Method for determining random variations in printed patterns

Abstract

A method for determining measurement data of a printed pattern on a substrate is described herein. The method involves obtaining (i) an original image of the substrate, including a printed pattern corresponding to a reference pattern, (ii) an average image of the original image, and (iii) a composite profile based on the average image. Further, the composite profile is aligned relative to a reference profile of the reference pattern, and the original profile is extracted from the original image based on the aligned composite profile and the output of a die-to-database alignment of the composite profile. Further, the method determines a plurality of pattern measurements based on the original profile, and determines measurement data corresponding to the printed pattern based on the plurality of pattern measurements. Further, the method determines a plurality of process variations, such as random variations, die-to-die variations, intra-die variations, and total variations.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to European / US application 62 / 809,838, filed on February 25, 2019, which is incorporated herein by reference in its entirety. Technical Field

[0003] The description herein relates to lithographic apparatus and processes, and more specifically to tools for determining random variations in printed patterns, for example, in a resist layer on a wafer, which can be used to model the random variations for process variation prediction and defect detection, detect defects on the wafer, and optimize patterning processes, such as mask optimization and source optimization. Background Art

[0004] A lithographic projection apparatus may be used, for example, in the manufacture of integrated circuits (ICs). In this case, a patterning device (e.g., a mask) may contain or provide a circuit pattern (a "design layout") corresponding to a single layer of the IC, and the circuit pattern may be transferred to a target portion (e.g., comprising one or more dies) on a substrate (e.g., a silicon wafer) that has been coated with a layer of radiation-sensitive material ("resist"), such as by irradiating the target portion through the circuit pattern on the patterning device. Typically, a single substrate contains a plurality of adjacent target portions to which the circuit pattern is transferred successively, one target portion at a time, by the lithographic projection apparatus. In one type of lithographic projection apparatus, the circuit pattern on the entire patterning device is transferred to one target portion at a time; such an apparatus is generally referred to as a wafer stepper. In an alternative apparatus, generally referred to as a stepper-scan apparatus, the projection beam is scanned over the patterning device in a given reference direction (the "scanning" direction) while the substrate is synchronously moved parallel or antiparallel to the reference direction. Different portions of the circuit pattern on the patterning device are progressively transferred to one target portion. Typically, since the lithographic projection apparatus will have a magnification factor M (typically <1), the speed F at which the substrate is moved will be a factor M of the projection beam scanning patterning device. More information on the lithographic apparatus described herein can be gleaned, for example, from US 6,046,792, which is incorporated herein by reference.

[0005] Before the circuit pattern is transferred from the pattern forming device to the substrate, the substrate may undergo various procedures, such as priming, resist coating and soft baking. After exposure, the substrate can undergo other procedures, such as post-exposure baking (PEB), development, hard baking and measurement / inspection of the transferred circuit pattern. This array of procedures is used as the basis for manufacturing a single layer of a device (e.g., IC). Then, the substrate can undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are intended to complete a single layer of the device. If multiple layers are required in the device, the entire procedure or its variant is repeated for each layer. Ultimately, the device will be present in each target portion on the substrate. Then, these devices are separated from each other by techniques such as cutting or sawing, so that a single device can be mounted on a carrier, connected to pins, etc.

[0006] As mentioned, microlithography is a central step in the fabrication of ICs, where patterns formed on substrates define the functional elements of the ICs, such as microprocessors, memory chips, etc. Similar lithographic techniques are also used in the formation of flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0007] As semiconductor manufacturing processes continue to advance, following a trend generally referred to as "Moore's Law," the size of functional elements has been continuously reduced, while the number of functional elements (such as transistors) per device has steadily increased for decades. At the current state of the art, the layers of a device are fabricated using a lithography projection apparatus that projects a design layout onto a substrate using illumination from a deep ultraviolet (DUV) or extreme ultraviolet (EUV) illumination source, thereby creating individual functional elements with dimensions well below 100 nm (i.e., less than half the wavelength of the radiation from the illumination source, such as 193 nm DUV and 13.5 nm EUV illumination sources).

[0008] The process in which features with dimensions smaller than the classical resolution limit of the lithographic projection apparatus are printed is generally referred to as low-k1 lithography, according to the resolution formula CD=k1×λ / NA, where λ is the wavelength of the radiation employed (currently 248 nm or 193 nm or 13.5 nm in most cases), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the "critical dimension", usually the smallest printed feature size, and k1 is an empirical resolution factor. In general, the smaller the k1, the more difficult it is to reproduce on the substrate a pattern similar in shape and size to that planned by the circuit designer in order to achieve specific electrical functionality and performance. In order to overcome these difficulties, complex fine-tuning steps are applied to the lithographic projection apparatus and / or the design layout. For example, these include, but are not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase-shifting pattern forming devices, optical proximity correction (OPC, sometimes also called "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement technology" (RET). The term "projection optics" as used herein should be broadly interpreted to cover various types of optical systems, including, for example, refractive optics, reflective optics, apertures, and reflective-refractive optics. The term "projection optics" may also include components that operate according to any of these design types to collectively or individually guide, shape, or control a projection beam of radiation. The term "projection optics" may include any optical component in a lithographic projection apparatus, regardless of where the optical component is located in the optical path of the lithographic projection apparatus. Projection optics may include optical components for shaping, adjusting, and / or projecting radiation from a source before the radiation passes through a patterning device and / or optical components for shaping, adjusting, and / or projecting radiation after the radiation passes through a patterning device. Projection optics typically do not include a source and a patterning device. Summary of the invention

[0009] In an embodiment, a method for determining random variation in measurement data of a printed pattern on a substrate is provided. The method involves: obtaining (i) multiple images of the substrate, each of the images including a printed pattern corresponding to a reference pattern, (ii) an average image of the multiple images, and (iii) a composite profile of the printed pattern based on the average image; aligning, via a processor, the composite profile of the average image relative to a reference profile of the reference pattern; extracting, via the processor, a profile of the printed pattern within the image from multiple original images, the extraction based on the aligned average profile; determining, via the processor, multiple pattern measurements based on the multiple original profiles, wherein the pattern measurements are characteristic of the printed pattern and the patterning process; and determining, via the processor, measurement data corresponding to the printed pattern based on the multiple pattern measurements. Further, the method determines multiple process variations, such as random variation, die-to-die variation, intra-die variation, and total variation.

[0010] In addition, in an embodiment, a device configured to extract a contour from a metrology image is provided. The device includes a processor configured to: obtain (i) a metrology image of a substrate having a printed pattern, (ii) an average image of the printed pattern, (iii) a composite contour from the average image, (iv) an aligned composite contour relative to a reference contour of a reference pattern, (v) an original contour from the metrology image, and (vi) a measurement statistic corresponding to the printed pattern based on the original contour.

[0011] Furthermore, in an embodiment, a computer program product is provided, including a non-transitory computer-readable medium having instructions recorded thereon, which, when executed by a computer system, implement the above method. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Embodiments will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0013] Figure 1 is a block diagram of various subsystems of a lithography system according to an embodiment.

[0014] Figure 2 is according to an embodiment corresponding to Figure 1 Block diagram of the simulation model of the subsystem in .

[0015] Figure 3 is a flow chart of a method for extracting contours from a raw image (eg, SEM) of a printed substrate and determining measurements from the extracted contours, according to an embodiment.

[0016] Figure 4A The diagram shows a method based on an embodiment of the present invention. Figure 3 Examples of extracted contours and measurement data (eg, random variations) of printed patterns determined by the method.

[0017] Figure 4B are example SEM images of printed patterns and signals within the SEM images according to an embodiment.

[0018] Figure 4C According to the embodiment Figure 4B Example of an average image of a printed pattern and the signal within the average image.

[0019] Figure 5 is an example of measurement results for determining a profile of an example printed pattern according to an embodiment.

[0020] Fig. 6A 2 is an example of an average image of an example one-dimensional (1D) pattern, corresponding random bands of the 1D pattern, and a distribution of CD values ​​of the 1D pattern, according to an embodiment.

[0021] Figure 6B2 is an example of an average image of an example two-dimensional (2D) pattern, corresponding random bands of the 2D pattern, and a distribution of CD values ​​of the 2D pattern, according to an embodiment.

[0022] Figure 6C is an example of an average image of another example of a two-dimensional (2D) pattern, corresponding random bands of the 2D pattern, and a distribution of CD values ​​of the 2D pattern according to an embodiment.

[0023] Fig. 7A An example image including different dies and printed patterns across the dies and the determination of the total variation, σall, according to an embodiment is illustrated.

[0024] Figure 7B illustrates an example image of a die across a printed pattern and the determination of intra-die variation, ie, σ intra-die .

[0025] Figure 7C ] illustrates example images and determination of die-to-die variation between different dies of a single printed pattern according to an embodiment, i.e., σ inter-die .

[0026] Fig.7D An example image field of view (FOV) of a single printed pattern and determination of the variation of the field of view (FOV) within the image, i.e., σ sepe .

[0027] Fig. 8A is an example die-to-die image alignment process according to an embodiment.

[0028] Figure 8B According to the embodiment Fig. 8A The process finds example sub-pixel offsets for common areas of the aligned images.

[0029] Fig.9A is an example die-to-database image alignment process according to an embodiment.

[0030] Fig. 9B According to the embodiment Fig.9A An example of the process of extracting contours and reference contours as well as the die-to-database alignment process.

[0031] Fig.10 An embodiment of a scanning electron microscope (SEM) according to an embodiment is schematically depicted.

[0032] Fig.11 Embodiments of electron beam inspection equipment according to embodiments are schematically depicted.

[0033] Fig.12is a flow chart illustrating aspects of an example method of joint optimization according to an embodiment.

[0034] Fig.13 An embodiment of another optimization method according to an embodiment is shown.

[0035] Fig.14A , 14B and 15 show example flow charts of various optimization processes according to embodiments.

[0036] Fig.16 is a block diagram of an example computer system according to an embodiment.

[0037] Fig.17 is a schematic diagram of a lithographic projection apparatus according to an embodiment.

[0038] Fig.18 is a schematic diagram of another lithography projection apparatus according to an embodiment.

[0039] Fig.19 According to the embodiment Fig.18 A more detailed view of the devices in the

[0040] Fig. 20 According to the embodiment Fig.18 and 19 A more detailed view of the source collector module SO of the device.

[0041] Embodiments will now be described in detail with reference to the accompanying drawings, which are provided as illustrative examples to enable those skilled in the art to practice the embodiments. It is noteworthy that the following figures and examples are not intended to limit the scope to a single embodiment, but other embodiments are possible by exchanging some or all of the described or illustrated elements. Where convenient, the same reference numerals will be used in the drawings to refer to the same or similar parts. In the case where some elements of these embodiments can be partially or completely implemented using known components, only those parts of such known components that are necessary for understanding the embodiments will be described, and the detailed description of other parts of such known components will be omitted to avoid confusing the description of the embodiments. In this specification, embodiments showing a single component should not be considered as limiting; on the contrary, the scope is intended to cover other embodiments including multiple identical components, and vice versa, unless otherwise expressly provided herein. Moreover, the applicant does not intend to give uncommon or special meanings to any term in the specification or claims unless explicitly stated as such. Further, the scope covers the current and future known equivalents of the components cited herein by way of illustration. DETAILED DESCRIPTION

[0042] Although specific reference may be made herein to the manufacture of ICs, it should be clearly understood that the description herein has many other possible applications. For example, it can be used to manufacture integrated optical systems, guide and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. Those skilled in the art will appreciate that in the context of such alternative applications, any use of the terms "reticle", "wafer" or "die" herein should be considered interchangeable with the more general terms "mask", "substrate" and "target portion", respectively.

[0043] In this document, the terms "radiation" and "beam" are used to cover all types of electromagnetic radiation, including UV radiation (e.g., wavelengths of 365, 248, 193, 157 or 126 nm) and EUV (extreme ultraviolet radiation, e.g., wavelengths in the range 5 to 20 nm).

[0044] The terms “optimizing” and “optimization” as used herein refer to adjusting the lithography projection equipment so that the results and / or process of lithography have more desired characteristics, such as higher projection accuracy of the design layout on the substrate, a larger process window, etc.

[0045] Further, the lithographic projection apparatus may be of a type having two or more substrate tables (and / or two or more patterning device tables). In such a "multi-stage" apparatus, additional tables may be used in parallel, or preparatory steps may be performed on one or more tables while one or more other tables are being used for exposure. A dual-stage lithographic projection apparatus is described, for example, in US 5,969,441, which is incorporated herein by reference.

[0046] The pattern forming device mentioned above includes or can form a design layout. The design layout can be generated using a CAD (computer-aided design) program, which is generally referred to as EDA (electronic design automation). Most CAD programs follow a predetermined set of design rules to create a functional design layout / pattern forming device. These rules are set by processing and design constraints. For example, the design rules define the spatial tolerances between circuit devices (such as gates, capacitors, etc.) or interconnects to ensure that the circuit devices or lines do not interact with each other in an undesirable manner. Design rule restrictions are generally referred to as "critical dimensions" (CD). The critical dimension of a circuit can be defined as the minimum width of a line or hole or the minimum space between two lines or two holes. Therefore, CD determines the overall size and density of the designed circuit. Of course, one of the goals in integrated circuit manufacturing is to faithfully reproduce the original circuit design (via a pattern forming device) on a substrate.

[0047] The terms "mask" or "patterning device" as used herein may be broadly interpreted as referring to a generic patterning device that can be used to impart a patterned cross-section to an incoming radiation beam, corresponding to the pattern to be created in a target portion of the substrate; in this context, the term "light valve" may also be used. In addition to classical masks (transmissive or reflective; binary, phase-shifting, hybrid, etc.), other examples of such patterning devices include:

[0048] -Programmable mirror array. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle behind such a device is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, while unaddressed areas reflect incident radiation as undiffracted radiation. Using appropriate filters, the undiffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation; in this way, the beam is patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic devices. More information about such mirror arrays can be gleaned, for example, from U.S. Patent Nos. 5,26,891 and 5,523,193, which are incorporated herein by reference.

[0049] - A programmable LCD array. An example of such a configuration is given in US Pat. No. 5,229,872, which is incorporated herein by reference.

[0050] As a brief introduction, Figure 1 An exemplary lithographic projection apparatus 10A is illustrated. The main components are a radiation source 12A, which may be a deep ultraviolet excimer laser source or other types of sources, including: an extreme ultraviolet (EUV) source (as discussed above, the lithographic projection apparatus itself does not require a radiation source); illumination optics, which define a partial coherence (denoted as σ) and may include optics 16Aa and 16Ab that shape the radiation from source 12A; a patterning device 14A; and transmission optics 16Ac that projects an image of the patterning device pattern onto a substrate plane 22A. An adjustable filter or aperture 20A at the pupil plane of the projection optics may limit the range of beam angles that impinge on the substrate plane 22A, where the maximum possible angle defines the numerical aperture NA of the projection optics = sin(θ max ).

