Repairing photolithography masks by simulating photoresist thickness evolution

Abstract

A system for mask design repair can develop a simulation-based model of layer thickness after one or more process steps for fabricating features on a specimen, develop a transformed model of a fabrication process that mimics the simulation-based model and has a faster evaluation speed than the simulation-based model, and wherein input to the transformed model includes an input mask design, and wherein output of the transformed model includes one or more output parameters associated with fabrication of the input mask design and one or more sensitivity metrics that describe sensitivity of the one or more output parameters to variations in the input mask design. The system can further receive a candidate mask design and generate a repaired mask design based on the transformed model and the candidate mask design.

Description

[0001] Cross Reference to Related Applications

[0002] This application claims the benefit under 35 U.S.C. § 119(e) of provisional U.S. Application No. 63 / 398,227, filed August 16, 2022, entitled REPAIR OF LITHOGRAPHY MASK PRINTING DEFECTS DISCOVERED BY RAPID RIGOROUS SIMULATION OF PHOTORESIST THICKNESS EVOLUTION, which is incorporated herein by reference in its entirety. TECHNICAL FIELD

[0003] The present disclosure relates generally to lithography mask design, and more particularly to repairing lithography mask designs to mitigate random defects. BACKGROUND

[0004] The need to reduce feature sizes in semiconductor devices leads to tighter tolerances for lithography printing processes. While the minimum feature size can be reduced generally by scaling down the wavelength of light used in the lithography process, it is often desirable to manufacture features near or below the classical resolution limit at a particular wavelength. Under this mechanism, random defects associated with the randomness of various processes become increasingly problematic. Random defects that occur during semiconductor manufacturing can be attributed to the inherent randomness of a large number of physical phenomena (such as, but not limited to, photon exposure and absorption, photo-product diffusion, chemical reactant spatial distribution, chemical reactions, or the like) that make up the lithography pattern transfer process. Significantly, randomness is different from uncertainty and is related to random variation within a process. Typical methods for characterizing random wafer defects include top-down scanning electron microscope (SEM)-based inspection, after-development inspection (ADI), and / or after-etching inspection (AEI) pattern edge placement, and top-down simulation thereof and inspection. However, such techniques can be too time-consuming and / or can not provide sufficient measurement of parameters leading to defect rates of manufactured samples that can ultimately be of interest. Therefore, there is a need to develop systems and methods that address such deficiencies. SUMMARY

[0005] According to one or more illustrative embodiments, a system is disclosed. In one illustrative embodiment, the system includes a controller including one or more processors. In another illustrative embodiment, the controller develops a simulation-based model of a thickness of a layer after one or more process steps for manufacturing a feature on a specimen, wherein the simulation-based model accepts an input mask design to be exposed on the specimen and provides at least the thickness of the layer after the one or more process steps as an output. In another illustrative embodiment, the controller develops a transformation model of a manufacturing process that mimics the simulation-based model and has a faster evaluation speed than the simulation-based model for a selected range of at least one of inputs or outputs, wherein the inputs to the transformation model include the input mask design, and wherein the outputs of the transformation model include one or more output parameters associated with manufacturing of the input mask design and one or more sensitivity metrics that describe sensitivity of the one or more output parameters to variations of the input mask design. In another illustrative embodiment, the one or more output parameters include at least one of the thickness of the layer after the one or more process steps or a random defect rate based on the thickness of the layer. In another illustrative embodiment, the controller receives a candidate mask design. In another illustrative embodiment, the controller generates a patched mask design based on the transformation model and the candidate mask design.

[0006] According to one or more illustrative embodiments, a method is disclosed. In one illustrative embodiment, the method includes developing a simulation-based model of a thickness of a layer after one or more process steps for manufacturing a feature on a specimen, wherein the simulation-based model accepts an input mask design to be exposed on the specimen and provides at least the thickness of the layer after the one or more process steps as an output. In another illustrative embodiment, the method includes developing a transformation model of a manufacturing process that mimics the simulation-based model and has a faster evaluation speed than the simulation-based model for a selected range of at least one of inputs or outputs, wherein the inputs to the transformation model include the input mask design, and wherein the outputs of the transformation model include one or more output parameters associated with manufacturing of the input mask design and one or more sensitivity metrics that describe sensitivity of the one or more output parameters to variations of the input mask design. In another illustrative embodiment, the one or more output parameters include at least one of the thickness of the layer after the one or more process steps or a random defect rate based on the thickness of the layer. In another illustrative embodiment, the method includes receiving a candidate mask design. In another illustrative embodiment, the method includes generating a patched mask design based on the transformation model and the candidate mask design.

[0007] According to one or more illustrative embodiments, a system is disclosed. In one illustrative embodiment, the system includes a controller including one or more processors. In another illustrative embodiment, the controller develops a simulation-based model of a thickness of a layer after one or more process steps for manufacturing a feature on a specimen, where inputs to the simulation-based model include an input mask design defining a mask to be exposed on the specimen and a recipe of one or more process parameters associated with the one or more process steps, and where outputs of the simulation-based model include at least the thickness of the layer after the one or more process steps. In another illustrative embodiment, the controller develops a transformation model of a manufacturing process that emulates the simulation-based model and has a faster evaluation speed than the simulation-based model for a selected range of at least one of inputs or outputs, where the inputs to the transformation model include at least one of the input mask design and the one or more process parameters, and where the outputs of the transformation model include one or more output parameters associated with manufacturing the input mask design with the one or more process steps and one or more sensitivity metrics describing a sensitivity of the one or more output parameters to the inputs to the transformation model. In another illustrative embodiment, the one or more output parameters include at least one of the thickness of the layer after the one or more process steps or a random defect rate based on the thickness of the layer. In another illustrative embodiment, the controller receives a candidate recipe including a candidate mask design and the at least one of the one or more process parameters. In another illustrative embodiment, the controller generates a patched recipe based on the transformation model and the candidate mask design.

[0008] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application as claimed. The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the application and together with the general description, serve to explain the principles of the application. BRIEF DESCRIPTION OF DRAWINGS

[0009] The many advantages of the present application will be better understood by reference to the drawings in conjunction with the accompanying description.

[0010] Figure 1A is a block diagram of a system in accordance with one or more embodiments of the present application.

[0011] Figure 1B is a conceptual diagram illustrating a lithography sub-system in accordance with one or more embodiments of the present application.

[0012] Figure 1C is a conceptual diagram illustrating a characterization sub-system in accordance with one or more embodiments of the present application.

[0013] Figure 2A is a top view of two mask designs according to one or more embodiments of the application.

[0014] Figure 2B is a top view of two mask designs according to one or more embodiments of the application. Figure 2A is a plot of average resist edge position for six slices of the mask designs of

[0015] Figure 2C is a plot of average resist edge position for six slices of the mask designs of Figure 2A

[0016] Figure 2D is a plot of random defect rate for six slices of the mask designs of Figure 2A

[0017] Figure 3A is a flowchart illustrating steps performed in a method for mask repair according to one or more embodiments of the application.

[0018] Figure 3B is a flowchart illustrating additional steps of the method of Figure 3A

[0019] Figure 4 is a conceptual illustration of trade-off of a transformation model according to one or more embodiments of the application.

[0020] Figure 5 is a simplified flowchart illustrating random defect mitigation according to one or more embodiments of the application.

[0021] Figure 6A is a simplified view of a repaired mask according to one or more embodiments of the application, shown in the form of update vectors on feature edges.

[0022] Figure 6B is a simplified view of a repaired mask according to one or more embodiments of the application, shown in the form of update vectors on feature edges, where only a subset of sample locations are repaired.

