] Optionally, the second condition includes the correlation between corresponding values ​​in different datasets of the plurality of datasets.

[0044] Optionally, the correlation condition may also include the correlation between values ​​in one of the plurality of datasets.

[0045] Optionally, the first condition and / or the second condition indicate the information content of the plurality of datasets.

[0046] Optionally, the method further includes estimating the unknown values ​​of at least one dataset based on a matrix completion algorithm.

[0047] Optionally, the matrix completion algorithm is based on convex optimization techniques.

[0048] Alternatively, convex optimization techniques include one of proximity splitting and primal duality algorithms.

[0049] Optionally, the method further includes a method based on Estimate the unknown values ​​in at least one dataset.

[0050] Where, d i It is a dataset that forms a row of matrix D, D M There are multiple known values. It is a value that assigns a weight to the smoothness condition compared to the correlation condition. is the error term for estimating the known values ​​in D, M is the mask for identifying multiple known values, and TV is the total variation.

[0051] Optionally, the method further includes estimating unknown values ​​in one or more datasets for each of a plurality of optical parameters and / or characteristic parameters, and generating a library of datasets that can be compared with a measured dataset obtained via measurements performed by a sensor.

[0052] Optionally, the method further includes estimating unknown values ​​in one or more datasets for each of a plurality of optical parameters and / or characteristic parameters, and generating a library of datasets that can be compared with a measured dataset obtained via measurements performed by a sensor.

[0053] Optionally, the method further includes matching the measured dataset with at least one of a plurality of datasets in the library to determine at least one parameter of the photolithography process performed on the substrate.

[0054] Optionally, the method further includes generating one or more of the known values ​​in the at least one dataset based on one or more of the following: at least one parameter of an optical system configured to direct radiation toward the one or more features fabricated in or on a substrate; at least one parameter of the radiation; and at least one parameter of the one or more features fabricated in or on a substrate.

[0055] Optionally, the method further includes generating one or more of the plurality of known values ​​at locations in the dataset where the information content is above a threshold.

[0056] Optionally, all values ​​in one or more of the plurality of datasets are known.

[0057] Optionally, all values ​​are known data sets associated with one or more additional features fabricated in or on the substrate or another substrate.

[0058] Optionally, one or more of the plurality of datasets represent pupil images, and one or more of the values ​​represent pixels of the pupil image.

[0059] Optionally, one or more of the pixels may include data indicating reflectivity or intensity.

[0060] According to an aspect of the invention, a computer program is provided, comprising instructions that, when executed on at least one processor, cause at least one processor to control a device to perform any method disclosed herein.

[0061] According to an aspect of the invention, a carrier is provided comprising the above-described computer program, wherein the carrier is one of an electronic signal, an optical signal, a radio signal, or a non-transitory computer-readable storage medium. Attached Figure Description

[0062] Embodiments of the invention will now be described by way of example only with reference to the accompanying schematic diagrams, in which:

[0063] Figure 1 A schematic overview of a photolithography apparatus is provided;

[0064] Figure 2 A schematic overview of the photolithography unit is described;

[0065] Figure 3 A schematic representation of the overall photolithography process is depicted, illustrating the collaboration between three key technologies to optimize semiconductor manufacturing.

[0066] Figure 4 It depicts a schematic representation of multiple datasets, including known and unknown values;

[0067] Figure 5 A flowchart illustrating a method for estimating multiple datasets;

[0068] Figure 6 It depicts a schematic representation of multiple datasets, including known and unknown values;

[0069] Figure 7 A flowchart illustrating a method for estimating multiple datasets; and

[0070] Figure 8 This is a block diagram illustrating a computer system that can assist in implementing the methods and processes disclosed herein. Detailed Implementation

[0071] In this document, the terms “radiation” and “beam” are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., with wavelengths of 365 nm, 248 nm, 193 nm, 157 nm or 126 nm) and soft X-rays and / or extreme ultraviolet radiation (EUV, e.g., with wavelengths in the range of about 1-100 nm).

[0072] As used herein, the terms “mask,” “mask,” or “patterning apparatus” can be broadly interpreted to refer to a general patterning apparatus capable of imparting a patterned cross-section to an incident radiation beam, the patterned cross-section corresponding to a pattern to be generated in a target portion of a substrate; the term “optical valve” can also be used in this context. Examples of other such patterning apparatuses besides classic masks (transmissive or reflective; binary, phase-shifting, hybrid, etc.) include:

[0073] - Programmable mirror array. More information about such mirror arrays is given in U.S. Patent Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference.

[0074] - Programmable LCD array. An example of such a construction is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0075] Figure 1 A lithography apparatus LA is schematically depicted. The lithography apparatus LA includes: an irradiation system (also called an irradiator) IL configured to modulate a radiation beam B (e.g., UV radiation, DUV radiation, or EUV radiation); a support structure (e.g., a mask stage) T configured to support a patterning apparatus (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning apparatus MA according to specific parameters; a substrate stage (e.g., a wafer stage) WT configured to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate according to specific parameters; and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted by the radiation beam B by the patterning apparatus MA onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0076] In operation, the irradiator IL receives a radiation beam from the radiation source SO, for example, via the beam delivery system BD. The irradiation system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic, or other types of optical components, or any combination thereof, to guide, shape, or control the radiation. The irradiator IL can be used to adjust the radiation beam B to have a desired spatial and angular intensity distribution in its cross-section at the plane of the pattern forming apparatus MA.

[0077] The term "projection system" PS as used herein should be interpreted broadly to encompass all types of projection systems, including refractive optical systems, reflective optical systems, reflective-refractive optical systems, anamorphic optical systems, magnetic optical systems, electromagnetic optical systems, and electrostatic optical systems, or any combination thereof, for example, as appropriate for the exposure radiation used or for other factors such as the use of immersion liquids or vacuum. Any term "projection lens" as used herein may be considered synonymous with the more general term "projection system" PS.

[0078] Photolithography equipment (LA) can be of the type in which at least a portion of the substrate can be covered with a liquid (e.g., water) having a relatively high refractive index to fill the space between the projection system and the substrate—this is also known as immersion lithography. More information about this immersion technique is given in U.S. Patent No. 6,952,253 and PCT Publication No. WO99-49504, which are incorporated herein by reference.

[0079] The lithography apparatus LA can also be of the type having two (dual-platform) or more substrate stages WT and, for example, two or more support structures T (not shown). In such a “multi-platform” machine, additional stages / structures can be used in parallel, or one or more other stages can be used to expose the design layout of the patterning apparatus MA onto the substrate W while preparatory steps are performed on one or more stages.

