Etching system, model and manufacturing process

Abstract

An etch bias is determined based on a curvature of a profile in a substrate pattern. The etch bias is configured to be used to improve accuracy of a semiconductor patterning process relative to a previous patterning process. In some embodiments, a representation of the substrate pattern is received, the representation including the profile in the substrate pattern. A curvature of the profile of the substrate pattern is determined and input to a simulation model. The simulation model includes a correlation between an etch bias and a curvature of a profile. The etch bias of the profile in the substrate pattern is output by the simulation model based on the curvature.

Description

Technical Field

[0001] This disclosure generally relates to etching simulations associated with computational lithography. Background Technology

[0002] Photolithography projection equipment can be used, for example, in the manufacture of integrated circuits (ICs). A patterning apparatus (e.g., a mask) can include or provide a pattern (“design layout”) corresponding to individual layers of the IC, and this pattern can be transferred onto target portions (e.g., comprising one or more dies) on a substrate (e.g., a silicon wafer) coated with a layer of radiation-sensitive material (“resist”) by methods such as irradiating the target portion through the pattern on the patterning apparatus. Typically, a single substrate comprises multiple adjacent target portions, and the pattern is transferred sequentially, one target portion at a time, by the photolithography projection apparatus onto these adjacent target portions. In one type of photolithography projection apparatus, the entire pattern on the patterning apparatus is transferred onto a single target portion in a single operation. Such an apparatus is often referred to as a stepper. In an alternative apparatus (often referred to as a step-scan apparatus), a projection beam scans over the patterning apparatus along a given reference direction (“scanning” direction) while the substrate moves synchronously parallel to or antiparallel to the reference direction. Different portions of the pattern on the patterning apparatus are progressively transferred onto a single target portion. Because, typically, the photolithography projection apparatus will have a reduction ratio M (e.g., 4), the speed F at which the substrate is moved will be 1 / M of the speed at which the projection beam scans the pattern forming apparatus. More information about photolithography apparatuses can be found, for example, in US 6,046,792, which is incorporated herein by reference.

[0003] Before the pattern is transferred from the patterning apparatus to the substrate, the substrate may undergo various processes, such as primer coating, resist coating, and soft baking. After exposure, the substrate may undergo other processes (“post-exposure processes”), such as post-exposure baking (PEB), development, hard baking, and measurement / inspection of the transferred pattern. This series of processes is used as the basis for fabricating individual layers of a device (e.g., an IC). The substrate may then undergo various processes, such as etching, ion implantation (doping), metallization, oxidation, chemical mechanical polishing, etc., all of which aim to ultimately complete the individual layers of the device. If multiple layers are required in the device, all processes or variations thereof are repeated for each layer. Ultimately, the device will exist in each target portion on the substrate. These devices are then separated from each other using techniques such as sawing or cutting, so that the individual devices can be mounted onto a carrier, connected to pins, etc.

[0004] Fabricating devices (such as semiconductor devices) typically involves processing a substrate (e.g., a semiconductor wafer) using multiple fabrication processes to form various features and multiple layers of the device. These layers and features are typically fabricated and processed using, for example, deposition, photolithography, etching, chemical mechanical polishing, and ion implantation. Multiple devices can be fabricated on multiple dies on a substrate, and then the multiple devices can be separated into individual devices. This device fabrication process can be considered a patterning process. A patterning process involves a patterning step using a patterning apparatus in a photolithography apparatus, such as optical and / or nanoimprint lithography, to transfer a pattern from the patterning apparatus onto the substrate, and the patterning process typically, but optionally, involves one or more associated patterning processing steps, such as resist development by a developing apparatus, baking the substrate using a baking tool, etching the pattern using an etching apparatus, etc.

[0005] Photolithography is a central step in the fabrication of devices such as integrated circuits (ICs), in which patterns formed on a substrate define the functional elements of the device, such as microprocessors and memory chips. Similar photolithography techniques are also used to form flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0006] With the continuous advancement of semiconductor manufacturing processes, the size of functional components has been constantly shrinking. Simultaneously, the number of functional components (such as transistors) per device has been steadily increasing, following a trend commonly known as "Moore's Law." In the current state of technology, photolithography projection equipment is used to fabricate layers of devices. This equipment projects a design layout onto a substrate using irradiation from a deep ultraviolet (DEUV) source, thereby forming individual functional components with dimensions well below 100 nm (i.e., less than half the wavelength of radiation from the DEUV source, e.g., a 193 nm source).

[0007] The process of printing features with dimensions smaller than the classical resolution limit of a photolithography projection apparatus is often referred to as low-k1 lithography, according to the resolution formula CD = k1 × λ / NA, where λ is the wavelength of the radiation used (currently mostly 248 nm or 193 nm), NA is the numerical aperture of the projection optics in the photolithography projection apparatus, CD is the "critical size"—typically the smallest feature size printed—and k1 is an empirical resolution factor. Generally, the smaller k1 is, the more difficult it becomes to reproduce patterns on the substrate that resemble the shape and size planned by the designer to achieve specific electrical functionality and performance. To overcome these difficulties, complex fine-tuning steps are applied to the photolithography projection apparatus, the design layout, or the patterning apparatus. These steps include, for example, but not limited to: optimization of NA and optical coherence settings, custom illumination schemes, the use of phase-shifted patterning apparatus, optical proximity correction (OPC, sometimes also referred to as "optical and process correction") in the design layout, or other methods generally defined as "resolution enhancement techniques" (RET). Summary of the Invention

[0008] Etching effects are frequently considered during OPC and / or other processes (e.g., for patterning process optimization and / or other purposes). For example, simulation models can be used to predict etching effects such as etch deviations. Previous simulation models included different terms configured to simulate various etching effects. For example, previous simulation models included terms configured to simulate the effect of nearby features in the wafer (substrate) pattern on etch deviations at local etch locations. Meanwhile, density mapping and / or other tools can be used to simulate long-range wafer pattern geometry effects on said (local) etch deviations. However, previous simulation models did not consider the effect of the in-plane curvature of the contours in the wafer pattern on said etch deviations.

[0009] Therefore, according to an embodiment, a non-transitory computer-readable medium is provided having instructions on it. When executed by a computer, the instructions cause the computer to receive a representation of the outline of a substrate (e.g., a wafer) pattern, determine the curvature of the outline, and determine an etching effect using a simulation model. The simulation model includes a correlation between etching deviation and the curvature of the outline. In some embodiments, the etching effect is an etching deviation, and the instructions cause the computer to output an etching deviation of the substrate pattern based on the curvature, based on the simulation model.

[0010] In some embodiments, the curvature is determined based on (1) the slope of the contour and (2) the maximum or minimum value in the contour.

[0011] In some embodiments, the curvature is determined based on the first and second derivatives of the contour.

[0012] In some embodiments, the curvature is determined by the ratio between the second derivative and the first derivative.

[0013] In some embodiments, the simulation model includes a multidimensional algorithm. In some embodiments, the multidimensional algorithm includes one or more nonlinear functions, linear functions, or quadratic functions representing parameters of the etching process.

[0014] In some embodiments, the simulation model includes a physical etching model or a semi-physical etching model.

[0015] In some embodiments, the simulation model is an etching model. In some embodiments, the etching model includes a multidimensional algorithm comprising a curvature term configured to correlate the curvature with the etching deviation.

[0016] In some embodiments, the contour is obtained from a representation of the substrate pattern obtained from a post-development inspection of the substrate pattern.

[0017] In some embodiments, the profile is obtained from a resist model and / or an optical model.

[0018] In some embodiments, the etching effect is an etching deviation, and the etching deviation is configured to be provided to a cost function to determine the cost associated with individual patterning process variables.

[0019] According to another embodiment, a method for determining an etching effect on a substrate pattern is provided. The method includes: receiving a representation of a contour of the substrate pattern; determining the curvature of the contour; and using a simulation model to determine the etching effect on the substrate pattern based on the curvature. The simulation model includes a correlation between etching deviation and the curvature of the contour. In some embodiments, the etching effect is an etching deviation.

[0020] In some embodiments, the curvature is determined based on (1) the slope of the contour and (2) the maximum or minimum value in the contour.

[0021] In some embodiments, the curvature is determined based on the first and second derivatives of the contour.

[0022] In some embodiments, the curvature is determined by the ratio between the second derivative and the first derivative.

[0023] In some embodiments, the simulation model includes a multidimensional algorithm, wherein the multidimensional algorithm includes one or more nonlinear functions, linear functions, or quadratic functions representing parameters of the etching process.

[0024] In some embodiments, the simulation model includes a physical etching model or a semi-physical etching model. In some embodiments, the simulation model is an etching model, and the etching model includes a multidimensional algorithm containing a curvature term configured to correlate the curvature with the etching deviation.

[0025] In some embodiments, the contour is obtained from a representation of the substrate pattern obtained from a post-development inspection of the substrate pattern.

[0026] In some embodiments, the profile is obtained from a resist model and / or an optical model.

[0027] In some embodiments, the etching effect is an etching deviation, and the etching deviation is configured to be provided to a cost function to determine the cost associated with individual patterning process variables.

[0028] According to another embodiment, a system for determining an etch effect on a substrate pattern is provided. The system includes one or more hardware processors configured by machine-readable instructions to: receive a representation of a contour of the substrate pattern; determine the curvature of the contour; and use a simulation model to determine the etch effect on the substrate pattern based on the curvature. The simulation model includes a correlation between etch deviation and the curvature of the contour. In some embodiments, the etch effect is an etch deviation.

[0029] In some embodiments, the curvature is determined based on (1) the slope of the contour and (2) the maximum or minimum value in the contour.

[0030] In some embodiments, the curvature is determined based on the first and second derivatives of the contour.

[0031] In some embodiments, the curvature is determined by the ratio between the second derivative and the first derivative.

[0032] In some embodiments, the simulation model includes a multidimensional algorithm, wherein the multidimensional algorithm includes one or more nonlinear functions, linear functions, or quadratic functions representing parameters of the etching process.