[0051] In the optimization process of the system, the merit of the system can be expressed as a cost function. The optimization process is reduced to the process of finding a set of parameters (design variables) of the system that minimizes the cost function. Depending on the goal of the optimization, the cost function can have any suitable form. For example, the cost function can be the weighted root mean square (RMS) of the deviations of certain characteristics (evaluation points) of the system relative to the expected values ​​(e.g., ideal values) of these characteristics; the cost function can also be the maximum value (i.e., the worst deviation) of these deviations. The term "evaluation point" in this article should be broadly interpreted as including any characteristics of the system. Due to the practicality of the implementation of the system, the design variables of the system can be limited to a limited range and / or interdependent. In the case of a lithographic projection device, the constraints are usually associated with the physical properties and characteristics of the hardware, such as an adjustable range and / or a pattern forming device manufacturability design rule, and the evaluation points can include physical points on the resist image on the substrate as well as non-physical characteristics (such as dose and focus).

[0052] In a lithographic projection apparatus, a source provides illumination (i.e., light); the projection optics directs and shapes the illumination onto a substrate via a pattern forming device. The term "projection optics" is broadly defined here to include any optical component that can modify the wavefront of a radiation beam. For example, the projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. The aerial image (AI) is the radiation intensity distribution at the substrate level. The resist layer on the substrate is exposed, and the aerial image is transferred to the resist layer as a potential "resist image" (RI) therein. The resist image (RI) can be defined as the spatial distribution of the solubility of the resist in the resist layer. Resist models can be used to calculate resist images from aerial images, examples of which can be found in commonly assigned U.S. patent application serial number 12 / 315,849, the disclosure of which is incorporated herein by reference in its entirety. The resist model is only related to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). The optical properties of a lithographic projection apparatus, such as the properties of the source, patterning device and projection optics, specify the aerial image. Since the patterning device used in a lithographic projection apparatus can be changed, it is desirable to separate the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, including at least the source and projection optics.

[0053] An exemplary flow chart for simulating lithography in a lithographic projection apparatus is shown in Figure 2. Source model 31 represents the optical properties of the source (including radiation intensity distribution and / or phase distribution). Projection optics model 32 represents the optical properties of the projection optics (including changes in radiation intensity distribution and / or phase distribution caused by the projection optics). Design layout model 35 represents the optical properties of the design layout (including changes in radiation intensity distribution and / or phase distribution caused by a given design layout 33), which is a representation of the arrangement of features on or by the pattern forming device. Aerial image 36 can be simulated by design layout model 35, projection optics model 32 and design layout model 35. Resist image 38 can be simulated from aerial image 36 using resist model 37. Simulation of lithography can, for example, predict the profile and CD in the resist image.

[0054] More specifically, it is noted that the source model 31 can represent the optical properties of the source, including but not limited to the NA sigma (σ) settings and any specific illumination source shapes (e.g., off-axis radiation sources, such as toroidal, quadrupole, and dipole, etc.). The projection optical model 32 can represent the optical properties of the projection optical device, including aberrations, distortions, refractive indices, physical dimensions, physical dimensions, etc. The design layout model 35 can also represent the physical properties of the physical pattern forming device, such as described in U.S. Patent No. 7,587,704, which is incorporated herein by reference in its entirety. The purpose of the simulation is to accurately predict, for example, edge positioning, spatial image intensity slope, and CD, which can then be compared with the expected design. The expected design is typically defined as a pre-OPC design layout, which can be provided in a standardized digital file format (e.g., GDSII or OASIS) or other file format.

[0055] From the design layout, one or more portions may be identified, which are referred to as "clips". In an embodiment, a collection of clips is extracted that represent complex patterns in the design layout (typically about 50 to 1000 clips, but any number of clips may be used). As will be appreciated by those skilled in the art, these patterns or clips represent small portions of the design (i.e., circuits, cells, or patterns), and in particular, clips represent small portions that require special attention and / or verification. In other words, a clip may be a portion of the design layout, or may be similar or have similar behavior to a portion of the design layout, where key features are identified through experience (including clips provided by customers), through trial and error, or by running full-chip simulations. A clip typically contains one or more test patterns or gauge patterns.

[0056] An initial larger set of clips may be provided a priori by the customer based on known key feature areas in the design layout that require specific image optimization. Alternatively, in another embodiment, an initial larger set of clips may be extracted from the entire design layout using some automatic (such as machine vision) or manual algorithm that identifies key feature areas.

[0057] Random variations in patterning processes (e.g., resist processes) potentially limit EUV lithography implementation for semiconductor high-volume manufacturing (e.g., HVM) due to the combination of "few" photons per millijoule dose and preferred low-dose processes, e.g., in terms of shrink potential for feature and exposure dose specifications, which in turn impacts product yield or wafer output of the patterning process, or both. In embodiments, random variations in the resist layer can manifest as different failure modes described by, for example, line width roughness (LWR), line edge roughness (LER), local CD non-uniformity, closed holes or trenches, and / or broken lines under extreme conditions. Such random variations impact and limit successful HVM EUV adoption. To characterize, understand, and predict random variations, the industry needs a reliable method to measure such variations for a variety of design patterns, not just 1D line space patterns or limited dense contact array patterns.

[0058] Existing methods for measuring random variations involve different measurement techniques for one-dimensional (1D) and two-dimensional (2D) patterns, such as 1D line / space and 2D repeating dense contact array patterns printed on a substrate. Based on such measurements, performance metrics of the patterning process (e.g., random variations) are determined to optimize the patterning process. For example, the 1D pattern measurement result is line width roughness (LWR), and the 2D repeating dense contact array measurement result is local CD uniformity (LCDU).

[0059] Currently, there is no unified solution to measure 1D and 2D patterns with the same algorithm. Different SEM algorithms are used for LWR and LCDU measurements. Moreover, there are significant algorithm differences between different SEM machines. It is difficult to compare apples to apples between the LWR of 1D line / space and the LCDU of 2D repeated dense contact arrays, and accurately estimate the SEPE of different patterns. Moreover, there is no method to estimate the SEPE of irregular 2D patterns except for 2D repeated dense contact arrays. Having a combined measurement system as suggested by the present disclosure allows 1D patterns and 2D patterns to be measured with the same algorithm, and SEPE is estimated with the same ruler (i.e., the same measurement algorithm), thereby improving the consistency, accuracy and efficiency of measurement. Due to the random variations of 1D and 2D patterns in the same measurement system, unlike in different measurement systems (such as in the case of LWR and LCDU), the combined measurement used during the modeling and optimization of the patterning process will lead to improved modeling and optimization accuracy of, for example, patterning matching schemes, hotspot identification and prediction, source and mask optimization or other patterning related processes.

[0060] Traditionally, the measurement of printed patterns is based on waveforms extracted from an image of the printed pattern (e.g., a SEM image) at a gage location (e.g., where CD measurements are taken). The waveform of the printed pattern is measured by detecting edges on the waveform using a mathematical algorithm. The simplest algorithm is thresholding of the image intensity. This algorithm has been widely used in the metrology industry, especially for defect and CD metrology in the semiconductor industry.

[0061] Prior applications (e.g., in U.S. Application No. 62 / 680,284, filed on June 4, 2018, which is incorporated herein by reference in its entirety) provide contour-based measurements for average images. For example, the extraction is based on accurate die-to-die alignment, average images, and contour extraction methods. The application enables fast and accurate contour-based measurements, such as CD and EPE measurements, to be achieved by averaging images to obtain very high signal-to-noise ratios. Unfortunately, during the image averaging process, random variation information is lost. The present disclosure provides a more accurate and improved contour extraction method for raw images, rather than average images of these raw contours and measurement data (e.g., CD or EPE) to determine random variations in the patterning process. In an embodiment, the concepts of the present disclosure are not limited to specific measurement results.

[0062] For ease of reading, these methods are described with reference to random edge positioning error (SEPE) as an example, which is a performance limiting factor in the EUV era. To control, reduce and predict SEPE, the semiconductor industry needs a robust, unified and manufacturable solution to accurately measure SEPE. As mentioned earlier, the semiconductor industry does not have a unified solution to measure 1D and 2D SEPE with the same algorithm. Currently, the industry measures the LWR of 1D lines and the LCDU of repeating 2D contact arrays to estimate SEPE. Moreover, these metrics only focus on the pattern level (e.g., one number per pattern), not the edge point level where hot spots occur (e.g., points along the pattern contour). Therefore, the measurement of random variations in edge point levels requires a profile-based SEPE measurement method.

[0063] In order to measure the true edge positioning error of each edge point (i.e., a point along the pattern profile), an accurate and reliable profile should be extracted from the original image rather than from an average image of the printed pattern (e.g., a raw SEM image). The industry is working hard to extract such reliable profiles from raw SEM images, especially low-dose SEM images, which are preferred, because the signal-to-noise ratio of raw SEM images is low.

[0064] Various image denoising filters are used to improve the quality of the original contours. Unfortunately, denoising filtering may distort the characteristics of the image so much that it cannot represent the true value of the random effects. The contour quality depends heavily on the image quality or image contrast. If the image quality is low, the contour quality will also be low. To improve the contour quality, averaging methods are used either by extracting contours from an averaged image or by averaging contours extracted from many original images. For example, the ASML MXP product (previous application) extracts very high quality contours from an averaged image, but the question of how to extract high quality contours from the original images remains.

[0065] The method of the present disclosure has several advantages. The method extracts high-quality composite contours from an average image of multiple repeated images corresponding to the same design pattern collected from different positions across the wafer. In an embodiment, the method uses the contours reliably extracted from the average image as a reference to guide the extraction of contours from the original image. This improves the quality of the original contour by avoiding or reducing, for example, inaccurate contour points at positions where the original image contrast is relatively poor, to obtain more realistic random measurement information. Moreover, the accurate sub-pixel alignment resolution between the original images provides better accuracy in SEPE bandwidth extraction and subsequent statistical data analysis to determine random variations and other process variations. According to an embodiment, the present disclosure is able to capture random variations of 1D and 2D patterns by contour-based measurement with the same contour extraction algorithm, thereby providing a joint SEPE measurement solution for the industry. In addition, the method provides faster, more accurate and contour point-specific measurements.

[0066] According to an embodiment, the terms "original image" and "measurement image" refer to an image of a printed substrate (e.g., a SEM image). The original image may be a portion of a substrate (e.g., a first die, a second die, a third die, etc. having a desired pattern), an entire printed substrate, or a different substrate having a desired pattern. In an embodiment, an image may refer to a desired printed pattern for which measurement results are collected and the measurement results are also used for different patterning process simulations (e.g., OPC, resist images, mask images, etc.). In an embodiment, a desired pattern refers to any pattern to be printed on a substrate, which may be referred to as a desired printed pattern when printed. For example, a desired pattern corresponds to a design pattern, such as a contact hole, a line, and any irregular pattern found in a memory, logic, or other IC circuit.

[0067] Figure 31 is a flow chart of a method for extracting contours from an image of a printed substrate (also referred to as an original image or a metrology image). Further, based on the extracted contours, measurement data (e.g., random variation / standard deviation or other relevant measurement statistics) can be determined to characterize the printed pattern and its printing process. Such measurement data related to the printed pattern and its printing process can also be used to generate a printed image through process simulation (e.g., Figure 2 The method is further described in detail as follows:

[0068] In processes P301 and P302, the method involves obtaining (i) a plurality of images 302 of a substrate, each of the images comprising a printed pattern corresponding to a reference pattern 301, (ii) an average image 303 of the plurality of images 302, and (iii) a composite profile 304 of the printed pattern based on the average image 303. In an embodiment, the reference pattern 301 is a design pattern or a simulated pattern corresponding to the design pattern provided in a GDS / OASIS file format.

[0069] In an embodiment, multiple images 302 of a substrate are obtained via a measurement tool. In an embodiment, obtaining refers to receiving images captured by a measurement tool via a processor (e.g., 104). In an embodiment, multiple images 302 are scanning electron microscope (SEM) images. In an embodiment, the images can be represented in the form of a vector including a signal value and a noise value. In an embodiment, the image is a pixelated image, and each pixel includes a signal value and a noise value. The signal value of the image corresponds to a feature of a printed pattern. In an embodiment, the signal value includes a pixel intensity of a pixel at a specific location of the image. The noise value corresponds to, for example, measurement noise during a measurement process. An example of multiple images 402 is shown in FIG. Figure 4A , and discussed later in this disclosure.

[0070] In an embodiment, the plurality of images 302 includes a plurality of first images of a printed pattern within a particular die, referred to as an intra-die image of the printed pattern. The plurality of first images may be used to determine an intra-die variation σ in the measurement of the printed pattern of the substrate. intra-die ). In-die variations are discussed later in this disclosure with respect to Figure 7C Further discussion.

[0071] In addition, the plurality of images 302 may include a plurality of second images corresponding to the printed pattern of the plurality of dies of the substrate. The second images are referred to as inter-die images of the printed pattern. The plurality of second images may be used to determine the inter-die variation σ in the measurement results of the printed pattern of the substrate. intra-die ). Die-to-die variations are discussed later in this disclosure with respect to Figure 7C Further discussion.

[0072] In an embodiment, obtaining (e.g., in process P301) an average image 303 involves aligning printed patterns of multiple images 302 relative to each other; identifying locations along the printed patterns of multiple images 302 having relatively high signal values, and aligning the identified locations; and determining the average image by calculating an average of the signal values ​​of the aligned multiple images 302. In an embodiment, aligning the printed patterns of multiple images 302 involves shifting one or more of the multiple images 302 to align corresponding printed patterns of the one or more images with the reference pattern 301 so that differences between the printed patterns of the multiple images 302 are reduced. An example of an average image 403 is shown in FIG. Figure 4A , discussed later in this disclosure. A detailed description of an example method of averaging images can be found in U.S. Application No. 62 / 680,284, filed on June 4, 2018, which is incorporated herein by reference in its entirety.