[0080] In operation, the radiation beam B is incident on the patterning apparatus (e.g., mask MA) held on a support structure (e.g., mask stage T) and patterned by the patterning apparatus MA. Having traversed the mask MA, the radiation beam B is passed through a projection system PS, which focuses the beam onto a target portion C of the substrate W. The substrate stage WT can be accurately moved, for example, to position different target portions C within the path of the radiation beam B, by means of a second positioner PW and a position sensor IF (e.g., an interferometer device, linear encoder, 2-D encoder, or capacitive sensor). Similarly, a first positioner PM and possibly another position sensor (…) can be used… Figure 1(Not explicitly depicted) The mask MA is used to accurately position itself relative to the path of the radiation beam B. The mask MA and the substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the illustrated substrate alignment marks occupy dedicated target portions, they can be located in the space between multiple target portions (these are known as scribing alignment marks).

[0081] like Figure 2 As shown, a lithography apparatus LA can constitute part of a lithography unit LC, sometimes also called a lithography cell or (lithography) cluster, which often includes equipment for performing pre-exposure and post-exposure processes on a substrate W. Typically, these devices include: a spin coater SC for depositing a resist layer, a developer DE for developing the exposed resist, and chillers CH and bake plates BK, for example, for regulating the temperature of the substrate W (e.g., for regulating the solvent in the resist layer). A substrate handler or robot RO picks up the substrate W from input / output ports I / O1, I / O2, moves the substrate between different process devices, and then transfers the substrate W to the loading stage LB of the lithography apparatus LA. These devices in the lithography cell are often collectively referred to as a coating and developing system and are typically controlled by a coating and developing system control unit TCU, which itself can be controlled by a management and control system SCS, which can also control the lithography apparatus LA, for example, via a lithography control unit LACU.

[0082] To ensure correct and consistent exposure of the substrate W by the lithography apparatus LA, it is desirable to inspect the substrate to measure properties of the patterned structure, such as overlap error between subsequent layers, line thickness, critical dimension (CD), etc. For this purpose, an inspection tool (not shown) may be included in the lithography unit LC. If an error is detected, adjustments can be made, for example, to the subsequent exposure of the substrate or other processing steps to be performed on the substrate W, especially if the inspection is performed before other substrates W in the same batch or leg are still awaiting exposure or processing.

[0083] Inspection equipment (which may also be referred to as measurement equipment) is used to determine the properties of a substrate W, particularly how the properties of different substrates W vary or how properties associated with different layers of the same substrate W vary between different layers. Inspection equipment can alternatively be configured to identify defects on the substrate W and may, for example, be part of a photolithography unit LC, or may be integrated into a photolithography apparatus LA, or may even be a standalone device. Inspection equipment can measure the properties of latent images (patterns in a photoresist layer after exposure), semi-latent images (images in a photoresist layer after a post-exposure baking (PEB) step), or developed photoresist images (where exposed or unexposed portions of the photoresist have been removed), or even etched images (after a pattern transfer step such as etching).

[0084] Typically, the patterning process in a photolithography (LA) apparatus is one of the most critical steps in this process, which requires the high-precision sizing and placement of structures on a substrate W. To ensure this high accuracy, three systems can be combined into a so-called "holistic" control environment, such as... Figure 3 The diagram is illustrative. One of these systems is a lithography apparatus LA, which is (essentially) connected to a metrology tool MT (second system) and a computer system CL (third system). The key to this “holistic” environment is optimizing the collaboration between these three systems to enhance the overall process window and provide tight control loops to ensure that the patterning performed by the lithography apparatus LA remains within the process window. The process window defines a range of process parameters (e.g., dose, focus, overlap) within which a particular manufacturing process produces a defined result (e.g., a functional semiconductor device), typically allowing for variations in process parameters during the lithography or patterning process.

[0085] The computer system CL can use a portion of the design layout to be patterned to predict which resolution enhancement technique to use and perform computational lithography simulations and calculations to determine which mask layouts and lithography equipment settings are used to achieve the largest overall process window (within) the patterning process. Figure 3 (Depicted by double arrows in the first scale SC1). Typically, resolution enhancement techniques are arranged to match the patterning possibilities of the lithography apparatus LA. The computer system CL can also be used to detect where the lithography apparatus LA is currently processing within its window (e.g., using input from a metrology tool MT) to predict whether defects exist due to, for example, suboptimal processing (in... Figure 3 (The arrow in the second scale SC2 points to "0").

[0086] The measurement tool MT can provide input to the computer system CL for accurate simulation and prediction, and can provide feedback to the lithography equipment LA to identify possible drifts, for example, in the calibrated state of the lithography equipment LA (in Figure 3 (This is depicted by multiple arrows in the third scale SC3).

[0087] During photolithography, it is desirable to frequently measure the resulting structure, for example, for process control and verification. The tools used to perform these measurements are typically called metrology tools (MTs). Different types of metrology tools (MTs) are known for performing these measurements, including scanning electron microscopes (SEMs) or various forms of scatterometer metrology tools (MTs). A scatterometer is a versatile instrument that allows the measurement of parameters of the photolithography process by placing a sensor in the pupil of the scatterometer objective or in a plane conjugate to that pupil (this measurement is often referred to as pupil-based measurement), or by placing a sensor in the image plane or in a plane conjugate to that image plane (in this case, the measurement is often referred to as image- or field-based measurement). Such scatterometers and associated measurement techniques are further described in patent applications US20100328655, US2011102753A1, US20120044470A, US20110249244, US20110026032, or EP1,628,164A, which are incorporated herein by reference in their entirety. The aforementioned scatterer can use light ranging from soft X-rays and visible light to near-IR wavelengths to measure gratings.

[0088] In the first embodiment, the scatterer MT is an angle-resolved scatterer. In such a scatterer, a reconstruction method can be applied to the measured signal to reconstruct or calculate the properties of the grating. This reconstruction can, for example, be produced by simulating the interaction between the scattered radiation and a mathematical model of the target structure and comparing the simulation results with the measurement results. The parameters of the mathematical model are adjusted until the simulated interaction produces a diffraction pattern similar to the diffraction pattern observed from an actual target.