[0033] In some embodiments, the simulation model includes a physical etching model or a semi-physical etching model. In some embodiments, the simulation model is an etching model, and the etching model includes a multidimensional algorithm containing a curvature term configured to correlate the curvature with the etching deviation.

[0034] In some embodiments, the contour is obtained from a representation of the substrate pattern obtained from a post-development inspection of the substrate pattern.

[0035] In some embodiments, the profile is obtained from a resist model and / or an optical model.

[0036] In some embodiments, the etching effect is an etching deviation, and the etching deviation is configured to be provided to a cost function to determine the cost associated with individual patterning process variables.

[0037] According to another embodiment, a non-transitory computer-readable medium is provided having instructions. When executed by a computer, the instructions cause the computer to execute a simulation model for determining an etch deviation for a pattern on a substrate. The etch deviation is determined based on the curvature of a contour in the pattern. The etch deviation is configured to be used to improve the accuracy of a patterning process relative to a previous patterning process. The instructions cause operations including: receiving a representation of the pattern, wherein the representation includes a contour in the pattern; determining the curvature of the contour of the pattern; inputting the curvature to the simulation model, wherein the simulation model includes a correlation between the etch deviation and the curvature of the contour; and, based on the simulation model, outputting the etch deviation for the contour in the pattern. The etch deviation from the simulation model is configured to be used in a cost function to facilitate the determination of costs associated with individual patterning process variables. The costs associated with individual patterning variables are configured to be used to facilitate optimization of the patterning process.

[0038] In some embodiments, the simulation model is an etching model.

[0039] In some embodiments, the representation of the pattern includes (1) an inspection result from a post-development inspection of the pattern; or (2) a model of the contour in the pattern.

[0040] In some embodiments, the representation of the pattern includes the results of a post-development inspection of the pattern, and the results of the post-development inspection of the pattern are obtained from a scanning electron microscope or an optical metrology tool.

[0041] In some embodiments, the curvature is determined based on (1) the slope of the contour in the pattern and (2) the maximum or minimum value of the contour in the pattern. Attached Figure Description

[0042] The accompanying drawings, which are incorporated in and form part of this specification, illustrate one or more embodiments and, together with the specification, serve to explain these embodiments. Embodiments of the invention will now be described by way of example only with reference to the accompanying illustrative drawings, in which corresponding reference numerals indicate corresponding parts, and in the drawings:

[0043] Figure 1 The figure shows a block diagram of the various subsystems of the photolithography projection apparatus according to an embodiment.

[0044] Figure 2 The figure illustrates an exemplary flowchart of simulated lithography in a lithography projection apparatus according to an embodiment.

[0045] Figure 3 The figure illustrates the method according to an embodiment.

[0046] Figure 4 The figure illustrates how this simulation model, according to an embodiment, can be used to predict the feature profile of an etched pattern based on etch effects (such as etch deviation).

[0047] Figure 5 The figure illustrates the determination of the curvature of a contour in a substrate (e.g., wafer) pattern according to an embodiment.

[0048] Figure 6 The figures illustrate quantified examples of improvements over previous systems, models, and / or manufacturing processes provided by this system, model, and / or manufacturing process according to embodiments.

[0049] Figure 7 This is a block diagram of an exemplary computer system according to an embodiment.

[0050] Figure 8 This is a schematic diagram of a photolithography projection apparatus according to an embodiment.

[0051] Figure 9 This is a schematic diagram of another photolithography projection device according to an embodiment.

[0052] Figure 10 This is a detailed view of a photolithography projection apparatus according to an embodiment.

[0053] Figure 11 This is a detailed view of the source collector module of the photolithography projection apparatus according to an embodiment. Detailed Implementation

[0054] As described above, etching effects are frequently taken into account during OPC and / or other processes (e.g., for patterning process optimization and / or other purposes). For example, simulation models can be used to predict the profile of etched pattern features based on etching effects such as etch deviation. Etching deviation can be considered as the change in the size of a given substrate pattern feature between after-development inspection (ADI) and after-etch inspection (AEI). Typically, simulation models (such as effective etch deviation (EEB) models) simulate and / or otherwise determine the etch deviation mapping for wafer patterning based on the dimensional differences in various pattern features between ADI and AEI. This etch deviation mapping is used to determine the post-etch profile of the pattern features.

[0055] Previous simulation models included different terms configured to simulate various types of etch effects, including etch deviations. For example, previous simulation models included terms configured to simulate the effect of nearby features from the substrate (e.g., wafer) pattern on etch deviations at local etch sites. Meanwhile, density mapping and / or other tools could be used to simulate long-range wafer pattern geometry effects on said (local) etch deviations. However, previous simulation models did not account for the effect of the in-plane curvature of the contours in the wafer pattern on etch deviations.

[0056] Advantageously, this disclosure describes systems, models, and manufacturing processes (methods) for determining the etching effect of a pattern on a substrate (e.g., a wafer) based on the curvature of a contour in the pattern. For example, the etching effect may be represented by etching deviation or etching contour, etc. The determined etching deviation is configured to improve the accuracy of the post-etching contour determination, and thus improve the overall accuracy of the patterning process relative to previous patterning processes. As described herein, a representation of the pattern is received, the representation including a given contour in the pattern. The curvature of the contour of the pattern is determined and input into a simulation model. The simulation model includes the correlation between the etching deviation and the curvature of the contour. The etching deviation of the contour in the pattern is output by the simulation model. In other possible uses, the etching deviation from the simulation model can be used to determine a post-etched feature contour, which is used in a cost function to determine the cost associated with individual patterning process variables and / or for other purposes. For example, the post-etched feature contour and / or the cost associated with individual patterning variables can be used to facilitate the optimization of the patterning process.

[0057] Embodiments of this disclosure are described in detail with reference to the accompanying drawings, which are provided as illustrative examples to enable those skilled in the art to practice this disclosure. It is important to note that the figures and examples below are not intended to limit the scope of this disclosure to a single embodiment, but rather to make other embodiments possible by exchanging some or all of the described or illustrated elements. Furthermore, certain elements of this disclosure may be implemented partially or entirely using known components; only those portions of these known components necessary for understanding this disclosure will be described, and detailed descriptions of other portions of these known components will be omitted so as not to obscure this disclosure. As will be appreciated by those skilled in the art, embodiments described as being implemented in software are not intended to be limited thereto, but may include embodiments implemented in hardware, or a combination of software and hardware, and vice versa. Embodiments showing a singular number of components in this specification should not be considered limiting; rather, unless expressly stated otherwise herein, this disclosure is intended to cover other embodiments including a plurality of identical components, and vice versa. Furthermore, unless expressly stated otherwise, the applicant does not intend to assign any terminology in this specification or claims an uncommon or special meaning. In addition, this disclosure covers present and future known equivalents of known components mentioned herein by way of illustration or description.

[0058] While this document has specifically referenced IC manufacturing, it should be clearly understood that the descriptions herein have many other possible applications. For example, it can be used in the fabrication of integrated optical systems, the patterning and detection of magnetic domain memories, liquid crystal display panels, thin-film magnetic heads, etc. Those skilled in the art will understand that, in the context of such alternative applications, any use of the terms “mask,” “wafer,” or “die” herein should be considered interchangeable with the more general terms “mask,” “substrate,” and “target portion,” respectively.

[0059] In this document, the terms “radiation” and “beam” are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., with wavelengths of 365 nm, 248 mm, 193 nm, 157 mm, or 126 mm) and EUV (extreme ultraviolet radiation, e.g., with wavelengths in the range of about 5 nm to 100 nm).

[0060] As used herein, the term "projection optics" should be broadly interpreted to encompass various types of optical systems, including, for example, refractive optics, reflective optics, apertures, and reflective-refractive optics. The term "projection optics" may also collectively or individually include components that operate according to any of these design types for guiding, shaping, or controlling the projected radiation beam. The term "projection optics" can include any optical component in the lithography projection apparatus, regardless of its location on the optical path of the lithography projection apparatus. Projection optics can include optical components for shaping, adjusting, and / or projecting radiation from the source before the radiation passes through (e.g., semiconductor) patterning apparatus, and / or for shaping, adjusting, and / or projecting the radiation after the radiation passes through the patterning apparatus. Projection optics typically do not include the source and the patterning apparatus.

[0061] (For example, semiconductor) patterning apparatuses may include or constitute one or more design layouts. These design layouts can be generated using CAD (Computer-Aided Design) programs, a process often referred to as EDA (Electronic Design Automation). Most CAD programs follow a predetermined set of design rules to generate functional design layouts / patterning apparatuses. These rules are set through processing and design constraints. For example, design rules define spacing tolerances between devices (such as gates, capacitors, etc.) or interconnects to ensure that devices or lines do not interact in undesirable ways. The design rules may include and / or specify particular parameters, limitations and / or ranges of parameters, and / or other information. One or more of the design rule constraints and / or parameters may be referred to as “critical dimensions” (CDs). A critical dimension of a device may be defined as the minimum width of a line or via, or the minimum spacing between two lines or two vias, or other characteristics. Thus, CDs determine the overall size and density of the designed device. One of the goals in device fabrication is (via the patterning apparatus) to faithfully reproduce the original design intent on the substrate.

[0062] As used in this invention, the terms "mask" or "patterning apparatus" can be broadly interpreted to refer to a general semiconductor patterning apparatus that can be used to impart a patterned cross-section to an incident radiation beam, the patterned cross-section corresponding to a pattern to be generated in a target portion of the substrate; in this context, the term "light valve" may also be used. Examples of other such patterning apparatuses besides classic masks (transmissive or reflective; binary, phase-shifting, hybrid, etc.) include programmable mirror arrays and programmable LCD arrays.

