Accelerating forward electromagnetic calculations for SXR reconstruction

Abstract

A computer-implemented method for generating a spectral model representation of an electromagnetic element for determining an electromagnetic response to electromagnetic radiation interacting with the electromagnetic element is presented. The spectral representation contains a two-dimensional array of elements corresponding to respective wave vectors, each of which is defined by (different) respective pairs of wave numbers in two directions transverse to each other. The electromagnetic elements are geometrically described as a plurality of slices stacked transversely to these directions, and each slice contains one or more polygons. The method includes determining points along each of the polygon edges, a calculation coefficient being calculated based on a range of the corresponding polygon edge in a lateral direction. By performing a fast Fourier transform (FFT) algorithm using the coefficients, Fourier components are generated in each of the lateral directions for each of the wave vectors.

Description

Cross-references to related applications

[0001] This application claims priority to EP application 23200829.2, filed on September 29, 2023, which is incorporated herein by reference in its entirety. Technical Field

[0002] This invention relates to a computer-implemented method for generating a spectral representation of an electromagnetic element (e.g., a grating) in an electromagnetic system for determining an electromagnetic response (e.g., a reflection coefficient) to electromagnetic radiation interacting with the electromagnetic element. The invention also relates to a computer system arranged to perform the method, and a computer program product comprising instructions for performing the method when implemented by a computer processor. Background Technology

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

[0004] To project patterns onto a substrate, photolithography apparatuses 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. Compared to photolithography apparatuses using radiation with a wavelength of, for example, 193 nm, extreme ultraviolet (EUV) radiation (with wavelengths ranging from 4 nm to 20 nm, such as 6.7 nm or 13.5 nm) can be used to form smaller features on the substrate.

[0005] Low-k1 lithography can be used to process features with dimensions smaller than the classical resolution limit of a lithography apparatus. In such a 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 apparatus, 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 is to reproduce patterns on the substrate that are similar in shape and size to those 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 apparatus and / or design layout. These include, for example, but not limited to, optimizing NA, customizing the illumination scheme, using phase-shifting patterning equipment, various optimizations of the design layout (such as optical proximity correction (OPC, sometimes also referred to as “optical and process correction”) in the design layout), or other methods generally defined as “resolution enhancement techniques” (RET). Alternatively, a tight control loop for controlling the stability of the lithography apparatus can be used to improve pattern reproduction at low k1.

[0006] In photolithography and other manufacturing processes, it is often desirable to measure the created structures, for example, for process control and verification. Various tools are known for performing such measurements, including scanning electron microscopes commonly used to measure critical dimension CD and specialized tools for measuring overlay (the alignment accuracy of two layers in a device). Recently, various forms of scatterometers have been developed for use in the field of photolithography.

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

[0008] Examples of known scatterers typically rely on the availability of a dedicated measurement target. For instance, a method might require a target in the form of a simple grating, large enough that the measurement beam generates a spot smaller than the grating (i.e., the grating is underfilled). In so-called reconstruction methods, the properties of the grating can be calculated by simulating the interaction between the scattered radiation and a mathematical model of the target structure. The model's parameters are tuned until the simulated interaction produces a diffraction pattern similar to that observed from a real target.

[0009] Besides measuring feature shapes through reconstruction, diffraction-based overlay measurements can be performed using devices such as those described in published patent application US2006066855A1. Diffraction-based overlay measurements utilize dark-field imaging of diffraction orders, enabling overlay measurements on small targets. These targets can be smaller than the illumination spot and can be surrounded by the product structure on the wafer. Examples of dark-field imaging measurements can be found in numerous published patent applications such as US2011102753A1 and US20120044470A. Multiple gratings can be measured in a single image using a composite grating target. Known scatterometers tend to use light in the visible or near-infrared (IR) wavelength range, requiring grating pitches much coarser than the actual product structure, whose characteristics are of real interest. Such product features can be defined using deep ultraviolet (DUV), extreme ultraviolet (EUV), or X-ray radiation with much shorter wavelengths. Unfortunately, such wavelengths are generally unsuitable or unavailable for measurement.

[0010] On the other hand, modern product structures are so small that they cannot be imaged using optical metrology techniques. Small features include, for example, features formed by multiple patterning processes and / or pitch multiplication. Therefore, targets used for high-volume metrology typically use features much larger than the product itself, where overlay errors or critical dimensions are the characteristics of interest. Measurement results are only indirectly related to the dimensions of the actual product structure and may be inaccurate because the measured target does not suffer the same distortion under different optical projections in the lithography apparatus and / or different treatments in other steps of the manufacturing process. While scanning electron microscopy (SEM) can directly resolve these modern product structures, SEM is much more time-consuming than optical measurements. Furthermore, electrons cannot penetrate thick process layers, making them unsuitable for metrology applications. Other techniques, such as using contact pads to measure electrical properties, are also known, but they only provide indirect evidence of the actual product structure.

[0011] By reducing the wavelength of the radiation used during measurement, smaller structures can be resolved, increasing sensitivity to structural changes and / or further penetration into the product structure. One method for generating appropriate high-frequency radiation (e.g., hard X-rays, soft X-rays, and / or EUV radiation) is to use pump radiation (e.g., infrared IR radiation) to excite the generating medium, thereby generating the emitted radiation, optionally including the generation of higher harmonics of the high-frequency radiation.

[0012] As the feature sizes of manufactured products (e.g., patterned wafers or gratings) continue to shrink, metrology continues to use increasingly higher frequencies of electromagnetic radiation (e.g., soft X-ray SXR) to accurately resolve and characterize these products. SXR can, for example, be used to resolve nanoscale feature sizes (i.e., feature sizes with dimensions less than 100 nm).

[0013] One known way to characterize an electromagnetic element (i.e., an object that exhibits interaction with an electromagnetic field) is to compare the measured electromagnetic response (e.g., the scattered electric field) with the electromagnetic response predicted by the solver.

[0014] A solver is an algorithm used to calculate the electromagnetic response of electromagnetic radiation interacting with an electromagnetic element (e.g., through, reflected from, and / or scattered by the element). The solver takes simulated incident electromagnetic radiation and a geometric representation of the electromagnetic element as input and outputs the electromagnetic response. The geometric representation of the electromagnetic element can then be iteratively refined until the predicted output from the solver matches the experiment within a predetermined error. This method is explained in detail in, for example, Proc. SPIE 12496, Metrology, Inspection, and Process Control XXXVII (doi: 10.1117 / 12.2658495), which is incorporated herein by reference.

[0015] In a broad sense, the process of characterizing electromagnetic components can be divided into two processing stages: (i) the initialization stage and (ii) the solver stage.

[0016] In the initialization phase, the geometric and spectral representations of the electromagnetic element are constructed. The initialization phase involves slicing the electromagnetic element into multiple stacked slices and characterizing the electromagnetic element according to the polygons that make up each of these slices.

[0017] The geometric representation of an electromagnetic element may include an array for each polygon in each of these slices, the array containing the polygon vertices.

[0018] The spectral representation of an electromagnetic element can include an array of Fourier coefficients, where each Fourier coefficient corresponds to a wave vector for each polygon in the slice.

[0019] In the solver phase, Maxwell equation solvers (e.g., COMPASS) are used to predict the effects of electromagnetic components on incident electromagnetic radiation.

[0020] In some examples, the solver stage involves solving a system of linear equations that describe the scattering effect of the electromagnetic element geometry on incident electromagnetic radiation. These linear equations are solved iteratively. Typically, the total number of iterations converging in the output scattered field increases with the scattering amplitude (i.e., the contrast between the scattered field and the incident field).

[0021] The total computation time for predicting the electromagnetic response therefore depends on the sum of the computation times for each of the initialization and solver phases. For higher frequency radiation, the initialization phase is impractically slow to compute (e.g., tens of hours) because evaluating the Fourier coefficients... Array (where and The computation time required for the existence of fourier modes (representing the number of Fourier modes required in the x and y directions, respectively) is given by the number of modes. In the case of polygonal edges, directly use a scale of The analytical formula for the Fourier transform of these frequencies can be excessively large. Meanwhile, at these frequencies, the relative permittivity of many materials is close to one, and therefore the contrast caused by electromagnetic elements in the scattered electric field is relatively small. This means that the solver stage is typically much faster than the initialization stage because the number of iterations required can be very low (e.g., as low as 1 if the Born approximation applies). Therefore, at such frequencies, the initialization stage can become a bottleneck in processing.

[0022] The initialization phase is expected to improve the solver. Summary of the Invention

[0023] This disclosure provides methods, computer program products, and computers as set forth in the appended set of claims.

[0024] Overall, this disclosure aims to provide new and useful methods, systems, and computer program products that improve the initialization phase of a solver, particularly for use in performing high-fidelity optical measurements.

[0025] More specifically, this disclosure provides a computer-implemented method for generating a spectral model representation of an electromagnetic element (e.g., a grating) in an electromagnetic system (e.g., a lithography apparatus) to determine the electromagnetic response (e.g., reflection coefficient) to electromagnetic radiation (e.g., SXR) interacting with the electromagnetic element.

[0026] A spectrum represents a two-dimensional array containing elements. Each "element" in the array corresponds to a corresponding wave vector, and each wave vector is defined by a pair of (different) corresponding wave numbers in each of a first mutually transverse direction and a second mutually transverse direction (e.g., the x and y directions). Electromagnetic elements are geometrically described as multiple slices stacked transversely to these transverse directions (i.e., the z-direction). Each slice is a cross-section and defines one or more polygons (onto the background). Typically, the slices are planar.

[0027] The method involves determining a plurality of corresponding points for each polygon. These points represent points along each polygon edge in the polygon. For each of these points, a first coefficient and a second coefficient are calculated based on the extent of the corresponding polygon edge in each of the first and second lateral directions (i.e., the distance the edge extends across each of the first and second directions; or in other words, the lengths of the two components if the edge is decomposed into two components in the corresponding directions).

[0028] The method also includes generating Fourier components in each of the transverse directions for each wave vector by performing a Fast Fourier Transform (FFT) algorithm on multiple points, and using corresponding first and second coefficients for each of these points. FFT is a Discrete Fourier Transform algorithm that transforms one domain (e.g., the spatial domain) to another domain (e.g., the spatial frequency domain) by decomposing the Discrete Fourier Transform matrix into a product of sparse factors (i.e., mostly zero). The FFT algorithm can be performed at a time cost that increases more slowly than the square of the number of points N in the first domain considered (e.g., N log N).

[0029] The spectral representation of the electromagnetic element is then generated based on the first and second Fourier components generated for each polygon.

[0030] Advantageously, using the proposed method, multiple points, as well as the first and second coefficients, are independent of the wave vector. The same multiple points, first and second coefficients are therefore used to evaluate the Fourier coefficients for each polygon in the transverse slice. As a result, the computation time of the proposed method exhibits excellent scalability with increasing number of Fourier modes, and in particular, it is significantly faster than... slow.