[0089] In the second embodiment, the scatterer MT is a spectroscopic scatterer. In such a spectroscopic scatterer MT, radiation emitted by a radiation source is directed onto the target, and radiation reflected or scattered from the target is directed to a spectroscopic detector that measures the spectrum of the specularly reflected radiation (i.e., a measurement of intensity as a function of wavelength). Based on this data, the structure or profile of the target that produces the detected spectrum can be reconstructed, for example, through rigorous coupled-wave analysis and nonlinear regression or by comparison with a simulated spectral library.

[0090] In the third embodiment, the scatterer MT is an ellipsometer. An ellipsometer allows the determination of parameters of a photolithography process by measuring the scattered radiation of each of a plurality of polarization states. This metrology device emits polarized light (such as linear, circular, or elliptical) using, for example, a suitable polarization filter in the illumination section of the metrology device. The source suitable for the metrology device can also provide polarized radiation. Various embodiments of existing ellipsometers are described in U.S. Patent Applications 11 / 451,599, 11 / 708,678, 12 / 256,780, 12 / 486,449, 12 / 920,968, 12 / 922,587, 13 / 000,229, 13 / 033,135, 13 / 533,110, and 13 / 891,410, which are incorporated herein by reference in their entirety.

[0091] In one embodiment of a scattering instrument (MT), the scattering instrument MT is adapted to measure the overlap of two misaligned gratings or periodic structures by measuring the reflectance spectrum and / or detecting an asymmetry in the configuration, the asymmetry being related to the degree of overlap. Two (typically overlapping) grating structures may be applied in two different layers (not necessarily consecutive layers) and may be formed at substantially the same location on a wafer. The scattering instrument may have a symmetrical detection configuration, for example, as described in the co-owned patent application EP1,628,164A, so that any asymmetry can be clearly distinguished. This provides a simple method for measuring misalignment in gratings. Other examples for measuring the overlap error between two layers containing a periodic structure by the asymmetry of the periodic structure can be found in PCT Patent Application Publication No. WO 2011 / 012624 or U.S. Patent Application US 20160161863, which are incorporated herein by reference in their entirety.

[0092] Other parameters of interest may be focus and dose. As described in U.S. Patent Application US2011-0249244, focus and dose can be determined simultaneously by scattering measurements (or alternatively by scanning electron microscopy), which is incorporated herein by reference in its entirety. A single structure can be used that has a unique combination of critical size and sidewall angle measurements for each point in the focus energy matrix (FEM—also known as the focus exposure matrix). If these unique combinations of critical size and sidewall angles are available, the focus and dose values ​​can be uniquely determined based on these measurements.

[0093] The measurement target can be an entire ensemble of a composite grating formed primarily in a resist during a photolithography process, but it can also be formed after, for example, an etching process. Typically, the pitch and linewidth of the structure within the grating are highly dependent on the measurement optics (particularly the NA of the optics) to capture the diffraction order from the measurement target. As previously mentioned, the diffraction signal can be used to determine the offset between two layers (also known as “overlap”), or to reconstruct at least a portion of the original grating produced by the photolithography process. This reconstruction can be used to provide guidance on the quality of the photolithography process and can be used to control at least a portion of the photolithography process. The target can have small subsegments and be configured to mimic the dimensions of functional portions of the design layout within the target. Due to these subsegments, the target will behave more similarly to the functional portions of the design layout, thus the overall process parameter measurements are better analogous to the functional portions of the design layout. The target can be measured in either an underfilled or overfilled mode. In an underfilled mode, the measurement beam produces a spot smaller than the entire target. In an overfilled mode, the measurement beam produces a spot larger than the entire target. In this overfilled mode, different targets may be measured simultaneously, thereby determining different processing parameters at the same time.

[0094] The overall measurement quality of a lithography parameter used for a specific target is determined at least in part by the measurement configuration used to measure that lithography parameter. The term "substrate measurement configuration" can include one or more parameters of the measurement itself, one or more parameters of one or more patterns being measured, or both. For example, if the measurement used in the substrate measurement configuration is a diffraction-based optical measurement, then one or more parameters of the measurement can include the wavelength of the radiation, the polarization of the radiation, the angle of incidence of the radiation relative to the substrate, the direction of the radiation relative to the pattern on the substrate, etc. One of the criteria for selecting a measurement configuration can be, for example, the sensitivity of one of the measurement parameters to processing variations. Further examples are described in U.S. Patent Application US2016-0161863 and U.S. Patent Application US2016-0370717, which are incorporated herein by reference in their entirety.

[0095] During photolithography, it is desirable to frequently measure the resulting structure, for example, for process control and verification. Various tools are known for performing such measurements, including scanning electron microscopes or various forms of metrology equipment, such as scatterometers. Examples of known scatterometers often rely on the provision of a dedicated measurement target, such as an underfilled target (in the form of a simple grating or overlapping gratings in different layers, large enough that the measurement beam produces a spot smaller than the grating) or an overfilled target (thus the spot partially or completely contains the target). Alternatively, the use of metrological tools (e.g., an angle-resolved scatterometer illuminating an underfilled target such as a grating) allows for the use of so-called reconstruction methods, where the properties of the grating can be calculated by simulating the interaction of scattered radiation with a mathematical model of the target structure and comparing the simulation results with the measured results. The parameters of the model are adjusted until the simulated interaction produces a diffraction pattern similar to that observed from an actual target. To accelerate the reconstruction process, a library of simulated scattering signals (or optical responses) is simulated and stored for each specific set of grating parameters and / or measurement parameters, resulting in the simulated scattering signals. By using already simulated responses, the generation of this library allows for faster refactoring times.

[0096] A scatterometer is a multifunctional instrument that allows for the measurement of parameters of a photolithography process by placing a sensor in the pupil of the scatterometer objective or in a plane conjugate to the pupil (this measurement is typically referred to as a pupil-based measurement), or by placing a sensor in the image plane or in a plane conjugate to the image plane (in this case, the measurement is typically referred to as an image- or field-based measurement). Such scatterometers and associated measurement techniques are further described in patent applications US20100328655, US2011102753A1, US20120044470A, US20110249244, US20110026032, or EP1,628,164A, all of which are incorporated herein by reference in their entirety. The aforementioned scatterometers are capable of measuring multiple targets from multiple gratings using light ranging from soft X-rays and visible light to near-IR wavelengths within a single image.