[0073] Further, in process P302, a composite contour 304 can be obtained from the average image 303. The composite contour 304 of the printed pattern is the contour of the printed pattern obtained from the combined image of the plurality of images 302. In an embodiment, the combined image is the average image 303, and the composite contour 304 is the average contour of the contours of the plurality of images 302 or the average image 303. In an embodiment, obtaining the composite contour 304 involves aligning the images of the printed pattern relative to each other so that the difference between the images is reduced; calculating the average image of all aligned images, and extracting the composite contour 304 from the average image based on a relatively high signal value at a position relative to the reference pattern 301. A detailed description of an example method of averaging images and extracting conforming contours can be found in U.S. Application No. 62 / 680,284 filed on June 4, 2018, which is incorporated herein by reference in its entirety.

[0074] In process P303, the method involves aligning the composite profile 304 of the average image 303 relative to the reference profile of the reference pattern 301, thereby producing an aligned composite profile 313. This process is similar to aligning the composite profile 304 of the average image 303 relative to the reference profile of the reference pattern 301. Fig.9A The discussion is related to the more general die-to-database alignment process.

[0075] In an embodiment, the alignment of the composite contour 304 involves overlapping the composite contour 304 with a reference contour; and offsetting the composite contour 304 within a predefined range so that the difference between the composite contour 304 and the reference contour (of 301) is reduced. In an embodiment, the offsetting of the composite contour 304 involves offsetting the composite contour 304 relative to the center of the predefined range so that the total contour-to-contour distance is reduced; and offsetting the composite contour 304 in a first direction to reduce the difference between the first contour and the contour in the first direction, and / or offsetting in a second direction to reduce the difference between the second contour and the contour in the second direction.

[0076] In process P305, the method involves extracting a primitive contour 315 from a given image in the plurality of images 302 (the primitive image) relative to the aligned composite contour 313. The primitive contour extraction is based on the aligned composite contour 313, the primitive image 302, and the normal direction of each contour point on the aligned composite contour (relative to the angle of the composite contour output in process P303). In an embodiment, extracting a contour in the plurality of contours 315 involves: i) identifying a starting point in the given image relative to the composite contour, ii) finding a direction with the aid of a primitive contour edge search from the output of process P303, and iii) determining the edge position of the primitive contour of the given image in the plurality of images.

[0077] In process P307, the method involves determining a plurality of pattern measurements 317 based on the plurality of contours 315. The pattern measurements 317 are characteristics of the printed pattern and its printing process (e.g., CD, EPE, etc.). In an embodiment, the determination of the pattern measurements involves: defining a set of cutting lines (e.g., referring to Figure 5 traversing a given contour among a plurality of contours; defining a plurality of measuring gauges along the given contour, wherein the measuring gauges are defined at intersections of the cutting line and the given contour; and determining pattern measurements relative to the measuring gauges.

[0078] In an embodiment, pattern measurement 317 is a critical dimension of the printed pattern and / or an edge positioning measurement of the printed pattern relative to reference pattern 301. In an embodiment, the critical dimension in the critical dimension is the distance between two measurement gauges along a horizontal cut line that intersects a given contour (see, e.g., Figure 5 ).

[0079] In an embodiment, the edge location measurement is an edge location error determined along a given profile at a measuring gauge, wherein the edge location error is a difference between the given profile and a reference profile at the given measuring gauge.

[0080] In process P309, the method involves determining measurement data 319, which involves determining a first statistic (σ) corresponding to the printed pattern based on a plurality of measurements associated with a particular die of the substrate (eg, within an image). inter-die ); and / or determining a second statistic (σ ) corresponding to the printed pattern based on a plurality of measurements associated with a particular field position of different dies across the substrate. inter-die ); and / or determining a third statistic associated with the printed pattern (e.g., σ ) based on a plurality of measurements associated with a particular feature within each image field of view (FOV) SEPE ). In an embodiment, the total variation is included as all portions of the measurement data 319 of the printed pattern.

[0081] In an embodiment, the third statistic is the random variation in the measurements of the printed pattern.All other statistics (eg, the first statistic and the second statistic) are the result of other process variations.

[0082] In an embodiment, the first statistic is within-die variation in measurements of a printed pattern of the substrate.

[0083] In an embodiment, the second statistic is the die-to-die variation in measurements of the printed pattern of the substrate, and the third statistic is the within-image field of view (FOV) variation, ie, random variation, where other process variations are assumed to be negligible within the image FOV.

[0084] Figure 4A An example of extracting the outline of a printed pattern from an original image and an example random variation band determined based on the outline of the printed pattern are illustrated.

[0085] exist Figure 4A In the embodiment, reference pattern 401 can be received (e.g., via processor 104), for example, in the form of a GDS / OASIS file format, which is a format different from the SEM image format. Accordingly, the coordinates or positions of the patterns in the image and the GDS format will be different. In an embodiment, reference pattern 401 can be a design layout, or a simulated layout obtained as an output of a process simulation. Reference pattern 401 includes a plurality of features that are desired to be printed on a substrate imaged via a lithographic device. In this example, reference pattern 401 includes horizontal lines and vertical lines with spacing. In another example, reference pattern 401 may include contact holes or other geometric structures corresponding to the IC to be printed on the substrate.

[0086] Reference pattern 401 can be printed at different locations on the substrate. For example, reference pattern 401 can be printed at different locations within a particular die and / or printed across different dies on the substrate. For example, the printed substrate can include thousands or even millions of printed pattern instances corresponding to reference pattern 401. In an embodiment, an image of the printed substrate can be obtained via a measurement tool (e.g., SEM, optical tool, or other image capture tool). Typically, such an image of the substrate is obtained to measure the characteristics of the printed pattern (e.g., CD, EPE, etc.), check the quality of the printed pattern, identify defects in the printed pattern, hot spots, etc.

[0087] A plurality of images 402 (also referred to as raw images 402 for better readability) corresponding to the reference pattern 401 are obtained, for example, by a SEM tool (e.g. Figures 10 to 11 In an embodiment, a plurality of first images are captured from a first die, a plurality of second images are captured from a second die of a substrate, and so on. Each such image includes a printed pattern corresponding to the reference pattern 401. For example, the printed pattern includes horizontal and vertical lines corresponding to the reference pattern 401. However, the printed pattern in the original image 402 may be inconsistent, distorted, and / or include variations due to patterning processes and / or metrology tools.

[0088] In an embodiment, the raw image 402 is distorted, blurred, and / or includes noise components, which makes it difficult to accurately identify the shape, size, and / or contour of the printed pattern. Nevertheless, a denoising filter may be applied to partially or completely remove noise from the image, from which the contour and corresponding measurement may be inaccurate because the SEM measurement process itself may involve process inaccuracies, such as the electron beam may affect the resist during the capture of the substrate image, thereby capturing a distorted image. Therefore, in order to accurately measure the printed pattern, additional image processing (e.g., averaging process, process P303 and P305) is performed as shown in Figure 3 In an embodiment, the combined image reduces the effects of noise or other forms of error that may be present in any individual image. In one embodiment, the combined image may be generated by averaging multiple measurement images. In other embodiments, the multiple measurement images may be aligned prior to combining or averaging. An example method for obtaining an averaged image is discussed in U.S. Application No. 62 / 680,284, filed on June 4, 2018, which is incorporated herein by reference in its entirety.

[0089] In an embodiment, the raw images 402 are aligned relative to each other to determine the average image 403. Such alignment involves raw images corresponding to different dies by shifting one or more raw images relative to each other. For example, the alignment involves offsetting one or more images so that portions of the images with relatively high signal-to-noise ratios are overlapped. In an embodiment, the offset is limited to a specific range (e.g., within a range of 0.05 nm to 1 nm) around pixel locations where signal values ​​are relatively high. Examples of signals in an image are as follows: Figure 4B shown.

[0090] exist Figure 4B , an example raw image 402 and a signal 402sig along a line at the center of the raw image 402 are shown. The peak value of the signal 402sig (e.g., approximately 200) indicates a strong signal and a weak signal (e.g., approximately 75 to 100 values). The signal 402sig also includes noise, so the signal 402sig is noisy (e.g., approximately a value of 100). Due to the noise, the raw image 402 is noisy, and a denoising filter may be required to remove the noise and improve the signal-to-noise ratio. On the other hand, the average image 403 has relatively little or no noise. Therefore, compared to the raw image 402, the signal along the line at the center has less noise and a relatively higher signal-to-noise ratio.

[0091] In an embodiment, the original image 402 can be a pixelated image, in which case pixels with relatively high intensity values ​​are aligned relative to corresponding positions of pixels in other images. For example, pixel positions within a first original image with relatively high pixel values ​​can be identified and aligned with corresponding pixel positions of a second original image. However, the other images may not have high pixel intensities at the same location, but are very close near a given pixel location. Therefore, sub-pixel adjustments of the second image can be performed to better align the printed patterns of the first image and the second image. Once the images 402 are aligned, the average image 403 can be calculated by taking the average of each of the positions within the image 402.

[0092] Average image 403 includes an average printed pattern having relatively sharper boundaries than those seen in original image 402 (see, for example, Figure 4B Further, a composite contour 404 is extracted from the average image 403, thereby averaging out any inaccuracies in the original image 402.

[0093] In an embodiment, (for example, in Figure 3303), an aligned composite profile can be determined by aligning the composite profile from the average image 403 with a simulated profile of a reference pattern 401 (not shown). The alignment process can be an iterative process in which the difference between the composite profile and the reference profile of the reference pattern 401 is reduced (in an embodiment, minimized). This alignment process also ensures that the resulting composite profile 404 corresponds to the position (e.g., GDS position) of the design pattern typically used during patterning process simulation. In an embodiment, this composite profile 404 can be used for patterning process simulation to optimize various aspects of the patterning process such as OPC, mask, resist, etc. However, the use of the composite profile 404 does not retain information related to the random variations of the printed pattern, which may help to further improve pattern measurement and optimization of the patterning process.

[0094] In an embodiment, (e.g., as discussed in process P305), the aligned composite contour from the average image is also used to guide the extraction of the contour 415 of the printed pattern in the original image 402 (e.g., SEM image). Extracting the contour from the SEM image 402 involves i) identifying the starting point in the given image relative to the composite contour, ii) finding the direction of the point used for contour edge search with the output of process P303, and iii) determining the edge position of each contour point of the original image.

[0095] Once the outline of the printed pattern in the original image 402 is extracted, the extracted outlines 415 can be overlapped with each other to determine the variation band (e.g., band 419) of the printed pattern. The variation band indicates that the reference pattern 401 is not printed uniformly or has different sizes / shapes at different locations on the substrate. The band is an estimate of the total variation. Part of this variation is due to random variation, and the other part comes from the patterning process and / or the measurement process (e.g., in a SEM tool or other measurement tool). Therefore, each variation information (e.g., random variation, inter-die variation, intra-die variation, etc.) associated with each original image 402 in the original image 402 is decomposed and retrieved in subsequent data analysis. In an embodiment, a random variation band 419 can be determined based on the measurement results associated with the extracted original outline (e.g., discussed in processes P307 and P309). This random variation band 419 can also be used to improve the existing patterning process, thereby improving the yield of the patterning process (e.g., printed patterns with fewer defects).

[0096] In an embodiment, measurements may be performed on the random variation band 419 and / or the original contour 415, as illustrated in the measurements 425 performed along the edge of the extracted contour relative to the reference contour. Figure 3 As discussed in , measurement 425 involves defining a cut line and a gauge along a contour, such as at the intersection of the cut line and the contour. Example measurement based on gauge positioning relative to Figure 5Illustrations and discussion.

[0097] exist Figure 5 In the figure, the profile 501 can be an extracted profile, a profile from an average image or an original image, or a reference profile. For measurement, different cutting lines can be defined based on the geometry of the profile and the location that needs to be measured. For example, for a curved portion, cutting lines CL1 and CL5 are angular cutting lines originating from the corresponding centers of the curved portion of the profile 501. For a relatively straight portion, cutting lines CL2, CL3, and CL4 are horizontal cutting lines vertically separated along the length of the profile 501. Cutting line CL1 intersects the profile 501 at EP1 to EP8, which are example gauge points where measurement results can be determined. For example, the vertical distance D1 between the cutting lines associated with gauge points EP7 and EP8 can be determined, or the cutting lines can be positioned using a uniform angle between EP7 and EP8, the distance D2 between gauge points EP11 and EP13 can be determined, and the horizontal dimension (example of CD) between EP10 and EP11 (EP12 and EP13, or EP14 and EP15) can be measured. In an embodiment, the measurement result is a characteristic of a feature and / or a printed pattern. Such a measurement may be determined for each of the contours extracted from the original image (eg, 415 ), which may also be used to determine the random variation band (eg, 419 ).

[0098] One of the advantages of measurements based on profiles extracted according to the present disclosure is that separate methods for measuring 1D features (e.g., LWR) and 2D features (e.g., LCDU) of a printed pattern do not need to be used. The present method provides a joint solution (e.g., in the form of random variation bands) for measuring different feature types (e.g., 1D, 2D, etc.), thereby providing a joint basis for comparing and modeling the effects of random variation and modifying different aspects of the patterning process to improve the yield of the patterning process.

[0099] Fig. 6A An example measurement related to a 1D pattern including vertical lines is illustrated. Fig. 6A , the average image 603 includes three vertical lines with similar CD specifications (e.g., width of 55 nm). Figure 4A ), when an original image corresponding to such a pattern is obtained and a measurement is performed, a random variation band 619 associated with the average profile of the average image 603 is obtained. Band 619A is just an enlarged version of a portion of the random band 619 provided for better visual understanding. In an embodiment, the measurement result may be a CD value illustrated by a bar graph. The bar graph illustrates the variation of the CD value of the printed pattern based on the average image 603. This information of the CD value variation can also be used to extract die-to-die, intra-die, intra-image FOV and total variation, and improve the patterning process (e.g., OPC).

[0100] Figure 6B An example measurement related to a 2D pattern including contact holes is shown. Average image 623 includes multiple contact holes with similar CD specifications (e.g., a diameter of 75 nm). As discussed above (e.g., in Figure 4A ), when an original image corresponding to such a pattern is obtained and a measurement is performed, a random variation band 629 associated with the average profile of the average image 623 is obtained. Band 629A is just an enlarged version of a portion of the random band 629 provided for better visual understanding. In an embodiment, the measurement result may be a CD value (e.g., diameter) illustrated by a bar graph 627. The bar graph 627 illustrates the variation of the CD value of the printed pattern based on the average image 623. Similar to a 1D pattern, the information of the CD value variation can also be used to extract die-to-die, intra-die, intra-image FOV and total variation, and improve the patterning process (e.g., OPC).