[0031] Therefore, accurate model reconstruction of electromagnetic components can be achieved with acceptable computational effort. Attached Figure Description

[0032] Embodiments will now be described by way of example only with reference to the accompanying schematic diagrams, in which: Figure 1A schematic overview of the photolithography apparatus is depicted; Figure 2 A schematic overview of the photolithography unit is depicted; Figure 3 A schematic representation of monolithography is depicted, which represents the collaboration between three key technologies to optimize semiconductor manufacturing; Figure 4 The scattering measurement device is illustrated schematically. Figure 5 The transmission scattering measurement device is illustrated schematically. Figure 6 A schematic representation of a measurement apparatus using EUV and / or SXR radiation is depicted; Figure 7 A simplified schematic diagram of the irradiation source is depicted; Figure 8A and Figure 8B The diagram schematically illustrates two transverse sections of an electromagnetic component; Figure 9 A comparative example of computation time from the prior art (Equation 1) and the present disclosure (Equation 2) is depicted; Figure 10 This is a flowchart of the steps in the method for generating a spectral model representation; Figure 11 This is a flowchart of the steps in the method for determining the electromagnetic response; and Figure 12 An example computer system that can implement the embodiments is schematically depicted. Detailed Implementation

[0033] In this document, the terms “radiation” and “beam” are used to encompass all types of electromagnetic and particle radiation, including ultraviolet radiation (e.g., with wavelengths of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm), EUV (extreme ultraviolet radiation, e.g., with wavelengths in the range of about 5 nm to 100 nm), X-ray radiation (e.g., soft X-rays), electron beam radiation, and other particle radiation.

[0034] As used herein, the terms “mask,” “mask,” or “patterning apparatus” can be broadly interpreted to refer to a general patterning apparatus that can be used to impart a patterned cross-section to an incoming radiation beam, the patterned cross-section corresponding to a pattern to be created in a target portion of a substrate. The term “optical valve” may also be used in this context. Examples of other such patterning apparatuses, besides classic masks (transmissive or reflective, binary, phase-shifting, hybrid, etc.), include programmable mirror arrays and programmable LCD arrays.

[0035] Figure 1A lithography apparatus LA is schematically depicted. The lithography apparatus LA includes: an irradiation system (also referred to as an irradiator) IL configured to modulate a radiation beam B (e.g., UV radiation, DUV radiation, EUV radiation, or X-ray radiation); a mask support (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 certain parameters; a substrate support (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 support according to certain 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., including one or more dies) of the substrate W.

[0036] In operation, the irradiation system IL receives a radiation beam from the radiation source SO, for example, via a beam delivery system BD. The irradiation system IL may include various types of optical components, such as refractive, reflective, diffractive, magnetic, electromagnetic, electrostatic, and / or other types of optical components, or any combination thereof, for guiding, shaping, and / or controlling the radiation. The irradiator IL can be used to modulate the radiation beam B at the plane of the patterning device MA to have a desired spatial and angular intensity distribution in its cross-section.

[0037] Depending on the exposure radiation used and / or other factors (such as the use of immersion liquid or vacuum), the term "projection system" PS as used herein should be interpreted broadly to encompass all types of projection systems, including refractive, reflective, diffractive, catadioptric, distorting, magnetic, electromagnetic, and / or electrostatic optical systems, or any combination thereof. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system" PS.

[0038] A lithography apparatus LA can be of the type in which at least a portion of the substrate can be covered by an immersion liquid (e.g., water) having a relatively high refractive index to fill the space between the projection system PS and the substrate W; this is also known as immersion lithography. Further information regarding immersion techniques is given in US6952253, which is incorporated herein by reference in its entirety.

[0039] The lithography apparatus LA can be of the type having two or more substrate supports WT (also known as "dual platforms"). In such a "multi-platform" machine, the substrate supports WT can be used in parallel, and / or steps in the subsequent exposure of the substrate W can be performed on the substrate W located on one of the substrate supports WT, while another substrate W on another substrate support WT is used to expose a pattern on the other substrate W.

[0040] In addition to the substrate support WT, the lithography apparatus LA may also include a measurement platform. The measurement platform is arranged to hold sensors and / or cleaning equipment. The sensors may be arranged to measure characteristics of the projection system PS or the radiation beam B. The measurement platform may hold multiple sensors. The cleaning equipment may be arranged to clean parts of the lithography apparatus, such as parts of the projection system PS or parts of the system providing the immersion solution. When the substrate support WT is moved away from the projection system PS, the measurement platform may move below the projection system PS.

[0041] In operation, a radiation beam B is incident on a patterning apparatus (e.g., a mask MA held on a mask support T) and patterned by the pattern (design layout) present on the patterning apparatus MA. After passing through 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. With the aid of a second positioner PW and a position measurement system IF, the substrate support WT can be moved precisely, for example, to position different target portions C in the path of the radiation beam B at a focused and aligned location. Similarly, a first positioner PM and possibly another position sensor (which...) Figure 1 (Not explicitly depicted) can be used to accurately position the patterning apparatus MA relative to the path of the radiation beam B. The patterning apparatus MA and the substrate W can be aligned using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks P1, P2 occupy dedicated target portions as shown, they can be located in the space between target portions. When the substrate alignment marks P1, P2 are located between target portions C, they are referred to as scribe alignment marks.

[0042] like Figure 2As shown, the lithography apparatus LA can form part of the lithography unit LC, sometimes referred to as a lithography pool or (lithography) cluster. It typically also includes apparatus for performing pre-exposure and post-exposure processes on the substrate W. Traditionally, the apparatus includes: a spin coater SC for depositing a resist layer; a developer DE for developing the exposed resist; a chiller CH and a baking plate BK, for example, to regulate the temperature of the substrate W, and for example, to regulate the solvent in the resist layer. A substrate processor or robot RO picks up the substrate W from input / output ports I / O1, I / O2, moves the substrate between different process units, and transfers the substrate W to the feed stage LB of the lithography apparatus LA. The equipment in the lithography pool, often collectively referred to as a track, is under the control of a track control unit TCU. The track control unit TCU itself can be controlled by a supervisory control system SCS, which can also control the lithography apparatus LA, for example, via a lithography control unit LACU.

[0043] During photolithography, it is desirable to perform frequent measurements on the created structure, for example, for process control and verification. The tools used to perform such measurements are called measurement tools (MTs). Different types of MTs for such measurements are known, including scanning electron microscopes (SEMs) or various forms of scatterometer MTs. A scatterometer is a versatile instrument that allows the measurement of parameters of the photolithography process by placing a sensor in or near the pupil of the scatterometer's objective lens; these measurements are typically referred to as pupil-based measurements. Alternatively, the parameters can be measured by placing the sensor in or near the image plane, in which case these measurements are typically referred to as image- or field-based measurements. Such scattering instruments 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 scattering instruments can measure gratings using light from hard X-rays (HXR), soft X-rays (SXR), extreme ultraviolet (EUV), visible to near-infrared (IR), and the IR wavelength range. In the case of hard or soft X-ray radiation, the aforementioned scattering instrument may optionally be a small-angle X-ray scattering measurement tool.

[0044] To ensure correct and consistent exposure of the substrate W exposed by the lithography apparatus LA, it is desirable to inspect the substrate to measure characteristics of the patterned structure, such as overlay error between subsequent layers, line thickness, critical dimension (CD), and structural shape. For this purpose, inspection tools and / or measurement tools (not shown) may be included in the lithography pool LC. If errors are detected, especially if the inspection is performed before other substrates W in the same batch or batch still need to be exposed or processed, adjustments can be made, for example, to the exposure of subsequent substrates or other processing steps to be performed on substrate W.

[0045] An inspection apparatus, also known as a measurement apparatus, is used to determine the characteristics of a substrate W, and specifically to determine how the characteristics of different substrates W vary or how the characteristics associated with different layers of the same substrate W vary layer by layer. The inspection apparatus may alternatively be configured to identify defects on the substrate W, and may be, for example, part of a photolithography pool (LC), or integrated into a photolithography apparatus (LA), or even a stand-alone device. The inspection apparatus can measure characteristics on latent images (images in the resist layer after exposure), or semi-latent images (images in the resist layer after a post-exposure baking (PEB) step), or developed resist images (where exposed or unexposed portions of the resist have been removed), or even etched images (after a pattern transfer step such as etching).

[0046] 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 characteristics of the grating. Such reconstruction can, for example, result from 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 that observed from a real target.

[0047] In the second embodiment, the scatterer MT is a spectroscopic scatterer MT. In such a spectroscopic scatterer MT, radiation emitted by a radiation source is directed onto a target, and radiation reflected, transmitted, or scattered from the target is directed to a spectroscopic detector, which measures the spectrum of the specularly reflected radiation (i.e., the intensity according to 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 library of simulated spectra.

[0048] In the third embodiment, the scatterer MT is an elliptically polarized scatterer. An elliptically polarized scatterer allows the determination of parameters of the photolithography process by measuring the scattered or transmitted radiation for each polarization state. Such a measurement device emits polarized light (such as linear, circular, or elliptical) by, for example, using an appropriate polarization filter in the illumination section of the measurement device. A source suitable for the measurement device can also provide polarized radiation. Various embodiments of existing elliptically polarized scatterers 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.

[0049] In one embodiment of the scattering instrument MT, the scattering instrument MT is adapted to measure the overlay of two misaligned gratings or periodic structures by measuring the reflectance spectrum and / or detecting asymmetry in the configuration, the asymmetry being related to the degree of overlay. Two (potentially overlapping) grating structures can be applied in two different layers (not necessarily consecutive layers) and can be formed substantially at the same location on the wafer. The scattering instrument can have a symmetrical detection configuration, for example, described in the co-owned patent application EP1,628,164A, such that any asymmetry can be clearly distinguished. This provides a simple method for measuring grating misalignment. Other examples of overlay errors between two layers containing a periodic structure when the target is measured by means of asymmetry in a 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.

[0050] 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 optionally by scanning electron microscopy), which is incorporated herein by reference in its entirety. A single structure can be used, having 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 from these measurements.

[0051] The measurement target can be an assembly of composite gratings formed by a photolithography process, primarily in a resist, but can also be formed after other manufacturing processes, such as etching. The pitch and linewidth of the structures in the gratings may be strongly dependent on the measurement optics (particularly the NA of the optics) to be able 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 it can be used 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 a small sub-segment configured to mimic the dimensions of functional portions of the design layout in the target. Due to this sub-segmentation, the target will behave more like the functional portions of the design layout, making the overall process parameter measurements closer to the functional portions of the design layout. The target can be measured in underfill or overfill modes. In underfill mode, the measurement beam generates a spot smaller than the overall target. In overfill mode, the measurement beam generates a spot larger than the overall target. In such overfill mode, it is also possible to measure different targets simultaneously, thus determining different processing parameters simultaneously.

[0052] The overall measurement quality of a lithography parameter for a specific target is at least partially determined by the measurement formulation used to measure that lithography parameter. The term "substrate measurement formulation" 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 formulation is a diffraction-based optical measurement, the one or more parameters measured can include the wavelength of the radiation, the polarization of the radiation, the angle of incidence of the radiation relative to the substrate, the orientation of the radiation relative to the pattern on the substrate, etc. One criterion for selecting the measurement formulation can be, for example, the sensitivity of one of the measurement parameters to handling variations. Further examples are described in U.S. Patent Application US2016-0161863 and published U.S. Patent Application US2016 / 0370717A1, which are incorporated herein by reference in their entirety.

[0053] The patterning process in a photolithography (LA) apparatus is arguably one of the most critical steps in the process, requiring high accuracy in determining and placing the structure on the substrate W. To ensure this high accuracy, three systems can be combined, such as... Figure 3The diagram illustrates a so-called "holistic" control environment. One of these systems is a lithography apparatus (LA), which is (virtually) connected to a metrology tool (MT) (a second system) and a computer system (CL) (a third system). The key to such a "holistic" environment is optimizing the collaboration between these three systems to enhance the overall process window and provide a tight control loop, thereby ensuring 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, overlay) within which a specific manufacturing process produces a defined result (e.g., a functional semiconductor device). This range of process parameters allows for variations in process parameters during the lithography or patterning process.

