Method for determining a pattern in a patterning process - Patents.com

Abstract

To provide a tool for training a model, and using the trained model to determine patterns that will be printed on a substrate in a patterning process.SOLUTION: The invention provides a method for training a model, the model being configured to predict a pattern that will be formed by a patterning process. The method involves: obtaining an image data associated with a desired pattern, a measured pattern of a substrate, a first model including a first set of parameters, and a machine learning model including a second set of parameters; and iteratively determining values of the first and second sets of parameters to train the model. The iteration involves: executing, using the image data, the first model and the machine learning model to cooperatively predict a printed pattern; and modifying the values of the first and second sets of parameters such that a difference between the measured pattern and the predicted pattern is reduced.SELECTED DRAWING: Figure 3

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to U.S. patent application Ser. No. 62 / 823,029, filed March 25, 2019, and U.S. patent application Ser. No. 62 / 951,097, filed December 20, 2019, which are incorporated by reference in their entireties herein.

[0002]

[0002] The description herein relates to lithographic apparatus and processes, and more particularly to tools for training patterning process models and using the trained models to determine the pattern to be printed on a substrate in a patterning process. [Background technology]

[0003] Lithographic projection apparatus may be used, for example, in the manufacture of integrated circuits (ICs). In such cases, a patterning device (e.g. a mask) may contain or be provided with a circuit pattern (a "design layout") corresponding to an individual layer of the IC, and this circuit pattern may be transferred onto a target portion (e.g. comprising one or more dies) on a substrate (e.g. a silicon wafer) that is coated with a layer of radiation-sensitive material ("resist"), such as by irradiating the target portion through the circuit pattern on the patterning device. Typically, a single substrate will contain several adjacent target portions (one target portion at a time) onto which the circuit pattern is successively transferred by the lithographic projection apparatus. In one type of lithographic projection apparatus, the circuit pattern on the entire patterning device is transferred onto one target portion at a time; such an apparatus is commonly referred to as a wafer stepper. In an alternative apparatus, commonly referred to as a step-and-scan apparatus, the projection beam is moved synchronously with scanning the patterning device in a given reference direction (the "scan" direction) and the substrate is moved parallel or anti-parallel to this reference direction. Different parts of the circuit pattern on the patterning device are transferred progressively onto one target portion. Typically, a lithographic projection apparatus has a magnification factor M (typically <1), so that the speed F at which the substrate is moved is a factor M times the speed at which the projection beam scans the patterning device. More information on lithographic devices as described herein can be learned, for example, from U.S. Pat. No. 6,046,792, incorporated herein by reference.

[0004]

[0004] Before transferring the circuit pattern from the patterning device to the substrate, the substrate may undergo various procedures such as priming, resist coating, and soft baking. After exposure, the substrate may undergo other procedures such as post-baking (PEB), developing, hard baking, and measurement / inspection of the transferred circuit pattern. This multiplicity of procedures is used as a basis for making the 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 intended to finish off the individual layers of the device. If several layers are required for the device, the entire procedure, or a variant of it, is repeated for each layer. Finally, a device is present on each target portion on the substrate. These devices are then separated from each other by techniques such as dicing or sawing, so that the individual devices can be mounted on a carrier, connected to pins, etc.

[0005]

[0005] As mentioned above, microlithography is a central step in the manufacture of ICs, in which patterns formed on a substrate define the functional elements of the IC, such as microprocessors, memory chips, etc. Similar lithographic techniques are also used in the formation of flat panel displays, microelectromechanical systems (MEMS), and other devices.

[0006]

[0006] As semiconductor manufacturing processes continue to advance, the dimensions of functional elements are continually decreasing, while the amount of functional elements, such as transistors, per device has been steadily increasing for decades, following a trend commonly referred to as "Moore's Law". In the current state of the art, device layers are fabricated using lithographic projection apparatus that projects a design layout onto a substrate using illumination from a deep ultraviolet illumination source, producing individual functional elements with dimensions well below 100 nm (i.e., less than half the wavelength of the radiation from the illumination source (e.g., a 193 nm illumination source)).

[0007]

[0007] This process, in which features with dimensions below the classical resolution limit of the lithographic projection apparatus are printed, is commonly known as low k1 lithography, with the resolution formula CD=k1×λ / NA, where λ is the wavelength of the radiation used (currently most often 248 nm or 193 nm), NA is the numerical aperture of the projection optics in the lithographic projection apparatus, CD is the "critical dimension" (typically the smallest feature size to be printed), and k1 is an empirical resolution factor. In general, the smaller k1 is, the more difficult it is to reproduce a pattern on a substrate that closely resembles the shape and dimensions planned by the circuit designer to achieve a particular electrical functionality and performance. To overcome these difficulties, sophisticated fine-tuning steps are applied to the lithographic projection apparatus and / or the design layout. These include, for example, but are not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase-shifting patterning devices, optical proximity correction (OPC, sometimes also called "optical and process correction") in the design layout, or other methods commonly defined as "resolution enhancement techniques" (RET). 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 catadioptric optics. The term "projection optics" may also include components that collectively or independently operate according to any of these design types to direct, shape, or control a projection beam of radiation. The term "projection optics" may include any optical component in a lithographic projection apparatus, regardless of where the optical component is located on the optical path of the lithographic projection apparatus. The projection optics may include optical components for shaping, conditioning, and / or projecting radiation from the source before it passes through the patterning device and / or optical components for shaping, conditioning, and / or projecting radiation after it has passed through the patterning device. The projection optics generally excludes the source and the patterning device. Summary of the Invention

[0008]

[0008] The present disclosure provides several improvements in the field of computational lithography. In particular, training a patterning process model, including a first model and a machine learning model, in a framework such as a deep learning convolutional neural network. The trained model can be further used to determine the pattern to be printed on the substrate in the patterning process. An advantage of the present disclosure is, but is not limited to, providing an improved method for measuring features of the pattern to be printed on the substrate and making accurate predictions of metrology images, thereby saving metrology time and resources.

[0009] According to one embodiment, a method for training a patterning process model is provided, the patterning process model being configured to predict a pattern to be formed during a patterning process. The method includes obtaining (i) image data associated with a desired pattern, (ii) a measured pattern of a substrate, the measured pattern being associated with the desired pattern, (iii) a first model associated with an aspect of the patterning process, the first model including a first set of parameters, and (iv) a machine learning model associated with another aspect of the patterning process, the first model including a second set of parameters, and iteratively determining values ​​of the first set of parameters and the second set of parameters to train the patterning process model. The iteration includes using the image data to run the first model and the machine learning model to jointly predict a printed pattern of the substrate, and modifying the values ​​of the first set of parameters and the second set of parameters such that a difference between the measured pattern and the predicted pattern of the patterning process model is reduced.

[0010]

[0010] In one embodiment, the first model and the machine learning model are constructed and trained in a convolutional deep neural network framework.

[0011]

[0011] In one embodiment, training includes predicting the printed pattern by forward propagation of outputs of the first model and the machine learning model, determining a difference between the measured pattern and the predicted pattern of the patterning process model, determining a difference-of-difference for the first set of parameters and the second set of parameters, and determining values ​​for the first set of parameters and the second set of parameters based on the difference-of-difference by backpropagating outputs of the first model and the machine learning model.

[0012]

[0012] Further, according to one embodiment, a method is provided for determining optical proximity corrections for a patterning process, the method including obtaining image data associated with a desired pattern, using the image data to execute a trained patterning process model to predict the pattern to be printed on a substrate, and determining optical proximity corrections and / or defects using the predicted pattern to be printed on a substrate subjected to the patterning process.

[0013]

[0013] Further, according to an embodiment, there is provided a method for training a machine learning model configured to determine an etch bias associated with an etch process, the method including obtaining (i) resist pattern data associated with a target pattern to be printed on a substrate, (ii) physical effect data characterizing an effect of an etch process on the target pattern, and (iii) a measured bias between an etch pattern formed on the printed substrate and a resist pattern, and training a machine learning model based on the resist pattern data, the physical effect data, and the measured bias to reduce a difference between the measured bias and a predicted etch bias.

[0014]

[0014] Further, according to one embodiment, a system for determining an etch bias associated with an etch process is provided, the system including a semiconductor processing apparatus and a processor, the processor configured to determine physical effect data characterizing an effect of the etch process on a substrate via execution of a physical effect model, execute a trained machine learning model using the resist pattern and the physical effect data as inputs to determine an etch bias, and control the semiconductor apparatus or etch process based on the etch bias.

[0015] Further, according to an embodiment, there is provided a method for calibrating a process model, the process model being configured to generate a simulated contour, the method including: (i) obtaining measurement data at a plurality of measurement locations on a pattern; (ii) a contour constraint defined based on the measurement data; and calibrating the process model by adjusting values ​​of model parameters of the process model until the simulated contour satisfies the contour constraint.

[0016] Further, according to one embodiment, there is provided a method for calibrating a process model configured to predict an image of a target pattern, the method including obtaining (i) a reference image associated with the target pattern, (ii) a gradient constraint defined with respect to the reference image, and calibrating the process model such that the process model produces a simulated image that (i) minimizes an intensity or frequency difference between the simulated image and the reference image and (ii) satisfies the gradient constraint.

[0017]

[0017] Further, according to an embodiment, a system for calibrating a process model is provided, the process model configured to generate a simulated contour. The system includes a metrology tool configured to acquire measurement data at a plurality of measurement locations on the pattern, and a processor. The processor is configured to calibrate the process model by adjusting values ​​of model parameters of the process model until the simulated contour satisfies a contour constraint, the contour constraint being based on the measurement data.

[0018]

[0018] Further, according to one embodiment, there is provided a system for calibrating a process model configured to predict an image of a target pattern. The system includes a metrology tool configured to acquire a reference image associated with the target pattern, and a processor. The processor is configured to calibrate the process model such that the process model produces a simulated image that (i) minimizes an intensity or frequency difference between the simulated image and the reference image, and (ii) satisfies a gradient constraint associated with the reference image.

[0019]

[0019] Further, according to one embodiment, a non-transitory computer-readable medium is provided that includes instructions which, when executed by one or more processors, cause operations including obtaining (i) resist pattern data associated with a target pattern to be printed on a substrate, (ii) physical effect data characterizing the effect of an etching process on the target pattern, and (iii) a measured bias between the etch pattern formed on the printed substrate and the resist pattern, and training a machine learning model based on the resist pattern data, the physical effect data, and the measured bias to reduce the difference between the measured bias and a predicted etch bias.

[0020]

[0020] Further, according to one embodiment, a non-transitory computer-readable medium is provided that contains instructions which, when executed by one or more processors, cause operations including: (i) obtaining measurement data at multiple measurement locations on a pattern; and (ii) contour constraints defined based on the measurement data; and calibrating a process model by adjusting values ​​of model parameters of the process model until a simulated contour satisfies the contour constraints.

[0021]

[0021] Further, according to one embodiment, a non-transitory computer-readable medium is provided that contains instructions which, when executed by one or more processors, cause operations including: (i) obtaining a reference image associated with a target pattern, (ii) a gradient constraint defined with respect to the reference image, and (i) minimizing an intensity difference or a frequency difference between the simulated image and the reference image, and (ii) calibrating a process model such that the process model produces a simulated image that satisfies the gradient constraint.

[0022]

[0022] Embodiments will now be described, by way of example only, with reference to the accompanying drawings, in which: [Brief description of the drawings]

[0023] [Figure 1] FIG. 1 is a block diagram of various subsystems of a lithography system, according to one embodiment. [Diagram 2]

[0024] FIG. 2 is a block diagram of a simulation model corresponding to the subsystems of FIG. 1 according to one embodiment. [Diagram 3]

[0025] 1 is a flow diagram of a method for training a patterning process model, according to one embodiment, the patterning process model being configured to predict a pattern to be formed in a patterning process. [Figure 4A]

[0026] 1 illustrates an exemplary configuration of a patterning process model including a first model and a second model (eg, a machine learning model), according to one embodiment. [Figure 4B] 1 illustrates an exemplary configuration of a patterning process model including a first model and a second model (eg, a machine learning model), according to one embodiment. [Figure 4C] 1 illustrates an exemplary configuration of a patterning process model including a first model and a second model (eg, a machine learning model), according to one embodiment. [Diagram 5]

[0027] 4 is a flow diagram of a method for determining optical proximity corrections for a patterning process based on a predicted pattern of the trained patterning process model of FIG. 3, according to one embodiment. [Figure 6]

[0028] 1 is a flow diagram of a method for training a machine learning model to determine an etch bias associated with an etch process, according to an embodiment. [Figure 7]

[0029] 1 is an exemplary resist pattern, according to one embodiment. [Figure 8]

[0030] 1 is exemplary physical effect data based on resist patterns, according to one embodiment. [Figure 9]

[0031] 1 is an exemplary acid-base concentration in a resist, according to one embodiment. [Figure 10]

[0032] 1 is exemplary physical effect data based on acid-base distribution, according to one embodiment. [Figure 11]

[0033] 1 is an exemplary etch bias applied to an after development image (ADI) contour, according to one embodiment. [Figure 12]

[0034] 1 is a flow diagram of a method for calibrating a process model based on physical constraints related to a contour shape (or outline) of a pattern, according to one embodiment. [Figure 13A]

[0035] 12 illustrates an example model output that satisfies the physical constraints associated with FIG. 11 , according to one embodiment. [Figure 13B]

[0036] 12 illustrates an example model output that does not satisfy the physical constraints of FIG. 11 , according to one embodiment. [Figure 14]

[0037] 11 is a flow diagram of another method for calibrating a process model based on another physical constraint, according to one embodiment. [Figure 15A]

[0038] 4 illustrates a reference intensity profile of an aerial or resist image according to one embodiment. [Figure 15B]

[0039] 15B illustrates an intensity profile associated with a model that satisfies the physical constraints of FIG. 15A, according to one embodiment. [Figure 15C]

[0040] 15B illustrates an intensity profile associated with a model that does not satisfy the physical constraints of FIG. 15A, according to one embodiment. [Figure 16]

[0041] 1 illustrates a schematic diagram of an embodiment of a scanning electron microscope (SEM), according to one embodiment. [Figure 17]

[0042] 1 illustrates a schematic diagram of an embodiment of an electron beam inspection apparatus, according to one embodiment. [Figure 18]

[0043] 1 is a flow diagram illustrating aspects of an exemplary methodology for joint optimization, according to one embodiment. [Figure 19]

[0044] 1 illustrates an embodiment of another optimization method, according to one embodiment. [Figure 20A]

[0045] 1 illustrates an example flow diagram of various optimization processes, according to one embodiment. [Figure 20B]

[0045] An exemplary flow diagram of various optimization processes according to one embodiment is shown. [Figure 21]

[0045] An exemplary flow diagram of various optimization processes according to one embodiment is shown. [Figure 22]

[0046] FIG. 1 is a block diagram of an example computer system, according to an embodiment. [Diagram 23]

[0047] 1 is a schematic diagram of a lithographic projection apparatus according to an embodiment; [Figure 24]

[0048] 1 is a schematic diagram of another lithographic projection apparatus, according to an embodiment; [Diagram 25]

[0049] FIG. 25 is a more detailed view of the device of FIG. 24, according to an embodiment. [Figure 26]

[0050] FIG. 26 is a more detailed diagram of the source collector module SO of the apparatus of FIGS. 24 and 25 according to one embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0024]

[0051] The embodiments will now be described in detail with reference to the drawings. The drawings are provided as illustrative examples to enable those skilled in the art to implement the embodiments. In particular, the following figures and examples are not intended to limit the scope to a single embodiment, and other embodiments are possible by replacing some or all of the elements described or shown. For convenience, the same reference numbers are used throughout the drawings to refer to the same or similar parts. Where certain elements of the embodiments can be partially or completely implemented using known components, only those parts of such known components that are necessary to understand the embodiment are described, and detailed descriptions of other parts of such known components are omitted so as not to obscure the description of the embodiment. In this specification, an embodiment showing a single component should not be considered as limiting. Rather, unless otherwise specified, the scope is intended to include other embodiments including multiple identical components, and vice versa. Furthermore, unless otherwise specified, the applicant does not intend any term in this specification or claims to be considered to have a general or special meaning. Additionally, the scope includes present and future known equivalents of the components referred to herein by way of example.

[0025]

[0052] While specific reference may be made herein to the manufacture of ICs, it should be expressly understood that what is described herein has many other possible applications. For example, it may be used in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, liquid crystal display panels, thin film magnetic heads, etc. Those skilled in the art will recognize that in the context of such alternative applications, any use of the terms "reticle," "wafer," or "die" herein should be considered synonymous with the more general terms "mask," "substrate," and "target portion," respectively.

[0026]

[0053] In this specification, the terms "radiation" and "beam" are used to encompass all types of electromagnetic radiation, including ultraviolet (e.g., having wavelengths of 365, 248, 193, 157, or 126 nm) and EUV (extreme ultraviolet, e.g., having wavelengths within the range of 5 to 20 nm).

[0027]

[0054] As used herein, the terms "optimizing" and "optimization" refer to adjusting a lithographic projection apparatus so that the lithographic results and / or process have more desirable characteristics, such as greater accuracy in projecting the design layout onto the substrate, a larger process window, etc.

[0028]

[0055] Further, the lithographic projection apparatus may be of a type having two or more substrate tables (and / or two or more patterning device tables). In such "multi-stage" devices, the additional tables may be used in parallel, or one or more tables may be used for exposure while preparatory steps are carried out on one or more of the other tables. A twin-stage lithographic projection apparatus is described, for example, in U.S. Patent No. 5,969,441, which is incorporated herein by reference.

[0029]

[0056] The patterning device mentioned above may include or form a design layout. The design layout may be generated using a CAD (Computer Aided Design) program, a process often referred to as EDA (Electronic Design Automation). Most CAD programs follow a predefined set of design rules to generate a functional design layout / patterning device. These rules are set by process and design limitations. For example, design rules may define the space tolerance between circuit devices (gates, capacitors, etc.) or interconnect lines, which is done to ensure that they do not interact with each other in an undesirable manner. The limitations of the design rules are usually referred to as "critical dimensions" (CD). A critical dimension of a circuit may be defined as the smallest width of a line or hole, or the smallest space between two lines or two holes. Thus, the CD determines the overall size and density of the designed circuit. Of course, one of the goals of integrated circuit manufacturing is to faithfully reproduce the original circuit design on the substrate (via the patterning device).