[0023] Figure 7 is an illustration of iterative mask repair in a region of interest (ROI) according to one or more embodiments of the application.

[0024] Figure 8A is a simplified flowchart illustrating training of a machine learning model using a transformation model according to one or more embodiments of the application.

[0025] Figure 8B ​​​is a flowchart illustrating non-limiting examples of training a machine learning model based on training data generated by a transformation model in accordance with one or more embodiments of the present disclosure.

[0026] Figures 9A to 9D is a series of plots including illustrations of additional non-limiting examples of repair masks in accordance with one or more embodiments of the present disclosure.

[0027] Figure 10 is a simplified flowchart illustrating random defect mitigation in accordance with one or more embodiments of the present disclosure. DETAILED DESCRIPTION

[0028] Reference will now be made in detail to the disclosed subject matter, which is illustrated in the accompanying drawings. The present application has been particularly shown and described with particular embodiments and specific features thereof. The embodiments set forth herein are illustrative and not restrictive. Those skilled in the art will readily appreciate that various modifications and adaptations of the embodiments set forth herein are possible and within the spirit and scope of the present application.

[0029] Embodiments of the present application relate to systems and methods that provide repair mask pattern design changes that attempt to mitigate or control random wafer defects within acceptable tolerances. For example, embodiments of the present application can evaluate the sensitivity of an input mask design to random defects and provide repair changes to the input mask design to reduce the sensitivity to such random defects. Notably, the systems and methods disclosed herein can provide repair changes to masks that have undergone other modifications, such as but not limited to optical proximity correction (OPC) variations, to facilitate accurate manufacturing according to the intended design. It should be noted that OPC and other techniques can be prone to error when based on "rule-based" or other "compact" modeling techniques that can include approximations to provide full chip evaluation with high throughput. However, the systems and methods disclosed herein can incorporate more accurate and potentially computationally more intensive modeling to provide superior random defect mitigation, and can provide acceptable throughput. Furthermore, the repair process can be flexibly applied to the full design (e.g., full chip) or in a targeted manner to specific regions of interest and / or regions most susceptible to random defects of interest.

[0030] Techniques for measuring and controlling semiconductor manufacturing in the presence of random defects are generally described in U.S. Patent No. 10,474,042, issued November 12, 2019, which is incorporated herein by reference in its entirety. Random defects can be attributed to the inherent randomness of a large number of physical phenomena that make up a lithographic pattern transfer process, such as but not limited to, photon exposure and absorption, photo-product diffusion, chemical reactant spatial distribution, or chemical reactions. In this way, when nominally identical conditions are used to manufacture nominally identical structures, such as but not limited to, at multiple locations within a field, at a given location across multiple fields on a single wafer, or at a given location across a sample of multiple wafers, randomly occurring manufacturing defects can occur with a certain probability.

[0031] In some embodiments, a rigorous simulation-based model (e.g., physics-based model) that predicts a sample layer thickness after one or more process steps (e.g., lithography, etching, polishing, or the like) is first generated, which can enable an accurate understanding of the random defectivity. For example, the simulation-based model can predict a thickness of a photoresist layer after a lithography exposure (e.g., after a development step). As another example, the simulation-based model can predict a thickness of a process layer after an etching and / or polishing step. Further, the simulation-based model can incorporate the effects of random variations and / or variations in process parameters that naturally occur during processing, such as but not limited to, dose, focus position, illumination numerical aperture, illumination source shape, post-exposure bake temperature, development time, or the like.

[0032] Subsequently, a transformation model can be developed that reproduces the results of the simulation-based model for a selected input and / or output space while providing a faster evaluation speed (e.g., faster computation time) than the simulation-based model. For example, the transformation model can mimic the simulation-based model for a selected range of inputs (e.g., a particular range of inputs, such as but not limited to, mask design and / or manufacturing process parameters) and / or outputs (e.g., a particular range of outputs, such as but not limited to, corrections to a mask design, a relatively lower pixel density associated with corrections to a mask design, and / or process parameters) that are within acceptable tolerances while providing a faster evaluation speed (e.g., faster computation time) than the simulation-based model. The transformation model can be, but is not required to be, a machine learning model. In a general sense, the transformation model can be tuned to balance the input space coverage, speed, and accuracy for a given application. The transformation model can further provide mathematical differentiability, such that the transformation model can provide a direct and efficient estimate of the sensitivity of a particular mask design (or variations thereof) to an output parameter of interest (such as but not limited to, random defectivity). Such sensitivity estimates can be provided in the form of a sensitivity metric (e.g., analyzing model gradients or the like) and can be used to provide remedial design changes to improve the performance of a mask.

[0033] Within the spirit and scope of the present invention, the transformation model and associated sensitivity metrics can be utilized in various ways to provide a repairative mask design change that mitigates random defects.

[0034] In some embodiments, the transformation model evaluates a candidate mask design and provides an output in the form of an output parameter of interest (e.g., random defect rate, resist edge placement error, distance field violation, mask rule check violation, etc.) and a sensitivity metric that characterizes the sensitivity of the candidate mask design to the output parameter. In the case of multiple output parameters, the sensitivity metric can provide a measure of the sensitivity of the candidate mask design to the output parameters individually or in combination. If the output parameter is unacceptable (e.g., outside of a selected tolerance), the candidate mask design is updated based on the sensitivity metric. This process can be iterated as needed to provide a repaired mask design that meets the selected tolerance. It should be noted that within the spirit and scope of the present invention, the mask design can be provided in various forms (e.g., but not limited to, binary representation, polygonal representation, distance field representation, or level set representation). In a general sense, the mask design can be represented by any parameter for which a sensitivity metric can be generated using the transformation model.

[0035] In some embodiments, the transformation model is used to provide training data for a machine learning model used for mask repair. For example, a machine learning model can be developed to generate a repaired mask design from an input mask design, where the machine learning model is trained based at least in part on the training data generated by the transformation model. To illustrate, the transformation model can evaluate a repaired mask design by generating an output parameter and associated sensitivity metric. Further, in the case where the repaired mask design provided by the machine learning model does not meet an application tolerance, the sensitivity metric from the transformation model can be used to train the machine learning model (e.g., weights within the machine learning model).

[0036] Additional embodiments of the present invention are directed to providing corrective modifications to additional aspects of a manufacturing recipe, such as but not limited to the properties of the illumination used during lithography (e.g., source distribution, wavelength, polarization, angle of incidence, or the like) or the properties of the sample (e.g., thickness of a processing layer, thickness of a photoresist, or the like). In this way, in addition to and / or in place of the mask design, such recipe parameters can be adjusted to reduce the probability of random defects during manufacturing.

[0037] Reference will now be made to Figures 1A to 10 , systems and methods are described in greater detail that provide a repairative mask design change to mitigate random defects in accordance with one or more embodiments of the present invention.

[0038] Figure 1Ais a block diagram of a system 100 in accordance with one or more embodiments of the present disclosure. In some embodiments, the system 100 includes a lithography sub-system 102 for lithographically printing one or more patterns on a sample 104 based on a mask 106 (e.g., a photolithography mask, a pattern mask, a reticle, or the like). For example, the lithography sub-system 102 can operate by illuminating the mask 106 and projecting an image of the mask 106 onto the sample 104.

[0039] The lithography sub-system 102 can include any type of lithographic printing tool known in the art, including but not limited to a scanner or a stepper. Moreover, the lithography sub-system 102 can utilize any type of illumination. For example, the lithography sub-system 102 can utilize extreme ultraviolet (EUV) illumination and thus be characterized as an EUV lithography sub-system.

