Method for determining patterns in the patterning process

Abstract

To provide a tool for training a patterning process model, and the use of the trained model to determine patterns that will be printed on a substrate in a patterning process.SOLUTION: A method involves: obtaining image data associated with a desired pattern, a measured pattern of the 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 set of parameters and the second set of parameters to train the patterning process model. An iteration involves executing, using the image data, the first model and the machine learning model to cooperatively 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.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] Cross-reference of related applications

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

[0002]

[0002] The description herein relates to lithography apparatus and processes, more specifically to tools for training a patterning process model, and to determining the pattern to be printed on a substrate in the patterning process using the trained model. [Background technology]

[0003]

[0003] Lithography projection equipment can be used, for example, in the manufacture of integrated circuits (ICs). In such cases, a patterning device (e.g., a mask) can include or provide circuit patterns ("design layouts") corresponding to individual layers of the IC, and these circuit patterns can be transferred onto target portions (e.g., including one or more dies) on a substrate (e.g., a silicon wafer) coated with a layer of radiation-sensitive material ("resist") by methods such as irradiating target portions through the circuit patterns on the patterning device. Generally, a single substrate includes multiple adjacent target portions (one target portion at a time) onto which the circuit patterns are successively transferred by the lithography projection equipment. In some types of lithography projection equipment, the circuit pattern on the entire patterning device is transferred onto one target portion at a time, and such equipment is generally called a wafer stepper. In alternative equipment, generally called a step-and-scan device, the projection beam moves the substrate parallel or antiparallel to a given reference direction ("scan" direction) in synchronization with scanning the patterning device in this reference direction. Different portions of a circuit pattern on a patterning device are progressively transferred to a single target portion. Generally, a lithography projection device has a magnification factor M (generally < 1), so the speed F at which the substrate is moved is equal to the speed at which the projection beam scans the patterning device multiplied by the factor M. Further information regarding lithography devices such as those described herein can be found, for example, in U.S. Patent 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-bake (PEB), development, hard baking, and measurement / inspection of the transferred circuit pattern. These numerous procedures are used as a basis for creating the individual layers of a device, such as an IC. The substrate may then undergo various processes such as etching, ion implantation (doping), metallization, oxidation, and chemical mechanical polishing (all intended to finish the individual layers of the device). If several layers are required for the device, the entire procedure or variations thereof are repeated for each layer. Finally, the device is present in 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 described above, microlithography is a central step in the manufacturing of ICs, in which patterns formed on a substrate define the functional elements of ICs such as microprocessors and memory chips. Similar lithography 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 continuously decreasing, while the number of functional elements, such as transistors, per device has steadily increased over decades, following a trend generally known as "Moore's Law." In the current technological state, layers of devices are manufactured using lithography projection equipment that projects a design layout onto a substrate using illumination from a deep ultraviolet illumination source, producing individual functional elements with dimensions far below 100 nm (i.e., less than half the wavelength of radiation from the illumination source (e.g., a 193 nm illumination source)).

[0007]

[0007] This process, in which features with dimensions below the classical limiting resolution of a lithography projector are printed, is generally known as low-k1 lithography, given by the resolution formula CD = k1 × λ / NA, where λ is the wavelength of the radiation used (currently, in most cases, 248 nm or 193 nm), NA is the numerical aperture of the projection optical system in the lithography projector, CD is the "critical dimension" (generally the smallest feature size to be printed), and k1 is the empirical resolution coefficient. Generally, the smaller k1, the more difficult it becomes to reproduce on the substrate a pattern that closely resembles the shape and dimensions planned by the circuit designer to achieve a particular electrical functionality and performance. To overcome these difficulties, state-of-the-art fine-tuning steps are applied to the lithography projector and / or design layout. These include, for example, but are not limited to, optimization of NA and optical coherence settings, customized illumination schemes, use of phase-shift patterning devices, optical proximity effect correction (OPC, sometimes also called "optical and process correction") in design layouts, or other methods generally defined as “resolution enhancement techniques” (RET). As used herein, the term “projection optics” is to be broadly interpreted to encompass a variety of optical systems, including, for example, refractive optics, reflective optics, apertures, and reflective-refractory optics. The term “projection optics” may also include components that operate collectively or individually according to any of these design types to guide, shape, or control the projected beam of radiation. The term “projection optics” may include any optical component within a lithography projection apparatus, regardless of where the optical component is located in the optical path of the lithography projection apparatus. A projection optical system may include optical components for shaping, adjusting, and / or projecting radiation before it passes through a patterning device, and / or optical components for shaping, adjusting, and / or projecting radiation after it has passed through a patterning device. Generally, the projection optical system excludes the source and the patterning device. [Overview of the project]

[0008]

[0008] This disclosure brings several improvements to the field of computer 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 that will be printed on the substrate in the patterning process. The advantages of this disclosure are, but are not limited to, to provide an improved method for measuring the features of the pattern that will be printed on the substrate, making an accurate prediction of the metrological image, and thereby saving metrological time and resources.

[0009]

[0009] According to one embodiment, a method is provided for training a patterning process model, which is configured to predict the pattern that will 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, which is associated with the desired pattern; (iii) a first model, which is associated with one aspect of the patterning process and includes a first set of parameters; and (iv) a machine learning model, which is associated with another aspect of the patterning process and includes a second set of parameters; and training the patterning process model by iteratively determining the values ​​of the first set of parameters and the second set of parameters. The iterations include: using the image data to run the first model and the machine learning model to collaboratively predict the printed pattern on the substrate; and modifying the values ​​of the first set of parameters and the second set of parameters so that the 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 configured and trained in a convolutional deep neural network framework.

[0011]

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

[0012]

[0012] Furthermore, according to one embodiment, a method is provided for determining optical proximity effect correction for a patterning process, the method comprising: acquiring image data associated with a desired pattern; using the image data to run a trained patterning process model to predict the pattern that will be printed on the substrate; and using the predicted pattern that will be printed on the substrate to be patterned, determining optical proximity effect correction and / or defects.

[0013]

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

[0014]

[0014] Furthermore, according to one embodiment, a system is provided for determining an etching bias related to an etching process. The system includes a semiconductor processing apparatus and a processor. The processor is configured to determine physical effect data characterizing the effect of the etching process on a substrate through the execution of a physical effect model, to run a trained machine learning model using a resist pattern and the physical effect data as input to determine an etching bias, and to control a semiconductor device or etching process based on the etching bias.

[0015]

[0015] Furthermore, according to one embodiment, a method is provided for calibrating a process model, which is configured to generate simulated contours. This method includes (i) obtaining measurement data at a plurality of measurement locations on a pattern, and (ii) contour constraints defined based on the measurement data, and calibrating the process model by adjusting the values ​​of the model parameters of the process model until the simulated contours satisfy the contour constraints.

[0016]

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

[0017]

[0017] Furthermore, according to one embodiment, a system is provided for calibrating a process model, which is configured to generate simulated contours. The system includes a metronome tool and a processor configured to acquire measurement data at a plurality of measurement locations on a pattern. The processor is configured to calibrate the process model by adjusting the values ​​of model parameters of the process model until the simulated contours satisfy contour constraints, which are based on the measurement data.

[0018]

[0018] Furthermore, according to one embodiment, a system is provided 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 (i) the process model produces a simulated image that minimizes the difference in intensity or frequency between the simulated image and the reference image, and (ii) satisfies gradient constraints associated with the reference image.

[0019]

[0019] Furthermore, according to one embodiment, a non-temporary computer-readable medium containing instructions is provided, which, when executed by one or more processors, triggers an operation that includes: (i) resist pattern data associated with a target pattern to be printed on a substrate; (ii) physical effect data characterizing the effect of the etching process on the target pattern; and (iii) a measured bias between the etching pattern and the resist pattern formed on the substrate to be printed; 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 the predicted etching bias.

[0020]

[0020] Furthermore, according to one embodiment, a non-temporary computer-readable medium containing instructions is provided, which, when executed by one or more processors, triggers an operation that includes (i) obtaining measurement data at a plurality of measurement locations on a pattern, and (ii) contour constraints defined based on the measurement data, and calibrating a process model by adjusting the values ​​of model parameters of the process model until the simulated contours satisfy the contour constraints.

[0021]

[0021] Furthermore, according to one embodiment, a non-temporary computer-readable medium containing instructions is provided, which, when executed by one or more processors, triggers an operation including (i) obtaining a reference image associated with a target pattern, and (ii) gradient constraints defined with respect to the reference image, and (i) calibrating a process model so that the process model produces a simulated image that minimizes the difference in intensity or frequency between the simulated image and the reference image, and (ii) satisfies the gradient constraints.

[0022]

[0022] Herein, an embodiment will be described as merely an example with reference to the attached drawings. [Brief explanation of the drawing]

[0023] [Figure 1]

[0023] This is a block diagram of various subsystems of a lithography system according to one embodiment. [Figure 2]

[0024] This is a block diagram of a simulation model corresponding to the subsystem in Figure 1, according to one embodiment. [Figure 3]

[0025] This is a flowchart of a method for training a patterning process model according to one embodiment, the patterning process model being configured to predict the patterns that will be formed in the patterning process. [Figure 4A]

[0026] An exemplary configuration of a patterning process model, including a first model and a second model (e.g., a machine learning model), according to one embodiment, is shown. [Figure 4B]

[0026] An exemplary configuration of a patterning process model, including a first model and a second model (e.g., a machine learning model), according to one embodiment is shown. [Figure 4C]

[0026] An exemplary configuration of a patterning process model, including a first model and a second model (e.g., a machine learning model), according to one embodiment is shown. [Figure 5]

[0027] This is a flowchart of a method for determining optical proximity effect corrections for a patterning process based on the predicted pattern of the trained patterning process model shown in Figure 3, according to one embodiment. [Figure 6]

[0028] This is a flowchart of a method for training a machine learning model to determine etching biases related to an etching process, according to one embodiment. [Figure 7]

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

[0030] This is exemplary physical effect data based on a resist pattern according to one embodiment. [Figure 9]

[0031] This is an example of acid-base concentration in the resist according to one embodiment. [Figure 10]

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

[0033] This is an exemplary etching bias applied to a post-development image (ADI) contour according to one embodiment. [Figure 12]

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

[0035] An exemplary model output satisfying the physical constraints related to Figure 11, according to one embodiment, is shown. [Figure 13B]

[0036] An exemplary model output that does not satisfy the physical constraints of Figure 11, according to one embodiment, is shown. [Figure 14]

[0037] This is a flowchart of another method for calibrating a process model based on different physical constraints, according to one embodiment. [Figure 15A]

[0038] This shows a reference intensity profile of a spatial image or resist image according to one embodiment. [Figure 15B]

[0039] The intensity profile associated with a model satisfying the physical constraints of Figure 15A, according to one embodiment, is shown. [Figure 15C]

[0040] The intensity profile associated with a model that does not satisfy the physical constraints of Figure 15A, according to one embodiment, is shown. [Figure 16]

[0041] One embodiment of a scanning electron microscope (SEM) according to one embodiment is schematically shown. [Figure 17]

[0042] One embodiment of an electron beam inspection apparatus according to one embodiment is schematically shown. [Figure 18]

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

[0044] One embodiment of another optimization method according to one embodiment is shown. [Figure 20A]

[0045] This diagram shows an exemplary flowchart of various optimization processes according to one embodiment. [Figure 20B]

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

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

[0046] This is a block diagram of an example computer system according to one embodiment. [Figure 23]

[0047] This is a schematic diagram of a lithography projection device according to one embodiment. [Figure 24]

[0048] This is a schematic diagram of another lithography projection apparatus according to one embodiment. [Figure 25]

[0049] This is a more detailed diagram of the apparatus shown in Figure 24, according to one embodiment. [Figure 26]

[0050] This is a more detailed view of the source collector module SO of the apparatus shown in Figures 24 and 25, according to one embodiment. [Modes for carrying out the invention]

[0024]

[0051] Herein, embodiments will be described in detail with reference to the drawings. The drawings are provided as illustrative examples so that those skilled in the art can carry out those 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 substituting some or all of the elements described or illustrated. For convenience, the same reference numerals are used throughout the drawings to refer to the same or similar parts. Where certain elements of those embodiments can be implemented in part or in whole using known components, only the portion of such known components necessary to understand the embodiment is described, and detailed descriptions of other parts of such known components are omitted so as not to obscure the description of the embodiment. Embodiments showing a single component should not be considered limiting. Rather, unless otherwise specified, the scope is intended to encompass other embodiments containing multiple identical components, and vice versa. Furthermore, unless otherwise specified, the applicant does not intend that any term in this specification or in the claims be non-generic or special in meaning. Furthermore, the scope includes current and future known equivalents of the components referenced herein by example.

[0025]

[0052] While specific references to the manufacture of ICs may be made in this specification, it should be clearly understood that the descriptions herein have many other possible applications. For example, they may be used in the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memory, liquid crystal display panels, thin-film magnetic heads, and the like. Those skilled in the art will recognize that in the context of such alternative applications, the terms “reticle,” “wafer,” or “die” used 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 radiation (e.g., having wavelengths of 365, 248, 193, 157, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having wavelengths in the range of 5 to 20 nm).

[0027]

[0054] As used herein, the terms “optimizing” and “optimization” mean adjusting a lithography projection apparatus so that the lithography results and / or process have more desirable characteristics, such as higher accuracy in projecting the design layout onto the substrate, a larger process window, and so on.

[0028]

[0055] Furthermore, lithography projection systems may be of a type having two or more substrate tables (and / or two or more patterning device tables). In such “multistage” devices, additional tables may be used in parallel, or preparation steps may be performed on one or more other tables while one or more tables are being used for exposure. A twin-stage lithography projection system is described, for example, in U.S. Patent No. 5,969,441, which is incorporated herein by reference.

[0029]

[0056] The patterning devices mentioned above may include or form design layouts. Design layouts can be generated using CAD (Computer-Aided Design) programs, a process often referred to as EDA (Electronic Design Automation). Most CAD programs follow a set of design rules to generate functional design layouts / patterning devices. These rules are defined by processing and design limits. For example, design rules define space tolerances between circuit devices (gates, capacitors, etc.) or interconnection lines, ensuring that these circuit devices or lines do not interact with each other in undesirable ways. The limits of design rules are usually called "critical dimensions" (CD). The critical dimension of a circuit can be defined as the minimum width of a line or hole, or the minimum space between two lines or two holes. Thus, the CD determines the overall size and density of the circuit being designed. Naturally, one of the goals of integrated circuit manufacturing is to faithfully reproduce the original circuit design on the substrate (via patterning devices).

