Method for determining control parameters of a device manufacturing process

Abstract

Disclosed herein is a method for determining one or more control parameters of a manufacturing process, the manufacturing process including a lithography process and one or more additional processes, the method including: obtaining an image of at least a portion of a substrate, wherein the image includes at least one feature fabricated on the substrate by the manufacturing process; calculating one or more image-related metrics depending on a profile determined from the image, wherein one of the image-related metrics is an edge position error EPE of the at least one feature; and determining one or more control parameters of the lithography process and / or one or more additional processes depending on the edge position error, wherein at least one control parameter is determined to minimize the edge position error of the at least one feature.

Description

[0001] This application is a divisional application of International Application No. PCT / EP2018 / 072706, filed on August 22, 2018, which entered the Chinese national phase on March 20, 2020, with application number 201880062857.2 and invention title "Method for Determining Control Parameters of a Device Manufacturing Process".

[0002] Cross - Reference to Related Applications

[0003] This application claims priority to European Application No. 17193430.0, filed on September 27, 2017, European Application No. 17200255.2, filed on November 7, 2017, and European Application No. 18155070.8, filed on February 5, 2018, which are hereby incorporated by reference in their entirety. Technical Field

[0004] The description herein relates to processes in the manufacture of semiconductor devices, and more particularly to a method, non-transitory computer-readable medium, and system for improving any of these processes depending on an image of a feature of a device being manufactured. Background Art

[0005] A lithographic projection apparatus can be used, for example, in the manufacture of integrated circuits (ICs). In such a case, a patterning device (e.g., a mask) can contain or provide a circuit pattern ("design layout") corresponding to an individual layer of the IC, and the circuit pattern can be transferred to a target portion (e.g., including one or more dies) on a substrate (e.g., a silicon wafer) that has been coated with a layer of radiation-sensitive material ("resist") by methods such as irradiating a target portion through the circuit pattern on the patterning device. Typically, a single substrate contains a plurality of adjacent target portions, and the circuit pattern is transferred to the plurality of adjacent target portions in sequence by the lithographic projection apparatus, one target portion at a time. In one type of lithographic projection apparatus, the circuit pattern over the entire patterning device is transferred to one target portion at a time; such an apparatus is commonly referred to as a stepper. In an alternative apparatus, commonly referred to as a stepper-scanner, the projection beam scans the patterning device in a given reference direction ("scan" direction) while synchronously moving the substrate parallel or antiparallel to this reference direction. Different portions of the circuit pattern on the patterning device are transferred progressively to one target portion. Since typically the lithographic projection apparatus will have a magnification factor M (usually <1), the speed F of the substrate movement will be M times the speed at which the projection beam scans the patterning device. More information about the lithographic apparatus described herein can be gathered, for example, from US 6,046,792, which is hereby incorporated by reference.

[0006] Before transferring the circuit pattern from the pattern forming apparatus to the substrate, the substrate may undergo various processes such as underlayer coating, resist coating, and soft baking. After exposure, the substrate may be subjected to other processes such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred circuit pattern. The array of these processes is used as a basis for fabricating a single layer of a device such as an IC. Then, the substrate may undergo various processes such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which are aimed at completing the individual layers of the device. If several layers are required in the device, the entire process and its variations are repeated for each layer. Eventually, the devices will appear in each target portion on the substrate. Then, these devices are separated from each other by techniques such as dicing or sawing so that individual devices can be mounted on carriers, connected to pins, etc.

[0007] As noted, lithography is a central step in integrated circuit fabrication, where the pattern formed on the substrate defines the functional elements of the IC, such as microprocessors, memory chips, etc. Similar lithography techniques are also used to form flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0008] With the continuous development of semiconductor manufacturing processes, the size of functional elements has been continuously reduced, while the number of functional elements (such as transistors) per device has been steadily increasing over the past few decades following a trend commonly known as "Moore's Law". At the current state of the art, the layers of a device are fabricated using a lithographic projection apparatus that uses irradiation from a deep ultraviolet radiation source to project a design layout onto the substrate, thereby creating individual functional elements with dimensions far below 100 nm, i.e., less than half the wavelength of the radiation from the radiation source (e.g., a 193 nm radiation source).

[0009] According to the resolution formula CD = k1 × λ / NA, 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, where λ is the wavelength of the radiation employed (currently mostly 248 nm or 193 nm), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the "critical dimension", typically the smallest feature size printed, and k1 is the empirical resolution. Generally, the smaller k1 is, the more difficult it is to reproduce on the substrate a pattern similar to the shape and size planned by the circuit designer in order to achieve specific electrical functions and performances. To overcome these difficulties, it is necessary to accurately determine the control parameters of all processes in device manufacturing. SUMMARY OF THE INVENTION

[0010] According to a first aspect of the present invention, there is provided a method for determining one or more control parameters of a manufacturing process, the manufacturing process including a lithography process and one or more additional processes, the method comprising: obtaining an image of at least a part of a substrate, wherein the image includes at least one feature fabricated on the substrate by the manufacturing process; calculating one or more image-related metrics depending on a profile determined from the image, wherein one of the image-related metrics is an edge position error EPE of the at least one feature; and determining one or more control parameters of the lithography process and / or the one or more additional processes depending on the edge position error, wherein at least one control parameter is determined so as to minimize the edge position error of the at least one feature.

[0011] Preferably, the method further comprises: controlling at least one of the following depending on the one or more determined control parameters: a lithography apparatus and the one or more additional processes in the manufacturing process of the device.

[0012] Preferably, the additional processes in the manufacturing process of the device include one or more of the following: a lithography process, a bottoming process, a resist coating process, a soft bake process, a post-exposure bake process, a development process, a hard bake process, a measurement / inspection process, an etching process, an ion implantation process, a metallization process, an oxidation process, and a chemical mechanical polishing process.

[0013] Preferably, the image-related metric is the edge position error EPE of the feature.

[0014] Preferably, the image-related metric is calculated depending on a comparison of the profile with a target profile.

[0015] Preferably, the image-related metric is generated depending on a plurality of images of the feature.

[0016] Preferably, the plurality of images of the feature are in a corresponding plurality of layers of the substrate.

[0017] Preferably, the method further comprises: determining a plurality of segments of the profile of the feature; determining a corresponding weight for each of the plurality of segments; calculating, for each segment, the image-related metric of the segment; and calculating the image-related metric of the feature depending on the weight and the image-related metric of each segment.

[0018] Preferably, the weight of each segment depends on a tolerance value of the image-related metric of the segment.

[0019] Preferably, the one or more control parameters are determined depending on the sensitivity of each segment.

[0020] Preferably, the one or more control parameters are determined so as to minimize the EPE of the feature.

[0021] Preferably, the method includes generating an image - related metric for each of a plurality of features in an image, wherein each image - related metric of a feature is generated by performing the method according to claim 8 or any of its dependent claims.

[0022] Preferably, the method further includes determining a weight for each of a plurality of features in the image; and calculating an image - related metric of the image depending on the image - related metric of each feature and the weight of each feature.

[0023] Preferably, the image - related metric of the image is the EPE of the image, and one or more control parameters are determined to minimize the EPE of the image.

[0024] Preferably, the method further includes: obtaining a plurality of images of different parts of the same layer of a substrate; and calculating an image - related metric for each image; wherein one or more control parameters are determined depending on the image - related metric of each image.

[0025] Preferably, each image is a field of view of 10μm×10μm.

[0026] Preferably, the method further includes: calculating an image - related metric for each of a plurality of features in one or more images of a layer of a substrate; wherein the one or more control parameters are determined depending on each of the plurality of image - related metrics.

[0027] Preferably, one or more control parameters define a dose distribution to be applied in a manufacturing process of a device.

[0028] Preferably, the method further includes calculating a global image - related metric; wherein the one or more control parameters are additionally determined depending on the global image - related metric.

[0029] Preferably, the method further includes calculating the EPE, wherein the one or more control parameters are determined to minimize the EPE.

[0030] Preferably, the EPE is determined depending on one or more of the following: global critical dimension uniformity, line - width roughness, local critical dimension uniformity, and critical dimension amplitude.

[0031] Preferably, the EPE is calculated as a weighted combination of global critical dimension uniformity and local critical dimension uniformity.

[0032] Preferably, the method includes: obtaining a plurality of images of a substrate; determining an image - related metric of a feature in each image; wherein one or more control parameters are determined depending on the image - related metric of each image and the dependence of the determined image - related metric on a change in the one or more control parameters.

[0033] Preferably, the image - related metrics include one or more of the following: the size of a block pattern in the image, the size difference of block patterns in the image, the pitch difference in a grating in the image, the overall offset of a blocking layer relative to a grating layer, and the offset between two LELE layers.

[0034] Preferably, the images are different parts of the same layer of the substrate.

[0035] Preferably, the images are of the same part of the substrate; and the images are acquired during different manufacturing processes of the layers of the substrate.

[0036] Preferably, the method further includes controlling the proximity effect depending on the differences between the images.

[0037] Preferably, the image - related metrics are obtained by: mapping the measured image to a reference image; and / or averaging parameters derived from lines across the image.

[0038] According to a second aspect of the present invention, there is provided a non - transitory computer - readable medium comprising instructions which, when executed, cause a manufacturing process of a device on a substrate to be controlled according to the method of the first aspect.

[0039] According to a third aspect of the present invention, there is provided a system for manufacturing a device on a substrate, wherein the system is configured to execute the method of the first aspect. Description of the Drawings

[0040] Figure 1 is a block diagram of various subsystems of a lithography system.

[0041] Figure 2 is related to Figure 1 a block diagram of an analog model corresponding to the subsystem in

[0042] Figure 3A schematically depicts LER.

[0043] Figure 3B schematically depicts LWR.

[0044] Figure 3C schematically shows how random variations affect lithography.

[0045] Figure 4A and Figure 4B schematically shows a method for determining the relationship between random variations in the characteristics of a spatial image or a resist image and one or more design variables.

[0046] Figure 5A and Figure 5B shows the fitting results of using the relationship.

[0047] Figure 6 Shows an exemplary flowchart for calculating and graphing random variations.

[0048] Figure 7 Shows hotspots identified using random variations.

[0049] Figure 8 Shows a non - transient computer - readable medium containing random variation values at multiple conditions and at multiple values of design variables.

[0050] Figure 9A and Figure 9B Both show the intensity of an image (spatial or resist) across an edge in a direction (x) perpendicular to the edge of the pattern.

[0051] Figure 10 Schematically shows the curve of the EPE ILS term.

[0052] Figure 11 Is a flowchart showing aspects of an example methodology for joint optimization / co - optimization.

[0053] Figure 12 Shows an example of an additional optimization method.

[0054] Figure 13A , Figure 13B and Figure 14 Show example flowcharts of various optimization processes.

[0055] Figure 15A Shows a flowchart of a method for identifying hotspots on a spatial image or a resist image based on characteristic - based random variations (e.g., LER) or a function thereof (e.g., bl_ILS, ILS, or NILS).

[0056] Figure 15B Shows a flowchart of an additional method for identifying hotspots on a spatial image or a resist image based on random variations (e.g., LER) or a function thereof (e.g., bl_ILS, ILS, or NILS) of a characteristic (e.g., edge position) of the spatial image or the resist image.

[0057] Figure 16 Shows a flowchart of a method for reducing random variations (e.g., LER) of one or more characteristics (e.g., edge position) of a spatial image or a resist image.

[0058] Figure 17 Is a block diagram of an example computer system.

[0059] Figure 18 Is a schematic diagram of a lithographic projection apparatus.

[0060] Figure 19 is a schematic view of another lithographic projection apparatus.

[0061] Figure 20 is Figure 19 a more detailed view of the apparatus in

[0062] Figure 21 is Figure 19 and Figure 20 a more detailed view of the source collector module SO of the apparatus of

[0063] Figure 22 shows several relationships between throughput and measures of random variation.

[0064] Figure 23 Schematically shows a flow chart of a method for performing optimization on a set of values of one or more design variables and presenting various characteristics of a process, a spatial image, and / or a resist image to a user such that the user can select a set of values of one or more design variables based on user-desired characteristics.

[0065] Figures 24(a) and 24(b) generally show a process for determining control parameters and a control process according to an embodiment.

[0066] Figure 25 shows an image of features on a substrate.

[0067] Figure 26 shows a via in a layer, which should be positioned above features on an adjacent layer.

[0068] Figures 27(a), 27(b), 27(c), and 27(d) show different relationships between a feature profile and a target profile.

[0069] Figure 28 shows an image of a patterned area on a substrate.

[0070] Figure 29 is a flow chart of a method according to an embodiment. Detailed Description

[0071] Although specific reference may be made in this text to the manufacture of ICs, it should be clearly understood that the description herein has many other possible applications. For example, it can be employed in the manufacture of: integrated optical systems, guidance 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 to be interchangeable with the more general terms "mask", "substrate" and "target portion", respectively.

[0072] In this document, the terms "radiation" and "beam" are used to encompass all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of 5 - 20 nm).

[0073] As used herein, the terms "optimize", "performing optimization" refer to or mean adjusting a lithographic projection apparatus, a lithographic process, etc., such that the result of lithography and / or the process has more desirable characteristics, such as higher accuracy of the projection of a design layout onto a substrate, a larger process window, etc. Thus, the term "optimize" as used herein refers to or means the process of identifying one or more values of one or more parameters, which provide at least one relevant metric improvement (e.g., a local optimum) compared to an initial set of one or more values of the one or more parameters. "Optimal" and other related terms should be interpreted accordingly. In one embodiment, the optimization step can be applied iteratively to provide further improvement of one or more metrics.

[0074] Furthermore, the lithographic projection apparatus may be of the type having two or more platforms (e.g., two or more substrate tables, a substrate table and a measurement table, two or more patterning device tables, etc.). In such a "multi - platform" device, the multiple platforms can be used in parallel, or preparation steps can be performed on one or more platforms while one or more other platforms are being used for exposure. A dual - platform lithographic projection apparatus is described, for example, in U.S. Patent 5,969,441, which is incorporated herein by reference.

[0075] The above-mentioned pattern forming apparatus includes or can form one or more design layouts. The design layout can be generated using a CAD (Computer-Aided Design) program, and this process is generally referred to as EDA (Electronic Design Automation). Most CAD programs follow a set of predefined design rules in order to create a functional design layout / pattern forming apparatus. These rules are set by processing and design limitations. For example, the design rules define the space tolerances between circuit devices (such as gates, capacitors, etc.) or interconnecting lines, thereby ensuring that the circuit devices or lines do not interact with each other in an undesirable manner. One or more of the design rule limitations can be referred to as "critical dimension" (CD). The critical dimension of a circuit can be defined as the minimum width of a line or a hole, or the minimum spacing between two lines or two holes. Thus, the CD determines the overall size and density of the designed circuit. Of course, one of the goals of integrated circuit fabrication is to faithfully reproduce the original circuit design (via the pattern forming apparatus) on a substrate.