[0030]

[0057] The terms "mask" or "patterning device" as used herein may be broadly interpreted to refer to any general patterning device that can be used to impart an incoming radiation beam with a patterned cross-section that corresponds to the pattern to be created in a target portion of a substrate, and the term "light valve" is also sometimes used in this context. In addition to traditional masks (transmissive or reflective; binary, phase-shifting, hybrid, etc.), examples of other such patterning devices include: -programmable mirror arrays. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and a reflective surface. The basic principle behind such an apparatus is that (for example) addressed areas of the reflective surface reflect incident radiation as diffracted radiation, and unaddressed areas reflect incident radiation as undiffracted radiation. Using appropriate filters, said undiffracted radiation can be filtered out of the reflected beam, leaving behind only the diffracted radiation, and in this way the beam is patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using suitable electronic means. More information on such mirror arrays can be gleaned, for example, from U.S. Pat. Nos. 5,296,891 and 5,523,193, which are incorporated herein by reference. - A programmable LCD array. An example of such a construction is given in US Patent No. 5,229,872, which is incorporated herein by reference.

[0031]

[0058] As a brief introduction, Figure 1 shows an exemplary lithographic projection apparatus 10A. The main components are a radiation source 12A, which may be a deep ultraviolet excimer laser source, or other type of source including an extreme ultraviolet (EUV) source (as explained above, the lithographic projection apparatus itself need not have a radiation source), illumination optics, which may include optics 14A, 16Aa, and 16Ab that define the partial coherence (denoted by sigma) and shape the radiation from source 12A; a patterning device 14A; and a transmission optics 16Ac that projects an image of the patterning device pattern onto a substrate surface 22A. An adjustable filter or aperture 20A in a pupil plane of the projection optics can limit the range of beam angles that impinge on the substrate surface 22A, where the maximum possible angle defines the numerical aperture NA=sin(Θmax) of the projection optics.

[0032]

[0059] In the optimization process of a system, the figure of merit of the system can be expressed as a cost function. The optimization process boils down to a process of finding a set of parameters (design variables) of the system that minimizes the cost function. The cost function may be in any suitable form depending on the goal of the optimization. For example, the cost function may be the weighted root mean square (RMS) of the deviations of certain features (e.g. evaluation points) of the system from their intended values ​​(e.g. ideal values). The cost function may be the maximum of those deviations (i.e. the worst deviation). The term "evaluation point" in this specification should be interpreted broadly to include any feature of the system. The design variables of the system may be limited to a finite range and / or interdependent due to the feasibility of the implementation of the system. In the case of a lithographic projection apparatus, the constraints are often related to the physical properties and characteristics of the hardware, such as the adjustable range, and / or the patterning device manufacturability design rules, and the evaluation points may include physical points on the resist image on the substrate, as well as non-physical features such as dose and focus.

[0033]

[0060] In a lithographic projection apparatus, a radiation source provides illumination (i.e., light) and a projection optics system guides and shapes the illumination through a patterning device and onto a substrate. The term "projection optics system" is broadly defined herein to include any optical component capable of modifying the wavefront of a radiation beam. For example, a projection optics system may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. The aerial image (AI) is the radiation intensity distribution at the substrate level. A resist layer on the substrate is exposed and the aerial image is transferred to the resist layer as a potential "resist image" (RI) therein. The resist image (RI) can be defined as the spatial distribution of resist solubility in the resist layer. A resist model can be used to calculate the resist image from the aerial image, an example of which can be found in commonly assigned U.S. patent application Ser. No. 12 / 315,849, the disclosure of which is incorporated herein in its entirety. The resist model is only concerned with the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). The optical properties of the lithographic projection apparatus (e.g. properties of the source, the patterning device and the projection optics) determine the aerial image. Because the patterning devices used in a lithographic projection apparatus may vary, it is desirable to decouple the optical properties of the patterning device from the optical properties of the rest of the lithographic projection apparatus, which includes at least the source and the projection optics.

[0034]

[0061] An exemplary flow chart for simulating lithography in a lithographic projection apparatus is shown in FIG. 2. The radiation source model 31 represents the optical characteristics of the radiation source (including radiation intensity distribution and / or phase distribution). The projection optics model 32 represents the optical characteristics of the projection optics (including changes to the radiation intensity distribution and / or phase distribution caused by the projection optics). The design layout model 35 represents the optical characteristics of the design layout (which is a representation of the arrangement of features on or formed by the patterning device) (including changes to the radiation intensity distribution and / or phase distribution caused by a given design layout 33). An aerial image 36 can be simulated using the design layout model 35, the projection optics model 32, and the design layout model 35. A resist image 38 can be simulated from the aerial image 36 using the resist model 37. For example, the lithography simulation can predict the contour and CD of the resist image.

[0035]

[0062] More specifically, it is noted that the radiation source model 31 can represent the optical characteristics of the radiation source, including, but not limited to, the NA-sigma (σ) setting, and any particular illumination radiation source shape (e.g., off-axis radiation sources such as annular, quadrupole, and dipole). The projection optics model 32 can represent the optical characteristics of the projection optics, including aberrations, distortion, refractive index, physical size, physical dimensions, and the like. The design layout model 35 can represent the physical characteristics of a physical patterning device, for example, as described in U.S. Pat. No. 7,587,704, which is incorporated by reference in its entirety. The goal of the simulation is to accurately predict, for example, edge placement, aerial image intensity slope, and CD, which can then be compared to the intended design. The intended design is generally defined as a pre-OPC design layout, which can be provided in a standard digital file format, such as GDSII, or OASIS, or another file format.

[0036]

[0063] From this design layout, one or more portions (these are called "clips") can be identified. In one embodiment, a set of clips is extracted (typically about 50-1000 clips, although any number of clips may be used) that represent complex patterns in the design layout. As will be appreciated by those skilled in the art, these patterns or clips represent small portions of the design (i.e., circuits, cells, or patterns), and in particular clips represent small portions that require special attention and / or validation. That is, clips may be portions of the design layout that are similar or have similar behavior to portions of the design layout whose critical features are identified by experience (including customer provided clips), by trial and error, or by running full chip simulations. Clips typically include one or more test or gauge patterns.

[0037]

[0064] The initial set of larger clips may be provided a priori by a customer based on known critical feature areas in the design layout that require specific image optimization, or in another embodiment, the initial set of larger clips may be extracted from the entire design layout by using some type of automatic (such as machine vision) or manual algorithm that identifies the critical feature areas.

[0038]

[0065] Stochastic variations in patterning processes (e.g., resist processes) can limit lithography (e.g., EUV lithography) in some cases, for example, in terms of possible feature shrinkage and exposure dose specifications, which impacts wafer throughput of the patterning process. In one embodiment, stochastic variations in a resist layer can be manifested as stochastic damage, such as closed holes or trenches, or broken lines. Such resist-related stochastic variations can be more impactful and limiting to high volume manufacturing (HVM) success, for example, compared to stochastic CD variations, which are traditional metrics of interest for measuring and adjusting the performance of a patterning process.

[0039]

[0066] In a patterning process (e.g., photolithography, e-beam lithography, etc.), an energy-sensitive material (e.g., photoresist) deposited on a substrate is subjected to a pattern transfer step (e.g., exposure). Following the pattern transfer step, various post-steps such as resist baking and subtractive processes such as resist development, etching, etc. are applied. These post-exposure steps or processes have various effects that lead to the patterned layer or etched substrate forming structures with dimensions different from the targeted dimensions.

[0040]

[0067] In computational lithography, patterning process models (e.g., those discussed in FIG. 2) related to different aspects of the patterning process, such as mask model, optical model, resist model, and post-exposure model, can be used to predict the pattern that will be printed on a substrate. When properly calibrated (e.g., using measurement data associated with printed wafers), the patterning process models can generate accurate predictions of the pattern dimensions output from the patterning process. For example, the patterning process models for the post-exposure process are calibrated based on empirical measurements. The calibration process includes exposing test substrates by varying different process parameters (e.g., dose, focus, etc.), measuring the resulting critical dimension printed pattern after the post-exposure process, and calibrating the patterning process model against the measured results. In practice, fast and accurate models contribute to improved device performance (e.g., yield), enhanced process window, patterning recipe, and / or increased complexity of the design pattern.

[0041]

[0068] The patterning process is a complex process, and not all aspects can be modeled based on the physical / chemical phenomena involved in the patterning process. For example, some effects of post-exposure processes are well understood and can be modeled using mathematical expressions of physical terms (e.g., parameters associated with the resist process) that describe the physics / chemistry of the process. For example, acid-base diffusion after exposure can be modeled by a Gaussian filter on the aerial image. In an embodiment, some of the physical terms (e.g., associated with dose, focus, intensity, pupil, etc.) are related to the lithography apparatus and are adjustable via adjustable parameters (e.g., adjustable knobs), thereby allowing real-time control of the patterning process via adjustable knobs. In an embodiment, some physical terms may not be directly adjustable via adjustable knobs, but can describe the physics / chemistry of the process (e.g., aerial image formation, resist image formation, etc.). For example, the resist model includes a Gaussian filter on the aerial image to model acid-base diffusion in the resist after exposure. This sigma term is typically not adjustable via adjustable knobs. Nonetheless, the values ​​of such physical terms (eg, sigma) can be determined based on empirical or physics-based equations that model the effects of the process (eg, resist).

[0042]

[0069] However, some aspects or effects of other post-exposure effects are not well understood and therefore difficult to model using physics / chemistry based formulas. In such cases, in the present disclosure, a machine learning model, such as a convolutional deep neural network (CNN), is trained to model the less understood aspects of the patterning process (e.g., post-exposure). The process model of the present disclosure reduces the requirement for understanding the post-exposure process, etc., for model development and eliminates the reliance on the engineer's personal experience for model tuning. In one embodiment of the present disclosure, the trained CNN produces model accuracy that is comparable to or exceeds that of models generated by conventional techniques.

[0043]

[0070] FIG. 3 is a flow diagram of a method for training a patterning process model, which is configured to predict a pattern that will be formed in a patterning process. As mentioned above, some aspects of the patterning process are well understood and can be modeled using mathematical equations that utilize physical terms configured to accurately describe the physical effects of the patterning process. Furthermore, there are some aspects that cannot be accurately modeled using physical terms. The method employs two different models, a first model configured to describe the known aspects via physical terms (e.g., parameters related to the optics, parameters related to the resist of the patterning process) and a second model (i.e., a machine learning model) configured to describe the aspects that are not well understood (in terms of physics / chemistry).

[0044]

[0071] Using a mixed model (i.e., a first model and a second model) to jointly predict the pattern of the patterning process has several advantages. For example, the physical terms are relatively simple to calculate, and models that use such physical terms are less susceptible to overfitting. For example, incorporating the physical terms in conjunction with a CNN model reduces the complexity of the CNN by several times, reducing the risk of overfitting and improving the run time of the patterning process simulation. On the other hand, existing models use CNNs to model both known and unknown effects, which can result in unnecessarily complex CNN models that are prone to overfitting and have slow run times.

[0045]

[0072] The method 300 includes, in process P301, obtaining (i) image data 302 associated with a desired pattern, (ii) a measured pattern 304 of a substrate, the measured pattern 304 being associated with the desired pattern, (iii) a first model associated with an aspect of the patterning process (e.g., whose effect can be accurately modeled by a physics / chemistry based equation), the first model including a first set of parameters 307, and (iv) a machine learning model associated with another aspect of the patterning process (e.g., whose effect cannot be accurately modeled by a physics / chemistry based equation), the machine learning model including a second set of parameters 308.

[0046]

[0073] In one embodiment, image data 302 generally refers to any input to a patterning process model configured to predict the effect of an aspect of a patterning process or the effect of a final pattern to be printed on a substrate. In one embodiment, image data 302 is an aerial image, a mask image, a resist image, or other output related to one or more aspects of a patterning process. In one embodiment, obtaining an aerial image, a mask image, a resist image, etc. includes simulating a patterning process, as discussed in FIG.

[0047]

[0074] In one embodiment, the patterning process model includes a first model coupled to a second model (e.g., a machine learning model). The first model may be connected to the machine learning model in a serial or parallel combination (e.g., as discussed in conjunction with FIGS. 4A-4C). In an exemplary configuration (e.g., FIG. 4A), the serial combination of models includes providing an output of the first model as an input to the machine learning model. In another exemplary configuration, the serial combination of models includes providing an output of the machine learning model as an input to the first model. In yet another example (e.g., FIG. 4B), the parallel combination of models includes providing the same input to the first model and the machine learning model, combining the output of the first model and the machine learning model, and determining a predicted print pattern based on the combined output of each model. In yet another example (e.g., FIG. 4C), the patterning process model may be configured to include both serial and parallel configurations of the first model, the machine learning model, and / or another physics-based model or machine learning model.

[0048]

[0075] In one embodiment, the first model is an empirical model that includes physical terms that accurately describe the effect of a first aspect of the patterning process. In one embodiment, the first model corresponds to a first aspect related to acid-based diffusion after exposure of the substrate. In one embodiment, an exemplary first model is a resist model. The first set of parameters of the resist model corresponds to at least one of the following physical terms: initial acid distribution, acid diffusion, image contrast, long-range pattern loading effect, acid concentration after neutralization, base concentration after neutralization, diffusion due to high acid concentration, diffusion due to high base concentration, resist shrinkage, resist development, or two-dimensional convex curvature effect. Examples of empirical models that utilize physical terms are as follows: R=cA×A+cMav×MAV+cAp×Ap*GAp+cBp×Bp*GBp+cAm×A*GAm+...

[0049]

[0076] In the above formula, R is the predicted resist image based on the physical terms and their associated coefficients (example of the first set of parameters). In the above formula, cA is the coefficient of the initial acid distribution A, which can be represented by an aerial image, cMav is the coefficient of the long-range pattern loading effect MAV, which can be determined as an average of the mask image, and similarly, other physical terms are associated with one or more coefficients. These coefficients are determined during the training process discussed below.

[0050]

[0077] In one embodiment, the machine learning model is a neural network that models a second aspect of the patterning process that is relatively less understood based on physics. In one embodiment, the second set of parameters includes weights and biases of one or more layers of the neural network. During the training process (e.g., including P303, P307), the weights and biases are adjusted in conjunction with the first set of parameters such that the difference between the predicted pattern and the measured pattern is reduced. In one embodiment, the patterning process model corresponds to a second aspect of the post-exposure process of the patterning process.

[0051]

[0078] In one embodiment, the method further includes iteratively determining values ​​for the first set of parameters 307 and the second set of parameters 308 to train the patterning process model. In one embodiment, the iterations include performing processes P303, P305, and P307.

[0052]

[0079] The method 300 includes, in process P303, using the image data 302 to execute the first model and the machine learning model to jointly predict a pattern for the substrate. Process P305 includes determining a difference between the measured pattern 304 and the predicted pattern 305 of the patterning process model, and determining whether the difference is reduced or minimized. Process P307 includes modifying values ​​of the first set of parameters 307 and the second set of parameters 308 such that the difference between the measured pattern 304 and the predicted pattern 305 of the patterning process model is reduced.

[0053]

[0080] In one embodiment, the modified values ​​are determined based on an optimization technique such as a gradient leveling method that derives how the values ​​of the first and second set of parameters should be modified such that the gradient of the difference for each parameter is reduced. After several iterations, global or local optimum values ​​of the parameters are obtained such that the difference between the prediction and the measurement is minimized. Thus, the patterning process model is calibrated (or trained) and can be further utilized to improve the patterning process via OPC, defect detection, hot spot ranking, or other known applications of the patterning process model.

[0054]

[0081] 4A, 4B, and 4C show an example configuration of a patterning process model including a first model and a second model (CNN) that are trained together during which a first set of parameters of the first model and a second set of parameters of the CNN are determined.

[0055]

[0082] FIG. 4A shows a serial combination of a first model and a second model, where the first model is represented as a function of physical parameters and the second model is represented as a CNN. The training process is iterative, and an iteration (or each iteration) is i (which are coefficients related to the physical terms), as well as the values ​​of the first set of parameters, such as the w iand u i The method further includes determining values ​​for a second set of parameters, such as weights c i is the physical term i The first model may then be operated on directly (e.g., via multiplication, exponentiation, addition, or other mathematical operation) with values ​​of variables (e.g., variables associated with the patterning process, such as dose, focus, acid concentration, etc.) to determine a first output of the first model. In one embodiment, the physical term term i The parameter param i The weights of a CNN may be a function (e.g., a, b of a Gaussian filter) associated with a particular physical term (e.g., a, b of a Gaussian filter). Although the weights of a CNN do not directly interact with a particular physical term, the CNN can take as input a first output from a first model and predict a second output associated with another aspect of the patterning process (e.g., that is less well understood).

[0056]

[0083] In one embodiment, the simulation process may begin with initial values ​​for the first and second parameter sets. In one embodiment, the input to the first model is, for example, an aerial image of a desired pattern to be printed on a substrate. Based on the input (e.g., the aerial image), the first model predicts a first output (e.g., a resist pattern) of an aspect of the patterning process (e.g., exposure of the resist with the aerial image). The first output is further input to a CNN, which further predicts the pattern to be printed on the substrate. The predicted pattern is compared to a desired output. The desired output may be a measured pattern that corresponds to the desired pattern, for example, measured via a SEM tool. The comparison includes calculating the difference between the predicted pattern and the measured pattern. Based on this difference, a backpropagation may be performed, where the CNN's w i and u i Weight values ​​such as c may be calculated such that this difference is reduced. i and / or param iFor example, a gradient-based method can be utilized, where a delta of differences on the weights is calculated to generate a gradient map. The gradient map is used to scale the weights and / or c such that the difference between the prediction and the desired output is reduced (and in one embodiment, minimized). i and / or param i After the patterning process model is trained, it can determine patterns that account for both well-understood and poorly understood physical effects of the patterning process (e.g., post-exposure processes).

[0057]

[0084] FIG. 4B illustrates a parallel combination of a first model and a second model. The first model and the second model are represented in a manner similar to that described above in FIG. 4A. Also, the initial values ​​of the first and second parameter sets may be similar to start the training process and determine the final values ​​of the first and second parameter sets. In the parallel combination, the same input (e.g., an aerial image of the desired pattern) is provided to both the first model and the second model simultaneously. Each model predicts an output, which may be combined to form the pattern to be printed on the substrate. The predicted output may be compared to the desired output (e.g., the measured pattern of the printed substrate), as described above. Backpropagation may then be performed, and a gradient constant leveling method may be utilized to determine the difference delta for each of the first and second parameters, as previously described. Furthermore, the values ​​of the first and second parameters are selected such that the difference is reduced (in one embodiment, minimized). After several iterations, the predicted pattern converges to the desired pattern, and the training of the model is said to be complete.