[0097] As discussed above, the reconstruction process may include developing a library of simulated optical responses for one or more features fabricated in or on a substrate under certain optical conditions. The simulated optical response of the feature can be determined by assuming that the feature exhibits one or more lithographic parameters, such as CD, overlap, focus, dose, and pitchwalk, to varying degrees. The optical response (simulated or measured) may include values ​​representing the light diffracted by the substrate and measured in the pupil plane of the optical tool or the re-imaging pupil plane to form a pupil image. In this arrangement, the values ​​produced in the simulated optical response represent pixels of the pupil image. However, it should be understood that the methods and apparatus disclosed herein can be applied to more general situations where the library comprises datasets, each available via a sensor and including multiple values ​​indicating radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate. These values ​​may be reflectivity coefficients, which may include multiple (e.g., four) complex coefficients. The reflectivity coefficient provides information for determining the intensity measured at a pixel of a sensor when given the radiation irradiated onto a feature on a substrate in use with a device such as those disclosed herein, and the optical system of said device through which the diffracted / reflected / scattered radiation propagates to the sensor. The following description pertains to a situation where each element in the dataset is applied to a simulated pupil image, but this should be understood as exemplary only.

[0098] In a broad sense, the pixels of a simulated pupil image can be determined using Maxwell's equations, knowledge of the structure of a substrate feature, and / or by assuming a specific degree of lithographic parameters seen in the feature. This will be understood by those skilled in the art and will not be discussed in detail here. However, a full simulation of each pupil image is computationally expensive and time-consuming. Therefore, there are various methods for more efficiently determining the simulated pupil images and thereby generating the library. For example, in approximation methods, a linear approximation of the pixels in the pupil image to be simulated is based on the reflectance of a subset of principal pixels. Approximation methods establish relationships across the pixels in the pupil and apply these relationships to the simulated pupil using the principal pixels to estimate the remaining pixels. In other words, employing redundancy in the pupil space makes it necessary to determine only a small subset of the pixels in the pupil to be simulated using Maxwell's equations, and the remaining pixels can be estimated based on the principal pixels. Typically, approximation methods are based on a large number of full pupils to determine the relationships between pixels in a pupil image. Essentially, the method looks at a large collection of one or more stacked full pupil images, finds the principal pixels of that collection representing the full pupil image, and the relationships between the pixels in the full pupil image. The method then checks the accuracy of the approximation determined based on the principal pixels and the relationship to the other stacked pupil images. If the approximation is poor, more principal pixels and stacks are added and the process is repeated.

[0099] The inventors have learned that further improvements to the approximation methods for library generation can improve the time to perform matching schemes (T2R), thereby making library generation more efficient. In particular, the exemplary methods and apparatuses disclosed herein are intended to avoid or reduce the number of redundant computations in the early stages of library generation. In some cases, this can be achieved using transfer learning, which can reuse data from similar libraries (which may correspond to different features (different stacks)) to generate a pupil image of the library associated with the features that will become the object of metrology. It should be noted that, as used herein, the term “stack” encompasses the parameterization of geometry and / or specific layer structures fabricated in or on a substrate. Additionally, “stack simulation” encompasses a model of a stack, where one or more parameters are fixed at specific values. As part of the approximation method, the tool is “trained” by determining the redundancy of pixels across the pupil image (i.e., within the pupil image) based on Maxwell's equations, but as mentioned above, this is computationally expensive. The methods and apparatuses disclosed herein seek to determine redundancy within the pupil image with less computational effort. Specifically, known approximation methods use the full pupil to find redundancy, while the methods and apparatus disclosed herein use the knowledge that the data in the pupil image includes redundant data and one or more characteristics of said redundancy to determine an estimate of the pupil image without having to look at all the data in any pupil image.

[0100] Exemplary methods and apparatuses can be configured to estimate multiple unknown values ​​in one or more datasets based on at least one known value in one of the datasets, a first condition imposed between values ​​within one dataset, and a second condition imposed between values ​​in different datasets. In a specific example, the datasets may represent pupil images, and the known and unknown values ​​may represent known and unknown pixel values. In the specific examples discussed herein, the first condition may be the smoothness between pixel values ​​within a pupil image, and / or the second condition may be the correlation between pixel values ​​in different pupil images. Exemplary methods and apparatuses can “fill in” gaps in pixel image data by utilizing assumptions about correlation (which indicates redundancy in pupil images) and smoothness in the pixel image data. The inventors have recognized that such methods can be used to address the problem of generating simulated pixel image libraries. Numerical results show that the methods and apparatuses disclosed herein achieve an accuracy of one order of magnitude better than the techniques discussed in one of the preceding paragraphs, with only 10% of the data in the pupil images used as training data. It should be noted that the required training data is the amount of data that must be generated by the Maxwell solver to determine the relationships (or the first and second conditions) between pixels in the pupil image.

[0101] Figure 4 A schematic representation of multiple pupil images 400 is shown. Each pupil image includes pixels 402, which may indicate the reflectivity or intensity of radiation reflected or diffracted from or on one or more features in the substrate (stack). It should be noted that the pixel values ​​in each of the pupil images 400 are concatenated into a single vector. These vectors can be processed collectively as matrices, such as... Figure 4 As shown. Each of the plurality of pupil images 400 includes at least one known pixel value 402. The known pixel value 402 may be a simulated pixel value determined using the techniques mentioned above and known to those skilled in the art, a pixel value passed from a previous process, or a mixture of both. Figure 4In the exemplary embodiment shown, each of the pixel images 400 is a pixel image to be estimated and includes a plurality of pixels 402 that have been simulated based on Maxwell's equations. Each of the pupil images is associated with the same feature fabricated in or on a substrate because they each represent the simulated pupil image that would be expected when diffracted and / or reflected and / or scattered by those features, although this is not required. In the exemplary arrangement, one or more of the pupil images in the plurality of pupil images 400 may have been determined based on additional features of the substrate or different substrates. In fact, the smoothness and correlation conditions imposed by the methods and apparatus disclosed herein may be similar for different features. Therefore, pixel values ​​determined for another set of features can be used to estimate the pupil image associated with the feature to which the metrology will be performed.

[0102] Figure 5 A flowchart is shown for a method used to estimate pupil image 400. Initially, smoothness and correlation conditions are determined. This can be done based on empirical data of pupil images measured or simulated from one or more features fabricated in or on a substrate. As previously discussed, these features may correspond to the features to be measured or may correspond to other features.