[0101] Figure 6C Another example measurement related to a 2D pattern including a combination of horizontal and vertical lines is illustrated. Fig. 6A , the average image 633 and the original image associated with the desired 2D pattern are used to obtain the measurement results and the random variation band 639 (and the magnified portion 639A) associated with the average profile of the average image 633. In an embodiment, the measurement results may be CD values ​​illustrated by the bar graph 637. The bar graph 637 illustrates the variation of the CD value of the printed pattern based on the average image 633. Such information of the variation of the CD value can also be used to extract the inter-die, intra-die, intra-image FOV and total variation, improving the patterning process (e.g., OPC).

[0102] It should be noted that in Fig. 6A , 6B In 6C, although the patterns are of different types, including 1D and 2D patterns, the measurements are performed in the same measurement system, as opposed to being performed in separate systems, such as LWR for 1D and LCDU for 2D. Furthermore, in an embodiment, not only are the measurements joint, but LWR and LCDU can also be determined based on the original image and random variation bands (e.g., using a gauge).

[0103] In an embodiment, different variations of the measurements may be determined based on raw images corresponding to inter-die and / or intra-die and / or intra-image FOVs, for example using Figure 7B , 7C Discussed with 7D.

[0104] Fig. 7A An example raw image is shown that accounts for all variations (e.g., die-to-die and intra-die process variations as well as measurement-related variations). Figure 7B , 7C7D illustrate how separate changes called intra-die, inter-die, and intra-image FOV changes are calculated. Fig. 7A contributes significantly to or explains most of the variation in .

[0105] exist Fig. 7A In the figure, the original images correspond to different tube cores (e.g., Die1, Die2, Die3) of the substrate. Each original image includes a set of patterns, which includes five contact holes. Such printed patterns in the image are associated with a reference pattern (not shown) including five reference contact holes (not shown). For example, the first original image Die1 is an animation of an SEM image of a first tube core of a printed substrate, which includes four patterns (e.g., P11, P12, P13, P14), each having five contact holes. Similarly, the second original image Die2 of the second tube core includes four patterns (e.g., P21, P22, ...), each having five contact holes, and the third original image Die3 of the third tube core includes four patterns (e.g., P31, P32, ...), each having five contact holes. In an embodiment, a probability distribution function of a metric such as CD pdf is associated with such a change represented as σ-all.

[0106] Figure 7B Four patterns P11, P12, P13, and P14 are illustrated, each having a set of five contact holes. In this case, the intra-die variation σ-intra_die of a particular die (e.g., a first die image) is determined based on the variation of the four patterns P11 to P14 within the particular die. Similarly, the intra-die variation of the second die and the third die can be determined based on the four patterns within each of the dies. In an embodiment, a probability distribution function of a metric (e.g., CD pdf) for each die is associated with each such variation denoted as σ-intra_die.

[0107] Figure 7C The diagram shows die-to-die variations, i.e., variations in a particular pattern on different dies. For example, a variation (e.g., in CD) is a variation in a third pattern set P13, P23, P33 (e.g., in Fig. 7A The upper left corner of each die in is determined in σ-inter_die). Similarly, variations of other pattern sets may be determined. In an embodiment, a probability distribution function of a metric (eg, CDpdf) on different dies is associated with this variation denoted as σ-inter_die.

[0108] Additionally, random variations in the image (e.g., FOV within the image) (e.g., random edge location errors SEPE) can be determined. Fig.7DThe variation σ-SEPE in five contact holes within the FOV and the pdf associated with the variation σ-SEPE are illustrated. Similarly, this variation can be determined for other sets of images. The final σ-SEPE can be from a single image or a set of images with various combinations.

[0109] Fig. 8A is an example flow chart of a process for obtaining an average image based on a die-to-die alignment process that may be used in process P301. In an embodiment, the raw images may be pre-processed to remove noise, such as via a denoising filter. In an embodiment, averaging of raw images 302 may involve, in step P801, grouping raw images that include similar patterns, or grouping raw images of a particular die having similar printed patterns, or other grouping methods. In step P803, the process involves aligning the printed patterns of the plurality of images relative to each other. In an embodiment, the alignment of the printed patterns is such that the aligned images best match the reference pattern.

[0110] In step P805, the process involves identifying locations along the printed patterns of the plurality of images, e.g., having relatively high signal values, and performing alignment based on the identified locations. In an embodiment, aligning based on the signal value involves shifting one or more of the plurality of images to align the corresponding printed patterns of the one or more images with the reference pattern such that the difference between the printed patterns of the plurality of images is reduced (in an embodiment, minimized). In an embodiment, the shifting of the one or more images is limited to a certain predefined range. After shifting in an iterative manner, a common region of the image having a high signal-to-noise ratio is obtained. Figure 8B An example sub-pixel alignment is shown, such as used in step P805. Figure 8B , images I1 , I2 , and I3 (which are examples of original image 302 ) are offset relative to each other, resulting in a common area CA having a relatively high signal-to-noise ratio compared to other offset combinations of images 302 .

[0111] Once the original images 302 are aligned, in step P807, an average image 303 is determined by calculating the average of the signal values ​​of the aligned multiple images. The resulting average image 303 has a better defined contour than the original image 302, which has a very high signal-to-noise ratio. Further, a high-quality composite contour 304 of the average image can be extracted and also used to guide the original image contour extraction, for example in Fig.9A discussed in .

[0112] Fig.9Ais an example flow chart of a die-to-database alignment process 900. In an embodiment, the D2DB alignment converts the SEM contour addresses from SEM image coordinates to GDS coordinates so that the SEM contour can be compared with a reference contour (a simulated contour on the GDS). According to an embodiment, this D2DB operation allows finding contour point directions, for example for contour adjustment in a subsequent stage such as extracting contours from an original image.

[0113] The die-to-database alignment can be used to align a composite contour (e.g., 304) or contour of an original image 302 (e.g., contour of a printed pattern in an SEM image) with a reference pattern 301 (e.g., a design layout in a GDS, other desired pattern). This die-to-database alignment ensures that locations within an image (original image or average image) are converted to locations in a format for a reference pattern (e.g., GDS locations). Process 900 can be used, for example, in process P303 to align contours, such as average contours or contours extracted from an original image 302 based on average contours.

[0114] In step P901, process 900 involves aligning, for example, composite contour 304 (or contours of the original image) with reference contours of reference pattern 301 such that contour-to-contour differences are reduced (in an embodiment, minimized). In step P901, contour alignment may be iterative, wherein composite contour 304 is moved within a range relative to the reference contour such that contour-to-contour differences are minimized. For example, Fig. 9B An example alignment of a composite contour 904 with a reference contour 901 including four contact holes and a vertical line is illustrated. The reference contour 901 has a center 901c and the average contour has a center 904c. The composite contour 904 is also associated with a predefined range 910 for movement / offset of the average contour. In an embodiment, the contour-to-contour difference includes a distance 912, which can be gradually reduced, e.g., minimized, by moving (e.g., leftward) the average contour within the predefined range 910. In an embodiment, the contour-to-contour distance can be relative to an edge of the reference contour and a corresponding edge of the composite contour.

[0115] In an embodiment, the difference from profile to profile is an absolute error value (e.g., the sum of the EPE at different gauge points). In an embodiment, the difference from profile to profile can be expressed in terms of angles, such as the cut line angle at a bend (e.g., see Figure 5 Cutting lines CL1 and CL5).

[0116] Further, in step P903, process 900 involves a second alignment, for example to minimize profile-to-profile differences in a particular direction, such as misalignment errors in the X and / or Y directions.

[0117] In an embodiment, the device may be configured to extract contours based on the measurement data 319 (e.g., random variations). In an embodiment, such extraction may be real-time, such as a metrology tool deployed in a high volume manufacturing (HVM) setting. In an embodiment, the metrology tool includes, for example, a processor 104 that executes method 300, or simply receives a predetermined SEPE. In addition, the device may be configured to update (via a processor), for example, a SEPE band based on a new image. Prior to the update, the contours may be extracted from the new image, as discussed in method 300, such as in process P305.

[0118] In an embodiment, an apparatus is configured to extract a contour from a metrology or raw image, the apparatus comprising a processor (e.g., processor 104) configured to: obtain (i) a metrology image of a substrate having a printed pattern, (ii) an average image of the printed pattern, (iii) extract a composite contour from the average image, (iv) align the composite contour with a reference pattern, (v) extract a raw contour from the raw image, (vi) measure the raw contour based on a pre-positioned cutting line, and (vii) extract measurement static data, such as intra-die variation, inter-die variation, and intra-image FOV variation, i.e., random variation σ sepe .

[0119] In an embodiment, extracting the contour from the original image involves: using a point on the composite contour from the average image as a starting point, and using the normal direction angle of the D2DB alignment of the composite contour to the reference contour at the point as a direction for contour edge finding and determining the original contour edge position. In an embodiment, the processor is also configured to determine pattern measurements based on the extracted contour (e.g., discussed earlier in method 300).

[0120] In some embodiments, a scanning electron microscope (SEM) produces images of structures exposed or transferred onto a substrate (eg, some or all of the structures of a device). Fig.10 Depicted is an embodiment of a SEM 200. A primary electron beam 202 emitted from an electron source 201 is converged by a condenser lens 203 and then passes through a beam deflector 204, an ExB deflector 205 and an objective lens 206 to illuminate a substrate 100 on a substrate stage 101 at a focal point.

[0121] When the substrate 100 is irradiated with the electron beam 202, secondary electrons are generated from the substrate 100. The secondary electrons are deflected by the ExB deflector 205 and detected by the secondary electron detector 207. The two-dimensional electron beam image can detect the electrons generated from the sample by synchronizing with, for example, two-dimensional scanning of the electron beam by the beam deflector 204 or repeated scanning of the electron beam 202 in the X or Y direction by the beam deflector 204, together with continuous movement of the substrate stage 101 to the substrate 100 in the other of the X or Y directions.

[0122] The signal detected by the secondary electron detector 207 is converted into a digital signal by an analog / digital (A / D) converter 208, and the digital signal is sent to the image processing system 3000. In an embodiment, the image processing system 3000 may have a memory 3003 to store all or part of the digital image for processing by a processing unit 3004. The processing unit 3004 (e.g., specially designed hardware or a combination of hardware and software) is configured to convert or process the digital image into a data set representing the digital image. Further, the image processing system 3000 may have a storage medium 3001, which is configured to store the digital image and the corresponding data set in a reference database. A display device 3002 may be connected to the image processing system 3000 so that an operator can perform necessary operations on the device with the aid of a graphical user interface.

[0123] Fig.18 A further embodiment of the inspection device is schematically illustrated. The system is used to inspect a sample 90 (such as a substrate) on a sample stage 89 and includes a charged particle beam generator 81, a focusing lens module 82, a probe forming objective lens module 83, a charged particle beam deflection module 84, a secondary charged particle detector module 85 and an image forming module 86.

[0124] The charged particle beam generator 81 generates a primary charged particle beam 91. The focusing lens module 82 converges the generated primary charged particle beam 91. The probe forming objective module 83 focuses the converged primary charged particle beam into the charged particle beam probe 92. The charged particle beam deflection module 84 scans the formed charged particle beam probe 92 across the surface of the region of interest on the sample 90 fixed on the sample stage 89. In an embodiment, the charged particle beam generator 81, the focusing lens module 82 and the probe forming objective module 83 or their equivalent designs, substitutes or any combination thereof together form a charged particle beam probe generator, which generates a scanning charged particle beam probe 92.

[0125] The secondary charged particle detector module 85 detects the secondary charged particles 93 emitted from the sample surface (and possibly also together with other reflected or scattered charged particles from the sample surface) when bombarded by the charged particle beam probe 92 to generate a secondary charged particle detection signal 94. An image forming module 86 (e.g., a computing device) is coupled to the secondary charged particle detector module 85 to receive the secondary charged particle detection signal 94 from the secondary charged particle detector module 85 and thereby form at least one scanned image. In an embodiment, the secondary charged particle detector module 85 and the image forming module 86 or their equivalent designs, substitutes, or any combination thereof together form an image forming device that forms a scanned image from the detected secondary charged particles emitted by the sample 90 bombarded by the charged particle beam probe 92.

[0126] As mentioned above, SEM images can be processed to extract contours describing the edges of objects in the image that represent device structures. These contours are then quantified via metrics such as CD. Therefore, typically, images of device structures are compared and quantified via simple metrics, such as edge-to-edge distance (CD) or simple pixel differences between images. Typical contour models for detecting object edges in images to measure CD use image gradients. In fact, these models rely on strong image gradients. However, in practice, images are usually noisy and have discontinuous boundaries. Techniques such as smoothing, adaptive thresholding, edge detection, erosion, and dilation can be used to process the results of image gradient contour models to resolve noisy and discontinuous images, but ultimately result in low-resolution quantization of high-resolution images. Therefore, in most instances, mathematical operations and automatic edge detection of device structure images to reduce noise result in a loss of image resolution, resulting in information loss. Therefore, the result is a low-resolution quantization that is equivalent to a simple representation of a complex high-resolution structure.

[0127] Thus, it is desirable to have a mathematical representation of a structure (e.g., a circuit feature, an alignment mark, or a portion of a metrology target (e.g., a grating feature), etc.) produced or expected to be produced using a patterning process, whether, for example, the structure is in a latent resist image, in a developed resist image, or a layer transferred to a substrate, for example, by etching, which can maintain resolution and also describe the general shape of the structure. In the context of a lithography or other patterning process, the structure can be a device being manufactured or a portion thereof, and the image can be a SEM image of the structure. In some instances, the structure can be a feature of a semiconductor device (e.g., an integrated circuit). In some instances, the structure can be an alignment mark or a portion thereof (e.g., a grating of an alignment mark) that is used in an alignment measurement process to determine the alignment of an object (e.g., a substrate) with another object (e.g., a patterning device) or a metrology target or a portion thereof (e.g., a grating of a metrology target) for measuring parameters of the patterning process (e.g., overlay, focus, dose, etc.). In an embodiment, the metrology target is a diffraction grating for measuring, for example, overlay.

[0128] In the embodiment, according to Figure 3The measured data (e.g., random variations) associated with the printed pattern determined by the method can be used to optimize the patterning process or adjust the parameters of the patterning process. As an example, OPC addresses the fact that the final size and positioning of the image of the design layout projected onto the substrate will not be the same as, or will only depend on, the size and positioning of the design layout on the pattern forming device. It should be noted that the terms "mask", "reticle", and "pattern forming device" are used interchangeably herein. Moreover, those skilled in the art will recognize that, particularly in the context of lithography simulation / optimization, the terms "mask" / "pattern forming device" and "design layout" can be used interchangeably, because in lithography simulation / optimization, a physical pattern forming device is not necessarily used, but a design layout can be used to represent a physical pattern forming device. For the small feature sizes and high feature densities present on a certain design layout, the position of a particular edge of a given feature will be affected to some extent by the presence or absence of other adjacent features. These proximity effects are caused by trace radiation and / or non-geometric optical effects (such as diffraction and interference) coupled from one feature to another. Similarly, proximity effects may be caused by diffusion and other chemical effects during the post-exposure bake (PEB), resist development, and etching that typically follows lithography.