[0054] The computer system CL can use the design layout (partial) to be patterned to predict which resolution enhancement techniques to use and perform computational lithography simulations and calculations to determine which mask layouts and lithography setups achieve the maximum overall process window for the patterning process (e.g., ...). Figure 3 (Depicted by the double arrows at the first scale SC1). Resolution enhancement techniques can be arranged to match the patterning capabilities of the lithography apparatus LA. The computer system CL can also be used to detect the current position of the lithography apparatus LA within the process window (e.g., using input from the metrology tool MET) to predict whether defects (such as those caused by suboptimal processing) may exist. Figure 3 (Depicted by the arrow pointing to "0" in the second scale SC2).

[0055] The measurement tool MT can provide input to the computer system CL to enable accurate simulation and prediction, and can also provide feedback to the lithography apparatus LA to, for example, identify possible drifts in the calibration state of the lithography apparatus LA (e.g., Figure 3 (Depicted by multiple arrows at the third scale SC3).

[0056] Various types of measurement tools (MTs) can be provided for measuring structures created using photolithographic patterning apparatuses. The measurement tool (MT) can probe the structure using electromagnetic radiation. The characteristics of the radiation (e.g., wavelength, bandwidth, power) can affect different measurement characteristics of the tool, with shorter wavelengths generally allowing for higher resolution. The radiation wavelength affects the resolution achievable by the measurement tool. Therefore, measurement tools (MTs) with short-wavelength radiation sources are preferred for measuring structures with small-sized features.

[0057] Another way radiation wavelength can affect measurement characteristics is through-penetration depth and the transparency / opacity of the material being inspected at that wavelength. Depending on opacity and / or through-penetration depth, radiation can be used for measurements in either transmission or reflection. The type of measurement can affect whether information relating to the surface and / or bulk interior of a structure / substrate is obtained. Therefore, through-penetration depth and opacity are another factor to consider when selecting a radiation wavelength for a measurement tool.

[0058] To achieve high-resolution measurements of photolithographically patterned structures, measurement tools (MTs) with short wavelengths are preferred. This can include wavelengths shorter than visible wavelengths, such as those in the UV, EUV, and X-ray portions of the electromagnetic spectrum. Hard X-ray methods, such as transmission small-angle X-ray scattering (TSAXS), utilize the high resolution and high penetration depth of hard X-rays and can therefore operate in transmission. On the other hand, soft X-rays and EUV do not penetrate the target that far, but can induce rich optical responses in the material being probed. This is likely due to the optical properties of many semiconductor materials, and because the structure is sized to match the probe wavelength. As a result, EUV and / or soft X-ray measurement tools (MTs) can operate in reflection, for example, by imaging or by analyzing the diffraction patterns from the photolithographically patterned structure.

[0059] For hard X-rays, soft X-rays, and EUV radiation, their application in high-volume manufacturing (HVM) applications may be limited due to the lack of available high-brightness sources at the required wavelengths. In the case of hard X-rays, commonly used sources in industrial applications include X-ray tubes. X-ray tubes include, for example, advanced X-ray tubes based on liquid metal anodes or rotating anodes. X-ray tubes may be relatively inexpensive and compact, but may lack the brightness required for HVM applications. High-brightness X-ray sources, such as synchrotron light sources (SLS) and X-ray free-electron lasers (XFELs), currently exist, but their size (>100 meters) and high cost (hundreds of millions of euros) make them too large and expensive for metrological applications. Similarly, sufficiently bright EUV and soft X-ray radiation sources are also lacking in availability.

[0060] Figure 4 An example of a measurement device, such as a scatterer, is depicted. It may include a broadband (e.g., white light) radiation projector 2, which projects radiation 5 onto a substrate W. The reflected or scattered radiation 10 is passed to a spectrometer detector 4, which measures the spectrum 6 of the specularly reflected radiation (i.e., the intensity I according to the wavelength λ). Based on this data, the structure or profile 8 of the detected spectrum can be generated by a processing unit PU, for example, through rigorous coupled-wave analysis and nonlinear regression, or through methods such as... Figure 4The bottom of the image shows a comparison with a simulated spectral library for reconstruction. Typically, for reconstruction, the overall form of the structure is known, and some parameters are assumed based on knowledge of the structure's fabrication process, allowing only a small number of parameters to be determined from scattering measurements. Such a scatterometer can be configured as a normal-incident scatterometer or an oblique-incident scatterometer.

[0061] Figure 5 The text describes measuring devices (such as...) Figure 4 The example shown is a transmission version of the scatterer. The transmitted radiation 11 is passed to the spectrometer detector 4, which measures the radiation as follows: Figure 4 The spectrum discussed is 6. Such a scatterer can be configured as a normal-incident scatterer or an oblique-incident scatterer. Optionally, the transmission version uses hard X-ray radiation with wavelengths of <1 nm, optionally <0.1 nm, and optionally <0.01 nm.

[0062] As alternatives to optical measurement methods, the use of hard X-rays, soft X-rays, or EUV radiation, for example, radiation having at least one of the following wavelength ranges: <0.01 nm, <0.1 nm, <1 nm, between 0.01 nm and 100 nm, between 0.01 nm and 50 nm, between 1 nm and 50 nm, between 1 nm and 20 nm, between 5 nm and 20 nm, and between 10 nm and 20 nm. An example of a measurement instrument operating within one of the wavelength ranges given above is transmitted small-angle X-ray scattering (such as T-SAXS in US 2007224518A, the contents of which are incorporated herein by reference in their entirety). Lemaillet et al. discuss profile (CD) measurements using T-SAXS in “Intercomparison between optical and X-ray scatterometry measurements of FinFET structures”, Proc. of SPIE, 2013, 8681. Note that the use of laser-generated plasma (LPP) X-ray sources is described in U.S. Patent Publication No. 2019 / 003988A1 and U.S. Patent Publication No. 2019 / 215940A1, which are incorporated herein by reference in their entirety. Reflectance measurement techniques using grazing incidence X-rays (GI-XRS) and extreme ultraviolet (EUV) radiation can be used to measure the properties of films and layer stacks on substrates. Within the general field of reflectance measurement, goniometric and / or spectroscopic techniques can be applied. In goniometrics, the variation of reflected beams at different incident angles can be measured. On the other hand, spectroscopic reflectance measurement measures the spectrum of wavelengths reflected at a given angle (using broadband radiation). For example, EUV reflectance measurement has been used to inspect mask blanks before fabricating masks (patterning apparatus) for use in EUV lithography.

[0063] The application scope may render the use of wavelengths in, for example, the hard X-ray, soft X-ray, or EUV domains insufficient. Published patent applications US 20130304424A1 and US2014019097A1 (Bakeman et al / KLA) describe hybrid metrology techniques in which measurements using X-rays are combined with optical measurements utilizing wavelengths in the range of 120 nm to 2000 nm to obtain measurements of parameters such as CD. CD measurements are obtained by coupling X-ray mathematical models and optical mathematical models using one or more common parameters. The contents of the cited US patent applications are incorporated herein by reference in their entirety.

[0064] Figure 6A schematic representation of the measuring device 302 is depicted, wherein the aforementioned radiation can be used to measure parameters of a structure on a substrate. Figure 6 The measurement device 302 presented herein can be applied to the hard X-ray, soft X-ray and / or EUV domains.

[0065] Figure 6 The illustration shows a schematic physical arrangement of the measurement device 302, which includes a spectroradiometer. By way of example only, the spectroradiometer uses optional grazing-incidence hard X-rays, soft X-rays, and / or EUV radiation. Alternatively, the inspection device can be provided as an angle-resolved scatterer, which can use radiation with normal or near-normal incidence similar to conventional scatterers operating at longer wavelengths, and can also use radiation with a direction greater than 1° or 2° relative to the direction parallel to the substrate. Another alternative inspection device can be provided as a transmission scatterer. Figure 5 The configuration in the document is applied to this alternative form of inspection device.

[0066] The inspection device 302 includes a radiation source or so-called irradiation source 310, an irradiation system 312, a substrate support 316, detection systems 318 and 398, and a measurement processing unit (MPU) 320.

[0067] In this example, the irradiation source 310 is used to generate EUV, hard X-ray, or soft X-ray radiation. The irradiation source 310 can be based on, for example... Figure 6 The high harmonic generation (HHG) technique shown can also be other types of irradiation sources, such as liquid metal jet sources, inverse Compton scattering (ICS) sources, plasma channel sources, magnetic wave generator sources, free electron laser (FEL) sources, compact storage ring sources, discharge-generated plasma sources, soft X-ray laser sources, rotating anode sources, solid anode sources, particle accelerator sources, microfocus sources, or laser-generated plasma sources.

[0068] HHG sources can be gas jet / nozzle sources, capillary / fiber sources, or gas chamber sources.

[0069] For example, HHG source, such as Figure 6As shown, the main components of the radiation source are a pump radiation source 330 operable to emit pump radiation and a gas delivery system 332. Optionally, the pump radiation source 330 is a laser, and optionally, it is a pulsed high-power infrared or optical laser. The pump radiation source 330 can be, for example, a fiber-based laser with an optical amplifier, generating pulses of infrared radiation that, if desired, can last for, for example, less than 1 ns (1 nanosecond) per pulse, with a pulse repetition rate up to several megahertz. The wavelength of the infrared radiation can be in the range of 200 nm to 10 µm, for example, in the region of 1 μm (1 micrometer). Optionally, the laser pulse is delivered to the gas delivery system 332 as a first pump radiation 340, wherein in the gas, a portion of the radiation is converted to a higher frequency than the first radiation to form emitted radiation 342. A gas supply device 334 supplies a suitable gas to the gas delivery system 332, wherein the gas is optionally ionized by a power source 336. The gas delivery system 332 can be a cut tube.

[0070] The gas provided by the gas delivery system 332 defines the gas target, which can be a gas flow or a static volume. The gas can be, for example, air, neon (Ne), helium (He), nitrogen (N2), oxygen (O2), argon (Ar), krypton (Kr), xenon (Xe), carbon dioxide, and combinations thereof. These can be optional options within the same apparatus. The emitted radiation can contain multiple wavelengths. If the emitted radiation is monochromatic, measurement calculations (e.g., reconstruction) can be simplified, but it is easier to generate radiation with several wavelengths. The emission divergence angle of the emitted radiation may be wavelength-dependent. Different wavelengths will, for example, provide different levels of contrast when imaging structures of different materials. For the inspection of metallic or silicon structures, for example, different wavelengths can be selected for imaging the characteristics of (carbon-based) resists or for detecting contamination in such different materials. One or more filtering devices 344 can be provided. For example, a thin-film filter such as aluminum (Al) or zirconium (Zr) can be used to block further transmission of fundamental frequency IR radiation into the inspection apparatus. A grating (not shown) may be provided to select one or more specific wavelengths from the generated wavelengths. Optionally, the irradiation source includes a space configured to be emptied, and a gas delivery system is configured to provide a gaseous target within that space. Optionally, part or all of the beam path may be contained within a vacuum environment to account for absorption of SXR and / or EUV radiation as it travels in air. The various components of the radiation source 310 and the irradiation optics 312 may be adjusted to achieve different measurement “recipes” within the same apparatus. For example, different wavelengths and / or polarizations may be optional.