[0058]

[0085] FIG. 4C illustrates a more general patterning process model, which is configured to include (i) one or more models including physical terms of the patterning process (e.g., variables of the patterning process); and (ii) one or more machine learning models (CNNs). In an embodiment, inputs and outputs can be communicated between the various models as illustrated to collaboratively predict the pattern to be printed on the substrate. The predicted pattern may be compared to the desired pattern for determined values ​​of the parameters of each model. As previously mentioned, these values ​​can be determined, for example, using gradient leveling. These values ​​are modified during backpropagation of the output of the different layers of the CNN and / or models, as shown in FIG. 4C.

[0059]

[0086] Thus, in one embodiment, the first model and the machine learning model are configured and trained together in a deep convolutional neural network framework (DCNN) as described above in Figures 4A-4C. Training includes predicting the pattern to be printed by forward propagation of the outputs (e.g., x, y, z, etc., in Figures 4A-4C) of the first model and the machine learning model, determining the difference (e.g., loss in Figures 4A-4C) between the measured pattern and the predicted pattern (e.g., output) of the patterning process model, and determining the first set of parameters (e.g., c i ,param i , z i , u i , w i and determining values ​​of the first and second parameter sets by backpropagating the outputs of the first model and the machine learning model based on the difference of differences. For example, in Figures 4A-4C, during backpropagation, the following differences can be calculated and used to adjust the first and second parameter sets: d(loss) / dt, d(loss) / dz, d(loss) / du, d(loss) / dw, etc.

[0060]

[0087] 5 is a flow diagram of a method for determining optical proximity corrections for a patterning process. The optical proximity corrections are associated with a desired pattern to be printed on a substrate. Method 500 includes, in process P501, acquiring image data 502 associated with the desired pattern. In one embodiment, image data 502 is an aerial image and / or a mask image of the desired pattern.

[0061]

[0088] Process P503 further includes using the image data 502 to execute a trained patterning process model 310 to predict a pattern to be printed on a substrate. As previously described in method 300, the trained patterning process model 310 includes a first model of a first aspect of the patterning process and a machine learning model of a second aspect of the patterning process configured to jointly predict a pattern to be printed on a substrate. The first model and the machine learning model are in a serial and / or parallel combination as discussed with respect to FIGS. 4A-4C. In one embodiment, the first model is an empirical model (e.g., the resist model described above) that accurately models the physical phenomena of the first aspect of the post-exposure process of the patterning process. In one embodiment, the first model corresponds to a first aspect related to acid-based diffusion after exposure of the substrate. In one embodiment, the machine learning model is a neural network that models the second aspect of the patterning process for which there is relatively little physics-based understanding.

[0062]

[0089] Based on the predicted pattern, process P505 includes determining optical proximity corrections and / or defects. In one embodiment, determining optical proximity corrections includes adjusting the desired pattern and / or placing assist features around the desired pattern such that differences between the predicted pattern and the desired pattern are reduced. Examples of OPC processes are described in conjunction with FIGS. 18-21 later in this disclosure.

[0063]

[0090] In one embodiment, determining the defects includes performing a lithographic manufacturability check (LMC) on the predicted pattern. The LMC determines whether features of the printed pattern meet desired specifications. If the LMC determines that the specifications are not met, the features are considered defective. Such defect information may help determine the yield of the patterning process. Furthermore, based on the defects (or yield), one or more variables of the patterning process may be modified to improve the yield.

[0064]

[0091] As mentioned above, some effects of the patterning process or post-exposure process are well understood and can be modeled using mathematical equations that include physical terms related to the pattern formed on the substrate. For example, some of the physical terms (e.g., associated with dose, focus, intensity, pupil, etc.) are related to the lithography apparatus and can be adjusted via adjustable parameters (e.g., adjustable knobs), thereby allowing real-time control of the patterning process via the adjustable knobs. In an embodiment, some physical terms may not be directly adjustable via adjustable knobs, but can account for the physical / chemical phenomena of the process (e.g., aerial image formation, resist image formation, etc.). For example, the resist model includes a Gaussian filter (including a sigma or dispersion term) on the aerial image to model acid-base diffusion in the resist after exposure. This sigma term is typically not adjustable via an adjustable knob. Even so, the values ​​of such physical terms (e.g., sigma) can be determined based on empirical equations or physics-based equations that model the effects of the process (e.g., resist).

[0065]

[0092] As discussed herein, there are various methods (e.g., FIGS. 4A-4C) provided for training a patterning process model based on physical terms. Utilizing physical terms to train or calibrate a patterning process model has several advantages. For example, physical terms are relatively simple to compute, and models utilizing such physical terms are less susceptible to overfitting. In one embodiment, for example, incorporating physical terms in conjunction with a CNN model reduces the complexity of the CNN by several times, reduces the risk of overfitting, and improves the run time of the patterning process simulation. In the following discussion, additional methods for training and calibrating a process model based on physical terms are discussed.

[0066]

[0093] 6 is a flow diagram of a method 600 for training a machine learning model to determine an etch bias associated with an etch process. In an embodiment, predicting such an etch bias may be beneficial in improving an etch recipe or settings of a current lithography apparatus. The method 600 includes several steps, which are described in detail as follows.

[0067]

[0094] Step P601 includes obtaining (i) resist pattern data 602 associated with a target pattern to be printed on a substrate, (ii) physical effect data 604 characterizing the effect of an etch process on the target pattern, and (iii) a measured bias 606 between the resist pattern and the etch pattern formed on the printed substrate.

[0068]

[0095] In one embodiment, the measured bias 606 data may be determined based on metrology data of a previously patterned substrate. For example, the measured bias 606 may be the difference between a resist pattern formed on a substrate and an etch pattern formed on a printed substrate. The resist pattern may be determined via a metrology tool or a simulation of the patterning process. In one embodiment, the etch pattern formed on the printed pattern is measured via a metrology tool (e.g., an SEM tool as described with respect to FIG. 16 and FIG. 17, or an optical metrology tool). In one embodiment, the dimensions of the resist pattern (e.g., CD of a feature) may be larger than the etch pattern, for example, due to removal of material (e.g., via a descum process). This difference between the resist pattern and the etch pattern on the printed substrate includes variations caused due to the etch process. For example, the variations are caused due to varying etch rates, variations in the amount of plasma concentration, variations in aspect ratios (e.g., feature height / feature width), or other physical aspects associated with the resist pattern, the etch process, or a combination thereof.

[0069]

[0096] In one embodiment, the resist pattern data 602 is represented as a resist image. The resist image may be a pixelated image, where the intensity of a pixel indicates the resist area and the pattern portion formed within the resist portion. For example, the pattern portion may be an edge / contour of the resist pattern. In one embodiment, obtaining the resist pattern data 602 includes running one or more process models, including a resist model of the patterning process, using a target pattern to be printed on a substrate.

[0070]

[0097] In one embodiment, the physical effect data 604 may be data related to etching terms that characterize the etching effect, including at least one of a concentration of plasma inside a trench of a resist pattern associated with the target pattern, a concentration of plasma on top of a resist layer of a substrate, a loading effect determined by convolving the resist pattern with a Gaussian Kernel having specified model parameters, a change in the loading effect on the resist pattern during the etching process, a relative position of the resist pattern with respect to an adjacent pattern on the substrate, an aspect ratio of the resist pattern, or a term related to the combined effect of two or more etching process parameters.

[0071]

[0098] In one embodiment, obtaining the physical effects data 604 includes executing a physical effects model, where the physical effects model includes one or more etch terms and a Gaussian kernel specified for each of the one or more etch terms. In one embodiment, the physical effects data 604 is represented as a pixelated image, where each pixel intensity indicates a physical effect on the resist pattern associated with the target pattern. Figures 7-10 show some examples of the physical effects data 604.

[0072]

[0099] FIG. 7 is an exemplary resist image including a resist pattern formed in resist 702. The resist pattern includes a trench region 704 formed within resist 702. In one embodiment, the etching model may be calibrated based on a plasma focused etching method (CEM). The CEM method uses plasma loading to the edge of the resist trench 704 to characterize the bias behavior induced by etching. In one embodiment, the evaluation point, e.g., 706, may be located at the edge of the resist trench, e.g., 704, and CEM_range is the etching proximity range that the etching model is considering. In one embodiment, the etching physics term may be a CT image or a CR image related to the plasma loading effect generated from the resist pattern. For example, CT0 is defined as the plasma loading from the plasma from the trench region (e.g., 704) to a unit edge length at the start of etching, and CR0 is defined as the plasma loading from the plasma from the resist region (e.g., 702) to a unit edge length at the start of etching. At time t, CT0 and CR0 become CT and CR, respectively, and the transformation with respect to time may be based on exponential terms that include parameters related to sidewall deposition or etch kinetic constants. In one embodiment, the product of the CT and CR images may be used to characterize the etch bias due to the proximity effect.

[0073]

[0100] FIG. 8 illustrates an exemplary etch physics term (e.g., CR image) generated from a resist pattern 801. The resist pattern 801 includes resist contours 802 (or resist pattern edges), and then the plasma loading effect from the resist region (e.g., CR as described above) can be calculated, which is shown as CR image 810. In one embodiment, a CT image may be generated, where the CT image is a flip-tone image of the CR. For example, a bright pixel in the CR becomes a dark pixel in the CT, and vice versa. The CR image 810 can be used to characterize the etch bias from the proximity effect. This exemplary etch bias is an exemplary bias applied to the resist contours 802 to compensate for such proximity effects.

[0074]

[0101] 9 illustrates another exemplary modeling of physical terms, such as acid-base reactions. In one embodiment, the acid-base reaction can be modeled by truncating the acid concentration by a quencher base. For example, the acid-base reaction (e.g., shown as image 901) can characterize the linear combination coefficients of the acid concentration 910 and the base concentration 920. In one embodiment, the truncation terms (e.g., 903) simulate the reaction and diffusion of the acid and base in forming the final acid density distribution image 901. The multiple truncation terms represent different times during the post-exposure bake. Depending on the truncation terms 903 (e.g., the truncation values ​​of the truncation terms), the acid concentration 910 and the base concentration 920 change.

[0075]

[0102] FIG. 10 is another exemplary physical term generated using an aerial image 1010. For example, the physical term can be an initial acid distribution 1020 at a particular location of the aerial image. In one embodiment, a linear transformation of the aerial image can be performed using Gaussian filtering of the aerial image. In one embodiment, the Gaussian filter includes a sigma term that is not typically adjustable via an adjustable knob, but can be set to determine long-term, mid-range, and short-range effects associated with etching. For example, the sigma value can be set based on data from previously printed and etched substrate data.

[0076]

[0103] Referring back to FIG. 6 , step P603 includes training a machine learning model 603 based on the resist pattern data 602, the physical effects data 604, and the measured bias 606 to reduce the difference between the measured bias 606 and the predicted etch bias. After this training process is completed, the machine learning model 603 can be referred to as a trained machine learning model 603. This trained machine learning model 603 can be utilized in a patterning process to improve performance metrics, such as the yield of printed substrates. For example, based on the etch bias predicted by the trained machine learning model 603, process parameters can be adjusted to reduce the number of pattern breaks, thereby improving yield.

[0077]

[0104] In one embodiment, the machine learning model 603 is configured to receive the resist pattern data 602 at a first tier of the machine learning model 603, and the physical effect data 604 is received at a last tier of the machine learning model 603. In one embodiment, the machine learning model 603 is configured to receive the resist pattern data 602 and the physical effect data 604 at a first tier of the machine learning model 603. One skilled in the art will appreciate that the present disclosure is not limited to a particular configuration of the machine learning model 603.

[0078]

[0105] In one embodiment, the output of the final layer of the machine learning model 603 is a linear combination of (i) an etch bias predicted by running the machine learning model 603 using the resist pattern data 602 as input, and (ii) another etch bias determined based on the physical effects data 604 related to the etch process.

[0079]

[0106] In one embodiment, the output of the last layer of the machine learning model 603 is an etch bias map from which the etch bias is extracted. The etch bias map is generated through running the machine learning model 603 using resist pattern data 602 as input to output an etch bias map, where the etch bias map includes a biased resist pattern, and combining the etch bias map with physical effects data 604.

[0080]

[0107] In one embodiment, training the machine learning model 603 is an iterative process that includes: (a) predicting the etch bias via running the machine learning model 603 using the resist pattern data 602 and the physical effects data 604 as inputs; (b) determining the difference between the measured bias 606 and the predicted etch bias; (c) determining the gradient of the difference with respect to the model parameters (e.g., weights associated with layers) of the machine learning model 603; (d) using the gradient as a guide, adjusting the model parameter values ​​such that the difference between the measured bias 606 and the predicted etch bias is reduced; (e) determining whether the difference has been minimized or a training threshold has been exceeded; and (f) performing steps (a)-(e) in response to the difference not being minimized or the training threshold not being exceeded.

[0081]

[0108] In one embodiment, the method 600 may further include, in step P605, obtaining a resist contour of a resist pattern (e.g., 602 described above) and generating an etch contour 605 by applying an etch bias (e.g., determined by running a trained machine learning model 603) to the resist contour (e.g., of 602).

[0082]

[0109] FIG. 11 shows an example of an etch bias determined via an etch model. In one embodiment, the etch model calculates an after etch image (AEI) contour (e.g., 1130) by directly biasing (e.g., 1120) an after development image (ADI) contour (e.g., 1110). In one embodiment, the bias direction of 1120 is perpendicular to the ADI contour 1110. The amount of bias of 1120 is variable depending on the ADI environment (e.g., feature density) and the physical terms associated with the etch. For example, a positive bias amount moves the ADI contour outward, while a negative bias (e.g., 1120) amount moves the ADI contour 1110 inward. In other words, the etch bias can be positive if the size of the pattern 1110 elements is larger before the etch than after the etch, and negative if the size is smaller before the etch than after the etch. In one embodiment, the etch model utilizes a calibration / check gauge, and the perpendicular direction of the ADI contour is relative to such gauge. The model can then directly output AEI contours for LMC / OPC applications. For example, LMC can determine whether the AEI contours meet size constraints associated with the target pattern. The AEI contours can be used to determine the OPC of the mask pattern such that the overall yield of the patterning process is improved. For example, in an OPC process, a simulated contour (e.g., based on a patterning process simulation) can be compared to the AEI contours, and the OPC can be determined based on this comparison. For example, the mask pattern is modified such that the simulated pattern closely matches the AEI contours. Thus, accurate prediction of the AEI contours improves the OPC of the mask pattern.

[0083]

[0110] In one embodiment, the amount of bias determined by the model (e.g., 603) is calculated based on some physical term, Term i where the physical terms are functions of the environment of one evaluation point i.

number

[0084]

[0111] In one embodiment, the physical term Term i can be, for example, local or long-range loading effects. In one embodiment, the effects may be determined by rasterization, for example, by convolving the resist contour with a Gaussian Kernel or a filter having a first set of parameters (e.g., sigma between 90-100 nm). Another physical term can be intermediate stage loading, determined using a Gaussian Kernel or a filter having a second set of parameters (e.g., sigma between 100-200 nm). Another exemplary physical term can be aspect ratio. In one embodiment, this term can be a higher order, non-linear, or complex effect.

[0085]

[0112] By mathematically modeling the etching bias, the production of the final device feature dimensions can be improved. The results of this modeling can be used for various purposes. For example, such results can be used to adjust the patterning process in terms of changing the design, control parameters, etc. For example, the results can be used to adjust one or more spatial properties of one or more elements provided by the patterned device, the pattern of the patterned device being used to generate a device that will be used to etch the substrate pattern. Thus, once the patterned device pattern is transferred to the substrate, the device pattern on the substrate is effectively adjusted prior to etching to compensate for the expected etching variations that occur during etching. As another example, one or more adjustments can be made to the lithography apparatus in terms of adjusting the dose, focus, etc. As can be appreciated, there may be many more applications. Thus, compensating for the etching variations can lead to devices having uniform feature sizes, uniform electrical properties, and / or improved (e.g., closer to the desired result) performance characteristics.

[0086]

[0113] Furthermore, the etching bias can be used to generate desired structures on the substrate, although the etching variations are sometimes detrimental to the fabrication of devices on the substrate. By considering the degree of etching bias when fabricating the patterned device, it is possible to fabricate device features in the device on the substrate that are smaller than the optical resolution limit of the pattern transfer procedure from the patterned device to the substrate. In this respect, the modeled results of the etching bias can therefore be used to adjust the patterning process in terms of changing the design, control parameters, etc. Modeling the etching bias in the etching process can therefore help to generate more accurate device features, such as by compensating for the etching variations, such as by adapting the patterned device to (accurately) anticipate the possible etching variations of the etching process (e.g., depending on the pattern density). This variation allows the actual features generated by the etching process after the (adjusted) lithography to be closer to the desired product specifications.

[0087]

[0114] In one embodiment, a system for determining an etch bias associated with an etch process performing a procedure discussed herein (e.g., of method 600) is described. For example, the system may include semiconductor processing equipment (e.g., FIGS. 1, 23, 24, 25) and one or more processors (e.g., 104 / 105 of FIG. 22) configured to determine physical effect data 604 characterizing an effect of the etch process on a substrate via execution of a physical effect model, and to execute a trained machine learning model 603 using the resist pattern and the physical effect data 604 as input to determine an etch bias, and to control a semiconductor device (e.g., FIG. 1) or an etch process based on the etch bias.

[0088]

[0115] In one embodiment, the trained machine learning model 603 is trained, for example, according to the method 600. For example, the trained machine learning model 603 is trained using a plurality of resist patterns, the physical effects data 604 associated with each of the resist patterns, and the measured bias 606 associated with each of the resist patterns, such that the difference between the measured bias 606 and the determined etch bias is minimized.

[0089]

[0116] In one embodiment, the trained machine learning model 603 is a convolutional neural network (CNN) that includes specific weights and biases that are determined via a training process that uses multiple resist patterns, physical effects data 604 associated with each of the resist patterns, and measured biases 606 associated with each of the resist patterns, such that the difference between the measured biases 606 and the determined etch bias is minimized.

[0090]

[0117] In one embodiment, controlling the semiconductor processing equipment (e.g., FIGS. 1, 23, 24, 25) includes adjusting values ​​of one or more parameters of the semiconductor processing equipment such that the yield of the patterning process is improved. In one embodiment, adjusting values ​​of one or more parameters of the semiconductor processing equipment is an iterative process. The iterative process includes: (a) changing current values ​​of one or more parameters via an adjustment mechanism of the semiconductor processing equipment; (b) acquiring a resist pattern to be printed on a substrate via the semiconductor processing equipment; (c) determining an etch bias via execution of the trained machine learning model 603 using the resist pattern, and further determining an etch pattern by applying the etch bias to the resist pattern; (d) determining whether the yield of the patterning process is within a desired yield range based on the etch pattern; and performing steps (a)-(d) in response to not being within the yield range.