[0030]

[0057] As used herein, the terms “mask” or “patterning device” can be broadly interpreted to refer to any general patterning device that can be used to give an incoming radiation beam a patterned cross-section corresponding to a pattern to be generated on a target portion of a substrate, and the term “light bulb” may also be used in this context. In addition to conventional masks (transmissive or reflective; binary, phase-shifted, hybrid, etc.), other examples of such patterning devices include: - Programmable mirror arrays. An example of such a device is a matrix-addressable surface having a viscoelastic control layer and reflective surfaces. The basic principle behind such a device is that (for example) the addressable areas of the reflective surface reflect incident radiation as diffracted radiation, and the non-addressable areas reflect incident radiation as non-diffracted radiation. Using appropriate filters, the above non-diffracted radiation can be removed from the reflected beam, leaving only the diffracted radiation behind, so that the beam is patterned according to the addressing pattern of the matrix-addressable surface. The required matrix addressing can be performed using appropriate electronic means. More information on such mirror arrays can be gathered, for example, from U.S. Patents 5,296,891 and 5,523,193, which are incorporated herein by reference. - Programmable LCD array. An example of such a structure is given in U.S. Patent No. 5,229,872, which is incorporated herein by reference.

[0031]

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

[0032]

[0059] In the system optimization process, the performance index of the system can be expressed as a cost function. The optimization process can be summarized as finding the set of system parameters (design variables) that minimize the cost function. The cost function may take any appropriate form depending on the optimization goal. For example, the cost function may be the weighted root mean square (RMS) of the deviations of specific features (evaluation points) of the system from their intended values ​​(e.g., ideal values). The cost function may also be the maximum value (i.e., the worst-case deviation) of those deviations. In this specification, the term “evaluation point” should be interpreted broadly to include any feature of the system. The design variables of a system may be limited to a finite range and / or interdependent due to the feasibility of implementing the system. In the case of a lithography projector, constraints are often related to the physical properties and characteristics of the hardware, such as adjustable ranges, and / or patterning device manufacturability design rules, and 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 lithography projection system, a radiation source provides illumination (i.e., light), and a projection optics system guides and shapes the illumination onto the substrate via a patterning device. The term “projection optics system” is broadly defined here to include any optical components that can alter the wavefront of the radiation beam. For example, the projection optics system may include at least some of components 14A, 16Aa, 16Ab, and 16Ac. The spatial image (AI) is the radiation intensity distribution at the substrate level. A resist layer on the substrate is exposed, and the spatial image is transferred to the resist layer as a potential “resist image” (RI). 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 spatial image, an example of which can be found in U.S. Patent Application No. 12 / 315,849 by the same applicant, the disclosure of which is incorporated herein by reference in whole. The resist model is relevant only to the properties of the resist layer (e.g., the effects of chemical processes occurring during exposure, PEB, and development). The optical properties of a lithography projection system (e.g., the properties of the radiation source, patterning device, and projection optics) determine the spatial image. Since the patterning device used in a lithography projection system may be changed, it is desirable to decouple the optical properties of the patterning device from the optical properties of the rest of the lithography projection system, including at least the source and projection optics.

[0034]

[0061] Figure 2 shows an exemplary flowchart for simulating lithography in a lithography projection system. The radiation source model 31 represents the optical features of the radiation source (including the radiation intensity distribution and / or phase distribution). The projection optics model 32 represents the optical features of the projection optics (including the changes to the radiation intensity distribution and / or phase distribution caused by the projection optics). The design layout model 35 represents the optical features of the design layout (which is a representation of the arrangement of features on or formed by the patterning device) (including the changes to the radiation intensity distribution and / or phase distribution caused by a given design layout 33). The spatial image 36 can be simulated using the design layout model 35, the projection optics model 32, and the design layout model 35. The resist image 38 can be simulated from the spatial image 36 using the resist model 37. For example, lithography simulation can predict the contours and CD of the resist image.

[0035]

[0062] More specifically, it should be noted that the radiation source model 31 can represent the optical characteristics of a radiation source, including, but not limited to, NA-sigma (σ) settings and any specific illumination 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 a projection optics system, including aberrations, distortions, refractive index, physical size, and physical dimensions. The design layout model 35 can represent the physical properties of a physical patterning device, such as that described in U.S. Patent No. 7,587,704, which is incorporated in its entirety by reference. The purpose of the simulation is to accurately predict, for example, edge placement, spatial 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 may 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 parts (these are called "clips") can be identified. In one embodiment, a set of clips representing complex patterns within the design layout is extracted (any number of clips may be used, but typically around 50 to 1000 clips). As those skilled in the art will understand, these patterns or clips represent small parts of the design (i.e., circuits, cells, or patterns), and clips in particular represent small parts that require special attention and / or verification. That is, clips may be parts of the design layout, or similar, or critical features may have similar behavior to parts of the design layout identified by experience (including clips provided by the customer), by trial and error, or by performing a full chip simulation. Clips typically include one or more test patterns or gauge patterns.

[0037]

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

[0038]

[0065] Stochastic variations in the patterning process (e.g., the resist process) can, in some cases, limit lithography (e.g., EUV lithography) in terms of, for example, the possibility of feature shrinkage and exposure dose specifications, which affects the wafer throughput of the patterning process. In one embodiment, stochastic variations in the resist layer may manifest as stochastic damage, such as closed holes or trenches, or broken lines. Such stochastic variations related to the resist have a greater impact on and limit the success of high-volume production (HVM) compared to, for example, stochastic CD variations, which are a conventional metric of interest for measuring and regulating the performance of the patterning process.

[0039]

[0066] In patterning processes (e.g., photolithography, electron 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 and etching are applied. These post-exposure steps or processes have various effects, leading to the patterned layer or etched substrate forming a structure with dimensions different from the target dimensions.

[0040]

[0067] In computer lithography, patterning process models (e.g., those discussed in Figure 2) related to different aspects of the patterning process, such as mask models, optical models, resist models, and post-exposure models, can be used to predict the patterns that will be printed on a substrate. When properly calibrated (e.g., using measurement data associated with printed wafers), patterning process models can generate accurate predictions of the pattern dimensions that will emerge from the patterning process. For example, a post-exposure patterning process model is calibrated based on empirical measurements. The calibration process includes exposing a test substrate by varying different process parameters (e.g., dose, focus, etc.), measuring the critical dimension printed pattern that occurs 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), process windows, enhanced patterning recipes, and / or increased design pattern complexity.

[0041]

[0068] The patterning process is a complex process, and not all aspects can be modeled based on the physical / chemical phenomena involved. For example, some effects of the post-exposure process are well understood and can be modeled using mathematical formulas for physical terms (e.g., parameters associated with the resist process) that describe the physical / chemical phenomena of the process. For example, post-exposure acid-base diffusion can be modeled by a Gaussian filter on the spatial image. In one 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 enabling real-time control of the patterning process via the adjustable knobs. In one embodiment, some physical terms may not be directly adjustable via the adjustable knobs, but can still describe the physical / chemical phenomena of the process (e.g., spatial image formation, resist image formation, etc.). For example, a resist model includes a Gaussian filter on the spatial image to model acid-base diffusion in the resist after exposure. This sigma term is typically not adjustable via the adjustable knobs. Even so, the values ​​of such physical terms (e.g., sigma) can be determined based on empirical formulas or physics-based formulas that model the effects of the process (e.g., resist).

[0042]

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

[0043]

[0070] Figure 3 is a flowchart of a method for training a patterning process model, which is configured to predict the patterns that will be formed in the patterning process. As mentioned above, several aspects of the patterning process are well understood and can be modeled using mathematical formulas that utilize physical terms configured to accurately describe the physical effects of the patterning process. Furthermore, there are several aspects that cannot be accurately modeled using physical terms. This method employs two different models: a first model configured to describe known aspects through physical terms (e.g., parameters related to the optics, parameters related to the resist in the patterning process), and a second model (i.e., a machine learning model) configured to describe aspects that are not well understood (from a physical / chemical perspective).

[0044]

[0071] There are several advantages to using a mixed model (i.e., a first and second model) to collaboratively predict patterns in a patterning process. For example, physical terms are relatively simple to compute, and models that utilize such physical terms are less susceptible to overfitting. For instance, incorporating physical terms in conjunction with a CNN model can reduce the complexity of the CNN several times over, reduce the risk of overfitting, and improve the execution 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 execution times.

[0045]

[0072] Method 300 includes obtaining, in process P301, (i) image data 302 associated with a desired pattern, (ii) a measured pattern 304 on a substrate, the measured pattern 304 associated with the desired pattern, (iii) a first model associated with an aspect of the patterning process (e.g., its effect can be accurately modeled by a physics / chemistry-based formula), comprising a first set of parameters 307, and (iv) a machine learning model associated with another aspect of the patterning process (e.g., its effect cannot be accurately modeled by a physics / chemistry-based formula), comprising 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 effects of aspects of the patterning process or the effects of the final pattern that will be printed on the substrate. In one embodiment, image data 302 is a spatial image, a mask image, a resist image, or other output related to one or more aspects of the patterning process. In one embodiment, obtaining a spatial image, a mask image, a resist image, etc., involves simulating the patterning process, as discussed in Figure 2.

[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 series or parallel combination (e.g., as considered with Figures 4A-4C). In an exemplary configuration (e.g., Figure 4A), the series combination of models includes providing the output of the first model as input to the machine learning model. In another exemplary configuration, the series combination of models includes providing the output of the machine learning model as input to the first model. In yet another example (e.g., Figure 4B), the parallel combination of models includes providing the same input to the first model and the machine learning model, composing the outputs of the first model and the machine learning model, and determining the predicted print pattern based on the combined outputs of each model. In yet another example (e.g., Figure 4C), the patterning process model may be configured to include both series 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, the 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. An example of an empirical model utilizing physical terms is as follows: R=cA×A+cMav×MAV+cAp×Ap*GAp+cBp×Bp*GBp+cAm×A*GAm+...

[0049]

[0076] In the above equation, R is the predicted resist image based on the physical terms and their associated coefficients (an example of the first set of parameters). In the above equation, cA is the coefficient of the initial acid distribution A, which can be represented by the spatial image, and cMav is the coefficient of the long-range pattern loading effect MAV, which can be determined as the mean of the mask image. Similarly, other physical terms are associated with one or more coefficients. These coefficients are determined during the training process, which will be 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 poorly understood from a physics perspective. In one embodiment, the second set of parameters includes the 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 so 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 the values ​​of a first set of parameters 307 and a second set of parameters 308 in order to train a patterning process model. In one embodiment, the iteration includes performing processes P303, P305, and P307.

[0052]

[0079] This method 300 includes, in process P303, using image data 302 to run a first model and a machine learning model to collaboratively predict the pattern on the substrate. Process P305 includes determining the difference between the measured pattern 304 and the predicted pattern 305 of the patterning process model, and further determining whether this difference is reduced or minimized. Process P307 includes modifying the values ​​of the first set of parameters 307 and the second set of parameters 308 so 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 values ​​to be modified are determined based on optimization techniques such as a constant gradient level method, which guides how to modify the values ​​of a first set of parameters and a second set of parameters so that the gradient of the difference with respect to each parameter is reduced. After several iterations, global or local optimal values ​​of the parameters are obtained so that the difference between prediction and measurement is minimized. Thus, the patterning process model can be calibrated (or trained) and further utilized to improve the patterning process through OPC, defect detection, hotspot ranking, or other known applications of the patterning process model.

[0054]

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

[0055]

[0082] Figure 4A shows a serial combination of the first and second models, where the first model is expressed as a function of physical parameters and the second model is expressed as a CNN. The training process is iterative, and each iteration (or each iteration) is c i The values ​​of the first set of parameters, such as (these are coefficients related to the physical term), as well as the w of the CNN. iand u i including determining values of a set of second parameters such as weights such as coefficient c i Coefficient c i acts directly on the value of a physical term term (for example, variables such as dose amount, focus, acid concentration related to the patterning process) and (for example, through multiplication, exponentiation, addition, or other mathematical operations) to determine the first output of the first model. In one embodiment, the physical term term i can be a function (for example, a Gaussian filter) associated with a parameter param i (for example, a, b of a Gaussian filter). The weights of the CNN do not act directly on a specific physical term, but the CNN can receive the first output from the first model as input and predict a second output associated with another aspect of the patterning process (for example, not well understood).

[0056]

[0083] In one embodiment, initial values of the set of first parameters and the set of second parameters may be assigned to start a simulation process. In one embodiment, the input to the first model is, for example, a spatial image of a desired pattern to be printed on a substrate. Based on the input (for example, the spatial image), the first model predicts a first output (for example, a resist pattern) of an aspect of the patterning process (for example, exposure of the resist using the spatial image). The first output is further input to the CNN, and the CNN further predicts the pattern to be printed on the substrate. The predicted pattern is compared with the desired output. The desired output can be, for example, a measured pattern corresponding to the desired pattern measured via a SEM tool. The comparison includes calculating the difference between the predicted pattern and the measured pattern. Based on this difference, backpropagation can be performed, where the values of weights such as w i and u i of the CNN may be calculated such that this difference is reduced. Further, c i and / or param iThe value of can be calculated. For example, a gradient-based method can be used, where the difference of the weights is calculated to generate a gradient map. The gradient map is calculated so that the difference between the prediction and the desired output is reduced (in one embodiment, minimized) by the weights and / or c i and / or param i It serves as a guide for correcting the values. After the patterning process model is trained, it can determine patterns that explain both well-understood and not-so-understood physical effects of the patterning process (e.g., post-exposure processes).

[0057]

[0084] Figure 4B shows a parallel combination of the first and second models. The first and second models are represented in the same manner as described above in Figure 4A. The initial values ​​of the first and second parameter sets may also be similar in order 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., a spatial image of the desired pattern) is provided simultaneously to both the first and second models. Each model predicts an output, which can be combined to form a pattern that will be printed on the substrate. The predicted output may be compared to the desired output (e.g., a measured pattern on the printed substrate), as described above. Backpropagation may then be performed, and as previously mentioned, the difference of the difference with respect to each of the first and second parameters can be determined using the constant gradient level method. Furthermore, the values ​​of the first and second parameters are selected so that the difference is reduced (minimized in one embodiment). After several iterations, the predicted pattern converges to the desired pattern, and the model training can be said to be complete.