[0040] In some embodiments, the system 100 includes a characterization sub-system 108 configured to generate one or more measurements of the mask 106 and / or the sample 104 having features associated with the mask 106 via lithographic exposure and potentially additional processing steps. The characterization sub-system 108 can include any type of characterization tool known in the art, such as but not limited to an optical characterization tool (e.g., an optical imaging tool or the like), an x-ray characterization tool, or a particle beam characterization tool (e.g., a scanning electron microscope (SEM), a transmission electron microscope (TEM), a focused ion beam (FIB) tool, or the like). Moreover, the characterization sub-system 108 or any portion thereof can be characterized as an inspection tool and / or a metrology. In this way, the characterization sub-system 108 can perform various functions, including but not limited to identifying defects in the mask 106 or performing one or more measurements of portions of the mask (e.g., critical dimension (CD) measurements, feature thickness measurements, film thickness measurements, composition measurements, edge placement measurements, or the like).

[0041] In some embodiments, the system 100 includes a controller 110. In some embodiments, the controller 110 includes one or more processors 112 configured to execute program instructions maintained in a memory 114 (e.g., a memory device). The controller 110 can be communicatively coupled with any component of the system 100 to provide unidirectional and / or bidirectional communication. In this way, the controller 110 can perform (e.g., via the one or more processors 112) any of the various process steps described throughout the present disclosure, such as but not limited to developing an analog-based model of a manufacturing process, developing a transformation model that mimics the analog-based model for a selected input space and provides a sensitivity metric that describes a sensitivity of one or more output parameters to variations in the mask, receiving a candidate mask design, or generating a patched mask design based on iteratively updating the candidate mask design using the transformation model.

[0042] The one or more processors 112 of the controller 110 can include any processing element known in the art. In this regard, the one or more processors 112 can include any microprocessor-type device configured to execute algorithms and / or instructions. In some embodiments, the one or more processors 112 can be comprised of a desktop computer, a mainframe computer system, a workstation, a graphics computer, a parallel processor, or any other computer system (e.g., networked computers) configured to execute programs configured to operate the system 100, as described throughout the present disclosure. It is further recognized that the term "processor" can be broadly defined to encompass any device having one or more processing elements that execute program instructions from a non-transitory memory 114. Moreover, the steps described throughout the present disclosure can be carried out by a single controller 110 or, alternatively, multiple controllers. Additionally, the controller 110 can include one or more controllers housed in a common housing or within multiple housings. In this manner, any controller or combination of controllers can be individually packaged as a module suitable for integration into the system 100.

[0043] The memory 114 can include any storage media suitable for storing program instructions executable by the associated one or more processors 112 known in the art. For example, the memory 114 can include a non-transitory memory medium. By way of another example, the memory 114 can include, but is not limited to, read-only memory, random access memory, magnetic or optical memory devices (e.g., magnetic disks), magnetic tape, solid state drives, and the like. It is further noted that the memory 114 can be housed in a common controller housing with the one or more processors 112. In some embodiments, the memory 114 can be remotely located relative to the physical location of the one or more processors 112 and the controller 110. For example, the one or more processors 112 of the controller 110 can access a remote memory (e.g., a server) that can be accessed through a network (e.g., the Internet, an intranet, and the like). Accordingly, the above description should not be interpreted as a limitation on the present disclosure but merely an illustration.

[0044] Mask design repair is described in more detail in FIGS. 2-10. Typical methods of stochastic defect control focus on modeling the placement of edges in photoresist (e.g., resist) or some intermediate metric such as aerial images (e.g., continuous or thresholded and typically contoured to approximate resist edges). The edges in such techniques are typically defined as the boundary separating resist area from space, with defects typically defined as locations where edges intersect or show a tendency to intersect. For example, typical methods of stochastic defect control are generally described in U.S. Patent No. 11,126,090, entitled “Model for calculating a stochastic variation in an arbitrary pattern” and issued September 21, 2021; “Full-chip lithography simulation and design analysis: how OPC is changing IC design” by Chris. Spence (Emerging Lithographic Technologies IX, Volume 5751, SPIE, 2005); “Fast pixel-based mask optimization for inverse lithography” by Yuri. Granik (Journal of Micro / Nanolithography, MEMS, and MOEMS 5.4 (2006): 043002-043002); “Fast stochastic proximity effect correction for optical proximity correction” by Daniel S. Abrams, et al. (Proc. SPIE 5374, Optical Microlithography XIV, 2004); “Fast stochastic proximity effect correction for optical proximity correction” by Daniel S. Abrams, et al. (Proc. SPIE 5374, Optical Microlithography XIV, 2004); “Fast stochastic proximity effect correction for optical proximity correction” by Daniel S. Abrams, et al. (Proc. SPIE 5374, Optical Microlithography XIV, 2004); “Fast stochastic proximity effect correction for optical proximity correction” by Daniel S. Abrams, et al. (Proc. SPIE 5374, Optical Microlithography XIV, 2004); “Fast stochastic proximity effect correction for optical proximity correction” by Daniel S. Abrams, et al. (Proc. SPIE 5374, Optical Microlithography XIV, 2004); “Fast stochastic proximity effect correction for optical proximity correction” by Daniel S.Fast inverse lithography technology, by Pang, Linyong, et al., Optical Microlithography XIX, Vol. 6154, SPIE, 2006; Source mask optimization (SMO) at full chip scale using inverse lithography technology (ILT) based on level set methods, by Pang, Linyong, et al., Lithography Asia 2009, Vol. 7520, SPIE, 2009; and Gaussian random field EUV stochastic models, their generalizations and lithographically meaningful stochastic metrics, by Latypov, Azat, et al., Extreme Ultraviolet (EUV) Lithography XII, Vol. 11609, SPIE, 2021; all of which are incorporated herein by reference in their entireties.

[0045] However, it is contemplated herein that stochastic defectivity can be estimated more directly and accurately based on local resist thickness at a region of interest on a sample (e.g., wafer) rather than through edge position. This is because edge position encodes an approximation of resist thickness by definition. Moreover, existing techniques can not be suitable for relatively rare stochastic errors. Advantages of stochastic defect characterization based on local resist thickness are generally described in: U.S. Patent Publication No. 2022 / 0129775, entitled “Prediction and metrology of stochastic photoresist thickness defects” and published on April 28, 2022; Mack, Chris A., et al. “Stochastic exposure kinetics of extreme ultraviolet photoresists: simulation study” (Journal of Micro / Nanolithography, MEMS, and MOEMS 10.3 (2011): 033019-033019); and Mack, Chris A., John J. Biafore, and Mark D. Smith. “Stochastic exposure kinetics of extreme ultraviolet photoresists: trapping model” (Journal of Vacuum Science & Technology B 31.6 (2013)); all of which are incorporated herein in their entirety.

[0046] As illustration, Figures 2A to 2D A series of plots demonstrating stochastic defectivity for two mask designs providing similar edge positions, but different local resist thicknesses and different error rates, in accordance with one or more embodiments of the present application. Figure 2A is a top view of two mask designs (labeled “Mask 1” and “Mask 2”) in accordance with one or more embodiments of the present application. Figure 2B is a top view of two mask designs (labeled “Mask 1” and “Mask 2”) in accordance with one or more embodiments of the present application. Figure 2A is a plot of average resist edge position (EP) for six slices (p1 to p6) of two mask designs in accordance with one or more embodiments of the present application. Figure 2Cis a plot of the average resist height (RH) of six slices of a mask design Figure 2A Figure 2D is a plot of the random defect rate (DR) of six slices of a mask design Figure 2A

[0047] As illustrated by Figures 2A to 2D both mask designs provide substantially the same edge placement when fabricated on the sample 104 (see, e.g., Figure 2A and 2B ). However, the mask designs exhibit substantial deviations in both average resist height and random defect rate in certain locations. For example, for slices pi, p4, and p6, both the average resist height data (see, e.g., Figure 2C ) and the random defect rate (see, e.g., Figure 2D ) of the two mask designs exhibit substantial deviations. In this way, resist height is a more accurate predictor of random defect rate than resist edge placement.