[0076] The term "mask" or "pattern forming device" as used herein can be broadly interpreted to mean a general pattern forming device that can be used to impart to an incident radiation beam a cross-section corresponding to a pattern to be patterned, which cross-section corresponds to the pattern to be created in a target portion of a substrate; the term "light valve" can also be used in this context. In addition to classical masks (transmission or reflection; binary, phase-shift, hybrid, etc.), examples of other such pattern forming devices include:

[0077] - A 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), the addressed areas of the reflective surface reflect the incident radiation as diffracted radiation, while the non-addressed areas reflect the incident radiation as non-diffracted radiation. Using an appropriate filter, the above-mentioned non-diffracted radiation can be filtered out of the reflected beam, leaving only the diffracted radiation; in this way, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic components. More information about such mirror arrays can be gleaned from, for example, U.S. Patent Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference.

[0078] - A programmable LCD array. An example of such a structure is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0079] As a brief introduction, Figure 1An exemplary lithographic projection apparatus 10A is shown. The main components are a radiation source 12A, which may be a deep ultraviolet excimer laser source or other type of source, including an extreme ultraviolet (EUV) source (as mentioned above, the lithographic projection apparatus itself does not need to have a radiation source); illumination optics, which define the partial coherence (represented as σ) and may include optics 14A, 16Aa and 16Ab, which shape the radiation from source 12A; a patterning device 14A; and projection optics 16Ac, which project 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 angular range of the beam incident on the substrate plane 22A, where the maximum possible angle defines the numerical aperture NA = n sin(Θ max ), where n is the refractive index of the medium between the last element of the projection optical element and the substrate.

[0080] In the optimization process of the system, the figure of merit of the system can be expressed as a cost function. The optimization process boils down to the process of finding a set of parameters (design variables) of the system that optimize (e.g., minimize or maximize) the cost function. The cost function can have any suitable form, depending on the optimization objective. For example, the cost function can be the weighted root mean square (RMS) of the deviation of certain characteristics (evaluation points) of the system from their expected values (e.g., ideal values); the cost function can also be the maximum value among these deviations (i.e., the worst deviation). The term "evaluation point" in this article should be interpreted broadly to include any feature of the system. Due to the practicality of system implementation, the design variables of the system can be constrained within a limited range and / or be interdependent. In the case of a lithographic projection apparatus, the constraints are usually associated with the physical nature and characteristics of the hardware (such as the adjustable range and / or the manufacturability design rules of the patterning device), 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 focal length.

[0081] In a lithographic projection apparatus, a light source provides illumination (i.e., radiation) to a patterning device, and projection optics direct and shape the illumination via the patterning device onto a substrate. The term "projection optics" is here defined in a broad sense to include any optical components that can alter the wavefront of a radiation beam. For example, the projection optics may include at least some of the components 14A, 16Aa, 16Ab, and 16Ac. A spatial image (AI) is the radiation intensity distribution at the substrate level. A resist layer on the substrate is exposed, and the spatial 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. A resist model can be used to calculate the resist image from the spatial image, an example of which can be found in U.S. Patent Application Publication No. US 2009-0157360, the entire disclosure of which is incorporated herein by reference. 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 characteristics of the lithographic projection apparatus (e.g., the properties of the source, patterning device, and projection optics) determine the spatial 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 remainder of the lithographic projection apparatus, which at least includes the source and projection optics.

[0082] In Figure 2 FIG. shows an exemplary flow chart for simulating lithography in a lithographic projection apparatus. A source model 31 represents the optical characteristics of the source (including radiation intensity distribution and / or phase distribution). A projection optics model 32 represents the optical characteristics of the projection optics (including the alteration of the radiation intensity distribution and / or phase distribution caused by the projection optics). A design layout model 35 represents the optical characteristics of a design layout (including the alteration of the 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 formed by a patterning device. A spatial image 36 can be simulated from the design layout model 35, projection optics model 32, and design layout model 35. A resist image 38 can be simulated from the spatial image 36 using a resist model 37. For example, simulation of lithography can predict the profiles and CDs in the resist image.

[0083] More specifically, it should be noted that the source model 31 can represent the optical characteristics of the source, including but not limited to NA settings, sigma (σ) settings, and any specific illumination shape (e.g., off-axis radiation sources such as annular, quadrupole, bipolar). The projection optical model 32 can represent the optical characteristics of the projection optics, including aberration, distortion, one or more refractive indices, one or more physical sizes, one or more physical dimensions, etc. The design layout model 35 can represent the physical properties of one or more physical pattern formation devices, such as those 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 positions, spatial image intensity slopes, and / or CDs, which can then be compared to the expected design. The expected design is typically defined as the pre-OPC (pre-optical proximity correction) design layout, which can be provided in a standard digital file format (such as GDSII or OASIS) or other file formats.

[0084] According to the design layout, one or more portions can be identified, which are referred to as "fragments". In one example, a set of fragments is extracted, which represents a complex pattern in the design layout (usually about 50 to 1000 fragments can be used, although any number of fragments can be used). These patterns or fragments represent small parts of the design (i.e., circuits, cells, or patterns), and more specifically, fragments typically represent small parts that require special attention and / or verification. In other words, a fragment can be a part of the design layout, be similar to a part of the design layout, or have a similar behavior to a part of the design layout, where one or more key features can be identified empirically (including fragments provided by the customer), by trial and error, or by running a full-chip simulation. A fragment can contain one or more test patterns or metrology patterns.

[0085] A larger set of initial fragments can be provided a priori by the customer based on one or more known critical feature regions in the design layout that require special image optimization. Alternatively, in another example, a larger set of initial fragments can be extracted from the entire design layout by using some automation (such as machine vision) or manual algorithm that identifies one or more critical feature regions.

[0086] In a lithographic projection apparatus, such as one using an EUV (extreme ultraviolet radiation, e.g. having a wavelength in the range of 5 - 20 nm) source or a non-EUV source, a reduced radiation intensity may lead to stronger stochastic variations, such as significant linewidth roughness and / or local CD variations of small two-dimensional features, such as holes. In a lithographic projection apparatus using an EUV source, the reduced radiation intensity can be attributed to a low total radiation amount output from the source, radiation losses in the optics shaping the radiation from the source, transmission losses through the projection optics, high photon energy resulting in fewer photons at a constant dose, etc. The stochastic variations can be attributed to factors such as photon shot noise, secondary electrons generated by photons, photon absorption variations, and / or acid generated by photons in the resist. The small size of the features further exacerbates such stochastic variations. The stochastic variations of smaller features are an important factor in production yield and justify the inclusion of various optimization processes of the lithography process and / or the lithographic projection apparatus.

[0087] At the same radiation intensity, a shorter exposure time per substrate results in a higher throughput of the lithographic projection apparatus, but leads to stronger stochastic variations. The photon shot noise in a given feature at a given radiation intensity is proportional to the square root of the exposure time. In lithography using EUV and other radiation sources, there is a desire to shorten the exposure time to increase throughput. Therefore, the methods and apparatus described herein for considering stochastic variations in the optimization process are not limited to EUV lithography.

[0088] The throughput may also be affected by the total amount of radiation directed onto the substrate. In some lithographic projection apparatuses, a portion of the radiation from the source is discarded in order to achieve a desired illumination shape.

[0089] Figure 3A The line edge roughness (LER) is schematically depicted. Assuming all conditions are the same in three exposures or exposure simulations of the edge 903 of a feature in a design layout, the resist images 903A, 903B, and 903C of the edge 903 may have slightly different shapes and positions. The positions 904A, 904B, and 904C of the resist images 903A, 903B, and 903C can be measured by averaging the resist images 903A, 903B, and 903C, respectively. Stochastic variations, such as line edge roughness, are typically represented by a parameter of the distribution of the underlying characteristics. In this example, assuming the distribution is a normal distribution, the LER of the edge 903 can be represented by 3σ of the spatial distribution of the edge 903. 3σ can be derived from the positions (e.g., positions 904A, 904B, and 904C) of the edge 903 in many exposures or simulations of the edge 903. The LER represents the range within which the edge 903 may fall due to random effects. Therefore, the LER can also be referred to as the stochastic edge position error (SEPE). The LER can be larger than the change in the position of the edge 903 caused by non-stochastic effects.

[0090] Figure 3B Schematically depicts line width roughness (LWR). Assuming all conditions are the same in three exposures or exposure simulations of a long rectangular feature 910 with width 911 on a design layout, the widths 911A, 911B, and 911C of the resist images 910A, 910B, and 910C of the rectangular feature 910 can be slightly different respectively. The LWR of the rectangular feature 910 can be a measure of the distribution of the widths 911A, 911B, and 911C. For example, assuming the distribution is a normal distribution, the LWR can be 3σ of the distribution of the width 911. The LWR can be derived from many exposures or simulations of the width 911 (e.g., widths 911A, 911B, and 911C) of the rectangular feature 910. In the context of short features (e.g., contact holes), the width of their images cannot be well defined because long edges are not available for averaging their positions. A similar quantity, LCDU, can be used to characterize this random variation. LCDU is 3σ of the distribution of the measured CDs of the images of short features (assuming the distribution is a normal distribution).

[0091] Figure 3C Schematically shows how random variation affects lithography. In Figure 3C the example, the expected position of the edge of a feature in a space image or a resist image is represented by a dashed line 982. The actual edge is represented by a curve 995, which includes random variation (LER in this example), and errors not related to random effects (e.g., caused by other factors such as dose variation, focal length variation, source shape, patterning device (e.g., mask) errors, etc.). The average position of the actual edge is represented by a solid line 981. The difference 980 between the average position (solid line 981) and the expected position (dashed line 982) is an error not related to random effects, which can be called edge position error (EPE). The variation of the actual edge relative to the average position is random variation. The band 990 around the average position (solid line 981) can be called the random variation band, which encloses the random variation, indicating the extent to which the actual local edge position can reach due to random effects. The width of the random variation band can be greater than the EPE. Therefore, the total probability deviation from the expected position (dashed line 982) of the edge can be the sum of the EPE and the random variation band. If there is no random variation, the actual position of the edge in this example would be at the position indicated by the solid line 981, and it would not merge with the adjacent feature 983, and thus no defect would be generated. However, when there is random variation and the random variation band is large enough (e.g., band 990), the actual edge may merge with the adjacent feature 983 (the position marked by the dashed circle) and thus generate a defect. Therefore, it is desirable to evaluate, simulate, or reduce random variation.

[0092] In Figure 4AThe flowchart of and Figure 4B The method for determining the relationship between the stochastic variations of the characteristics of a spatial image or a resist image and one or more design variables is depicted in the schematic diagram of. In step 1301, the value 1503 of the characteristic is measured from a plurality of spatial images or resist images 1502 (either through actual exposure or simulation), and the plurality of spatial images or resist images 1502 are formed for each set of values 1501 of one or more sets of values of the design variables. In step 1302, from the distribution 1504 of the values 1503 of the characteristic measured from the spatial images or resist images formed for each set of values 1501 of one or more design variables, the values 1505 of the stochastic variations are determined for each set of values 1501 of one or more design variables. In step 1303, the relationship 1506 is determined by fitting with one or more parameters of a model from the values 1504 of the stochastic variations and one or more sets of values 1501 of the design variables.

[0093] In one example, the stochastic variation is LER, and the one or more design variables are the blurred image ILS (bl_ILS), dose, and image intensity. The model can be:

[0094] LER = a × bl_ILS b × (dose × image intensity) c (Equation 30)

[0095] The parameters a, b, and c can be determined by fitting. The blurred image ILS (bl_ILS) is the image logarithmic slope ILS on which spatial blur is imposed. The spatial blur can represent the blur of the resist image caused by the diffusion of chemical species generated in the resist layer by exposure to radiation.

[0096] Figure 5A Shows the result of fitting using the model in Equation 30. The values of LER1400 (as an example of the stochastic variation) for more than 900 different features, which include long trenches 1401, long lines 1402, short lines 1403, short trenches 1404, short line ends 1405, and short trench ends 1406 at a constant image intensity and a constant dose, are determined according to Figure 4A and Figure 4B The method in. The parameters a and b in Equation 30 (since the dose-weighted blurred image intensity is constant, the parameter c is incorporated into the parameter a) are determined by fitting the values of LER with the values of the design variable bl_ILS. The fitting result is shown in curve 1410.

[0097] Figure 5BShows the results of fitting 1510 using the model in Equation 30. Values of LCDU 1500 (as an example of random variation) of CDs in the width direction of the 20×40 nm trench 1505 and CDs in its length direction, at various doses and various image intensities, are determined using Figure 4A and Figure 4B the methods in. The parameters a, b, and c in Equation 30 are determined by fitting the values of LWR to the values of the design variables bl_ILS, dose, and image intensity.

[0098] Once the relationship between the random variation of the characteristics of the aerial image or the resist image and one or more design variables is determined by a method (such as Figure 4A and Figure 4B the methods in), for that characteristic, the relationship can be used to calculate the value of the random variation. Figure 6 Shows an exemplary flowchart for this calculation. In step 1610, a set of conditions (e.g., NA, σ, dose, focal length, resist chemical composition, one or more projection optical device parameters, one or more illumination parameters, etc.) are selected. In step 1620, the values of one or more design variables are calculated under these conditions. For example, the values of the resist image along the edge and the edge position of bl_ILS. In step 1630, the value of the random variation is calculated according to the relationship between the random variation and one or more design variables. For example, in one example, the random variation is the LER of the edge. In optional step 1640, a noise vector can be defined, the frequency distribution of which approximately matches the actual substrate measurement values. In optional step 1650, the noise vector is overlaid on the result (e.g., the random edge of the aerial image or the resist image).

[0099] The relationship between the random variation of the characteristics of the aerial image or the resist image and one or more design variables can also be used to identify one or more “hot spots” of the aerial image or the resist image, as Figure 7 shown. A “hot spot” can be defined as a position on the image where the random variation exceeds a certain amplitude. For example, if the LER values of two positions on two nearby edges are large, then these two positions have a high chance of being interconnected.

[0100] In one example, the values of the random variation (and / or its function) at multiple conditions and at multiple values of one or more design variables can be calculated and compiled in a non-transitory computer-readable medium 1800 (such as a database stored on a hard drive), as Figure 8 shown. The computer can query the medium 1800 and calculate the value of the random variation according to the content of the medium 1800.

[0101] Determination of random variations in the characteristics of the space / resist image can be useful in lithography processes in many ways. In one example, the random variations can be taken into account in optical proximity correction (OPC).