[0129] To ensure that the projected image of the design layout is in accordance with the requirements of a given target circuit design, proximity effects need to be predicted and compensated using, for example, complex numerical models, corrections or pre-distortions of the design layout. An overview of the current "model-based" optical proximity correction process is provided by C. Spence in the 2005 Proc. SPIE, Vol. 5751, pp. 1-14. Almost every feature of the design layout is modified in some way in a typical high-end design so that the projected image has high fidelity to the target design. These modifications can include shifting or biasing of edge locations or line widths and the application of "helper" features designed to assist in the projection of other features.

[0130] Given that there are typically millions of features in a chip design, applying model-based OPC to a target design involves good process models and significant computational resources. However, applying OPC is typically not an “exact science” but rather an empirical, iterative process that does not always compensate for all possible proximity effects. Therefore, the effects of OPC (e.g., on the design layout after applying OPC and any other RET) need to be verified through design checking, i.e., intensive full-chip simulations using calibrated digital process models to minimize the likelihood of design defects making their way into the patterning device pattern. This is driven by the enormous cost of manufacturing high-end patterning devices, which run in the multi-million dollar range, and by the impact on turnaround time of rework or repair after the actual patterning device has been fabricated.

[0131] OPC and full-chip RET verification can be based on digital modeling systems and methods, such as those described in U.S. patent application Ser. No. 10 / 815,573 and in an article by Y. Cao et al. entitled “Optimized Hardware and Software For Fast, Full Chip Simulation” published in Proc. SPIE, Vol. 5754, p. 405, 2005.

[0132] A RET is related to adjusting the global bias of the design layout. The global bias is the difference between the pattern in the design layout and the pattern intended to be printed on the substrate. For example, a circular pattern with a diameter of 25nm can be printed on the substrate by using a pattern with a diameter of 50nm in the design layout or a pattern with a diameter of 20nm in the design layout but using a high dose.

[0133] In addition to optimizing the design layout or patterning device (e.g., OPC), the illumination source can also be optimized, either in conjunction with or separately from patterning device optimization, to improve overall lithography fidelity. The terms "irradiation source" and "source" are used interchangeably in this document. Since the 1990s, a variety of off-axis illumination sources, such as annular, quadrupole, and dipole, have been introduced and provide greater freedom for OPC design, thereby improving imaging results. As is well known, off-axis illumination is a proven method for resolving fine structures (i.e., target features) contained in patterning devices. However, off-axis illumination sources typically provide less radiation intensity for aerial images (AI) than conventional illumination sources. Therefore, it is desirable to attempt to optimize the illumination source to achieve an optimal balance between finer resolution and reduced radiation intensity.

[0134] Many illumination source optimization methods can be found, for example, in an article by Rosenbluth et al., entitled “Optimum Mask and Source Patterns to Print AGiven Shape”, published in Microlithography, Microfabrication Microsystems 1 (1), pp. 13-20, 2002. The source is divided into a plurality of regions, each corresponding to a certain region of the pupil spectrum. It is then assumed that the source distribution in each source region is uniform and that the brightness of each region is optimized for the process window. However, this assumption of uniform source distribution in each source region is not always valid, and thus the effectiveness of this method is affected. In another example set forth in an article by Granik, entitled “Source Optimization for Image Fidelity and Throughput”, published in Microlithography, Microfabrication Microsystems 3 (4), pp. 509-522, 2004, a variety of existing source optimization methods are outlined, and an illuminator pixel-based method that converts the source optimization problem into a series of non-negative least squares optimizations is proposed. Although these methods have demonstrated some success, they typically require multiple complex iterations to converge. In addition, it may be difficult to determine the appropriate / optimal values ​​of some additional parameters, such as γ in Granik's method, which specifies the trade-off between the source and the smoothness requirement of the source to optimize substrate image fidelity.

[0135] For low k1 lithography, optimization of source and pattern forming device is very useful to ensure feasible process window for projection of key circuit patterns. Some algorithms (such as Socha et al., published in Proc. SPIE Vol. 5853, p. 180 in 2005) discretize the illumination into independent source points and the mask into diffraction orders in the spatial frequency domain, and separately formulate cost functions (defined as functions of selected design variables) based on process window metrics (such as exposure latitude), which can be predicted by optical imaging models through source point intensity and pattern forming device diffraction orders. The term "design variables" used in this article includes a set of parameters of a lithography projection device or a lithography process, such as parameters that a user of a lithography projection device can adjust, or image characteristics that a user can adjust by adjusting those parameters. It should be understood that any characteristics of the lithography projection process (including those characteristics of the source, pattern forming device, projection optical device, and / or resist characteristics) can be design variables in optimization. The cost function is usually a nonlinear function of the design variables. Standard optimization techniques are then used to minimize the cost function.

[0136] Relatedly, the pressure of ever-reducing design rules has driven semiconductor chip manufacturers to move deeper into the low-k1 lithography era using existing 193nm ArF lithography. The move toward lower k1 lithography places high demands on RET, exposure tools, and the need for lithography-friendly design. 1.35ArF ultra-numerical aperture (NA) exposure tools may be used in the future. To help ensure that circuit designs can be produced on substrates with a viable process window, source patterning device optimization (referred to herein as source mask optimization or SMO) is becoming an important RET for the 2xnm node.

[0137] Source and pattern forming device (design layout) optimization methods and systems that allow the use of cost functions to simultaneously optimize the source and pattern forming devices without constraints and within the available time amount are described in commonly assigned International Patent Application No. PCT / US2009 / 065359, which was filed on November 20, 2009 and published as WO2010 / 059954, entitled "Fast Freeform Source and Mask Co-Optimization Method", which is incorporated herein by reference in its entirety.

[0138] Another source and mask optimization method and system involving optimizing a source by adjusting pixels of the source is described in commonly assigned U.S. patent application Ser. No. 12 / 813,456, filed on Jun. 10, 2010 and published as U.S. Patent Application Publication No. 2010 / 0315614, entitled “Source-Mask Optimization in Lithographic Apparatus,” which is incorporated herein by reference in its entirety.

[0139] As an example, in a lithographic projection apparatus, the cost function is expressed as

[0140]

[0141] where (z1,z2,…,z N ) are N design variables or their values. p (z1,z2,…,z N ) can be the design variables (z1,z2,…,z N ), such as for (z1,z2,…,z N ) is the difference between the actual and expected values ​​of a characteristic at the evaluation points for a set of values ​​of the design variables. p is with f p (z1,z2,…,z N) is associated with a weight constant. A more critical evaluation point or pattern can be assigned a higher w than other p Patterns and / or evaluation points that occur more often may also be assigned higher values ​​of w p Examples of evaluation points may be any physical point or pattern on the substrate, any point on the virtual design layout or resist image or aerial image, or a combination thereof. p (z1,z2,…,z N ) can also be a function of one or more random effects, such as LWR, which are the design variables (z1,z2,…,z N ). The cost function may represent any suitable characteristic of the lithographic projection apparatus or substrate, such as a failure rate of a feature, focus, CD, image offset, image distortion, image rotation, random effects, yield, CDU, or a combination thereof. CDU is the local CD variation (e.g., three times the standard deviation of the local CD distribution). CDU may be interchangeably referred to as LCDU. In one embodiment, the cost function represents (i.e., is a function of) CDU, yield, and random effects. In one embodiment, the cost function represents (i.e., is a function of) EPE, yield, and random effects. In one embodiment, the design variables (z1, z2, ..., z N ) may include dose, global bias of the patterning device, shape of the illumination from the source, or a combination thereof. Since the resist image typically defines the circuit pattern on the substrate, the cost function typically includes a function representing some characteristic of the resist image. For example, f at such an evaluation point p (z1,z2,…,z N ) can simply be the distance between a point in the resist image and the expected position of that point (i.e., the edge positioning error EPE p (z1,z2,…,z N )). The design variables can be any adjustable parameters, such as adjustable parameters of the source, pattern forming device, projection optical device, dose, focus, etc. The projection optical device may include components collectively referred to as "wavefront manipulators", which can be used to adjust the shape and intensity distribution of the wavefront and / or the phase shift of the radiation beam. The projection optical device can preferably adjust the wavefront and intensity distribution at any position along the optical path of the lithographic projection device, such as before the pattern forming device, near the pupil plane, near the image plane, near the focal plane. The projection optical device can be used to correct or compensate for certain distortions of the wavefront and intensity distribution caused by, for example, temperature changes in the source, pattern forming device, lithographic projection device, thermal expansion of components of the lithographic projection device. Adjusting the wavefront and intensity distribution can change the value of the evaluation point and the cost function. This change can be simulated from a model or actually measured. Of course, CF(z1,z2,…,z N ) is not limited to the form in Equation 1. CF(z1,z2,…,zN ) may be in any other suitable form.

[0142] It should be noted that f p (z1,z2,…,z N ) is defined as Therefore, minimizing f p (z1,z2,…,z N ) is equivalent to minimizing the cost function defined in Equation 1 Therefore, for simplicity of notation in this paper, f p (z1,z2,…,z N ) and the weighted RMS of Equation 1 can be used interchangeably.

[0143] Further, if maximizing PW (process window) is considered, the same physical location from different PW conditions can be regarded as different evaluation points in the cost function in (Equation 1). For example, if N PW conditions are considered, the evaluation points can be classified according to their PW conditions, and the cost function can be written as:

[0144]

[0145] in Under the u-th PW condition u=1,…,U, it is f p (z1,z2,…,z N ) value. When f p (z1,z2,…,z N ) is the EPE, then minimizing the above cost function is equivalent to minimizing the edge offset under various PW conditions, resulting in maximizing PW. Specifically, if PW also consists of different mask biases, then minimizing the above cost function also includes minimizing MEEF (mask error enhancement factor), which is defined as the ratio between the substrate EPE and the induced mask edge bias.

[0146] The design variables may have constraints, which can be expressed as (z1,z2,…,z N)∈Z, where Z is a set of possible values ​​of the design variables. One possible constraint on the design variables may be imposed by the yield or expected output of the lithography projection equipment. The expected yield or output may limit the dose and therefore have an impact on the random effects (e.g., impose a lower limit on the random effects). Higher yields typically result in lower doses, shorter exposure times, and larger random effects. Higher yields typically result in constrained designs that can be sensitive to random risks. Since random effects are functions of design variables, minimization of substrate yield, yield, and random effects may constrain the possible values ​​of the design variables. In the absence of such constraints imposed by the expected output, optimization may produce a set of unrealistic values ​​of the design variables. For example, if the dose is in the design variable, without such constraints, the optimization may produce dose values ​​that make the output economically impossible. However, the usefulness of the constraint should not be interpreted as necessity. The output may be affected by the adjustment of patterning process parameters based on the failure rate. It is desirable to have a lower feature failure rate while maintaining a high output. The output may also be affected by the resist chemistry. Slower resists (e.g., those that require more light to be properly exposed) result in lower yields. Therefore, appropriate parameters for the patterning process can be determined based on an optimization process involving feature failure rates due to resist chemistry or fluctuations and dose requirements for higher yields.

[0147] Therefore, the optimization process is performed under the constraints (z1,z2,…,z N )∈Z, find the set of design variable values ​​that minimizes the cost function, that is, find

[0148]

[0149] According to an embodiment, a general method for optimizing a lithographic projection apparatus is Fig.12. The method includes a step S1202 of defining a multivariate cost function for a plurality of design variables. The design variables may include any suitable combination selected from characteristics of the illumination source (1200A) (e.g., pupil fill rate, i.e., the percentage of radiation of the source that passes through the pupil or aperture), characteristics of the projection optics (1200B), and characteristics of the design layout (1200C). For example, the design variables may include characteristics of the illumination source (1200A) and characteristics of the design layout (1200C) (e.g., global bias), but not characteristics of the projection optics (1200B) that result in SMO. Alternatively, the design variables may include characteristics of the illumination source (1200A), characteristics of the projection optics (1200B), and characteristics of the design layout (1200C), which result in source-mask-lens optimization (SMLO). In step S1204, the design variables are adjusted simultaneously so that the cost function moves toward convergence. In step S1206, it is determined whether a predefined termination condition is met. The predefined termination conditions may include various possibilities, namely, the cost function may be minimized or maximized, the value of the cost function has equaled a threshold or has exceeded a threshold, depending on the requirements of the numerical technique used, the value of the cost function has reached a preset error limit, or a preset number of iterations has been reached. If any of the conditions in step S1206 is met, the method ends. If no condition in step S1206 is met, steps S1204 and S1206 are iteratively repeated until the desired result is obtained. Optimization does not necessarily result in a single set of design variable values, as there may be physical limitations caused by factors such as failure rate, pupil fill factor, resist chemistry, output, etc. Optimization may provide multiple sets of values ​​for design variables and associated performance characteristics (e.g., output), and allow a user of the lithographic apparatus to select one or more sets.

[0150] In a lithographic projection apparatus, a source, a patterning device, and a projection optics may be optimized alternatively (referred to as alternative optimization) or simultaneously (referred to as simultaneous optimization). As used herein, the terms "simultaneously," "simultaneously," "jointly," and "jointly" refer to design variables of characteristics of a source, a patterning device, a projection optics, and / or any other design variables being allowed to be changed at the same time. As used herein, the terms "alternatively" and "alternatively" mean that not all design variables are allowed to be changed simultaneously.

[0151] exist Fig.13 In the process, the optimization of all design variables is performed simultaneously. This process can be called a simultaneous process or a collaborative optimization process. Alternatively, the optimization of all design variables is performed alternatively, such as Fig.13As shown in the figure. In this process, in each step, some design variables are fixed while other design variables are optimized to minimize the cost function; then in the next step, a different set of variables is fixed while other variables are optimized to minimize the cost function. These steps are performed alternately until convergence or some termination condition is met.