[0048] Figure 3A is a flowchart illustrating steps performed in a method 300 for mask repair in accordance with one or more embodiments of the present application. Applicant notes that embodiments and implementation techniques previously described herein in the context of the system 100 should be interpreted to extend to the method 300. For example, one or more processors 112 of the system 100 can execute program instructions that cause the one or more processors 112 to implement any of the various steps of the method 300. However, it is further noted that the method 300 is not limited to the architecture of the system 100.

[0049] In some embodiments, the method 300 includes a step 302 of developing a simulation-based model of sample layer thickness after one or more process steps for fabricating a feature on the sample 104. As an illustration, the simulation-based model can provide a distribution of sample layer thickness as a function of location across the sample 104 or a portion thereof. The distribution of sample layer thickness can be expressed as a single output value for each location on the sample 104 or a probability distribution of thickness for each location on the sample 104.

[0050] ​​Step 302 can describe features on the sample 104 after any number of process steps. For example, process steps can be used to fabricate features on the sample 104 (e.g., on a particular layer of the sample 104), such as, but not limited to, deposition of one or more layers (e.g., a treatment layer and / or a photoresist layer), lithographic exposure from a pattern of the mask 106, post-exposure bake, etching, ion implantation (e.g., doping), metallization oxidation, polishing, or the like. Moreover, such steps can be repeated multiple times to build a semiconductor device. In some embodiments, the simulation-based model of step 302 provides a photoresist thickness after a lithographic exposure process, which can be similar to a photoresist thickness that can be measured at an after-development inspection (ADI) step. The simulation-based model can model any type of commercial or custom photoresist, including, but not limited to, a Positive-Tone-Develop (PTD CAR), a Negative-Tone-Develop (NTD) resist, or a metal oxide (MOx) resist. In some embodiments, the simulation-based model of step 302 provides a treatment layer thickness after an etching step, which can be similar to a treatment layer thickness that can be measured at an after-etch inspection (AEI) step. Moreover, the simulation-based model of step 302 can provide various additional outputs after any process step, such as, but not limited to, edge placement, line edge roughness (LER), or critical dimension uniformity (CDU).

[0051] Step 302 can include developing a simulation-based model of a sample layer thickness using any suitable technique. Input parameters to the simulation-based model can include, but are not limited to, a design of the mask 106, properties of the sample 104 (e.g., composition, thickness, or the like), and / or process parameters. For example, process parameters can include, but are not limited to, properties of illumination during lithography (e.g., intensity, spectrum, polarization, numerical aperture, angle of incidence, source shape, total dose, or the like), focus position, development time, post-exposure bake temperature, or the like. As used herein, an input space defines a range of various input parameters that can be utilized by the model.

[0052] In some embodiments, the simulation-based model includes modeling the optical interaction of light with the sample 104 during lithographic exposure of the mask 106 utilizing techniques such as, but not limited to, rigorous coupled wave analysis (RCWA), finite difference time domain (FDTD) analysis, finite element method (FEM) analysis, method of moments analysis, surface integral techniques, or volume integral techniques. In this manner, the simulation-based model can be characterized as a physics-based model. In some embodiments, a simulator such as, but not limited to, PROLITH (Positive Resist Optical Lithography), which is a physics-based simulator sold by KLA Corporation, can be used to simulate photoresist thickness. Physics-based simulation of photoresist thickness is generally described in the above-referenced and incorporated by reference in its entirety herein U.S. Patent Publication No. 2022 / 0129775 entitled “Prediction and metrology of stochastic photoresist thickness defects” and published on April 28, 2022.

[0053] It is contemplated herein that the simulation-based model developed in step 302 can be adapted to characterize stochastic defects during a manufacturing process. For example, Monte Carlo techniques can be used to apply the simulation-based model multiple times to stochastically sample a stochastic process (e.g., photon absorption or the like). In this case, the output of the simulation can provide a probability distribution of an output parameter (e.g., local photoresist thickness). This technique can theoretically provide accurate characterization of a wide range of process steps under a wide range of conditions. Further, the simulation-based model can incorporate or otherwise account for variations in process parameters that can naturally occur during manufacturing (e.g., process variations). For example, the simulation-based model can provide a probability of any output parameter (e.g., sample layer thickness or the like) based on known or expected variations in process parameters and / or stochastic processes.

[0054] However, it is further contemplated herein that this technique can require a large number of samples to adequately characterize relatively rare stochastic defects (e.g., defects having a defect rate of one in a million or one in a billion). Further, the run time of this model can be relatively slow. Thus, relying solely on this simulation-based model to characterize stochastic defect rates can be undesirable or impractical.

[0055] In some embodiments, the method 300 includes a step 304 of developing a surrogate model of the manufacturing process that mimics the simulation-based model and has a faster evaluation speed than the simulation-based model for a selected range of inputs and / or outputs. The surrogate model can accept an input mask design, input parameters (e.g., as fixed or floating parameters) within at least a portion of the input space of the simulation-based model, output one or more output parameters associated with the manufacturing of the input mask design, and output one or more sensitivity metrics that describe the sensitivity of the one or more output parameters to variations in the input mask design. The output parameters provided by the surrogate model can include, but are not limited to, sample layer thicknesses (e.g., photoresist and / or process layer thicknesses) or random defect rates based on sample layer thicknesses. Further, the surrogate model can incorporate or otherwise account for variations in process parameters that can naturally occur during manufacturing (e.g., process variations). For example, the surrogate model can provide a probability of any output parameter (e.g., sample layer thickness or the like) based on known or expected variations in process parameters and / or stochastic processes. In this way, the surrogate model can be adapted to characterize the robustness of a mask design to process variations.

[0056] The step 304 can include developing a surrogate model of at least sample layer thicknesses using any suitable technique. In some embodiments, a machine learning technique is used to produce the surrogate model. In this way, the surrogate model can be a trained machine learning model. This machine learning model can be trained using any suitable training data. For example, this machine learning model can be trained using simulation data and / or metrology data from training samples manufactured with different variations in input parameters. The metrology data can be produced using any suitable characterization subsystem 108 such as, but not limited to, a scanning electron microscope (SEM) tool, a transmission electron microscope tool (TEM), an x-ray tool, or the like. Further, this machine learning model can incorporate any type of supervised machine learning model such as, but not limited to, a general linear model, a neural network, a Bayesian inference model, a Bayesian neural network, a deep neural network, a convolutional neural network, or a support vector machine. In some embodiments, the machine learning further incorporates other techniques such as, but not limited to, unsupervised learning, semi-supervised learning, or reinforcement learning.

[0057] In some embodiments, the transformation model is designed to provide faster evaluation speed for at least a subset of the input space and / or output space of the simulation-based model. In this way, development and utilization of the transformation model can provide increased throughput relative to the simulation-based model while maintaining performance tolerance for at least the subset of the input space. In a general sense, the transformation model can be tunable to provide a desired tradeoff between accuracy, speed (e.g., evaluation speed), and size of the input space (e.g., size of the input parameter range for which the transformation model mimics the simulation-based model within acceptable tolerance). Use of machine learning models that mimic simulation-based models for photoresist thickness is generally described in U.S. Patent Publication No. 2022 / 0129775, entitled “Prediction and metrology of stochastic photoresist thickness defects” and published on April 28, 2022, which is cited above and incorporated herein by reference in its entirety.