[0063] An example of a programmable mirror array can be a matrix-addressable surface with a viscoelastic control layer and a reflective surface. The basic principle underlying such a device is that, for example, addressed regions of the reflective surface reflect incident radiation as diffracted radiation, while unaddressed regions reflect incident radiation as non-diffracted radiation. With the use of suitable filters, the non-diffracted radiation can be filtered out from the reflected beam, leaving only the diffracted radiation; thus, the beam becomes patterned according to the addressing pattern of the matrix-addressable surface. Suitable electronics can be used to perform the desired matrix addressing. An example of a programmable LCD array is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0064] As used herein, the term “patterning process” generally refers to a process of producing an etched substrate by applying a specified light pattern as part of a photolithography process. However, a “patterning process” may also include (e.g., plasma) etching, as many of the features described herein can benefit the formation of printed patterns using etching (e.g., plasma) processes.

[0065] As used herein, the term “pattern” refers to an idealized pattern to be etched onto a substrate (e.g., a wafer).

[0066] As used herein, the term "printed pattern" refers to a physical pattern etched onto a substrate based on a target pattern. The printed pattern may include, for example, trenches, channels, recesses, edges, or other two-dimensional or three-dimensional features produced by a photolithography process.

[0067] As used herein, the terms “predictive model,” “process model,” “electronic model,” and / or “simulation model” (these models may be used interchangeably) refer to a model that includes one or more models simulating the patterning process. For example, the model may include an optical model (e.g., modeling a lens system / projection system used to transmit light during the photolithography process and may include modeling the final optical image of the light traveling onto the photoresist), a resist model (e.g., modeling the physical effects of the resist, such as chemical effects due to the light), and an OPC model (e.g., the OPC model can be used to create the target pattern and may include sub-resolution resist features (SRAF), etc.), an etching (or etching deviation) model (e.g., the etching model simulates the physical effects of the etching process on the printed wafer pattern), and / or other models.

[0068] As used herein, the term “calibration” means to modify (e.g., improve or tune) and / or verify something, such as a model.

[0069] A patterning system can be a system that includes any or all of the components described above, as well as other components configured to perform any or all of the operations associated with these components. For example, a patterning system may include a photolithography projection device, a scanner, a system configured to apply and / or remove resist, an etching system, and / or other systems.

[0070] As an introduction, Figure 1 The diagram illustrates the various subsystems of an exemplary photolithography projection apparatus 10A. The main components are: a radiation source 12A, which may be a deep ultraviolet excimer laser source or another type of source including extreme ultraviolet (EUV) sources (as discussed above, the photolithography projection apparatus itself does not need to have such a radiation source); irradiation optics, which, for example, define partial coherence (denoted as sigma) and may include optical components 14A, 16Aa, and 16Ab for shaping the radiation from the source 12A; a pattern forming apparatus 18A; and a transmission optics 16Ac that projects an image of the pattern formed by the pattern forming apparatus onto a substrate plane 22A. An adjustable filter or aperture or aperture stop 20A at the pupil surface of the projection optics can limit the range of beam angles incident on the substrate plane 22A, wherein the maximum possible angle defines the numerical aperture NA of the projection optics as n sin(θmax), where n is the refractive index of the medium between the substrate and the final element of the projection optics, and θmax is the maximum angle of the beam emitted from the projection optics that can still be incident on the substrate plane 22A.

[0071] In a photolithography projection apparatus, a source provides illumination (i.e., radiation) to a patterning apparatus, and projection optics guide and shape the illumination onto a substrate via the patterning apparatus. The projection optics may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. A spatial image (AI) is the distribution of radiation intensity at the substrate level. The resist image can be calculated using a resist model based on the spatial image; examples of such a scheme can be found in U.S. Patent Application Publication No. 2009-0157630, the entire contents of which are hereby incorporated by reference. The resist model relates to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking (PEB), and development). The optical properties of the photolithography projection apparatus (e.g., the properties of the illumination, the patterning apparatus, and the projection optics) define the spatial image and can be confined within the optical model. Since the pattern forming apparatus used in the photolithography projection apparatus can be modified, it is desirable to separate the optical properties of the pattern forming apparatus from the optical properties of the rest of the photolithography projection apparatus, including at least the source and the projection optics. Techniques and models for transforming design layouts into various photolithographic images (e.g., spatial images, resist images, etc.), applying OPC using those techniques and models, and evaluating performance (e.g., in terms of process windows) are described in U.S. Patent Application Publications Nos. US 2008-0301620, 2007-0050749, 2007-0031745, 2008-0309897, 2010-0162197, and 2010-0180251, the entire disclosure of each of these U.S. patent applications is hereby incorporated herein by reference.

[0072] It may be desirable to use one or more tools to produce results that can be used for designing, controlling, monitoring, etc., of the patterning process. One or more tools may be provided for use in one or more aspects of the patterning process, such as pattern design for a patterning apparatus (including, for example, adding sub-resolution auxiliary features or optical proximity correction), illumination for the patterning apparatus, etc. Therefore, in a system for computationally controlling, designing, etc., a manufacturing process involving patterning, the manufacturing system components and / or processes can be described by various functional modules and / or models. In some embodiments, one or more electronic (e.g., mathematical, parametric, etc.) models describing one or more steps and / or apparatus of the patterning process (e.g., etching) can be provided. In some embodiments, simulation of the patterning process can be performed using one or more electronic models to simulate how the patterning process forms a patterned substrate using a pattern provided by the patterning apparatus.

[0073] Figure 2 The figure shows an exemplary flowchart for simulating a photolithography projection apparatus. Irradiation model 231 represents the optical characteristics of the irradiation (including the radiation intensity distribution and / or phase distribution). Projection optics model 232 represents the optical characteristics of the projection optics (including changes in the radiation intensity distribution and / or phase distribution caused by the projection optics). Design layout model 235 represents the optical characteristics of a design layout (including changes in the radiation intensity distribution and / or phase distribution caused by a given design layout), which is a representation of the arrangement of features formed on or by a pattern forming apparatus. Spatial image 236 can be simulated using the irradiation model 231, the projection optics model 232, and the design layout model 235. Resist model 237 can be used to simulate resist image 238 based on spatial image 236. The simulation of photolithography can, for example, predict the contours and / or CDs in the resist image.

[0074] More specifically, illumination model 231 may represent the optical characteristics of the illumination, including but not limited to NA-sigma (σ) settings and any particular illumination shape (e.g., off-axis illumination, such as annular, quadrupole, and dipole illumination). Projection optics model 232 may represent the optical characteristics of the projection optics, including, for example, aberrations, distortion, refractive index, physical size, or dimensions. Design layout model 235 may also represent one or more physical properties of a physical patterning apparatus, for example, as described in U.S. Patent No. 7,587,704, the entire contents of which are incorporated herein by reference. The optical properties associated with the photolithography projection apparatus (e.g., the properties of the illumination, the patterning apparatus, and the projection optics) define the spatial image. Since the patterning apparatus used in the photolithography projection apparatus can be modified, it is desirable to separate the optical properties of the patterning apparatus from the optical properties of at least the rest of the photolithography projection apparatus, including the illumination and the projection optics (and thus design layout model 235).

[0075] The resist model 237 can be used to calculate the resist image based on the spatial image. Examples of such a scheme can be found in U.S. Patent Application No. 8,200,468, the entire contents of which are hereby incorporated herein by reference. The resist model typically relates to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, post-exposure baking, and / or development).

[0076] One of the objectives of full simulation is to accurately predict, for example, edge placement, spatial image intensity slope, and / or CD, which can then be compared with the intended design. The intended design is typically defined as a pre-OPC design layout, which can be provided in a standardized digital file format (such as GDS, GDSII, OASIS, or other file formats).

[0077] Based on the design layout, one or more portions referred to as "segments" can be identified. In embodiments, a set of segments is extracted, representing complex patterns in the design layout (typically around 50 to 1000 segments, but any number of segments can be used). As those skilled in the art will understand, these patterns or segments represent smaller parts of the design (e.g., circuits, cells, etc.), and in particular, the segments represent smaller parts that require special attention and / or verification. In other words, a segment can be a part of the design layout, or a similar behavior of a part of the design layout that has critical features identified empirically (including segments provided by the customer), identified through trial and error, or identified by performing full-chip simulation. Segments often contain one or more test patterns or gauge patterns. An initial large set of segments can be provided a priori by the customer based on known critical feature regions in the design layout that require specific image optimization. Alternatively, in another embodiment, an initial large set of segments can be extracted from the entire design layout by using automated (e.g., machine vision) or manual algorithms to identify critical feature regions.

[0078] For example, the simulation and modeling can be used to configure one or more features of the pattern forming apparatus pattern (e.g., performing optical proximity correction), one or more features of the illumination (e.g., changing one or more characteristics of the spatial / angular intensity distribution of the illumination (such as changing the shape)), and / or one or more features of the projection optics (e.g., numerical aperture, etc.). Such configurations can generally be referred to as mask optimization, source optimization, and projection optimization, respectively. Such optimizations can be performed individually or combined in different ways. One such example is source-mask optimization (SMO), which involves configuring one or more features of the pattern forming apparatus pattern together with one or more features of the illumination. These optimization techniques can focus on one or more of these segments. The optimizations can use the machine learning models described herein to predict values ​​for various parameters, including images, etc.

[0079] Similar modeling techniques can be applied to optimize processes such as etching and / or other processes. In some embodiments, for example, illumination model 231, projection optics model 232, design layout model 235, resist model 237, and / or other models can be used in conjunction with the etching model. For example, output from an Acrylic Inspection (ADI) model (e.g., included as all and / or some of the design layout model 235, resist model 237, and / or other models) can be used to determine an ADI profile, which can be provided to an Effective Etching Bias (EEB) model to produce a predicted Acrylic Inspection (AEI) profile.