[0091]

[0118] In one embodiment, controlling the etching process includes determining an etching pattern by applying an etching bias to the resist pattern, determining a yield of the patterning process based on the etching pattern, and determining an etch recipe for the etching process based on the etching pattern such that the yield of the patterning process is improved. In one embodiment, the yield of the patterning process is the percentage of the etch pattern across the substrate that meets the design specifications. In one embodiment, the semiconductor processing equipment is a lithography equipment (e.g., FIGS. 1, 23, 24, 25).

[0092]

[0119] In today's semiconductor world, technology nodes continue to shrink, and there is a desire to have better models of lithography and etching. A good model meets both accuracy (e.g., matches model results with real wafer metrology results) and good wafer prediction (e.g., behaves according to physical limitations). Meeting both accuracy and prediction specifications can be difficult with current complex model formats, because a better fit indicates overfitting of the model. Overfitted models can usually produce irregularly shaped patterns that may be undesirable to print on the substrate.

[0093]

[0120] The current method to solve the problem of overfitting or problems related to prediction is to have more metrology information during model calibration. For example, more information includes data related to more pattern coverage or more evaluation points. For example, a SEM tool can be configured to generate a large number of EP gauges for a particular pattern. However, increasing metrology increases the cost and time of the patterning process. Typically, the pattern coverage is significantly less than 100% of the total number of patterns in the design layout. Therefore, model calibration cannot be performed for all patterns that may be printed on the wafer. Increasing the pattern coverage is time-consuming and not cost-effective. This requires several recalibrations and data collections. Furthermore, if the model is of significant complexity, it still proceeds to overfit. Therefore, instead of dealing with the problems arising from feeding more data to the model calibration, a more fundamental solution is proposed to make the model physics-aware by performing the model calibration based on physical constraints.

[0094]

[0121] In one embodiment, the physical constraints may be related to a contour shape obtained from a metrology tool (e.g., SEM), a physical image (e.g., resist image, aerial image) obtained from a metrology tool (e.g., SEM), or a combination thereof. Examples of methods for implementing physical constraints are discussed herein, such as the methods of Figures 12 and 14.

[0095]

[0122] 12 is a flow diagram of a method 2000 for calibrating a process model based on physical constraints related to the contour shape (or outline) of a pattern. The method 2000 calibrates the process model to generate a simulated contour that satisfies the shape constraints. Detailed steps of the method 2000 are described below.

[0096]

[0123] Procedure P2001 includes obtaining (i) measurement data 2002 at a plurality of measurement locations on a pattern, and (ii) a contour constraint 2004 defined based on the measurement data 2002. In one embodiment, the plurality of measurement locations are edge placement (EP) gauges placed on the printed pattern or on a printed contour of the printed pattern.

[0097]

[0124] In one embodiment, the measurement data 2002 includes a plurality of angles, each angle being defined at each measurement location located on the pattern or on the printed contour of the printed pattern. In one embodiment, each angle at each measurement location defines a direction for determining the edge placement error between the printed contour and the target contour. Figures 13A and 13B show exemplary measurement locations EP1, EP2, and EP3. The angle associated with each measurement location EP1-EP3 is then an angle or direction from which the EPE can be calculated. In other words, for example, at point EP1, the distance between the contour 1110 (or 1120 in Figure 13B) is measured in the direction indicated by the arrow pointing away from the contour 1110 (or 1120). Depending on the shape of the contour 1110 / 1120, such measurements may vary.

[0098]

[0125] In one embodiment, each contour constraint is a function of the tangent angle between a tangent to a simulated contour (e.g., contour 1110 or 1120) at a given measurement location (e.g., EP1-EP3) and the angle of the measurement data 2002 at the given location. For example, referring to FIG. 13A, a contour constraint may be that the angle θ1 between a tangent to the simulated contour 1110 and an arrow at EP1 (which indicates the angle of the measurement data 2002) should be within a vertical range. In one embodiment, the vertical range is the value of the angle θ1, which should be between 88° and 92°, preferably 90°. Each point EP1, EP2, and EP3 may be associated with such a vertical constraint.

[0099]

[0126] In another example, FIG. 13B shows the result of a calibrated model that produces a simulated contour 1120 that does not satisfy the physical constraints. For example, the calibrated model may be overfitted to make a good prediction to the measured data. For example, a model overfitted due to excess data, where fitting is focused on minimizing EP error, may produce an irregularly shaped contour, such as contour 1120. Then, the tangent to contour 1120 at EP1, EP2, and EP3 may not be perpendicular to the measured data (e.g., the measurement angle indicated by the arrows at EP1-EP3, respectively). For example, as seen in FIG. 13B, the line perpendicular to the arrows at EP1, EP2, and EP3 is not a tangent to contour 1120. Thus, the simulated contour 1120 is fitted to the measured data (e.g., EPE or CD values) such that the sum of errors associated with the simulated contour 1120 is minimized, but the shape of the contour 1120 may not be physically exact.

[0100]

[0127] 12, procedure P2003 includes calibrating the process model 2003 by adjusting values ​​of model parameters of the process model until the simulated contour (e.g., 1110) satisfies the contour constraint 2004. After the calibration process, the process model may be referred to as a calibrated process model 2003. In one example, the model 2003 that produces the simulated contour 1120 may be considered uncalibrated because it does not satisfy the contour constraint 2004 at some points EP1, EP2, and EP3. In one embodiment, calibrating the process model may be limited to a selected number of points EP1 and EP3, or all points, e.g., EP, EP2, and EP3.

[0101]

[0128] In one embodiment, adjusting the value of the model parameter is an iterative process that includes (a) executing the process model 2003 with given values ​​of the model parameters to generate a simulated contour, the given values ​​being random values ​​in a first iteration and adjusted values ​​in subsequent iterations, (c) determining a tangent to the simulated contour at each of the measurement locations, (d) determining a tangent angle between the tangent and an angle of the measurement data 2002 at each of the measurement locations, (e) determining whether the tangent angle is within a vertical range at one or more of the measurement locations, and (f) in response to the tangent angle not being within the vertical range, adjusting the value of the model parameter, and performing steps (a)-(d).

[0102]

[0129] In one embodiment, at each iteration, a simulated contour can be obtained and a tangent can be drawn or calculated (e.g., via the trigonometric relationship "tan") at the measurement location. The angle between the tangent and the EPE angle of the measurement data 2002 can then be determined to check whether the tangent angle is within the vertical range, e.g., between 88° and 92°, preferably 90°.

[0103]

[0130] In one embodiment, the adjustment is based on the gradient of each tangent angle with respect to the model parameter, which gradient indicates how sensitive the tangent angle is to changes in the model parameter value.

[0104]

[0131] In one embodiment, the process model 2003 is a data-driven model, including empirical models and / or machine learning models. For example, the machine learning model is a convolutional neural network, and the model parameters are weights and biases associated with multiple layers. This disclosure is not limited to a particular type of model or a particular process of a patterning process. The method 2000 can be modified or adapted for any process model and any process (or combination of processes) of a patterning process.

[0105]

[0132] In one embodiment, the method 2000 may further include, in step P2005, obtaining a resist contour of the resist pattern (e.g., 602 described above) and generating an etch contour 2005 by applying an etch bias (e.g., determined by running a calibrated model) to the resist contour.

[0106]

[0133] 14 is a flow diagram of another method 3000 for calibrating a process model based on physical constraints. In one embodiment, the process model is configured to predict an image of a target pattern. The calibration may then be based on image-based constraints. The method 3000 includes the following steps:

[0107]

[0134] Procedure P3001 includes obtaining (i) a reference image 3002 associated with the target pattern, and (ii) a gradient constraint 3004 defined relative to the reference image 3002. In one embodiment, the reference image 3002 is obtained via simulating a physics-based model of the patterning process using the target pattern. The reference image 3002 includes, but is not limited to, at least one of an aerial image of the target pattern, a resist image of the target pattern, or an etched image of the target pattern. In one embodiment, the simulated gradient is determined by taking the first derivative of the signal along a given line passing through the simulated image. In one embodiment, the gradient constraint 3004 is obtained by taking the first derivative of the signal along a given line passing through the reference image 3002.

[0108]

[0135] Procedure P3003 includes calibrating the process model 3003 such that the process model 3003 produces a simulated image that (i) minimizes the intensity or frequency difference between the simulated image and the reference image 3002, and (ii) satisfies the gradient constraint 3004. After calibration, the process model 3003 may be referred to as a calibrated process model 3003.

[0109]

[0136] 15A-15C show examples of gradient constraints 3004. FIG. 15A shows an example reference intensity distribution 1510 at a given location in a physical image (e.g., an aerial image, a resist image, and an ADI). In one embodiment, the similarity between the reference image 3002 and the simulated image can be used to quantify the resist model stability and the risk of overfitting. For example, the similarity can be evaluated as the intensity difference between the reference image 3002 and the simulated image, or the frequency difference between the reference image 3002 and the simulated image (e.g., via an FFT of the images).

[0110]

[0137] Thus, in one embodiment, the gradient of the intensity difference or frequency difference may be applied as a constraint during calibration of the process model (e.g., 3003). For example, after applying a gradient constraint with respect to the reference intensity distribution 1510 during the calibration process, the process model may generate a simulated contour having an intensity distribution 1520 (of FIG. 15B), which has a similar shape (e.g., similar peaks and valleys) as the reference intensity distribution 1510. Thus, the calibrated process model (e.g., 3003) is deemed to follow the physical terms (e.g., intensity profile or frequency profile) of the reference image associated with the patterning process. In one embodiment, a process model that is not calibrated according to the gradients associated with the physical terms (e.g., AI / RI), such a process model may generate an unacceptable intensity distribution 1530 (of FIG. 15C) compared to the reference intensity distribution. For example, the peaks of 1510 and 1530 are significantly different.

[0111]

[0138] In one embodiment, the calibration of the process model is an iterative process that includes: (a) executing the process model using the target pattern to generate a simulated image, (b) determining an intensity difference between the intensity values ​​of the simulated image and the intensity values ​​of the reference image 3002, and / or transforming the simulated image and the reference image 3002 into the frequency domain via a Fourier transform and determining a frequency difference between the frequencies associated with the simulated image and the frequencies associated with the reference image 3002, (c) determining a simulated gradient of a signal in the simulated image, the signal being along a given line passing through the simulated image, (d) determining the following conditions: (i) the intensity difference or frequency difference is minimized, (ii) the simulated gradient satisfies the gradient constraint 3004 associated with the reference image 3002, (e) in response to conditions (i) and (ii) not being satisfied, adjusting values ​​of model parameters of the process model, and performing steps (a)-(d) until conditions (i) and (ii) are satisfied.

[0112]

[0139] In one embodiment, the method 3000 further includes, in step P3005, extracting a simulated contour from the simulated image and a reference contour from the reference image 3002, and calibrating the process model such that the simulated contour satisfies the contour shape constraint. For example, the contour can be extracted from the image using an edge detection algorithm or other contour extraction technique used to extract a contour related to the target pattern. In one embodiment, the simulated contour and the reference contour are associated with the target pattern, and the contour shape constraint ensures that the simulated contour matches the shape of the reference contour. In one embodiment, the contour shape constraint may be implemented as an invariant condition that the model output must satisfy. If the invariant condition is not satisfied, the values ​​of the model parameters are adjusted until such invariant condition is satisfied.

[0113]

[0140] In one embodiment, determining whether the contour shape constraint is satisfied includes determining that a second derivative of the simulated contour is within a desired range of a second derivative of a reference contour, in one embodiment, the contour shape is represented as a polygon, and thus the second derivative of the polygon may be calculated using computational software.

[0114]

[0141] In one embodiment, the process model may be configured to satisfy contour constraints (e.g., as discussed in method 2000 of FIG. 12) that are defined with respect to the printed contour of the pattern on the printed substrate. For example, each contour constraint may be a function of the tangent angle between a tangent to the simulated contour at a given measurement location and the angle of the measurement data 2002 at that given location, where the simulated contour is the contour of the simulated pattern as determined via running the process model with the target pattern.

[0115]

[0142] In one embodiment, the method 3000 may further include, in step P3005, obtaining a resist contour of the resist pattern (e.g., 602 described above) and generating an etch contour 3005 by applying an etch bias (e.g., determined by running a calibrated model) to the resist contour.

[0116]

[0143] In one embodiment, a system for calibrating a process model implementing the procedures discussed herein (e.g., of method 2000) is described. The process model is configured to generate a simulated contour. The system includes a metrology tool (e.g., SEM tool of FIGS. 16 and 17) configured to acquire measurement data 2002 at a plurality of measurement locations on the pattern, and one or more processors (e.g., 104 / 105 of FIG. 22). The processor (e.g., 104 / 105) may be configured to calibrate the process model by adjusting values ​​of model parameters of the process model until the simulated contour satisfies a contour constraint 2004, where the contour constraint 2004 is based on the measurement data 2002.

[0117]

[0144] In one embodiment, a metrology tool, e.g., an SEM, is configured to obtain measurements at multiple measurement locations, such as edge placement (EP) gauges, located on the printed pattern or on the printed contour of the printed pattern. In one embodiment, the measurement data 2002 includes multiple angles, each angle defined at each measurement location located on the pattern or on the printed contour of the printed pattern. In one embodiment, each angle at each measurement location defines a direction that determines the edge placement error between the printed contour and the target contour. As previously described, the metrology tool can be an electron beam device (e.g., the SEM of Figs. 16 and 17). In one embodiment, the metrology tool is a scanning electron microscope configured to identify and extract contours from a captured image of the pattern on the printed substrate.

[0118]

[0145] In one embodiment, the processor is configured to include each contour constraint as a function of the tangent angle between the tangent to the simulated contour at a given measurement location and the angle of the measurement data 2002 at that given location.

[0119]

[0146] In one embodiment, the processor is configured to iteratively adjust the value of the model parameter, for example, the iterations including: (a) executing the process model using a given value of the model parameter to generate a simulated contour, the given value being a random value in a first iteration and an adjusted value in a subsequent iteration, (c) determining a tangent to the simulated contour at each of the measurement locations, (d) determining a tangent angle between the tangent and an angle of the measurement data 2002 at each of the measurement locations, (e) determining whether the tangent angle is within a vertical range at one or more of the measurement locations, (f) in response to the tangent angle not being within the vertical range, adjusting the value of the model parameter, and performing steps (a)-(d).

[0120]

[0147] In one embodiment, the vertical range is between 88° and 92°, preferably an angle value of 90°. In one embodiment, the processor is configured to adjust based on a gradient of each tangent angle with respect to the model parameter, the gradient indicating how sensitive the tangent angle is to changes in the model parameter value. In one embodiment, the process model is a data-driven model, including an empirical model and / or a machine learning model.

[0121]

[0148] In one embodiment, the machine learning model is a convolutional neural network and the model parameters are weights and biases associated with multiple layers.

[0122]

[0149] Similarly, in one embodiment, a system for calibrating a process model, e.g., according to a procedure of method 3000 discussed herein, is described. The process model may be configured to predict an image of a target pattern. The system includes a metrology tool (e.g., SEM tool of FIGS. 16 and 17) configured to acquire a reference image 3002 associated with the target pattern, and one or more processors (104 / 105 of FIG. 22). The processor may be configured to calibrate the process model such that the process model produces a simulated image that (i) minimizes an intensity or frequency difference between the simulated image and the reference image 3002, and (ii) satisfies a gradient constraint 3004 associated with the reference image 3002.

[0123]

[0150] In one embodiment, the processor is configured to iteratively calibrate the process model, which includes (a) executing the process model using the target pattern to generate a simulated image, (b) determining an intensity difference between intensity values ​​of the simulated image and the reference image 3002 and / or transforming the simulated image and the reference image 3002 into the frequency domain via a Fourier transform and determining a frequency difference between a frequency associated with the simulated image and a frequency associated with the reference image 3002, (c) determining a simulated gradient of a signal in the simulated image, the signal being along a given line passing through the simulated image, (d) determining the following conditions: (i) the intensity or frequency difference is minimized, (ii) the simulated gradient satisfies the gradient constraint 3004 associated with the reference image 3002, (e) in response to conditions (i) and (ii) not being satisfied, adjusting values ​​of model parameters of the process model, and performing steps (a)-(d) until conditions (i) and (ii) are satisfied.

[0124]

[0151] As mentioned above, in one embodiment, the simulated gradient is determined by taking the first derivative of the signal along a given line passing through the simulated image. In one embodiment, the gradient constraint 3004 is obtained by taking the first derivative of the signal along a given line passing through the reference image 3002.

[0125]

[0152] In one embodiment, the processor is further configured to extract a simulated contour from the simulated image and a reference contour from the reference image 3002, where the simulated contour and the reference contour are associated with the target pattern, and the processor is further configured to calibrate the process model so that the simulated contour satisfies a contour shape constraint, where the contour shape constraint ensures that the simulated contour matches the shape of the reference contour.

[0126]

[0153] In one embodiment, determining whether the contour shape constraint is satisfied includes determining that a second derivative of the simulated contour is within a desired range of a second derivative of a reference contour.

[0127]

[0154] In one embodiment, the reference image 3002 is obtained via simulating a physics-based model of the patterning process using the target pattern. The simulation may be performed on a processor. In one embodiment, the reference image 3002 may be obtained from a metrology tool (e.g., SEM). In one embodiment, the reference image 3002 includes an aerial image of the target pattern, a resist image of the target pattern, and / or an etched image of the target pattern.

[0128]

[0155] In one embodiment, the process model is configured to satisfy contour constraints 2004 defined with respect to the printed contour of the pattern on the printed substrate, as discussed in Figure 12. For example, each contour constraint will be a function of the tangent angle between a tangent to the simulated contour at a given measurement location and the angle of the measurement data 2002 at that given location, where the simulated contour is the contour of the simulated pattern, as determined via running the process model with the target pattern.

[0129]

[0156] In one embodiment, a non-transitory computer readable medium is provided that includes instructions that, when executed by one or more processors, cause operations including obtaining (i) resist pattern data 602 associated with a target pattern to be printed on a substrate, (ii) physical effect data 604 characterizing the effect of an etch process on the target pattern, and (iii) a measured bias 606 between the etch pattern formed on the printed substrate and the resist pattern, and training a machine learning model based on the resist pattern data 602, the physical effect data 604, and the measured bias 606 to reduce the difference between the measured bias 606 and a predicted etch bias. Additionally, the non-transitory computer readable medium may include additional instructions discussed with respect to FIG. 6 (e.g., associated with P601, P603, and P605).