[0058] Figure 4 is a conceptual illustration of tradeoff of a transformation model according to one or more embodiments of the present disclosure. Plot 402 is a conceptual illustration of speed of a transformation model as a function of encompassed input space of a simulation-based model. Plot 404 is a conceptual illustration of accuracy of a transformation model as a function of speed of the transformation model. As illustrated, speed of the transformation model can generally decrease with an increase in encompassed input space. Further, accuracy of the transformation model can generally decrease with an increase in speed. However, there can be a condition in which the transformation model provides sufficient accuracy (e.g., within a selected tolerance) while also providing a substantial speed enhancement relative to the simulation-based model, within a suitable subset of the input space of the simulation-based model.

[0059] In some embodiments, the transformation model further provides mathematical differentiability. For example, the transformation model can produce a sensitivity metric associated with an estimate of the sensitivity of any of the output parameters to variations in the process parameters of interest. Any suitable sensitivity metric can be produced, such as but not limited to an analytical model gradient. Analytical model gradients are generally described in Andreas Griewank, “Who invented the reverse mode of differentiation,” Documenta Mathematica, Extra Volume ISMP 389400 (2012), and in Baydin, Atilim Gunes, et al., “Automatic differentiation in machine learning: a survey,” Journal of Machine Learning Research 18 (2018): 1-43, both of which are incorporated by reference herein in their entirety.

[0060] Further, the transformation model can provide a sensitivity metric for each output parameter (e.g., local photoresist thickness, random defect rate based on photoresist thickness, or the like) individually to a selected input parameter or a sensitivity metric for a combination of output parameters. By way of illustration, the sensitivity metric can provide an indication of the degree of sensitivity of the local photoresist thickness and / or random defect rate (e.g., output parameters of the transformation model) of a particular candidate mask design to variations in the process parameters. In other words, the sensitivity metric can provide an indication of how deviations in the process parameters that occur during manufacturing can affect the photoresist thickness and / or random defect rate. With this information in mind, corrective design changes can be made to reduce the sensitivity of the design to these process variations.

[0061] In some embodiments, the method 300 includes a step 306 of receiving a candidate mask design. In some embodiments, the method 300 includes a step 308 of generating a patched mask design based on the transformation model. The candidate mask design and / or the patched mask design can be provided in any suitable format, such as but not limited to a binary representation, a polygonal representation, a distance field representation, or a level set representation. Further, the patched mask design can be provided as a complete design or as an update vector describing modifications to the candidate mask design.

[0062] It is contemplated herein that step 308 can utilize the transformation model in a wide variety of ways to produce a repaired mask design. In any case, the repaired mask design can provide a reduced random defect rate and can further be robust to process variations (e.g., as characterized by the transformation model).

[0063] Figure 3B is a flowchart illustrating sub-steps of step 308 of generating a repaired mask design according to one or more embodiments of the present disclosure.

[0064] In some embodiments, step 308 includes step 310 of utilizing the candidate mask design as an input mask design to the transformation model to generate one or more output parameters of the candidate mask design and one or more sensitivity metrics. In some embodiments, step 308 includes step 312 of updating the candidate mask design based on the one or more sensitivity metrics when the candidate mask design fails to meet the application tolerance (e.g., within a selected tolerance). For example, step 312 can include updating the design of mask 106 based on the sensitivity metrics such that the updated candidate design is less sensitive to variations in input parameters (e.g., process parameters).

[0065] In some embodiments, steps 310 and 312 are iterated as necessary until a repaired mask design is generated that meets the application tolerance. Any application tolerance can be considered, such as but not limited to a tolerance related random defect rate.

[0066] Figure 5 is a simplified flowchart illustrating random defect mitigation according to one or more embodiments of the present disclosure. In particular, Figure 5 depicts a process in which a candidate mask design 500-C (e.g., a design of candidate mask design 500-C) is provided as input to a transformation model 502 (e.g., as generated in step 304) along with additional focus process parameters 504. For example, process parameters 504 can include values and / or ranges of process parameters 504 within an input space encompassed by transformation model 502. Transformation model 502 can then generate (e.g., in step 310) any number of output parameters 506, such as but not limited to, local photoresist thickness, a random defect rate based at least in part on local photoresist thickness, edge placement error, LER, CDU, distance field violations, or mask rule check parameters. Transformation model 502 can also generate (e.g., in step 310) sensitivity metrics 508 associated with any output parameters 506 individually or in one or more combinations.

[0067] Figure 5Further, it is determined (e.g., block 510) whether the application tolerance is met (e.g., as part of step 312). If the tolerance is met, then the repaired mask design 500-R (e.g., the design of the repaired mask design 500-R) is provided. Otherwise, the design is updated (e.g., block 512) to produce an updated candidate mask design 500-C. This process can be repeated as necessary until the application tolerance is met (e.g., satisfied). Any application tolerance can be considered, such as, but not limited to, a tolerance related random defect rate.

[0068] Referring now to Figures 6A to 8B , a non-limiting variation of the method 300 (and flowchart in Figure 5 ) is described.

[0069] The method 300 (e.g., step 308) can apply the correction or repair to the entire candidate mask design 500-C or to a portion of the candidate mask design 500-C. For example, applying the correction to a portion of the candidate mask design 500-C rather than the entire candidate mask design 500-C can reduce the computational speed. In cases where only a portion of the candidate mask design 500-C is corrected, any suitable technique can be used to determine the portion.

[0070] In some embodiments, regions of interest (ROIs) can be selected for repair (all or for particular iterations) using the method 300. Any criteria can be used to select these ROIs. For example, the ROIs can correspond to features or sample locations that are prone to random defects. In another example, the ROIs can correspond to features or sample locations that are particularly critical to device performance.

[0071] In some embodiments, the selection of portions of the candidate mask design 500-C selected for repair (e.g., prior to updating the candidate mask design 500-C) is based on screening. For example, the output parameters 506 of the transformation model can identify one or more areas on the specimen 104 as potentially problematic based on the current candidate mask design 500-C. For example, the output parameters 506 of the transformation model can predict one or more hotspots as having a relatively high probability of random defects when manufacturing using the candidate mask design 500-C. Such problematic areas can be mitigated by making a large number of adjustments to various portions of the candidate mask design 500-C (e.g., a large number of different combinations of adjustments to different edge locations). However, it can not be desirable to incorporate all of the identified potential adjustments to the candidate mask design 500-C. For example, some adjustments can be redundant. As another example, some adjustments can repair the identified problematic areas but can adversely affect different areas. Accordingly, in some embodiments, only a subset of the potential adjustments to the candidate mask design 500-C are implemented in a particular iteration. By way of illustration, a selected percentage of the locations for adjustment having the sensitivity metrics 508 indicating the highest sensitivity to the output parameters 506 can be selected for repair (e.g., the top X% of locations, where X can be any selected value, such as but not limited to 10%). By way of another illustration, locations having sensitivity metrics exceeding a selected threshold (e.g., defining a magnitude of sensitivity) can be selected for repair. Further, the screening criteria can be adjusted individually for each iteration, either dynamically or based on pre-defined rules. By way of illustration, it can be desirable to gradually reduce the number and / or magnitude of corrections to the candidate mask design 500-C over successive iterations to facilitate convergence to a robust design.