[0152] like Fig.13 As shown in the non-limiting example flow chart of , first the design layout (step S1302) is obtained, and then the source optimization step is performed in step S1304, where all design variables of the illumination source are optimized (SO) to minimize the cost function, while all other design variables are fixed. Then in the next step S1306, the mask optimization (MO) is performed, where all design variables of the pattern forming device are optimized to minimize the cost function, while all other design variables are fixed. These two steps are alternatively performed until some termination conditions are met in step S1308. Various termination conditions can be used, such as the value of the cost function becomes equal to a threshold, the value of the cost function exceeds a threshold, the value of the cost function reaches a preset error limit, or a preset number of iterations is reached, etc. It is noted that SO-MO alternative optimization is used as an example of an alternative process. The alternative process can take many different forms, such as SO-LO-MO alternative optimization, where SO, LO (lens optimization) are performed, and MO is alternatively and iteratively performed; or SMO can be performed first, and then LO and MO are alternatively and iteratively performed; and so on. The output of the final optimization result is obtained in step S1310, and the process stops.

[0153] As previously discussed, the pattern selection algorithm can be integrated with simultaneous or alternative optimization. For example, when alternative optimization is employed, first the full chip SO can be performed, the 'hot spots' and / or 'warm spots' are identified, and then the MO is performed. In view of the present disclosure, multiple permutations and combinations of sub-optimizations are possible in order to achieve the desired optimization results.

[0154] Fig.14AAn exemplary optimization method is shown in which a cost function is minimized. In step S502, initial values ​​of the design variables are obtained, including their tuning ranges, if any. In step S504, a multivariate cost function is set. In step S506, the cost function is expanded within a sufficiently small neighborhood around the starting point values ​​of the design variables for the first iteration step (i=0). In step S508, standard multivariate optimization techniques are applied to minimize the cost function. It is noted that the optimization problem may apply constraints, such as tuning ranges, during the optimization process of S508 or at a later stage of the optimization process. Step S520 indicates that each iteration is performed for a given test pattern (also referred to as a "gauge") for an identified evaluation point that has been selected to optimize the lithography process. In step S510, the lithography response is predicted. In step S512, the results of step S510 are compared with the expected or ideal lithography response values ​​obtained in step S522. If the termination condition is met in step S514, that is, the optimization generates a lithographic response value that is close enough to the expected value, then the final value of the design variable is output in step S518. The output step may also include outputting other functions using the final value of the design variable, such as outputting a wavefront aberration adjustment map at the pupil plane (or other plane), an optimized source map, and an optimized design layout, etc. If the termination condition is not met, then in step S516, the value of the design variable is updated with the result of the i-th iteration, and the process returns to step S506. Fig.14A The process is explained in detail below.

[0155] In the exemplary optimization process, it is assumed or approximated that the design variables (z1, z2, ..., z N ) and f p (z1,z2,…,z N ) have no relationship unless f p (z1,z2,…,z N ) is smooth enough (e.g. the first-order derivative exists), which is usually effective in lithography projection equipment. Algorithms such as Gauss-Newton algorithm, Levenberg-Marquardt algorithm, gradient descent algorithm, simulated annealing, genetic algorithm, etc. can be applied to find

[0156] Here, the Gauss-Newton algorithm is used as an example. The Gauss-Newton algorithm is an iterative method applicable to general nonlinear multivariable optimization problems. In the i-th iteration, the design variables (z1, z2, …, z N ) takes the value (z 1i ,z 2i ,…,z Ni ), Gauss-Newton algorithm in (z 1i ,z 2i ,…,zNi ) linearized around f p (z1,z2,…,z N ), and then give CF(z1,z2,…,z N ) of the minimum value (z 1i ,z 2i ,…,z Ni ) near the calculated value (z 1(i+1) ,z 2(i+1) ,…,z N(i+1) ). Design variables (z1, z2, …, z N ) uses the (z in the (i+1)th iteration 1(i+1) ,z 2(i+1) ,…,z N(i+1) ) value. This iteration continues until convergence is reached (i.e., CF(z1,z2,…,z N ) is no longer reduced further) or until the preset number of iterations.

[0157] Specifically, in the i-th iteration, in (z 1i ,z 2i ,…,z Ni )nearby,

[0158]

[0159] Under the approximation of Equation 3, the cost function becomes:

[0160]

[0161] This is the design variable (z1,z2,…,z N ). In addition to the design variables (z1, z2, …, z N ), each term is a constant.

[0162] If the design variables (z1, z2, …, z N ) is not subject to any constraints, (z 1(i+1) ,z 2(i+1) ,…,z N(i+1) ) can be derived by solving N linear equations:

[0163]

[0164] If for j = 1, 2, ... J, the design variables (z1, z2, ..., z N ) is subject to the constraints of the form of J inequalities (e.g. (z1,z2,…,z N ) tuning range and for k = 1, 2, ... K, K equations (e.g., interdependencies between design variables) The optimization process becomes a classic quadratic programming problem, where A nj , B j , C nk , D k is a constant. Additional constraints can be imposed for each iteration. For example, the “damping factor” Δ D can be introduced to limit (z 1(i+1) ,z 2(i+1) ,…,z N(i+1) ) and (z 1i ,z 2i ,…,z Ni ), so that the approximation of Equation 3 holds. This constraint can be expressed as z ni -Δ D ≤z n ≤z ni +Δ D . (z 1(i+1) ,z 2(i+1) ,…,z N(i+1) ) can be derived using, for example, the method described in Numerical Optimization (2nd ed.) by Jorge Nocedal and Stephen J. Wright (Berlin New York: Vandenberghe Cambridge University Press).

[0165] Instead of minimizing f, the optimization process can minimize the magnitude of the maximum deviation (worst defect) between the evaluation point and its expected value. p (z1,z2,…,z N ). In this approach, the cost function can alternatively be expressed as

[0166]

[0167] Among them, CL p Yes p (z1,z2,…,z N ). The cost function represents the worst defect among the evaluation points. Optimization using this cost function minimizes the magnitude of the worst defect. An iterative greedy algorithm can be used for this optimization.

[0168] The cost function of Equation 5 can be approximated as:

[0169]

[0170] Where q is an even positive integer, such as at least 4, preferably at least 10. Equation 6 mimics the behavior of Equation 5 while allowing the optimization to be performed analytically and accelerated using methods such as the deepest descent method, the conjugate gradient method, and the like.

[0171] Minimizing the worst defect size can also be done with the linearization fp (z1,z2,…,z N ) combination. Specifically, f p (z1,z2,…,z N ) is approximated by Equation 3. Then the constraint on the worst defect size is written as the inequality E Lp ≤f p (z1,z2,…,z N )≤E Up , where E Lp and E Up are two constants, specifying f p (z1,z2,…,z N ). Inserting into Equation 3, for p = 1, ... P, these constraints are transformed into

[0172]

[0173] as well as

[0174]

[0175] Since Equation 3 is usually only valid for (z 1i ,z 2i ,…,z Ni ) is valid near to prevent the desired constraint E Lp ≤f p (z1,z2,…,z N )≤E Up cannot be achieved in this vicinity, which can be determined by any conflict between the inequalities, the constant E Lp and E Up can be relaxed until the constraints are achievable. The optimization process minimizes (z 1i ,z 2i ,…,z Ni ). Each step then gradually reduces the worst defect size, and each step is iteratively performed until a certain termination condition is met. This will result in an optimal reduction in the worst defect size.

[0176] Another way to minimize the worst-case defect is to adjust the weight w in each iteration p For example, after the i-th iteration, if the r-th evaluation point is the worst defect, then w r can be increased in the (i+1)th iteration so that reducing the defect size of this evaluation point is given higher priority.

[0177] In addition, the cost functions in Eq. 4 and Eq. 5 can be modified by introducing Lagrange multipliers to achieve a trade-off between RMS optimization of defect size and optimization of the worst defect size, i.e.,

[0178]

[0179] Where λ is a preset constant that specifies the trade-off or compromise between optimization of the RMS of defect size and optimization of the worst defect size. Specifically, if λ=0, then this becomes Equation 4 and only the RMS of defect size is minimized; while if λ=1, then this becomes Equation 5 and only the worst defect size is minimized; if 0<λ<1, then both are considered in the optimization. This optimization can be solved using a variety of methods. For example, the weighting in each iteration can be adjusted, similar to that described previously. Alternatively, similar to minimizing the worst defect size from inequalities, the inequalities of Equations 6' and 6" are treated as constraints on the design variables during the solution of the quadratic programming problem. Then, the bounds on the worst defect size can be gradually relaxed or the weights of the worst defect size can be increased, the cost function values ​​for each achievable worst defect size are calculated, and the design variable values ​​that minimize the total cost function are selected as the initial point for the next step. By doing this iteratively, minimization of this new cost function can be achieved.

[0180] Optimizing the lithography projection equipment can expand the process window. A larger process window provides greater flexibility for process design and chip design. The process window can be defined as a set of focus and dose values, where the resist image is within specific limits of the design target of the resist image. It should be noted that all methods discussed herein can also be extended to a generalized process window definition, which can be established by different or additional basis parameters in addition to exposure dose and defocus. These may include, but are not limited to, optical settings such as NA, σ, aberrations, polarization or optical constants of the resist layer. For example, as described earlier, if the PW is also composed of different mask biases, then the optimization includes minimization of MEEF (mask error enhancement factor), which is defined as the ratio between the substrate EPE and the mask edge bias caused. The process window defined on the focus and dose values ​​is used only as an example in the present disclosure. A method for maximizing the process window according to an embodiment is described below.

[0181] In the first step, starting from the known conditions (f0, ε0) in the process window, where f0 is the nominal focus and ε0 is the nominal dose, one of the cost functions around (f0±Δf, ε0±Δε) is minimized as follows:

[0182]

[0183] or

[0184]

[0185] or

[0186]

[0187] If the nominal focus f0 and the nominal dose ε0 are allowed to shift, they can be related to the design variables (z1, z2, …, z N ) joint optimization. In the next step, if (z1,z2,…,z N If a set of values ​​of (f0±Δf,ε0±Δε) can be found such that the cost function is within preset limits, then (f0±Δf,ε0±Δε) is accepted as part of the process window.

[0188] Alternatively, if the focus and dose are not allowed to shift, the design variables (z1, z2, ..., z N ) is optimized, where the focus and dose are fixed to the nominal focus f0 and nominal dose ε0. In an alternative embodiment, if (z1, z2, ..., z N ) can be found such that the cost function is within the preset limits, then (f0±Δf,ε0±Δε)(z1,z2,…,z N ) is accepted as part of the process window.

[0189] The methods described earlier in this disclosure can be used to minimize the respective cost functions of Eq. 7, 7' or 7". If the design variables are characteristics of the projection optics, such as Zernike coefficients, then minimizing the cost function of Eq. 7, 7' or 7" results in maximizing the process window based on projection optics optimization (i.e., LO). If the design variables are characteristics of the source and pattern forming device in addition to the characteristics of the projection optics, then minimizing the cost function of Eq. 7, 7' or 7" results in maximizing the process window based on SMLO, such as Fig.13 If the design variables are characteristics of the source and the patterning device, then minimizing the cost function of Eq. 7, 7' or 7" results in maximizing the SMO-based process window. The cost function of Eq. 7, 7' or 7" may also include at least one f p (z1,z2,…,z N ), such as in Equation 7 or Equation 8, which is a function of one or more random effects, such as the LWR or local CD variation of the 2D feature and the output.

[0190] Fig.15A specific example of how a simultaneous SMLO process can be optimized using the Gauss-Newton algorithm is shown. In step S702, starting values ​​for the design variables are identified. The tuning range for each variable can also be identified. In step S704, a cost function is defined using the design variables. In step S706, the cost function is expanded around the starting values ​​for all evaluation points in the design layout. In optional step S710, a full chip simulation is performed to cover all key patterns in the full chip design layout. The expected lithography response metrics (such as CD or EPE) are obtained in step S714 and compared to the predicted values ​​of those quantities in step S712. In step S716, the process window is determined. Steps S718, S720, and S722 are similar to those with respect to Fig.14A The corresponding steps S514, S516 and S518 are described. As mentioned before, the final output may be a wavefront aberration map in the pupil plane, optimized to produce the desired imaging performance. The final output may also be an optimized source map and / or an optimized design layout.

[0191] Fig. 14B An exemplary method for optimizing a cost function is shown, where the design variables (z1, z2, ..., z N ) include design variables that may take only discrete values.

[0192] The method begins by defining pixel groups of an illumination source and patterning device tiles of a patterning device (step S802). In general, pixel groups or patterning device tiles may also be referred to as subdivisions of a lithography process component. In an exemplary method, the illumination source is divided into 117 pixel groups, and 94 patterning device tiles are defined for the patterning device, substantially as described above, resulting in a total of 211 subdivisions.

[0193] In step S804, a lithography model is selected as the basis for a lithography simulation. The results generated by the lithography simulation are used to calculate lithography metrics or responses. Specific lithography metrics are defined as performance metrics to be optimized (step S806). In step S808, initial (pre-optimization) conditions for the illumination source and the patterning device are set. The initial conditions include the initial state of the pixel group of the illumination source and the patterning device block of the patterning device, so that the initial illumination shape and the initial patterning device pattern can be referenced. The initial conditions may also include mask bias, NA, and focus slope range. Although steps S802, S804, S806, and S808 are depicted as sequential steps, it is to be understood that in other embodiments of the present invention, these steps may be performed in other orders.

[0194] In step S810, the pixel groups and patterning device tiles are sorted. The pixel groups and patterning device tiles may be interleaved in the sorting. Various sorting methods may be employed, including: sequentially (e.g., from pixel group 1 to pixel group 117 and from patterning device tile 1 to patterning device tile 94), randomly, based on the physical location of the pixel groups and patterning device tiles (e.g., sorting pixel groups closer to the center of the illumination source higher), and based on how changes to the pixel groups or patterning device tiles affect the performance metric.

[0195] Once the pixel groups and patterning device tiles are sorted, the illumination source and patterning device are adjusted to improve the performance metric (step S812). In step S812, each of the pixel groups and patterning device tiles is analyzed in the order of sorting to determine whether the change of the pixel group or patterning device tile will result in an improved performance metric. If it is determined that the performance metric will be improved, the pixel group or patterning device tile is changed accordingly, and the resulting improved performance metric and the modified illumination shape or modified patterning device pattern form a baseline for comparison for subsequent analysis of lower sorted pixel groups and patterning device tiles. In other words, the change to improve the performance metric is retained. As the change of the state of the pixel groups and patterning device tiles is made and retained, the initial illumination shape and the initial patterning device pattern are changed accordingly, so that the modified illumination shape and the modified patterning device pattern are produced by the optimization process in step S812.

[0196] In other approaches, patterning device polygon shape adjustment and paired polling of pixel groups and / or patterning device tiles are also performed within the optimization process of S812.