[0080] In some embodiments, the optimization process of a system can be represented as a cost function. The optimization process may include finding the set of parameters (design variables, process variables, etc.) that minimize the cost function. The cost function can have any suitable form depending on the optimization objective. For example, the cost function may be the weighted root mean square (RMS) of the deviations of certain characteristics (estimated points) of the system relative to expected values ​​(e.g., ideal values) of these characteristics. The cost function may also be the maximum value of these deviations (i.e., the worst-case deviation). The term "estimated point" should be interpreted broadly to include any characteristic of the system or fabrication method. Due to the practicality of the implementation of the system and / or method, the design and / or process variables of the system may be limited to a finite range and / or interdependent. In the case of photolithography projection equipment, these constraints are often associated with the physical properties and characteristics of the hardware (such as tunability range) and / or manufacturability design rules of the patterning apparatus. For example, the estimated point may include physical points on a resist image on a substrate, as well as non-physical characteristics (such as one or more etching parameters, dose, and focal length, etc.).

[0081] In an etching system, as an example, the cost function (CF) can be expressed as:

[0082]

[0083] Where (z1, z2, ..., z N ) represents either N design variables or the values ​​of N design variables, and f p (z1, z2, ..., z N ) can be the design variables (z1, z2, ..., z N Functions such as (z1, z2, ..., z) N The difference between the actual and expected values ​​of the set of design variables. In some embodiments, w p Is with f p (z1, z2, ..., z N The associated weighting constant. For example, the characteristic could be the position of the edge measured at a given point on the edge of the image. Different f p (z1, z2, ..., z N ) can have different weights w p For example, if a particular edge has a narrow range of permissible locations, then f represents the difference between the actual location and the expected location of the edge. p (z1, z2, ..., z N The weight w p It can be assigned a large value. p (z1, z2, ..., z NThe design variables (z1, z2, ..., z) can also be functions of intermediate layer characteristics, which are themselves the design variables (z1, z2, ..., z). N The function is CF(z1, z2, ..., z). N The equation is not limited to the form of the above equation, and CF(z1, z2, ..., z) N It can take any other suitable form.

[0084] The cost function may represent any one or more suitable characteristics of the etching system, etching process, photolithography equipment, photolithography process, or substrate, such as focal length, CD, raster offset, image distortion, image rotation, random variation, yield, local CD variation, process window, intermediate layer characteristics, or a combination thereof. In some embodiments, the cost function may include functions representing one or more characteristics of the resist image. For example, f p (z1, z2, ..., z N It can simply be the distance between a point in the resist image and the expected location of that point, for example, after etching and / or some other process (i.e., edge placement error EPE). p (z1, z2, ..., z N The parameters (e.g., design variables) may include any adjustable parameters, such as adjustable parameters of the etching system, the source, the patterning apparatus, the projection optics, dose, focal length, etc.

[0085] The parameters (e.g., design variables) may have constraints, which can be represented as (z1, z2, ..., z...). N )∈Z, where Z is the set of possible values ​​for the design variable. A possible constraint on the design variable can be imposed by the expected production volume of the photolithography projection equipment. Without the constraint imposed by the expected production volume, the optimization can produce a set of unrealistic values ​​for the design variable. Constraints should not be interpreted as necessities.

[0086] In some embodiments, the irradiation model 231, the projection optics model 232, the design layout model 235, the resist model 237, and the etching model, and / or other models associated with and / or included in the integrated circuit manufacturing process, may be empirical models and / or other simulation models of at least some of the operations performed in the methods described herein. The empirical model may predict the output based on the correlation between various inputs (e.g., one or more characteristics of the pattern (such as curvature), one or more characteristics of the pattern forming apparatus, one or more characteristics of the irradiation used in the photolithography process (such as wavelength), etc.).

[0087] As an example, the empirical model can be a machine learning model and / or any other parameterized model. In some embodiments, the machine learning model can be, for example, and / or include mathematical equations, algorithms, graphs, charts, networks (e.g., neural networks) and / or other tools and machine learning model components. For example, the machine learning model can be and / or include one or more neural networks having an input layer, an output layer, and one or more intermediate or hidden layers. In some embodiments, the one or more neural networks can be and / or include deep neural networks (e.g., neural networks with one or more intermediate or hidden layers between the input and output layers).

[0088] As an example, the one or more neural networks may be based on a large number of neural units (or artificial neurons). The one or more neural networks may loosely mimic the way a biological brain works (e.g., via a large cluster of biological neurons connected by axons). Each neural unit of the neural network may be connected to many other neural units of the neural network. These connections may strengthen or inhibit their influence on the activation state of the connected neural units. In some embodiments, each individual neural unit may have a summation function that combines the values ​​of all its inputs. In some embodiments, each connection (or the neural unit itself) may have a threshold function such that a signal must exceed a threshold before it is allowed to propagate to other neural units. These neural network systems may be self-learning and trained rather than explicitly programmed, and they may perform significantly better in certain areas of problem-solving compared to conventional computer programs. In some embodiments, the one or more neural networks may include multiple layers (e.g., where signal paths traverse from previous layers to subsequent layers). In some embodiments, the neural network may utilize backpropagation techniques, where forward stimulation is used to reset weights on “previous” neural units. In some embodiments, stimulation and inhibition against the one or more neural networks can flow more freely, and the connections interact in a more chaotic and complex manner. In some embodiments, the intermediate layers of the one or more neural networks include one or more convolutional layers, one or more recurrent layers, and / or other layers.

[0089] One or more neural networks can be trained (i.e., their parameters are determined) using a set of training information. The training information may include a set of training samples. Each sample may be a pair comprising an input object (typically a vector, which may be called a feature vector) and a desired output value (also called a supervision signal). The training algorithm analyzes the training information and adjusts the behavior of the neural network by adjusting the parameters of the neural network (e.g., the weights of one or more layers) based on the training information. For example, given the form {(x1, y1), (x2, y2), ..., (x... N y N Let be a set of N training samples, such that xi is the feature vector of the i-th example and y i The supervisory signal is used to train the neural network g: X→Y, where X is the input space and Y is the output space. Feature vectors are n-dimensional vectors representing the numerical features of certain objects (e.g., simulated spatial images, wafer designs, fragments, etc.). The vector space associated with these vectors is often called the feature space. After training, the neural network can be used to make predictions using new samples.

[0090] As another example, the empirical (simulation) model may include one or more algorithms. The one or more algorithms may be and / or include mathematical equations, graphs, charts, and / or other tools and model components. For example, in some embodiments, the system and method include (or use) an empirical simulation model comprising one or more multidimensional algorithms. The one or more multidimensional algorithms include one or more nonlinear, linear, or quadratic functions representing physical parameters of the etching process. In some embodiments, the one or more multidimensional algorithms include curvature terms configured to correlate curvature with etching deviation, either alone or in conjunction with other algorithm terms. In some embodiments, the empirical simulation model including the one or more algorithms may be considered a physical etching model. The physical etching model may be and / or include an effective etching deviation (EEB) model, a resist model combined with an etching deviation model (e.g., resist model 237), and / or other models. This is further described below.

[0091] Figure 3The figure illustrates an exemplary method 300 according to an embodiment of the present disclosure. In some embodiments, method 300 includes: receiving 302 a representation of a contour in a substrate pattern; determining 304 the curvature of the contour; inputting the curvature 306 to the simulation model; and outputting 308 an etch deviation for the substrate pattern based on the curvature. In some embodiments, method 300 includes: using 310 the etch deviation in a cost function to predict a post-etched feature contour in a substrate (wafer) pattern to facilitate the determination of costs associated with individual patterning process variables, and / or costs in other operations. It will be understood that the present disclosure is not limited to any particular method or algorithm for determining or obtaining a contour.

[0092] In some embodiments, a non-transitory computer-readable medium stores instructions that, when executed by a computer, cause the computer to perform one or more operations 302 to 310 and / or other operations. These operations of method 300 are intended to be illustrative. In some embodiments, method 300 may be implemented using one or more additional operations not described, and / or without using one or more of the operations discussed. For example, operations 310 and / or other operations may be optional. Additionally, in Figure 3 The order of operations of method 300, as illustrated in the figure and described herein, is not intended to be limiting.

[0093] At operation 302, a representation of a contour in a substrate pattern is received. The representation includes the contour in the pattern and / or other information. For example, the representation may include information describing the geometry of the contour in the pattern, and / or information related to the geometry. For example, the geometry of the contour in the pattern may be a two-dimensional geometry. The received representation includes data describing the characteristics of the contour (e.g., XY dimension data points, mathematical equations describing the geometry, etc.), processing parameters associated with the contour, and / or other data. In some embodiments, the representation of the pattern includes inspection results from an auto-division (ADI) of the pattern, a model of the contour in the pattern, and / or other information. The inspection results from the auto-division of the pattern can be obtained from a scanning electron microscope, optical metrology tools, and / or other sources. In some embodiments, from a resist model (e.g., such as...) Figure 2 (shown in and described above), optical models (e.g., such as) Figure 2 (as shown in the diagram and described above) and / or other modeling sources are used to obtain the contour.

[0094] The representation may be received electronically from one or more other parts of the system (e.g., from different processors, or from different parts of a single processor), from a remote computing system not associated with the system, and / or from other sources. The representation may be received wirelessly and / or via wire, via portable storage media, and / or from other sources. The representation may be uploaded and / or downloaded, for example, from another source (such as cloud storage), and / or otherwise received.

[0095] By way of non-restrictive examples, Figure 4 The diagram illustrates how simulation model 400 can be used, for example, to predict the post-etched pattern profile based on etching effects (such as etching deviation 404). Figure 4 As shown, the etch deviation describes the dimensional change between the Advanced Development (ADI) profile 408 and the Advanced Etching (AEI) profile 410 for a given substrate pattern feature 406 at a given location. (The pattern feature 406 may be generated via a corresponding portion of a mask 407.) The deviation direction 412 may be perpendicular to the ADI profile 408, but this disclosure is not limited thereto. The simulation model 400 simulates and / or otherwise determines the etch deviation 404 for the wafer pattern based on the ADI profile 408 (and / or other information) to generate the AEI profile 410. More generally, the etch deviation from the model 400 can be used to determine various pattern features (e.g., pattern feature 406 and / or...) Figure 4 The etched outline (other pattern features not shown in the figure).