[0103] Smoothness conditions can be defined by the difference in amplitude between two pixel values ​​within the pupil image. The lower the amplitude difference, the higher the smoothness. Smoothness conditions can impose a minimum threshold of smoothness on the estimated pixel values ​​of the pupil image. The amplitude difference can be defined between neighboring pixel values, and the amplitude difference can be related to multiple pairs of neighboring pixel values. It should be noted that the dataset can be an abstract representation of the 2-D pixel reflectance structure in the "real" world, and "neighboring" can mean adjacent in the 2-D pixel reflectance structure. That is, the term "neighboring," as used herein, encompasses pixel values ​​that are adjacent when the pupil image is formed, but this may not be the case when the pupil image is in vector form. Additionally, the amplitude difference can be the average difference in amplitude across multiple pixels within the pupil image. Smoothness conditions can indicate the information content in the pupil image. In particular, higher smoothness indicates less high-frequency data in the pupil image. High-frequency data can indicate information content.

[0104] A correlation condition can be defined as the correlation between pixel values ​​in different pupil images and / or the correlation between pixel values ​​in the same pupil image. The higher the correlation between pixel values, the lower the information content in the pupil image. A correlation condition can impose a maximum threshold (or, in another way, a minimum threshold) on the estimated pixel values ​​in a pupil image regarding the correlation. More specifically, a correlation condition can be defined as the correlation between corresponding pixel values ​​in different pupil images. As used herein, the term "corresponding" refers to pixel values ​​that have the same location in the pupil image when the pupil image is formed. A correlation condition can indicate the information content in multiple pupil images 400. When the information content in pupil image 400 is low, the methods and apparatus disclosed herein can be applied to estimate the pixel values ​​in pupil image 400 with greater accuracy.

[0105] In an exemplary arrangement, smoothness conditions and relevance conditions can be imposed jointly. That is, a combination of smoothness conditions and relevance conditions can be imposed. This combination can be the sum of smoothness conditions and information content associated with relevance conditions. The combination of smoothness conditions and information content associated with relevance conditions can impose a single combined (or third) condition. In this arrangement, the combined conditions can be minimized.

[0106] Obtain the known pixel value 402 (step 502). This can be achieved by obtaining the known pixel value 402 from a previous process or by simulating the known pixel value 402 using methods known to those skilled in the art. Figure 4 As can be seen, each of the pupil images 400 includes some known pixel values ​​402. In the example described, each of the pupil images 400 also includes unknown pixel values.

[0107] Then, a matrix completion algorithm (step 504) is performed to complete the matrix formed by the vectorized pupil image 400. More specifically, the matrix completion algorithm can use imposed smoothness conditions and imposed correlation conditions as regularization in a self-imposed ill-posed problem that is solved using convex optimization techniques such as nearest neighbor splitting and primal duality algorithms.

[0108] In a specific example, the matrix completion algorithm can be defined by solving the following optimization task for D, although other definitions of the matrix completion algorithm are also possible:

[0109]

[0110] Where D is the matrix of the vectorized stacked pupil image to be simulated, in Figure 4 The matrix D is schematically represented by 400. Each row d of matrix D...i This represents a full-pupil image. To perform an approximation, the methods and apparatus disclosed herein are configured to simulate several pixels D for each pupil using Maxwell's equations. M Pixel D M The pixels can be randomly selected, or they can be selected based on one or more parameters, such as the location of a pixel in the pupil image, or the correlation value of a specific pixel across the pupil image. The pixels to be simulated are identified via a selection mask M. The optimization task described above imposes the difference between the simulated matrices (with known pixel values) of the pupil image, and the estimated pixel values ​​have a very small error, which is caused by... As a regularization, the method imposes a specific smoothness on each pupil image, for example, ensuring that the difference in amplitude between pixels in each pupil image is below a threshold or minimized (i.e., smoothness is maximized). In some exemplary methods and devices, this can be achieved by searching for a smoothness level where the error in the measured data is below a certain threshold. Under the constraint of minimizing the kernel norm of D, the smoothest pupil image is generated to maximize smoothness. Furthermore, the algorithm imposes pixel correlation between pupil images; that is, the resulting matrix D has low information content (low level), thus resulting in high correlation between pupil images. The low information condition is relaxed by minimizing the kernel norm of matrix D to ensure the problem is convex.

[0111] To solve the aforementioned optimization problem and generate the estimated pupil image 400, convex optimization techniques, such as proximity splitting and primal-dual methods, can be applied. Since the function used is non-differentiable, approximate splitting methods can be applied. These methods can be, for example, based on forward-backward algorithms, primal-dual algorithms, or augmented Lagrangian methods. Alternative approaches include using smooth approximations to non-differentiable kernels and the TV norm, replacing the data fidelity term with an L2 term, and using gradient / Hessian-based first / second-order methods. The imposed first and second conditions, namely the smoothness and correlation conditions, represent a strong knowledge transfer from previously known stacked simulations. In an exemplary arrangement, multiple full-pupil image simulations performed for multiple applications include known stacked simulations. These simulations can be analyzed to extract one or more attributes common to the applications, stacks, and / or pupil images. The extracted attributes can then be used to determine the correlation and smoothness conditions. The inventors have observed that the first and second conditions are satisfied for all applications encountered to date, which means that data from previous processes associated with different stacks can be used.

[0112] The estimated pupil images can then be formed into a library (step 506), and the measured pupil images can be compared with the library. Exemplary methods and apparatus can measure the pupil images by directing radiation onto one or more features fabricated in or on a substrate and sensing radiation diffracted and / or reflected and / or scattered by said one or more features (step 508). The measured pupil images can then be compared with estimated pupil images in the library (step 510), and a suitable close match can be found. Based on one or more estimated pupil images that most closely match the measured pupil image, one or more parameters of one or more features can be determined (step 512), such as CD, overlap, focus, dose, and pitch shift.