[0102] As an example, OPC addresses the fact that the final size and placement of the image of the design layout projected onto the substrate will not be the same as the size and placement of the design layout on the patterning device, or simply depend only on the size and placement of the design layout on the patterning device. Note that the terms “mask”, “reticle”, “patterning device” may be used interchangeably herein. Also, those skilled in the art will recognize that, especially in the context of lithography simulation / optimization, the terms “mask” / “patterning device” and “design layout” may be used interchangeably, as in lithography simulation / optimization, a physical patterning device is not necessarily used, but the design layout can be used to represent the physical patterning device. For small feature sizes and high feature densities present in some design layouts, 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 minute radiation coupled from one feature to another and / or non-geometric optical effects such as diffraction and interference. Similarly, during processes such as post-exposure bake (PEB), resist development, and etching, which typically occur after lithography, proximity effects may be caused by diffusion and other chemical effects.

[0103] To help ensure that the projected image of the design layout meets the requirements of a given target circuit design, proximity effects should be predicted and compensated for using complex numerical models, corrections, or pre-deformations of the design layout. The article “Full-Chip Lithography Simulation and Design Analysis - How OPC Is Changing IC Design”, C. Spence, Proc. SPIE, Vol. 5751, pp. 1 - 14 (2005) provides a review of “model-based” optical proximity correction processes. In typical high-end designs, almost every feature of the design layout requires some modification in order to achieve a high fidelity of the projected image to the target design. These modifications can include offsets or biases in edge position or line width, and the application of “assist” features designed to aid the projection of other features.

[0104] Given the millions of features typically present in chip designs, the application of model-based OPC in a target design involves good process models and significant computational resources. However, applying OPC is generally not an "exact science", but an empirical, iterative process that does not always compensate for all possible proximity effects. Therefore, the impact of OPC (e.g., the design layout after applying OPC and / or any other RET) should be verified through design checks, namely using intensive full-chip simulations with calibrated numerical process models, to reduce or minimize the likelihood that design defects are built into the patterns of the patterning device. This is driven by the high cost of fabricating high-end patterning devices (which vary in the millions of dollars range), and the impact on turnaround time of reworking or repairing the actual patterning device once it has been manufactured.

[0105] Both OPC and full-chip RET verification can be based on, for example, the numerical modeling systems and methods described in U.S. Patent Application Publication No. US 2005-0076322, and the article by Y. Cao et al., titled "Optimized Hardware and Software For Fast, Full-Chip Simulation", Proc. SPIE, Vol. 5754, 405 (2005).

[0106] The adjustment of a global deviation of a RET from a design layout (also referred to as a "mask bias") is relevant. The overall deviation is the difference between the pattern in the design layout and the pattern intended to be printed on the substrate. For example, ignoring the (reduction) magnification of the projection optics, a circular pattern with a diameter of 25 nm can be printed on the substrate as follows: by a pattern with a diameter of 50 nm in the design layout, or by a pattern with a diameter of 20 nm in the design layout but with a high dose.

[0107] In addition to optimizing the design layout or the patterning device (e.g., OPC), the illumination can also be optimized, which can be done together with or separately from patterning device optimization, in an effort to improve overall lithography fidelity. The terms "illumination source" and "source" are used interchangeably in this document. Many off-axis illuminations (such as annular, quadrupole, and dipole illuminations) have been introduced, and these off-axis illuminations provide greater degrees of freedom for OPC design, thus improving the imaging effect. Off-axis illumination is a way to resolve fine structures (i.e., target features) contained in the patterning device. However, when compared with conventional illumination, off-axis illumination generally provides less radiation intensity for the aerial image (AI). Therefore, it is desirable to attempt to optimize the illumination to achieve an optimal balance between finer resolution and reduced radiation intensity.

[0108] Several irradiation optimization methods can be found, for example, in the article by Rosenbluth et al. entitled “Optimum Mask and Source Patterns to Print a Given Shape”, Journal of Microlithography, Microfabrication, Microsystems 1(1), pages 13-20 (2002). The source is divided into several regions, each corresponding to a certain region of the pupil spectrum. Then, the source distribution is assumed to be uniform within each source region, and the intensity of each region is optimized for the process window. However, the assumption that the source distribution is uniform within each source region is not always valid, and thus the effectiveness of this scheme is affected. In another example described in the article by Granik entitled “Source Optimization for Image Fidelity and Throughput”, Journal of Microlithography, Microfabrication, Microsystems 3(4), pages 509-522 (2004), several existing source optimization schemes are reviewed and a method based on illuminator pixels is proposed, which transforms the source optimization problem into a series of non-negative least squares optimizations. Although these methods have shown some success, they typically require multiple complex iterations to converge. Additionally, it may be difficult to determine the appropriate / optimal values for some additional parameters, such as γ in the Granik method, which determines the trade-off between optimizing the source for substrate image fidelity and the smoothness requirements of the source.

[0109] For low k1 lithography, the optimization of both the source and the patterning device is useful for helping to ensure a viable process window for projecting critical circuit patterns. Some algorithms (e.g., Socha et al., Proc. SPIE, vol. 5853, 2005, page 180) discretize the irradiation into independent source points and the patterning device into diffraction orders in the spatial frequency domain, and formulate a cost function (which is defined as a function of one or more selected design variables) based on process window metrics such as exposure latitude, which can be predicted by an optical imaging model from the source point intensities and the patterning device diffraction orders.

[0110] As used herein, the term "design variables" includes a set of parameters of a lithographic projection apparatus or a lithographic process, e.g., parameters that can be adjusted by a user of the lithographic projection apparatus, or image characteristics that a user can adjust by adjusting these parameters. It should be understood that any one or more characteristics of the lithographic projection process, which includes one or more characteristics of illumination, patterning device, projection optics and / or resist, can be represented by design variables in an optimization. The cost function is typically a non-linear function of the design variables. Then, standard optimization techniques are used to optimize the cost function.

[0111] Correspondingly, the pressure of continuously decreasing design rules has driven semiconductor chip manufacturers to use existing 193nm ArF lithography technology to further enter the era of low k1 lithography technology. The lithography technology towards lower k1 poses heavy requirements on the needs of RET, exposure tools, and lithography-friendly designs. 1.35 ArF extreme numerical aperture (NA) exposure tools can be used in the future. To help ensure that circuit designs can be produced onto a substrate using a viable process window, the optimization of illumination - patterning device (referred to herein as source mask optimization or SMO) is becoming an important RET for the 2×nm node.

[0112] In U.S. Patent Application Publication No. 2011 - 0230999, the entire content of which is incorporated herein by reference, an illumination and patterning device (design layout) optimization method and system are described, which allow the use of a cost function without constraints and the simultaneous optimization of the illumination and patterning device within a practicable amount of time. In U.S. Patent Application Publication No. 2010 / 0315614, the entire content of which is incorporated herein by reference, another SMO method and system are described, which involve optimizing the source by adjusting the pixels of the source.

[0113] In a lithographic projection apparatus, as an example, the cost function can be expressed as

[0114]

[0115] where (z1, z2,..., z N ) are N design variables or their values. f p (z1, z2,..., z N ) can be a function of the design variables (z1, z2,..., z N ), such as the difference between the actual value and the expected value of a characteristic at an evaluation point for a set of values of the design variables (z1, z2,..., z N ). w p is related to f p (z1, z2,..., z N) associated weight constants. Evaluation points or patterns that are more critical than other evaluation points or patterns can be assigned a higher w p value. Patterns and / or evaluation points with a higher number of occurrences can also be assigned a higher w p value. Examples of evaluation points can be any physical point or pattern on a substrate, any point on a virtual design layout, or a resist image or aerial image, or a combination thereof. f p (z1, z2,..., z N ) can also be a function of one or more random variations (such as LWR, LER, and / or LCDU), which in turn is a function of design variables (z1, z2,..., z N ). f p (z1, z2,..., z N ) can be an explicit function of random variations, such as f p (LER) = LER 2 (z1, z2,..., z N ). f p (z1, z2,..., z N ) can be an explicit function of a variable that is a function of a random variation such as LER. For example, bl_ILS can be a function of LER as indicated by Equation 30, and f p (z1, z2,..., z N ) can be a variable that affects a random variation such as LER.

[0116] Thus, optimizing a cost function that includes f p (z1, z2,..., z N ) representing random variations may result in values of one or more design variables that reduce or minimize the random variations. The cost function can represent any one or more suitable characteristics of a lithographic projection apparatus, a lithographic process, or a substrate, such as focal length, CD, image shift, image distortion, image rotation, random variations, throughput, LCDU, or a combination thereof. LCDU is the local CD variation (e.g., three times the standard deviation of the local CD distribution). In one example, the cost function represents LCDU, throughput, and random variations (i.e., is a function thereof). In one example, the cost function represents EPE, throughput, and random variations (e.g., including f p (z1, z2,..., z N ), which is a function of these terms). In one example, the cost function includes f p (z1, z2,..., z N ) as a function of EPE, and f p (z1, z2,..., z N)。In one example, the design variables (z1, z2, …, z N ) include one or more selected from the following: dose, overall deviation of the patterning device, shape of the irradiation, or a combination thereof. Since it is typically the resist image that determines the pattern on the substrate, the cost function may include a function representing one or more characteristics of the resist image. For example, the f of such an evaluation point p (z1, z2, …, z N ) may simply be the distance between a point in the resist image and the expected position of that point (i.e., the edge position error EPE p (z1, z2, …, z N ). The design variables may include any adjustable parameters, such as adjustable parameters of a light source, patterning device, projection optics, dose, focal length, etc.

[0117] A lithographic apparatus may include components collectively referred to as a "wavefront manipulator", which may be used to adjust the shape of the wavefront and the intensity distribution and / or phase shift of the radiation beam. In one example, the lithographic apparatus may adjust the wavefront and intensity distribution at any position along the optical path of the lithographic projection apparatus, such as before the patterning device, near the pupil plane, near the image plane, and / or near the focal plane. The wavefront manipulator may be used to correct or compensate for certain deformations and / or phase shifts of the wavefront and intensity distribution caused by, for example, temperature variations in the source, patterning device, lithographic projection apparatus, thermal expansion of components of the lithographic projection apparatus, etc. Adjusting the wavefront and intensity distribution and / or phase shift may change the values of the evaluation points and the cost function. Such changes may be simulated from the model or measured in practice. Of course, CF(z1, z2, …, z N ) is not limited to the form in Equation 1. CF(z1, z2, …, z N ) may be in any other suitable form.

[0118] According to one example, a cost function representing both EPE and LER may have the following form:

[0119]

[0120] This is because both EPE and LER have a length dimension. Therefore, they can be directly added. Alternative cost functions may be used, including cost functions in which LER is included in EPE.

[0121] Equation 30 links bl_ILS to LER. Thus, optimizing using a cost function representing bl_ILS is similar to optimizing using a cost function representing LER. A larger bl_ILS results in a smaller LER, and vice versa. According to one example, the cost function can represent EPE and bl_ILS (or normalized ILS (NILS)). However, since bl_ILS does not measure length while EPE measures length, or NILS is dimensionless while EPE has a length dimension, EPE and bl_ILS (or NILS) may not be directly added. Thus, representing bl_ILS (or NILS) by a function representing length can enable the representation to be directly added to EPE.

[0122] ILS is defined as bl_ILS is the spatially blurred ILS. NILS is defined as = CD × ILS. These definitions suggest functions that can represent ILS, bl_ILS, or NILS and represent length, and thus allow direct addition to EPE. Figure 9A and Figure 9B respectively show the intensity of the image (spatial or resist) across the edge perpendicular to the edge of the pattern in the direction (x). A higher slope of the intensity with respect to x means higher ILS, bl_ILS, and NILS. Thus, Figure 9A the example of Figure 9B has higher ILS, bl_ILS, and NILS than the example of e The edge position X e is shifted with the intensity sufficient to expose the resist I. When the exposure duration is fixed, the intensity sufficient to expose the resist I changes with the dose. Thus, the offset of the edge position X ILS (hereinafter referred to as "EPE Figure 9A " in the example of ILS is less than the EPE Figure 9B in the example of ILS because Figure 9A the example of Figure 9B thus has higher ILS, bl_ILS, and NILS than the example of ILS is an example of a function that can represent ILS, bl_ILS, or NILS and represent length, thus allowing direct addition to the EPE in the cost function. EPE ILS can be written as

[0123]

[0124] where ILS(x e (0)) is a function of the design variables (z1, z2, …, z N ). According to one example, the cost functions representing EPE and either ILS, bl_ILS, or NILS can have the following form:

[0125]

[0126] where EPE p (z1, z2, …, z N )| δ＝0 is the EPE value at the nominal dose, p is the p-th evaluation point, and S p is the weight for the EPE ILS term. Thus, for example, the optimization that minimizes this cost function maximizes ILS(x e (0)), and thus minimizes LER.

[0127] According to one example, when the EPE term increases, the weight of the EPE ILS term can be decreased relative to the weight of the EPE term (e.g., ), such that the EPE ILS term is not dominant over the EPE term . If the EPE ILS term is dominant, the EPE term cannot be sufficiently reduced by the optimization. For example, when |EPE p | is higher than a user-selected offset, when |EPE p | > OF, s p = 0 (thus the optimization ignores the EPE ILS term and only reduces the EPE term), while when |EPE p | ≤ OF, s p ≠ 0, where OF is the offset. For example, a higher weight for the EPE term will cause the optimization using the cost function to favor reducing the EPE term.

[0128] Figure 10 A curve schematically showing the relationship between the cost function and EPE p is shown, where the weight is as Figure 10 shown, and when |EPE p | > OF, because the weight w p has a larger value, the EPE term accounts for a larger proportion of the cost function.

[0129] The design variables can have constraints, which can be expressed as (z1, z2, …, zN ) ∈ Z, where Z is the set of possible values of the design variables. A possible constraint on the design variables can be imposed by the desired production volume of the lithographic projection apparatus. A lower limit on the desired production volume results in an upper limit on the dose and thus has an impact on the stochastic variations (e.g., imposing a lower limit on the stochastic variations). Shorter exposure times and / or lower doses generally result in higher production volumes, but with larger stochastic variations. Since the stochastic variations are a function of the design variables, the consideration of the substrate production volume and the minimization of the stochastic variations may limit the possible values of the design variables. In the absence of such constraints imposed by the desired production volume, the optimization may yield a set of values of the design variables that are unrealistic. For example, if the dose is a design variable, in the absence of such constraints, the optimization may yield dose values that make the production volume economically unfeasible. However, the usefulness of the constraints should not be construed as necessary. For example, the production volume may be affected by the pupil fill factor. For some illumination designs, a low pupil fill factor may discard radiation, resulting in a lower production volume. The production volume may also be affected by the resist chemical composition. A slower resist (e.g., a resist that requires a large amount of radiation to be correctly exposed) results in a lower production volume.