[0072] Figure 6A and 6B The repair of selected portions of the specimen 104 is illustrated. In Figure 6A and 6B In the example of FIG. 5B, the transformation model 502 provides output parameters 506 including a rate of random defects in photoresist and edge placement error (e.g., after a lithographic exposure). Figure 6A is a simplified view of a repaired mask 500-R in the form of update vectors on feature edges generated by multiple iterations of step 308 according to one or more embodiments of the application. For example, the various arrows indicate the direction and magnitude of edge location modifications identified for adjustment in a particular iteration. As illustrated, the magnitude and / or direction of the update vectors in the repaired mask design 500-R can vary across the specimen 104 and between different iterations. Figure 6B is a simplified view of a repaired mask design 500-R in the form of update vectors on feature edges generated by multiple iterations of step 308 according to one or more embodiments of the application, where only a subset of the specimen locations are repaired. For example, Figure 6B is generally similar toFigure 6A except that it only contains updates associated with a portion of the sample 104, where the locations shown can be selected based on defining a ROI, screening, or any other suitable technique. In particular, Figure 6B is generated according to screening a set of potential modifications to the candidate mask design 500-C based on the sensitivity metric 508 to include a selected percentage of modifications that provide the highest sensitivity to the output parameter 506.

[0073] Figure 7 is an illustration of the iterative mask repair performed in the ROI 702 using the method 300 according to one or more embodiments of the disclosure. In Figure 7 , the transformation model 502 provides the output parameter 506 (e.g., after a lithographic exposure) that includes a random defect rate within the ROI 702, a random defect rate outside the ROI 702, and edge placement error in photoresist.

[0074] In particular, Figure 7 depicts a view of the initial candidate mask design 500-C (e.g., a pre-repair candidate mask design 500-C), two interim masks associated with iterations of the step 308, and the final repaired mask design 500-R. In this way, the two interim masks represent both the repaired mask design 500-R from one iteration and the candidate mask design 500-C of a subsequent iteration. Further, Figure 7 depicts arrows 704 that illustrate the reparative modifications (e.g., in Figure 5 , block 512) to the candidate mask design 500-C shown. For reference, the initial design is also shown as a dashed line so that the impact of the design changes within each iteration can be visualized.

[0075] In the flow shown in Figure 7 , the decision as to whether the design as a whole meets the selected tolerance (e.g., block 510 in Figure 5 ) is based at least in part on the ROI 702 (e.g., the random defect rate within the ROI 702). In particular, the method 300 can continue iterations until the locations within the ROI 702 meet the selected tolerance. In some embodiments, the method 300 can additionally iterate until the locations outside the ROI 702 meet an additional tolerance, which can be different from the tolerance for the regions within the ROI 702. Further, it should be noted that the screening techniques as described previously herein (e.g., with respect to Figures 6A to 6B ) can also be applied to limit reparative corrections based on any of the output parameters 506.

[0076] Referring generally again to FIGS. 3 and 5, step 312 of updating the candidate mask design 500-C (e.g., block 512) can be customized for the manner in which the design is expressed. For example, step 312 of updating the candidate mask design 500-C (e.g., block 512) can include updating mask polygons, where the mask polygons can directly correspond to feature designs or as parameters in distance field and / or level set techniques. Further, updating mask polygons is not limited to modifying existing polygons, but can also include adding new polygons and / or removing existing polygons. Any type of update or optimization technique can be utilized, including but not limited to gradient descent optimization techniques. As another example, step 312 of updating the candidate mask design 500-C (e.g., block 512) can include updating distance field and / or level set parameters (when used to represent the design). In some embodiments, step 312 of updating the candidate mask design 500-C (e.g., block 512) can further control and / or manage parameters related to the manner in which the design is expressed. For example, step 312 of updating the candidate mask design 500-C (e.g., block 512) can further control and / or manage velocity fields to adhere to Courant-Friedrichs-Lewy (CFL) condition or similar when using level set or fast marching techniques.

[0077] In some embodiments, the method 300 (e.g., step 308) can generate the repaired mask design 500-R in two or more stages with different tolerance conditions, where steps 310 and 312 can be iterated as necessary to achieve the associated tolerance conditions.

[0078] For example, the flow in Figure 5 may be performed a first time in a first stage to generate a first repaired mask design 500-R of the initial candidate mask design 500-C. Subsequently, the flow in Figure 5 may be performed a second time in a second stage, where the first repaired mask design 500-R is provided as the candidate mask design 500-C of the second stage to generate a second (e.g., final) repaired mask design 500-R. By way of illustration, the output parameters 506 of the first stage can include random defect rates within one or more ROIs (e.g., as described in Figure 7The one or more ROI-external random defect rates and edge placement errors are illustratively shown. Then, an update to the candidate mask design 500-C can be performed (e.g., block 512) for the entire sample 104, for the ROIs only, or for a set of filtered locations as described above. Then, the output parameters 506 in the second stage can further include mask rule check violations. It is contemplated herein that this one-two stage operation can provide efficient patching during the first stage without spending computational resources and associated time on mask rule check violations until a certain performance level is reached in the first stage. Then, the second stage can make any additional modifications as needed to avoid mask rule check violations. It is noted, however, that this example is provided for illustration only and should not be construed as limiting. In general, a multi-stage implementation can allow for mask correction based on multiple combinations of output parameters in a controlled and efficient manner.

[0079] Referring now to Figure 8A and 8B In some embodiments, the transformation model 502 (e.g., generated in step 304) can be used to train a machine learning model (e.g., an inverse machine learning model) to directly generate a patched mask design 500-R from a candidate mask design 500-C.

[0080] Figure 8A is a simplified flowchart illustrating training of a machine learning model 802 using the transformation model 502 in accordance with one or more embodiments of the present disclosure.

[0081] In some embodiments, the machine learning model 802 generates a patched mask design 500-R from an input candidate mask design 500-C. Then, this patched mask design 500-R can be provided as input to the transformation model 502 (e.g., generated in step 304) that can provide the output parameters 506 and the sensitivity metrics 508. Further, in some embodiments, the sensitivity metrics 508 include the sensitivity of the machine learning weights of the machine learning model 802 to the output parameters 506. In this way, the sensitivity metrics 508 can characterize the sensitivity of the machine learning model 802 to the output parameters 506 (e.g., random defect rates or the like). If the patched mask design 500-R from the machine learning model 802 does not comply with the selected application tolerances, the machine learning model 802 can be updated (block 804) based on the sensitivity metrics 508. Further, this process can be repeated until the patched mask design 500-R generated by the machine learning model 802 complies (e.g., meets) the application tolerances.

[0082] Figure 8B is a flowchart illustrating a non-limiting example of training a machine learning model 802 based on training data generated by the transformation model 502 in accordance with one or more embodiments of the present disclosure. It is noted thatFigure 8B A particular non-limiting case is illustrated in which the output parameters 506-T include local resist thickness and resist edge placement values.

[0083] In some embodiments, the transformation model 502 generates output parameters 506-T as training data based on a plurality of input candidate mask designs 500-T. For example, the input candidate mask designs 500-T can be fabricated with known variations in process parameters (e.g., within the encompassed input space). Upon training, the machine learning model 802 can directly generate a repaired mask design 500-R based on any suitable input, including but not limited to an input candidate mask design 500-C or a desired value of the output parameters as illustrated in Figure 8B

[0084] Reference is now made to Figures 9A to 9D , Figures 9A to 9D A series of plots including additional non-limiting examples of repairing mask designs 500 using the method 300 according to one or more embodiments of the present application. Figures 9A to 9D Each of the plots in Figures 9A to 9D Each of the plots in Figures 9A to 9D Each of the plots in Figures 9A to 9C depicts a configuration in which repair is provided based on a single ROI 900, while Figure 9D depicts a configuration in which repair is provided based on a plurality of ROIs 900. In each case, the method 300 provides a substantial reduction in the probability of random defects. Additionally, in each case, the random defect rate of the associated repaired mask design 500-R is below the application tolerance (e.g., illustrated as the dashed line 902).