[0071] Depending on the material of the structure being inspected, different wavelengths can provide the desired level of penetration into the underlying layers. Shorter wavelengths may be preferred for distinguishing between minimum device features and defects within them. For example, one or more wavelengths in the range of 0.01 nm to 20 nm, or optionally one or more wavelengths in the range of 1 nm to 10 nm, or optionally one or more wavelengths in the range of 10 nm to 20 nm, can be selected. Wavelengths shorter than 5 nm may suffer from very low critical angles when reflected from the material of interest in semiconductor manufacturing. Therefore, selecting wavelengths greater than 5 nm can provide a stronger signal at larger incident angles. On the other hand, if the inspection task is to detect the presence of specific materials, such as contamination, wavelengths up to 50 nm may be useful.

[0072] From radiation source 310, a filtered beam 342 can enter inspection chamber 350, in which a substrate W, including the structure of interest, is held in a measurement position by substrate support 316 for inspection. The structure of interest is designated T. Optionally, the atmosphere within inspection chamber 350 can be maintained near vacuum by vacuum pump 352, allowing SXR and / or EUV radiation to pass through the atmosphere without excessive attenuation. As described in the aforementioned disclosed U.S. patent application US2017 / 0184981A1 (the contents of which are incorporated herein by reference in their entirety), the irradiation system 312 has the function of focusing radiation into a focused beam 356 and may include, for example, a two-dimensional curved mirror or a series of one-dimensional curved mirrors. Focusing is performed to achieve a circular or elliptical spot S with a diameter less than 10 μm when projected onto the structure of interest. Substrate support 316 includes, for example, an XY translation platform and a rotation platform, any portion of the substrate W can be moved to the focal point of the beam in a desired orientation by means of the XY translation platform and the rotation platform. Therefore, the radiation spot S is formed on the structure of interest. Alternatively or additionally, the substrate support 316 includes, for example, a tilting platform that can tilt the substrate W at an angle to control the incident angle of the focused beam on the structure of interest T.

[0073] Optionally, the illumination system 312 provides a reference radiation beam to a reference detector 314, which can be configured to measure the spectrum and / or intensity of different wavelengths in the filtered beam 342. The reference detector 314 can be configured to generate a signal 315, which is provided to the processor 320, and the filter can include information related to the spectrum of the filtered beam 342 and / or the intensity of different wavelengths in the filtered beam.

[0074] The reflected radiation 360 is captured by detector 318, and the spectrum is provided to processor 320 for calculating the properties of the target structure T. The irradiation system 312 and detection system 318 thus form an inspection apparatus. This inspection apparatus may include hard X-ray, soft X-ray, and / or EUV spectroreflectometers of the type described in US2016282282A1, the contents of which are incorporated herein by reference in their entirety.

[0075] If the target Ta has a specific periodicity, the radiation from the focused beam 356 can also be partially diffracted. The diffracted radiation 397 follows a different path, angularly determined relative to the angle of incidence, unlike the reflected radiation 360. Figure 6 In the diagram, the diffraction radiation 397 is drawn schematically, and the diffraction radiation 397 may follow many other paths besides the drawn path. The inspection device 302 may also include an additional detection system 398 that detects and / or images at least a portion of the diffraction radiation 397. Figure 6 A single additional detection system 398 is depicted in the diagram, but embodiments of the inspection apparatus 302 may also include more than one additional detection system 398 arranged at different locations to detect and / or image the diffracted radiation 397 in multiple diffraction directions. In other words, the (higher) diffraction order of the focused radiation beam striking the target Ta is detected and / or imaged by one or more additional detection systems 398. One or more detection systems 398 generate a signal 399, which is provided to the measurement processor 320. The signal 399 may include information about the diffracted light 397 and / or may include an image obtained from the diffracted light 397.

[0076] To assist in aligning and focusing the spot S with the desired product structure, the inspection apparatus 302 may also provide auxiliary optics using auxiliary radiation under the control of the measurement processor 320. The measurement processor 320 may also communicate with a position controller 372, which operates a translation platform, a rotation platform, and / or a tilting platform. The processor 320 receives highly accurate feedback on the position and orientation of the substrate via sensors. The sensor 374 may include an interferometer, for example, an interferometer capable of providing accuracy in a picometer-scale region. During the operation of the inspection apparatus 302, spectral data 382 captured by the detection system 318 is transmitted to the measurement processing unit 320.

[0077] As previously described, alternative forms of inspection apparatus use hard X-rays, soft X-rays, and / or EUV radiation incident optionally at or near normal, for example, to perform diffraction-based asymmetry measurements. Another alternative form of inspection apparatus uses hard X-rays, soft X-rays, and / or EUV radiation with a direction greater than 1° or 2° relative to the direction parallel to the substrate. Both types of inspection apparatus can be provided in a hybrid metrology system. The performance parameters to be measured can include overlay (OVL), critical dimension (CD), the focal point of the lithography apparatus when printing the target structure, coherent diffraction imaging (CDI), and resolution overlay (ARO) measurements. Hard X-rays, soft X-rays, and / or EUV radiation can, for example, have wavelengths less than 100 nm, such as radiation in the range of 5 nm to 30 nm, or optionally radiation in the range of 10 nm to 20 nm. The radiation can be narrowband or broadband in characteristics. The radiation can have discrete peaks in a specific wavelength band or can have more continuous characteristics.

[0078] Similar to optical scattering instruments used in modern manufacturing facilities, inspection device 302 can be used to measure structures within resist materials treated in a photolithography bath (after development inspection or ADI), and / or to measure structures that have already formed in harder materials (after etching inspection or AEI). For example, substrates can be inspected using inspection device 302 after they have been treated by development, etching, annealing, and / or other equipment.

[0079] Measurement tools (MTs), including but not limited to the aforementioned scatterers, can perform measurements using radiation from a radiation source. The radiation used by the measurement tool MT can be electromagnetic radiation. The radiation can be optical radiation, such as radiation in the infrared, visible, and / or ultraviolet portions of the electromagnetic spectrum. The measurement tool MT can use radiation to measure or inspect the properties and aspects of a substrate, such as a photolithographically exposed pattern on a semiconductor substrate. The type and quality of the measurement may depend on several characteristics of the radiation used by the measurement tool MT. For example, the resolution of an electromagnetic measurement may depend on the wavelength of the radiation; for example, due to the diffraction limit, shorter wavelengths can measure smaller features. To measure features with small dimensions, radiation with short wavelengths, such as EUV, hard X-rays (HXR), and / or soft X-rays (SXR), can preferably be used to perform the measurement. To perform a measurement at a specific wavelength or wavelength range, the measurement tool MT needs access to a source that provides radiation at that one or more wavelengths. Different types of sources exist to provide radiation at different wavelengths. Depending on the wavelength(s) provided by the source(s), different types of radiation generation methods can be used. For extreme ultraviolet (EUV) radiation (e.g., 1 nm to 100 nm) and / or soft X-ray (SXR) radiation (e.g., 0.1 nm to 10 nm), the source can use higher harmonic generation (HHG) or any other type of source described above to obtain radiation at the desired wavelength(s).

[0080] Figure 7 A simplified schematic diagram of embodiment 600 of the irradiation source 310 is shown. The irradiation source 310 can be an irradiation source for high-order harmonic generation (HHG). Regarding Figure 6 One or more features of the irradiation source in the described measurement tool may also be present in the irradiation source 600 as needed. The irradiation source 600 includes a chamber 601 and is configured to receive pump radiation 611 having a propagation direction indicated by the arrow. (As...) Figure 6As shown, the pump radiation 611 illustrated here is an example of pump radiation 340 from pump radiation source 330. Pump radiation 611 can be directed into chamber 601 via radiation input 605, which can be a viewport and optionally made of fused silica or a similar material. Pump radiation 611 can have a Gaussian or hollow, e.g., annular, transverse cross-sectional profile and can be incident (optionally focused) onto a gas flow 615 within chamber 601, the gas flow 615 having a flow direction indicated by a second arrow. Gas flow 615 comprises a small volume of a specific gas (e.g., air, neon (Ne), helium (He), nitrogen (N2), oxygen (O2), argon (Ar), krypton (Kr), xenon (Xe), carbon dioxide, and combinations thereof) with a gas pressure above a certain value, referred to as a gas volume or gas target (e.g., several cubic millimeters). Gas flow 615 can be a steady-state flow. Other media, such as metallic plasma (e.g., aluminum plasma), can also be used.

[0081] The gas delivery system of the irradiation source 600 is configured to provide a gas flow 615. The irradiation source 600 is configured to provide pump radiation 611 in the gas flow 615 to drive the generation of emitted radiation 613. The region where at least most of the emitted radiation 613 is generated is referred to as the interaction region. The interaction region can range from tens of micrometers (for compact focused pump radiation) to several millimeters or centimeters (for medium focused pump radiation), or even up to several meters (for extremely loosely focused pump radiation). The gas delivery system is configured to provide a gas target for generating emitted radiation at the interaction region of the gas target, and optionally, the irradiation source is configured to receive pump radiation and provide pump radiation at the interaction region. Optionally, the gas flow 615 is provided by the gas delivery system to an empty or near-empty space. The gas delivery system may include a gas nozzle 609, such as... Figure 6 As shown, the gas nozzle 609 includes an opening 617 in its outlet plane. A gas flow 615 is supplied from the opening 617. A gas trap is used to confine the gas flow 615 to a specific volume by extracting residual gas flow and maintaining a vacuum or near-vacuum environment within the chamber 601. Optionally, the gas nozzle 609 may be made of a thick-walled tube and / or a material with high thermal conductivity to avoid thermal deformation due to high-power pump radiation 611.

[0082] The size of the gas nozzle 609 can also be conceivably used in scaled-up or scaled-down versions ranging from micrometer-level nozzles to meter-level nozzles. This wide range of sizes stems from the fact that the setup can be scaled to achieve a specific range of pump radiation intensity at the gas flow that is favorable for emitted radiation. This requires different size designs for different pump radiation energies, which can be pulsed lasers, and the pulse energy can vary from tens of microjoules to joules. Optionally, the gas nozzle 609 has thicker walls to reduce nozzle deformation due to thermal expansion effects, which can be detected by, for example, a camera. A gas nozzle with thicker walls can produce a stable gas volume with reduced deformation. Optionally, the irradiation source includes a gas trap located near the gas nozzle to maintain the pressure in chamber 601.

[0083] Due to the interaction between the pump radiation 611 and the gas atoms of the gas flow 615, the gas flow 615 converts a portion of the pump radiation 611 into emitted radiation 613. The emitted radiation 613 can be... Figure 6 The example shown is the emitted radiation 342. The central axis of the emitted radiation 613 may be collinear with the central axis of the incident pump radiation 611. The emitted radiation 613 may have a wavelength in the X-ray or EUV range, wherein the wavelength is in the range of 0.01 nm to 100 nm, optionally in the range of 0.1 nm to 100 nm, optionally in the range of 1 nm to 100 nm, optionally in the range of 1 nm to 50 nm, or optionally in the range of 10 nm to 20 nm.

[0084] In operation, the emitted radiation beam 613 can be transmitted through radiation output 607 and can subsequently be manipulated and guided by irradiation system 603 to the substrate to be inspected for measurement purposes. Irradiation system 603 can be... Figure 6 An example of the irradiation system 312. The emitted radiation 613 can be guided, and optionally focused, onto the structure on the substrate.