[0130] Thus, the optimization process is to find a set of values of one or more design variables under the constraint (z1, z2, …, z N ) ∈ Z that optimizes a cost function, such as:

[0131]

[0132] According to one example, the overall optimization method is in Figure 11is shown in. The method includes step 302 of defining a multi-variable cost function of a plurality of design variables. The design variables may include any suitable combination of design variables selected from those representing the following: one or more characteristics of the illumination (300A) (e.g., the pupil fill factor, i.e., the percentage of the radiation of the illumination passing through the pupil or the opening), one or more characteristics of the projection optics (300B), and / or one or more characteristics of the design layout (300C). For example, the design variables may include design variables representing one or more characteristics of the illumination (300A) and one or more characteristics of the design layout (300C) (e.g., global deviation), but not design variables representing one or more characteristics of the projection optics (300B), which results in SMO. Alternatively, the design variables may include design variables representing one or more characteristics of the illumination (300A) (optionally polarization), one or more characteristics of the projection optics (300B), and one or more characteristics of the design layout (300C), which results in illumination-pattern formation device (e.g., mask)-projection system (e.g., lens) optimization (SMLO). In step 304, the design variables are simultaneously adjusted such that the cost function moves towards convergence. In step 306, it is determined whether a predefined termination condition is met. The predefined termination condition may include various possibilities, such as one or more selected from the following: according to the requirements of the numerical technique used, the value of the cost function has been minimized or maximized, the value of the cost function has been equal to or exceeded a threshold, the value of the cost function has reached within a preset error limit, and / or a preset number of iterations has been reached. If the condition in step 306 is met, the method ends. If one or more of the conditions in step 306 are not met, steps 304 and 306 are iteratively repeated until the desired result is obtained. The optimization does not necessarily result in a single set of values for one or more design variables because there may be physical limitations caused by factors such as the pupil fill factor, resist chemical composition, production volume, etc. The optimization may provide multiple sets of values for one or more design variables and associated performance characteristics (e.g., production volume), and allow the user of the lithographic apparatus to select one or more sets. Figure 22Shows several relationships between the production volume (in units of the number of substrates per hour) on the horizontal axis and a measure of random variation (e.g., the average of the worst corner CDU and LER) on the vertical axis, and the resist chemistry (which can be represented by the dose required to expose the resist), the pupil fill factor (also known as the "pupil fill factor"), the illumination efficiency (e.g., the ratio of the mirrors that direct radiation to the patterning device to the total available mirrors in the illuminator), and the mask bias. Trace 1811 shows these relationships for a 100% pupil fill factor and a fast resist. Trace 1812 shows these relationships for a 100% pupil fill factor and a slow resist. Trace 1821 shows these relationships for a 60% pupil fill factor and a fast resist. Trace 1822 shows these relationships for a 60% pupil fill factor and a slow resist. Trace 1831 shows these relationships for a 29% pupil fill factor and a fast resist. Trace 1832 shows these relationships for a 29% pupil fill factor and a slow resist. Optimization can present all these possibilities to the user, so that the user can select the pupil factor and the resist chemical composition based on his specific requirements for random variation and / or production volume. Optimization can also include calculating the relationships between the production volume and the pupil fill factor, the resist chemical composition, and the mask bias. Optimization can also include calculating the relationships between the measure of random variation and the pupil fill factor, the resist chemical composition, and the mask bias.

[0133] According to one example, as also Figure 23 illustrated in the flowchart of, the optimization can be performed (step 1910) for each item in a set of values of one or more design variables (e.g., an array, matrix, or list of values of global deviation and mask anchor deviation). In one example, the cost function of the optimization is a function of one or more measures of random variation (e.g., LCDU). Then, in step 1920, for the optimization of each set of values of one or more design variables, various characteristics of the process, the aerial image, and / or the resist image (e.g., critical dimension uniformity (CDU), depth of focus (DOF), exposure latitude (EL), mask error enhancement factor (MEEF), LCDU, production volume, etc.) can be presented to the user (e.g., in the form of a 3D graph). In the optional step 1930, the user selects a set of values of one or more design variables based on his one or more desired characteristics. This process can be implemented via an XML file or any scripting language.

[0134] The illumination, patterning device, and projection optical device can be optimized selectively (referred to as selective optimization) or simultaneously (referred to as simultaneous optimization). As used herein, the terms "simultaneously," "simultaneously," "collectively," and "collectively" mean that one or more design variables of one or more characteristics of the illumination, patterning device, projection optical device, and / or any other design variables are allowed to change at the same time. As used herein, the terms "selective" and "selectively" mean that not all design variables are allowed to change at the same time.

[0135] In Figure 11 , the optimization of all design variables is performed simultaneously. Such a process can be referred to as a simultaneous process or a co-optimization process. Alternatively, the optimization of all design variables can also be performed selectively, as shown in Figure 12 . In this process, in each step, some design variables are fixed while other design variables are optimized to optimize the cost function; then in the next step, a different set of variables is fixed while other variables are optimized to minimize or maximize the cost function. These steps are performed selectively until convergence or a certain termination condition is met. As shown in the non-limiting example flowchart of Figure 12 , first, the design layout is obtained (step 402), and then in step 404, the illumination optimization step is performed, where one or more design variables of the illumination are optimized (SO) to minimize or maximize the cost function while other design variables are fixed. Then in the next step 406, the patterning device (e.g., mask) optimization (MO) is performed, where the design variables of the patterning device are optimized to minimize or maximize the cost function while other design variables are fixed. These two steps are performed selectively until a certain termination condition is met in step 408. One or more 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 crosses a threshold, the value of the cost function reaches within a preset error range, a preset number of iterations has been reached, etc. Note that taking SO-MO-selective-optimization as an example of a selective process. The selective process can take many different forms, such as SO-LO-MO-selective-optimization, where SO and LO (projection optical optimization) are performed while MO is performed selectively and iteratively; or first SMO is performed once, and then LO and MO are performed selectively and iteratively; and so on. Another option is SO-PO-MO (illumination optimization, polarization optimization, and patterning device optimization). Finally, in step 410, the output of the optimization result is obtained, and the process stops.

[0136] As discussed previously, the pattern selection algorithm can be integrated with simultaneous optimization or alternative optimization. For example, when alternative optimization is employed, first full-chip SO can be performed, one or more "hot spots" and / or "warm spots" are identified, and then MO is performed. Given the present disclosure, several permutations and combinations of sub-optimizations are possible in order to obtain the desired optimization result.

[0137] Figure 13A An exemplary method of optimization is shown, in which a cost function is minimized or maximized. In step S502, initial values of one or more design variables are obtained, including one or more associated adjustment ranges (if any). In step S504, a multi-variable cost function is established. In step S506, the cost function is expanded in a sufficiently small neighborhood around the starting point values of the one or more design variables at the first iteration step (i = 0). In step S508, standard multi-variable optimization techniques are applied to the cost function. Note that the optimization problem can refer to constraints, such as one or more adjustment ranges, during the optimization process in S508 or at a later stage of the optimization process. Step S520 indicates that each iteration has been completed for one or more given test patterns (also referred to as "gauges"), and one or more given test patterns are for the identified evaluation points that have been selected to optimize the lithography process. In step S510, the lithography response is predicted. In step S512, the result of step S510 is compared with the desired or ideal lithography response value obtained in step S522. If the termination condition is satisfied in step S514, i.e., the optimization generates a lithography response value that is sufficiently close to the desired value, then the final values of the design variables are output in step S518. The output step may also include outputting one or more other functions using the final values of the design variables, such as outputting a wavefront aberration adjustment map at the pupil plane (or other plane), an optimized illumination map, and / or an optimized design layout, etc. If the termination condition is not satisfied, then in step S516, the values of one or more design variables are updated using the results of the i-th iteration, and the process returns to step S506. The process described below is detailed Figure 13A of the process.

[0138] In the exemplary optimization process, in addition to f p (z1, z2, …, z N ) being sufficiently smooth (e.g., there exists a first derivative (n = 1, 2, … N)), no design variables (z1, z2, …, z N ) are related to f p (z1, z2, …, z N) The relationship between is assumed or approximated, which is usually valid in a lithographic projection apparatus. Algorithms such as the Gauss - Newton algorithm, Levenberg - Marquardt algorithm, Broyden - Fletcher - Goldfarb - Shanno algorithm, gradient descent algorithm, simulated annealing algorithm, interior point algorithm, and genetic algorithm can be applied to find

[0139] Here, take the Gauss - Newton algorithm as an example. The Gauss - Newton algorithm is an iterative method that is applicable to general non - linear multivariable optimization problems. In the i - th iteration, where the design variables (z1, z2, …, z N ) take the values (z 1i , z 2i , …, z Ni ), the Gauss - Newton algorithm linearizes f 1i , z 2i , …, z Ni ) around (z p (z1, z2, …, z N ), and then calculates the values (z 1i , z 2i , …, z Ni ) around (z 1(i+1) , z 2(i+1) , …, z N(i+1) ) that give the minimum of CF(z1, z2, …, z N ). The design variables (z1, z2, …, z N ) take the values (z 1(i+1) , z 2(i+1) , …, z N(i+1) ) in the (i + 1)-th iteration. This iteration continues until convergence (i.e., CF(z1, z2, …, z N ) no longer decreases further) or a preset number of iterations has been reached.

[0140] Specifically, in the i - th iteration, around (z 1i , z 2i , …, z Ni ),

[0141]

[0142] Under the approximation of Equation 3, the cost function becomes:

[0143]

[0144] which is the design variables (z1, z2, …, zN ) of the quadratic function. Except for the design variables (z1, z2, …, z N ), each term is a constant.

[0145] If the design variables (z1, z2, …, z N ) are not subject to any constraints, then (z 1(i+1) , z 2(i+1) , …, z N(i+1) ) can be obtained by solving N linear equations: where n = 1, 2, …, N.

[0146] If the design variables (z1, z2, …, z N ) are subject to constraints in the following form: in the form of J inequalities (for example, the adjustment range of (z1, z2, …, z N )) where j = 1, 2, …, J; and in the form of K equalities (for example, the mutual dependencies between design variables) where k = 1, 2, …, K, then the optimization process will become a classical quadratic programming problem, where A nj , B j , C nk , D k are constants. Additional constraints can be imposed for each iteration. For example, a "damping factor" Δ D can be introduced to limit the difference between (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 is maintained. Such a constraint can be expressed as z ni - Δ D ≤ z n ≤ z ni + Δ D . For example, (z 1(i+1) , z 2(i+1) , …, z N(i+1) ) can be obtained using the method described in "Numerical Optimization" (Second Edition) by Jorge Nocedal and Stephen J. Wright (Berlin New York: Springer. Cambridge University Press).

[0147] Instead of minimizing f p (z1, z2, …, z N)'s RMS, the optimization process can also minimize the magnitude of the maximum deviation (worst defect) of the evaluation points from their expected values. In this method, the cost function can be expressed as

[0148]

[0149] where CL p is the maximum allowable value of f p (z1, z2,..., z N ). This cost function represents the worst defect among the evaluation points. Optimization using this cost function can minimize the magnitude of the worst defect. An iterative greedy algorithm can be used for this optimization.

[0150] The cost function of Equation 5 can be approximated as:

[0151]

[0152] where q is an even positive integer, such as at least 4 or at least 10. Equation 6 mimics the behavior of Equation 5, while allowing the optimization to be performed analytically and using methods such as the steepest descent method, conjugate gradient method, etc. to accelerate.

[0153] Minimizing the worst defect size can also be combined with the linearization of f p (z1, z2,..., z N ). Specifically, f p (z1, z2,..., z N ) is approximated as in 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 that specify the minimum and maximum allowable deviations of f p (z1, z2,..., z N ). Inserting Equation 3, for p = 1,..., P, these constraints are transformed into

[0154]

[0155] and

[0156]

[0157] Since Equation 3 is usually only valid near (z1, z2,..., z N ), if the desired constraint E Lp ≤ f p (z1, z2,..., z N) ≤ E Up cannot be achieved in the vicinity of this, which can be determined by any conflict among the inequalities, then the constraint E Lp and E Up can be relaxed until the constraint is achievable. This optimization process minimizes the worst defect size in the vicinity of (z1, z2, …, z N ). Then, the worst defect size is gradually reduced in each step, and each step is executed iteratively until some termination condition is satisfied. This will result in an optimal reduction of the worst defect size.

[0158] Another way to minimize the worst 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 a higher priority is given to reducing the defect size at this evaluation point.

[0159] In addition, the cost functions in Equation 4 and Equation 5 can be modified by introducing Lagrange multipliers to achieve a compromise between optimizing the RMS of the defect size and optimizing the worst defect size, that is,[[]]

[0160]

[0161] where λ is a preset constant that specifies the trade-off between optimizing the RMS of the defect size and optimizing the worst defect size. In particular, if λ = 0, then Equation 6''' becomes Equation 4, and only the RMS of the defect size is minimized; if λ = 1, then it becomes Equation 5 and only the worst defect size is minimized; if 0 < λ < 1, then both are taken into account in the optimization. Such an optimization problem can be solved using various methods. For example, similar to what was described previously, the weights in each iteration can be adjusted. Alternatively, similar to minimizing the worst defect size from inequalities, during the solution of the quadratic programming problem, the inequalities in Equations 6' and 6'' are regarded as constraints on the design variables. Then, the bounds of the worst defect size can be relaxed incrementally, or the weight of the worst defect size can be increased incrementally, the cost function values are calculated for each achievable worst defect size, and the values of the design variables that minimize the total cost function are selected as the initial points for the next step. By performing this operation iteratively, the minimization of this new cost function can be achieved.

[0162] Optimizing a lithographic projection apparatus 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 for which the resist image is within certain limits of the design target of the resist image. Note that all methods discussed herein can also be extended to a general process window definition, which can be established by different or additional basic parameters in addition to the exposure dose and defocus. These parameters can include but are not limited to optical settings such as NA, σ, aberration, polarization, or the optical constants of the resist layer. For example, as previously mentioned, if the process window (PW) also includes different mask biases, the optimization includes minimizing the MEEF, which is defined as the ratio between the substrate EPE and the induced mask edge bias. The process window defined over focus and dose values is only used as an example in this disclosure. A method for maximizing the process window according to an example is described below.

[0163] In a first step, starting from the known conditions (f0, ε0) within the process window, where f0 is the nominal focus and ε0 is the nominal dose, one of the following cost functions is minimized in the vicinity of (f0 ± Δf, ε0 ± ε):

[0164]

[0165] Or

[0166]

[0167] Or

[0168]

[0169] If the nominal focus f0 and the nominal dose ε0 are allowed to move, they can be optimized jointly with the design variables (z1, z2,..., z N ). In the next step, if a set of values (z1, z2,..., z N , f, ε) can be found such that the cost function is within a preset limit, then (f0 + Δf, ε0 ± ε) is accepted as part of the process window.