[0130]

[0157] In one embodiment, a non-transitory computer readable medium is provided that includes instructions that, when executed by one or more processors, cause operations including: acquiring (i) measurement data 2002 at a plurality of measurement locations on a pattern, (ii) a contour constraint 2004 defined based on the measurement data 2002, and calibrating a process model by adjusting values ​​of model parameters of the process model until a simulated contour satisfies the contour constraint 2004. Additionally, the non-transitory computer readable medium may include additional instructions discussed with respect to FIG. 12 (e.g., associated with procedures P2001, P2003, and P2005).

[0131]

[0158] In one embodiment, a non-transitory computer readable medium is provided that includes instructions that, when executed by one or more processors, cause operations including: (i) obtaining a reference image 3002 associated with a target pattern, (ii) a gradient constraint 3004 defined with respect to the reference image 3002, and (i) calibrating a process model such that the process model produces a simulated image that minimizes an intensity or frequency difference between the simulated image and the reference image 3002 and (ii) satisfies the gradient constraint 3004. Additionally, the non-transitory computer readable medium may include additional instructions discussed with respect to FIG. 14 (e.g., associated with steps P3001, P3003, and P3005).

[0132]

[0159] In accordance with the present disclosure, combinations and subcombinations of the disclosed elements constitute separate embodiments. For example, a first combination includes determining an etch contour based on a trained machine learning model. In another example, the combination includes determining a simulated contour based on a model calibrated according to physical constraints.

[0133]

[0160] In some embodiments, a scanning electron microscope (SEM) generates an image of the exposed or transferred structure (e.g., part or all of a device structure) on the substrate. Figure 16 shows one embodiment of an SEM 200. A primary electron beam 202 emitted from an electron emitter 201 is focused by a collector lens 203 and then passes through a beam deflector 204, an E x B deflector 205, and an objective lens 206 to focus and illuminate a substrate 100 on a substrate table 101.

[0134]

[0161] When the substrate 100 is irradiated with the electron beam 202, secondary electrons are generated from the substrate 100. The secondary electrons are deflected by the E x B deflector 205 and detected by the secondary electron detector 207. A two-dimensional electron beam image can be obtained by detecting the electrons generated from the sample, for example, in synchronization with a two-dimensional scanning of the electron beam by the beam deflector 204, or a repetitive scanning of the electron beam 202 by the beam deflector 204 in the X or Y direction (with a continuous movement of the substrate 100 by the substrate table 101 in the other of the X or Y directions).

[0135]

[0162] The signal detected by the secondary electron detector 207 is converted into a digital signal by an analog-to-digital (A / D) converter 208, which is sent to an image processing system 300. In an embodiment, the image processing system 300 may comprise a memory 303 to store all or part of the digital image for processing by a processing unit 304. The processing unit 304 (e.g., a specially designed hardware or a combination of hardware and software) is configured to convert or process the digital image into a data set representative of the digital image. Furthermore, the image processing system 300 may comprise a storage medium 301 configured to store the digital image and the corresponding data set in a reference database. A display device 302 may be connected to the image processing system 300, so that an operator can perform the required operations of the apparatus with the aid of a graphical user interface.

[0136]

[0163] 17 shows a schematic representation of a further embodiment of an inspection apparatus, which is used to inspect a sample 90 (such as a substrate) on a sample stage 89 and comprises a charged particle beam generator 81, a condenser lens module 82, a probe-forming objective lens module 83, a charged particle beam deflection module 84, a secondary charged particle detector module 85, and an image formation module 86.

[0137]

[0164] The charged particle beam generator 81 generates a primary charged particle beam 91. The collector lens module 82 collects the generated primary charged particle beam 91. The probe-forming objective lens module 83 focuses the collected primary charged particle beam onto a charged particle beam probe 92. The charged particle beam deflection module 84 scans the formed charged particle beam probe 92 across a surface of a region of interest on a sample 90 fixed to a sample stage 89. In one embodiment, the charged particle beam generator 81, the collector lens module 82, and the probe-forming objective lens module 83, or equivalent designs, alternatives, or any combination thereof, together form a charged particle beam probe generator that generates the scanning charged particle beam probe 92.

[0138]

[0165] The secondary charged particle detector module 85 detects secondary charged particles 93 (possibly along with other reflected or scattered charged particles from the sample surface) emitted from the sample surface when impacted by the charged particle beam probe 92 to generate a secondary charged particle detection signal 94. An imaging module 86 (e.g., a computing device) is coupled to the secondary charged particle detector module 85 to receive the secondary charged particle detection signal 94 from the secondary charged particle detector module 85 and, in response, form at least one scanned image. In one embodiment, the secondary charged particle detector module 85 and the imaging module 86, or equivalent designs, alternatives, or any combination thereof, together form an imaging device that forms a scanned image from detection of secondary charged particles emitted from the sample 90 impacted by the charged particle beam probe 92.

[0139]

[0166] As mentioned above, SEM images can be processed to extract contours that describe the edges of objects in the images, which represent device structures. These contours are then quantified via a metric such as CD. Thus, images of device structures are usually compared and quantified via simple metrics such as edge-to-edge distance (CD) or simple pixel differences between images. A typical contour model to detect the edges of objects in an image to measure CD uses image gradients. Indeed, these models rely on strong image gradients. However, in reality, images are usually noisy and have discontinuous boundaries. Techniques such as smoothing, adaptive thresholding, edge detection, erosion, and dilation can be used to process the results of the image gradient contour models to deal with noisy and discontinuous images, but this ultimately leads to low-resolution quantification of high-resolution images. Thus, in most cases, mathematical manipulation of device structure images to reduce noise and automate edge detection leads to a loss of image resolution and thereby to a loss of information. Thus, the result is a low-resolution quantification that is a simple representation of the complex high-resolution structures.

[0140]

[0167] For this, it is desirable to have a mathematical representation of a structure (e.g., a circuit feature, an alignment mark, or a metrology target portion (e.g., a grating feature), etc.) that is produced or predicted to be produced using a patterning process, whether that structure is in a latent resist image, in a developed resist image, or transferred, e.g., by etching, to a layer on a substrate that can retain resolution and still represent the general shape of the structure. In the context of lithography or other patterning processes, the structure may be a device or part thereof being fabricated, and the image may be an SEM image of the structure. In some cases, the structure may be a feature of a semiconductor device, e.g., an integrated circuit. In some cases, the structure may be an alignment mark, or a portion thereof (e.g., a grating of an alignment mark), used in an alignment measurement process to determine the alignment of an object (e.g., a substrate) with another object (e.g., a patterning device), or may be a metrology target, or a portion thereof (e.g., a grating of a metrology target), used to measure a parameter of a patterning process (e.g., overlay, focus, dose, etc.). In one embodiment, the metrology target is, for example, a diffraction grating used to measure overlay.

[0141]

[0168] In one embodiment, the measurement data associated with the printed pattern is used to train a model in the method of FIG. 3. The trained model may be further utilized to optimize the patterning process or adjust the parameters of the patterning process. In one example, OPC addresses the fact that the final size and location of the image of the design layout projected onto the substrate may not be identical to or solely dependent on the size and location of the design layout on the patterning device. Note that the terms "mask", "reticle" and "patterning device" are used interchangeably herein. Those skilled in the art will also recognize that, particularly in the context of lithography simulation / optimization, the terms "mask" / "patterning device" and "design layout" may be used interchangeably because in lithography simulation / optimization, a physical patterning device is not necessarily used, but a design layout can be used to represent a physical patterning device. With small feature sizes and high feature density, as exists in some design layouts, the location of a particular edge of a given feature is influenced to a certain extent by the presence or absence of other adjacent features. These proximity effects arise from small amounts of radiation coupling from one feature to another, and / or non-geometric optical effects such as diffraction and interference. Similarly, proximity effects can also arise from diffusion and other chemical effects during the post-exposure bake (PEB), resist development, and etching that typically follow lithography.

[0142]

[0169] To ensure that the projected image of a design layout conforms to the requirements of a given target circuit design, it is necessary to predict and compensate for the proximity effect using advanced numerical models, corrections or pre-distortions of the design layout. The paper “Full-Chip Lithography Simulation and Design Analysis - How OPC Is Changing IC Design”, C. Spence, Proc.SPIE, Vol. 5751, pp 1-14 (2005) provides an overview of current “model-based” optical proximity correction processes. In a typical high-end design, almost every feature of the design layout undergoes some modification to improve the fidelity of the projected image to the target design. These modifications may include shifting or biasing edge positions or line widths, as well as the application of “assist” features intended to assist the projection of other features.

[0143]

[0170] Applying model-based OPC to a target design typically requires good process models and substantial computational resources, given that millions of features exist in a chip design. However, applying OPC is generally not an "exact science" but an empirical iterative process that does not always compensate for all possible proximity effects. Therefore, the effect of OPC, e.g., the design layout after application of OPC and any other RET, needs to be verified by design verification, i.e., intensive full-chip simulation using a calibrated numerical process model, to minimize the possibility of design defects being incorporated into the patterning device pattern. This is driven by the enormous cost of manufacturing high-end patterning devices, which can range from millions of dollars, as well as the impact on turnaround time of reworking or repairing the actual patterning device once it is manufactured.

[0144]

[0171] Both OPC verification and full-chip RET verification may be based on numerical modeling systems and methods such as those described in U.S. patent application Ser. No. 10 / 815,573 and the paper entitled “Optimized Hardware and Software For Fast, Full Chip Simulation” by Y. Cao et al., Proc. SPIE, Vol. 5754, 405 (2005).

[0145]

[0172] One RET is related to adjusting the global bias of the design layout. The global bias is the difference between the pattern in the design layout and the pattern intended to be printed on the substrate. For example, a circular pattern with a diameter of 25 nm may be printed on the substrate by a pattern with a diameter of 50 nm in the design layout, or may be printed on the substrate by a pattern with a diameter of 20 nm in the design layout, but at a higher dose.

[0146]

[0173] In addition to optimization for the design layout or patterning device (e.g., OPC), the illumination radiation source may be optimized together with or separately from the patterning device optimization to enhance the overall lithography fidelity. The terms "illumination radiation source" and "radiation source" are used interchangeably in this document. Since the 1990s, many off-axis illumination radiation sources, such as annular, quadrupole, and dipole, have been introduced to provide more freedom in the design of the OPC, thereby improving the imaging results. As is known, off-axis illumination is a proven method for resolving fine structures (i.e., target features) contained in a patterning device. However, compared to conventional illumination radiation sources, off-axis illumination radiation sources usually provide smaller radiation intensity for the aerial image (AI). Therefore, it becomes desirable to optimize the illumination radiation source to try to achieve an optimal balance between finer resolution and reduced radiation intensity.

[0147]

[0174] A number of illumination source optimization methods can be found, for example, in the paper by Rosenbluth et al. entitled "Optimum Mask and Source Patterns to Print A Given Shape" published in Journal of Microlithography, Microfabrication, Microsystems 1(1), pp.13-20, (2002). The source is divided into several regions, each of which corresponds to a specific region of the pupil spectrum. The source distribution is then assumed to be uniform in each source region, and the brightness of each region is optimized for the process window. However, the assumption that the source distribution is uniform in each source region is not always valid, which reduces the effectiveness of the method. Another example, described in a paper by Granik entitled "Source Optimization for Image Fidelity and Throughput" published in Journal of Microlithography, Microfabrication, Microsystems 3(4), pp.509-522, (2004), reviews some existing source optimization methods and proposes an illuminator pixel-based method that transforms the source optimization problem into a series of non-negative least squares optimizations. These methods have demonstrated some success, but typically require multiple complex iterations to converge. Furthermore, it can be difficult to determine the appropriate / optimal values ​​of some additional parameters, such as γ in Granik's method, which defines a trade-off between source optimization for substrate image fidelity and the requirement of source smoothness.

[0148]

[0175] For low k1 photolithography, optimizing both the radiation source and the patterning device helps to guarantee a viable process window for projecting critical circuit patterns. Some algorithms (e.g., Socha et al. Proc.SPIE vol. 5853,2005, p.180) discretize the illumination into independent radiation source points, mask into diffraction orders in the spatial frequency domain, and separately formulate a cost function (defined as a function of selected design variables) based on a process window metric, such as exposure latitude, that can be predicted by an optical imaging model from the radiation source point intensity and the patterning device diffraction orders. As used herein, the term "design variables" includes a set of parameters of a lithographic projection apparatus or lithographic process, such as parameters that a user of the lithographic projection apparatus can adjust, or image features that a user can adjust by adjusting those parameters. It should be understood that any feature of a lithographic projection process, including features of the radiation source, the patterning device, the projection optics, and / or the resist features, can be included in the design variables in the optimization. The cost function, which is often a nonlinear function of the design variables, is then minimized using standard optimization techniques.

[0149]

[0176] In this context, the pressure to continually reduce design rules has led semiconductor chipmakers to move deeper into the era of low k1 lithography with existing 193 nm ArF lithography. Lithography towards lower k1 places strong demands on RET, exposure tools, and the need for litho-friendly design. 1.35 ArF high numerical aperture (NA) exposure tools can be used in the future. Source-patterning device optimization (herein referred to as source-mask optimization or SMO) is becoming a critical RET for the 2x nm node to ensure that circuit designs can be manufactured on a substrate with a feasible process window.

[0150]

[0177] A source and patterning device (design layout) optimization method and system capable of co-optimizing the source and patterning device using a cost function without constraints and in a reasonable time frame is described in commonly assigned International Patent Application No. PCT / US2009 / 065359, entitled "Fast Freeform Source and Mask Co-Optimization Method," filed on November 20, 2009, and published as WO 2010 / 059954, which is incorporated herein by reference in its entirety.

[0151]

[0178] Another source and mask optimization method and system, which involves optimizing the source by adjusting the pixels of the source, is described in commonly assigned U.S. patent application Ser. No. 12 / 813,456, entitled "Source-Mask Optimization in Lithographic Apparatus," filed Jun. 10, 2010, and published as U.S. Patent Application Publication No. 2010 / 0315614, which is incorporated herein by reference in its entirety.

[0152]

[0179] In a lithographic projection apparatus, as an example, the cost function may be expressed as:

number

[0153]

[0180] In addition, f p (z1, z2, ..., z N The usual weighted root mean square (RMS) of

number

number

[0154]

[0181] Furthermore, when considering the maximization of the PW (process window), the same physical locations from different PW conditions can be considered as different evaluation points in the cost function of (Equation 1). For example, when considering N PW conditions, we can classify the evaluation points according to the PW conditions and write the cost function as follows:

number

[0155]

[0182] There may be constraints on the design variables, which are expressed as (z1, z2, ..., z N)∈Z, where Z is the set of possible values ​​of the design variables. One possible constraint on the design variables may be imposed by the desired throughput of the lithographic projection apparatus. The desired throughput may limit the dose and thus have implications on stochastic effects (e.g., imposing a lower limit on stochastic effects). Higher throughput generally equates to lower doses, shorter and longer exposure times, and greater stochastic effects. Considerations of substrate throughput and minimization of stochastic effects may constrain the possible values ​​of the design variables, since stochastic effects are a function of the design variables. In the absence of such constraints imposed by the desired throughput, optimization may produce unrealistic sets of design variable values. For example, if dose is included in the design variables, in the absence of such constraints, optimization may produce dose values ​​that make the throughput economically unfeasible. However, the usefulness of the constraints should not be interpreted as necessary. Throughput may be affected by defect rate-based adjustments to parameters of the patterning process. It is desirable to have a lower defect rate of features while maintaining a high throughput. Throughput can also be affected by the resist chemistry. A slower resist (e.g., a resist that requires more light to be properly exposed) results in a lower throughput. Therefore, appropriate parameters of the patterning process can be determined based on an optimization process involving the defect rate of features due to resist chemistry or variations, and the dose requirements for higher throughput.

[0156]

[0183] Thus, the optimization process is a process in which the constraints (z1, z2, ..., z N ) ∈Z, the goal is to find a set of values ​​of the design variables that minimizes the cost function, i.e., to find:

number

[0157]

[0184] In a lithographic projection apparatus, the radiation source, the patterning device and the projection optics may be selectively optimized (referred to as selective optimization) or simultaneously optimized (referred to as simultaneous optimization). The terms "simultaneous", "concurrently", "together" and "together" as used herein mean that design variables of the radiation source, the patterning device, the projection optics features and / or any other design variables can be varied at the same time. The terms "selectively" and "selectively" as used herein mean that not all of the design variables can be varied at the same time.

[0158]

[0185] In FIG. 19, the optimization of all design variables is performed simultaneously. Such a flow may be called a simultaneous flow or a joint optimization flow. Alternatively, the optimization of all design variables may be performed selectively, as shown in FIG. 19. In this flow, at each step, some design variables are fixed while other design variables are optimized to minimize a cost function. Then, at the next step, a different set of variables is fixed while other variables are optimized to minimize a cost function. These steps are performed selectively until a convergence condition or a specific termination condition is met.

[0159]

[0186] As shown in the non-limiting example of the flowchart in FIG. 19, first, a design layout (step S1302) is obtained, and then a step of radiation source optimization is performed in step S1304, in which all design variables of the illumination radiation source are optimized to minimize a cost function while all other design variables are fixed (SO). Then, in the next step S1306, a mask optimization (MO) is performed, in which all design variables of the patterning device are optimized to minimize a cost function while all other design variables are fixed. These two steps are selectively performed until a certain termination condition is met in step S1308. Various termination conditions can be used, such as: the value of the cost function is equal to a threshold value; the value of the cost function exceeds a threshold value; the value of the cost function reaches a preset error limit range; or a preset number of iterations is reached; etc. Note that SO-MO-selective-optimization is used as an example of the selective flow. The selective flow can take many different forms, such as SO-LO-MO-selective-optimization, where SO, LO (lens optimization) are performed, and MO is selective and iterative, or SMO can be performed once first, and then LO and MO can be selectively and iteratively performed, etc. Finally, an optimization result output is obtained in step S1310, and the process stops.

[0160]

[0187] As mentioned above, the pattern selection algorithm may be integrated with joint optimization or selective optimization. For example, if selective optimization is employed, full-chip SO may be performed first to identify "hot spots" and / or "warm spots" and then MO is performed. Given the present disclosure, numerous permutations and combinations of sub-optimizations are possible to achieve the desired optimization results.