[0197] In an alternative embodiment, the staggered simultaneous optimization procedure may include changing the pixel groups of the illumination source, and if an improvement in the performance metric is found, the dose is stepped up and down to seek further improvements in the simultaneous optimization procedure. In yet another alternative embodiment, the stepwise increase and decrease of the dose or intensity may be replaced by a bias change of the patterning device pattern to seek further improvements in the simultaneous optimization procedure.

[0198] In step S814, it is determined whether the performance metric has converged. For example, if little or no improvement to the performance metric has been witnessed in the last few iterations of steps S810 and S812, then the performance metric may be considered to have converged. If the performance metric has not converged, then the steps of S810 and S812 are repeated in the next iteration, where the modified illumination shape and modified patterning device from the current iteration are used as the initial illumination shape and initial patterning device for the next iteration (step S816).

[0199] The above optimization method can be used to increase the output of a lithographic projection apparatus. For example, the cost function may include f as a function of exposure time. p (z1,z2,…,z N ). The optimization of such a cost function is preferably constrained or influenced by a measure of the random effects or other measures. Specifically, a computer-implemented method for increasing the output of a lithography process may include optimizing a cost function as a function of one or more random effects of the lithography process and an exposure time of the substrate to minimize the exposure time.

[0200] In one embodiment, the cost function includes at least one f p (z1,z2,…,z N ), which is a function of one or more random effects. Random effects may include characteristic failures, Figure 3 The measured data determined by the method (such as SEPE), σ sepe or LWR or local CD variations of 2D features. In one embodiment, the random effects include random variations in resist image characteristics. For example, such random variations may include the failure rate of features, σ sepe , line edge roughness (LER), line width roughness (LWR), and critical dimension uniformity (CDU). Including random variation in the cost function allows finding values ​​of the design variables that minimize the random variation, thereby reducing the risk of defects due to random effects.

[0201] Fig.16 1 is a block diagram illustrating a computer system 100 that can assist in implementing the preferred methods and processes disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, which is coupled to the bus 102 for storing information and instructions to be executed by the processor 104. The main memory 106 can also be used to store temporary variables or other intermediate information during the execution of instructions to be executed by the processor 104. The computer system 100 also includes a read-only memory (ROM) 108 or other static storage device, which is coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110, such as a magnetic disk or optical disk, is provided and coupled to the bus 102 for storing information and instructions.

[0202] The computer system 100 may be coupled to a display 112, such as a cathode ray tube (CRT) or a flat panel or touch pad display, via the bus 102 for displaying information to a computer user. An input device 114 including alphanumeric and other keys is coupled to the bus 102 for communicating information and command selections to the processor 104. Another type of user input device is a cursor control 116, such as a mouse, trackball, or cursor direction keys, for communicating direction information and command selections to the processor 104 and controlling cursor movement on the display 112. The input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), which allows the device to specify a position in a plane. A touch pad (screen) display may also be used as an input device.

[0203] According to one embodiment, in response to processor 104 executing one or more sequences of one or more instructions contained in main memory 106, portions of the optimization process may be performed by computer system 100. Such instructions may be read into main memory 106 from another computer-readable medium such as storage device 110. Execution of the sequence of instructions contained in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multi-processing arrangement may also be employed to execute the sequence of instructions contained in main memory 106. 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 specific combination of hardware circuitry and software.

[0204] The term "computer-readable medium" as used herein refers to any medium that participates in providing instructions to processor 104 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 or magnetic disks, such as storage device 110. Volatile media include dynamic memory, such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers, including the wires that make up bus 102. Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, foldable disks, hard disks, magnetic tape, any other magnetic media, CD-ROMs, DVDs, any other optical media, punch cards, paper tape, any other physical media with a pattern of holes, RAM, PROMs and EPROMs, flash EPROMs, any other memory chips or memory cartridges, carrier waves described below, or any other media from which a computer can read.

[0205] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to processor 104 for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer can load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to computer system 100 can receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to bus 102 can receive the data carried in the infrared signal and place the data on bus 102. Bus 102 carries the data to main memory 106, from which processor 104 retrieves and executes the instructions. The instructions received by main memory 106 may optionally be stored on storage device 110 before or after execution by processor 104.

[0206] Preferably, the computer system 100 also includes a communication interface 118 coupled to the bus 102. The communication interface 118 provides a two-way data communication coupled to a network link 120, which is connected to a local network 122. For example, the communication interface 118 can be an integrated services digital network (ISDN) card or a modem to provide a data communication connection with a corresponding type of telephone line. As another example, the communication interface 118 can be a local area network (LAN) card to provide a data communication connection with a compatible LAN. A wireless link can also be implemented. In any such implementation, the communication interface 118 sends and receives electrical signals, electromagnetic signals, or optical signals that carry digital data streams representing various types of information.

[0207] The network link 120 typically provides data communication through one or more networks to other data devices. For example, the network link 120 may provide a connection through a local network 122 to a host computer 124 or a data device operated by an Internet service provider (ISP) 126. The ISP 126, in turn, provides data communication services through a global packet data communication network, now generally referred to as the "Internet" 128. Both the local network 122 and the Internet 128 use electrical, electromagnetic, or optical signals that carry digital data streams. The signals through the various networks and the signals on the network link 120 and through the communication interface 118, which carry the digital data to and from the computer system 100, are exemplary forms of carrier waves that transport the information.

[0208] The computer system 100 can send messages and receive data, including program code, through the network(s), network link 120, and communication interface 118. In the Internet example, the server 130 can transmit the requested code for the application program through the Internet 128, ISP 126, local network 122, and communication interface 118. For example, one such downloaded application can provide illumination optimization of an embodiment. The received code can be executed by the processor 104 as it is received, and / or stored in the storage device 110 or other non-volatile storage device for later execution. In this way, the computer system 100 can obtain the application code in the form of a carrier wave.

[0209] Fig.17 An exemplary lithographic projection apparatus is schematically depicted, the illumination source of which can be optimized using the methods described herein. The apparatus comprises:

[0210] - an illumination system IL to condition the radiation beam B. In this particular case, the illumination system also comprises a radiation source SO;

[0211] a first stage (e.g. mask table) MT provided with a patterning device holder for holding a patterning device MA (e.g. reticle) and connected to a first positioner for accurately positioning the patterning device relative to the object PS;

[0212] a second object table (substrate table) WT provided with a substrate holder for holding a substrate W (e.g. a silicon wafer coated with resist) and connected to a second positioner for accurately positioning the substrate relative to the item PS;

[0213] - a projection system ("lens") PS (eg a refractive, reflective or catadioptric optical system) to image the radiation portion of the patterning device MA onto a target portion C of the substrate W (eg comprising one or more dies).

[0214] As depicted herein, the apparatus is transmissive (e.g., with a transmissive mask). However, in general, it may also be reflective, e.g., with a reflective mask). Alternatively, the apparatus may employ another class of patterning devices as an alternative to using a classical mask; examples include a programmable mirror array or an LCD matrix.

[0215] A source SO (e.g. a mercury lamp or an excimer laser) generates a radiation beam. This beam is fed into an illumination system (illuminator) IL, for example directly or after traversing conditioning components such as a beam expander Ex. The illuminator IL may include adjustment components AD for setting the outer and / or inner radial extent of the intensity distribution in the beam (commonly referred to as σ outer and σ inner, respectively). In addition, it will typically include various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the patterning device MA has a desired uniformity and intensity distribution in its cross section.

[0216] about Fig.17 It should be noted that the source SO can be within the housing of the lithographic projection device (for example, this is usually the case when the source SO is a mercury lamp), but it can also be remote from the lithographic projection device, the radiation beam it produces being introduced into the device (for example with the aid of suitable guide mirrors); this latter scenario is usually the case when the source SO is an excimer laser (for example, based on KrF, ArF or F2 laser irradiation).

[0217] The beam PB then intercepts the patterning device MA which is held on the patterning device table MT. After traversing the patterning device MA, the beam PB passes through a lens PL which focuses the beam B onto a target portion C of the substrate W. With the aid of the second positioning means (and the interferometry means IF), the substrate table WT can be accurately moved, for example to position a different target portion C in the path of the beam PB. Similarly, the first positioning means can be used to accurately position the patterning device MA relative to the path of the beam B, for example after mechanically retrieving the patterning device MA from a patterning device library or during a scan. Typically, movement of the stage MT, WT will be realized with the aid of a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which are used in the embodiment of the present invention. Fig.17 However, in the case of a wafer stepper (as opposed to a step-and-scan tool), the patterning device table MT may be connected to a short-stroke actuator only, or may be fixed.

[0218] The depicted tool can be used in two different modes:

[0219] - in step mode, the patterning device table MT is kept essentially stationary and the entire patterning device image is projected once (i.e. a single "flash") onto a target portion C. The substrate table WT is then shifted in the x and / or y direction so that a different target portion C can be irradiated by the beam PB;

[0220] - In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single "flash". Instead, the patterning device table MT is movable in a given direction (the so-called "scanning direction", e.g. the y-direction) at a speed v, so that the projection beam B is used to scan over the patterning device image; concurrently, the substrate table WT is simultaneously moved in the same or opposite direction at a speed V=Mv, where M is the magnification of the lens PL (typically M=1 / 4 or 1 / 5). In this way, a relatively large target portion C can be exposed without having to sacrifice resolution.

[0221] Fig.18 Another exemplary lithographic projection apparatus 1000 is schematically depicted, whose illumination source may be optimized using the methods described herein.

[0222] The lithography projection apparatus 1000 comprises:

[0223] -Source Collector Module SO

[0224] - an illumination system (illuminator) IL configured to condition a radiation beam B (eg EUV radiation).

[0225] a support structure (e.g. mask table) MT configured to support a patterning device (e.g. mask or reticle) MA and connected to a first positioner PM configured to accurately position the patterning device;

[0226] a substrate table (eg wafer stage) WT configured to hold a substrate (eg resist coated wafer) W and connected to a second positioner PW configured to accurately position the substrate; and

[0227] - a projection system (eg a reflective projection system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C of the substrate W (eg comprising one or more dies).

[0228] As depicted here, the apparatus 1000 is reflective (e.g., employing a reflective mask). Note that because most materials are absorptive in the EUV wavelength range, the mask can have a multilayer reflector comprising multiple stacks of, for example, molybdenum and silicon. In one example, the multilayer reflector has 40 layer pairs of molybdenum and silicon, where each layer is a quarter wavelength thick. Even smaller wavelengths can be produced with X-ray lithography. Since most materials are absorptive at both EUV and X-ray wavelengths, a thin sheet of patterned absorbing material on the patterning device topography (e.g., a TaN absorber on top of a multilayer reflector) defines where features will be printed (positive resist) or not (negative resist).

[0229] Reference Fig.18, illuminator IL receives a beam of extreme ultraviolet radiation from a source collector module SO. Methods of generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element (e.g., xenon, lithium, or tin) having one or more emission lines in the EUV range. In one such method, generally referred to as laser produced plasma ("LPP"), a plasma may be generated by irradiating a fuel (such as a droplet, stream, or cluster of a material having a line emitting element) with a laser beam. The source collector module SO may be part of an EUV radiation system that includes a device not provided in the EUV radiation system. Fig.18 The laser shown in Figure 1 is used to provide a laser beam for exciting the fuel. The resulting plasma emits output radiation, such as EUV radiation, which is collected using a radiation collector disposed in a source collector module. The laser and source collector module can be separate entities, such as when a CO2 laser is used to provide a laser beam for fuel excitation.

[0230] In this case, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is passed from the laser to the source collector module with the aid of a beam delivery system including, for example, suitable guide mirrors and / or a beam expander. In other cases, the source may be an integrated part of the source collector module, for example when the source is a discharge produced plasma EUV generator, often referred to as a DPP source.

[0231] The illuminator IL may include an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent of the intensity distribution in a pupil plane of the illuminator (commonly referred to as σ outer and σ inner, respectively) may be adjusted. In addition, the illuminator IL may include various other components, such as a facet field and a pupil mirror arrangement. The illuminator may be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0232] A radiation beam B is incident on and patterned by a patterning device (e.g. a mask) MA, which is held on a support structure (e.g. a mask table) MT. After reflection from the patterning device (e.g. a mask) MA, the radiation beam B passes through a projection system PS which focuses the beam onto a target portion C of a substrate W. With the aid of a second positioner PW and a position sensor PS2 (e.g. an interferometric device, a linear encoder or a capacitive sensor), the substrate table WT can be accurately moved, for example to position different target portions C in the path of the radiation beam B. Similarly, a first positioner PM and a further position sensor PS1 can be used to accurately position the patterning device (e.g. a mask) MA relative to the path of the radiation beam B. The patterning device (e.g. a mask) MA and the substrate W can be aligned using the patterning device alignment marks M1, M2 and the substrate alignment marks P1, P2.

[0233] The depicted device 1000 may be used in at least one of the following modes:

[0234] 1. In step mode, the support structure (e.g. mask table) MT and the substrate table WT remain substantially stationary while the entire pattern imparted to the radiation beam is projected at one time onto a target portion C (i.e. a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that a different target portion C can be exposed.

[0235] 2. In scan mode, the support structure (e.g. mask table) MT and substrate table WT are scanned synchronously as a pattern imparted to the radiation beam is projected onto a target portion C (i.e. a single dynamic exposure). The speed and direction of the substrate table WT relative to the support structure (e.g. mask table) MT may be determined by the (de-)magnification and image reversal characteristics of the projection system PS.

[0236] 3. In another mode, the support structure (e.g. mask table) MT remains essentially stationary, thereby holding the programmable patterning device, and the substrate table WT is moved or scanned, while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, typically a pulsed radiation source is employed, and the programmable patterning device is updated as required after each movement of the substrate table WT or between successive radiation pulses during a scan. This mode of operation can readily be applied to maskless lithography, which makes use of a programmable patterning device (such as a programmable mirror array of the type cited above).

[0237] Fig.19 The apparatus 1000 is shown in more detail and includes a source collector module SO, an illumination system IL, and a projection system PS. The source collector module SO is constructed and arranged so that a vacuum environment can be maintained in a closed structure 220 of the source collector module SO. The EUV radiation emitting plasma 210 can be formed by a plasma source generated by a discharge. EUV radiation can be generated by a gas or vapor, such as xenon, lithium vapor, or tin vapor, wherein a very hot plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. The very hot plasma 210 is generated by, for example, a discharge that causes a plasma that is at least partially ionized. In order to effectively generate radiation, a partial pressure of, for example, 10Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required. In an embodiment, a plasma that excites tin (Sn) is provided to generate EUV radiation.