[0170] If the focus and dose are not allowed to move, the design variables (z1, z2,..., z N ) are optimized with the focus and dose fixed at the nominal focus f0 and the nominal dose ε0. In an alternative example, if a set of values can be found such that the cost function is within the preset limit, then (f0 ± Δf, ε0 ± ε) is accepted as part of the process window.

[0171] The methods described earlier in this disclosure can be used to minimize the respective cost functions of Equation 7, Equation 7', or Equation 7". If the design variables represent one or more characteristics of a projection optical device (such as Zernike coefficients), minimizing the cost function of Equation 7, Equation 7', or Equation 7" results in maximizing the process window based on projection optical device optimization (i.e., LO). If the design variables also represent one or more characteristics of the illumination and patterning devices in addition to the characteristics of the projection optical device, minimizing the cost function of Equation 7, Equation 7', or Equation 7" results in maximizing the process window based on SMLO, as Figure 11 shown. If the design variables represent one or more characteristics of the source and patterning devices, minimizing the cost function of Equation 7, Equation 7', or Equation 7" results in maximizing the process window based on SMO. The cost functions of Equation 7, Equation 7', or Equation 7" can also include at least one f p (z1, z2, …, z N ), which is a function of one or more random variations such as LWR, local CD variations of 2D features, and / or production volume.

[0172] Figure 14 shows a specific example of how the simultaneous SMLO process can be optimized using the Gauss-Newton algorithm. In step S702, the starting values of one or more design variables are identified. The adjustment range for each variable can also be identified. In step S704, the cost function is defined using one or more design variables. In step S706, the cost function is extended near the starting values of all evaluation points in the design layout. In optional step S710, full-chip simulation is performed to cover all critical patterns in the full-chip design layout. In step S714, the desired lithography response metric (such as CD or EPE) is obtained, and in step S712, the desired lithography response metric is compared with the predicted values of these quantities. In step S716, the process window is determined. Steps S718, S720, and S722 are similar to the corresponding steps S514, S516, and S518 as described with respect to Figure 13A described. As previously mentioned, the final output can be, for example, a wavefront aberration map in the pupil plane, which is optimized to produce the desired imaging performance. The final output can be, for example, an optimized illumination map and / or an optimized design layout.

[0173] Figure 13B shows an exemplary method for optimizing a cost function, where the design variables (z1, z2, …, z N ) include such design variables that can only take discrete values.

[0174] The method begins with defining a group of pixels to be irradiated and a patterning device tile of a patterning device (step 802). Generally, the group of pixels or the patterning device tile may also be referred to as a partitioning of a lithography process component. In one exemplary scenario, irradiation is partitioned into 117 groups of pixels and, for the patterning device, 94 patterning device tiles are defined, resulting in a total of 211 partitions, substantially as described above.

[0175] In step 804, a lithography model is selected as the basis for lithography simulation. The results generated by the lithography simulation are used in the calculation of one or more optical metrics or responses. A specific optical metric is defined as a performance metric to be optimized (step 806). In step 808, initial (pre-optimized) conditions for the irradiation and the patterning device are set. The initial conditions include the initial states of the group of pixels to be irradiated and the patterning device tile of the patterning device such that an initial irradiation shape and an initial patterning device pattern can be referenced. The initial conditions may also include mask bias, NA, and / or focus ramp range. Although steps 802, 804, 806, and 808 are depicted as sequential steps, it should be understood that in other examples, these steps may be performed in other orders.

[0176] In step 810, the groups of pixels and the patterning device tiles are sorted. The groups of pixels and the 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, according to the physical location of the groups of pixels and the patterning device tiles (e.g., sorting the groups of pixels closer to the center of the irradiation higher), and / or according to how the change of a group of pixels or a patterning device tile affects the performance metric.

[0177] Once the groups of pixels and the patterning device tiles are sorted, the irradiation and the patterning device are adjusted to improve the performance metric (step 812). In step 812, each of the groups of pixels and the patterning device tiles is analyzed in the sorted order to determine whether a change in the group of pixels or the patterning device tile will result in an improved performance metric. If it is determined that the performance metric will be improved, the group of pixels or the patterning device tile is changed accordingly, and then the resulting improved performance metric and the modified irradiation shape or the modified patterning device pattern form a baseline for comparison for the subsequent analysis of the lower-sorted groups of pixels and patterning device tiles. In other words, the changes that improve the performance metric are retained. Since changes to the states of the groups of pixels and the patterning device tiles are made and retained, the initial irradiation shape and the initial patterning device pattern are changed accordingly, such that the modified irradiation shape and the modified patterning device pattern are obtained from the optimization process in step 812.

[0178] In other scenarios, the adjustment of the polygon shape of the patterning device and the paired polling of pixel groups and / or patterning device tiles are also performed within the optimization process of step 812.

[0179] In one example, the interleaved simultaneous optimization process can include changing the illuminated pixel groups, and if an improvement in the performance metric is detected, the dose or intensity is stepped up and / or stepped down to search for further improvements. In additional examples, the stepping up and / or stepping down of the dose or intensity can be replaced by: changing the deviation of the patterning device pattern to search for further improvements in the simultaneous optimization process.

[0180] In step 814, it is determined whether the performance metric has converged. For example, if little or no improvement in the performance metric has been witnessed in the last few iterations of steps 810 and 812, the performance metric can be considered to have converged. If the performance metric has not converged, steps 810 and 812 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 816).

[0181] The above optimization method can be used to increase the throughput of a lithographic projection apparatus. For example, the cost function can include f as a function of the exposure time p (z1, z2, …, z N ). In one example, the optimization of such a cost function is constrained or influenced by a measure of random variation or other measures. Specifically, a computer-implemented method for increasing the throughput of a lithographic process can include: optimizing a cost function that is a function of one or more random variations of the lithographic process and a function of the exposure time of the substrate in order to reduce or minimize the exposure time.

[0182] In one example, the cost function includes at least one f p (z1, z2, …, z N ) that is a function of one or more random variations. The one or more random variations can include LWR of 2D features and / or local CD variations. In one example, the one or more random variations include one or more random variations of one or more characteristics of a spatial image or a resist image. For example, such random variations can include line edge roughness (LER), line width roughness (LWR), and / or local critical dimension uniformity (LCDU). Including one or more random variations in the cost function allows finding values of one or more design variables that minimize the one or more random variations, thereby reducing the risk of defects due to random variations.

[0183] Figure 15A A flowchart of a method for identifying hotspots in a spatial image or a resist image based on a feature-based random variation (e.g., LER), or on a variable that is a function of or affects the random variation (e.g., bl_ILS, ILS, or NILS), according to one example, is shown. In an optional step 2510, a value of a random variation (e.g., LER) that is a function of a characteristic (e.g., edge position) of the spatial image or the resist image, or a variable (e.g., bl_ILS, ILS, or NILS) that affects such a random variation, is obtained. In step 2520, a value of the random variation (e.g., LER) of the characteristic (e.g., from the value of the variable) is obtained. In step 2530, a range of the characteristic is obtained. The range can be due to any suitable limitation. For example, when the random variation is LER, the range can be determined by the geometry of the pattern of the design layout. For example, the maximum value of LER can not exceed the width of the gap from an edge to its adjacent edge. In step 2540, the value of the random variation is compared with the range. If the random variation exceeds the range, then in step 2550, the characteristic is identified as a hotspot. Further processing such as optimization to reduce the random variation can be performed on the characteristic identified as a hotspot.

[0184] Figure 15B A flowchart of a method for identifying hotspots in a spatial image or a resist image based on a random variation (e.g., LER) of a characteristic (e.g., edge position) of the spatial image or the resist image, or on a variable that is a function of or affects the random variation (e.g., bl_ILS, ILS, or NILS), according to one example, is shown. In step 2610, a range of the characteristic is obtained. In step 2620, a range of the random variation (e.g., LER) or a range of the variable (e.g., bl_ILS, ILS, or NILS) is obtained based on the range of the characteristic. In step 2630, a value of the random variation or a value of the variable is obtained. In step 2640, the value of the random variation or the value of the variable is compared with its corresponding range. If the value of the random variation or the value of the variable exceeds its corresponding range, then in step 2650, the characteristic is identified as a hotspot. For the characteristic identified as a hotspot, further processing such as optimization to reduce the random variation can be performed.

[0185] Figure 16 A flowchart of a method for reducing random variation (e.g., LER) of one or more characteristics (e.g., edge position) of a spatial image or a resist image, according to one example, is shown. In step 2710, by, for example, using Figure 15A or Figure 15BA method of obtaining one or more features by identifying one or more features as hotspots from a portion of a design layout. In step 2720, for example, a cost function is used to reduce random variations of one or more features, the cost function representing at least a random variation or variable (e.g., bl_ILS, ILS, or NILS), which is a function of or affects the random variation. In step 2730, hotspots are re-identified from a portion of the design layout. In step 2740, it is determined whether a hotspot is identified. If a hotspot is identified, proceed to step 2750; if no hotspot is identified, the method ends. In step 2750, one or more parameters of the optimization are changed (e.g., δ and / or a user-selected offset), and the method repeats again to step 2720 and performs the optimization with the changed one or more parameters. In an alternative, one or more parameters can be part of the design layout, and steps 2740 and 2750 can be omitted.

[0186] Figure 17 is a block diagram showing a computer system 100 that can help implement the optimization methods and processes disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for transferring information, and a processor 104 (or 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, coupled to the bus 102 to store 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 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.

[0187] The computer system 100 can be coupled via the bus 102 to a display 112 for displaying information to a computer user, such as a cathode ray tube (CRT) or a flat panel or touch panel display. An input device 114 including alphanumeric keys and other keys is coupled to the bus 102 for transmitting 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, which is used to transmit direction information and command selections to the processor 104 and to control the movement of a cursor on the display 112. The input device typically has two degrees of freedom on 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 panel (screen) display can also be used as an input device.

[0188] According to one example, in response to one or more sequences of one or more instructions included in main memory 106 being executed by processor 104, a portion 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 instruction sequence included in main memory 106 causes processor 104 to perform the process steps described herein. One or more processors in a multiprocessing arrangement may also be employed to execute the instruction sequence included in main memory 106. In an alternative example, hardwired circuitry may be used in place of, or in combination with, software instructions. Accordingly, the description herein is not limited to any specific combination of hardware circuitry and software.

[0189] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to processor 104 for execution. Such a medium may take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media includes, for example, optical or magnetic disks, such as storage device 110. Volatile media includes dynamic memory, such as main memory 106. Transmission media includes coaxial cables, copper wire, and fiber optics, including the wires that comprise bus 102. Transmission media can also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and in infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape, any other magnetic medium, CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with patterns of holes, RAM, PROM, and EPROM, FLASH-EPROM, any other memory chip or cartridge, a carrier wave as described hereinafter, or any other medium from which a computer can read.

[0190] 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 borne on a magnetic disk of a remote computer. The remote computer can load the instructions into its dynamic memory and then 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 convert the data to an infrared signal using an infrared transmitter. 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 either before or after execution by processor 104.

[0191] The computer system 100 may also include a communication interface 118 coupled to the bus 102. The communication interface 118 provides two-way data communication coupled to a network link 120, and the network link 120 is connected to a local area network 122. For example, the communication interface 118 may be an integrated services digital network (ISDN) card or a modem for providing a data communication connection to a corresponding type of telephone line. As another example, the communication interface 118 may be a local area network (LAN) card for providing a data communication connection to a compatible LAN. A wireless link may also be implemented. In any such implementation, the communication interface 118 transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0192] The network link 120 generally provides data communication to other data devices through one or more networks. For example, the network link 120 may provide a connection to a host computer 124 through the local network 122, or a connection to a data device operated by an Internet service provider (ISP) 126. The ISP 126 in turn provides data communication services through the global packet data communication network (now commonly referred to as the "Internet" 128). Both the local area network 122 and the Internet 128 use electrical, electromagnetic, or optical signals carrying digital data streams. Signals through various networks and signals on the network link 120 and through the communication interface 118, which carry digital data to and from the computer system 100, are exemplary forms of carriers for conveying information.

[0193] The computer system 100 can send messages and receive data, including program code, through the (one or more) networks, the network link 120, and the communication interface 118. In the Internet example, the server 130 can transmit the code requested by the application through the Internet 128, the ISP 126, the local network 122, and the communication interface 118. For example, one such downloaded application can provide exemplary irradiation optimization. The received code can be executed by the processor 104 when it is received, and / or stored in the storage device 110 or other non-volatile storage for later execution. In this way, the computer system 100 can obtain application code in the form of a carrier wave.

[0194] Figure 18 An exemplary lithographic projection apparatus is schematically depicted, the irradiation of which can be optimized using the methods described herein. The apparatus includes:

[0195] - An illumination system IL for conditioning a radiation beam B. In this particular case, the illumination system also includes a radiation source SO;

[0196] - A first stage (e.g., a patterning device stage) MT, which is provided with a patterning device holder for holding a patterning device MA (e.g., a mask), and the first stage is connected to a first locator to accurately position the patterning device relative to an article PS;

[0197] - A second stage (substrate stage) WT, which is provided with a substrate holder for holding a substrate W (e.g., a silicon wafer coated with resist), and the second stage is connected to a second locator to accurately position the substrate relative to the article PS.

[0198] - A projection system (“lens”) PS (e.g., a refractive system, a catadioptric system, or a catadioptric optical system), for imaging an irradiated portion of the patterning device MA onto a target portion C (e.g., including one or more dies) of the substrate W.

[0199] As depicted herein, the device is transmissive (i.e., has a transmissive patterning device). However, in general, the device can also be, for example, reflective (with a reflective patterning device). The device can employ a patterning device different from a conventional mask; examples include a programmable mirror array or an LCD matrix.

[0200] A source SO (e.g., a mercury lamp or an excimer laser, an LPP (laser-produced plasma) EUV source) generates a radiation beam. The beam is fed directly or after passing through an adjusting device such as a beam expander Ex into an illumination system (illuminator) IL. The illuminator IL can include adjusting devices AD for setting the external and / or internal radial range (commonly referred to as σ - outer and σ - inner, respectively) of the intensity distribution in the beam. Additionally, the illuminator will typically include various other components, such as an integrator IN and a condenser CO. In this way, the beam B incident on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0201] Regarding Figure 18 It should be noted that the source SO can be within the housing of the lithographic projection apparatus (e.g., this is usually the case when the source SO is a mercury lamp), but it can also be remote from the lithographic projection apparatus, and the radiation beam generated by it is introduced into the apparatus (e.g., by means of a suitable guiding mirror); the latter scenario is typically the case when the source SO is an excimer laser (e.g., based on KrF, ArF, or F2 laser).