[0096] Figure 4 The diagram also illustrates a representation of a contour (e.g., ADI contour 408 in this example) within a substrate pattern of receiving 414. As described above, the representation of the contour (e.g., ADI contour 408) can be derived from the results of an after-development inspection (ADI) of the pattern, a model of the contour within the pattern, and / or any other suitable information. Figure 4 In the example shown, profile 415 408 is obtained from resist model and / or optical model 416.

[0097] Return to Figure 3 At operation 304, the curvature of the contour in the substrate pattern is determined. The curvature is (e.g., as...) Figure 4The curvature is shown as an in-plane curvature of a two-dimensional profile. This curvature corresponds to an in-plane bending effect near a local etch location. The curvature can be an indication of the activation energy at a given local etch location, which affects the etching effect. This disclosure is not limited to any particular method, process, operation, or algorithm for determining the curvature. The curvature can be determined based on the slope of the profile in the pattern, the maximum or minimum value of the profile in the pattern, and / or other information. For example, the slope, the maximum value, and / or the minimum value can be determined based on the first and / or second derivatives of the profile. In some embodiments, the curvature is determined by the ratio between the second derivative and the first derivative, and / or other mathematical operations. It should be noted that although this disclosure describes the determination of a single curvature, the curvature can be determined (and input into the simulation model, as described below) at one or more locations along the profile.

[0098] By way of non-restrictive examples, Figure 5 The figure illustrates the curvature 500 at a given location 501 in the contour 502 of a substrate (e.g., a wafer) pattern 504. Figure 5 As shown, curvature 500 is an in-plane curvature (e.g., of a two-dimensional profile 502). In some embodiments, curvature 500 is determined based on the slope (e.g., a sloping or skewed portion) of profile 502 in pattern 504, the maximum or minimum value (e.g., an inflection point) of profile 502 in pattern 504, and / or other information. For example, the slope, the maximum value, and / or the minimum value may be determined based on the first and / or second derivatives of profile 502. Curvature 500 is also determined by the ratio between the second derivative and the first derivative. For example, profile 502 may be described by a function 506y = f(x). Using function 506, curvature 500 may be determined based on the following equation:

[0099]

[0100] Where f' is the first derivative of function 506 and f″ is the second derivative. In the equations shown above, the curvature 500 is determined by dividing the absolute value of the second derivative of function 506 by the first derivative of function 506 (modified by various constants and exponents) (or by ratioing it to the first derivative). In some embodiments, it may be possible to determine the curvature using the first derivative, the second derivative, and / or various other constants and other combinations of equation terms. These embodiments should be considered within the spirit and scope of the invention.

[0101] Return to Figure 3At operation 306, the curvature is input to the simulation model. Input may include electronically transmitting, uploading, and / or otherwise providing the curvature to the simulation model. In some embodiments, the simulation model may be programmed integrated with instructions causing other operations in operations 302 through 310 (e.g., so that "input" is not required, and instead, data simply flows directly to the simulation model). The simulation model is configured to predict the impact of pattern profile curvature on local etching deviations. The simulation model is configured to receive pattern profile curvature and determine etching deviations. In contrast to previous systems, the simulation model includes an in-plane curvature term not included in previous models. The simulation model includes a correlation between etching deviations and profile curvature. For example, the model is configured to correlate the in-plane curvature with an in-plane bending effect near the local etching location.

[0102] The simulation model is a physical etching (or etching deviation) model or a semi-physical etching (or etching deviation) model. The physical or semi-physical etching model describes the physical parameters of the etching process, which depends on chemical / physical / mathematical principles in the algorithm (e.g., where different terms are used for different physical parameters) and / or other forms. The physical or semi-physical etching model is configured based on the ADI profile (e.g., Figure 4 Outline 408 or Figure 5 The contour 502 in the image is used to determine the AEI contour (see, for example, the contour 502 in the image). Figure 4 Model 400 and contour 410 (as shown in the text). It has various terms corresponding to various physical etching effects. The physical or semi-physical etching model may be and / or include an effective etch bias (EEB) model, a resist model combined with an etch bias model, and / or other models. In some embodiments, the simulation model includes a multidimensional algorithm (or more than one multidimensional algorithm). The multidimensional algorithm includes one or more nonlinear, linear, or quadratic functions representing parameters of the etching process. The simulation model includes a curvature term configured to correlate the curvature with the etch bias. For example, the curvature term may be combined with one or more additional terms of the multidimensional algorithm to determine the etch bias.

[0103] In some embodiments, for example, the simulation model is a calibrated predictive model. The simulation model is calibrated using curvature calibration data and corresponding etching deviation calibration data. Calibration may include model generation, training, adjustment, and / or other operations. The curvature calibration data and corresponding etching deviation calibration data include known and / or otherwise previously determined data. The curvature and / or etching deviation calibration data may be measured, simulated, and / or otherwise determined. In some embodiments, the calibration data is obtained by performing a full simulation model (e.g., where the full simulation model may include one or more of an illumination model 231, a projection optics model 232, a design layout model 235, a resist model 237, and / or other models).

[0104] In some embodiments, the simulation model is calibrated by providing the curvature calibration data to a base (simulation) model to obtain predicted values ​​of the etching deviation calibration data, and using the etching deviation calibration data as feedback to update one or more configurations of the base model. For example, the one or more configurations of the simulation model may be updated based on a comparison between the etching deviation calibration data and the predicted values ​​of the etching deviation calibration data. The calibration data used to calibrate the simulation model may include pairs or sets of inputs (e.g., known curvature) and corresponding known outputs (e.g., known corresponding etching deviations). The calibrated simulation model can then be used to make predictions based on the new curvature (e.g., the etching deviation).

[0105] This disclosure is not limited to any particular form or algorithm of the simulation model. In some embodiments, the simulation model includes the multidimensional algorithm described above. In some embodiments, calibrating the model includes updating one or more configurations of the base model by adjusting and / or otherwise modifying one or more parameters of the algorithm. In some embodiments, modification includes adjusting one or more model parameters such that the predicted etching deviation data better matches, or better corresponds to, known etching deviation data for the corresponding curvature. In some embodiments, modification includes training or retraining the model using additional calibration information including new and / or additional input / output calibration data pairs.

[0106] In some embodiments, the simulation model (e.g., the multidimensional algorithm) includes one or more of nonlinear algorithms, linear algorithms, quadratic algorithms, or combinations thereof, but may and / or include any suitable arbitrary mathematical function. For example, the function may have a power polynomial form, a piecewise polynomial form, an exponential form, a Gaussian form, a sigmoid form, a decision tree type form, etc. These algorithms may include any number of parameters, weights, and / or other features in any combination, such that the function is configured to mathematically correlate curvature with etching deviation.

[0107] In some embodiments, the form of the algorithm (e.g., nonlinear, linear, quadratic, etc.), the parameters of the algorithm, the weights in the algorithm, and / or other characteristics of the algorithm can be determined automatically based on the calibration described above, based on accuracy and runtime performance specifications provided by the user, based on manual input and / or information selection by the user through a user interface included in the system, and / or by other methods. In some embodiments, the form of the algorithm (e.g., nonlinear, linear, quadratic, etc.), the parameters of the algorithm, and / or other characteristics of the algorithm can vary with individual layers of the substrate (e.g., with processing parameters and / or other conditions that may cause and / or affect etching changes), and / or based on other information. For example, different models can be calibrated for different layers of the substrate produced during etching operations in semiconductor device fabrication.

[0108] At operation 308, an etching deviation is output from the simulation model. The etching deviation is for a defined contour within the pattern. The etching deviation may be output electronically to one or more other parts of the system (e.g., to a different processor), a remote computing system not associated with this system, and / or other locations. The etching deviation may be output wirelessly and / or via wire, via portable storage media, and / or using other components. The etching deviation may be uploaded and / or downloaded, for example, to another source (such as cloud storage), and / or otherwise output.

[0109] At operation 310, the etching deviation is used in the cost function to facilitate the determination of costs associated with individual patterning process variables and / or metrics. The costs associated with individual patterning variables are configured to be used to facilitate the optimization of the patterning process. In some embodiments, the costs associated with individual patterning process variables are configured to be provided to an optimizer for (e.g., co-optimization) of the etching process, the patterning system (e.g., a scanner), and / or other semiconductor manufacturing processes and / or systems. Typically, the optimizer is a computer algorithm that finds the minimum of a given cost function. For example, the optimizer may be a gradient-based nonlinear optimizer configured to co-determine multiple etching process variables. The optimizer may consist of one or more processors configured to balance different possible process variables (e.g., each process variable within its own tolerance range) relative to manufacturing capabilities or costs associated with different metrics (e.g., critical size, pattern placement error, edge placement error, critical size asymmetry, defect count associated with the etching process, and / or other metrics).

[0110] Figure 6 The figure illustrates an exemplary quantification of the improvements provided by this system, model, and / or manufacturing process compared to previous systems, models, and / or manufacturing processes. Figure 6 The figure illustrates how the pattern RMS (root mean square – a measure of surface roughness) decreases for DUV600 and EUV602 applications when curvature is used to determine the etching deviation as described above. Experimental results show a 12.8% reduction for DUV600 applications and a 21.3% reduction for EUV 602 applications.

[0111] Figure 7 This is a diagram of an exemplary computer system CS that can be used in one or more of the operations described herein. The computer system CS includes a bus BS or other communication mechanism for communicating information, and a processor PRO (or multiple processors) connected to the bus BS for processing information. The computer system CS also includes a main memory MM (such as random access memory (RAM) or other dynamic memory), which is connected to the bus BS for storing information and instructions to be executed by the processor PRO. The main memory MM can also be used to store temporary variables or other intermediate information during the execution of instructions by the processor PRO. The computer system CS also includes a read-only memory (ROM) or other static storage device connected to the bus BS for storing static information and instructions for the processor PRO. A storage device SD, such as a disk or optical disk, is provided and connected to the bus BS for storing information and instructions.