[0058]

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

[0059]

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

[0060]

[0087] Figure 5 is a flowchart of a method for determining optical proximity effect correction for a patterning process. Optical proximity effect correction is associated with a desired pattern to be printed on a substrate. Method 500 includes acquiring image data 502 associated with the desired pattern in process P501. In one embodiment, the image data 502 is a spatial image and / or mask image of the desired pattern.

[0061]

[0088] Furthermore, process P503 includes using image data 502 to run a trained patterning process model 310 to predict the pattern that will be printed on the 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 collectively predict the pattern that will be printed on the substrate. The first model and the machine learning model are in series and / or parallel combinations, as discussed with respect to Figures 4A to 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 the acid-based diffusion of the substrate after exposure. In one embodiment, the machine learning model is a neural network that models a second aspect of the patterning process for which a relatively poor physics-based understanding exists.

[0062]

[0089] Based on the predicted pattern, process P505 includes determining optical proximity effect correction and / or defects. In one embodiment, determining optical proximity effect correction includes adjusting the desired pattern so that the difference between the predicted pattern and the desired pattern is reduced, and / or placing assist features around the desired pattern. An example of the OPC process is described later in this disclosure with reference to Figures 18–21.

[0063]

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

[0064]

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

[0065]

[0092] As discussed herein, there are various methods (e.g., Figures 4A-4C) provided for training patterning process models based on physical terms. There are several advantages to using physical terms to train or calibrate patterning process models. For example, physical terms are relatively simple to compute, and models that utilize 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 several times over, reduces the risk of overfitting, and improves the execution time of patterning process simulations. The following description discusses additional methods for training and calibrating process models based on physical terms.

[0066]

[0093] Figure 6 is a flowchart of Method 600 for training a machine learning model to determine etching biases associated with the etching process. In one embodiment, predicting such etching biases may be useful in improving etching recipes or current lithography equipment settings. Method 600 includes several steps, which are described in detail below.

[0067]

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

[0068]

[0095] In one embodiment, the measured bias 606 data may be determined based on metronome data of a previously patterned substrate. For example, the measured bias 606 may be the difference between a resist pattern formed on the substrate and an etching pattern formed on the printed substrate. The resist pattern may be determined through a metronome tool or a simulation of the patterning process. In one embodiment, the etching pattern formed on the printed pattern is measured through a metronome tool (e.g., an SEM tool or optical metronome tool as described with respect to Figures 16 and 17). In one embodiment, the dimensions of the resist pattern (e.g., CD of features) may be greater than those of the etching pattern, for example, due to material removal (e.g., via a descam treatment). This difference between the resist pattern and the etching pattern on the printed substrate includes variations caused by the etching process. For example, variations may be caused by a fluctuating etching rate, variations in the amount of plasma concentration, variations in the aspect ratio (e.g., feature height / feature width), or other physical aspects related to the resist pattern, the etching 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 the pixels indicates the resist region and the pattern portion formed within the resist portion. For example, the pattern portion may be the edges / contours of the resist pattern. In one embodiment, obtaining the resist pattern data 602 involves performing one or more process models, including a resist model of the patterning process, using a target pattern to be printed on the substrate.

[0070]

[0097] In one embodiment, the physical effect data 604 may be data relating to an etching term that characterizes the etching effect, the etching term including at least one of the following: the plasma concentration inside the trench of the resist pattern associated with the target pattern; the plasma concentration on top of the resist layer on the substrate; the loading effect determined by convolving the resist pattern with a Gaussian Kernel having specified model parameters; the 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 a term relating to the combined effect of two or more etching process parameters.

[0071]

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

[0072]

[0099] Figure 7 is an exemplary resist image including a resist pattern formed in resist 702. The resist pattern includes trench regions 704 formed within resist 702. In one embodiment, the etching model may be calibrated based on a concentrated plasma etching (CEM) method. The CEM method uses plasma loading to the edges of the resist trenches 704 to characterize the bias behavior induced by etching. In one embodiment, evaluation points, e.g., 706, may be located at the edges of the resist trenches, e.g., 704, and CEM_range is the etching proximity range considered by the etching model. In one embodiment, the etching physical terms may be CT or CR images related to the plasma loading effect generated from the resist pattern. For example, CT0 is defined as plasma loading from the trench region (e.g., 704) to a unit edge length at the start of etching, and CR0 is defined as plasma loading 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 time-dependent conversion may be based on an exponential term that includes parameters related to sidewall adhesion or etching reaction constants. In one embodiment, the product of the CT image and the CR image may be used to characterize the etching bias due to the proximity effect.

[0073]

[0100] Figure 8 shows an exemplary etching physical term (e.g., CR image) generated from the resist pattern 801. The resist pattern 801 includes the resist contour 802 (or resist pattern edge), and the plasma loading effect from the resist region (e.g., the CR described above) can then be calculated, which is shown as the 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, bright pixels in the CR become dark pixels in the CT, and vice versa. The CR image 810 can be used to characterize the etching bias from the proximity effect. This exemplary etching bias is an exemplary bias applied to the resist contour 802 to compensate for such a proximity effect.

[0074]

[0101] Figure 9 shows another exemplary modeling of a physical term, such as an acid-base reaction. In one embodiment, an acid-base reaction can be modeled by truncating the acid concentration with a quencher base. For example, an acid-base reaction (shown, e.g., as image 901) can be characterized by a linear combination coefficient of acid concentration 910 and base concentration 920. In one embodiment, a truncation term (e.g., 903) simulates the reaction and diffusion of the acid and base in the formation of the final acid density distribution image 901. Multiple truncation terms represent different time periods during post-exposure baking. Depending on the truncation term 903 (e.g., the truncation value of the truncation term), the acid concentration 910 and base concentration 920 change.

[0075]

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

[0076]

[0103] Returning to Figure 6, step P603 includes training a machine learning model 603 based on resist pattern data 602, physical effect data 604, and measured bias 606 to reduce the difference between the measured bias 606 and the predicted etching bias. After this training process is complete, the machine learning model 603 can be called the trained machine learning model 603. This trained machine learning model 603 can be used in the patterning process to improve performance metrics, such as the yield of printed substrates. For example, process parameters can be adjusted based on the etching bias predicted by the trained machine learning model 603 to reduce the number of pattern failures and thereby improve the yield.

[0077]

[0104] In one embodiment, the machine learning model 603 is configured to receive resist pattern data 602 in a first layer of the machine learning model 603, and physical effect data 604 is received in a last layer of the machine learning model 603. In another embodiment, the machine learning model 603 is configured to receive resist pattern data 602 and physical effect data 604 in a first layer of the machine learning model 603. Those skilled in the art will understand that this disclosure is not limited to any 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 etching bias predicted by running the machine learning model 603 with resist pattern data 602 as input, and (ii) another etching bias determined based on physical effect data 604 related to the etching process.

[0079]

[0106] In one embodiment, the output of the last layer of the machine learning model 603 is an etching bias map from which the etching bias is extracted. The etching bias map is generated by running the machine learning model 603 with resist pattern data 602 as input to output an etching bias map, the etching bias map containing biased resist patterns, and combining the etching bias map with physical effect data 604.

[0080]

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

[0081]

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

[0082]

[0109] Figure 11 shows an example of etching bias determined via an etching model. In one embodiment, the etching model calculates the post-etched image (AEI) contour (e.g., 1130) by directly biasing (e.g., 1120) the post-developed 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 environment of the ADI (e.g., feature density) and the physical terms associated with etching. For example, a positive bias shifts the ADI contour outward, while a negative bias (e.g., 1120) shifts the ADI contour 1110 inward. In other words, the etching bias may be positive if the size of the pattern 1110 elements is larger before etching than after etching, and negative if the size is smaller before etching than after etching. In one embodiment, the etching model utilizes a calibration / check gauge, and the perpendicular direction of the ADI contour is relative to such a gauge. Next, this model can directly output AEI contours for LMC / OPC applications. For example, an LMC can determine whether the AEI contours meet the size constraints related to the target pattern. The OPC of a mask pattern can be determined using the AEI contours to improve the overall yield of the patterning process. For example, in an OPC process, simulated contours (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 so 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 bias amount determined by the model (e.g., 603) is several physical terms. i It may be a linear combination of these terms, and their physical terms are functions of the environment at one evaluation point i.

number

[0084]

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

[0085]

[0112] By mathematically modeling the etching bias, the generation 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 changes to the design, control parameters, etc. For example, these results can be used to adjust one or more spatial properties of one or more elements provided by the patterned device, and the pattern of the patterned device is used to generate the 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 etching variations that are expected to 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 understood, there may be many more applications. Thus, by compensating for etching variations, the device may have multiple uniform feature sizes, one or more uniform electrical properties, and / or one or more improved (e.g., closer to the desired result) performance features.

[0086]

[0113] Furthermore, although etching variations can sometimes be detrimental to the manufacturing of devices on a substrate, etching bias can be used to generate desired structures on the substrate. By considering the degree of etching bias when manufacturing patterned devices, it becomes possible to manufacture device features smaller than the optical resolution limit of the pattern transfer procedure from the patterned device to the substrate within the device on the substrate. In this respect, the patterning process can be tuned in terms of changes to design, control parameters, etc., using the modeled results of the etching bias. Thus, modeling the etching bias in the etching process can help generate more accurate device features by compensating for etching variations, such as by fitting the patterned device to (accurately) anticipate the possible etching variations of the etching process (e.g., depending on the pattern density). This variation makes it possible to bring the actual features generated by the etching process after (adjusted) lithography closer to the desired product specifications.

[0087]

[0114] In one embodiment, a system for determining an etching bias associated with an etching process that carries out a procedure discussed herein (e.g., Method 600) is described. For example, this system includes a semiconductor processing apparatus (e.g., Figures 1, 23, 24, 25) and one or more processors (e.g., 104 / 105 in Figure 22) which are configured to determine physical effect data 604 that characterize the effect of the etching process on a substrate through the execution of a physical effect model, and to determine an etching bias by executing a trained machine learning model 603 using a resist pattern and the physical effect data 604 as input, and to control a semiconductor device (e.g., Figure 1) or an etching process based on the etching bias.

[0088]

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

[0089]

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

[0090]

[0117] In one embodiment, the control of a semiconductor processing apparatus (e.g., Figures 1, 23, 24, 25) includes adjusting the values ​​of one or more parameters of the semiconductor device so as to improve the yield of the patterning process. In one embodiment, adjusting the values ​​of one or more parameters of the semiconductor processing apparatus is an iterative process. This iterative process includes (a) changing the current values ​​of one or more parameters via a control mechanism of the semiconductor processing apparatus; (b) obtaining a resist pattern to be printed on a substrate via the semiconductor processing apparatus; (c) determining an etching bias via the execution of a trained machine learning model 603 using the resist pattern, and further determining an etching pattern by applying the etching bias to the resist pattern; and (d) determining, based on the etching pattern, whether the yield of the patterning process is within a desired yield range, and in response to not being within the yield range, performing steps (a) to (d).

[0091]

[0118] In one embodiment, the control of the etching process includes determining the etching pattern by applying an etching bias to the resist pattern, determining the yield of the patterning process based on the etching pattern, and determining the etching recipe of the etching process based on the etching pattern so as to improve the yield of the patterning process. In one embodiment, the yield of the patterning process is the percentage of the etching pattern across the entire substrate that satisfies the design specifications. In one embodiment, the semiconductor processing apparatus is a lithography apparatus (e.g., Figures 1, 23, 24, 25).

[0092]

[0119] In today's semiconductor field, technology nodes continue to shrink, and there is a demand for better models for lithography and etching. A good model satisfies both accuracy (e.g., matching the model's results to the actual wafer's metrometry results) and good wafer prediction (e.g., behaving according to physical constraints). Satisfying both accuracy and prediction specifications can be difficult with current complex model forms, because the force of better fitting often indicates overfitting. Overfitted models can produce irregularly shaped patterns that are often undesirable to print on substrates.

[0093]

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

[0094]

[0121] In one embodiment, physical constraints may relate to contour shapes obtained from a metronome tool (e.g., SEM), physical images (e.g., resist images, spatial images) obtained from a metronome tool (e.g., SEM), or a combination thereof. Examples of methods for implementing physical constraints, such as the methods shown in Figures 12 and 14, are discussed herein.

[0095]

[0122] Figure 12 is a flowchart of Method 2000 for calibrating a process model based on physical constraints related to the contour shape (or outline) of a pattern. Method 2000 calibrates the process model to generate simulated contours that satisfy the shape constraints. The detailed procedure of Method 2000 is described below.

[0096]

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

[0097]

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

[0098]

[0125] In one embodiment, each contour constraint is a function of the tangent angle between the tangent to a simulated contour (e.g., contour 1110 or 1120) at a given measurement location (e.g., EP1 to EP3) and the angle of the measurement data 2002 at a given location. For example, referring to Figure 13A, the contour constraint may be that the angle θ1 between the tangent to the simulated contour 1110 and the arrow at EP1 (which indicates the angle of the measurement data 2002) should be within the vertical range. In one embodiment, the vertical range is a value of angle θ1 that 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, Figure 13B shows the result of a calibrated model that produces a simulated contour 1120 that does not satisfy physical constraints. For example, a calibrated model may be overfitted to make good predictions for measurement data. For example, an overfitted model due to excessive data, where the fitting focuses on minimizing the EP error. Such an overfitted model may produce contours with irregular shapes, such as contour 1120. In this case, the tangents to contour 1120 at EP1, EP2, and EP3 may not be perpendicular to the measurement data (e.g., the measurement angles indicated by the arrows at EP1 to EP3, respectively). For example, as seen in Figure 13B, the lines perpendicular to the arrows at EP1, EP2, and EP3 are not tangents to contour 1120. Therefore, although the simulated contour 1120 is fitted to the measurement data (e.g., EPE or CD value) such that the sum of errors associated with the simulated contour 1120 is minimized, the shape of the contour 1120 may not be physically accurate.