[0113] Figure 6 Another exemplary schematic representation of multiple pupil images 600 is shown. (With) Figure 4 Similarly, the pupil image 600 includes pixels 402, which can indicate the reflectivity or intensity of radiation reflected or diffracted from or on one or more features in the substrate (stack). Figure 6 In the example, one or more pixels of one or more first pupil images 602 are obtained from a prior process. The one or more first pupil images 602 therefore include multiple known pixel values. In the illustrated example, all pixel values ​​of the one or more first pupil images 602 are known, but the method and apparatus may use other percentages of known pixel values, such as at least 50%, at least 75%, or at least 90%. Additionally, in some exemplary arrangements, one or more first pupil images 602 may include as few as one known pixel value, but this would reduce the accuracy of estimating unknown pixel values. Generally, it can be said that the fewer known pixel values ​​in the first pupil image 602 (and the second pupil image 604 – discussed below), the less accurate the estimation of unknown pixel values. The known pixel values ​​of one or more first pupil images 602 may be associated with one or more features of the substrate to which the metrology will be performed. The known pixel values ​​of one or more first pupil images 602 may be associated with one or more features of a substrate having a shape similar to one or more features of the substrate to which the metrology will be performed. Alternatively, and in Figure 6 In this case, the known pixel values ​​of one or more first pupil images 602 can be associated with other features of the same or different substrates, and the known pixel values ​​have been previously determined and / or estimated. The known pixel values ​​of one or more first pupil images 602 can be obtained from an existing pupil image library. One or more first pupil images 602 can be represented as blocks or matrices, but it should be understood that a block may include multiple vectorized pupil images.

[0114] One or more second pupil images 604 are pupil images to be estimated. One or more second pupil images 604 include known pixel values ​​606 and unknown pixel values.

[0115] In relation to the above text Figure 4 and Figure 5 A similar approach can be used to impose first and second conditions (e.g., smoothness and correlation) on a sequence of one or more first pupil images 602, which may be full pupil images known from previous processes, and one or more second pupil images 604, whose pixel values ​​are known only partially. As mentioned above, pixel values ​​known from previous processes may be associated with the same or additional features.

[0116] Figure 7 A flowchart is shown for another method for estimating pupil image 604. Figure 7 Multiple steps and Figure 5 The steps are the same or similar, and will not be explained in detail again here. Initially, smoothness conditions and correlation conditions are determined (step 700). Known pixel values ​​of one or more first pupil images 602 and one or more second pupil images 604 are obtained (step 702). This can be achieved by obtaining known pixel values ​​from a previous process, simulating known pixel values ​​using methods known to those skilled in the art, or a combination of both. Figure 6 In the example, one or more first pupil images 602 are obtained from a previous process, and known pixel values ​​606 of one or more second pupil images 604 are simulated. From Figure 6 It can be seen that each of the pupil images 600 includes some known pixel values.

[0117] A matrix completion algorithm is then performed (step 704) to complete the matrix formed by the vectorized pupil image 600. The estimated pupil images can then be formed into a library (step 706), and the measured pupil image can be compared with the library. Exemplary methods and apparatus can measure the pupil image by directing radiation to one or more features fabricated in or on a substrate and sensing radiation that has been diffracted and / or reflected and / or scattered by the one or more features (step 708). The measured pupil image can then be compared with the estimated pupil images in the library (step 710), and a suitable close match can be found. Based on one or more estimated pupil images that most closely match the measured pupil image, one or more parameters of one or more features can be determined (step 712), such as CD, overlap, focus, dose, and pitch shift.

[0118] In exemplary methods and apparatuses that use Maxwell's solver to generate known pixel values, one or more strategies can be used to determine which pixel values ​​in the pupil image are identified. In some exemplary arrangements, more known pixel values ​​may be generated at locations with higher information content in the pixel image. In some pupil images, this may mean that the concentration of generated known pixel values ​​is higher in the central and peripheral areas. The area between the central and peripheral areas may include fewer generated known pixel values ​​compared to the central and peripheral areas. In exemplary arrangements, known pixel values ​​may be generated at locations where the information content is above a threshold. Therefore, the concentration of generated known pixel values ​​is higher at such locations.

[0119] Figure 8 This is a block diagram illustrating a computer system 1600 that can assist in implementing the methods and processes disclosed herein. The computer system 1600 includes a bus 1602 or other communication mechanism for communicating information, and a processor 1604 (or multiple processors 1604 and 1605) coupled to the bus 1602 for processing information. The computer system 1600 also includes a main memory 1606, such as random access memory (RAM) or other dynamic storage device, coupled to the bus 1602 for storing information and instructions to be executed by the processor 1604. The main memory 1606 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 1604. The computer system 1600 also includes a read-only memory (ROM) 1608 or other static storage device coupled to the bus 1602 for storing static information and instructions for the processor 1604. A storage device 1610, such as a magnetic disk or optical disk, is provided and coupled to the bus 1602 for storing information and instructions.

[0120] Computer system 1600 may be coupled via bus 1602 to display 1612 for displaying information to a computer user, such as a cathode ray tube (CRT), flat panel display, or touch panel display. Input device 1614, including alphanumeric keys and other keys, is coupled to bus 1602 for communicating information and command selections to processor 1604. Another type of user input device is a cursor controller 1616 (such as a mouse, trackball, or arrow keys) for communicating directional information and command selections to processor 1604 and for controlling cursor movement on display 1612. Such input devices typically have two degrees of freedom on two axes (a first axis (e.g., x) and a second axis (e.g., y)), allowing the device to specify a position in a plane. Touch panel (screen) displays can also be used as input devices.

[0121] One or more of the methods described herein can be executed by computer system 1600 in response to processor 1604 executing one or more sequences of instructions contained in main memory 1606. Such instructions can be read into main memory 1606 from another computer-readable medium, such as storage device 1610. Execution of the sequence of instructions contained in main memory 1606 causes processor 1604 to perform the process steps described herein. In a multiprocessor arrangement, one or more processors can also be used to execute the sequence of instructions contained in main memory 1606. In alternative embodiments, hardwired circuitry can be used in place of or in combination with software instructions. Therefore, the description herein is not limited to any particular combination of hardware circuitry and software.

[0122] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 1604 for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical discs or magnetic disks, such as storage device 1610. Volatile media include dynamic memory, such as main memory 1606. Transmission media include coaxial cables, copper wires, and optical fibers, including wires containing bus 1602. Transmission media can also take the form of sound waves or light waves, such as sound waves or light waves generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punched cards, paper tape, any other physical media with a perforated pattern, RAM, PROMs and EPROMs, FLASH-EPROMs, any other memory chips or cartridges, carrier waves as described below, or any other media from which a computer can read.

[0123] Various forms of computer-readable media may involve transmitting one or more sequences of instructions to processor 1604 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and transmit them over a telephone line using a modem. A modem local to computer system 1600 may receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 1602 may receive the data carried in the infrared signal and place the data on bus 1602. Bus 1602 transmits the data to main memory 1606, from which processor 1604 retrieves and executes the instructions. The instructions received by main memory 1606 may optionally be stored on storage device 1610 before or after execution by processor 1604.