[0085] Because air (in fact, any gas) heavily absorbs SXR or EUV radiation, the volume between the gas flow 615 and the wafer under inspection can be emptied or nearly emptied. Since the central axis of the emitted radiation 613 can be collinear with the central axis of the incident pump radiation 611, the pump radiation 611 may need to be blocked to prevent it from passing through the radiation output 607 and entering the irradiation system 603. This can be achieved by... Figure 6The filter 344 shown is incorporated into the radiation output 607. The filter 344 is positioned in the path of the emitted beam and is opaque or nearly opaque to the pump radiation (e.g., opaque or nearly opaque to infrared or visible light), but at least partially transparent to the emitted radiation beam. The filter can be fabricated using zirconium or a combination of materials in multiple layers. When the pump radiation 611 has a hollow, optional annular cross-sectional profile, the filter can be a hollow, optional annular block. Optionally, the filter is neither perpendicular nor parallel to the propagation direction of the emitted radiation beam to achieve efficient pump radiation filtering. Optionally, the filter 344 includes a hollow block and a thin-film filter, such as an aluminum (Al) or zirconium (Zr) film filter. Optionally, the filter 344 may also include a mirror that efficiently reflects the emitted radiation but poorly reflects the pump radiation, or a mesh that efficiently transmits the emitted radiation but poorly transmits the pump radiation.

[0086] This document describes methods, apparatus, and components for optionally obtaining emitted radiation at higher harmonic frequencies of pump radiation. The radiation generated by the process, optionally employing nonlinear effects to generate an HHG of radiation at the harmonic frequencies of the provided pump radiation, can be provided as radiation in a metrology instrument (MT) for inspecting and / or measuring a substrate. If the pump radiation comprises short pulses (i.e., few periods), the generated radiation is not necessarily exactly at the harmonics of the pump radiation frequency. The substrate can be a photolithographically patterned substrate. The radiation obtained by the process can also be provided in a photolithography apparatus (LA) and / or a photolithography cell (LC). The pump radiation can be pulsed radiation, which can provide high peak intensity up to a short burst.

[0087] Pump radiation 611 may include radiation having one or more wavelengths higher than one or more wavelengths of emitted radiation. Pump radiation may include infrared radiation. Pump radiation may include radiation having multiple wavelengths in the range of 500 nm to 1500 nm. Pump radiation may include radiation having multiple wavelengths in the range of 800 nm to 1300 nm. Pump radiation may include radiation having multiple wavelengths in the range of 900 nm to 1300 nm. Pump radiation may be pulsed radiation. Pulsed pump radiation may include pulses having a duration in the femtosecond range.

[0088] In some embodiments, the emitted radiation, optionally higher harmonic radiation, may include one or more harmonics of the pump radiation wavelength(s). The emitted radiation may include wavelengths in the extreme ultraviolet, soft X-ray, and / or hard X-ray portions of the electromagnetic spectrum. The emitted radiation 613 may include wavelengths in one or more ranges from less than 1 nm, less than 0.1 nm, less than 0.01 nm, 0.01 nm to 100 nm, 0.1 nm to 100 nm, 0.1 nm to 50 nm, 1 nm to 50 nm, and 10 nm to 20 nm.

[0089] Radiation, such as the aforementioned higher harmonic radiation, can be provided as source radiation in a metrology tool (MT). The metrology tool (MT) can use this source radiation to perform measurements on a substrate exposed by a photolithography apparatus. The measurements can be used to determine one or more parameters of the structure on the substrate. Using radiation at shorter wavelengths, such as EUV, SXR, and / or HXR wavelengths included in the aforementioned wavelength range, allows the metrology tool to resolve smaller features of the structure compared to using longer wavelengths (e.g., visible radiation, infrared radiation). Radiation with shorter wavelengths, such as EUV, SXR, and / or HXR radiation, can also penetrate deeper into materials such as patterned substrates, meaning that measurements of deeper layers on the substrate are possible. These deeper layers may not be reachable by radiation with longer wavelengths.

[0090] In a metrology tool (MT), source radiation can be emitted from a radiation source and directed onto a target structure (or other structure) on a substrate. The source radiation can include EUV XR and / or HXR radiation. The target structure can reflect, transmit, and / or diffract the incident source radiation onto the target structure. The metrology tool (MT) can include one or more sensors for detecting diffracted radiation. For example, the metrology tool (MT) can include detectors for detecting the positive (+1) and negative (-1) first diffraction orders. The metrology tool (MT) can also measure specular reflection or transmission radiation (0th-order diffraction radiation). Other sensors for measurement can be present in the metrology tool (MT), for example, to measure other diffraction orders (e.g., higher diffraction orders).

[0091] In example photolithography applications, the radiation generated by HHG can be focused onto a target on a substrate using an optical column, which can be referred to as an irradiator, to transfer radiation from the HHG source to the target. The HHG radiation can then be reflected from the target, detected, and processed, for example, to measure and / or infer the characteristics of the target.

[0092] Gas target HHG configurations can be broadly classified into three separate categories: gas jet, gas pool, and gas capillary. Figure 7An example gas jet configuration is depicted, in which a gas volume is introduced into a pump / drive radiation laser beam. In the gas jet configuration, the interaction between the drive radiation and the solid-state component is kept to a minimum. The gas volume may, for example, comprise a gas flow perpendicular to the drive radiation beam, wherein the gas volume is enclosed within a gas pool. In a gas capillary arrangement, the capillary structure holding the gas has a small dimension in the transverse direction, such that it significantly affects the propagation of the drive radiation laser beam. The capillary structure may, for example, be a hollow fiber, wherein the hollow portion is configured to hold the gas.

[0093] Gas-jet HHG configurations offer relative freedom in shaping the spatial profile of the driving radiation beam in the far field, as they are not constrained by the gas capillary structure. Gas-jet configurations may also have less stringent alignment tolerances. On the other hand, the gas capillary can provide an increased interaction zone between the driving radiation and the gaseous medium, which can optimize the HHG process.

[0094] For example, in measurement applications, HHG radiation is separated from the driving radiation downstream of the gas target. This separation of HHG and driving radiation can differ for gas jet and gas capillary configurations. In both cases, driving radiation suppression schemes can include metallic transmission filters to filter out any remaining driving radiation from the short-wavelength radiation. However, before such a filter can be used, the intensity of the driving radiation should be significantly reduced from its intensity at the gas target to avoid damaging the filter. Methods for this intensity reduction can differ for gas jet and capillary configurations. For gas jet HHG, due to the relative degrees of freedom in the shape and spatial profile (which may also be referred to as spatial distribution and / or spatial frequency) of the driving radiation beam focused onto the gas target, it can be designed such that it has low intensity in the far field along the direction of propagation of the short-wavelength radiation. This spatial separation in the far field means that the aperture can be used to block the driving radiation and reduce its intensity.

[0095] Conversely, in gas capillary structures, the spatial profile of the beam as it propagates through the gaseous medium can be largely determined by the capillary. The spatial profile of the driving radiation can be determined by the shape and material of the capillary structure. For example, when hollow fibers are used as the capillary structure, the shape and material of the fiber structure determine which modes of the driving radiation are supported for propagation through the fiber. For most standard fibers, the supported propagation modes result in a spatial profile where the high intensity of the driving radiation overlaps with the high intensity of the HHG radiation. For example, the driving radiation intensity can be centered in the far field with a Gaussian or near-Gaussian profile.

[0096] Although HHG is specifically referenced, it will be understood that the invention can be practiced using any radiation source where the context permits. In one embodiment, the radiation source is a laser-generated plasma (LPP) source as described above, used for generating hard X-rays, soft X-rays, EUV, DUV, and visible radiation. In one embodiment, the radiation source is one of a liquid metal jet source, an inverse Compton scattering (ICS) source, a plasma channel source, a magnetic wave generator source, a free electron laser (FEL) source, a compact reservoir ring source, a discharge-generated plasma source, a rotating anode source, a solid anode source, a particle accelerator source, and a microfocus source.

[0097] Figure 8A It is the cross section 802 of the electromagnetic element 800 in the first plane. Figure 8B The electromagnetic element 800 has a cross-section 804 in the second plane, along... Figure 8A The dashed line AA' shown indicates that the second plane is transverse to the first plane. In a specific example, the electromagnetic element can be a product manufactured through a production process such as photolithography or etching, or an element used in the photolithography process, such as a periodic grating.

[0098] exist Figure 8A and Figure 8B In one example, the electromagnetic element 800 includes a layered substrate 801 (whose main surface is parallel to the second plane) supporting a matrix layer 802 having an upper surface 803. Figure 8A Optionally, a component 804 with a trapezoidal cross-section is embedded in a matrix layer 802.

[0099] Electromagnetic component 800 interacts with electromagnetic EM radiation. This interaction allows for microscopic inspection of the electromagnetic component 800. The interaction may include the scattering, reflection, and / or transmission of EM radiation incident on the electromagnetic component. Figure 8A In the example shown, the incident EM radiation 805 is partially reflected by element 800 to produce reflected radiation 806. A small portion of the incident EM radiation may also pass through the electromagnetic element 800.

[0100] observe Figure 8A and Figure 8B The first and second planes of the cross section can be based on, in some cases, such as Figure 5 The transmission direction of the incident electromagnetic radiation 805 is shown. More typically, as shown, the plane is chosen such that the region of interest in the electromagnetic element 800 varies relatively smoothly in a direction transverse to the second plane. For example, component 804 in Figure 8A The vertical direction changes relatively smoothly, while the vertical direction is transverse to the second plane.

[0101] Electromagnetic element 800 can be composed of multiple stacked transverse sections or parallel to the second plane (i.e., transverse to). Figure 8A It is represented by slices (in the vertical direction) in the middle. Figure 8B An example of such a slice is shown. The geometry of the slice can be modeled as having a background component 806 (shown in white) and at least one component 808 (shown in a darker color), the at least one component 808 being referred to as a "polygonal component" and having a polygonal shape in a plane. In the example shown, the polygonal component 808 is a square, but polygons can generally be any closed polygon, and the slice can contain any arrangement of closed polygons in the background. In this way, a geometric representation of any arbitrary electromagnetic element can be generated. The electromagnetic element 800 can have more than two material components, each defining one or more corresponding polygonal components in one or more slices.

[0102] The geometry of each polygon can be characterized by the coordinates of its vertices. The two lateral directions can be confined within a second plane and are represented as follows: x and y In the example shown, polygonal part 808 can be represented by the Cartesian coordinates ((x1, y1), (x2, y2), …, (x4, y4)) of its corresponding vertices. Other coordinate systems may also be used.

[0103] Technicians will understand that, for any given slice, the constraints on the background and polygonal parts are, to some extent, arbitrary. That is to say, Figure 8B The colored squares in the image can theoretically be considered background components, and the white frame-shaped region 806 can be considered polygonal components. However, in practice, polygonal components 808 are usually limited to components with the simplest polygonal shapes or arrangements in the slice (i.e., those with the fewest total sides). This ensures that the computational overhead during initialization and solver phases is minimized.

[0104] As mentioned earlier, the spectral representation of an electromagnetic element can include a two-dimensional array of Fourier coefficients, where for each polygon in each slice of the element, the Fourier coefficients correspond to a different wave vector k. The wave vector can be defined by the corresponding wave number in each of the x and y directions.