[0202] The beam bundle PB subsequently intercepts the patterning device MA, which is held on the patterning device table MT. After having passed through the patterning device MA, the beam B passes through the lens PL, which focuses the beam B onto the target portion C of the substrate W. By means of the second positioning device (and the interferometric device IF), the substrate table WT can be accurately moved, for example, so as to position different target portions C on the path of the beam bundle PB. Similarly, for example, after mechanically retrieving the patterning device MA from the patterning device library or during scanning, the first positioning device can be used to accurately position the patterning device MA relative to the path of the beam B. Generally, the movement of the tables MT, WT will be effected by means of long stroke modules (coarse positioning) and short stroke modules (fine positioning) (not explicitly shown in Figure 18 ). However, in the case of a stepper (as opposed to a step-and-scan tool), the patterning device table MT may be connected only to a short stroke actuator or may be fixed.

[0203] The tool depicted can be used in two different modes:

[0204] - In the step mode, the patterning device table MT remains substantially stationary and the entire patterning device image is projected onto the target portion C in one go (i.e., a single "flash"). The substrate table WT is then moved in the x and / or y direction so that different target portions C can be irradiated by the beam bundle PB;

[0205] - In the scan mode, substantially the same scenario applies, except that a given target portion C is not exposed in one "flash". Instead, the patterning device table MT is movable in a given direction (the so-called "scan direction", e.g., the y direction) with a velocity v such that the projection beam B is caused to scan over the patterning device image; simultaneously, the substrate table WT is moved synchronously in the same or opposite direction with a velocity V = Mv, where M is the magnification of the lens PL (generally, M = 1 / 4 or 1 / 5). In this way, a relatively large target portion C can be exposed without sacrificing resolution.

[0206] Figure 19 Another exemplary lithographic projection apparatus 1000 is schematically depicted, the illumination of which can be optimized by the methods described herein.

[0207] The lithographic projection apparatus 1000 comprises:

[0208] - a source collector module SO

[0209] - an illumination system (illuminator) IL, which is configured to condition the radiation beam B (e.g., EUV radiation).

[0210] - A support structure (e.g., a patterning device stage) MT, which is configured to support a patterning device (e.g., a mask or a reticle) MA and is connected to a first positioner PM, the first positioner PM being configured to accurately position the patterning device;

[0211] - A substrate stage (e.g., a wafer stage) WT, which is configured to hold a substrate (e.g., a wafer coated with resist) W and is connected to a second positioner PW, the second positioner PW being configured to accurately position the substrate; and

[0212] - A projection system (e.g., a reflective projection system) PS, which is configured to project the pattern imparted to a radiation beam B by the patterning device MA onto a target portion C (e.g., including one or more dies) of the substrate W.

[0213] As depicted herein, the apparatus 1000 is reflective (e.g., employing a reflective patterning device). It should be noted that since most materials are absorptive in the EUV wavelength range, the patterning device may have a multilayer reflector, which includes a multi-stack of, for example, molybdenum and silicon. In one example, the multi-stack reflector has 40 pairs of molybdenum and silicon layers, where the thickness of each layer is a quarter wavelength. Even smaller wavelengths can be generated with X-ray lithography. Since most materials are absorptive at EUV and X-ray wavelengths, a thin sheet of patterned absorptive material (e.g., a TaN absorber on a multilayer reflector) on the topography of the patterning device defines where the features will be printed (positive resist) or not printed (negative resist).

[0214] Reference Figure 19 , the illuminator IL receives an extreme ultraviolet radiation beam from the source collector module SO. Methods for generating EUV radiation include, but are not limited to, converting a material into a plasma state of at least one element (e.g., xenon, lithium, or tin) having one or more emission lines in the EUV range. In one such method, which is commonly referred to as laser-produced plasma (“LPP”), the plasma can be generated by irradiating a fuel (such as droplets, streams, or clusters of material having line-emitting elements) with a laser beam. The source collector module SO may be part of an EUV radiation system, which includes a laser (not shown in Figure 19 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 the source collector module. For example, when a CO2 laser is used to provide a laser beam for fuel excitation, the laser and the source collector module may be separate entities.

[0215] In this case, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is transmitted from the laser to the source collector module by means of a beam delivery system including, for example, suitable directing mirrors / or beam expanders. In other cases, for example, when the source is a discharge produced plasma EUV generator (commonly referred to as a DPP source), the source may be an integral part of the source collector module.

[0216] The illuminator IL may include regulators for adjusting the angular intensity distribution of the radiation beam. In general, at least the outer and / or inner radial extent of the intensity distribution in the pupil plane of the illuminator (commonly referred to as σ-out and σ-in respectively) may be adjusted. Additionally, the illuminator IL may include various other components such as faceted field and pupil mirror devices. The illuminator may be used to adjust the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0217] The radiation beam B is incident on a patterning device (e.g., a mask) MA, which is held on a support structure (e.g., a patterning device table) MT and patterned by the patterning device. After reflection from the patterning device (e.g., a mask) MA, the radiation beam B passes through a projection system PL, which focuses the beam onto a target portion C of the substrate W. By means 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, in order to position different target portions C in the path of the radiation beam B. Similarly, a first positioner PM and another 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 may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0218] The depicted apparatus 1000 can be used in at least one of the following modes:

[0219] 1. In step mode, the support structure (e.g., the patterning device table) MT and the substrate table WT remain substantially stationary while the entire pattern imparted to the radiation beam is projected onto the target portion C in one go (i.e., a single static exposure). The substrate table WT is then shifted in the X and / or Y direction so that different target portions C can be exposed.

[0220] 2. In scan mode, the support structure (e.g., the patterning device table) MT and the substrate table WT are scanned synchronously while the pattern imparted to the radiation beam is projected onto the target portion C (i.e., a single dynamic exposure). The rate and direction of the substrate table WT relative to the support structure (e.g., the patterning device table) MT can be determined by the (reduction) magnification and image reversal characteristics of the projection system PS.

[0221] 3. In another mode, the support structure (e.g., the patterning device table) MT remains substantially stationary to hold the programmable patterning device, and the substrate table WT is moved or scanned while the pattern imparted to the radiation beam is projected onto the target portion C. In this mode, typically, a pulsed radiation source is employed, and the programmable patterning device is updated as needed after each movement of the substrate table WT, or between successive radiation pulses during the scan. This operating mode can be readily applied to maskless lithography using a programmable patterning device, such as the type of programmable mirror array described above.

[0222] Figure 20 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 such that a vacuum environment can be maintained within the enclosure structure 220 of the source collector module SO. The EUV radiation emitting plasma 210 can be formed by a discharge-produced plasma source. The EUV radiation can be generated from a gas or vapor (e.g., xenon, lithium vapor, or tin vapor), where 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, for example, by a discharge that causes at least a partially ionized plasma. For efficient radiation generation, a partial pressure of, for example, 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required. In one example, a plasma of excited tin (Sn) is provided to generate EUV radiation.

[0223] The 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 in some cases as a contaminant barrier or fin trap), which is positioned in or after an opening in the source chamber 211. The contaminant trap 230 can include a channel structure. The contaminant trap 230 can 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 described herein includes at least a channel structure.

[0224] The collector chamber 211 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 passing through the collector CO may be reflected by the grating spectral filter 240 to be focused at 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 the intermediate focus, and the source collector module is arranged such that the intermediate focus IF is located at or near the opening 221 in the enclosure structure 220. The virtual source point IF is an image of the radiation-emitting plasma 210.

[0225] Subsequently, the radiation passes through the illumination system IL, which may include a faceted field mirror device 22 and a faceted pupil mirror device 24, arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA, and a desired radiation intensity uniformity at the patterning device MA. When the radiation beam 21 is reflected at the patterning device MA held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged onto a substrate W held by the substrate table WT via the reflective elements 28, 30 by the projection system PS.

[0226] More elements than those shown may generally be present in the illumination optical unit IL and the projection system PS. Depending on the type of lithographic apparatus, the grating spectral filter 240 may optionally be present. In addition, more mirrors than those shown in the figure may be present, for example, compared with Figure 20 as shown, 1 - 6 additional reflective elements may be present in the projection system PS.

[0227] As Figure 20 illustrated, the collector optics CO is depicted as a nested collector having grazing incidence reflectors 253, 254, and 255, which is only one example of a collector (or collector mirror). The grazing incidence reflectors 253, 254, and 255 are arranged axially symmetrically about the optical axis O, and this type of collector optics CO can be used in combination with a discharge-produced plasma source commonly referred to as a DPP source.

[0228] Alternatively, the source collector module SO may be part of an LPP radiation system as Figure 21 shown. A laser LA is arranged to deposit laser energy into a fuel such as xenon (Xe), tin (Sn), or lithium (Li) to generate a highly ionized plasma 210 having an electron temperature of several tens of eV. The high-energy radiation generated during the de-excitation and recombination of these ions is emitted from the plasma, collected by a near-normal incidence collector optics CO, and focused onto the opening 221 in the enclosure structure 220.

[0229] U.S. Patent Application Publication No. US 2013-0179847 is hereby incorporated by reference in its entirety.

[0230] The concepts disclosed herein can simulate or be mathematically modeled for any general imaging system used for imaging sub-wavelength features and are particularly useful for emerging imaging technologies capable of generating increasingly shorter wavelengths. Emerging technologies already in use include EUV (extreme ultraviolet), DUV lithography, which can generate a wavelength of 193 nm when using an ArF laser and even 157 nm when using a fluorine laser. Moreover, EUV lithography can generate photons in the range of 20 - 5 nm by using a synchrotron or by bombarding a material (solid or plasma) with high-energy electrons in order to generate wavelengths in that range.

[0231] Although the concepts disclosed herein can be used for imaging on a substrate such as a silicon wafer, it should be understood that the disclosed concepts can be used with any type of lithographic imaging system, e.g., a system for imaging on substrates other than silicon wafers.

[0232] Embodiments generally provide techniques for improving any manufacturing process of a device on a substrate using image-related metrics. The above techniques have been described for a specific application of improving a specific lithography process that uses a lithographic apparatus to image a portion of a design layout onto a substrate. Embodiments more generally provide techniques for improving the determination of control parameters for any process performed during the manufacture of a substrate depending on image-related metrics determined from one or more images of the substrate. Each image can be a portion of the substrate within the field of view (FOV) of an imaging device, which is typically an electron-beam based metrology device. Such an electron-beam device (e.g., manufactured by HMI) typically has a FOV of 10 μm × 10 μm. Processes that can be improved by the techniques of the embodiments include any of the following: lithography process, scanning process, priming process, resist coating process, soft bake process, post-exposure bake process, development process, hard bake process, measurement / inspection process, etching process, ion implantation process, metallization process, oxidation process, and chemical mechanical polishing process. The techniques described in all of the above examples can be used to determine improved control parameters for these processes depending on image-related metrics.

[0233] Figures 24(a) and (b) illustrate an overall process for determining control parameters and a control process according to an embodiment. In both Figures 24(a) and (b), there are computational measurement processes and control processes. The computational process includes obtaining one or more images of a substrate, and each image is a FOV of a portion of the substrate. The acquired images include features included in a device fabricated on the substrate. Image-related metrics are calculated depending on the nature of the features (such as the profile of the features). Then, depending on the image-related metrics, control parameters for processes in the manufacturing process of the features are determined.

[0234] In Figure 24(a), image-related metrics are calculated for multiple features on one or more substrates. In Figure 24(b), image-related metrics are calculated for multiple features on multiple layers of one or more substrates.

[0235] Figure 25 An image of a feature on a substrate is shown. The image can represent, for example, a 10μm×10μm area on the substrate. The thick line in the image is the target profile of one of the features. Although the ideal shape of the feature can be rectangular, the target profile is curved / rounded because this is the closest possible shape to a rectangle that can be fabricated and thus is the best profile that can be actually achieved. For Figure 25 For one of the features shown, the image has been constructed as a stacked image of multiple images of the feature. Each of the stacked images can have been acquired from one or more images of the same feature in different layers of the substrate, one or more images of multiple features on the same layer of the substrate, one or more images of features on multiple substrates, and / or one or more images of the same feature on the same layer of the substrate but taken by different imaging devices. By stacking multiple images of the same feature together with the target profile, as Figure 25 shown, random variations can be measured. However, the embodiment also includes comparing only one image of the profile of the feature with the target profile.

[0236] Image-related metrics can be calculated depending on the difference between the profile of the feature and the corresponding target profile. The difference between the profile of the feature and the target profile can be measured by multiple well-known specific image-related metrics, such as critical dimension uniformity (CDU), line width roughness (LWR), and overlay error. However, the preferred image-related metric is "edge position error" (EPE) because this metric provides an overall representation of the difference between the profile of the feature and the target profile.

[0237] In a preferred embodiment, the profile of each feature is divided into a plurality of segments, and each segment in the segments has a corresponding weight. How the profile is divided into a plurality of segments and the weight of each segment can be automatically defined by an image processing program or manually defined by a user. The segments and weights can depend on a variety of factors, including: the shape of the feature, the proximity of other features to the segments of the feature, the positioning of the feature relative to features on other layers, the tolerance value of the profile, the importance of the correct positioning of the profile for the correct manufacture of the device, the tolerance value of the image-related metric, and the sensitivity of the segment or the image-related metric of the segment to changes in the control parameters.

[0238] Controllable parameters that affect the profile of a feature can include: focal length, dose, illumination pupil shape (e.g., ellipticity), aberration (e.g., coma, spherical, astigmatism), etch rate, and other controllable parameters. For each controllable parameter, the sensitivity of each segment of the profile is determined. This sensitivity can be determined, for example, by simulating or measuring the known response to the control parameter.

[0239] The image-related metric of a feature is calculated depending on the image-related metric of each segment and the weight of each segment.

[0240] To determine more appropriate control parameters for a feature, the sensitivity of the segments of the feature to changes in the control parameters can be used to simulate the effect of changing the control parameters on the image-related metric of the feature. Thus, the control parameters can be determined to minimize the image-related metric of the feature.

[0241] The calculated and minimized image-related metric of the feature is preferably the EPE of the feature.

[0242] In an alternative embodiment, the image-related metric of a feature, in the case where the feature is not segmented, is generated depending on the comparison of the entire profile of the feature with a corresponding target profile. Control parameters are determined to minimize the image-related metric of the entire profile in a similar manner as described above, but without including the effects at the segment level.

[0243] Embodiments include determining an image-related metric of an image depending on each of a plurality of features in the image. There may be thousands of features in the image, and the image-related metric may be calculated for some or all of these features. As described above, the image-related metric for each feature may be calculated depending on the weights of the segments of the contour of the feature, or may be calculated without the segments of the contour. Each of the plurality of features in the field of view is assigned a weight. The weight for each feature may depend on various factors such as the importance of each feature for the correct fabrication of the device and the proximity of the feature to hot spots. Then, the image-related metric of the image is generated based on the image-related metric of each feature and the weight of each feature. If multiple exposures (such as using lithography-etch-lithography-etch (LELE)) have been used, the pattern offset / overlap between the two exposures may be calculated. An optimization process of the control parameters is then performed to minimize the image-related metric of the image. The image-related metric of the image is preferably the EPE of the image.