[0124] Computer system 1600 also preferably includes a communication interface 1618 coupled to bus 1602. Communication interface 1618 provides bidirectional data communication coupled to network link 1620, which is connected to local network 1622. For example, communication interface 1618 may be an Integrated Services Digital Network (ISDN) card or modem for providing data communication connectivity with a corresponding type of telephone line. As another example, communication interface 1618 may be a Local Area Network (LAN) card for providing data communication connectivity with a compatible LAN. A wireless link may also be implemented. In any such implementation, communication interface 1618 transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0125] Network link 1620 typically provides data communication to other data devices via one or more networks. For example, network link 1620 may provide a connection to host computer 1624 or to data devices operated by Internet service provider (ISP) 1626 via local network 1622. ISP 1626, in turn, provides data communication services via a global packet data communication network now commonly referred to as the “Internet” 1628. Both local network 1622 and Internet 1628 use electrical, electromagnetic, or optical signals carrying digital data streams. Signals through various networks and signals on network link 1620 and through communication interface 1618 (which transmits digital data to and from computer system 1600) are exemplary forms of carrier waves for conveying information.

[0126] Computer system 1600 can send and receive messages, including program code, via a network, network link 1620, and communication interface 1618. In the example of the Internet, server 1630 can transmit requested code for an application via the Internet 1628, ISP 1626, local network 1622, and communication interface 1618. For example, a downloaded application may provide one or more of the techniques described herein. The received code may be executed by processor 1604 upon receipt and / or stored in storage device 1610 or other non-volatile storage for later execution. In this way, computer system 1600 can acquire application code in carrier-based form.

[0127] Other embodiments are provided in aspects numbered subsequently:

[0128] 1. An apparatus for estimating unknown values ​​in at least one of a plurality of datasets, each dataset comprising a plurality of values ​​indicating radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate.

[0129] The plurality of datasets mentioned therein include at least one known value.

[0130] And wherein at least one of the plurality of datasets includes unknown values, the device includes a processor configured to estimate the unknown values ​​of the at least one dataset based on:

[0131] The known values ​​of the multiple datasets;

[0132] A first condition between two or more values ​​within one of the multiple datasets; and

[0133] A second condition between two or more values ​​that are parts of different datasets of the multiple datasets.

[0134] 2. The device according to aspect 1, wherein the first condition includes a smoothness condition.

[0135] 3. The device according to aspect 1 or 2, wherein the first condition includes data indicating the difference in magnitude between one or more values ​​within the plurality of datasets.

[0136] 4. The device according to any one of the preceding aspects, wherein the processor is configured to apply the first condition between two or more values, including adjacent values, within the plurality of datasets.

[0137] 5. The device according to any one of the preceding aspects, wherein the second condition includes a correlation condition.

[0138] 6. The device according to any one of the preceding aspects, wherein the second condition includes the correlation between corresponding values ​​in different datasets of the plurality of datasets.

[0139] 7. The device according to aspect 6, wherein the correlation condition further includes the correlation between multiple values ​​in one of the multiple datasets.

[0140] 8. The device according to any one of the foregoing aspects, wherein the first condition and / or the second condition indicates the information content of the plurality of datasets.

[0141] 9. The device according to any one of the preceding aspects, wherein the processor is configured to estimate the unknown values ​​of the at least one dataset based on a matrix completion algorithm.

[0142] 10. The device according to aspect 9, wherein the matrix completion algorithm is based on convex optimization techniques.

[0143] 11. The apparatus according to aspect 10, wherein the convex optimization technique includes one of the nearest neighbor splitting algorithm and the primal dual algorithm.

[0144] 12. The device according to any one of the foregoing aspects, wherein the processor is configured to be based on

[0145] Estimate the unknown values ​​in at least one dataset.

[0146] Where, d i It is a dataset that forms a row of matrix D, D M There are multiple known values. This is a weighted value assigned to the smoothness condition compared to the correlation condition. is the error term for estimating the known values ​​in D, M is the mask for identifying the multiple known values, and TV is the total variation.

[0147] 13. The device according to any one of the preceding aspects, wherein the processor is configured to estimate an unknown value in one or more datasets for each of a plurality of optical parameters and / or characteristic parameters, and to generate a library of datasets that can be compared with a measured dataset obtained via measurements performed by a sensor.

[0148] 14. The apparatus according to aspect 13, wherein the processor is configured to match a measured dataset with at least one of a plurality of datasets in the library to determine at least one parameter of a photolithography process performed on the substrate.

[0149] 15. The device according to any one of the foregoing aspects, wherein the processor is further configured to generate one or more of the known values ​​in the at least one dataset based on one or more of the following:

[0150] At least one parameter of the optical system, the optical system being configured to direct radiation toward one or more features fabricated in or on a substrate;

[0151] At least one parameter of the radiation; and

[0152] At least one parameter of the one or more features formed in or on a substrate.

[0153] 16. The apparatus according to aspect 15, wherein the processor is configured to generate one or more of the known values ​​at locations in a dataset where the information content is above a threshold.

[0154] 17. The device according to any one of the preceding aspects, wherein all values ​​in one or more of the plurality of datasets are known.

[0155] 18. The apparatus according to aspect 17, wherein the one or more datasets, all of which are known, are associated with one or more additional features fabricated in or on the substrate or another substrate.

[0156] 19. The device according to any one of the preceding aspects, wherein one or more of the plurality of datasets represent a pupil image, and one or more of the values ​​represent pixels of the pupil image.

[0157] 20. The device according to any one of the preceding aspects, wherein one or more of the pixels include data indicating reflectivity or intensity.

[0158] 21. The device according to any one of the foregoing aspects further includes a sensor configured to receive radiation diffracted and / or reflected and / or scattered by the one or more features.

[0159] 22. An inspection device comprising the device described in any of the preceding aspects.

[0160] 23. The inspection device according to aspect 22, wherein the inspection device is a measuring device.

[0161] 24. A photolithography apparatus comprising the apparatus according to any one of aspects 1-21.

[0162] 25. A photolithography unit comprising the apparatus according to any one of aspects 1-24.

[0163] 26. A method for estimating unknown values ​​in at least one of a plurality of datasets, each dataset including a plurality of values ​​indicating radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate.

[0164] The plurality of datasets mentioned therein include at least one known value.