[0105] It can be shown that for a number of N E The (straight) edges and vertices (x1, y1), (x2, y2), …, A closed polygon for any given wave vector k Fourier coefficients f k We can evaluate this based on Equation 1: Integer index p Mark the vertices of the polygon (in clockwise or counterclockwise order around the outer perimeter of the polygon); y p = y p+1 – y p and x p = x p+1 - x p These represent the distance between vertex p and vertex p+1 (or, in...). p equals N E In the case of vertex N E The distance between the edge and vertex 1 in the y-direction and the x-direction (i.e., the range between these vertices in the y-direction and the x-direction, respectively); L p It is between vertex p and vertex p+1 (or, in p equals N E In the case of vertex N E The length of the polygon's side (the side between vertex 1 and vertex 1). ;r p It is a vector It describes the first polygon. p The position of the vertex in the xy plane; and τ p It is a normalized vector It describes the relationship between vertex p and vertex p+1 (or, in p equals N E In the case of vertex N E The direction of the polygon's edges (the edges between vertex 1 and vertex 2).

[0106] The time complexity of Equation 1 is O( ),in and These are the numbers of Fourier modes in the horizontal directions x and y, respectively. Each Fourier mode is a wave in the spatial domain, and it corresponds to k in the x and y directions with its corresponding static wavenumber. x , k y The given frequencies exhibit sinusoidal oscillations. The Discrete Fourier Transform transforms these Fourier modes into their corresponding values ​​in the spatial frequency domain (representing the corresponding wave functions).

[0107] For complex-shaped electromagnetic components (i.e., those with a minimum feature size of less than 10 nm), this scaling imposes a practical upper limit on accuracy because the number of Fourier modes, or the number of polygon edges, must be truncated to keep computation time within acceptable levels (e.g., less than tens of hours). Inherent errors in the spectral representation of the electromagnetic component also propagate to the predicted electromagnetic response made using the solver during the solver phase. To some extent, this can particularly obscure proper characterization of electromagnetic components at higher frequencies (e.g., frequencies greater than 10,000 THz), as such frequencies typically require modeling nanoscale (i.e., <10 nm) printing defects in the electromagnetic component. This is because the wavelengths of electromagnetic radiation at these frequencies are less than 30 nm (in free space), small enough to begin probing nanoscale printing defects. At these frequencies, the wavelength within the electromagnetic component is approximately equal to the wavelength in free space because the relative permittivity of the material comprising the electromagnetic component will be approximately equal to 1.

[0108] This paper proposes an alternative method for generating spectral model representations of electromagnetic components, which can be more efficient than O( It can be computed more efficiently.

[0109] It can be proven that, for vertices , ,…, The number represented is The Fourier coefficients f of any given non-zero wave vector k of a closed polygon with sides k We can evaluate this based on Equation 2: Where k x, y It is a wave vector k The wavenumbers in the horizontal directions x and y, respectively; and where These represent the "first" Fourier component and the "second" Fourier component, respectively.

[0110] However, in practice, for each Fourier coefficient f k Assessment 2N E Line integrals are computationally infeasible. To address this problem, this disclosure proposes to approximate the line integral using a numerical orthogonality rule at multiple discrete points along each polygon edge. These discrete points form a set.

[0111] More specifically, line integrals can be approximated using the numerical orthogonality rule (Equation 3): Where N QThis is the number of sampling points for each edge of the polygon (for simplicity, we assume the number of sampling points is the same for each edge, but this is not the case in the variant). It is along the first p Vertex to the p+1 The edges of the vertex (or, in) p equals N E In the case of vertex N E The unit vector in the direction of the edge between vertex 1 and vertex 2; for integer indices q=1,… N Q of {l q } It applies to each polygon edge, between 0 and L. p A set of values ​​between, where each q The value corresponds to the distance from the first p Vertex distance l q At the corresponding sampling point (also called the orthogonal point), the integrand from Equation 2 will be numerically evaluated; and {W q} represents the set of orthogonal weights, where each orthogonal weight corresponds to a sampling point q. Note that, for simplicity, the values ​​are... {l q } They are written without a subscript p, i.e., it is assumed that they are the same for every edge. However, more generally, they may differ for different edges, in which case they would be written as {l pq}

[0112] In a specific example, the numerical orthogonality rule is the Gaussian-Legendre orthogonality rule. The orthogonality points and weights for this rule are known from the literature and can be determined from a lookup table (i.e., they do not need to be computed themselves). However, those skilled in the art will understand that the Gaussian orthogonality rule relates to an integral over the interval [-1, 1], and therefore its orthogonality points and weights require mapping the interval [-1, 1] to the interval [0, L] in Equation 2. p ] above, to calculate {l q} and {W q Generally, orthogonal weights and points can be scaled according to the length of the polygon edges to which they are associated. For the Gaussian orthogonality rule, a linear mapping between the orthogonal points and weights is applied: x' = L p / 2 (x+1) and W' = L p W / 2 is applied, meaning that if the orthogonal points are x = -1 and 1, then the mapped orthogonal points x' are 0 and L respectively. p Other orthogonal rules and appropriate mapping rules can also be applied.

[0113] Substituting the numerical orthogonal approximation for the line integral into Equation 2, we obtain the first Fourier component {X}. k} and the second Fourier component {Y k The following expression for} (Equation 4): Where r pq =r p +τ p l q , represents the set of positions along each edge of the polygon, where each position corresponds to a corresponding l. q At this position, the integrand from Equation 2 is evaluated numerically; x pq Form a set of coefficients ("first coefficients"), each first coefficient equal to ;and y pq Form another set of coefficients ("second coefficients"), each of which is equal to Set x pq and y pq Each coefficient in the equation represents the weight of the corresponding polygon edge p in the x and y directions through the corresponding orthogonal weight W. q The range of magnitude to be modified.

[0114] As shown in Equation 4, the first Fourier component and the second Fourier component X k Or Y k Each of these is a sampling position r along the edge of the polygon. pq The first set of coefficients at {x} pq} or the second set of coefficients {y pq The two-dimensional Discrete Fourier Transform (DFT) of the expression is given. This DFT can be efficiently evaluated using the Fast Fourier Transform (FFT) algorithm.

[0115] Advantageously, the coefficient set {x} pq} and {y pq} and sampling position {r pq (The DFT will be evaluated above the sampling location) does not depend on the wave vector k. This means that for each polygon, {x} pq}、{y pq} and {r pq These coefficients only need to be calculated once, and can subsequently be used to evaluate any of the Fourier coefficients. If the number of Fourier coefficients is large enough, this can reduce the total computation time used to generate the spectral model representation of the electromagnetic element.

[0116] More specifically, the sampling location {r pq The set of coefficients at} {x pq} and {y pqIt can be done with a time complexity of O( ) to perform calculations.

[0117] As mentioned earlier, some orthogonal points are known from the literature and can be determined from a lookup table. In some examples, the sampling location {r} pq By mapping these known orthogonal points for each polygon edge to a length of L p It is determined on the corresponding polygon edges. For each polygon edge, the set x pq and y pq The coefficients are then calculated based on the range of the polygon's edges in each of the x and y directions, modified by the corresponding orthogonal weights.

[0118] In other examples, the sampling position r for each polygon edge pq By defining a set {l} for the sides of this polygon q And calculate r numerically. p +τ p l q And thus determined. With set l q The orthogonal weight corresponding to each element (i.e., orthogonal point) in the set can then be calculated according to the numerical orthogonality rule. As mentioned above, the set {x} pq} and {y pq The first and second coefficients in} can be calculated for each polygon edge, based on the range of that polygon edge in each of the x and y directions, respectively, with magnitude modified by the corresponding orthogonal weights.

[0119] For each polygon's set of edges {l q The orthogonality can be defined in several different ways. In one example, the locations along the edges of the polygon are sampled uniformly or randomly. In this case, the Newton-Cotes orthogonality rule (e.g., the trapezoidal or Simpson rule) can be applied to determine the orthogonal weights. In another example, the sampling locations correspond to the roots of orthogonal polynomials such as Legendre or Chebyshev polynomials. The orthogonal weights are then Gauss-Legendre orthogonal weights or Gauss-Chebyshev orthogonal weights, respectively. As mentioned above, the roots and weights can be obtained from a lookup table and then mapped to the edges of the polygon. In some examples, the Clenshaw-Curtis orthogonality rule is applied. In these examples, the integrand (and its intervals) is transformed into a series containing cosines, the integral of which is approximated using the discrete cosine transform of the sampling locations. In these examples, the sampling locations and orthogonal weights are typically not available from a “known” lookup table, but in theory, a custom lookup table can be pre-computed.

[0120] In some examples, the element {l q The elements are distributed non-uniformly along each polygon edge. In other examples, element l... q They are evenly distributed along each edge of the polygon. Furthermore, as mentioned earlier, they may differ for different edges, making them more appropriately represented as {l}. pq In this case, l pq Replace the equation (3) l q and r pq In the limitation l q Generally speaking, although it's not mandatory, but point r... pq The FFT algorithm used to evaluate the 2D-DFT in Equation 4 is therefore typically a non-uniform or non-equidistant FFT algorithm, given the perimeter of the polygon and the non-uniform distribution across a given transverse slice. However, r pq It can be evenly distributed, and if so, then l pq They are also evenly distributed.

[0121] The time complexity of using a non-uniform FFT algorithm to evaluate the 2D-DFT from Equation 4 is O(N). k log(N k )+log(N Q N E / ε)), where ε represents the predetermined accuracy of NFFT, and N k Represents the product N x N y The total time complexity for evaluating Equation 4 is therefore O(N). Q N E + N k log(N k )+log(N Q N E This is typically much smaller than O(N). E N x N y ), because in almost all examples, in order to accurately evaluate Equation 4, it is necessary to adjust r. pq The sampled set {l q The number of values ​​N in} Q Much smaller than the required number (N) of Fourier coefficients k In other words, generally speaking, O(N) Q N E ) is much smaller than O(N) k N E ).

[0122] In many non-uniform FFT algorithms, the FFT is computed by interpolating points from a non-uniform distribution to points from a uniform distribution and then performing the FFT on these uniformly distributed points. The predetermined accuracy of the NFFT can be set by controlling the number of non-uniformly distributed points used to sample each uniformly distributed point. Increasing the number improves accuracy, while decreasing the number decreases accuracy.

[0123] However, in some examples, O(N) Q N E ) greater than O(N k N E This can occur in the case of polygons with relatively long sides and large amplitudes of wave vector k. In such an example, O(N) Q N E ) can be artificially made smaller than O(N) through the following methods. k N E ): Divide one or more polygon edges into shorter segments to reduce N. Q And the Fourier coefficients for each of these segments are evaluated individually. Specifically, N k (It is greater than N) Q Those polygon edges can be selected for this segmentation process. Generally, at least within the SXR range, as long as the length of each polygon edge is less than approximately 1 nm, O(N) Q N E ) is less than O(N) k N E ).

[0124] In some examples, the number of orthogonal points required for each polygon edge and a given numerical orthogonality rule can be derived based on a pre-defined upper limit on the error. That is, if the upper limit on the error is set relatively low, a larger number of orthogonal points will be needed, and if the upper limit is set even lower, fewer orthogonal points will be needed. The number of orthogonal points can then be adjusted according to the desired accuracy, and the set {l} q The element N of} Q This can be determined accordingly. In a specific example, the Nyquist criterion is used to determine the required number of orthogonal points based on the magnitude of the maximum wavenumber k. That is, the number of orthogonal points is the product of (a) the length of the polygon's sides and (b) at least twice the maximum wavenumber.