[0161]

[0188] FIG. 20A shows one exemplary method of optimization, in which a cost function is minimized. In step S502, initial values ​​of the design variables are obtained, including their adjustment ranges, if any. In step S504, a multivariate cost function is set. In step S506, the cost function is expanded in a sufficiently small neighborhood around the starting point values ​​of the design variables for the first iteration step (i=0). In step S508, standard multivariate optimization techniques are applied to minimize the cost function. Note that the optimization problem may add constraints, such as adjustment ranges, during the optimization process in S508 or at a later stage in the optimization process. Step S520 shows that each iteration is performed for a given test pattern (also known as a "gauge") of identified evaluation points selected to optimize the lithography process. In step S510, the lithography response is predicted. In step S512, the results of step S510 are compared to the desired or ideal lithography response values ​​obtained in step S522. If the termination condition is met in step S514, i.e., the optimization produces lithographic response values ​​that are sufficiently close to the desired values, the final values ​​of the design variables are output in step S518. The output step may also include outputting other functions using the final values ​​of the design variables, such as outputting a wavefront aberration adjusted map at the pupil plane (or other plane), an optimized source map, and an optimized design layout. If the termination condition is not met, in step S516, the values ​​of the design variables are updated with the results of the i-th iteration, and the process returns to step S506. The process of FIG. 20A is described in more detail below.

[0162]

[0189] In the exemplary optimization process, the design variables (z1, z2, ..., z N ) and f p (z1, z2, ..., z N ), but no relationship is assumed or approximated between f p (z1, z2, ..., z N ) is sufficiently smooth (e.g., the first derivative

number

number

[0163]

[0190] Here, we use the Gauss-Newton algorithm as an example. The Gauss-Newton algorithm is an iterative method that can be applied to general nonlinear multivariable optimization problems. N ) is (z 1i , z 2i , ..., z Ni At the iteration, which takes a value of (z 1i , z 2i , ..., z Ni ) in the neighborhood of f p (z1, z2, ..., z N ) and then linearize CF(z1, z2, ..., z N ), which gives the minimum value of (z 1i , z 2i , ..., z Ni ) in the neighborhood of z 1(i+1) , z 2(i+1) , ..., z N(i+1) ) is calculated by the design variables (z1, z2, ..., z N ) in the (i+1)th iteration, (z 1(i+1) , z 2(i+1) , ..., z N(i+1) ) value. This iteration converges (i.e., CF(z1, z2, ..., z N This continues until either ) does not decrease any further) or a preset number of iterations is reached.

[0164]

[0191] In particular, at the i-th iteration, (z 1i , z 2i , ..., z Ni ) in the vicinity of

number

[0165]

[0192] Under the approximation of Equation 3, the cost function becomes:

number

[0166]

[0193] The design variables (z1, z2, ..., z N ) is not subject to any constraints, then (z 1(i+1) , z 2(i+1) , ..., z N(i+1) ) can be derived by solving the following N linear equations:

number

[0167]

[0194] The design variables (z1, z2, ..., z N ) is a set of J inequalities (say, (z1, z2, ..., z N ) Adjustment range)

number

number

[0168]

[0195] f p (z1, z2, ..., z N Instead of minimizing the RMS of , the optimization process can minimize the magnitude of the maximum deviation (worst defect) among the evaluation points from the intended value. In this approach, the cost function can alternatively be expressed as

number

[0169]

[0196] The cost function in Equation 5 can be approximated as follows:

number

[0170]

[0197] Minimizing the size of the worst defect is f p (z1, z2, ..., z N ) can be combined with the linearization of f p (z1, z2, ..., z N ) is approximated as in Equation 3. The constraint on the size of the worst defect is then given by the inequality E Lp ≦f p (z1, z2, ..., z N )≦E Up where E Lp and E Up f p (z1, z2, ..., z N ) are two constants that define the minimum and maximum allowable deviations of the vectors. Substituting Equation 3, these constraints translate to the following for p=1,...,P:

number

[0171]

[0198] Equation 3 can be written in general as (z1, z2, ..., z N ), so that in such a neighborhood, the desired constraint E Lp ≦f p (z1, z2, ..., z N )≦E Up If it is not possible to achieve this (which may depend on some contradiction between the inequalities), then the constant E Lp and E Upmay be relaxed until the constraints are achievable. This optimization process is N ), where each step incrementally reduces the size of the worst defect, and each step is performed iteratively until a certain termination condition is met, resulting in an optimal reduction in the size of the worst defect.

[0172]

[0199] Another way to minimize the worst defects is to use the weights w p For example, after the i-th iteration, if the r-th evaluation point has the worst defect, we adjust w to give it a higher priority by reducing its defect size. r can be increased in the (i+1)th iteration.

[0173]

[0200] Furthermore, the cost functions in Eqs. 4 and 5 can be modified by introducing the Lagrange multiplier method to achieve a compromise between optimizing the RMS of defect sizes and optimizing the size of the worst defect, i.e.

number

[0174]

[0201] Optimizing the lithographic projection apparatus can expand the process window. The larger the process window, the more flexibility in process and chip design. The process window can be defined as a set of focus and dose values ​​for which the resist image is within a certain limit of the resist image design target. It should be noted that all methods described herein can also be extended to a generalized process window definition that can be established with different or additional basic parameters in addition to the exposure dose and defocus. These may include, but are not limited to, optical settings such as NA, sigma, aberration, polarization, or optical constants of the resist layer. For example, as mentioned above, when the PW is composed of different mask biases, optimizing includes minimizing the MEEF (mask error enhancement factor), which is defined as the ratio between the substrate EPE and the induced mask edge bias. The process window defined for focus and dose values ​​serves as an example only in this disclosure. A method for maximizing the process window according to an embodiment is described below.

[0175]

[0202] In the first step, we start with known conditions (f0, ε0) in the process window, where f0 is the nominal focus and ε0 is the nominal dose, and minimize one of the following cost functions in the neighborhood (f0±Δf, ε0±Δε):

number

[0176]

[0203] If the nominal focus f0 and the nominal dose ε0 are allowed to shift, they are N ) can be optimized together. In the next step, we choose the optimal set of (z1, z2, ..., z) such that the cost function is within a preset limit. N , f, ε) can be found, then (f0±Δf, ε0±Δε) is accepted as part of the process window.

[0177]

[0204] Alternatively, if the focus and dose cannot be shifted, the design variables (z1, z2, ..., z N ) is optimized by fixing the focus and dose at a nominal focus f0 and a nominal dose ε0. In an alternative embodiment, the cost function is optimized by choosing (z1, z2, ..., z) such that it is within preset limits. N ), then (f0±Δf, ε0±Δε) is accepted as part of the process window.

[0178]

[0205] The method described above in this disclosure can be used to minimize the cost function in Equation 7, 7', or 7'', respectively. If the design variables are the projection optics features, such as Zernike coefficients, minimizing the cost function in Equation 7, 7', or 7'' maximizes the process window based on projection optics optimization, i.e., LO. If the design variables are the source and patterning device features in addition to the projection optics features, minimizing the cost function in Equation 7, 7', or 7'' maximizes the process window based on SMLO, as shown in FIG. 19. If the design variables are the source and patterning device features, minimizing the cost function in Equation 7, 7', or 7'' maximizes the process window based on SMO. The cost function in Equation 7, 7', or 7'' may be calculated by minimizing at least one f, such as in Equation 7 or Equation 8. p (z1, z2, ..., z N ), which is a function of one or more stochastic effects, such as LWR or local CD variation of the 2D features, and throughput.

[0179]

[0206] FIG. 21 shows one particular example of how the simultaneous SMLO process uses the Gauss Newton algorithm for optimization. In step S702, starting values ​​of the design variables are identified. An adjustment range for each variable may also be identified. In step S704, a cost function is defined using the design variables. In step S706, the cost function is expanded around the starting values ​​of all evaluation points in the design layout. In optional step S710, a full-chip simulation is performed to cover all critical patterns in the full-chip design layout. The desired lithography response metrics (such as CD or EPE) are obtained in step S714 and compared with the predicted values ​​of those quantities in step S712. In step S716, a process window is determined. Steps S718, S720, and S722 are similar to the corresponding steps S514, S516, and S518 as described with respect to FIG. 20A. As mentioned above, the final output may be a wavefront aberration map at the pupil plane optimized to produce the desired imaging performance. The final output may also be an optimized source map and / or an optimized design layout.

[0180]

[0207] FIG. 20B illustrates an exemplary method for optimizing the cost function, in which the design variables (z1, z2, ..., z N ) contains design variables that can assume only discrete values.

[0181]

[0208] The method begins by defining pixel groups for the illumination radiation source and patterning device tiles for the patterning device (step S802). In general, pixel groups or patterning device tiles may also be referred to as divisions of lithographic process components. In one exemplary scheme, the illumination radiation source is divided into 117 pixel groups and 94 patterning device tiles are defined for the patterning device, resulting in a total of 211 divisions, essentially as described above.

[0182]

[0209] In step S804, a lithography model is selected as the basis for a photolithography simulation. The photolithography simulation produces results that are used in the calculation of a photolithography metric or response. A particular photolithography metric is defined (step S806) to be the performance metric to be optimized. In step S808, initial (pre-optimization) conditions of the illumination radiation source and the patterning device are set. The initial conditions include initial states of the pixel groups of the illumination radiation source and the patterning device tiles of the patterning device to reference an initial illumination shape and an initial patterning device pattern. The initial conditions may also include mask bias, NA, and focus lamp range. It should be understood that although steps S802, S804, S806, and S808 are shown as sequential steps, in other embodiments of the present invention, these steps may be performed in other orders.

[0183]

[0210] In step S810, the pixel groups and patterning device tiles are ranked. The pixel groups and patterning device tiles may be interleaved in the ranking. Various ranking methods may be used, including sequentially (e.g., from pixel group 1 to pixel group 117 and from patterning device tile 1 to patterning device tile 94), randomly, according to the physical location of the pixel groups and patterning device tiles (e.g., ranking pixel groups closer to the center of the illumination radiation source higher) and according to how changing the pixel group or patterning device tile affects the performance metrics.

[0184]

[0211] Once the pixel groups and patterning device tiles have been ranked, the illumination radiation source and the patterning device are adjusted to improve the performance metric (step S812). In step S812, each of the pixel groups and patterning device tiles is analyzed in order of rank to determine whether a change to the pixel group or patterning device tile leads to an improvement in the performance metric. If it is determined that the performance metric is improved, the pixel group or patterning device tile is correspondingly modified, and the resulting improved performance metric and modified illumination shape or modified patterning device pattern form a baseline of comparison for subsequent analysis of lower ranked pixel groups and patterning device tiles. In other words, the changes that improve the performance metric are retained. As changes to the states of the pixel groups and patterning device tiles are made and retained, the initial illumination shape and the initial patterning device pattern are correspondingly changed, resulting in modified illumination shape and modified patterning device pattern resulting from the optimization process of step S812.

[0185]

[0212] In other schemes, adjustments to patterning device polygon shapes and pairwise polling of pixel groups and / or patterning device tiles are also performed within the optimization process of S812.

[0186]

[0213] In an alternative embodiment, the interleaved joint optimization procedure may involve changing pixel groups of the illumination radiation source, and if an improvement in the performance metric is found, the dose is increased or decreased in search of further improvement. In a further alternative embodiment, the increase or decrease in dose or intensity may be replaced by a bias change of the patterning device pattern to look for further improvement in the joint optimization procedure.

[0187]

[0214] In step S814, a determination is made as to whether the performance metric has converged. The performance metric may be deemed to have converged, for example, if there is little or no improvement to the performance metric in the last few iterations of steps S810 and S812. If the performance metric has not converged, steps S810 and S812 are repeated for the next iteration, where the modified illumination shape and modified patterning device from the current iteration are used as the initial illumination shape and initial patterning device for the next iteration (step S816).

[0188]

[0215] The optimization method described above can be used to increase the throughput of a lithographic projection apparatus. For example, the cost function can be a function of exposure time, f p (z1, z2, ..., z N ) Optimization of such a cost function is preferably constrained or influenced by the magnitude or other metric of the stochastic effects. In particular, a computer-implemented method for increasing throughput of a lithographic process may include optimizing a cost function that is a function of one or more stochastic effects of the lithographic process and a function of exposure time of the substrate, in order to minimize the exposure time.

[0189]

[0216] In one embodiment, the cost function is at least one f that is a function of one or more stochastic effects. p (z1, z2, ..., z N ). The stochastic effects may include defects of the features, metrology data (e.g., SEPE) determined by the method of FIG. 3, LWR or local CD variations of 2D features. In an embodiment, the stochastic effects include stochastic variations of resist image features. For example, such stochastic variations may include defect rate, line edge roughness (LER), line width roughness (LWR), and critical dimension uniformity (CDU) of the features. Including the stochastic variations in the cost function allows finding values ​​of the design variables that minimize the stochastic variations, thereby reducing the risk of defects due to stochastic effects.

[0190]

[0217] 22 is a block diagram illustrating a computer system 100 that may assist in implementing the optimization methods and flows disclosed herein. The computer system 100 includes a bus 102 or other communication mechanism for communicating information, and a processor 104 (or multiple processors 104 and 105) coupled to the bus 102 for processing information. The computer system 100 also includes a main memory 106, such as a random access memory (RAM) or other dynamic storage device, coupled to the bus 102 for storing information and instructions executed by the processor 104. The main memory 106 may also be used to store temporary variables or other intermediate information during execution of instructions executed by the processor 104. The computer system 100 further includes a read-only memory (ROM) 108, or other static storage device, coupled to the bus 102 for storing static information and instructions for the processor 104. A storage device 110, such as a magnetic or optical disk, for storing information and instructions is provided and coupled to the bus 102.

[0191]

[0218] The computer system 100 may be coupled via bus 102 to a display 112, such as a cathode ray tube (CRT), flat panel, or touch panel display, for displaying information to a computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 for communicating information and command selections to the processor 104. Another type of user input device is a cursor control 116, such as a mouse, trackball, or cursor direction keys, for communicating directional information and command selections to the processor 104 and for controlling cursor movement on the display 112. This input device typically has two degrees of freedom in two axes, a first axis (e.g., x) and a second axis (e.g., y), allowing the device to be positioned in a plane. A touch panel (screen) display may also be used as an input device.

[0192]

[0219] According to an embodiment, portions of the optimization process may be performed by the computer system 100 in response to the processor 104 executing one or more sequences of one or more instructions contained in the main memory 106. Such instructions may be read into the main memory 106 from another computer-readable medium, such as the storage device 110. Execution of the sequences of instructions contained in the main memory 106 causes the processor 104 to perform the process steps described herein. One or more processors in a multi-processing arrangement may be used to execute the sequences of instructions contained in the main memory 106. In an alternative embodiment, hardwired circuitry may be used in place of or in combination with software instructions. Thus, the description herein is not limited to any specific combination of hardware circuitry and software.

[0193]

[0220] The term "computer-readable medium" as used herein refers to any medium that participates in providing instructions to the processor 104 for execution. Such media may take many forms, including but not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks, such as the storage device 110. Volatile media include dynamic memory, such as the main memory 106. Transmission media include coaxial cables, copper wire and fiber optics (including the wires that comprise the bus 102). Transmission media may also take the form of acoustic or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tape, other magnetic media, CD-ROMs, DVDs, other optical media, punch cards, paper tape, other physical media with patterns of holes, RAM, PROMs, and EPROMs, FLASH-EPROMs, other memory chips or cartridges, carrier waves as described below, or other media from which a computer can read.

[0194]

[0221] Various forms of computer readable media may be involved in carrying one or more sequences of one or more instructions to the processor 104 for execution. For example, the instructions may initially reside on a magnetic disk of a remote computer. The remote computer may load the instructions into its dynamic memory and send the instructions over a telephone line using a modem. A modem local to the computer system 100 may receive the data on the telephone line and use an infrared transmitter to convert the data to an infrared signal. An infrared detector coupled to the bus 102 may receive the data carried in the infrared signal and place the data on the bus 102. The bus 102 carries the data to the main memory 106, from which the processor 104 reads and executes the instructions. The instructions received by the main memory 106 may optionally be stored on a storage device 110 either before or after execution by the processor 104.

[0195]

[0222] Computer system 100 also preferably includes a communications interface 118 coupled to bus 102. Communications interface 118 also provides a two-way data communication coupling to a network link 120 that is connected to a local network 122. For example, communications interface 118 may be an Integrated Services Digital Network (ISDN) card or a modem to provide a data communication connection to a corresponding type of telephone line. As another example, communications interface 118 may be a Local Area Network (LAN) card to provide a data communication connection to a compatible LAN. A wireless link may also be implemented. In such an implementation, communications interface 118 sends and receives electrical, electromagnetic or optical signals that carry digital data streams representing various types of information.

[0196]

[0223] Network link 120 typically provides data communication through one or more networks to other data devices. For example, network link 120 may provide a connection through a local network 122 to a host computer 124 or to data equipment operated by an Internet Service Provider (ISP) 126. ISP 126 in turn provides data communication services through a world wide packet data communication network (now commonly referred to as the "Internet" 128). Local network 122 and Internet 128 both use electrical, electromagnetic or optical signals that carry digital data streams. The signals through the various networks and the signals on network link 120 and through communication interface 118, which carry the digital data to and from computer system 100, are exemplary forms of carrier waves transporting the information.

[0197]

[0224] Computer system 100 can send messages and receive data, including program code, through one or more networks, network link 120, and communication interface 118. In the Internet example, server 130 might send a requested code for an application program through Internet 128, ISP 126, local network 122, and communication interface 118. One such downloaded application may provide, for example, the lighting optimization of the embodiment. The received code may be executed by processor 104 as received, and / or stored in storage device 110 or other non-volatile storage for later execution. In this manner, computer system 100 may obtain application code in the form of a carrier wave.

[0198]

[0225] 23 illustrates a schematic diagram of an exemplary lithographic projection apparatus, the illumination radiation source of which may be optimized using the methods described herein. The apparatus includes: an illumination system IL, for conditioning a beam of radiation B. In this particular case, the illumination system also includes a radiation source SO. - a first object table (e.g. mask table) MT provided with a patterning device holder for holding a patterning device MA (e.g. reticle) and connected to a first positioner for accurately positioning the patterning device relative to the item PS. a second object table (substrate table) WT provided with a substrate holder for holding a substrate W (e.g. a resist-coated silicon wafer) and connected to a second positioner for accurately positioning the substrate relative to the item PS. - a projection system ("lens") PS (e.g. a refractive, reflective or catadioptric system) for imaging an irradiated portion of the patterning device MA onto a target portion C (e.g. comprising one or more dies) of the substrate W.