[0238] Radiation emitted by the hot plasma 210 enters the collector chamber 212 from the source chamber 211 via an optional gas barrier or contaminant trap 230 (also referred to as a contaminant barrier or fin trap in some cases) positioned in or behind an opening in the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. As is known in the art, the contaminant trap or contaminant barrier 230 further indicated herein includes at least a channel structure.

[0239] The collector chamber 212 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation traversing the collector CO may be reflected from the grating spectral filter 240 to be focused in a virtual source point IF along the optical axis indicated by the dotted line 'O'. The virtual source point IF is generally referred to as an intermediate focus, and the source collector module is arranged so that the intermediate focus IF is located at or near an opening 221 in the enclosure 220. The virtual source point IF is an image of the radiation emitting plasma 210.

[0240] The radiation then traverses an illumination system IL which may include a faceted field mirror arrangement 22 and a faceted pupil mirror arrangement 24 which are arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA and a desired uniformity of radiation intensity at the patterning device MA. Upon reflection of the radiation beam 21 at the patterning device MA held by the support structure MT, a patterned beam 26 is formed and the patterned beam 26 is imaged by the projection system PS via reflective elements 28, 30 onto a substrate W held by a substrate table WT.

[0241] More elements than shown may typically be present in the illumination optics unit IL and the projection system PS. Depending on the type of lithographic apparatus, a grating spectral filter 240 may optionally be present. Further, there may be more mirrors than shown in the figures, for example with Fig.19 Compared to that shown, there may be between 1 and 6 additional reflective elements in the projection system PS.

[0242] like Fig.19 As illustrated, the collector optics CO is depicted as a nested collector with grazing incidence reflectors 253, 254 and 255, merely as an example of a collector (or collector mirror). The grazing incidence reflectors 253, 254 and 255 are arranged axially symmetrically around the optical axis O, and preferably, this type of collector optics CO may be used in combination with a discharge produced plasma source, generally referred to as a DPP source.

[0243] Alternatively, the source collector module SO may be Fig. 20A portion of the LPP radiation system shown. The laser LA is arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn) or lithium (Li), thereby producing a highly ionized plasma 210 with an electron temperature of tens of eV. Energetic radiation generated during the deexcitation and recombination of these ions is emitted from the plasma, collected by a collector optics CO at near normal incidence and focused onto an opening 221 in a closed structure 220.

[0244] The concepts disclosed herein can simulate or mathematically model any general imaging system for imaging sub-wavelength features, and may be particularly useful for emerging imaging technologies that are capable of producing shorter and shorter wavelengths. Emerging technologies already in use include EUV (extreme ultraviolet), DUV lithography, which is capable of producing wavelengths of 193nm using ArF lasers, and even 157nm using fluorine lasers. Moreover, EUV lithography is capable of producing wavelengths in the range of 20 to 5nm by using synchrotrons or by bombarding materials (solid or plasma) with high-energy electrons to produce photons in this range.

[0245] Although the concepts disclosed herein may be used for imaging on substrates such as silicon wafers, it should be understood that the disclosed concepts may be used with any type of lithography imaging system, such as those used for imaging on substrates other than silicon wafers.

[0246] The above description is intended to be illustrative, rather than limiting. It will therefore be apparent to those skilled in the art that modifications may be made as described without departing from the scope of the claims set forth below.

[0247] The embodiments may also be described using the following terms:

[0248] 1. A method for determining measurement data of a printed pattern on a substrate, the method comprising:

[0249] obtaining (i) a plurality of images of the substrate, each of the images comprising a printed pattern corresponding to a reference pattern, (ii) an average image of the plurality of images, and (iii) a composite profile of the printed pattern based on the average image;

[0250] aligning, via a processor, a composite profile of the average image relative to a reference profile of a reference pattern;

[0251] extracting, via a processor, from the plurality of images, original contours of printed patterns within the images, the extraction being guided by the aligned composite contours;

[0252] determining, via a processor, a plurality of pattern measurements based on the plurality of profiles, wherein the pattern measurements are characteristics of the printed pattern; and

[0253] Measurement data corresponding to the printed pattern is determined, via a processor, based on the plurality of pattern measurements.

[0254] 2. The method of clause 1, wherein the aligning of the composite profile comprises:

[0255] Overlapping the composite contour with the reference contour; and

[0256] The composite profile is shifted within a predefined range such that the difference between the composite profile and the reference profile is reduced.

[0257] 3. A method according to clause 2, wherein the shifting of the composite profile comprises:

[0258] offsetting the composite contour relative to the center of the predefined range so that the overall contour-to-contour distance is reduced; and

[0259] The composite profile is offset in a first direction to reduce first profile-to-profile differences in the first direction, and / or offset in a second direction to reduce second profile-to-profile differences in the second direction.

[0260] 4. A method according to any one of clauses 1 to 3, wherein extracting the contour from a given image of the plurality of images comprises:

[0261] Identify the starting point in a given image relative to the composite contour;

[0262] Finding the direction to use for contour edge searching; and

[0263] Determine edge locations of a contour in a given image among multiple images.

[0264] 5. A method according to any one of clauses 1 to 4, wherein the image is a pixelated image.

[0265] 6. A method according to any of clauses 4 to 5, wherein the signal value comprises a pixel intensity of a pixel at a specific location of the image.

[0266] 7. The method according to any one of clauses 1 to 6, wherein the determining of the pattern measurement results comprises:

[0267] defining a set of cutting lines passing through a given contour among a plurality of contours;

[0268] defining a plurality of measuring gauges along a given contour, wherein the measuring gauges are defined at intersections of the cutting line and the given contour; and

[0269] Pattern measurements are determined relative to a measuring gauge.

[0270] 8. A method according to any of clauses 1 to 7, wherein the pattern measurements are critical dimension measurements of the printed pattern and / or edge positioning measurements of the printed pattern relative to a reference pattern.

[0271] 9. The method of clause 8, wherein the critical dimension in the critical dimension is the distance between two measuring gauges along a horizontal cut line that intersects the given contour.

[0272] 10. The method of clause 8, wherein the edge location measurement result is an edge location error determined along a given profile at a measuring gauge, wherein the edge location error is the difference between the given profile at the given measuring gauge and a reference profile.

[0273] 11. The method according to any one of clauses 1 to 10, wherein the determining of the measurement data comprises:

[0274] determining a first statistic corresponding to the printed pattern based on a plurality of measurements associated with a particular die of the substrate; and / or

[0275] determining a second statistic (σinter-die) corresponding to the printed pattern based on a plurality of measurements associated with specific field locations on different dies of the substrate; and / or

[0276] determining a third statistic associated with the printed pattern based on a plurality of measurements associated with a particular feature within each image field of view (FOV); and / or

[0277] A fourth statistic is determined by combining the first statistic, the second statistic, and the third statistic.

[0278] 12. A method according to any of clauses 1 to 11, wherein the measurement data, the first statistic and the second statistic are associated with process variations, and the third statistic is associated with random variations in the measurements of the printed pattern.

[0279] 13. The method of clause 12, wherein the first statistic is within-die variation in measurements of a printed pattern of the substrate.

[0280] 14. The method of clause 12, wherein the second statistic is die-to-die variation in measurements of a printed pattern of the substrate.

[0281] 15. The method of clause 12, wherein the third statistic is the random variation in the measurements of the printed pattern of the substrate.

[0282] 16. A method according to any one of clauses 1 to 15, wherein obtaining the average image comprises:

[0283] aligning printed patterns of the plurality of images relative to one another;

[0284] identifying locations having relatively high signal values ​​along a printed pattern of the plurality of images, and aligning the identified locations; and

[0285] The average image is determined by averaging the signal values ​​of the aligned multiple images.

[0286] 17. A method according to any one of clauses 1 to 16, wherein aligning the printed pattern of multiple images comprises:

[0287] One or more images of the plurality of images are shifted to align corresponding printed patterns of the one or more images with the reference pattern such that differences between the printed patterns of the plurality of images are reduced.

[0288] 18. A method according to any one of clauses 1 to 17, wherein obtaining the composite profile comprises:

[0289] aligning the printed pattern of the average image with the reference pattern such that differences between the patterns are reduced; and

[0290] Based on relatively high signal-to-noise ratio values ​​at locations around the reference pattern, a composite contour is extracted from the average image.

[0291] 19. A method according to any one of clauses 1 to 18, wherein the reference pattern is a designed pattern or a simulated pattern.

[0292] 20. A method according to any one of clauses 1 to 19, wherein the plurality of images are scanning electron microscope images.

[0293] 21. A device configured to extract a contour from a measurement image, the device comprising a processor configured to:

[0294] obtaining (i) a metrology image of a substrate having a printed pattern, (ii) an average image of the printed pattern, and (ii) a measurement statistic corresponding to the printed pattern based on the average image;

[0295] Based on the measurement statistics and the average image, the outline of the printed pattern is extracted from the metrology image.

[0296] 22. The apparatus according to clause 21, wherein the extracting of the contour comprises:

[0297] aligning the average image with the measurement image; and

[0298] identifying locations in the measurement image surrounding the mean image having signal values ​​within the measurement statistic; and

[0299] A contour is defined based on relatively high signal values ​​around the identified locations.

[0300] 23. The apparatus of any of clauses 21 to 22, wherein the processor is further configured to:

[0301] Pattern measurements are determined based on the extracted contours.

[0302] 24. Apparatus according to clause 23, wherein the pattern measurement result is a critical dimension of the printed pattern and / or an edge positioning of the printed pattern relative to a reference pattern.

[0303] 25. Apparatus according to any of clauses 21 to 24, wherein the measurement statistic is the random variation in the measurements of the printed pattern on the substrate.

[0304] 26. Apparatus according to any one of clauses 21 to 25, wherein the metrology image is a scanning electron microscope image.

[0305] 27. A computer program product comprising a non-transitory computer-readable medium having recorded thereon instructions which, when executed by a computer, implement the method of any one of clauses 1 to 26.

Claims

1. A method for determining measurement data of a printed pattern on a substrate, the method comprising: obtaining (i) a plurality of images of the substrate, each of the images comprising a printed pattern corresponding to a reference pattern, (ii) an average image of the plurality of images, and (iii) a composite profile of the printed pattern based on the average image; aligning, via a processor, the composite contour of the average image relative to a reference contour of the reference pattern; extracting, via the processor, from the plurality of images a plurality of contours of the printed pattern within the images to preserve at least some random variations in the plurality of images, the extracting being guided by the aligned composite contours; determining, via the processor, a plurality of pattern measurements based on the plurality of contours, wherein the pattern measurements are characteristics of the printed pattern; as well as The measurement data corresponding to the printed pattern is determined, via the processor, based on the plurality of the pattern measurements.

2. The method of claim 1 , wherein the aligning of the composite profile comprises: Overlaying the composite contour with the reference contour; as well as The composite profile is shifted within a predefined range such that a difference between the composite profile and the reference profile is reduced.

3. The method of claim 2, wherein the offset of the composite profile comprises: offsetting the composite contour relative to a center of the predefined range such that an overall contour-to-contour distance is reduced; as well as The composite profile is offset in a first direction to reduce first profile-to-profile differences in the first direction and / or in a second direction to reduce second profile-to-profile differences in the second direction.

4. The method according to any one of claims 1 to 3, wherein the extracting comprises extracting contours from a given image of the plurality of images, wherein the extracting of the contours comprises: identifying a starting point in the given image relative to the composite contour; Find the direction to use for contour edge search; as well as An edge location of the contour in the given image of the plurality of images is determined.

5. The method according to any one of claims 1-3, wherein the image is a pixelated image. The method of claim 4 , wherein the signal value comprises a pixel intensity of a pixel at a specific location of the image.

7. The method according to any one of claims 1 to 3, wherein the determining of the pattern measurement result comprises: defining a set of cutting lines passing through a given contour of said plurality of said contours; defining a plurality of measuring gauges along the given contour, wherein the measuring gauges are defined at intersections of a cutting line and the given contour; as well as The pattern measurements are determined relative to the measurement gauge.

8. The method according to any one of claims 1 to 3, wherein the pattern measurement result is a critical dimension of the printed pattern and / or an edge positioning measurement result of the printed pattern relative to the reference pattern.

9. The method of claim 8, wherein the critical dimension in the critical dimension is the distance between two measuring gauges along a horizontal cut line that intersects a given contour.

10. The method of claim 8, wherein the edge location measurement result is an edge location error determined at the measuring gauge along a given profile, wherein the edge location error is a difference between the given profile at the given measuring gauge and the reference profile.

11. The method according to any one of claims 1 to 3, wherein the determining of the measurement data comprises: determining a first statistic corresponding to the printed pattern based on the plurality of measurements associated with a particular die of the substrate; and / or determining a second statistic (σinter-die) corresponding to the printed pattern based on the plurality of measurements associated with specific field locations on different dies of the substrate; and / or determining a third statistic associated with the printed pattern based on the plurality of measurements associated with particular features within each image field of view (FOV); and / or A fourth statistic is determined by combining the first statistic, the second statistic, and the third statistic.

12. The method of claim 11, wherein the measurement data, the first statistic, and the second statistic are associated with process variations, and the third statistic is associated with random variations in measurements of the printed pattern.

13. The method of claim 12, wherein the first statistic is intra-die variation in measurements of the printed pattern of the substrate.

14. The method of claim 12, wherein the second statistic is die-to-die variation in measurements of the printed pattern of the substrate.

15. The method of claim 12, wherein the third statistic is random variation in measurements of the printed pattern of the substrate.

16. The method according to any one of claims 1 to 3, wherein obtaining an average image comprises: aligning printed patterns of the plurality of images relative to one another; identifying locations having relatively high signal values ​​along the printed pattern of the plurality of images, and aligning the identified locations; as well as The average image is determined by averaging the signal values ​​of the aligned multiple images.

17. The method of any one of claims 1-3, wherein said aligning said printed pattern of said plurality of images comprises: One or more images of the plurality of images are shifted to align corresponding printed patterns of the one or more images with the reference pattern such that differences between the printed patterns of the plurality of images are reduced.

18. The method according to any one of claims 1 to 3, wherein obtaining the composite profile comprises: aligning the printed pattern of the average image with the reference pattern such that differences between the patterns are reduced; as well as The composite contour is extracted from the average image based on signal-to-noise ratio values ​​at locations around the reference pattern.

19. The method according to any one of claims 1 to 3, wherein the reference pattern is a design pattern or a simulation pattern.

20. The method of any one of claims 1-3, wherein the plurality of images are scanning electron microscope images.

21. A computer program product comprising a non-transitory computer-readable medium having instructions recorded thereon, which when executed by a computer implement the method according to any one of claims 1-20.

Images