[0125] The proposed method is particularly suitable for determining the spectral model representation of electromagnetic components whose transverse slices define polygons with more than 50 sides, more preferably more than 250 sides, and even more preferably more than 500 sides. These polygons require numerous Fourier modes (e.g., >25, >50, or >100) for accurate modeling in each of the x and y directions. This is because the computation time of the proposed method exhibits excellent scalability (N0) as the number of Fourier modes increases. k log(N k Compared to N k This is unlike traditional methods. Therefore, the proposed method is particularly advantageous when used to determine the electromagnetic response of electromagnetic components to higher frequency electromagnetic radiation (e.g., SXR), at which even nanometer-scale (i.e., <10 nm) features need to be modeled to obtain accurate results.

[0126] In some examples, the number of points along any polygonal edge is less than 400, more preferably less than 150, and even more preferably less than 50.

[0127] A spectral model representation of an electromagnetic element, which can be geometrically described as multiple slices stacked transversely along the x and y directions, can be obtained by determining the spectral representation of one or more polygons defined by each transverse slice. The electromagnetic response can be determined by inputting this spectral model representation of the electromagnetic element into a Maxwell solver.

[0128] Examples of electromagnetic responses that can be calculated in this manner include: electromagnetic fields that are scattered or reflected; electromagnetic fields generated due to radiation transmitted through electromagnetic elements; and near-fields that describe the state / behavior of scattered / reflected electromagnetic fields.

[0129] Figure 9 The total computation time required to evaluate Fourier coefficients for a regular polygon with 500 sides and a fixed side length of 0.1 nm using Equations 1 and 2 is shown. The total computation time varies with the number of patterns (Nx, Ny) in each of the x- and y-directions.

[0130] In the specific example shown, Equation 2 is computed using Gauss-Legend de Gauss numerical orthogonality. However, it should be understood that the improvement in processing speed is not solely attributable to using this particular orthogonality rule. Other orthogonality rules will produce similar improvements.

[0131] An 11th-generation Intel® Core™ i5-1145G7'' 2.60GHz CPU with 16GB of RAM was used to generate... Figure 9The results are as described above, but technicians certainly understand that other computers with different specifications will produce similar results, but the absolute value of the computation time will differ.

[0132] Further results (not shown) confirm that these improvements in computation time do not significantly affect numerical accuracy.

[0133] As previously mentioned, the proposed method has particular applications in EUV / SXR-based optical measurements that are based on model reconstruction of the target object (i.e., electromagnetic components).

[0134] Figure 10 This is a flowchart illustrating the steps in a method for generating a spectral representation of an electromagnetic element. The electromagnetic element can be described as a plurality of stacked transverse slices, each transverse slice defining one or more polygons. The spectral representation of the electromagnetic element includes an array of Fourier coefficients for each polygon in the slice. Each array of Fourier coefficients has at least two dimensions, where the Fourier coefficients correspond to different wavenumbers k. x , k y .

[0135] In step 1002, multiple points are determined for each polygon. The multiple points represent points along the edges of the polygon.

[0136] In step 1004, the corresponding first coefficient and second coefficient for each of these plurality of points are calculated based on the range of the corresponding polygon edges in each of the first and second lateral directions (i.e., the x and y directions).

[0137] In step 1006, the first Fourier component (i.e., {X}) k For each polygon and multiple wave vectors, an FFT algorithm is performed based on the corresponding multiple points and corresponding first coefficients. That is, for each of the multiple points, the corresponding first coefficient is used in the FFT.

[0138] In step 1008, the second Fourier component (i.e., {Y}) k For each polygon and multiple wave vectors, an FFT algorithm is performed based on the corresponding multiple points and corresponding second coefficients. That is, for each of the multiple points, the corresponding first coefficient is used in the FFT.

[0139] In step 1010, the spectral representation of the electromagnetic element is generated, for example, by Equation 2 based on the first and second Fourier components for each polygon.

[0140] Figure 11This is a flowchart illustrating the steps in a method for determining the electromagnetic response of an electromagnetic element to electromagnetic radiation.

[0141] In step 1102, the spectral model of the electromagnetic element is represented, for example, according to... Figure 10 The method steps are generated.

[0142] In step 1104, the spectral model representation, along with the representation of the electromagnetic radiation incident on the electromagnetic element, is input into the Maxwell solver. The solver then evaluates the electromagnetic response based on these conditions. The incident electromagnetic radiation can be modeled as propagating along a direction perpendicular to the transverse slice of the electromagnetic element, or propagating at an angle to the transverse slice of the electromagnetic element.

[0143] Optionally, there may be an additional step of comparing the electromagnetic response obtained in step 1104 with experimental measurement data describing the electromagnetic response of the observed (real-world) electromagnetic element. The experimental measurement data can be obtained by any conventional measuring device, and the comparison can be performed using known techniques, such as based on obtaining numerical parameters indicating the difference between the electromagnetic response obtained in step 1104 and the experimental measurement data.

[0144] Embodiments may include computer programs comprising one or more sequences of machine-readable instructions describing methods for optical measurement and / or methods for analyzing measurements to obtain information related to the photolithography process. Embodiments may also include computer code comprising one or more sequences of machine-readable instructions or data describing methods. The computer program or code may, for example, be in... Figure 6 The unit MPU and / or Figure 3 The operation is executed within the control unit CL. A data storage medium (e.g., semiconductor memory, disk, or optical disk) storing such a computer program or code may also be provided. When existing measuring devices (e.g., Figure 6 When a measurement device of the type shown is already in production and / or use, embodiments of the invention can be implemented by providing an updated computer program product, causing a processor to execute one or more of the methods described herein. The computer program or code may optionally be arranged to control optical systems, substrate supports, etc., to perform methods for measuring parameters of a lithography process on suitable plurality of targets. The computer program or code may update lithography and / or measurement formulations for measuring other substrates. The computer program or code may be arranged to (directly or indirectly) control lithography apparatus to pattern and process other substrates.

[0145] The irradiation source can be provided in, for example, a measurement device (MT), an inspection device, a lithography device (LA), and / or a lithography unit (LC).

[0146] The characteristics of the emitted radiation used to perform a measurement can affect the quality of the resulting measurement. For example, the shape and size of the transverse beam profile (cross-section) of the radiation beam, the intensity of the radiation, and the power spectral density of the radiation can all influence the measurement performed by the radiation. Therefore, it is beneficial to have a source that provides radiation with characteristics that produce high-quality measurements.

[0147] Figure 12 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 transmitting 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. Storage device 1610 (such as a disk or optical disk) is provided and coupled to bus 1602 for storing information and instructions.

[0148] Computer system 1600 can be coupled to display 1612, such as a cathode ray tube (CRT), flat panel display, or touchscreen display, via bus 1602 for displaying information to the computer user. Input device 1614, including alphanumeric and other keys, is coupled to bus 1602 for transmitting information and command selection to processor 1604. Another type of user input device is cursor control 1616, such as a mouse, trackball, or arrow keys, for transmitting directional information and command selection to processor 1604 and for controlling cursor movement on display 1612. This input device typically has 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.

[0149] 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 one or more instructions contained in main memory 1606. Such instructions may be read into main memory 1606 from another computer-readable medium, such as storage device 1610. Executing the sequence of instructions contained in main memory 1606 causes processor 1604 to perform the process steps described herein. One or more processors in a multiprocessor arrangement may also be used to execute the sequence of instructions contained in main memory 1606. In alternative embodiments, hardwired circuitry may 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.

[0150] 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 conductors 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 tape, any other magnetic media, CD-ROMs, DVDs, any other optical media, punched cards, paper tape, any other physical media with a perforated pattern, RAM, PROM, EPROM, FLASH-EPROM, any other memory chip or card, the carrier wave described below, or any other medium from which a computer can read.

[0151] Various forms of computer-readable media may involve carrying one or more sequences of one or more 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 the instructions 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 carries the data to main memory 1606, from which processor 1604 retrieves and executes the instructions. The instructions received in main memory 1606 may optionally be stored on storage device 1610 before or after execution by processor 1604.

[0152] 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 a modem to provide data communication connectivity to a corresponding type of telephone line. As another example, communication interface 1618 may be a Local Area Network (LAN) card to provide data communication connectivity to 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.

[0153] 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 via local network 1622, or to data devices operated by Internet Service Provider (ISP) 1626. ISP 1626 then 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 to carry digital data streams. Signals through various networks, as well as signals on network link 1620 and through communication interface 1618 (which carries digital data to and from computer system 1600), are example forms of carrier waves for transmitting information.

[0154] Computer system 1600 can send messages and receive data, including program code, via networks (multiple), network link 1620, and communication interface 1618. In the Internet example, server 1630 can transmit application-requested code via the Internet 1628, ISP 1626, local network 1622, and communication interface 1618. An application thus downloaded can, for example, provide one or more of the techniques described herein. The received code can 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 obtain application code in carrier form.

[0155] While this article may specifically refer to the use of photolithography apparatus in IC manufacturing, it should be understood that the photolithography apparatus described herein can have other applications. Other possible applications include manufacturing integrated optical systems, guiding and detecting patterns for magnetic domain memory, flat panel displays, liquid crystal displays (LCDs), thin-film magnetic heads, etc.

[0156] Although specific reference to embodiments of the invention may be made herein in the context of a lithography apparatus, embodiments of the invention may also be used in other apparatuses. Embodiments of the invention can form mask inspection apparatuses, measurement apparatuses, or any apparatus for measuring or processing objects such as wafers (or other substrates) or masks (or other patterning devices). These apparatuses can be collectively referred to as lithography tools. Such lithography tools can use vacuum conditions or ambient (non-vacuum) conditions.

[0157] Although the terms "measuring apparatus / tool / system" or "inspection apparatus / tool / system" are specifically used, these terms can refer to tools, apparatus, or systems of the same or similar type. For example, an inspection or measuring apparatus including embodiments of the present invention can be used to determine the characteristics of a structure on a substrate or wafer. For example, an inspection or measuring apparatus including embodiments of the present invention can be used to detect defects in a substrate or defects in a structure on a substrate or wafer. In such embodiments, the characteristics of interest in a structure on a substrate may relate to defects in the structure, the absence of a specific portion of the structure, or the presence of unwanted structures on the substrate or wafer.

[0158] While the foregoing may specifically refer to the use of embodiments of the invention in the context of optical lithography, it should be understood that, where the context permits, the invention is not limited to optical lithography and can be used in other applications (e.g., imprint lithography).

[0159] 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. The above description is intended to be illustrative and not restrictive. Therefore, it will be apparent to those skilled in the art that modifications can be made to the invention without departing from the scope of the set forth claims.

[0160] Embodiments may include a method for calculating Fourier coefficients for calculating the electromagnetic scattering properties of a structure, wherein at least a portion of the structure is represented by a polygon, the method comprising: a first step of calculating a first portion of the Fourier coefficients, wherein the first portion is a function of the number of sides of the polygon; and a second step of calculating a second portion of the Fourier coefficients, wherein the second portion is a function of the number of Fourier models. Optionally, the first portion is a function of the number of sampling points per side. Optionally, the first portion does not depend on the number of Fourier models. Optionally, the second portion does not depend on the number of sides of the polygon and / or the number of sampling points per side.