[0112] The computer system CS can be connected via a bus BS to a display DS for displaying information to the computer user, such as a cathode ray tube (CRT), flat panel display, or touch panel display. Input devices ID, including alphanumeric keys and other keys, are connected to the bus BS for communicating information and command selections to the processor PRO. Another type of user input device is a cursor controller CC (such as a mouse, trackball, or arrow keys) for communicating directional information and command selections to the processor PRO and for controlling cursor movement on the display DS. This type of input device typically has two degrees of freedom on two axes (a first axis (e.g., x) and a second axis (e.g., y)), allowing the device to specify a position in a plane. Touch panel (screen) displays can also be used as input devices.

[0113] In some embodiments, portions of one or more methods described herein can be executed by a computer system CS in response to a processor PRO for executing one or more sequences of instructions contained in main memory MM. Such instructions may be read into main memory MM from another computer-readable medium, such as a storage device SD. Execution of the sequence of instructions contained in main memory MM causes the processor PRO to perform the process steps (operations) described herein. In a multiprocessor arrangement, one or more processors may also be used to execute the sequence of instructions contained in main memory MM. In some embodiments, hardwired circuitry may be used in place of or in combination with software instructions. Therefore, the description herein is not limited to any particular combination of hardware circuitry and software.

[0114] As used herein, the term "computer-readable medium" refers to any medium that participates in providing instructions to a processor (PRO) for execution. Such media can take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical discs or magnetic disks, such as storage devices (SDs). Volatile media include dynamic memory, such as main memory (MMs). Transmission media include coaxial cables, copper wires, and optical fibers, including wires containing a bus (BS). Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Computer-readable media can be non-transitory, such as floppy disks, floppy disks, hard disks, magnetic tapes, any other magnetic media, CD-ROMs, DVDs, any other optical media, punched cards, paper tape, any other physical media with a perforated pattern, RAM, PROMs, and EPROMs, FLASH-EPROMs, any other memory chips, or cassette memories. Non-transitory computer-readable media can have instructions recorded thereon. These instructions, when executed by a computer, perform any of the operations described above. For example, a temporary computer-readable medium may include a carrier wave or other means of propagating electromagnetic signals.

[0115] Various forms of computer-readable media can involve carrying one or more sequences of instructions to a processor PRO for execution. For example, the instructions may initially be carried on a disk of a remote computer. The remote computer may load the instructions into its dynamic memory and transmit them over a telephone line using a modem. A modem local to the computer system CS can receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to a bus BS can receive the data carried in the infrared signal and place the data on the bus BS. The bus BS carries the data to main memory MM, from which the processor PRO retrieves and executes the instructions. The instructions received by the main memory MM may optionally be stored on a storage device SD before or after execution by the processor PRO.

[0116] The computer system CS may also include a communication interface CI coupled to a bus BS. The communication interface CI provides bidirectional data communication to a network link NDL connected to a local area network (LAN). For example, the communication interface CI may be an Integrated Services Digital Network (ISDN) card or modem for providing data communication connectivity to a corresponding type of telephone line. As another example, the communication interface CI may be a LAN card for providing data communication connectivity to a compatible LAN. Wireless links may also be implemented. In any such implementation, the communication interface CI transmits and receives electrical, electromagnetic, or optical signals carrying digital data streams representing various types of information.

[0117] A network link (NDL) typically provides data communication to other data devices via one or more networks. For example, a network link (NDL) can provide a connection to a host computer (HC) via a local area network (LAN). This can include data communication services provided via a global packet data communication network now commonly referred to as the "Internet" (INT). A LAN (Internet) can use electrical, electromagnetic, or optical signals to carry digital data streams. Signals through various networks and signals on the network link (NDL) and through the communication interface (CI) (which carries digital data to and from the computer system (CS)) are exemplary forms of carriers for transmitting said information.

[0118] A computer system (CS) can send messages and receive data including program code via one or more networks, network data links (NDLs), and communication interfaces (CIs). In the example of the Internet, a host (HC) can transmit request codes for an application via the Internet (INT), network data links (NDLs), local area networks (LANs), and communication interfaces (CIs). For example, a downloaded application could provide all or part of the methods described herein. The received code can be executed by the processor (PRO) upon receipt and / or stored in storage devices (SDs) or other non-volatile memory for later execution. In this way, the computer system (CS) can acquire application code in carrier-like form.

[0119] Figure 8 This is a schematic diagram of a photolithography projection apparatus according to an embodiment. The photolithography projection apparatus may include an illumination system IL, a first stage MT, a second stage WT, and a projection system PS. The illumination system IL can adjust the radiation beam B. In this example, the illumination system also includes a radiation source SO. The first stage (e.g., a patterning apparatus stage) MT may be provided with a patterning apparatus holder for holding a patterning apparatus MA (e.g., a mask) and is connected to a first locator to accurately position the patterning apparatus relative to the article PS. The second stage (e.g., a substrate stage) WT may be provided with a substrate holder for holding a substrate W (e.g., a silicon wafer coated with resist) and is connected to a second locator to accurately position the substrate relative to the article PS. The projection system (e.g., the projection system includes a lens) PS (e.g., a refractive, reflective, or reflective-refractive optical system) can image the irradiated portion of the patterning apparatus MA onto a target portion C (e.g., comprising one or more dies) of the substrate W. For example, the pattern forming apparatus MA and the substrate W can be aligned using the pattern forming apparatus alignment marks M1, M2 and the substrate alignment marks P1, P2.

[0120] As depicted, the device can be of the transmissive type (i.e., having a transmissive pattern forming apparatus). However, it can also typically be of the reflective type (i.e., employing a reflective pattern forming apparatus). The device can employ a different kind of pattern forming apparatus than a classic mask; examples include programmable mirror arrays or LCD matrices.

[0121] The source SO (e.g., a mercury lamp or excimer laser, LPP (laser-generated plasma) EUV source) generates a radiation beam. This beam is fed directly into the irradiation system (irradiator) IL, either after passing through an adjustment device (such as a beam expander) or a beam delivery system BD (including a directional mirror, the beam expander, etc.). The irradiator IL may include an adjustment device AD ​​for setting the outer radial range and / or inner radial range (typically referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the beam. Additionally, the irradiator IL typically includes various other components, such as an integrator IN and a concentrator CO. In this way, the beam B incident on the pattern forming apparatus MA has the desired uniformity and intensity distribution in its cross-section.

[0122] In some embodiments, the source SO can be located within the housing of the photolithography projection apparatus (e.g., this is typically the case when the source SO is a mercury lamp), but the source SO can also be located away from the photolithography projection apparatus. For example, the radiation beam generated by the source SO can be directed into the apparatus (e.g., by means of a suitable directional mirror). This latter case can be, for example, when the source SO is an excimer laser (based on KrF, ArF, or F2 laser action).

[0123] The beam B can then be truncated by the pattern forming apparatus MA held on the pattern forming apparatus stage MT. Having traversed the pattern forming apparatus MA, the radiation beam B can pass through the lens PL, which focuses the beam B onto the target portion C of the substrate W. With the aid of the second positioning device (and the interferometric measurement device IF), the substrate stage WT can be accurately moved, for example, to position different target portions C within the path of the beam B. Similarly, for example, after mechanically retrieving the pattern forming apparatus MA from the pattern forming apparatus library, or during scanning, the first positioning device can be used to accurately position the pattern forming apparatus MA relative to the path of the radiation beam B. Typically, the movement of the stages MT and WT can be achieved using long-stroke modules (coarse positioning) and short-stroke modules (fine positioning). However, in the case of a stepper (as opposed to a stepping scanning tool), the pattern forming apparatus stage MT can be connected to a short-stroke actuator, or it can be fixed.

[0124] The described tool can be used in two different modes: step mode and scan mode. In step mode, the pattern forming apparatus stage MT is kept essentially stationary, and the entire pattern forming apparatus image is projected onto the target portion C in one operation (i.e., a single "flash"). The substrate stage WT can be offset along the x-direction and / or y-direction, so that different target portions C can be irradiated by the beam B. In scan mode, essentially the same situation applies, except that a given target portion C is not exposed in a single "flash". Alternatively, the pattern forming apparatus stage MT can be moved at a speed v in a given direction (the so-called "scanning direction," or y-direction), so that the projected beam B is caused to scan across the entire pattern forming apparatus image. Simultaneously, the substrate stage WT moves at a speed V = Mv in the same or opposite directions, where M is the magnification of the lens (typically M = 1 / 4 or = 1 / 5). In this way, a relatively large target portion C can be exposed without compromising resolution.

[0125] Figure 9 This is a schematic diagram of another lithographic projection apparatus (LPA) that can be used and / or facilitates one or more of the operations described herein. The LPA may include a source collector module SO, an illumination system (illuminator) IL, a support structure MT, a substrate stage WT, and a projection system PS, the illumination system being configured to modulate a radiation beam B (e.g., EUV radiation). The support structure (e.g., a patterning apparatus stage) MT may be configured to support a patterning apparatus (e.g., a mask or photomask) MA and is connected to a first positioner PM, the first positioner being configured to accurately position the patterning apparatus. The substrate stage (e.g., a wafer stage) WT is configured to hold a substrate (e.g., a resist-coated wafer) W and is connected to a second positioner PW, the second positioner being configured to accurately position the substrate. The projection system (e.g., a reflective projection system) PS may be configured to project a pattern imparted by the patterning apparatus MA to the radiation beam B onto a target portion C (e.g., comprising one or more dies) of the substrate W.

[0126] As illustrated in this example, the LPA can be of the reflective type (e.g., employing a reflective patterning apparatus). It should be noted that because most materials are absorptive in the EUV wavelength range, the patterning apparatus can have a multilayer reflector comprising multiple stacks of, for example, molybdenum and silicon. In one example, the multilayer reflector has 40 pairs of molybdenum and silicon layers, each layer being a quarter wavelength thick. Even smaller wavelengths can be produced using X-ray lithography. Since most materials are absorptive at both EUV and X-ray wavelengths, the patterned sheets of absorbing material on the morphology of the patterning apparatus (e.g., a TaN absorber on top of a multilayer reflector) define areas where features will be printed (positive resist) or not printed (negative resist).