[0244] Embodiments include determining an image-related metric of a substrate depending on each of a plurality of images of the substrate. The images may be acquired at a plurality of locations on the substrate. Preferably, the images are acquired at positions that provide a proper fingerprint of the substrate. The image-related metric for each image may be calculated as described above. The image-related metric of the substrate is determined depending on the image-related metric of the images. The image-related metric of the substrate is preferably the EPE of the substrate.

[0245] During the manufacturing process of the features on the substrate, the changes and range constraints of the control parameters are determined. For example, during the manufacturing of the device, due to the rate at which the focal length can change and the manufacturing speed, there will be a limit to the extent to which the focal length can change between two different positions on the substrate. Embodiments use the determined control parameter constraints to perform an optimization process on the control parameters such that the image-related metric of the substrate is minimized.

[0246] Advantageously, the control parameters are determined to minimize the image-related metric of the substrate (such as the EPE of the substrate). The segments of the contour contribute to the EPE of the substrate according to the appropriate weights of each segment.

[0247] Embodiments also include generating and minimizing an image-related metric depending on the image-related metrics of a plurality of substrates and the constraints on the control parameters between the plurality of substrates. The image-related metric for each image and / or substrate may be weighted, for example, depending on their importance for the correct fabrication of the device. Then, the image-related metric of one or more substrates may be calculated depending on the weights.

[0248] Embodiments are particularly suitable for improving the control parameters of the features of a device across multiple layers of a substrate. For example, Figure 26A via hole on a layer is shown, and the via hole should be positioned above features on an adjacent layer. In such a multi-layer scenario, the image-related metric depends on the overlapping area of the features to be determined. Thus, the optimization process of the image-related metric will determine the control parameters for maximizing the overlap between features, i.e., the positioning of the via hole above the features in another layer.

[0249] In one embodiment, EPE is calculated as the image-related metric and expressed as a percentage. For example, FIGS. 27(a) to (d) show different relationships between a feature profile and a target profile. In FIG. 27(a), EPE can be defined as the ratio of the overlapping area of the feature profile and the target profile expressed as a percentage. In FIG. 27(b), since the feature profile is too small, EPE is large. In FIG. 27(c), since the feature profile is too large, EPE is large. In FIG. 27(d), EPE is affected by the offset of the feature profile relative to the target profile. The different relationships between the feature profile and the target profile shown in FIGS. 27(a) to (d) can be controlled and changed by control parameters. By calculating and optimizing EPE depending on all features in the image / FOV as described above, more suitable control parameters can be determined.

[0250] Embodiments include using the image-related metric to improve the dose distribution. It is known to depend on the global critical dimension uniformity (GCDU) for the dose distribution to be controlled, and the global critical dimension uniformity is a specific single error measurement value. However, since even the local effects are related to the focal length and the dose, and the control parameters are not determined depending on the local effects, determining the control parameters depending on this global parameter may lead to more serious EPE errors.

[0251] According to one embodiment, the dose distribution is determined depending on the image-related metric, which depends on the local image-related metric, or depends on both the local image-related metric and the global image-related metric. For example, embodiments include optimizing the dose distribution by determining the control parameters that minimize EPE, and the control parameters are calculated based on any of the following:

[0252] - A function of both GCDU and line width roughness (LWR) and / or local critical dimension uniformity (LCDU);

[0253] - A function of the LWR and / or LCDU of critical (i.e., important) features; or

[0254] - The critical dimension (CD) amplitude of lithography and non-lithography CD interference sources.

[0255] Embodiments use EPE as the image-related metric. EPE can be calculated using the following simplified and approximate formula (based on empirical research):

[0256] EPE ≈ 1.5 * GCDU + 4.2 * LCDU

[0257] Therefore, EPE depends on both the global parameter GCDU and the local parameter LCDU. Embodiments include other coefficients used in the above formula, if applicable to a particular application and use case.

[0258] By using the techniques according to embodiments to replace known techniques based only on global image-related metrics, EPE can be significantly reduced.

[0259] Embodiments also include using the above techniques to determine the dose distribution through a scanner, and a combination of etching process conditions means for an etching device, in order to minimize EPE.

[0260] Embodiments also include co-determining the values of two or more control parameters. By co-determining the control parameters, the combined effect of the control parameters, as well as the interdependence of the effects of the control parameters, can be used to advantageously improve the determination of the control parameters for increasing the yield, or for optimizing with respect to any other objective.

[0261] In particular, embodiments include co-determining the values of the applied focal length and dose. When the focal length and dose are co-determined, the range of deviations that can be corrected by applying the focal length and dose increases. For example, the focal length required to correct the deviation may be outside the applicable focal length range. However, the deviation can be corrected by the combined effect of additionally adjusting the applied dose and the focal length. This is particularly advantageous for improving image-related metrics at the edge of the substrate, where large focal length changes may be required.

[0262] Furthermore, the determined value of the dose to be applied can depend on the determined value of the focal length to be applied, and the determined value of the focal length to be applied can depend on the value of the dose to be applied. Advantageously, instead of applying independently determined optimal focal lengths and doses at a particular part of the substrate to minimize image-related metrics such as CD, a focal length value different from the independently determined focal length value can be applied, and the applied dose is adjusted such that the image-related metrics remain suitable. The effect of this is that the range of focal lengths and doses applied at any particular part of the substrate can be increased.

[0263] The dependence of the image metric CD on both the applied focal length and the applied dose can be approximated by the following equation: CD = a * dose + b * focal length^2.

[0264] Thus, the change in focal length can be compensated by a change in dose, where the desired CD can still be achieved, and vice versa. The parameters of the above equations can be determined empirically or by other techniques. Additionally, known techniques can be used to model the interdependence of dose and focal length and their combined effects.

[0265] During the manufacturing process of features on a substrate, there are constraints on the rate at which the applied focal length can be changed, the range over which the applied focal length can be changed, the rate at which the applied dose can be changed, and the range over which the applied dose can be changed. As a result of these constraints, it is not always possible to apply the individually optimal values of focal length or dose at every part of the substrate. However, as explained above, the present embodiment advantageously increases the range of suitable focal lengths and doses that can be applied at any particular part of the substrate, and this reduces the impact of the above constraints. Thus, jointly determining the focal length and dose distribution can provide an increased overall yield compared to the case where the applied focal length is determined independently from the applied dose.

[0266] The embodiment also includes jointly determining more than two control parameters. For example, the effect of changing the focal length may also cause the contrast to change to an unsuitable value. In particular, in the case of low-contrast applications, the allowable reduction in contrast may be small. Therefore, all terms of focal length, dose, and contrast are preferably jointly determined. Additionally, the focal length and dose can be jointly determined with overlay control and / or contrast.

[0267] The embodiment is not limited to jointly determining the focal length and dose, and the embodiment includes jointly determining any control parameters. The combinations and interdependent effects of control parameters can be modeled using known techniques and used to optimize the control parameters according to any metric. In particular, the embodiment is not limited to jointly determining the control parameters to optimize CD. The control parameters can be jointly determined to optimize any metric, such as a combination of EPE, yield, and / or local and global metrics (such as GCDU and LCDU).

[0268] The present embodiment is particularly advantageous in reducing the LDCU variation across the substrate. Since regions of the substrate with large LCDU variations are more likely to include defects and thus reduce the yield, preferably, there is little or no LCDU variation across the substrate.

[0269] LCDU depends on imaging metrics such as focal length and dose. According to the embodiment, the applied focal length and dose are determined depending on the impact of the focal length and dose on LCDU, such that the focal length and dose are adjusted during the manufacturing process of features on the substrate to minimize the contribution of LCDU to the total CDU budget across the substrate.

[0270] In particular, the LCDU of a feature is related to the dose sensitivity of the feature. This correlation can be modeled by known simulation and / or actual measurement techniques such that the impact of scanner parameters (such as dose, focal length, and MSD) on dose sensitivity can be determined. Accordingly, scanner parameters (such as dose and focal length) can be determined depending on the impact of the scanner parameters on the LCDU such that the LCDU is reduced. Preferably, the focal length and dose are determined depending on both the GCDU and LCDU. Embodiments also include the focal length and dose being determined depending on both the local EPE or global EPE and the local EPE.

[0271] It is known to determine control parameters, such as overlay measurements at specific points, depending on measurements of sparse distributions of a single specific type of metric across a substrate. Embodiments include improving such known techniques by performing an optimization process for all controllable parameters using image-related metrics determined from images.

[0272] As Figure 28 shown, one or more images of several patterned regions on a substrate are acquired. The images may have been acquired by a scanning electron microscope (SEM) and / or an electron beam device (such as a device manufactured by HMI). Multiple such images can be used to obtain a fingerprint of process parameters across the substrate.

[0273] Each acquired image can be deconstructed in order to obtain image-related metrics. The dependence of the image-related metrics on changes in control parameters can be determined by simulation or measurement. An optimization process can then be performed that determines the control parameters for minimizing the image-related metrics. Accordingly, the image-related metrics are used to control processes in the manufacture of semiconductor devices (such as scanners or etch tools).

[0274] The image-related metrics include one or more of the following: the size of block patterns in the image, the size difference of block patterns in the image, the pitch difference of gratings in the image, the overall offset of a barrier layer relative to a grating layer, and the offset between two LELE layers.

[0275] Preferably, the image-related metrics are determined from each of multiple images of different parts of the same layer of the substrate. This allows for obtaining a fingerprint and potentially controlling the fingerprint (overlay fingerprint, dose fingerprint, etc.) from the images.

[0276] Preferably, the images are of the same part of the substrate and the images are acquired during different manufacturing processes of the layer of the substrate.

[0277] For example, if two scan operations are performed, a delta image, i.e., the difference between the two images, can be acquired and the EPE can be determined. These operations can be controlled in a manner that can improve the EPE.

[0278] If two other operations besides the scan operation are performed, the incremental image can be used to control the proximity effect caused by the lack of matching of the equipment for the process. For example, it is known that etchers can cause proximity effects such as microloading, and the proximity effect is different for each individual etcher.

[0279] For an image-related metric to be determined, the image can be decomposed into multiple process parameters. The method can include:

[0280] - Mapping the measured image to a reference image. Mapping properties such as scaling, tilting, rotating, shifting, deforming, etc. can be parameterized. Then the control parameters of processes such as lithography processes, etching processes, etc. can be determined depending on the parameterized mapping properties; and / or

[0281] - Averaging the parameters derived from image-related metrics (such as cut lines) across the image.

[0282] Accordingly, embodiments allow the optimization of control parameters to achieve a desired image-related metric. The optimization can be for a specific image property, such as minimizing the error in positioning a specific edge. Advantageously, embodiments allow an increase in pattern fidelity, i.e., improved overlay and CD control.

[0283] An additional advantage of image comparison is that image comparison can be used to verify the consistency of image data and can be used to reduce (image) noise and identify processing artifacts. As described above, HMI manufactures electron beam-based imaging devices for acquiring images of portions of a substrate. Images can be taken by multiple HMI tools, and the comparison of images from different HMI tools can be used to verify the consistency of the determined process parameters.

[0284] Embodiments also include applying techniques for reducing the amount of data processing required to generate and represent an image-related metric of the structure of features in one or more images of the patterned regions on the acquired substrate.

[0285] The analysis of the actual structure included in the features in the image includes comparing the actual structure with a reference structure to determine one or more image-related metrics. However, performing such a detailed analysis (i.e., on a per-pixel basis) for each individual structure requires processing a large amount of data and is thus slow.

[0286] Embodiments preferably reduce the amount of data processing required to analyze one or more acquired images of a patterned region on a substrate by generating a model of the differences between an actual structure and a reference structure. Individual structures in the image are detected and their contour shapes are extracted according to known techniques. Each contour shape is then compared to a reference contour shape, i.e., fitted to the reference contour shape.

[0287] The reference contour shape can be an ideal expected contour shape with or without deviations such that the ideal expected contour shape exactly corresponds to a contour shape that can be achieved and / or one or more other actual contour shapes. In particular, by comparing the actual contour shapes of the same structure in multiple layers, a measurement of overlay error can be obtained.

[0288] A model with N parameters is generated to represent the result of each comparison. For example, the model can include parameters that describe the translation, magnification, and rotation between the compared contour shapes. Translation corresponds to line placement error. Magnification corresponds to local CD differences. Rotation is not linked to a control parameter, but is still a determinable difference between the two contours. Thus, a six-parameter model can have X and Y parameters for translation, magnification, and rotation, respectively. The model according to embodiments can additionally or alternatively include other types of metrics of the comparison of the contour shapes and other parameters.

[0289] Preferably, the operations of extracting the contour shapes from the image and comparing the extracted contour shapes to the reference contour shape are performed together in the same operation. This can improve computational efficiency.

[0290] The reference contour shape can preferably also be used during the contour shape detection process. For example, a contour detection algorithm may incorrectly detect a single contour as two contours. The reference contour shape can be used to detect this error and thus improve the detection of the contour shape.

[0291] The amount of data processing required can also be further reduced in the following way: by further modeling the model parameters across an image or multiple images to generate one or more general models. Advantageously, such general models are each generated depending on the individual structures in the (multiple) images.

[0292] The generation of a model for representing the comparison of contour shapes is an efficient way to calculate image-related metrics. Compared to the amount of data required in the case of performing a per-pixel comparison between structures, the amount of data required to represent the comparison according to this embodiment can be approximately 1000 times less. Thus, the amount of data processing required to obtain image-related metrics, as well as the amount of data required to represent the image-related metrics, is significantly reduced.

[0293] Model parameters can be used in a variety of ways. For example, the model parameters of adjacent structures can be used to determine the relative positions and interactions of the structures.

[0294] Model parameters are image-related metrics. Embodiments include generating a feedback signal for adjusting a control parameter depending on the model parameters. For example, the feedback signal can be generated depending on the average value or a weighted combination of multiple model parameters. Additionally or alternatively, in order to adjust a control parameter depending on the model parameters, the model parameters can be used to improve any other process. For example, the model parameters can be used to calibrate an imaging process.

[0295] Figure 29 is a flowchart of a process according to one embodiment.

[0296] In step 2901, the process starts.

[0297] In step 2903, in a manufacturing process of a device on a substrate, wherein the manufacturing process includes a lithography process and one or more additional processes in the manufacturing process of the device, the lithography process uses a lithography apparatus to image a part of a design layout onto the substrate, an image of at least a part of the substrate is acquired, wherein the image includes at least one feature included by the device being manufactured on the substrate.

[0298] In step 2905, one or more image-related metrics are calculated depending on a profile determined from the image including at least one feature.

[0299] In step 2907, one or more control parameters of the lithography apparatus and / or one or more additional processes in the manufacturing process of the above-mentioned device are determined depending on one or more image-related metrics.

[0300] In step 2909, the process ends.