[0161] Further embodiments are disclosed in the following numbered clauses:

[0162] Clause 1: A computer-implemented method for generating a spectral model representation of an electromagnetic element in an electromagnetic system, for determining an electromagnetic response to electromagnetic radiation interacting with the electromagnetic element, the representation comprising a two-dimensional array of elements corresponding to respective wave vectors, the wave vectors being defined by corresponding wave numbers in each of a first and a second mutually transverse direction, wherein the electromagnetic element is geometrically described as a plurality of slices stacked transversely to the first and second transverse directions, each slice comprising one or more polygons, the method comprising: for each of the one or more polygons: determining a plurality of corresponding points, the points including points along each side of the polygon; For each of the plurality of points: calculate the corresponding first coefficient and second coefficient based on the range of the corresponding polygon edges in each of the first mutual lateral direction and the second mutual lateral direction; generate a first Fourier component for each wave vector by performing a Fast Fourier Transform (FFT) algorithm on the plurality of points and using the corresponding first coefficient for each point; generate a second Fourier component for each wave vector by performing a Fast Fourier Transform (FFT) algorithm on the plurality of points and using the corresponding second coefficient for each point; generate an array of elements based on the first Fourier component and the second Fourier component for each polygon.

[0163] Clause 2: The method according to Clause 1, wherein the points along each polygon edge are non-uniformly distributed along the edge.

[0164] Clause 3: The method according to Clause 1, wherein the points along each polygonal edge are uniformly distributed along the edge.

[0165] Clause 4: The method according to any one of Clauses 1 to 2, wherein the FFT is a non-uniform FFT.

[0166] Clause 5: The method according to any one of Clauses 1 to 4, wherein each step of calculating the corresponding first coefficient and the second coefficient is further based on the corresponding orthogonal weights from the numerical orthogonality rules, wherein each of the orthogonal weights is associated with a corresponding orthogonal point corresponding to one of the plurality of points along the edge of the polygon.

[0167] Clause 6: According to the method of Clause 5, each of the orthogonal weights and the corresponding orthogonal points is determined by scaling the corresponding orthogonal weights and orthogonal weights from the lookup table according to the length of the polygonal edge associated with the orthogonal point.

[0168] Clause 7: The method according to Clause 6, wherein the step of determining the corresponding plurality of points includes: mapping the orthogonal point for each polygon edge to the corresponding polygon edge.

[0169] Clause 8: The method according to any one of Clauses 5 to 7, wherein the numerical orthogonality rule is the Gauss-Legend orthogonality rule.

[0170] Clause 9: The method according to any one of the preceding clauses further comprises: dividing the polygon edge until the product of the number of wave numbers in each of (a) the first mutual lateral direction and (b) the second mutual lateral direction is greater than the number of points along the corresponding polygon edge.

[0171] Clause 10: The method according to any one of the preceding clauses, wherein the number of sides in any one of the one or more polygons is greater than 50, more preferably greater than 250, and even more preferably greater than 500.

[0172] Clause 11: The method according to any one of the preceding clauses, wherein, for any one of the one or more polygons, the number of points along any edge of the polygon is less than 400, more preferably less than 150, and even more preferably less than 50.

[0173] Clause 12: The method according to any one of the preceding clauses, wherein the number of waves in each of the first mutual lateral direction and the second mutual lateral direction is greater than 25, more preferably greater than 50, and even more preferably greater than 100.

[0174] Clause 13: The method according to any one of Clauses 1 to 9, wherein, for any polygon in the polygons, the maximum product of the following is greater than 60,000, more preferably greater than 1,850,000, and even more preferably greater than 20,000,000: (i) the number of sides of the polygon; (ii) the number of points along each polygonal side of the polygon; and (iii) the number of wave numbers on each of the first and second lateral directions.

[0175] Clause 14: The method according to any one of Clauses 5 to 13 further comprises: when using the numerical orthogonality rule, deriving the number of orthogonal points required for each polygon edge based on a predefined upper limit for the error; and determining a plurality of points for each polygon comprises: determining the derived number of points along each edge of the polygon.

[0176] Clause 15: A computer program product comprising instructions that, when executed by a computer processor, cause the computer processor to perform method steps according to any one of Clauses 1 to 14.

[0177] Clause 16: A computer system comprising one or more processors configured to perform the method according to any one of Clauses 1 to 14.

[0178] Clause 17: A computer-implemented method for determining the electromagnetic response to electromagnetic radiation interacting with an electromagnetic element, the method comprising: inputting a spectral model representation of the electromagnetic element obtained according to any one of Method Clauses 1 to 14 into a Maxwell solver.

[0179] Clause 18: The method according to Clause 17, wherein the electromagnetic radiation is in the soft X-ray band.

[0180] While this article may specifically refer to the use of photolithography apparatus in IC manufacturing, it should be understood that the photolithography apparatus described herein can have other applications. Other possible applications include manufacturing integrated optical systems, guiding and detecting patterns for magnetic domain memory, flat panel displays, liquid crystal displays (LCDs), thin-film magnetic heads, etc.

[0181] Although specific reference to embodiments of the invention may be made herein in the context of a lithography apparatus, embodiments may also be used in other apparatuses. Embodiments may form mask inspection apparatus, measurement apparatus, or any apparatus for measuring or processing an object (such as a wafer (or other substrate) or a mask (or other patterning apparatus)). These apparatuses may be collectively referred to as lithography tools. Such lithography tools may use vacuum conditions or ambient (non-vacuum) conditions.

[0182] While specific references to embodiments may be made herein in the context of inspection or measurement apparatus, embodiments may be used in other apparatuses. Embodiments may 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 devices). The term “measurement apparatus” (or “inspection apparatus”) may also refer to an inspection apparatus or inspection system (or a measurement apparatus or measurement system). For example, an inspection apparatus including embodiments may be used to detect defects in a substrate or defects in a structure on a substrate. In such embodiments, the characteristics of interest in the structure on the substrate may relate to defects in the structure, the absence of a specific portion of the structure, or the presence of unwanted structures on the substrate.

[0183] While the foregoing may specifically refer to the embodiments used in the context of optical lithography, it should be understood that the invention is not limited to optical lithography and may be used in other applications (e.g., imprint lithography) where the context permits.

[0184] While the aforementioned targets or target structures (more generally, structures on a substrate) are measurement target structures specifically designed and formed for measurement purposes, in other embodiments, the characteristics of interest may be measured on one or more structures that are functional parts of a device formed on the substrate. Many devices have regular, grating-like structures. The terms structure, target grating, and target structure used herein do not require that the structure has been specifically provided for the measurement being performed. Furthermore, the pitch of the measurement target may be close to the resolution limit of the scatterer's optical system, or may be smaller, but may be much larger than the size of a typical non-target structure (optionally a product structure fabricated in the target portion C by a photolithography process). In practice, the lines and / or spaces of the overlay grating within the target structure may be fabricated to include smaller structures similar in size to the non-target structures.

[0185] While specific embodiments have been described above, it should be understood that the invention can be practiced in ways different from those described. The foregoing description is intended to be illustrative and not restrictive. Therefore, it will be apparent to those skilled in the art that modifications can be made to the described invention without departing from the scope of the set forth claims.

[0186] Although the terms "measuring apparatus / tool / system" or "inspection apparatus / tool / system" are specifically used, these terms can refer to tools, apparatus, or systems of the same or similar type. For example, an inspection or measuring apparatus including embodiments of the present invention can be used to determine the characteristics of a structure on a substrate or wafer. For example, an inspection or measuring apparatus including embodiments of the present invention can be used to detect defects in a substrate or defects in a structure on a substrate or wafer. In such embodiments, the characteristics of interest in the structure on the substrate may relate to defects in the structure, the absence of a specific portion of the structure, or the presence of unwanted structures on the substrate or wafer.

[0187] While specific references are made to HXR, SXR, and EUV electromagnetic radiation, it should be understood that the invention can be practiced using all electromagnetic radiation, including radio waves, microwaves, infrared radiation, (visible) light, ultraviolet radiation, X-rays, and gamma rays, where the context permits.

[0188] Additional objects, advantages, and features of the invention are set forth in this specification and will become apparent in part to those skilled in the art upon examination of the following, or may be learned by practice of the invention. The invention disclosed in this application is not limited to any particular set or combination of the objects, advantages, and features. Various combinations of the stated objects, advantages, and features are contemplated to constitute the invention disclosed in this application.

Claims

1. A computer-implemented method for generating a spectral model representation of an electromagnetic element in an electromagnetic system, for determining an electromagnetic response to electromagnetic radiation interacting with the electromagnetic element, the representation comprising a two-dimensional array of elements corresponding to respective wave vectors, the wave vectors being defined by corresponding wave numbers in each of a first mutually transverse direction and a second mutually transverse direction, wherein the electromagnetic element is geometrically described as a plurality of slices stacked transversely to the first transverse direction and the second transverse direction, each slice comprising one or more polygons, the method comprising: For each of the one or more polygons: Determine a plurality of corresponding points, the points including points along each side of the polygon; For each of the plurality of points: Based on the range of the corresponding polygon edges in each of the first mutual lateral direction and the second mutual lateral direction, calculate the corresponding first coefficient and second coefficient. By performing a Fast Fourier Transform (FFT) algorithm based on the plurality of points and using the corresponding first coefficients for each point, a first Fourier component is generated for each wave vector in the wave vector. By performing the Fast Fourier Transform (FFT) algorithm based on the plurality of points and using the corresponding second coefficients for each point, a second Fourier component is generated for each wave vector in the wave vector. An array of elements is generated based on the first Fourier component and the second Fourier component for each polygon.

2. The method of claim 1, wherein the points along each polygonal edge are non-uniformly distributed along the edge.

3. The method of claim 1, wherein the points along each polygonal edge are uniformly distributed along the edge.

4. The method according to any one of claims 1 to 2, wherein the FFT is a non-uniform FFT.

5. The method according to any one of claims 1 to 4, wherein each step of calculating the corresponding first coefficient and the second coefficient is further based on a corresponding orthogonal weight from a numerical orthogonality rule, wherein each of the orthogonal weights is associated with a corresponding orthogonal point corresponding to one of the plurality of points along the edge of the polygon.

6. The method according to any one of the preceding claims further comprises: The polygon edges are divided under the condition that the product of the number of wave numbers in each of (a) the first mutual lateral direction and (b) the second mutual lateral direction is greater than the number of points along the corresponding polygon edge, until the product is less than the number of points.

7. The method according to any one of the preceding claims, wherein the number of sides in any one of the one or more polygons is greater than 50, more preferably greater than 250, and even more preferably greater than 500.

8. The method according to any one of the preceding claims, wherein, For any one of the one or more polygons, the number of points along any edge of the polygon is less than 400, more preferably less than 150, and even more preferably less than 50.

9. The method according to any one of the preceding claims, wherein the number of waves in each of the first mutual lateral direction and the second mutual lateral direction is greater than 25, more preferably greater than 50, and even more preferably greater than 100.

10. The method according to any one of claims 1 to 6, wherein, For any polygon in the polygon, the product of the number of waves in each of the first mutual lateral directions and the second mutual lateral directions is greater than the number of points along any polygon edge in the polygon.

11. The method according to any one of claims 5 to 10, further comprising: When using the numerical orthogonality rule, the number of orthogonal points required for each polygon edge is derived based on a predefined upper limit for the error. as well as Determining the corresponding number of points for each polygon includes: determining the derived number of points along each side of the polygon.

12. A computer program product comprising instructions that, when executed by a computer processor, cause the computer processor to perform the method steps according to any one of claims 1 to 11.

13. A computer system comprising one or more processors configured to perform the method according to any one of claims 1 to 11.

14. A computer-implemented method for determining the electromagnetic response to electromagnetic radiation interacting with an electromagnetic element, the method comprising: The spectral model representation of the electromagnetic element obtained according to any one of claims 1 to 11 is input into the Maxwell solver.

15. A method for characterizing an electromagnetic element, comprising: The measured electromagnetic response is compared with the electromagnetic response determined according to claim 14.

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