[0127] The irradiator IL can receive 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 having at least one element (e.g., xenon, lithium, or tin) with one or more emission lines in the EUV range. In one such method, often referred to as laser-generated plasma (“LPP”), the plasma can be generated by irradiating a fuel, such as a droplet, stream, or cluster of a material having a line-emitting element, with a laser beam. The source collector module SO can be an EUV radiation system including a laser for providing a laser beam to excite the fuel. Figure 9 (Not shown in the image) is part of the source collector module. The resulting plasma emission uses output radiation, such as EUV radiation, collected by a radiation collector disposed within 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 can be separate entities. In this example, the laser may not be considered part of the lithography apparatus, and the radiation beam can be delivered from the laser to the source collector module by means of a beam delivery system including, for example, suitable directional mirrors and / or beam expanders. In other examples, such as when the source is a discharge-generated plasma EUV generator (often referred to as a DPP source), the source can be part of the source collector module.

[0128] The irradiator IL may include adjusters for adjusting the angular intensity distribution of the radiation beam PB. Typically, at least the outer radial range and / or inner radial range (often referred to as σ-outer and σ-inner, respectively) of the intensity distribution in the pupil plane of the irradiator can be adjusted. Furthermore, the irradiator IL may include various other components, such as faceted field mirror assemblies and faceted pupil mirror assemblies. The irradiator can be used to adjust the radiation beam to achieve a desired uniformity and intensity distribution in its cross-section.

[0129] The radiation beam B can be incident on and patterned by the patterning apparatus (e.g., a mask) MA, which is held on the support structure (e.g., a patterning apparatus stage) MT. After being reflected from the patterning apparatus (e.g., the mask) MA, the radiation beam B passes through the projection system PS, which focuses the beam onto the target portion C of the substrate W. The substrate stage WT can be accurately moved (e.g., to position different target portions C in the path of the radiation beam B) by means of the second locator PW and the position sensor PS2 (e.g., an interferometer device, a linear encoder, or a capacitive sensor). Similarly, the first locator PM and another position sensor PS1 can be used to accurately position the patterning apparatus (e.g., the mask) MA relative to the path of the radiation beam B. The patterning apparatus (e.g., the mask) MA and the substrate W can be aligned using patterning apparatus alignment marks M1, M2 and substrate alignment marks P1, P2.

[0130] The described apparatus LPA can be used in at least one of the following modes: step mode, scan mode, and static mode. In step mode, the support structure (e.g., a patterning apparatus stage) MT and the substrate stage WT are held substantially stationary while the entire pattern to be applied to the radiation beam is projected onto the target portion C in a single pass (e.g., a single static exposure). The substrate stage WT is then moved along the X and / or Y directions, allowing exposure of different target portions C. In scan mode, the pattern to be applied to the radiation beam B is projected onto the target portion C while the support structure (e.g., a patterning apparatus stage) MT and the substrate stage WT are scanned synchronously (i.e., a single dynamic exposure). The velocity and direction of the substrate stage WT relative to the support structure (e.g., a patterning apparatus stage) MT can be determined by the (reduced) magnification and image inversion characteristics of the projection system PS. In the static mode, the support structure (e.g., a patterning apparatus stage) MT is held substantially stationary, holding the programmable patterning apparatus in place, and the substrate stage WT is moved or scanned while the pattern to be applied to the radiation beam is projected onto the target portion C. In this mode, a pulsed radiation source is typically used, and the programmable patterning apparatus is updated as needed after each movement of the substrate stage WT or between consecutive radiation pulses during scanning. This operating mode can be readily applied to maskless lithography utilizing programmable patterning apparatuses (such as programmable mirror arrays of the type mentioned above).

[0131] Figure 10 Is Figure 9 A detailed view of the photolithography projection apparatus is shown in the figure. Figure 10As shown, the LPA may include the source collector module SO, the irradiation system IL, and the projection system PS. The source collector module SO is configured such that a vacuum environment can be maintained within the enclosure structure 220 of the source collector module SO. The plasma 210 emitting EUV radiation can be formed by a discharge-generated plasma source. EUV radiation can be generated by a gas or vapor, such as xenon, lithium vapor, or tin vapor, wherein a thermal plasma 210 is generated to emit radiation in the EUV range of the electromagnetic spectrum. For example, the thermal plasma 210 is generated by a discharge that causes at least partial ionization of the plasma. Xe, Li, Sn vapor, or any other suitable gas or vapor with a partial pressure of 10 Pa may be required for efficient radiation generation. In some embodiments, an excited tin (Sn) plasma is provided to generate EUV radiation.

[0132] Radiation emitted by the thermal plasma 210 is transmitted from the source chamber 21l to the collector chamber 212 via an optional gas barrier or contaminant trap 230 (also referred to in some cases as a contaminant barrier or wing trap) positioned in or behind an opening in the source chamber 21l. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier, or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier trap 230 (described below) also includes a channel structure. The collector chamber 211 may include a radiation collector CO, which may be a grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation traversing the collector CO can be reflected away from the grating spectral filter 240 to be focused at the virtual source point IF along the optical axis indicated by the line "O". The virtual source point IF is typically 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 T is an image of the plasma 210 emitting radiation.

[0133] Subsequently, the radiation traverses the illumination system IL, which may include a faceted field mirror assembly 22 and a faceted pupil mirror assembly 24. The faceted field mirror assembly 22 and the faceted pupil mirror assembly 24 are arranged to provide a desired angular distribution of the radiation beam 21 at the patterning apparatus MA, and a desired uniformity of radiation intensity at the patterning apparatus MA. When the radiation beam 21 is reflected at the patterning apparatus MA held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged onto the substrate W held by the substrate stage WT via the projection system PS through reflective elements 28 and 30. More elements than are shown may typically be present in the illumination optics unit IL and the projection system PS. For example, the grating spectral filter 240 may be optionally present, depending on the type of lithography apparatus. Additionally, more mirrors than are shown in the figure may be present, for example, in the projection system PS, in addition to… Figure 10 In addition to the reflective element shown, there are 1 to 6 additional reflective elements.

[0134] Collector optics CO (e.g.) Figure 10 The image shown is depicted as a nested collector with grazing incidence reflectors 253, 254, and 255, which is only an 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 conjunction with a plasma source generated by discharge (often referred to as a DPP source).

[0135] Figure 11 This is a detailed view of the source collector module SO of the photolithography projection apparatus LPA (shown in the previous figure). The source collector module SO may be part of the LPA radiation system. The laser LA may be arranged to deposit laser energy into a fuel, such as xenon (Xe), tin (Sn), or lithium (Li), thereby generating a highly ionized plasma 210 with an electron temperature of tens of eV. The high-energy radiation generated during the deexcitation and recombination of these ions is emitted by the plasma, collected by the near-normal incident collector optics CO, and focused onto the opening 221 in the enclosure structure 220.

[0136] Further embodiments are disclosed in the subsequent catalogue of the numbered aspects:

[0137] 1. A non-transitory computer-readable medium having instructions thereon, the instructions causing the computer, when executed by the computer, to:

[0138] Representation of the outline of the receiving substrate pattern;

[0139] Determine the curvature of the contour; and

[0140] A simulation model is used to determine the etching effect on the substrate pattern based on the curvature, wherein the simulation model includes the correlation between etching deviation and the curvature of the profile.

[0141] 2. The medium according to aspect 1, wherein the etching effect is an etching deviation, and wherein the curvature is determined based on the slope of the profile (1) and the maximum or minimum value in the profile (2).

[0142] 3. The medium according to aspect 1, wherein the curvature is determined based on the first derivative of the profile.

[0143] 4. The medium according to aspect 1, wherein the curvature is determined based on the second derivative of the profile.

[0144] 5. The medium according to aspect 1, wherein the curvature is determined based on the first and second derivatives of the profile.

[0145] 6. The medium according to aspect 5, wherein the curvature is determined by the ratio between the second derivative and the first derivative.

[0146] 7. The medium according to any one of aspects 1 to 6, wherein the simulation model includes a multidimensional algorithm.

[0147] 8. The medium according to aspect 7, wherein the multidimensional algorithm comprises one or more nonlinear functions, linear functions or quadratic functions representing parameters of the etching process.

[0148] 9. The method according to aspect 8, wherein the simulation model includes a physical etching model or a semi-physical etching model.

[0149] 10. The medium according to aspect 8, wherein the simulation model is an etching model.

[0150] 11. The medium according to aspect 10, wherein the etching model includes a multidimensional algorithm comprising a curvature term configured to correlate the curvature with the etching deviation.

[0151] 12. The medium according to any one of aspects 1 to 11, wherein the profile is obtained from a representation of the substrate pattern obtained from a post-development inspection of the substrate pattern.

[0152] 13. The medium according to any one of aspects 1 to 11, wherein the profile is obtained from a resist model.

[0153] 14. The medium according to any one of aspects 1 to 11, wherein the profile is obtained from an optical model.

[0154] 15. The medium according to any one of aspects 1 to 14, wherein the etching effect includes etching deviation, and the etching deviation is configured to be provided to a cost function to determine the cost associated with individual patterning process variables.

[0155] 16. A method for determining an etching effect on a substrate pattern, the method comprising:

[0156] Receive a representation of the outline of the substrate pattern;

[0157] Determine the curvature of the contour; and

[0158] A simulation model is used to determine the etching effect on the substrate pattern based on the curvature, wherein the simulation model includes the correlation between etching deviation and the curvature of the profile.

[0159] 17. The method according to aspect 16, wherein the etching effect is an etching deviation, and wherein the curvature is determined based on (1) the slope of the profile and (2) the maximum or minimum value in the profile.

[0160] 18. The method according to aspect 16, wherein the curvature is determined based on the first derivative of the profile.