[0085] Reference is now made to Figure 10 , according to one or more embodiments of the present application, describe mitigating random defects by modification of process parameters instead of or in addition to the design of the mask 106. Considered herein, the defect rate (e.g., random defect rate) can be influenced not only by the design of the mask 106 used for lithography, but also by various process parameters such as, but not limited to, dose, focus position, illumination numerical aperture, illumination source shape, post-exposure bake temperature, development time, or the like. Therefore, in addition to or instead of the mask design, process parameters can also be adjusted to mitigate random defects. ​

[0086] In some embodiments, a manufacturing process is governed or otherwise described by a recipe, which can include parameters describing various aspects of the process tool (lithography tool, etching tool, polishing tool, or the like) to be used at any process step and / or the sample 104 to be manufactured. In this way, the recipe can include process parameters 504 associated with any process step. For example, the recipe can include process parameters 504 associated with the sample 104 at any process step, including but not limited to the thickness of a film to be deposited or the composition of a film to be deposited. As another example, the recipe can include the design of a mask 106 to be used in a lithography step. As another example, the recipe can include process parameters 504 for a lithography step, such as but not limited to the illumination dose, the illumination wavelength, the illumination polarization, the illumination source shape, the exposure time, or the focus position of the sample 104. As another example, the recipe can include process parameters 504 associated with an etching step, including but not limited to the composition of an etchant or the etching duration. As another example, the recipe can include process parameters 504 associated with a post-exposure bake step, including but not limited to the temperature or duration of the bake.

[0087] In some embodiments, any aspect of the recipe can be patched (e.g., updated) based on the transformation model 502 to mitigate random defects (e.g., to reduce the random defect rate). Thus, the teachings of the disclosure related to providing patching corrections to a mask design 500 can be extended to providing patching corrections to a recipe that more generally describes one or more process steps.

[0088] For example, any component of the recipe can be iteratively modified (e.g., updated) based on the transformation model 502. Figure 10 is a simplified flowchart illustrating random defect mitigation according to one or more embodiments of the disclosure. Note that, Figure 10 is generally similar to Figure 5 except that block 512, which represents updating the mask design 500, is replaced with block 1002, which represents updating a recipe that describes a manufacturing process. As Figure 5 illustrated in Figure 10 , the transformation model 502 can accept as input any process parameter 504 (e.g., candidate process parameter 504-C) as well as the mask design 500 (e.g., candidate mask design 500-C) and provide as output the output parameter 506 and the associated sensitivity metric 508. If the output parameter 506 is not within the application tolerance, then any aspect of the recipe can be updated (block 1002), including only the mask design 500, only any process parameter 504, and / or a combination of the mask design 500 and any process parameter 504. If the output parameter 506 is within the application tolerance, then the patched mask design 500-R and / or the patched process parameter 504-R (e.g., more generally, a patched recipe) can be provided as output.

[0089] As another example, Figures 8A to 8B The machine learning model 802 depicted in FIG. 8 can be extended to provide a repaired recipe based on a candidate recipe. For example, the machine learning model 802 can be trained to accept a candidate mask design 500-C and / or a candidate process parameter 504-C and generate a repaired mask design 500-R and / or a repaired process parameter 504-R based on training data that includes related process parameters. Thus, Figure 8B may be extended to include process parameters 504 within the training data set and provide associated outputs.

[0090] Referring now generally to Figures 1A to 1C Additional aspects of the system 100 are described in greater detail below, in accordance with one or more embodiments of the present disclosure.

[0091] Figure 1B is a conceptual diagram illustrating a lithography sub-system 102 in accordance with one or more embodiments of the present disclosure. In some embodiments, the lithography sub-system 102 includes an illumination source 116 configured to generate one or more illumination beams 118. The illumination beams 118 can include light of one or more selected wavelengths, including but not limited to EUV light. For example, at least a portion of the spectrum of the illumination beams 118 can include a wavelength of, for example but not limited to, 13.5 nm or similar. EUV-based lithography is generally described in U.S. Patent No. 8,916,831, issued December 23, 2014, which is incorporated herein by reference in its entirety.

[0092] In some embodiments, the illumination source 116 includes an extreme ultraviolet illumination source 116. For example, the EUV illumination source 116 can include a broadband plasma (BBP) illumination source. In this regard, the illumination beams 118 can include radiation emitted by a plasma. For example, the BBP illumination source 116 can include, but is not required to include, one or more pumps (e.g., one or more lasers) configured to focus illumination into a volume of gas, causing the gas to absorb energy to generate or sustain a plasma suitable for emitting radiation. Further, at least a portion of the plasma radiation can be used as the illumination beams 118. In some embodiments, the illumination source 116 can include one or more lasers capable of emitting radiation at one or more selected wavelengths.

[0093] In some embodiments, the illumination source 116 directs the illumination beam 118 to the mask 106 via an illumination path 120. The illumination path 120 can include one or more illumination optics 122 suitable for directing, focusing, and / or shaping the illumination beam 118 on the mask 106. For example, the illumination optics 122 can include one or more lenses, one or more focusing components, or the like. Further, the illumination optics 122 can include any reflective optical components known in the art suitable for directing and / or focusing the illumination beam 118. For example, the illumination optics 122 can include reflective optics suitable for directing and / or focusing low wavelength light (e.g., EUV light and the like), such as, but not limited to, flat mirrors or curved mirrors (e.g., elliptical mirrors, parabolic mirrors, or the like).

[0094] The illumination optics 122 can further include one or more additional illumination path components suitable for shaping the illumination beam 118 and / or controlling the range of angles of incidence (e.g., the illumination pupil distribution) of the illumination beam 118 on the mask 106. For example, the illumination path components can include, but are not limited to, one or more apertures, one or more apodizers, one or more homogenizers, one or more diffusers, one or more polarizers, or one or more filters.

[0095] In some embodiments, the lithography sub-system 102 includes a mask support device 124. The mask support device 124 can be configured to secure the mask 106.

[0096] In some embodiments, the lithography sub-system 102 includes a set of projection optics 126 configured to project an image of the mask 106 illuminated by the one or more illumination beams 118 onto a surface of the sample 104 disposed on a sample stage 128. For example, the set of projection optics 126 can be configured to project an image of the mask 106 onto a resist layer 130 on the sample 104 to produce (e.g., expose or the like) printed pattern elements on the resist layer 130 that correspond to the pattern elements on the mask 106. In some embodiments, the mask support device 124 can be configured to actuate or position the mask 106. For example, the mask support device 124 can actuate the mask 106 to a selected position relative to the projection optics 126 of the lithography sub-system 102.

[0097] The mask 106 can be used (e.g., by the lithography sub-system 102) in any imaging configuration known in the art. For example, the mask 106 can be a positive mask (e.g., a bright field mask) in which the pattern elements are positively imaged as printed pattern elements of the resist layer 130 of the sample 104. By another example, the mask 106 can be a negative mask (e.g., a dark field mask) in which the pattern elements of the mask 106 form negative printed pattern elements (e.g., gaps, spaces, or the like) of the resist layer 130 of the sample 104.