[0100]

[0127] Returning to Figure 12, step P2003 includes calibrating the process model 2003 by adjusting the values ​​of the 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 the calibrated process model 2003. In one example, model 2003 that produces the simulated contour 1120 may be considered uncalibrated because the model 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 to all points, e.g., EP1, EP2, and EP3.

[0101]

[0128] In one embodiment, adjusting the values ​​of the model parameters is an iterative process. This iteration includes (a) running the process model 2003 with model parameters of given values ​​to generate simulated contours, where the given values ​​are random in the first iteration and adjusted in subsequent iterations; (c) determining the tangent to the simulated contour at each measurement location; (d) determining the tangent angle between the tangent and the angle of the measurement data 2002 at each measurement location; (e) determining whether the tangent angle is within the vertical range at one or more measurement locations; (f) adjusting the values ​​of the model parameters in response to the tangent angle being outside the vertical range; and performing steps (a) to (d).

[0102]

[0129] In one embodiment, in each iteration, a simulated contour can be obtained, and a tangent can be drawn or calculated at the measurement location (for example, via the trigonometric relation "tan"). 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, for example, between 88° and 92°, preferably 90°.

[0103]

[0130] In one embodiment, the adjustment is based on the slope of each tangent angle with respect to the model parameter, where the slope 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 any particular type of model or particular process of a patterning process. 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, method 2000 may further include, in step P2005, obtaining a resist contour of a resist pattern (e.g., 602 described above) and generating an etching contour 2005 by applying an etching bias (e.g., determined by running a calibrated model) to the resist contour.

[0106]

[0133] Figure 14 is a flowchart 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. In this case, the calibration may be based on constraints based on the image. 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 in relation to the reference image 3002. In one embodiment, the reference image 3002 is obtained by simulating a physics-based model of the patterning process using the target pattern. The reference image 3002 includes, but is not limited to, a spatial 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 obtaining the first derivative of a signal along a given line passing through the simulated image. In one embodiment, the gradient constraint 3004 is obtained by obtaining the first derivative of a signal along a given line passing through the reference image 3002.

[0108]

[0135] Procedure P3003 includes calibrating the process model 3003 so that it generates a simulated image that (i) minimizes the difference in intensity or frequency 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 the calibrated process model 3003.

[0109]

[0136] Figures 15A to 15C illustrate an example of a gradient constraint 3004. Figure 15A shows an exemplary reference intensity distribution 1510 at a given location in a physical image (e.g., spatial image, resist image, and 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 determine 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 as the frequency difference between the reference image 3002 and the simulated image (e.g., via the FFT of the image).

[0110]

[0137] Accordingly, in one embodiment, a gradient of intensity difference or frequency difference may be applied as a constraint during the calibration of a process model (e.g., 3003). For example, after applying a gradient constraint with respect to a reference intensity distribution 1510 during the calibration process, the process model may generate a simulated contour having an intensity distribution 1520 (Figure 15B). This intensity distribution 1520 has a similar shape (e.g., similar peaks and troughs) to the reference intensity distribution 1510. Thus, the calibrated process model (e.g., 3003) is considered 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 not calibrated according to a gradient associated with a physical term (e.g., AI / RI), such a process model may generate an unacceptable intensity distribution 1530 (Figure 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. The iterations include (a) running the process model using a target pattern to generate a simulated image; (b) determining the 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 the frequency difference between the frequencies associated with the simulated image and the frequencies associated with the reference image 3002; (c) determining the simulated gradient of a signal in the simulated image, wherein the signal is a signal along a given line passing through the simulated image; (d) determining the conditions that (i) the intensity difference or frequency difference is minimized, and (ii) the simulated gradient satisfies the gradient constraint 3004 associated with the reference image 3002; (e) adjusting the values ​​of the model parameters of the process model in response to conditions (i) and (ii) not being met, and repeating steps (a) to (d) until conditions (i) and (ii) are met.

[0112]

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

[0113]

[0140] In one embodiment, determining whether the contour shape constraints are satisfied includes determining whether the second derivative of the simulated contour falls within a desired range of the second derivative of the reference contour. In one embodiment, the contour shape is represented as a polygon, and therefore 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 defined with respect to printed contours of a pattern on a printed substrate (e.g., as considered in Method 2000 in Figure 12). For example, each contour constraint is a function of the tangent angle between the tangent to a simulated contour at a given measurement position and the angle of the measurement data 2002 at that given position, where the simulated contour is the contour of a simulated pattern determined through the execution of the process model using the target pattern.

[0115]

[0142] In one embodiment, method 3000 may further include, in step P3005, obtaining a resist contour of a resist pattern (e.g., 602 described above) and generating an etching contour 3005 by applying an etching 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 that performs the procedure discussed herein (e.g., Method 2000) is described. The process model is configured to generate simulated contours. The system includes a metronome tool (e.g., the SEM tool in Figures 16 and 17) configured to acquire measurement data 2002 at multiple measurement locations on a pattern, and one or more processors (e.g., 104 / 105 in Figure 22). The processors (e.g., 104 / 105) may be configured to calibrate the process model by adjusting the values ​​of model parameters of the process model until the simulated contours satisfy contour constraints 2004, which are based on the measurement data 2002.

[0117]

[0144] In one embodiment, the metrology tool, such as a scanning electron microscope (SEM), is configured to acquire measurements at multiple measurement locations, such as edge alignment (EP) gauges, which are positioned on or on printed contours of a printed pattern. In one embodiment, the measurement data 2002 includes multiple angles, each angle defined at each measurement location positioned on or on printed contours of a printed pattern. In one embodiment, each angle at each measurement location defines a direction that determines the edge alignment error between the printed contour and the target contour. As previously stated, the metrology tool may be an electron beam apparatus (e.g., the SEM in Figures 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 a pattern on a 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 position and the angle of the measurement data 2002 at that given position.

[0119]

[0146] In one embodiment, the processor is configured to iteratively adjust the values ​​of model parameters. For example, this iteration includes (a) running a process model with model parameters of given values ​​to generate simulated contours, where the given values ​​are random in the first iteration and adjusted in subsequent iterations; (c) determining the tangent to the simulated contour at each measurement location; (d) determining the tangent angle between the tangent and the angle of the measurement data 2002 at each measurement location; (e) determining whether the tangent angle is within the vertical range at one or more measurement locations; (f) adjusting the values ​​of the model parameters in response to the tangent angle being outside the vertical range; and performing steps (a) to (d).

[0120]

[0147] In one embodiment, the vertical range is an angle value between 88° and 92°, preferably 90°. In one embodiment, the processor is configured to adjust based on the slope of each tangent angle with respect to the model parameter, where the slope indicates 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 empirical models and / or machine learning models.

[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 is described, following the procedure of, for example, Method 3000, which is discussed herein. The process model may be configured to predict an image of a target pattern. The system includes a metronome tool (e.g., the SEM tool in Figures 16 and 17) configured to acquire a reference image 3002 associated with the target pattern, and one or more processors (104 / 105 in Figure 22). The processors may be configured to calibrate the process model such that the process model produces a simulated image that (i) minimizes the intensity or frequency difference between the simulated image and the reference image 3002, and (ii) satisfies gradient constraints 3004 associated with the reference image 3002.

[0123]

[0150] In one embodiment, the processor is configured to iteratively calibrate a process model. The iterations include: (a) running the process model using a target pattern to generate a simulated image; (b) determining the 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 the frequency difference between the frequencies associated with the simulated image and the frequencies associated with the reference image 3002; (c) determining the simulated gradient of a signal in the simulated image, wherein the signal is a signal 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) adjusting the values ​​of the model parameters of the process model in response to conditions (i) and (ii) not being met, and repeating steps (a) to (d) until conditions (i) and (ii) are met.

[0124]

[0151] As described above, in one embodiment, the simulated gradient is determined by obtaining 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 obtaining 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 simulated contours from a simulated image and to extract reference contours from a reference image 3002, the simulated contours and reference contours being associated with a target pattern, and the processor is further configured to calibrate a process model so that the simulated contours satisfy contour shape constraints, the contour shape constraints ensuring that the simulated contours match the shape of the reference contours.

[0126]

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

[0127]

[0154] In one embodiment, the reference image 3002 is obtained by simulating a physics-based model of the patterning process using the target pattern. The simulation can be performed on a processor. In one embodiment, the reference image 3002 may be obtained from a metronome tool (e.g., SEM). In one embodiment, the reference image 3002 includes a spatial 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 printed contours of a pattern on a printed substrate, as discussed in Figure 12. For example, each contour constraint is a function of the tangent angle between the tangent to a simulated contour at a given measurement position and the angle of the measurement data 2002 at that given position, where the simulated contour is the contour of a simulated pattern determined through the execution of the process model using a target pattern.

[0129]

[0156] In one embodiment, a non-temporary computer-readable medium containing instructions is provided, which, when executed by one or more processors, triggers an operation that includes: (i) obtaining resist pattern data 602 associated with a target pattern to be printed on a substrate; (ii) physical effect data 604 characterizing the effect of the etching process on the target pattern; and (iii) a measured bias 606 between the etching pattern and the resist pattern formed on the substrate to be printed; 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 the predicted etching bias. Furthermore, the non-temporary computer-readable medium may include additional instructions (e.g., related to P601, P603, and P605) considered in relation to Figure 6.

[0130]

[0157] In one embodiment, a non-temporary computer-readable medium containing instructions is provided, which, when executed by one or more processors, triggers an operation that includes (i) obtaining measurement data 2002 at multiple measurement locations on a pattern, and (ii) contour constraints 2004 defined based on the measurement data 2002, and calibrating a process model by adjusting the values ​​of model parameters of the process model until the simulated contours satisfy the contour constraints 2004. Furthermore, the non-temporary computer-readable medium may include additional instructions considered with respect to Figure 12 (e.g., related to procedures P2001, P2003, and P2005).

[0131]

[0158] In one embodiment, a non-temporary computer-readable medium containing instructions is provided, which, when executed by one or more processors, triggers an operation including (i) obtaining a reference image 3002 associated with a target pattern, and (ii) gradient constraints 3004 defined with respect to the reference image 3002, and calibrating a process model so that the process model generates a simulated image that minimizes the intensity or frequency difference between the simulated image and the reference image 3002, and (ii) satisfies the gradient constraints 3004. Furthermore, the non-temporary computer-readable medium may include additional instructions considered with respect to Figure 14 (e.g., related to procedures P3001, P3003, and P3005).

[0132]

[0159] According to this disclosure, separate embodiments are formed by combinations and secondary combinations of the disclosed elements. For example, a first combination includes determining etching contours based on a trained machine learning model. In another example, the combination includes determining simulated contours based on a model calibrated according to physical constraints.

[0133]

[0160] In some embodiments, a scanning electron microscope (SEM) generates an image of a structure exposed or transferred onto a substrate (e.g., part or all of the structure of a device). Figure 16 shows one embodiment of the SEM 200. The primary electron beam 202 emitted from the electron source 201 is focused by the focusing lens 203 and then passes through the beam deflector 204, the Ex-B deflector 205, and the objective lens 206 to focus and illuminate the substrate 100 on the 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 Ex B deflector 205 and detected by the secondary electron detector 207. A two-dimensional electron beam image can be obtained, for example, by detecting electrons generated from the sample in synchronization with a two-dimensional scan of the electron beam by the beam deflector 204, or by a repetitive scan of the electron beam 202 by the beam deflector 204 in the X or Y direction (performed in conjunction with the continuous movement of the substrate 100 by the substrate table 101 in the other direction).

[0135]

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

[0136]

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

[0137]

[0164] A charged particle beam generator 81 generates a primary charged particle beam 91. A focusing lens module 82 focuses the generated primary charged particle beam 91. A probe-forming objective lens module 83 focuses the focused primary charged particle beam onto a charged particle beam probe 92. A charged particle beam deflection module 84 scans the formed charged particle beam probe 92 across the 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 focusing lens module 82, and the probe-forming objective lens module 83, or equivalent designs, substitutes, or any combination thereof, together form a charged particle beam probe generator that generates a 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 struck by the charged particle beam probe 92, and generates a secondary charged particle detection signal 94. The image forming module 86 (e.g., a computing instrument) is coupled with 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, forms at least one scanning image. In one embodiment, the secondary charged particle detector module 85 and the image forming module 86, or equivalent designs, substitutes, or any combination thereof, together form an image forming apparatus that forms a scanning image from the detection of secondary charged particles emitted from a sample 90 struck by the charged particle beam probe 92.

[0139]

[0166] As described above, SEM images can be processed to extract contours that describe the edges of objects representing device structures within the image. These contours are then quantified via metrics such as CD. Thus, images of device structures are typically compared and quantified via simple metrics such as the distance between edges (CD) or the simple pixel difference between images. Typical contour models that detect the edges of objects in an image to measure CD use the image gradient. 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 expansion can be used to process the results of image gradient contour models to address noisy and discontinuous images, but this ultimately leads to low-resolution quantification of high-resolution images. Thus, in most cases, mathematical manipulation of images of device structures to reduce noise and automate edge detection leads to a loss of image resolution, and thereby a loss of information. Consequently, the result is low-resolution quantification, which becomes a simple representation of complex, high-resolution structures.

[0140]

[0167] Therefore, it is desirable to have a mathematical representation of the structure (e.g., circuit features, alignment marks, or metrologic target portions (e.g., grid features), etc.) that is generated or expected to be generated using the patterning process, regardless of whether the structure is in a potential resist image, in a developed resist image, or transferred, for example, by etching, to a layer on the substrate that can represent the general shape of the structure while maintaining resolution. In the context of lithography or other patterning processes, the structure may be a manufactured device or a part thereof, and the image may be an SEM image of the structure. In some cases, the structure may be a feature of a semiconductor device, such as an integrated circuit. In some cases, the structure may be an alignment mark or a part thereof (e.g., a grid of alignment marks) used in an alignment measurement process to determine the alignment of one object (e.g., a substrate) with another object (e.g., a patterning device), or a metronome target or a part thereof (e.g., a grid of a metronome target) used to measure parameters of a patterning process (e.g., superposition, focus, dose, etc.). In one embodiment, the metronome target is, for example, a diffraction grating used to measure superposition.