[0165] Where at least one of the plurality of datasets includes unknown values, the method includes having a processor estimate the unknown values ​​of the at least one dataset based on the following:

[0166] The known values ​​of the multiple datasets;

[0167] A first condition between two or more values ​​within one of the multiple datasets; and

[0168] A second condition between two or more values ​​that are parts of different datasets of the multiple datasets.

[0169] 27. The method according to aspect 26, wherein the first condition includes a smoothness condition.

[0170] 28. The method according to aspect 26 or 27, wherein the first condition includes data indicating the difference in magnitude between one or more values ​​within the plurality of datasets.

[0171] 29. The method according to any one of aspects 26-28, further comprising the first condition applied between two or more values, including adjacent values, within the plurality of datasets.

[0172] 30. The method according to any one of aspects 26-29, wherein the second condition includes a correlation condition.

[0173] 31. The method according to any one of aspects 26-30, wherein the second condition includes the correlation between corresponding values ​​in different datasets of the plurality of datasets.

[0174] 32. The method according to aspect 31, wherein the correlation condition further includes the correlation between multiple values ​​in one of the datasets of the plurality of datasets.

[0175] 33. The method according to any one of aspects 26-32, wherein the first condition and / or the second condition indicates the information content of the plurality of datasets.

[0176] 34. The method according to any one of aspects 26-33 further includes estimating the unknown values ​​of the at least one dataset based on a matrix completion algorithm.

[0177] 35. The method according to aspect 34, wherein the matrix completion algorithm is based on convex optimization techniques.

[0178] 36. The method according to aspect 35, wherein the convex optimization technique includes one of the nearest neighbor splitting algorithm and the primal dual algorithm.

[0179] 37. The method according to any one of aspects 26-36 further includes a method based on Estimate the unknown values ​​of the at least one dataset.

[0180] Where, d i It is a dataset that forms a row of matrix D, D M There are multiple known values. This is a weighted value assigned to the smoothness condition compared to the correlation condition. is the error term for estimating the known values ​​in D, M is the mask for identifying the multiple known values, and TV is the total variation.

[0181] 38. The method according to any one of aspects 26-37 further includes estimating unknown values ​​in one or more datasets for each of a plurality of optical parameters and / or characteristic parameters, and generating a library of datasets that can be compared with a measured dataset obtained via measurements performed by a sensor.

[0182] 39. The method according to aspect 38 further includes matching the measured dataset with at least one dataset from a plurality of datasets in the library to determine at least one parameter of the photolithography process performed on the substrate.

[0183] 40. The method according to any one of aspects 26-39 further comprises generating one or more of the known values ​​in the at least one dataset based on one or more of the following:

[0184] At least one parameter of the optical system, the optical system being configured to direct radiation toward one or more features fabricated in or on a substrate;

[0185] At least one parameter of the radiation; and

[0186] At least one parameter of the one or more features formed in or on a substrate.

[0187] 41. The method according to aspect 40 further includes generating one or more of the known values ​​at locations in the dataset where the information content is above a threshold.

[0188] 42. The method according to any one of aspects 26-41, wherein all values ​​in one or more of the plurality of datasets are known.

[0189] 43. The method according to aspect 42, wherein the one or more datasets, in which all values ​​are known, are associated with one or more additional features fabricated in or on the substrate or another substrate.

[0190] 44. The method according to any one of aspects 26-43, wherein one or more of the plurality of datasets represent a pupil image, and one or more of the values ​​represent pixels of the pupil image.

[0191] 45. The method according to any one of aspects 26-44, wherein one or more of the pixels include data indicating reflectivity or intensity.

[0192] 46. ​​A computer program comprising instructions that, when executed on at least one processor, cause the at least one processor to control a device to perform the method according to any one of aspects 26-45.

[0193] 47. A carrier comprising the computer program of aspect 46, wherein the carrier is one of an electronic signal, an optical signal, a radio signal, or a non-transitory computer-readable storage medium.

[0194] Although embodiments of the invention are described in detail herein within the context of inspection or measurement equipment, embodiments of the invention can be used in other equipment. Embodiments of the invention can form part of a mask inspection apparatus, a lithography apparatus, or any apparatus for measuring or processing objects such as wafers (or other substrates) or masks (or other patterning apparatus).

[0195] While this article provides specific references to the use of lithography equipment in IC manufacturing, it should be understood that the lithography equipment described herein can have other applications. Possible other applications include manufacturing integrated optical systems, guiding and detecting patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin-film magnetic heads, etc.

[0196] Although embodiments of the invention are specifically referenced herein within the context of photolithography equipment, these embodiments can be used with other equipment. Embodiments of the invention can form part of mask inspection equipment, metrology equipment, or any equipment for measuring or processing objects such as wafers (or other substrates) or masks (or other patterning apparatus). These devices are generally referred to as photolithography tools. Such photolithography tools can use vacuum conditions or ambient (non-vacuum) conditions.

[0197] Although the use of embodiments of the present invention has been specifically referenced above in the context of optical lithography, it should be understood that, where the context permits, the present invention is not limited to optical lithography and can be used in other applications, such as imprint lithography.

[0198] While specific embodiments of the invention have been described above, it should be understood that the invention can be practiced in ways different from those described above. The above description is intended to be illustrative and not restrictive. Therefore, those skilled in the art will understand that modifications can be made to the described invention without departing from the scope of the claims set forth below.

Claims

1. An apparatus for generating simulated values ​​indicating radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate, wherein each of a plurality of datasets indicates a plurality of values ​​of radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate, wherein the plurality of datasets includes at least one known value indicating radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate, and wherein at least one of the plurality of datasets includes an unknown value indicating radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate, the apparatus comprising: A processor configured to generate simulated values ​​of estimates of the unknown values ​​in the at least one dataset based on: The known values ​​of the multiple datasets; A first condition between two or more values ​​within one of the multiple datasets; and A second condition between two or more values ​​that are parts of different datasets of the multiple datasets.

2. A method for estimating unknown values ​​in at least one of a plurality of datasets, each dataset including a plurality of values ​​indicating radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate. The plurality of datasets includes at least one known value, which indicates radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on the substrate. At least one of the plurality of datasets includes unknown values, the unknown values ​​indicating radiation diffracted and / or reflected and / or scattered by one or more features fabricated in or on a substrate, the method comprising: The processor estimates the unknown values ​​of the at least one dataset based on the following: The known values ​​of the multiple datasets; A first condition between two or more values ​​within one of the multiple datasets; and A second condition between two or more values ​​that are parts of different datasets of the multiple datasets.

Images