[0199]

[0226] As here depicted, the apparatus is of a transmissive type (i.e. has a transmissive mask). However, in general, the apparatus may be of a reflective type, for example (with a reflective mask). Alternatively, the apparatus may employ another type of patterning device as an alternative to the classical use of a mask. Examples include a programmable mirror array or an LCD matrix.

[0200]

[0227] A source SO (e.g. a mercury lamp or excimer laser) produces a beam of radiation. This beam is fed to an illumination system (illuminator) IL, either as is or after having traversed conditioning means, such as a beam expander Ex. The illuminator IL may comprise conditioning means AD for setting the outer and / or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution of the beam. Furthermore it will generally comprise various other components, such as an integrator IN and a condenser CO. In this way, the beam B impinging on the patterning device MA has a desired uniformity and intensity distribution in its cross-section.

[0201]

[0228] It should be noted, with regard to Figure 23, that the source SO may be located within the housing of the lithographic projection apparatus (as is often the case when the source SO is, for example, a mercury lamp), but it may also be remote from the lithographic projection apparatus and the radiation beam it generates may be directed into the apparatus (for example by the use of appropriate directing mirrors). This latter scenario is often the case when the source SO is an excimer laser (for example based on KrF, ArF or F2 lasing).

[0202]

[0229] The beam PB subsequently intersects the patterning device MA, which is held on a patterning device table MT. After traversing the patterning device MA, the beam B passes through a lens PL which focuses the beam B onto a target portion C of the substrate W. Using the second positioning means (and interferometric measurement means IF), the substrate table WT can be precisely moved, e.g. to position a different target portion C in the path of the beam PB. Similarly, the first positioning means can be used to precisely position the patterning device MA with respect to the path of the beam B, e.g. after mechanical retrieval of the patterning device MA from a patterning device library or during a scan. In general, movement of the object tables MT, WT is realized using a long-stroke module (coarse positioning) and a short-stroke module (fine positioning), which are not explicitly depicted in Fig. 23. However, in the case of a wafer stepper (as opposed to a step-and-scan tool) the patterning device table MT may be connected to a short-stroke actuator only or may be fixed.

[0203]

[0230] The depicted tools can be used in two different modes: in step mode, the patterning device table MT remains essentially stationary and the entire patterning device image is projected onto the target portion C in one go (i.e. in a single "flash"), and the substrate table WT is then shifted in the x and / or y directions so that a different target portion C can be irradiated by the beam PB; In scan mode, essentially the same scenario applies, except that a given target portion C is not exposed in a single "flash". Instead, the patterning device table MT is movable in a given direction (the so-called "scan direction", e.g. the y direction) with a speed v, such that the projection beam B is caused to scan over the patterning device image. In parallel, the substrate table WT is simultaneously moved in the same or opposite direction with a speed V = Mv, in which M is the magnification factor of the lens PL (typically M = 1 / 4 or 1 / 5). In this way, a relatively large target portion C can be exposed, without having to compromise on resolution.

[0204]

[0231] FIG. 24 depicts diagrammatically another exemplary lithographic projection apparatus LA, the illumination source of which may be optimized utilizing the methods described herein.

[0205]

[0232] The lithographic projection apparatus LA includes: - Source collector module SO - an illumination system (illuminator) IL configured to condition a radiation beam B (eg EUV radiation). - a support structure (e.g. mask table) MT constructed to support a patterning device (e.g. mask or reticle) MA and connected to a first positioner PM configured to accurately position the patterning device; a substrate table (e.g., a wafer table) WT constructed to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate; and a projection system (eg a reflective projection system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (eg comprising one or more dies) of the substrate W.

[0206]

[0233] As depicted here, the apparatus LA is reflective (e.g., using a reflective mask). Note that since most materials are absorbing in the EUV wavelength range, the mask can have a multi-layer reflector including, for example, a multi-stack of molybdenum and silicon. In one example, a multi-stack reflector has 40 layer pairs of molybdenum and silicon, with each layer being a quarter wavelength thick. Even smaller wavelengths can be produced using x-ray lithography. Since most materials are absorbing at EUV and x-ray wavelengths, a thin strip of patterned absorbing material (e.g., TaN absorber on a multi-layer reflector) on the patterning device topography defines where features will or will not be printed (positive resist) or printed (negative resist).

[0207]

[0234] Referring to FIG. 24, the illuminator IL receives an extreme ultraviolet radiation beam from a source collector module SO. Methods of generating EUV radiation include, but are not necessarily limited to, converting a material into a plasma state having at least one element (e.g., xenon, lithium, or tin) with one or more emission lines in the EUV range. In one such method, often referred to as laser-produced plasma ("LPP"), the plasma may be generated by irradiating a fuel, such as droplets, streams, or clusters of a material having a line-emitting element, with a laser beam. The source collector module SO may be part of an EUV radiation system that includes a laser (not shown in FIG. 24) that provides a laser beam that excites the fuel. The resulting plasma emits output radiation (e.g., EUV radiation), which is collected using a radiation collector disposed in the source collector module. The laser and the source collector module may be separate entities, for example, when a CO2 laser is used to provide the laser beam for fuel excitation.

[0208]

[0235] In such cases, the laser is not considered to form part of the lithographic apparatus, and the radiation beam is passed from the laser to the source collector module using a beam delivery system including, for example, appropriate directing mirrors and / or beam expanders. In other cases, the source may be an integral part of the source collector module, for example when the source is a discharge produced plasma EUV generator, often referred to as a DPP source.

[0209]

[0236] The illuminator IL may include an adjuster for adjusting the angular intensity distribution of the radiation beam. Typically, at least the outer and / or inner radial extent (commonly referred to as σ-outer and σ-inner, respectively) of the intensity distribution in a pupil plane of the illuminator may be adjusted. In addition, the illuminator IL may include various other components, such as facetted field and pupil mirror devices. The illuminator may be used to condition the radiation beam to have a desired uniformity and intensity distribution in its cross-section.

[0210]

[0237] The radiation beam B is incident on a patterning device (e.g. mask) MA, which is held on a support structure (e.g. mask table) MT, and is patterned by the patterning device. After being reflected from the patterning device (e.g. mask) MA, the radiation beam B passes through a projection system PS, which focuses the beam onto a target portion C of the substrate W. Using a second positioner PW and a position sensor PS2 (e.g. an interferometric device, a linear encoder or a capacitive sensor), the substrate table WT can be accurately moved, for example to position a different target portion C in the path of the radiation beam B. Similarly, using a first positioner PM and another position sensor PS1, the patterning device (e.g. mask) MA can be accurately positioned with respect to the path of the radiation beam B. The patterning device (e.g. mask) MA and substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0211]

[0238] The depicted apparatus LA could be used in at least one of the following modes: 1. In step mode, the support structure (e.g. mask table) MT and substrate table WT remain essentially stationary while an entire pattern imparted to the radiation beam is projected onto a target portion C in one go (i.e. a single static exposure), and the substrate table WT is then shifted in the X and / or Y directions so that a different target portion C can be exposed. 2. In scan mode, the support structure (e.g. mask table) MT and the substrate table WT are scanned synchronously (i.e. a single dynamic exposure) while a pattern imparted to the radiation beam is projected onto a target portion C. The velocity and direction of the substrate table WT relative to the support structure (e.g. mask table) MT may be determined by the de-magnification and image reversal characteristics of the projection system PS. 3. In another mode, the support structure (e.g. mask table) MT remains essentially stationary holding a programmable patterning device and the substrate table WT is moved or scanned while a pattern imparted to the radiation beam is projected onto a target portion C. In this mode, a pulsed radiation source is typically used and the programmable patterning device is updated as required after each movement of the substrate table WT, or between successive radiation pulses during a scan. This mode of operation can readily be applied to maskless lithography employing a programmable patterning device such as a programmable mirror array of the type referred to above.

[0212]

[0239] FIG. 25 shows the apparatus LA in more detail, including the source collector module SO, the illumination system IL, and the projection system PS. The source collector module SO is constructed and arranged such that a vacuum environment can be maintained within the closed structure 220 of the source collector module SO. The EUV radiation emitting plasma 210 can be formed by a discharge-produced plasma source. The EUV radiation can be generated by a gas or vapor, for example Xe gas, Li vapor, or Sn vapor, from which a very hot plasma 210 is created to emit radiation in the EUV range of the electromagnetic spectrum. The very hot plasma 210 is created, for example, by an electric discharge that produces an at least partially ionized plasma. A partial pressure of, for example, 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor, can be required for efficient generation of radiation. In an embodiment, a plasma of excited tin (Sn) is provided to generate the EUV radiation.

[0213]

[0240] Radiation emitted by the high temperature plasma 210 passes from the source chamber 211 into the collector chamber 212 through an optional gas barrier or contaminant trap 230 (sometimes also called a contaminant barrier or foil trap) located in or behind the opening of the source chamber 211. The contaminant trap 230 may include a channel structure. The contaminant trap 230 may also include a gas barrier or a combination of a gas barrier and a channel structure. The contaminant trap or contaminant barrier 230 as further illustrated herein includes at least a channel structure, as known in the art.

[0214]

[0241] The collector chamber 211 may include a radiation collector CO, which may be a so-called grazing incidence collector. The radiation collector CO has an upstream radiation collector side 251 and a downstream radiation collector side 252. Radiation traversing the collector CO may be reflected off a grating spectral filter 240 and focused to a virtual source point IF along an optical axis indicated by dashed-dotted line "O". The virtual source point IF is commonly referred to as an intermediate focus, and the source collector module is positioned such that the intermediate focus IF is at or near the opening 221 of the enclosure structure 220. The virtual source point IF is an image of the radiation emitting plasma 210.

[0215]

[0242] The radiation subsequently traverses the illumination system IL, which may include a faceted field mirror device 22 and a facetted pupil mirror device 24 arranged to provide a desired angular distribution of the radiation beam 21 at the patterning device MA, and a desired uniformity of the radiation intensity at the patterning device MA. Upon reflection of the radiation beam 21 off the patterning device MA, held by the support structure MT, a patterned beam 26 is formed, and the patterned beam 26 is imaged by the projection system PS via reflective elements 28, 30 onto the substrate W, held by the substrate table WT.

[0216]

[0243] Generally, more elements than shown may be present in the illumination optics unit IL and projection system PS. A grating spectral filter 240 may optionally be present, depending on the type of lithographic apparatus. Furthermore, there may be more mirrors than shown in the drawings, for example 1 to 6 additional reflective elements may be present in the projection system PS than shown in Figure 25.

[0217]

[0244] 25 is depicted as a nested collector with grazing incidence reflectors 253, 254, and 255, just as 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 system CO is preferably used in combination with a discharge produced plasma source, often referred to as a DPP source.

[0218]

[0245] Alternatively, the source collector module SO may be part of an LPP radiation system, as shown in Fig. 26. The laser LA is arranged to deposit laser energy into a fuel, such as xenon (Xe), tin (Sn) or lithium (Li), generating a highly ionized plasma 210 with an electron temperature of a few tens of eV. Energetic radiation generated during de-excitation and recombination of these ions is emitted from the plasma, collected by a near-normal incidence collector system CO and focused onto an opening 221 of a closing structure 220.

[0219]

[0246] The concepts disclosed herein can be used to simulate or mathematically model general imaging systems for imaging sub-wavelength features, and can be particularly useful for new imaging technologies capable of producing ever-shorter wavelengths. New technologies already in use include EUV (extreme ultraviolet), DUV lithography capable of producing wavelengths of 193 nm using ArF lasers, and even 157 nm using fluorine lasers. EUV lithography can also produce wavelengths in this range by using synchrotrons or by bombarding materials (solids or plasmas) with high energy electrons to produce photons in the 20-5 nm range.

[0220]