[0141]

[0168] In one embodiment, measurement data associated with a printed pattern is used to train a model in the method shown in Figure 3. The trained model may be further used to optimize the patterning process or to adjust the parameters of the patterning process. In one example, OPC addresses the fact that the final size and placement of the image of the design layout projected onto the substrate is not identical to, or does not depend solely on, the size and placement of the design layout on the patterning device. The terms “mask,” “reticle,” and “patterning device” are used interchangeably herein. Furthermore, those skilled in the art will recognize that the terms “mask” / “patterning device” and “design layout” may be used interchangeably, particularly in the context of lithography simulation / optimization, because, while physical patterning devices are not necessarily used in lithography simulation / optimization, a design layout can be used to represent a physical patterning device. When the feature size is small and the feature density is high, as is present in some design layouts, the position of a particular edge of a given feature is affected to some extent by the presence or absence of other adjacent features. These proximity effects arise from trace amounts of radiation joining from one feature to another, and / or from non-geometric optical effects such as diffraction and interference. Similarly, proximity effects can also arise from diffusion and other chemical effects during post-exposure baking (PEB), resist development, and etching, which commonly follow lithography.

[0142]

[0169] To ensure that the projected image of a design layout adheres reliably to the requirements of a given target circuit design, it is necessary to predict and compensate for proximity effects using advanced numerical models, design layout corrections, or pre-distortion. 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 effect correction processes. In typical high-end designs, almost every feature of the design layout is modified in some way to improve the fidelity of the projected image to the target design. These modifications may include shifts or biases of edge positions or line widths, as well as the application of “assist” features intended to support the projection of other features.

[0143]

[0170] Applying model-based OPC to target designs typically requires sophisticated process models and substantial computing resources, given the millions of features present in chip designs. However, applying OPC is generally an empirical iterative process, not a "precise science," and it does not always compensate for all possible proximity effects. Therefore, the effects of OPC, such as the design layout after applying OPC and any other RET, should be verified by design inspection—that is, intensive full-chip simulation using calibrated numerical process models—to minimize the possibility of design flaws being incorporated into the patterning device patterns. 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 lead time due to rework or repair of the devices once they are 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, for example, U.S. Patent Application 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 (Real-Effect Pattern) relates to adjusting the global bias of the design layout. 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 by a pattern with a diameter of 20 nm in the design layout, but at a higher dose.

[0146]

[0173] In addition to optimizing the design layout or patterning device (e.g., OPC), the illumination source may be optimized together with or separately from the patterning device optimization to enhance overall lithographic fidelity. The terms "illumination source" and "source" are used interchangeably in this document. Since the 1990s, numerous off-axis illumination sources have been introduced, such as annular, quadrupole, and dipole, providing greater design flexibility for OPCs and thereby improving imaging results. As is well known, off-axis illumination is a proven method for resolving fine structures (i.e., target features) contained within patterning devices. However, compared to conventional illumination sources, off-axis illumination sources typically provide lower radiation intensity for spatial images (AI). Therefore, it becomes desirable to optimize the illumination source to achieve the optimal balance between resolution refinement and radiation intensity reduction.

[0147]

[0174] An optimization method for multiple illumination sources can be found, for example, in the paper by Rosenbluth et al., titled "Optimum Mask and Source Patterns to Print A Given Shape," published in the Journal of Microlithography, Microfabrication, Microsystems 1(1), pp. 13-20, (2002). The emission source is divided into several regions, each corresponding to a specific region of the pupil spectrum. The emission source distribution is then assumed to be uniform in each emission source region, and the brightness of each region is optimized for the process window. However, the assumption that the emission source distribution is uniform in each emission source region is not always valid, and as a result, the effectiveness of this method is diminished. Another example described in Granik's paper, "Source Optimization for Image Fidelity and Throughput," published in Journal of Microlithography, Microfabrication, Microsystems 3(4), pp. 509-522, (2004), outlines several 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. While these methods have demonstrated some success, they typically require multiple complex iterations to converge. Furthermore, determining appropriate / optimal values ​​for several additional parameters, such as γ in Granik's method, can be difficult, imposing a trade-off between source optimization for substrate image fidelity and the requirement for source smoothness.

[0148]

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

[0149]

[0176] In this context, the constant pressure to reduce design rules has led semiconductor chip manufacturers to delve deeper into the era of low-k1 lithography using existing 193nm ArF lithography. Lithography toward lower k1 results in a strong demand for RET, exposure tools, and litho-friendly design. 1.35 ArF high numerical aperture (NA) exposure tools can be used in the future. To ensure that circuit designs can be reliably manufactured on substrates within a feasible process window, source-patterning device optimization (hereinafter referred to as source-mask optimization or SMO) is becoming a critical RET for the 2x nm node.

[0150]

[0177] A method and system for optimizing a radiation source and patterning device (design layout), which can simultaneously optimize the radiation source and patterning device using a cost function within a practical timeframe without constraints, is described in International Patent Application PCT / US2009 / 065359, filed on November 20, 2009, and published as International Publication No. 2010 / 059954 by the same applicant, entitled "Fast Freeform Source and Mask Co-Optimization Method," which is incorporated herein by reference in its entirety.

[0151]

[0178] Another method and system for optimizing a source and mask, including optimizing the source by adjusting the pixels of the source, is described in U.S. Patent Application No. 12 / 813456 by the same applicant, filed on June 10, 2010, and published as U.S. Patent Application Publication No. 2010 / 0315614, titled "Source-Mask Optimization in Lithographic Apparatus," which is incorporated herein by reference in its entirety.

[0152]

[0179] For example, in a lithography projection system, the cost function can be expressed as follows:

number

[0153]

[0180] Note that f p (z1, z2, ..., z N The normal weighted root mean square (RMS) of ) is:

number

number

[0154]

[0181] Furthermore, when considering maximizing the process window (PW), the same physical location from different PW conditions can be considered as different evaluation points in the cost function (Equation 1). For example, when considering N PW conditions, the evaluation points can be classified according to the PW conditions, and the cost function can be written as follows:

number

[0155]

[0182] Design variables may have constraints, and these constraints are (z1, z2, ..., z N) can be expressed as ∈ Z, where Z is the set of possible values ​​for the design variable. One possible constraint on the design variable may be imposed by the desired throughput of the lithography projector. The desired throughput may limit the dose and therefore be related to stochastic effects (e.g., imposing a lower bound on stochastic effects). As throughput increases, generally the dose decreases, the exposure time becomes shorter and longer, and the stochastic effects become larger. When considering minimizing substrate throughput and stochastic effects, the possible values ​​of the design variable may be constrained, since stochastic effects are a function of the design variable. Without such constraints imposed by the desired throughput, optimization may generate an unrealistic set of design variable values. For example, if the dose is included in the design variable, without such constraints, optimization may generate dose values ​​that make the throughput economically impossible. However, the usefulness of constraints should not be interpreted as necessary. Throughput may be affected by defect rate-based adjustments to the patterning process parameters. It is desirable to lower the feature defect rate while maintaining high throughput. Throughput can also be affected by the chemical properties of the resist. A slower resist (e.g., a resist that requires more light to be properly exposed) will result in lower throughput. Therefore, appropriate parameters for the patterning process may be determined based on the optimization process, which involves the feature defect rate due to the chemical properties or variations of the resist, and the dose requirements for higher throughput.

[0156]

[0183] Therefore, the optimization process is defined by constraints (z1, z2, ..., z N The goal is to find the set of design variable values ​​that minimizes the cost function under ∈ Z, i.e., to find the following:

number

[0157]

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

[0158]

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

[0159]

[0186] As shown in the example of an unrestricted flowchart in Figure 19, first the design layout (step S1302) is obtained, then the radiation source optimization step is performed in step S1304, where all design variables of the illumination radiation source are optimized to minimize the cost function while all other design variables are fixed (SO). Next, in the following step S1306, mask optimization (MO) is performed, where all design variables of the patterning device are optimized to minimize the cost function while all other design variables are fixed. These two steps are performed selectively until a specific termination condition is met in step S1308. Various termination conditions can be used, for example, the value of the cost function has become equal to a threshold; the value of the cost function has exceeded a threshold; the value of the cost function has reached a preset error limit range; or a preset number of iterations has been reached. Note that SO-MO-selective-optimization is used as an example of a selective flow. The selective flow can take many different forms, such as SO-LO-MO-selective-optimization, where SO and LO (lens optimization) are performed, MO is selective and iterative, or SMO can be performed once first, followed by LO and MO being selectively iterative, and so on. Finally, the output of the optimization result is obtained in step S1310, and the process stops.

[0160]

[0187] As mentioned above, the pattern selection algorithm may be integrated with simultaneous optimization or selective optimization. For example, if selective optimization is employed, a full chip SO can be performed first to identify "hot spots" and / or "warm spots," and then a MO can be performed. With this disclosure in mind, numerous rearrangements and combinations of secondary optimizations are possible to achieve the desired optimization result.

[0161]

[0188] Figure 20A shows an exemplary method of optimization in which the 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 multivariable cost function is set. In step S506, the cost function is expanded within a sufficiently small neighborhood around the starting point values ​​of the design variables for the first iteration step (i=0). In step S508, standard multivariable optimization techniques are applied to minimize the cost function. Note that the optimization problem may have constraints, such as adjustment ranges, added during or at a later stage of the optimization process in S508. Step S520 shows that each iteration has been 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 result from step S510 is compared with the desired or ideal lithography response value obtained in step S522. If the termination condition is met in step S514, i.e., if the optimization has produced a lithography response value that is sufficiently close to the desired value, 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 a wavefront aberration-adjusted map on the pupil (or other plane), an optimized radiation 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 using the results of the i-th iteration, and the process returns to step S506. The process in Figure 20A is described in detail below.

[0162]

[0189] In the example optimization process, the design variables (z1, z2, ..., z) N ) and f p (z1, z2, ..., z N No relationship is assumed or approximated between ) and f p (z1, z2, ..., z N ) is sufficiently smooth (for example, the first derivative)

number

number

[0163]

[0190] Here, we will 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. Design variables (z1, z2, ..., z N ) is (z 1i , z 2i ,..., z Ni In the i-th iteration, where the value of ) is taken, the Gauss-Newton algorithm is (z 1i , z 2i ,..., z Ni f in the neighborhood of ) p (z1, z2, ..., z N Linearize ) and then CF(z1, z2, ..., z N (z) gives the minimum value 1i , z 2i ,..., z Ni The value (z) in its neighborhood 1(i+1) , z 2(i+1) ,..., z N(i+1) ) calculates the design variables (z1, z2, ..., z N ) is (z 1(i+1) , z 2(i+1) ,..., z N(i+1) The value of ) is taken. This iteration converges (i.e., CF(z1, z2, ..., z N The process continues until the number of repetitions (which does not decrease further) or until a predetermined number of repetitions is reached.

[0164]

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

Number

[0165]

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

Number

[0166]

[0193] When the design variables (z1, z2,..., z N ) are not under any constraints, (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] When the design variables (z1, z2,..., z N ) are subject to J inequalities (e.g., the adjustment range of (z1, z2,..., z N ))

Number

Number

[0168] <00008​​​​​​​​​​​​​​​​​​​​​​​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 It can also be combined with the linearization of ). Specifically, f p (z1, z2, ..., z N ) is approximated as shown in Equation 3. Then, the constraint on the size of the worst defect is given by Inequality E Lp ≤f p (z1, z2, ..., z N )≦E Up It is described as, where E Lp and E Up is, f p (z1, z2, ..., z N These are two constants that define the minimum and maximum allowable deviations of ). Substituting Equation 3, these constraints are transformed for p=1, ..., P as follows:

number

[0171]

[0198] Equation 3 is generally (z1, z2, ..., z N Since this is only valid in the neighborhood of ), the desired constraint E is in such a neighborhood. Lp ≤f p (z1, z2, ..., z N )≦E Up If it is not possible to achieve this (which may be determined by some contradiction between the inequalities), the constant E Lp and E UpThe constraints may be relaxed until they become achievable. This optimization process involves (z1, z2, ..., z N The size of the worst defect in the vicinity of ) is minimized. In this process, each step gradually reduces the size of the worst defect, and each step is executed repeatedly until a specific termination condition is met. This optimally reduces the size of the worst defect.

[0172]

[0199] Another way to minimize the worst defect is to use weight w in each iteration. p The goal is to adjust the w. For example, if, after the i-th iteration, the r-th evaluation point is the worst defect, then the w is given higher priority by reducing the defect size of that evaluation point. r This can be increased in the (i+1)th iteration.

[0173]

[0200] Furthermore, by modifying the cost functions in Equations 4 and 5 by introducing the Lagrange multiplier method, a compromise can be reached between optimizing the RMS of the defect size and optimizing the size of the worst defect, i.e.,

number

[0174]

[0201] Optimizing the lithography projection system can enlarge the process window. A larger process window provides greater flexibility in process and chip design. The process window can be defined as a pair of focus and dose values ​​for the resist image to be within a specific limit range of the resist image design target. All methods described herein can be extended to generalized process window definitions that can be established by different or additional basic parameters in addition to exposure dose and focus. 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, if the PW consists of different mask biases, optimization 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 only as an example in this disclosure. A method for maximizing the process window according to one 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 nominal dose ε0 are shiftable, then they are the design variables (z1, z2, ..., z N ) can be optimized together. In the next step, the cost function is optimized so that it is within the pre-set limits (z1, z2, ..., z N If a set of values ​​(f0 ± Δf, ε0 ± Δε) is found, then (f0 ± Δf, ε0 ± Δε) is accepted as part of the process window.

[0177]

[0204] Alternatively, if the focus and dose are not shiftable, the design variables (z1, z2, ..., z N The cost function is optimized by fixing the focus and dose to the nominal focus f0 and nominal dose ε0. In an alternative embodiment, the cost function is optimized such that (z1, z2, ..., z) is within a predetermined limit. N If a pair of values ​​for (f0±Δf, ε0±Δε) is found, then it is accepted as part of the process window.