[0301] Further embodiments of the present invention are disclosed in the following numbered list of embodiments:

[0302] 1. A method of a manufacturing process of a device on a substrate, wherein the manufacturing process includes a lithography process and one or more additional processes in the manufacturing process of the device, the lithography process uses a lithography apparatus to image a part of a design layout onto the substrate, the method comprising:

[0303] acquiring an image of at least a part of the substrate, wherein the image includes at least one feature included by the device being manufactured on the substrate;

[0304] calculating one or more image-related metrics depending on a profile determined from the image including the at least one feature;

[0305] Determine one or more control parameters of the lithographic apparatus and / or of one or more further processes in the manufacturing process of the device, depending on the one or more image-related metrics.

[0306] 2. The method according to embodiment 1, the method further comprising controlling at least one of the following depending on the determined one or more control parameters: the lithographic apparatus and one or more further processes in the manufacturing process of the device.

[0307] 3. The method according to embodiment 1 or 2, wherein the further process in the manufacturing process of the device comprises one or more of the following: a lithography process, a priming process, a resist coating process, a soft bake process, a post-exposure bake process, a development process, a hard bake process, a measurement / inspection process, an etching process, an ion implantation process, a metallization process, an oxidation process, and a chemical mechanical polishing process.

[0308] 4. The method according to any one of the preceding embodiments, wherein the image-related metric is the Edge Position Error EPE of the feature.

[0309] 5. The method according to any one of the preceding embodiments, wherein the image-related metric is calculated depending on a comparison of the profile with a target profile.

[0310] 6. The method according to any one of the preceding embodiments, wherein the image-related metric is generated depending on a plurality of images of the feature.

[0311] 7. The method according to embodiment 6, wherein the plurality of images of the feature are in corresponding plurality of layers of the substrate.

[0312] 8. The method according to any one of the preceding embodiments, the method further comprising:

[0313] Determine a plurality of segments of the profile of the feature;

[0314] Determine a respective weight for each of the plurality of segments;

[0315] For each of the segments, calculate the image-related metric of the segment; and

[0316] Calculate the image-related metric of the feature depending on the weights and the image-related metrics of each of the segments.

[0317] 9. The method according to embodiment 8, wherein the weight of each segment depends on the tolerance value of the image-related metric of the segment.

[0318] 10. The method according to embodiment 8 or 9, wherein the one or more control parameters are determined depending on the sensitivity of each segment in the segmentation.

[0319] 11. The method according to embodiment 4 or any embodiment dependent on embodiment 4, wherein the one or more control parameters are determined to minimize the EPE of the feature.

[0320] 12. The method according to embodiment 8 or any embodiment dependent on embodiment 8, the method comprising generating an image-related metric for each of a plurality of features in the image, wherein each image-related metric of a feature is generated by performing the method according to embodiment 8 or any embodiment dependent on embodiment 8.

[0321] 13. The method according to embodiment 12, further comprising determining a weight for each of the plurality of features in the image; and

[0322] calculating an image-related metric of the image depending on the image-related metric of each feature and the weight of each feature.

[0323] 14. The method according to embodiment 13, wherein the image-related metric of the image is the EPE of the image, and the one or more control parameters are determined to minimize the EPE of the image.

[0324] 15. The method according to embodiment 13 or 14, further comprising:

[0325] acquiring a plurality of images of different parts of the same layer of the substrate; and

[0326] calculating an image-related metric of each image according to the method according to embodiment 13 or 14;

[0327] wherein the one or more control parameters are determined depending on the image-related metric of each image.

[0328] 16. The method according to any one of the preceding embodiments, wherein each image is a field of view of 10 μm × 10 μm.

[0329] 17. The method according to any one of the preceding embodiments, further comprising:

[0330] calculating an image-related metric of each of a plurality of features in one or more images of a layer of the substrate;

[0331] wherein the one or more control parameters are determined depending on each image-related metric among the plurality of image-related metrics.

[0332] 18. The method according to embodiment 17, wherein the one or more control parameters define a dose profile to be applied in the manufacturing process of the device.

[0333] 19. The method according to embodiment 17 or 18, the method further comprising calculating a global image correlation metric;

[0334] wherein the one or more control parameters are additionally determined depending on the global image correlation metric.

[0335] 20. The method according to any one of embodiments 17 to 19, the method further comprising calculating an EPE, wherein the one or more control parameters are determined to minimize the EPE.

[0336] 21. The method according to embodiment 20, wherein the EPE is determined depending on one or more of global critical dimension uniformity, line width roughness, local critical dimension uniformity, and critical dimension amplitude.

[0337] 22. The method according to embodiment 20, wherein the EPE is calculated as a weighted combination of global critical dimension uniformity and local critical dimension uniformity.

[0338] 23. The method according to any of the foregoing embodiments, wherein a plurality of control parameters are determined; and at least two of the control parameters are determined jointly.

[0339] 24. The method according to embodiment 23, wherein the joint determination of at least two of the control parameters comprises: determining the applied value of another control parameter depending on the applied value of one control parameter among the control parameters.

[0340] 25. The method according to embodiment 23 or 24, wherein the joint determination of at least two of the control parameters depends on:

[0341] the combined effect of the at least two control parameters; and / or

[0342] the interdependence of the at least two control parameters.

[0343] 26. The method according to any one of embodiments 23 to 25, wherein the jointly determined control parameters are focal length and dose.

[0344] 27. The method according to embodiment 26, wherein the jointly determined control parameters further comprise overlay and / or contrast.

[0345] 28. The method according to any one of embodiments 23 to 27, wherein the jointly determined control parameter is determined depending on the CD variation on a small spatial scale, or depending on both the CD variation on a small spatial scale and the CD variation on a large spatial scale.

[0346] 29. The method according to any one of embodiments 23 to 27, wherein the jointly determined control parameter is determined depending on one or more of the following: global EPE, local EPE, CD, CDU, CD variation on a small spatial scale, and CD variation on a large spatial scale.

[0347] 30. The method according to any of the foregoing embodiments, the method comprising:

[0348] acquiring a plurality of images of the substrate; and

[0349] determining an image-related metric of features in each image.

[0350] 31. The method according to embodiment 30, wherein the one or more control parameters are determined depending on the image-related metric of each image and the dependence of the determined image-related metric on the change of the one or more control parameters.

[0351] 32. The method according to embodiment 30 or 31, wherein the image-related metric comprises one or more of the following: the size of a block pattern in the image, the size difference of block patterns in the image, the pitch difference in a grating in the image, the overall offset of a barrier layer relative to a grating layer, and the offset between two LELE layers.

[0352] 33. The method according to any one of embodiments 30 to 32, wherein the images are images of different portions of the same layer of the substrate.

[0353] 34. The method according to any one of embodiments 30 to 33, wherein the images are images of the same portion of the substrate; and

[0354] the images are acquired during different manufacturing processes of the layer of the substrate.

[0355] 35. The method according to embodiment 34, further comprising controlling the proximity effect depending on the difference between the images.

[0356] 36. The method according to any one of embodiments 30 to 35, wherein the image-related metric is obtained by: mapping the measured image to a reference image; and / or

[0357] averaging parameters derived from lines across the images.

[0358] 37. The method according to any one of the foregoing embodiments, wherein obtaining the image-related metric comprises:

[0359] Determining a contour shape of a structure included in the feature in the image;

[0360] Comparing the determined contour shape with one or more reference contour shapes;

[0361] Generating a model of the comparison result.

[0362] 38. The method according to embodiment 37, wherein the reference contour shape is an expected contour shape or an actual contour shape.

[0363] 39. The method according to embodiment 37 or 38, wherein the reference contour shape is an actual contour shape of the same structure in another image of the structure.

[0364] 40. The method according to any one of embodiments 37 to 39, wherein the model comprises parameters representing one or more of the following: a translation difference, a magnification difference, and a rotation difference between the determined contour shape and the one or more reference contour shapes.

[0365] 41. The method according to any one of embodiments 37 to 40, wherein a plurality of image-related metrics are obtained for each of a corresponding plurality of structures included in features in one or more images; and

[0366] For each of the image-related metrics, generating a model of the comparison result between the determined structure contour shape and one or more reference contour shapes.

[0367] 42. The method according to embodiment 41, further comprising using a plurality of the models to generate one or more general models.

[0368] 43. The method according to any one of embodiments 41 or 42, wherein one or more image-related metrics are generated depending on a plurality of the models.

[0369] 44. A non-transitory computer-readable medium comprising instructions that, when executed, cause a manufacturing process of a device on a substrate to be controlled according to the method according to any one of embodiments 1 to 43.

[0370] 45. A system for manufacturing a device on a substrate, wherein the system is configured to perform the method according to any one of embodiments 1 to 43.

[0371] Embodiments include many modifications and variations of known processes.

[0372] Any of the techniques described throughout this document can be used to determine and optimize image-related metrics of embodiments.

[0373] Embodiments determine control parameters that are used to control processes in the manufacture of semiconductor devices. The process includes any process, including measurement processes, and can be performed by any known equipment. The process according to embodiments can be controlled by a computing system executing instructions for performing a process stored on a non-transitory computer-readable medium.

[0374] Other embodiments of the invention will be apparent to those skilled in the art by considering the specification and practice of the embodiments disclosed herein. The specification and embodiments are considered to be exemplary only, and the true scope and spirit of the invention are indicated by the appended claims. Additionally, where the steps of a method or process are listed in a particular order in this application, it is possible, and even convenient in some cases, to change the order in which some steps are performed, and it is intended that, unless the order particularity is explicitly stated in the claims, the particular steps of the method or process claims set forth should not be construed as being order-specific.

Claims

1. A method in a manufacturing process of a device on a substrate, wherein the manufacturing process includes a lithography process of imaging a part of a design layout onto the substrate using a lithography apparatus, and one or more other processes in the manufacturing process of the device, the method comprising: Obtaining an image of at least a part of the substrate, wherein the image includes at least one feature included in the device manufactured on the substrate; Calculating one or more image-related metrics based on a profile determined from the image including the at least one feature; And Determining a plurality of control parameters of the lithography apparatus and / or the one or more other processes in the manufacturing process of the device based on the one or more image-related metrics, wherein at least two of the control parameters are co-determined.

2. The method according to claim 1, wherein the joint determination of at least two of the control parameters comprises: Determining an applied value of another one of the control parameters based on an applied value of one of the control parameters.

3. The method according to claim 1, wherein the co-determination of at least two of the control parameters is based on: The combined effect of the at least two control parameters; and / or The interdependence of the at least two control parameters.

4. The method according to claim 1, wherein the co-determined control parameters are focus and dose.

5. The method according to claim 4, wherein the co-determined control parameters further include overlay and / or contrast.

6. The method according to claim 1, wherein the co-determined control parameters are determined based on CD variations on a small spatial scale, or both CD variations on a small spatial scale and CD variations on a large spatial scale.

7. The method according to claim 1, wherein the co-determined control parameters are determined based on one or more of the following: global EPE, local EPE, CD, CDU, CD variations on a small spatial scale, and CD variations on a large spatial scale.

8. The method according to claim 1, the method further comprising: Obtaining a plurality of images of the substrate; And Determining the image-related metrics of features in each image.

9. The method according to claim 8, wherein the one or more control parameters are determined based on the image-related metrics of each image and the dependence of the determined image-related metrics on changes in the one or more control parameters.

10. The method according to claim 8, wherein the image-related metrics include one or more of the following: the size of a block pattern in the image, the size difference of the block pattern in the image, the grating pitch difference in the image, the overall offset of a block layer relative to a grating layer, and the offset between two LELE layers.

11. The method according to claim 8, wherein the image is an image of different parts of the same layer of the substrate.

12. The method according to claim 8, wherein the image is an image of the same part of the substrate, and the image is obtained during different manufacturing processes of the layer of the substrate.

13. The method according to claim 12, further comprising controlling the proximity effect based on the differences between the images.

14. The method according to claim 1, wherein the image-related metric is obtained by: mapping the measurement image to a reference image; and / or averaging parameters derived from lines across the image.

15. The method according to claim 1, wherein obtaining the image-related metric comprises: determining the contour shape of the structure included in the feature in the image; comparing the determined contour shape with one or more reference contour shapes; and generating a model of the comparison result.

16. The method according to claim 15, wherein the reference contour shape is an expected contour shape or an actual contour shape.

17. The method according to claim 15, wherein the reference contour shape is the actual contour shape of the same structure in another image of the structure.

18. The method according to claim 15, wherein the model comprises parameters representing one or more of: translation, magnification, and rotation differences between the determined contour shape and the one or more reference contour shapes.

19. The method according to claim 15, wherein a plurality of image-related metrics are obtained for each of the respective plurality of structures included in the features in one or more images; and for each of the image-related metrics, a model with a comparison result between the determined contour shape of the structure and one or more reference contour shapes is generated.

20. The method according to claim 19, further comprising using the plurality of models to generate one or more general models.

21. The method according to claim 19, wherein one or more image-related metrics are generated based on the plurality of models.

22. A non-transitory computer-readable medium comprising instructions that, when executed, cause a manufacturing process of a device on a substrate to be controlled according to the method of any one of claims 1 to 21.

23. A computer program product comprising machine-readable instructions that, when executed, cause a manufacturing process of a device on a substrate to be controlled according to the method of any one of claims 1 to 21.

24. A computer program product comprising machine-readable instructions configured to, when executed, control a manufacturing process comprising a lithography process of imaging a portion of a design layout onto a substrate using a lithography apparatus and one or more other processes in the manufacturing process of the device, the instructions being configured to: obtain an image of at least a portion of the substrate, wherein the image comprises at least one feature included in the device manufactured on the substrate; calculate one or more image-related metrics based on a contour determined from the image comprising the at least one feature; and determine a plurality of control parameters of the lithography apparatus and / or the one or more other processes in the manufacturing process of the device based on the one or more image-related metrics, wherein at least two of the control parameters are co-determined.

25. The computer program product according to claim 24, wherein the joint determination of at least two of the control parameters comprises: Determine the application value of another control parameter among the control parameters according to the application value of one of the control parameters.

26. The computer program product according to claim 24, wherein the co-determination of at least two of the control parameters is based on: The combined effect of the at least two control parameters; and / or The interdependence of the at least two control parameters.

27. The computer program product according to claim 24, wherein the co-determined control parameters are focus and dose.

28. The computer program product according to claim 27, wherein the co-determined control parameters further include overlay and / or contrast.

29. The computer program product according to claim 24, wherein the co-determined control parameters are determined according to the CD variation on a small spatial scale, or both the CD variation on a small spatial scale and the CD variation on a large spatial scale.

30. The computer program product according to claim 24, wherein the co-determined control parameters are determined according to one or more of the following: global EPE, local EPE, CD, CDU, CD variation on a small spatial scale, and CD variation on a large spatial scale.

Images