[0161] 19. The method according to aspect 16, wherein the curvature is determined based on the second derivative of the profile.

[0162] 20. The method according to aspect 16, wherein the curvature is determined based on the first and second derivatives of the contour.

[0163] 21. The method according to aspect 20, wherein the curvature is determined by the ratio between the second derivative and the first derivative.

[0164] 22. The method according to any one of aspects 16 to 21, wherein the simulation model comprises a multidimensional algorithm.

[0165] 23. The method according to aspect 22, wherein the multidimensional algorithm comprises one or more nonlinear functions, linear functions or quadratic functions representing parameters of the etching process.

[0166] 24. The method according to aspect 22, wherein the simulation model includes a physical etching model or a semi-physical etching model.

[0167] 25. The medium according to aspect 22, wherein the simulation model is an etching model.

[0168] 26. The method according to aspect 25, wherein the etching model includes a multidimensional algorithm comprising a curvature term configured to correlate the curvature with the etching deviation.

[0169] 27. The method according to any one of aspects 16 to 26, wherein the contour is obtained from a representation of the substrate pattern obtained from a post-development inspection of the substrate pattern.

[0170] 28. The method according to any one of aspects 16 to 26, wherein the profile is obtained from a resist model.

[0171] 29. The method according to any one of aspects 16 to 26, wherein the profile is obtained from an optical model.

[0172] 30. The method according to any one of aspects 16 to 29, wherein the etching effect is an etching deviation, and the etching deviation is configured to be provided to a cost function to determine the cost associated with individual patterning process variables.

[0173] 31. A system for determining etch effects on a substrate pattern, the system comprising one or more hardware processors configured by machine-readable instructions to:

[0174] Receive a representation of the outline of the substrate pattern;

[0175] Determine the curvature of the contour; and

[0176] A simulation model is used to determine the etching effect on the substrate pattern based on the curvature, wherein the simulation model includes the correlation between etching deviation and the curvature of the profile.

[0177] 32. The system according to aspect 31, wherein the etching effect is an etching deviation, and wherein the curvature is determined based on (1) the slope of the profile and (2) the maximum or minimum value in the profile.

[0178] 33. The system according to aspect 31, wherein the curvature is determined based on the first derivative of the profile.

[0179] 34. The system according to aspect 31, wherein the curvature is determined based on the second derivative of the profile.

[0180] 35. The system according to aspect 31, wherein the curvature is determined based on the first and second derivatives of the contour.

[0181] 36. The system according to aspect 35, wherein the curvature is determined by the ratio between the second derivative and the first derivative.

[0182] 37. The system according to any one of aspects 31 to 36, wherein the simulation model includes a multidimensional algorithm.

[0183] 38. The system according to aspect 37, wherein the multidimensional algorithm comprises one or more nonlinear functions, linear functions or quadratic functions representing parameters of the etching process.

[0184] 39. The system according to aspect 38, wherein the simulation model includes a physical etching model or a semi-physical etching model.

[0185] 40. The system according to aspect 37, wherein the simulation model is an etching model.

[0186] 41. The system according to aspect 40, wherein the etching model includes a multidimensional algorithm comprising a curvature term configured to correlate the curvature with the etching deviation.

[0187] 42. The method according to any one of aspects 31 to 41, wherein the contour is obtained from a representation of the substrate pattern obtained from a post-development inspection of the substrate pattern.

[0188] 43. The system according to any one of aspects 31 to 41, wherein the profile is obtained from a resist model.

[0189] 44. The system according to any one of aspects 31 to 41, wherein the profile is obtained from an optical model.

[0190] 45. The system according to any one of aspects 31 to 44, wherein the etching effect is an etching deviation, and the etching deviation is configured to be provided to a cost function to determine the cost associated with individual patterning process variables.

[0191] 46. ​​A non-transitory computer-readable medium having instructions thereon, which, when executed by a computer, cause the computer to execute a simulation model for determining an etch deviation for a pattern on a substrate, the etch deviation being determined based on the curvature of a contour in the pattern, the etch deviation being configured to improve the accuracy of a patterning process relative to a previous patterning process, the instructions causing operations including:

[0192] Receive a representation of the pattern, wherein the representation includes an outline in the pattern;

[0193] Determine the curvature of the outline of the pattern;

[0194] The curvature is input into the simulation model, wherein the simulation model includes the correlation between etching deviation and the curvature of the contour; and

[0195] Based on the simulation model, the etching deviation for the contour in the pattern is output, wherein the etching deviation from the simulation model is configured to be used in a cost function to facilitate the determination of the cost associated with individual patterning process variables, and wherein the cost associated with individual patterning variables is configured to be used to facilitate the optimization of the patterning process.

[0196] 47. The medium according to aspect 46, wherein the simulation model is an etching model.

[0197] 48. The medium according to aspect 46 or 47, wherein the representation of the pattern comprises (1) an inspection result from a post-development inspection of the pattern; or (2) a model of the contour in the pattern.

[0198] 49. The medium according to aspect 46 or 47, wherein the representation of the pattern includes the result of an inspection of the pattern after development, and wherein the result of the inspection of the pattern after development is obtained from a scanning electron microscope or an optical measuring instrument.

[0199] 50. The medium according to any one of aspects 46 to 49, wherein the curvature is determined based on (1) the slope of the contour in the pattern and (2) the maximum or minimum value of the contour in the pattern.

[0200] 51. A non-transitory computer-readable medium having instructions thereon, which, when executed by a computer, cause the computer to execute a simulation model for determining an etch deviation for a pattern on a substrate, the etch deviation being determined based on the curvature of a contour in the pattern, the etch deviation being configured to improve the accuracy of a patterning process relative to a previous patterning process, the instructions causing operations including: receiving a representation of the pattern, wherein the representation includes a contour in the pattern; determining the curvature of the contour of the pattern; inputting the curvature to the simulation model, wherein the simulation model includes a correlation between the etch deviation and the curvature of the contour; and, based on the simulation model, outputting the etch deviation for the contour in the pattern, wherein the etch deviation from the simulation model is configured to be used in a cost function to facilitate the determination of costs associated with individual patterning process variables, and wherein the costs associated with individual patterning variables are configured to facilitate optimization of the patterning process.

[0201] 52. The medium according to aspect 51, wherein the simulation model is an etching model.

[0202] 53. The medium according to any of the foregoing aspects, wherein the representation of the pattern comprises (1) an inspection result from a post-development inspection of the pattern; or (2) a model of the contour in the pattern.

[0203] 54. The medium according to any one of aspects 51 to 53, wherein the representation of the pattern includes the result of an inspection of the pattern after development, and wherein the result of the inspection of the pattern after development is obtained from a scanning electron microscope or an optical measuring instrument.

[0204] 55. The medium according to any one of aspects 51 to 54, wherein the curvature is determined based on (1) the slope of the contour in the pattern and (2) the maximum or minimum value of the contour in the pattern.

[0205] The concepts disclosed herein can be used to simulate or mathematically model any general imaging, etching, polishing, inspection, etc., system targeting sub-wavelength characteristics, and can be useful for emerging imaging techniques capable of generating increasingly shorter wavelengths. Emerging techniques include EUV (Extreme Ultraviolet) and DUV lithography, which can generate wavelengths of 193 nm using ArF lasers and even 157 nm using fluorine lasers. Furthermore, EUV lithography can generate photons in the range of 20 nm to 50 nm by using synchrotrons or by bombarding materials (solid or plasma) with high-energy electrons.

[0206] While the concepts disclosed herein can be used in manufacturing on substrates such as silicon wafers, it should be understood that the disclosed concepts can be used with any type of manufacturing system, such as a manufacturing system for manufacturing on substrates other than silicon wafers.

[0207] Furthermore, combinations and sub-combinations of the disclosed elements or components may include discrete embodiments. For example, one or more of the etching simulation model and other models described herein may be included in discrete embodiments, or they may be included together in the same embodiment.

[0208] The foregoing description is intended to be exemplary and not restrictive. Therefore, those skilled in the art will understand that modifications can be made as described without departing from the scope of the claims set forth below.

Claims

1. A method for determining the etching effect on a substrate pattern, comprising: Receive a representation of the outline of the substrate pattern; Determine the curvature of the contour; as well as A simulation model is used to determine the etching effect on the substrate pattern based on the curvature, wherein the simulation model includes a correlation between etching deviation and the curvature of the profile, wherein the etching effect includes the etching deviation between the etched profile and the developed profile, and the etching deviation is configured to be provided to a cost function to determine the cost associated with individual patterning process variables.

2. The method according to claim 1, wherein, The curvature is determined based on the slope of the contour described in (1) and the maximum or minimum value in the contour described in (2).

3. The method according to claim 1, wherein, The curvature is determined based on the first or second derivative of the contour.

4. The method according to claim 1, wherein, The curvature is determined based on the first and second derivatives of the contour.

5. The method according to claim 4, wherein, The curvature is determined by the ratio between the second derivative and the first derivative.

6. The method according to claim 1, wherein, The simulation model includes a multidimensional algorithm.

7. The method according to claim 6, wherein, The multidimensional algorithm includes one or more nonlinear functions, linear functions, or quadratic functions representing parameters of the etching process.

8. The method according to claim 7, wherein, The simulation model includes a physical etching model or a semi-physical etching model.

9. The method according to claim 8, wherein, The etching model includes a multidimensional algorithm containing a curvature term configured to correlate the curvature with the etching deviation.

10. The method according to claim 1, wherein, The outline is obtained from a representation of the substrate pattern obtained from a post-development inspection of the substrate pattern.

11. The method according to claim 1, wherein, The contours are obtained from resist models or optical models.

12. A non-transitory computer-readable medium having instructions thereon that, when executed by a computer, cause the computer to perform the method according to any one of claims 1 to 11.

13. A system for determining etch effects on a substrate pattern, the system comprising one or more hardware processors configured by non-transitory machine-readable instructions to perform the method according to any one of claims 1 to 11.

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