[0178]

[0205] The cost functions of equations 7, 7', or 7'' can be minimized using the methods described above in this disclosure. When the design variables are features of the projection optical system, such as the Zernike coefficient, minimizing the cost functions of equations 7, 7', or 7'' maximizes the process window based on projection optical system optimization, i.e., LO. When the design variables are features of the radiation source and patterning device in addition to the projection optical system, minimizing the cost functions of equations 7, 7', or 7'' maximizes the process window based on SMLO, as shown in Figure 19. When the design variables are features of the radiation source and patterning device, minimizing the cost functions of equations 7, 7', or 7'' maximizes the process window based on SMO. The cost functions of equations 7, 7', or 7'' are at least one f, such as those in equation 7 or equation 8. p (z1, z2, ..., z N This may include, and is a function of one or more stochastic influences, such as LWR or local CD variation of 2D features and throughput.

[0179]

[0206] Figure 21 shows one specific example of how the simultaneous SMLO process uses the Gauss-Newton algorithm for optimization. In step S702, the starting values ​​of the design variables are identified. Adjustment ranges 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 the 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 to predicted values ​​of those quantities in step S712. In step S716, the process window is determined. Steps S718, S720, and S722 are similar to the corresponding steps S514, S516, and S518 as described with respect to Figure 20A. As previously mentioned, 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 radiation source map and / or an optimized design layout.

[0180]

[0207] Figure 20B shows an exemplary method for optimizing the cost function, in which the design variables (z1, z2, ..., z) are used. N ) includes design variables for which only discrete values ​​can be assumed.

[0181]

[0208] This method begins by defining pixel groups for the illumination source and patterning device tiles for the patterning device (step S802). Generally, pixel groups or patterning device tiles are sometimes referred to as divisions of lithography process components. In one exemplary scheme, the illumination 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, as described above.

[0182]

[0209] In step S804, a lithography model is selected as the basis for the photolithography simulation. The photolithography simulation generates results, which are used in the calculation of photolithography metrics or responses. A specific photolithography metric is defined to be a performance metric that will be optimized (step S806). In step S808, initial (pre-optimization) conditions are set for the illumination source and patterning device. The initial conditions include the initial state of the pixel groups of the illumination source and the patterning device tiles of the patterning device, so as to refer to the initial illumination shape and initial patterning device pattern. The initial conditions may also include the mask bias, NA, and focus ramp range. Although steps S802, S804, S806, and S808 are shown as consecutive steps, it should be understood that in other embodiments of the invention, these steps may be performed in a different order.

[0183]

[0210] In step S810, pixel groups and patterning device tiles are ranked. Pixel groups and patterning device tiles may be interleaved in the ranking. Various ranking methods may be used, including randomly, in sequence (for example, from pixel group 1 to pixel group 117 and from patterning device tile 1 to patterning device tile 94), according to the physical location of the pixel groups and patterning device tiles (for example, ranking pixel groups closer to the center of the light source higher) and according to how much changing the pixel group or patterning device tile affects the performance metric.

[0184]

[0211] Once the pixel groups and patterning device styles are 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 styles is analyzed in rank order to determine whether a change in the pixel group or patterning device style leads to an improvement in the performance metric. If it is determined that the performance metric is improved, the pixel group or patterning device style is correspondingly changed, and the resulting improved performance metric and modified illumination shape or modified patterning device pattern form a baseline for comparison for subsequent analysis of lower-ranked pixel groups and patterning device styles. In other words, changes that improve the performance metric are retained. When changes to the states of the pixel groups and patterning device styles are made and retained, the initial illumination shape and initial patterning device pattern change correspondingly, and as a result, the modified illumination shape and modified patterning device pattern result from the optimization process of step S812.

[0185]

[0212] In other ways, adjustment of the patterning device polygon shape, as well as polling of pairs of two of the pixel groups and / or patterning device styles, is also performed within the optimization process of S812.

[0186]

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

[0187]

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

[0188]

[0215] Using the optimization method described above, the throughput of a lithographic projection apparatus can be increased. For example, the cost function may be a function of exposure time f p (z1, z2,..., z N ) which may be included. The optimization of such a cost function is preferably constrained or affected by the magnitude of stochastic effects or other metrics. Specifically, a computer-implemented method for increasing the 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 the exposure time of the substrate in order to minimize the exposure time.

[0189]

[0216] In one embodiment, the cost function includes at least one f p (z1, z_{2},..., z N ) which is a function of one or more stochastic effects. Stochastic effects may include feature defects, measurement data (e.g., SEPE) determined by the method of FIG. 3, LWR of 2D features, or local CD variations. In one embodiment, the stochastic effects include stochastic variations in the characteristics of the resist image. For example, such stochastic variations may include feature defect rate, line edge roughness (LER), line width roughness (LWR), and critical dimension uniformity (CDU). Including stochastic variations in the cost function makes it possible to find the values of the design variables that minimize the stochastic variations, thereby reducing the risk of defects due to stochastic effects.

[0190]

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

[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 the computer user. An input device 114, including alphanumeric and other keys, is coupled to bus 102 to communicate information and command selections to the processor 104. Another type of user input device is a cursor control unit 116, such as a mouse, trackball, or cursor directional keys, for communicating directional information and command selections to the processor 104 and for controlling cursor movement on the display 112. This input device generally has two degrees of freedom (a first axis (e.g., x) and a second axis (e.g., y)) that allow the device to be positioned in a plane. A touch panel (screen) display may be used as an input device.

[0192]

[0219] According to one embodiment, a portion of the optimization process may be performed by the computer system 100 in response to a processor 104 executing one or more sequences of one or more instructions contained in main memory 106. Such instructions may be read into main memory 106 from another computer-readable medium, such as a storage device 110. The execution of the sequence of instructions contained in main memory 106 causes the processor 104 to perform the process steps described herein. One or more processors in a multiprocessing configuration may be used to execute the sequence of instructions contained in main memory 106. In one alternative embodiment, hardwired circuits may be used instead of, or together with, software instructions. Thus, the description herein is not limited to any particular combination of hardware circuits and software.

[0193]

[0220] As used herein, the term “computer-readable medium” refers to any medium involved in providing instructions to the processor 104 for execution. Such mediums can take many forms, but are not limited to non-volatile media, volatile media, and transmission media. Non-volatile media include, for example, optical or magnetic disks such as storage device 110. Volatile media include dynamic memory such as main memory 106. Transmission media include coaxial cables, copper wires, and optical fibers (including wires including bus 102). Transmission media can also take the form of sound waves or light waves, such as those generated during radio frequency (RF) and infrared (IR) data communications. Common forms of computer-readable media include, for example, floppy disks, flexible disks, hard disks, magnetic tapes, and other magnetic media, CD-ROMs, DVDs, and other optical media, punch cards, paper tapes, and other physical media having perforation patterns, RAM, PROMs, and EPROMs, FLASH-EPROMs, and other memory chips or cartridges, carrier waves as described below, or other media that can be read by a computer.

[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 can load the instructions into its dynamic memory and send them over a telephone line using a modem. A modem local to computer system 100 can receive data over the telephone line and convert the data into an infrared signal using an infrared transmitter. An infrared detector coupled to bus 102 can receive the data carried by the infrared signal and load that data onto bus 102. Bus 102 transports the data to main memory 106, from which the processor 104 reads and executes the instructions. Instructions received by main memory 106 may optionally be stored in a storage device 110 before or after execution by the processor 104.

[0195]

[0222] The computer system 100 also preferably includes a communication interface 118 coupled to the bus 102. The communication interface 118 also provides bidirectional data communication coupled to a network link 120 connected to a local network 122. For example, the communication interface 118 may be an ISDN (Integrated Services Digital Network) card or modem that provides data communication connectivity to a corresponding type of telephone line. Alternatively, the communication interface 118 may be a local area network (LAN) card that provides data communication connectivity to a compatible LAN. A wireless link may also be implemented. In such an implementation, the communication interface 118 transmits and receives electrical, electromagnetic, or optical signals that carry digital data streams representing various types of information.

[0196]

[0223] The network link 120 typically provides data communication to other data devices through one or more networks. For example, the network link 120 can provide connection to data equipment operated by a host computer 124 or an Internet service provider (ISP) 126 through a local network 122. The ISP 126 then provides data communication services via the World Wide Packet Data Network (now commonly referred to as the "Internet" 128). Both the local network 122 and the Internet 128 use electrical, electromagnetic, or optical signals to carry digital data streams. Signals across various networks, and signals on the network link 120 and through the communication interface 118, carrying digital data to and from the computer system 100, are examples of carrier wave forms that carry information.

[0197]

[0224] The computer system 100 can send messages and receive data, including program code, through one or more networks, network links 120, and communication interfaces 118. In the internet example, server 130 may send request code for an application program through the internet 128, ISP 126, local network 122, and communication interfaces 118. One such downloaded application might, for example, provide lighting optimization in its embodiment. The received code is executed by processor 104 upon receipt and / or stored in storage device 110 or other non-volatile storage for later execution. In this way, the computer system 100 can obtain application code in carrier form.

[0198]

[0225] Figure 23 schematically shows an exemplary lithography projection apparatus, the illumination source of this apparatus can be optimized using the method described herein. This apparatus includes: - Illumination system IL for adjusting beam B of radiation. In this particular case, the illumination system also includes radiation source SO. - A first object table (e.g., a mask table) MT, which is equipped with a patterning device holder for holding a patterning device MA (e.g., a reticle), and is connected to a first positioner for precisely positioning the patterning device relative to an item PS. - A second object table (substrate table) WT comprising a substrate holder for holding a substrate W (e.g., a resist-coated silicon wafer) and connected to a second positioner for precisely positioning the substrate relative to an item PS. - A projection system ("lens") PS (e.g., a refractive, reflective, or reflective-refracting optical system) for imaging an illuminated portion of a patterning device MA onto a target portion C of a substrate W (e.g., including one or more dies).

[0199]

[0226] As shown herein, the apparatus is transmissive (i.e., has a transmissive mask). However, generally, the apparatus may be reflective (equipped with a reflective mask), for example. Alternatively, the apparatus may utilize another type of patterning device as an alternative to the use of a typical mask. Examples include programmable mirror arrays or LCD matrices.

[0200]

[0227] The source SO (e.g., a mercury lamp or excimer laser) generates a radiant beam. This beam is supplied to the illumination system (illuminator) IL either directly or after passing through a regulating means such as a beam expander Ex. The illuminator IL may include regulating means AD for setting the outer and / or inner radial ranges of the beam's intensity distribution (commonly referred to as σ-outer and σ-inner, respectively). Furthermore, it generally includes various other components such as an integrator IN and a capacitor CO. In this way, the beam B that strikes the patterning device MA has the desired uniformity and intensity distribution in cross-section.

[0201]

[0228] Regarding Figure 23, it should be noted that the source SO may be located within the housing of the lithography projection apparatus (in most cases, when the source SO is, for example, a mercury lamp), or it may be located away from the lithography projection apparatus, with the emitted beam it generates being guided into the apparatus (for example, using appropriate guide mirrors). This latter scenario is often the case when the source SO is an excimer laser (e.g., based on KrF, ArF, or F2 lathing).

[0202]

[0229] Next, beam PB intersects with the patterning device MA held on the patterning device table MT. After traversing the patterning device MA, beam B passes through lens PL, which focuses beam B onto a target portion C of the substrate W. Using a second positioning means (and interferometric measurement means IF), the substrate table WT can be precisely moved to position, for example, a different target portion C within the path of beam PB. Similarly, for example, after or during a mechanical search of the patterning device MA from the patterning device library, the patterning device MA can be precisely positioned relative to the path of beam B using the first positioning means. In general, the movement of the object tables MT and WT is achieved using long-stroke modules (coarse positioning) and short-stroke modules (fine positioning), which are not explicitly shown in Figure 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 or fixed only to short-stroke actuators.

[0203]

[0230] The drawn tool 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 a single pass (i.e., a single "flash"). The substrate table WT is then shifted in the x and / or y directions so that different target portions C can be illuminated by the beam PB; - In the scanning mode, basically the same scenario applies, except that a given target portion C is not exposed with a single "flash". Instead, the patterning device table MT is movable at a speed v in a given direction (the so-called "scanning direction", e.g., the y-direction) such that the projection beam B is scanned over the patterning device image. In parallel, the substrate table WT is moved simultaneously at a speed V = Mv (M is the magnification of the lens PL (generally, M = 1 / 4 or 1 / 5)) in the same or opposite direction. In this way, a relatively large target portion C can be exposed without the need to compromise the resolution.

[0204]

[0231] FIG. 24 schematically shows another exemplary lithographic projection apparatus LA whose illumination source can be optimized using the method described herein.

[0205]

[0232] The lithographic projection apparatus LA includes the following: - A source collector module SO - An illumination system (illuminator) IL configured to condition a radiation beam B (e.g., EUV radiation). - A support structure (e.g., a mask table) MT constructed to support a patterning device (e.g., a 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 (e.g., a reflective projection system) PS configured to project the pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g., including 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 absorbent in the EUV wavelength range, the mask may have a multilayer reflector, for example, a multi-stack of molybdenum and silicon. In one example, the multi-stack reflector has 40 layers of molybdenum and silicon, with each layer having a thickness of one-quarter of a wavelength. Even smaller wavelengths can be generated using X-ray lithography. Since most materials are absorbent at EUV and X-ray wavelengths, a thin piece of patterned absorbent material on the patterning device topography (e.g., a TaN absorber on a multilayer reflector) defines where features are printed (positive resist) or not printed (negative resist).

[0207]

[0234] Referring to Figure 24, the illuminator IL receives an extreme ultraviolet radiation beam from the source collector module SO. Methods for generating EUV radiation are not necessarily limited but include 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 called laser-generated plasma ("LPP"), the plasma can be generated by irradiating a fuel, such as droplets, streams, or clusters of material having a line-emitting element, with a laser beam. The source collector module SO may also be part of an EUV radiation system including a laser (not shown in Figure 24) that provides the laser beam for exciting the fuel. The resulting plasma emits output radiation (e.g., EUV radiation), which is collected using a radiation collector located in the source collector module. The laser and source collector module may be separate entities, for example, if 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 lithography apparatus, and the emitted beam is delivered from the laser to the source collector module using a beam delivery system, for example, including appropriate guide mirrors and / or beam expanders. In other cases, for example, when the source is a discharge-generated plasma EUV generator, often called a DPP source, the source may be an integrated part of the source collector module.