[0247] The embodiments may be further described using the following clauses. 1. A method for training a patterning process model, the patterning process model configured to predict a pattern that will be formed during a patterning process, the method comprising: obtaining (i) image data associated with a desired pattern; (ii) a measured pattern of a substrate, the measured pattern being associated with the desired pattern; (iii) a first model associated with one aspect of the patterning process, the first model comprising a first set of parameters; and (iv) a machine learning model associated with another aspect of the patterning process, the first model comprising a second set of parameters; and iteratively determining values ​​of the first set of parameters and the second set of parameters to train the patterning process model, the iterations including: using the image data to execute the first model and the machine learning model to jointly predict a printed pattern of the substrate; and modifying values ​​of the first set of parameters and the second set of parameters such that a difference between the measured pattern and the predicted pattern of the patterning process model is reduced. 2. The method of claim 1, wherein the first model and the machine learning model are constructed and trained in a convolutional deep neural network framework. 3. The above training is predicting the printed pattern by forward propagation of outputs of the first model and the machine learning model; determining a difference between the measured pattern and the predicted pattern of the patterning process model; determining said difference between said first and second sets of parameters; The method of claim 2, comprising determining values ​​of the first set of parameters and the second set of parameters by backpropagating the outputs of the first model and the machine learning model based on the difference of the differences. 4. A method according to any one of clauses 1 to 3, wherein the first model is connected to the machine learning model in a serial or parallel combination. 5. The above series combination of the above models is 5. The method of claim 4, comprising providing an output of the first model as an input to the machine learning model. 6. The above series combination of the above models is 5. The method of claim 4, comprising providing an output of the machine learning model as an input to the first model. 7. The above parallel combination of the above models is providing identical inputs to the first model and to the machine learning model; combining outputs of the first model and the machine learning model; and and determining the predicted printing pattern based on the combined output of each model. 8. The method of any one of clauses 1 to 7, wherein the first model is a resist model and / or a spatial model. 9. The first set of parameters of the resist model: Initial acid distribution, Acid diffusion, Image contrast, Long distance pattern loading effect, Long distance pattern loading effect, Acid concentration after neutralization, Base concentration after neutralization, Diffusion due to high acid concentration, Diffusion due to high base concentration, Resist shrinkage, Resist development, or 9. The method of claim 8, wherein the method corresponds to at least one of: a two-dimensional convex curvature effect. 10. The method of any one of clauses 1 to 9, wherein the first model is an empirical model that accurately models the physical phenomena of the first aspect of the patterning process. 11. The method of any one of clauses 1 to 10, wherein the first model corresponds to the first aspect relating to diffusion of an acid base after exposure of the substrate. 12. The method of any one of clauses 1-9, wherein the machine learning model is a neural network that models a second aspect of the patterning process that is relatively poorly understood based on physics. 13. The method of claim 12, wherein the second set of parameters includes weights and biases for one or more layers of the neural network. 14. The method of any one of clauses 1 to 13, wherein the patterning process model corresponds to the second aspect of a post-exposure process of the patterning process. 15. The method of any one of clauses 1 to 14, wherein the first aspect and / or the second aspect of the post-exposure process comprises resist baking, resist developing, and / or etching. 16. A method for determining an optical proximity correction for a patterning process, comprising: acquiring image data associated with a desired pattern; using the image data to run a trained patterning process model to predict the pattern to be printed on the substrate; and determining optical proximity corrections and / or defects using the predicted pattern to be printed on the substrate subjected to the patterning process. 17. The method of claim 16, wherein the image data is an aerial image and / or a mask image of the desired pattern. 18. The method of claim 16, wherein the trained patterning process model includes a first model of a first aspect of the patterning process and a machine learning model of a second aspect of the patterning process configured to jointly predict the pattern to be printed on the substrate. 19. The method of claim 18, wherein the first model and the machine learning model are in a serial and / or parallel combination. 20. A method according to any one of clauses 16 to 19, wherein the first model is an empirical model that accurately models the physical phenomena of the first aspect of a post-exposure process of the patterning process. 21. The method of any one of clauses 16 to 20, wherein the first model corresponds to the first aspect relating to diffusion of an acid base after exposure of the substrate. 22. The method of any one of clauses 16 to 21, wherein the machine learning model is a neural network that models the second aspect of the patterning process that is relatively poorly understood in a physics-based manner. 23. The step of determining the optical proximity correction comprises: 23. The method of any one of clauses 16 to 22, comprising adjusting the desired pattern and / or placing assist features around the desired pattern such that a difference between the predicted pattern and the desired pattern is reduced. 24. The determination of the above deficiencies is 23. The method of any one of clauses 16 to 22, comprising performing a lithographic manufacturability check on the predicted pattern. 25. A method for training a machine learning model configured to determine an etching bias associated with an etching process, comprising: Obtaining (i) resist pattern data associated with a target pattern to be printed on a substrate, (ii) physical effect data characterizing an effect of the etch process on the target pattern, and (iii) a measured bias between the resist pattern and an etch pattern formed on the printed substrate; training the machine learning model based on the resist pattern data, the physical effects data, and the measured bias to reduce a difference between the measured bias and the predicted etch bias. 26. The method of claim 25, wherein the machine learning model is configured to receive the resist pattern data at a first layer of the machine learning model, and the physical effect data is received at a last layer of the machine learning model. 27. The method of claim 26, wherein the output of the final layer is a linear combination of (i) the etch bias predicted by running the machine learning model using the resist pattern data as input, and (ii) another etch bias determined based on the physical effects data related to the etch process. 28. The output of the last layer is an etch bias map, from which the etch bias is extracted, the etch bias map being running the machine learning model using the resist pattern data as input to output an etch bias map, the etch bias map including a biased resist pattern; and 28. The method of claim 27, wherein the etch bias map is generated by combining the etch bias map with the physical effects data. 29. The method of claim 28, wherein the machine learning model is configured to receive the resist pattern data and the physical effect data at the first layer of the machine learning model. 30. Training the machine learning model (a) predicting the etch bias by executing the machine learning model using the resist pattern data and the physical effects data as input; (b) determining the difference between the measured bias and the predicted etch bias; and (c) determining a gradient of the difference with respect to model parameters of the machine learning model; and (d) using the gradient as a guide, adjusting values ​​of model parameters such that the difference between the measured bias and the predicted etch bias is reduced; and (e) determining whether the difference has been minimized or exceeded a training threshold; and (f) in response to the difference not being minimized or the training threshold not being exceeded, performing steps (a) to (e). 31. The acquiring of the resist pattern data includes: 31. The method of any one of clauses 25 to 30, comprising running one or more process models including a resist model of the patterning process using the target pattern to be printed on the substrate. 32. The method of any one of clauses 25 to 31, wherein the resist pattern data is represented as a resist image, the resist image being a pixelated image. 33. The physical effect data is data related to an etching term that characterizes an etching effect, the etching term being: a concentration of plasma within the trenches of the resist pattern associated with the target pattern; a concentration of plasma on top of a resist layer of the substrate; The loading effect, which is determined by convolving the resist pattern with a Gaussian Kernel having specific model parameters; Changes in the loading effect on the resist pattern during the etching process; the relative position of the resist pattern with respect to adjacent patterns on the substrate; The aspect ratio of the resist pattern, or 33. The method of any one of clauses 25-32, including at least one of the following terms related to the combined effect of two or more etching process parameters. 34. The obtaining of the physical effect data comprises: 34. The method of any one of clauses 25 to 33, comprising executing a physical effects model comprising one or more of the etching terms and a Gaussian kernel defined for each of the one or more of the etching terms. 35. A method according to any one of clauses 25 to 34, wherein the physical effect data is represented as a pixelated image, each pixel intensity being indicative of a physical effect on the resist pattern associated with the target pattern. 36. Obtaining a resist contour of the resist pattern; 36. The method of any one of claims 25 to 35, further comprising: generating an etching contour by applying the etching bias to the resist contour. 37. A system for determining an etching bias associated with an etching process, comprising: Semiconductor processing equipment, and 1. A processor comprising: executing a physical effects model to determine physical effects data characterizing an effect of the etch process on a substrate; running a trained machine learning model using the resist pattern and the physical effects data as inputs to determine the etch bias; a processor configured to control the semiconductor device or the etching process based on the etching bias. 38. The system of clause 37, wherein the trained machine learning model is trained using a plurality of resist patterns, the physical effect data associated with each resist pattern of the plurality of resist patterns, and the measured bias associated with each resist pattern, such that a difference between the measured bias and the determined etch bias is minimized. 39. The system of any one of clauses 37-38, wherein the trained machine learning model is a convolutional neural network (CNN) including specific weights and biases, and the weights and biases of the CNN are determined via a training process using the plurality of resist patterns, the physical effect data associated with each resist pattern of the plurality of resist patterns, and the measured biases associated with each resist pattern, such that a difference between the measured biases and the determined etch bias is minimized. 40. The control of the semiconductor processing apparatus is 40. The system of any one of clauses 37 to 39, comprising adjusting values ​​of one or more parameters of the semiconductor device such that a yield of the patterning process is improved. 41. The adjusting of the value of the one or more parameters of the semiconductor processing apparatus comprises: (a) modifying a current value of the one or more parameters via an adjustment mechanism of the semiconductor processing equipment; (b) obtaining the resist pattern printed on a substrate via the semiconductor processing apparatus; and (c) determining the etch bias by executing the trained machine learning model using the resist pattern, and further determining the etch pattern by applying the etch bias to the resist pattern; (d) determining whether the yield of the patterning process is within a desired yield range based on the etch pattern; and and in response to not being within the yield range, performing steps (a)-(d). 42. The control of the etching process is determining the etch pattern by applying the etch bias to the resist pattern; determining the yield of the patterning process based on the etch pattern; and determining an etching recipe for the etching process based on the etching pattern, such that the yield of the patterning process is improved. 43. The system of any one of clauses 37-42, wherein the yield of the patterning process is the percentage of etched patterns across the substrate that meet design specifications. 44. A system according to any one of clauses 37 to 43, wherein the semiconductor processing equipment is a lithography equipment. 45. A method for calibrating a process model, the process model being configured to generate a simulated contour, the method comprising: (i) acquiring measurement data at a plurality of measurement locations on a pattern; and (ii) a contour constraint defined based on the measurement data; and calibrating the process model by adjusting values ​​of model parameters of the process model until the simulated contour satisfies the contour constraint. 46. ​​The method of claim 45, wherein the plurality of measurement locations are edge placement (EP) gauges positioned on the printed pattern or on a printed contour of the printed pattern. 47. A method according to any one of clauses 45 to 46, wherein the measurement data includes a plurality of angles, each angle being defined at a respective measurement location located on the pattern or on the printed contour of the printed pattern. 48. The method of claim 47, wherein each angle at each measurement location defines a direction for determining an edge placement error between the printed contour and a target contour. 49. A method according to any one of clauses 45 to 48, wherein each contour constraint is a function of the tangent angle between a tangent to the simulated contour at a given measurement location and the angle of the measurement data at the given location. 50. Adjusting the values ​​of the model parameters (a) running the process model using given values ​​of the model parameters to generate the simulated contour, the given values ​​being random values ​​in a first iteration and adjusted values ​​in subsequent iterations; (c) determining a tangent to the simulated contour at each of the measurement locations; and (d) determining a tangent angle between the tangent line and the angle of the measurement data at each of the measurement locations; (e) determining whether the tangent angle is within a normal range at one or more of the measurement locations; and (f) in response to the tangent angle not being within a normal range, adjusting the value of the model parameter and performing steps (a) to (d). 51. The method according to any one of clauses 45 to 50, wherein the vertical range is an angle value between 88° and 92°, preferably 90°. 52. A method according to any one of clauses 45 to 51, wherein the adjusting is based on the gradient of each tangent angle with respect to the model parameter, the gradient indicating how sensitive the tangent angle is to changes in model parameter value. 53. The method of any one of clauses 45 to 52, wherein the process model is a data-driven model, including an empirical model and / or a machine learning model. 54. A method according to any one of clauses 45 to 53, wherein the machine learning model is a convolutional neural network and the model parameters are weights and biases associated with multiple layers. 55. A method for calibrating a process model configured to predict an image of a target pattern, comprising: (i) obtaining a reference image associated with the target pattern; and (ii) a gradient constraint defined with respect to the reference image; (i) minimizing intensity or frequency differences between a simulated image and the reference image; and (ii) calibrating the process model such that the process model produces the simulated image that satisfies the gradient constraint. 56. The calibration of the process model is (a) executing the process model using the target pattern to generate the simulated image; (b) determining the intensity difference between intensity values ​​of the simulated image and intensity values ​​of the reference image, and / or transforming the simulated image and the reference image into the frequency domain via a Fourier transform and determining the frequency difference between frequencies associated with the simulated image and frequencies associated with the reference image; (c) determining a simulated gradient of a signal in the simulated image, the signal being along a given line passing through the simulated image; and (d) determining whether the conditions: (i) the intensity difference or the frequency difference is minimized; and (ii) the simulated gradients satisfy the gradient constraints associated with the reference image; (e) in response to conditions (i) and (ii) not being satisfied, adjusting values ​​of model parameters of the process model, and performing steps (a)-(d) until conditions (i) and (ii) are satisfied. 57. A method according to any one of clauses 55 to 56, wherein the simulated gradient is determined by taking the first derivative of the signal along the given line passing through the simulated image. 58. A method according to any one of clauses 55 to 57, wherein the gradient constraint is obtained by taking the first derivative of the signal along the given line passing through the reference image. 59. Extracting a simulated contour from the simulated image and a reference contour from the reference image, the simulated contour and the reference contour being associated with the target pattern; and 59. The method of any one of clauses 55 to 58, further comprising: calibrating the process model so that the simulated contour satisfies a contour shape constraint, the contour shape constraint ensuring that the simulated contour matches a shape of the reference contour. 60. Determining whether the contour shape constraint is satisfied comprises: 60. A method according to any one of clauses 55 to 59, comprising determining that a second derivative of the simulated contour is within a desired range of a second derivative of the reference contour. 61. The reference image is obtained by simulating a physics-based model of a patterning process using the target pattern, and the reference image is an aerial image of the target pattern; A resist image of the target pattern, and / or 61. The method of any one of clauses 55 to 60, including an etched image of the target pattern. 62. A method according to any one of clauses 55 to 61, wherein the process model is configured to satisfy a contour constraint defined in relation to a printed contour of a pattern on a printed substrate. 63. A method according to any one of clauses 55 to 62, wherein each contour constraint is a function of a tangent angle between a tangent to a simulated contour at a given measurement location and the angle of the measurement data at the given location, where the simulated contour is a contour of the simulated pattern determined via execution of the process model using the target pattern. 64. A system for calibrating a process model, the process model being configured to generate a simulated contour, the system comprising: a metrology tool configured to acquire measurement data at a plurality of measurement locations on the pattern; 1. A processor comprising: and a processor configured to calibrate the process model by adjusting values ​​of model parameters of the process model until the simulated contour satisfies the contour constraint, the contour constraint being based on the measured data. 65. The system of claim 64, wherein the plurality of measurement locations are edge placement (EP) gauges positioned on the printed pattern or on a printed contour of the printed pattern. 66. A system described in any one of clauses 64 to 65, wherein the measurement data includes a plurality of angles, each angle being defined at each measurement location located on the pattern or on the printed contour of the printed pattern. 67. The system of clause 66, wherein each angle at each measurement location defines a direction for determining an edge placement error between the printed contour and a target contour. 68. A system described in any one of clauses 64 to 67, wherein each contour constraint is a function of a tangent angle between a tangent to the simulated contour at a given measurement location and the angle of the measurement data at the given location. 69. The adjusting of the values ​​of the model parameters comprises: (a) running the process model using given values ​​of the model parameters to generate the simulated contour, the given values ​​being random values ​​in a first iteration and adjusted values ​​in subsequent iterations; (c) determining a tangent to the simulated contour at each of the measurement locations; and (d) determining a tangent angle between the tangent line and the angle of the measurement data at each of the measurement locations; (e) determining whether the tangent angle is within a normal range at one or more of the measurement locations; and (f) in response to the tangent angle not being within a vertical range, adjusting the value of the model parameter and performing steps (a) to (d). 70. A system according to any one of clauses 64 to 69, wherein the vertical range has an angle value between 88° and 92°, preferably 90°. 71. A system described in any one of clauses 64 to 70, wherein the adjusting is based on the gradient of each tangent angle with respect to the model parameter, the gradient indicating how sensitive the tangent angle is to changes in model parameter value. 72. The system of any one of clauses 64 to 71, wherein the process model is a data-driven model, including an empirical model and / or a machine learning model. 73. The system of any one of clauses 64 to 72, wherein the machine learning model is a convolutional neural network and the model parameters are weights and biases associated with multiple layers. 74. A system as described in any one of clauses 64 to 73, wherein the metrology tool is an electron beam device. 75. A system described in any one of clauses 64 to 74, wherein the metrology tool is a scanning electron microscope configured to identify and extract contours from a captured image of a pattern on a printed substrate. 76. A system for calibrating a process model configured to predict an image of a target pattern, comprising: a metrology tool configured to acquire a reference image associated with the target pattern; 1. A processor comprising: and a processor configured to: (i) minimize intensity or frequency differences between a simulated image and the reference image; and (ii) calibrate the process model such that the process model produces the simulated image that satisfies a gradient constraint relative to the reference image. 77. The calibration of the process model is (a) executing the process model using the target pattern to generate the simulated image; (b) determining the intensity difference between intensity values ​​of the simulated image and intensity values ​​of the reference image, and / or transforming the simulated image and the reference image into the frequency domain via a Fourier transform and determining the frequency difference between frequencies associated with the simulated image and frequencies associated with the reference image; (c) determining a simulated gradient of a signal in the simulated image, the signal being along a given line passing through the simulated image; and (d) determining whether the conditions: (i) the intensity difference or the frequency difference is minimized; and (ii) the simulated gradients satisfy the gradient constraints associated with the reference image; (e) in response to conditions (i) and (ii) not being satisfied, adjusting values ​​of model parameters of the process model, and performing steps (a)-(d) until conditions (i) and (ii) are satisfied. 78. A system described in any one of clauses 76-77, wherein the simulated gradient is determined by taking the first derivative of the signal along the given line passing through the simulated image. 79. A system according to any one of clauses 76 to 78, wherein the gradient constraint is obtained by taking the first derivative of the signal along the given line passing through the reference image. 80. The processor further comprises: configured to extract a simulated contour from the simulated image and a reference contour from the reference image, where the simulated contour and the reference contour are associated with the target pattern; The system of any one of clauses 76 to 79, further configured to calibrate the process model so that the simulated contour satisfies a contour shape constraint, wherein the contour shape constraint ensures that the simulated contour matches a shape of the reference contour. 81. Determining whether the contour shape constraint is satisfied comprises: 81. The system of any one of clauses 76 to 80, comprising determining that a second derivative of the simulated contour is within a desired range of a second derivative of the reference contour. 82. The reference image is obtained by simulating a physics-based model of a patterning process using the target pattern, and the reference image is an aerial image of the target pattern; A resist image of the target pattern, and / or 82. The system of any one of clauses 76-81, including an etched image of the target pattern. 83. A system according to any one of clauses 76 to 82, wherein the process model is configured to satisfy a contour constraint defined with respect to a printed contour of a pattern on a printed substrate. 84. A system described in any one of clauses 76 to 83, wherein each contour constraint is a function of a tangent angle between a tangent to a simulated contour at a given measurement location and the angle of the measurement data at the given location, where the simulated contour is a contour of the simulated pattern determined via execution of the process model using the target pattern. 85. A non-transitory computer-readable medium containing instructions that, when executed by one or more processors, Obtaining (i) resist pattern data associated with a target pattern to be printed on a substrate, (ii) physical effect data characterizing the effect of an etch process on the target pattern, and (iii) a measured bias between the resist pattern and an etch pattern formed on the printed substrate; training the machine learning model based on the resist pattern data, the physical effects data, and the measured bias to reduce a difference between the measured bias and the predicted etch bias. 86. A non-transitory computer-readable medium containing instructions that, when executed by one or more processors, (i) acquiring measurement data at a plurality of measurement locations on a pattern; and (ii) a contour constraint defined based on the measurement data; calibrating a process model by adjusting values ​​of model parameters of the process model until the simulated contour satisfies the contour constraint. 87. A non-transitory computer-readable medium containing instructions that, when executed by one or more processors, (i) obtaining a reference image associated with a target pattern; and (ii) a gradient constraint defined with respect to the reference image; A non-transitory computer-readable medium that causes operations including: (i) minimizing an intensity or frequency difference between a simulated image and the reference image; and (ii) calibrating the process model such that the process model produces the simulated image that satisfies the gradient constraint.

[0221]

[0248] The concepts disclosed herein may be used for imaging on substrates such as silicon wafers, although it is understood that the disclosed concepts may be used in any type of lithographic imaging system (e.g., those used for imaging on substrates other than silicon wafers).

[0222]

[0249] The above description is intended to be illustrative and not limiting. Thus, it will be apparent to one skilled in the art that modifications can be made as described without departing from the scope of the claims set forth below.

Claims

1. 1. A method for training a machine learning model configured to determine an etch bias associated with an etch process, comprising: Obtaining (i) resist pattern data associated with a target pattern to be printed on a substrate, (ii) physical effect data characterizing the effect of the etch process on the target pattern, and (iii) a measured bias between the resist pattern and an etch pattern formed on the printed substrate; training the machine learning model based on the resist pattern data, the physical effects data, and the measured bias to reduce a difference between the measured bias and an etch bias predicted by the trained machine learning model; 11. The method of claim 10, wherein the machine learning model is configured to receive the resist pattern data at one layer of the machine learning model and the physical effect data at another layer of the machine learning model.

2. The method of claim 1, wherein the output of the final layer of the machine learning model is a linear combination of (i) the etch bias predicted by running the machine learning model using the resist pattern data as input, and (ii) another etch bias determined based on the physical effects data related to the etching process.

3. The output of the final layer is an etch bias map from which the etch bias is extracted, the etch bias map being running the machine learning model using the resist pattern data as input to output an etch bias map, the etch bias map including a biased resist pattern; and The method of claim 2 , wherein the etch bias map is generated by combining the etch bias map with the physical effects data.

4. 4. The method of claim 3, wherein the machine learning model is configured to receive the resist pattern data and the physical effects data for the one layer of the machine learning model.

5. Training the machine learning model includes: (a) predicting the etch bias by running the machine learning model using the resist pattern data and the physical effects data as input; (b) determining the difference between the measured bias and the predicted etch bias; and (c) determining a gradient of the difference with respect to a model parameter of the machine learning model; and (d) using the gradient as a guide, adjusting values ​​of model parameters such that the difference between the measured bias and the predicted etch bias is reduced; and (e) determining whether the difference has been minimized or exceeded a training threshold; (f) in response to the difference not being minimized or the training threshold not being exceeded, performing steps (a)-(e).

6. The acquiring of the resist pattern data includes:

5. The method of claim 1 , further comprising: running one or more process models, including a resist model, of a patterning process using the target pattern to be printed on the substrate.

7. 5. The method of claim 1, wherein the resist pattern data is represented as a resist image, the resist image being a pixelated image.

8. The physical effect data is data related to an etching term that characterizes an etching effect, the etching term being: a concentration of plasma within a trench of the resist pattern associated with the target pattern; a concentration of plasma on top of a resist layer of the substrate; loading effect, determined by convolving the resist pattern with a Gaussian kernel having specific model parameters; change in the loading effect on the resist pattern during the etching process; the relative position of the resist pattern with respect to adjacent patterns on the substrate; the aspect ratio of the resist pattern, or 5. The method of claim 1, further comprising at least one of: a term related to the combined effect of two or more etching process parameters.

9. The obtaining of the physical effect data includes:

5. The method of claim 1 , comprising: executing a physical effects model comprising one or more etching terms characterizing an etching effect and a Gaussian kernel defined for each of the one or more of the etching terms.

10. 5. The method of claim 1, wherein the physical effect data is represented as a pixelated image, with each pixel intensity indicative of a physical effect on the resist pattern associated with the target pattern.

11. Obtaining a resist contour of the resist pattern; The method of claim 1 , further comprising: generating an etch contour by applying the etch bias to the resist contour.

12. 5. The method of claim 1, further comprising: running the trained machine learning model using the resist pattern and the physical effects data as inputs to determine the etch bias.

13. determining physical effects data characterizing an effect of the etch process on the substrate by executing a physical effects model; running a trained machine learning model using the resist pattern and the physical effects data as inputs to determine an etch bias; and controlling the semiconductor device or the etching process based on the etching bias.

11. The method of claim 10, wherein the trained machine learning model receives the resist pattern at one layer of the trained machine learning model and receives the physical effects data at another layer of the trained machine learning model.

14. 14. The method of claim 13, wherein the trained machine learning model is a convolutional neural network (CNN) that includes certain weights and biases, and the weights and biases of the CNN are determined via a training process that uses the plurality of resist patterns, the physical effect data associated with each resist pattern of the plurality of resist patterns, and the measured biases associated with each resist pattern, such that a difference between a measured bias and the determined etch bias is minimized.

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