[0209]

[0236] An illuminator (IL) may include adjusters for adjusting the angular intensity distribution of the radiated beam. Generally, at least the outer and / or inner radial ranges of the intensity distribution at the pupil surface of the illuminator (commonly referred to as σ-outer and σ-inner, respectively) can be adjusted. Furthermore, an illuminator (IL) may include various other components such as facet fields and pupil mirror devices. Using an illuminator, the radiated beam can be tuned to have desired uniformity and intensity distribution in cross-section.

[0210]

[0237] A radiant beam B is incident on a patterning device (e.g., a mask) MA held on a support structure (e.g., a mask table) MT, and is patterned by the patterning device. After being reflected from the patterning device (e.g., a mask) MA, the radiant beam B passes through a projection system PS that focuses the beam onto a target portion C of the substrate W. A second positioner PW and a position sensor PS2 (e.g., an interference device, a linear encoder, or a capacitance sensor) can be used to precisely move the substrate table WT to position, for example, different target portions C within the path of the radiant beam B. Similarly, a first positioner PM and another position sensor PS1 can be used to precisely position the patterning device (e.g., a mask) MA relative to the path of the radiant beam B. The patterning device (e.g., a mask) MA and the substrate W may be aligned using patterning device alignment marks M1, M2 and substrate alignment marks P1, P2.

[0211]

[0238] The depicted device LA can 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 (i.e., single static exposure) while the entire pattern applied to the radiation beam is projected onto the target portion C in a single pass. The substrate table WT is then shifted in the X and / or Y directions so that different target portions 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., single dynamic exposure) while the pattern applied to the radiation beam is projected onto the target portion C. The speed and direction of the substrate table WT relative to the support structure (e.g., mask table) MT can be determined by the reduction and image inversion characteristics of the projection system PS. 3. In another mode, while the pattern applied to the radiation beam is projected onto the target portion C, the support structure (e.g., mask table) MT remains essentially stationary, holding the programmable patterning device, while the substrate table WT is moved or scanned. In this mode, a pulsed radiation source is generally used, and the programmable patterning device is updated as needed after each movement of the substrate table WT or between consecutive radiation pulses during scanning. This operating mode can be readily applied to maskless lithography utilizing programmable patterning devices such as the type of programmable mirror array mentioned above.

[0212]

[0239] Figure 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 positioned so that a vacuum environment can be maintained within the enclosed structure 220 of the source collector module SO. The EUV radiation emission plasma 210 can be formed by a discharge-generated plasma source. EUV radiation can be generated by a gas or vapor (e.g., Xe gas, Li vapor, or Sn vapor, from which the ultra-high temperature plasma 210 is made to emit radiation in the EUV range of the electromagnetic spectrum). The ultra-high temperature plasma 210 is made, for example, by a discharge that produces at least a partially ionized plasma. A partial pressure of, for example, 10 Pa of Xe, Li, Sn vapor, or any other suitable gas or vapor may be required for efficient generation of radiation. In one embodiment, a plasma of excited tin (Sn) is provided to generate EUV radiation.

[0213]

[0240] Radiation emitted by the high-temperature plasma 210 is passed from the source chamber 211 into the collector chamber 212 via an optional gas barrier or contaminant trap 230 (sometimes also called a contaminant barrier or foil trap) located within 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 further described herein includes at least a channel structure, as is known in the art.

[0214]

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

[0215]

[0242] Next, the radiation traverses an illumination system IL which may include faceted field mirror devices 22 and faceted pupil mirror devices 24 arranged in the patterning device MA to provide a desired angular distribution of the radiation beam 21 and a desired uniformity of radiation intensity in the patterning device MA. Upon reflection of the radiation beam 21 in 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 onto a substrate W held by the substrate table WT via reflective elements 28, 30.

[0216]

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

[0217]

[0244] The collector-type CO system shown in Figure 25 is depicted as a nested collector with obliquely incident reflectors 253, 254, and 255, as just one example of a collector (or collector mirror). The obliquely incident reflectors 253, 254, and 255 are arranged axially with respect to the optical axis O, and this type of collector-type CO system is preferably used in combination with a discharge-generating plasma source, often referred to as a DPP source.

[0218]

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

[0219]

[0246] The concepts disclosed herein can be used to simulate or mathematically model general imaging systems for imaging subwavelength features and may be particularly useful for new imaging techniques capable of generating increasingly shorter wavelengths. New techniques already in use include DUV lithography, which can generate wavelengths as short as 193 nm using EUV (extreme ultraviolet) and ArF lasers, and even 157 nm using fluorine lasers. EUV lithography can also generate wavelengths in the 20-5 nm range by using a synchrotron to generate photons, or by bombarding a material (solid or plasma) with high-energy electrons.

[0220]

[0247] Embodiments can be further described using the following clauses. 1. A method for training a patterning process model, wherein the patterning process model is configured to predict the patterns that will be formed during the patterning process, and the method is (i) image data associated with a desired pattern, (ii) a measured pattern of a substrate associated with the desired pattern, (iii) a first model associated with one aspect of the patterning process, comprising a first set of parameters, and (iv) a machine learning model associated with another aspect of the patterning process, comprising a second set of parameters. This includes repeatedly determining the values ​​of the first set of parameters and the second set of parameters to train the patterning process model, and the iterations include: Using the above image data, the first model and the machine learning model are executed to collaboratively predict the printed pattern on the substrate, and A method comprising modifying the values ​​of the first set of parameters and the second set of parameters so as to reduce the difference between the measured pattern and the predicted pattern of the patterning process model described above. 2. The method according to Clause 1, wherein the first model and the machine learning model described above are constructed and trained within a convolutional deep neural network framework. 3. The above training is The forward propagation of the outputs of the first model and the machine learning model described above predicts the pattern to be printed. The difference between the measured pattern and the predicted pattern of the patterning process model described above is determined. Determine the difference of the above difference for the first set of parameters and the second set of parameters, The method according to Clause 2, comprising determining the 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 above differences. 4. The first model described above is connected to the machine learning model described above in a series or parallel configuration, as described in any one of the provisions 1 to 3. 5. The above series combination of the above models is: The method according to Clause 4, which includes providing the output of the first model described above as input to the machine learning model described above. 6. The above series combination of the above models is: The method according to Clause 4, which includes providing the output of the above-mentioned machine learning model as input to the above-mentioned first model. 7. The above parallel combinations of the above models are: Providing the same input to the first model and the machine learning model described above, Combining the output of the first model described above and the machine learning model described above, The method according to Clause 4, which includes determining the predicted print pattern based on the combined output of each model described above. 8. The method described in any one of the clauses 1 to 7, wherein the first model described above is a resist model and / or a spatial model. 9. The above first set of parameters for the resist model is: Initial acid distribution, Acid diffusion, The contrast of the statue, 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 caused by high base concentration, Resist shrinkage, Resist development, or The method according to clause 8, which corresponds to at least one of the two-dimensional convex curvature effects. 10. The method described in any one of the clauses 1 to 9, wherein the first model described above is an empirical model that accurately models the physical phenomena of the first aspect of the patterning process described above. 11. The method according to any one of the clauses 1 to 10, relating to the first aspect of the above-mentioned model relating to the diffusion of the acid base after exposure of the substrate. 12. The machine learning model described above is a neural network that models the second aspect of the patterning process described above, which is relatively poorly understood from a physics perspective, as described in any one of clauses 1 to 9. 13. The method according to clause 12, wherein the second set of parameters described above includes the weights and biases of one or more layers of the neural network described above. 14. The patterning process model described above is the method described in any one of the clauses 1 to 13, corresponding to the second aspect of the post-exposure process of the patterning process described above. 15. The first and / or second aspects of the above post-exposure process are the methods described in any one of the items 1 to 14, including resist baking, resist development, and / or etching. 16. A method for determining optical proximity effect correction for a patterning process, To obtain image data associated with the desired pattern, Using the above image data, a trained patterning process model is run to predict the pattern that will be printed on the substrate. A method comprising determining optical proximity effect correction and / or defects using the predicted pattern that will be printed on the substrate subjected to the patterning process described above. 17. The method according to clause 16, wherein the image data is a spatial image and / or mask image of the desired pattern. 18. The method according to Clause 16, wherein the trained patterning process model includes a first model for a first aspect of the patterning process and a machine learning model for a second aspect of the patterning process configured to collectively predict the pattern to be printed on the substrate. 19. The method described in Clause 18, wherein the first model and the machine learning model described above are in a series and / or parallel combination. 20. The method according to any one of the clauses 16 to 19, wherein the first model described above is an empirical model that accurately models the physical phenomena of the first aspect of the post-exposure process of the patterning process described above. 21. The method according to any one of the clauses 16 to 20, relating to the first aspect of the above-mentioned model relating to the diffusion of the acid base after exposure of the substrate. 22. The machine learning model described above is a neural network that models the second aspect of the patterning process described above, which is relatively poorly understood from a physics perspective, as described in any one of the provisions of 16 to 21. 23. Determining the above-mentioned optical proximity effect correction means that The method according to any one of the clauses 16 to 22, comprising adjusting the desired pattern so that the difference between the predicted pattern and the desired pattern is reduced, and / or placing assist features around the desired pattern. 24. The above-mentioned defect is determined to be: The method described in any one of the provisions of Clauses 16 to 22, which includes performing a lithographic manufacturability check on the predicted patterns described above. 25. A method for training a machine learning model configured to determine etching biases related to the etching process, (i) Resist pattern data associated with the target pattern to be printed on the substrate, (ii) Physical effect data characterizing the effect of the etching process on the target pattern, and (iii) Measured bias between the resist pattern and the etching pattern formed on the printed substrate. A method comprising training a machine learning model based on the above-mentioned resist pattern data, the above-mentioned physical effect data, and the above-mentioned measured bias to reduce the difference between the above-mentioned measured bias and the above-mentioned predicted etching bias. 26. The method according to Clause 25, wherein the machine learning model is configured to receive the resist pattern data in a first layer of the machine learning model, and the physical effect data is received in a last layer of the machine learning model. 27. The method according to Clause 26, wherein the output of the last layer is a linear combination of (i) the etching bias predicted by running the machine learning model using the resist pattern data as input, and (ii) another etching bias determined based on the physical effects data related to the etching process. 28. The output of the last layer above is an etching bias map, and the etching bias is extracted from the etching bias map, and the etching bias map is The process involves using the above resist pattern data as input to execute the above machine learning model and outputting an etching bias map, wherein the etching bias map includes a biased resist pattern, and The method according to Clause 27, which is generated by combining the above etching bias map with the above physical effect data. 29. The method according to Clause 28, wherein the machine learning model is configured to receive the resist pattern data and the physical effect data in the first layer of the machine learning model. 30. Training the above machine learning model as described above is (a) Predicting the etching bias by running the machine learning model using the resist pattern data and physical effect data as inputs, (b) Determining the difference between the measured bias and the predicted etching bias, (c) Determine the gradient of the above difference with respect to the model parameters of the above machine learning model, (d) Using the above gradient as a guide, adjust the values ​​of the model parameters so that the above difference between the measured bias and the above predicted etching bias is reduced, (e) Determining whether the above difference has been minimized or exceeded the training threshold, (f) The method of any one of the clauses 25 to 29, which is an iterative process comprising performing steps (a) to (e) in response to the above difference not being minimized or the above training threshold not being exceeded. 31. Obtaining the above resist pattern data is: The method according to any one of the clauses 25 to 30, comprising performing one or more process models, including a resist model for the patterning process, using the target pattern that will be printed on the substrate. 32. The method according to any one of the clauses 25 to 31, wherein the above resist pattern data is represented as a resist image, and the above resist image is a pixelated image. 33. The above physical effect data is related to the etching term that characterizes the etching effect, and the above etching term is, The plasma concentration inside the trench of the resist pattern associated with the target pattern, The plasma concentration on the upper part of the resist layer of the above substrate, The loading effect is determined by convolving the above resist pattern with a Gaussian kernel having specific model parameters. Changes in the loading effect on the resist pattern during the etching process described above, The relative position of the resist pattern with respect to the adjacent pattern on the substrate, The aspect ratio of the above resist pattern, or The method according to any one of the clauses 25 to 32, comprising at least one clause relating to the combined effect of two or more etching process parameters. 34. Obtaining the above physical effect data is The method according to any one of the clauses 25 to 33, comprising performing a physical effects model comprising one or more of the etching clauses described above and a Gaussian kernel defined for each of the one or more etching clauses described above. 35. The method according to any one of the clauses 25 to 34, wherein the above physical effect data is represented as a pixelated image, and each pixel intensity indicates the physical effect on the resist pattern associated with the target pattern. 36. Obtain the resist contour of the above resist pattern, The method according to clauses 25 to 35, further comprising generating an etching contour by applying the etching bias to the resist contour. 37. A system for determining the etching bias related to the etching process, Semiconductor processing apparatus, and It is a processor, By running a physical effects model, we determine physical effects data that characterize the effects of the etching process on the substrate. Using the above resist pattern and the above physical effect data as input, a trained machine learning model is run to determine the etching bias. A system including a processor configured to control the semiconductor device or the etching process based on the etching bias described above. 38. The system according to Clause 37, wherein the trained machine learning model is trained using a plurality of resist patterns, the physical effect data associated with each of the plurality of resist patterns, and the measured bias associated with each of the resist patterns, such that the difference between the measured bias and the determined etching bias is minimized. 39. The system described in any one of clauses 37-38, wherein the trained machine learning model is a convolutional neural network (CNN) including specific weights and biases, the weights and biases of the CNN being determined through a training process using the plurality of resist patterns, the physical effect data associated with each of the plurality of resist patterns, and the measured bias associated with each of the resist patterns, such that the difference between the measured bias and the determined etching bias is minimized. 40. The above control of the semiconductor processing apparatus is: The system according to any one of the clauses 37 to 39, including adjusting the values ​​of one or more parameters of the semiconductor device so as to improve the yield of the patterning process described above. 41. Adjusting the values ​​of one or more of the above-mentioned parameters of the above-mentioned semiconductor processing apparatus is: (a) Changing the current value of one or more of the above parameters via the adjustment mechanism of the semiconductor processing apparatus, (b) Obtaining the resist pattern printed on the substrate via the semiconductor processing apparatus described above, (c) Determining the etching bias by running the trained machine learning model using the resist pattern, and further determining the etching pattern by applying the etching bias to the resist pattern. (d) Based on the etching pattern, determine whether the yield of the patterning process is within the desired yield range, The system described in Clause 40 is an iterative process that includes performing steps (a) to (d) in response to the yield not being within the above range. 42. The above control of the etching process is, The etching pattern is determined by applying the above etching bias to the above resist pattern. Based on the etching pattern described above, the yield of the patterning process described above is determined. A system according to any one of clauses 37 to 41, comprising determining an etching recipe for the etching process based on the etching pattern so as to improve the yield of the patterning process. 43. The above yield of the patterning process is the percentage of the etching pattern on the entire substrate that meets the design specifications, as described in any one of clauses 37 to 42. 44. The above semiconductor processing apparatus is a lithography apparatus, as described in any one of the clauses 37 to 43. 45. A method for calibrating a process model, wherein the process model is configured to generate simulated contours, and the method is (i) obtaining measurement data at multiple measurement locations on the pattern, and (ii) obtaining contour constraints defined based on the above measurement data. A method comprising calibrating the process model by adjusting the values ​​of the model parameters of the process model until the simulated contour satisfies the contour constraints. 46. ​​The method according to Clause 45, wherein the plurality of measurement positions are edge placement (EP) gauges positioned on the printed pattern or on the printed contours of the printed pattern. 47. The measurement data described above includes multiple angles, each angle defined at each measurement location located on the pattern or on the printed contour of the printed pattern, as described in any one of the provisions of Clauses 45 to 46. 48. The method according to Clause 47, wherein each angle at each measurement position defines the direction that determines the edge placement error between the printed contour and the target contour. 49. The method according to any one of the clauses 45 to 48, wherein each contour constraint is a function of the tangent angle between the tangent to the simulated contour at a given measurement position and the angle of the measurement data at the given position. 50. Adjusting the above values ​​of the above model parameters is possible. (a) Running the process model using the given values ​​of the model parameters to generate the simulated contour, wherein the given values ​​are random in the first iteration and adjusted in subsequent iterations. (c) Determine the tangent to the simulated contour at each of the above measurement locations, (d) Determine the tangent angle between the tangent line and the angle of the measurement data at each of the above measurement positions, (e) Determining whether the tangent angle is within the vertical range at one or more of the above measurement locations, (f) The method according to any one of the clauses 45 to 49, which is an iterative process comprising: adjusting the above value of the model parameter in response to the above tangent angle not being within the vertical range, and performing steps (a) to (d). 51. The method according to any one of the clauses 45 to 50, wherein the above vertical range is an angle value between 88° and 92°, preferably 90°. 52. The adjustment described above is based on the gradient of each tangent angle with respect to the above model parameter, the gradient indicating how sensitive the above tangent angle is to changes in the model parameter value, as described in any one of the methods in clauses 45 to 51. 53. The process model described above is a data-driven model, including empirical models and / or machine learning models, as described in any one of the provisions of 45 to 52. 54. The machine learning model described above is a convolutional neural network, and the model parameters are weights and biases associated with multiple layers, as described in any one of clauses 45 to 53. 55. A method for calibrating a process model configured to predict an image of a target pattern, (i) obtaining a reference image associated with the target pattern, and (ii) obtaining gradient constraints defined with respect to the reference image. A method comprising (i) minimizing the intensity or frequency difference between a simulated image and the reference image, and (ii) calibrating the process model such that the process model generates the simulated image that satisfies the gradient constraint. 56. The above calibration of the process model is: (a) To run the process model using the target pattern described above to generate the simulated image described above, (b) Determining the intensity difference between the intensity values ​​of the simulated image and the intensity values ​​of the reference image, and / or converting the simulated image and the reference image to the frequency domain via the Fourier transform, and determining the frequency difference between the frequencies related to the simulated image and the frequencies related to the reference image, (c) Determining the simulated gradient of the signal in the simulated image, wherein the signal is a signal along a given line passing through the simulated image, (d) Conditions: (i) The intensity difference or frequency difference is minimized, (ii) The simulated gradient satisfies the gradient constraint associated with the reference image, The method according to Clause 55, which is an iterative process comprising (e) adjusting the values ​​of the model parameters of the process model in response to conditions (i) and (ii) not being met, and performing steps (a) to (d) until conditions (i) and (ii) are met. 57. The method according to any one of the clauses 55 to 56, wherein the simulated gradient is determined by obtaining the first derivative of the signal along the given line passing through the simulated image. 58. The gradient constraint is obtained by taking the first derivative of the signal along the given line passing through the reference image, as described in any one of the provisions of 55 to 57. 59. Extracting simulated contours from the simulated image and extracting reference contours from the reference image, wherein the simulated contours and reference contours are associated with the target pattern. The method of any one of the clauses 55 to 58, further comprising calibrating the process model such that the simulated contour satisfies contour shape constraints, wherein the contour shape constraints ensure that the simulated contour matches the shape of the reference contour. 60. Determining whether the above contour shape constraints are satisfied is: The method according to any one of the clauses 55 to 59, comprising determining that the second derivative of the simulated contour is within the desired range of the second derivative of the reference contour. 61. The above reference image is obtained by simulating a physics-based model of the patterning process using the above target pattern, and the above reference image is The spatial image of the target pattern described above, The resist image of the above target pattern, and / or, The method according to any one of the clauses 55 to 60, including an etched image of the target pattern described above. 62. The method according to any one of the clauses 55 to 61, wherein the process model described above is configured to satisfy contour constraints defined with respect to printed contours of a pattern on a printed substrate. 63. The method according to any one of the clauses 55 to 62, wherein each contour constraint is a function of the tangent angle between the tangent to the simulated contour at a given measurement position and the angle of the measurement data at the given position, where the simulated contour is the contour of the simulated pattern determined through the execution of the process model using the target pattern. 64. A system for calibrating a process model, wherein the process model is configured to generate simulated contours, and the system is: A metrology tool configured to acquire measurement data at multiple measurement locations on a pattern, It is a processor, A system comprising a processor configured to calibrate the process model by adjusting the values ​​of the model parameters of the process model until the simulated contour satisfies the contour constraints, wherein the contour constraints are based on the measured data. 65. The system according to Clause 64, wherein the multiple measurement positions are edge placement (EP) gauges positioned on a printed pattern or on printed contours of the printed pattern. 66. The above measurement data includes multiple angles, each angle defined at each measurement position located on the pattern or on the printed contour of the printed pattern, as described in any one of clauses 64 to 65. 67. The system described in Clause 66, wherein each angle at each measurement position defines the direction that determines the edge placement error between the printed contour and the target contour. 68. A system according to any one of clauses 64 to 67, in which each contour constraint is a function of the tangent angle between the tangent to the simulated contour at a given measurement position and the angle of the measurement data at the given position. 69. Adjusting the above values ​​of the above model parameters is, (a) Running the process model using the given values ​​of the model parameters to generate the simulated contour, wherein the given values ​​are random in the first iteration and adjusted in subsequent iterations. (c) Determine the tangent to the simulated contour at each of the above measurement locations, (d) Determine the tangent angle between the tangent line and the angle of the measurement data at each of the above measurement positions, (e) Determining whether the tangent angle is within the vertical range at one or more of the above measurement locations, (f) The system described in any one of the clauses 64 to 68, which is an iterative process comprising: adjusting the above values ​​of the model parameters in response to the above tangent angle not being within the vertical range, and performing steps (a) to (d). 70. The above vertical range is an angle value between 88° and 92°, preferably 90°, as described in any one of the clauses 64 to 69. 71. The above adjustment is based on the gradient of each tangent angle with respect to the above model parameter, and the gradient indicates how sensitive the above tangent angle is to changes in the model parameter value, as described in any one of the systems in Clauses 64-70. 72. The above process model is a data-driven model, including empirical models and / or machine learning models, as described in any one of the systems in Clauses 64 to 71. 73. The machine learning model described above is a convolutional neural network, and the model parameters are weights and biases associated with multiple layers, as described in any one of clauses 64 to 72. 74. The above-mentioned metrologic tool is an electron beam apparatus, a system as described in any one of clauses 64 to 73. 75. The metrologic tool described above is a scanning electron microscope configured to identify and extract contours from captured images of patterns on a printed substrate, as described in any one of the systems in Clauses 64 to 74. 76. A system for calibrating a process model configured to predict an image of a target pattern, A metrology tool configured to acquire a reference image associated with the above target pattern, It is a processor, A system including a processor configured to (i) minimize the intensity or frequency difference between a simulated image and a reference image, and (ii) calibrate the process model such that the process model generates a simulated image that satisfies gradient constraints related to the reference image. 77. The above calibration of the process model is: (a) To run the process model using the target pattern described above to generate the simulated image described above, (b) Determining the intensity difference between the intensity values ​​of the simulated image and the intensity values ​​of the reference image, and / or converting the simulated image and the reference image to the frequency domain via the Fourier transform, and determining the frequency difference between the frequencies related to the simulated image and the frequencies related to the reference image, (c) Determining the simulated gradient of the signal in the simulated image, wherein the signal is a signal along a given line passing through the simulated image, (d) Conditions: (i) The intensity difference or frequency difference is minimized, (ii) The simulated gradient satisfies the gradient constraint associated with the reference image, (e) The system according to Clause 76, which is an iterative process comprising adjusting the values ​​of the model parameters of the process model in response to conditions (i) and (ii) not being met, and performing steps (a) to (d) until conditions (i) and (ii) are met. 78. The 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. The above gradient constraint is obtained by taking the first derivative of the signal along the given line passing through the above reference image, in any one of the systems described in any one of clauses 76 to 78. 80. The above processor further, The system is configured to extract simulated contours from the simulated image and reference contours from the reference image, where the simulated contours and reference contours are associated with the target pattern. The system is configured to calibrate the process model such that the simulated contour satisfies contour shape constraints, where the contour shape constraints ensure that the simulated contour matches the shape of the reference contour, as described in any one of clauses 76 to 79. 81. Determining whether the above contour shape constraints are satisfied is: A system according to any one of the clauses 76 to 80, which includes determining whether the second derivative of the simulated contour is within the desired range of the second derivative of the reference contour. 82. The above reference image is obtained by simulating a physics-based model of the patterning process using the above target pattern, and the above reference image is The spatial image of the target pattern described above, The resist image of the above target pattern, and / or, A system as described in any one of clauses 76 to 81, including an etched image of the target pattern described above. 83. The process model described above is a system as described in any one of clauses 76 to 82, configured to satisfy contour constraints defined with respect to printed contours of a pattern on a printed substrate. 84. Each contour constraint is a function of the tangent angle between the tangent to the simulated contour at a given measurement position and the angle of the measurement data at the given position, where the simulated contour is the contour of the simulated pattern determined through the execution of the process model using the target pattern, as described in any one of clauses 76 to 83. 85. A non-temporary computer-readable medium containing instructions, wherein the instructions are executed by one or more processors. (i) Resist pattern data associated with the target pattern to be printed on the substrate, (ii) Physical effect data characterizing the effect of the etching process on the target pattern, and (iii) Measured bias between the resist pattern and the etching pattern formed on the printed substrate. A non-temporary computer-readable medium that causes an operation including training the machine learning model based on the above resist pattern data, the above physical effect data, and the above measured bias to reduce the difference between the above measured bias and the above predicted etching bias. 86. A non-temporary computer-readable medium containing instructions, wherein the instructions are executed by one or more processors. (i) obtaining measurement data at multiple measurement locations on the pattern, and (ii) obtaining contour constraints defined based on the above measurement data. A non-temporary computer-readable medium that causes an operation including calibrating the process model by adjusting the values ​​of the model parameters of the process model until the simulated contour satisfies the contour constraints. 87. A non-temporary computer-readable medium containing instructions, wherein the instructions are executed by one or more processors. (i) obtaining a reference image associated with the target pattern, and (ii) obtaining gradient constraints defined with respect to the above reference image, A non-temporary computer-readable medium that causes an operation including (i) minimizing the intensity or frequency difference between the simulated image and the reference image, and (ii) calibrating the process model so that the process model generates 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, but it should be understood that the disclosed concepts may be used in any type of lithography imaging system (e.g., those used for imaging on substrates other than silicon wafers).

[0222]

[0249] The above description is for illustrative purposes only and is not intended to limit the scope of the claims. Therefore, it will be apparent to those skilled in the art that modifications may be made as described below without departing from the scope of the claims.

Claims

1. A method for calibrating a process model configured to generate simulated contours, (i) obtaining measurement data at multiple measurement positions on a pattern, and (ii) obtaining contour constraints defined based on the measurement data, wherein the measurement data relates to the contour shape of the pattern, and each contour constraint is a function of the tangent angle between the tangent to the simulated contour at a given measurement position and the angle of the measurement data at the given measurement position. A method comprising calibrating the process model by adjusting the values ​​of the model parameters of the process model until the simulated contours satisfy the contour constraints.

2. The method according to claim 1, wherein the plurality of measurement positions are edge placement (EP) gauges positioned on a printed pattern or on printed contours of the printed pattern.

3. The method according to claim 2, wherein the measurement data includes a plurality of angles, each angle defined at each measurement position located on the printed pattern or on the printed contour of the printed pattern.

4. The method according to claim 3, wherein each angle at each measurement position defines a direction that determines the edge placement error between the printed contour and the target contour.

5. Adjusting the values ​​of the aforementioned model parameters is, (a) Running the process model using the given values ​​of the model parameters to generate the simulated contour, wherein the given values ​​are random in the first iteration and adjusted in subsequent iterations, (c) Determining the tangent to the simulated contour at each of the measurement positions, (d) Determining the tangent angle between the tangent and the angle of the measurement data at each of the measurement positions, (e) Determining whether the tangent angle is within the vertical range at one or more of the measurement positions, The method according to claim 1 or 2, which is an iterative process comprising (f) adjusting the value of the model parameter in response to the tangent angle not being within the vertical range, and performing steps (a) to (d).

6. The method according to claim 1 or 2, wherein the adjustment 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 the model parameter value.

7. The method according to claim 1 or 2, wherein the process model is a data-driven model that includes an empirical model and / or a machine learning model.

8. The method according to claim 7, wherein the machine learning model is a convolutional neural network, and the model parameters are weights and biases associated with a plurality of layers.

9. A non-temporary computer-readable medium containing instructions, wherein, when executed by one or more processors, the instructions cause the one or more processors to perform the method according to any one of claims 1 to 8.

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