[0098] As used throughout this disclosure, the term "sample" generally refers to a substrate (e.g., a wafer or the like) formed of semiconductor or non-semiconductor material. For example, the semiconductor or non-semiconductor material can include, but is not limited to, monocrystalline silicon, gallium arsenide, and indium phosphide. The sample can include one or more layers. For example, such layers can include, but are not limited to, resist, dielectric material, conductive material, and semiconductive material. Numerous different types of such layers are known in the art, and the term sample as used herein is intended to encompass samples on which all types of such layers can be formed. The one or more layers formed on the sample can be patterned or unpatterned. For example, the sample can include a plurality of dies each having repeatable patterned features. The formation and processing of such layers of material can ultimately result in finished devices. Numerous different types of devices can be formed on the sample, and the term sample as used herein is intended to encompass samples on which any type of device known in the art is manufactured. Furthermore, for purposes of this disclosure, the terms sample and wafer shall be construed to be interchangeable. Additionally, for purposes of this disclosure, the terms patterning device, pattern mask, mask, and reticle shall be construed to be interchangeable.

[0099] Figure 1C is a conceptual diagram illustrating a characterization subsystem 108 in accordance with one or more embodiments of the present disclosure. Note that, Figure 1C The characterization subsystem 108 is depicted as an optical system. However, this is illustrative only and not limiting. Indeed, the characterization subsystem 108 can include and / or be configured as a particle beam system (e.g., an electron beam system, an ion beam system, or the like) or an x-ray system (e.g., including an optical configuration suitable for light in the x-ray spectral region).

[0100] In some embodiments, the characterization subsystem 108 includes an illumination source 132 to generate an illumination beam 134. The illumination beam 134 can include light of one or more selected wavelengths, including but not limited to ultraviolet (UV) radiation, visible radiation, or infrared (IR) radiation. It is noted herein that the characterization subsystem 108 can include any type of characterization subsystem 108 known in the art without limiting the scope of the present disclosure. For example, although Figure 1C Not depicted in FIG. 1, but without limiting the scope of the present disclosure, the characterization subsystem 108 can include an extreme ultraviolet (EUV) characterization subsystem, a deep ultraviolet (DUV) characterization subsystem, or the like.

[0101] In some embodiments, the illumination source 132 directs the illumination beam 134 to the sample 104 via an illumination path 136. The illumination path 136 can include one or more lenses 138. Further, the illumination path 136 can include one or more additional optical components 140 suitable for modifying and / or conditioning the illumination beam 134. For example, the one or more optical components 140 can include, but are not limited to, one or more polarizers, one or more filters, one or more beam splitters, one or more diffusers, one or more homogenizers, one or more apodizers, or one or more beam shapers. In some embodiments, the illumination path 136 includes a beam splitter 142. In some embodiments, the characterization subsystem 108 includes an objective lens 144 to focus the illumination beam 134 onto the sample 104.

[0102] In some embodiments, the characterization subsystem 108 includes one or more detectors 146 configured to capture radiation emanating from the sample 104 through a collection path 148. The collection path 148 can include a number of optical components to direct and / or modify the illumination collected by the objective lens 144, including, but not limited to, one or more lenses 150, one or more filters, one or more polarizers, one or more beam stops, or one or more beam splitters.

[0103] For example, the detectors 146 can receive an image of the sample 104 provided by components in the collection path 148 (e.g., the objective lens 144, the one or more lenses 150, or the like). By another example, the detectors 146 can receive radiation reflected or scattered (e.g., via specular reflection, diffuse reflection, and the like) from the sample 104. By another example, the detectors 146 can receive radiation generated by the sample (e.g., luminescence associated with absorption of the illumination beam 134, and the like). Further, it is noted herein that the one or more detectors 146 can include any optical detector known in the art suitable for measuring illumination received from the sample 104. For example, the detectors 146 can include, but are not limited to, a CCD detector, a TDI detector, a photomultiplier tube (PMT), an avalanche photodiode (APD), or the like.

[0104] Additionally, in some embodiments, the characterization subsystem 108 includes a translation stage 152 to secure and position the sample 104.

[0105] The objects described herein sometimes illustrate different components contained within, or connected with, other components. It is to be understood that such depicted architectures are merely exemplary, and that in fact many other architectures can be implemented which achieve the same functionality. In a conceptual sense, any arrangement of components to achieve the same functionality is effectively "associated" such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as "associated with" each other such that the desired functionality is achieved, irrespective of architectures or intermediate components. Likewise, any two components so associated can also be viewed as being "connected" or "coupled" to each other to achieve the desired functionality, and any two components capable of being so associated can also be viewed as being "couplable" to each other to achieve the desired functionality. Specific examples of couplable include but are not limited to physically interactable and / or physically interacting components, and / or wirelessly interactable and / or wirelessly interacting components, and / or logically interactable and / or logically interacting components.

[0106] It is believed that the subject matter, which has been described, will be readily appreciated as it is made in the following claims, the scope of which is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. The structure and function of the all the systems along with the related advantages can be better understood by reference to the following claims.

Claims

1. A system comprising: a controller including one or more processors configured to execute program instructions causing the one or more processors to: develop a simulation-based model of a thickness of a layer after one or more process steps for fabricating a feature on a specimen, wherein the simulation-based model accepts an input mask design to be exposed on the specimen and provides at least the thickness of the layer after the one or more process steps as an output; develop a transformation model of a fabrication process that mimics the simulation-based model and has a faster evaluation speed than the simulation-based model for a selected range of at least one of inputs or outputs, wherein the input to the transformation model includes the input mask design, wherein the output of the transformation model includes one or more output parameters associated with fabrication of the input mask design and one or more sensitivity metrics that describe sensitivity of the one or more output parameters to variations of the input mask design, wherein the one or more output parameters include at least one of the thickness of the layer after the one or more process steps or a random defect rate based on the thickness of the layer; receive a candidate mask design; and generate a patched mask design based on the transformation model and the candidate mask design.

2. The system of claim 1, wherein the thickness of the layer comprises: at least one of a thickness of a photoresist layer after a lithography process step or a thickness of a process layer after an etching step.

3. The system of claim 1, wherein at least one of the simulation-based model or the transformation model provides at least one of the thickness of the layer or a probability of the thickness of the layer in the presence of process variations.

4. The system of claim 1, wherein the candidate mask design and the patched mask design are represented by at least one of a binary representation, a polygon representation, a distance field representation, or a level set representation.

5. The system of claim 1, wherein generating the patched mask design based on the transformation model and the candidate mask design comprises: generating update vectors for at least some edges in the candidate mask design; and updating the candidate mask design with the update vectors to provide the patched mask design.

6. The system of claim 1, wherein generating the patched mask design based on the transformation model and the candidate mask design comprises iteratively performing the following steps until one or more application tolerances are satisfied: utilizing the candidate mask design as the input mask design to the transformation model to generate the one or more output parameters and the one or more sensitivity metrics for the candidate mask design; and updating the candidate mask design based on the one or more sensitivity metrics to provide the patched mask design when the candidate mask design fails to meet the one or more application tolerances.

7. The system of claim 6, wherein the one or more application tolerances comprise: a random defect rate tolerance. ​ ​ 8. The system of claim 6, wherein updating the candidate mask design based on the one or more sensitivity metrics when the candidate mask design fails to meet the application tolerance comprises: generating update vectors for at least some edges in the candidate mask design based on the one or more sensitivity metrics; and updating the candidate mask design with the update vectors to generate the patched mask design.

9. The system of claim 8, wherein updating the candidate mask design based on the one or more sensitivity metrics when the candidate mask design fails to meet the application tolerance further comprises: screening the update vectors based on the one or more sensitivity metrics to include only a subset of the update vectors having a sensitivity above a selected sensitivity threshold before updating the candidate mask design with the update vectors to generate the patched mask design.

10. The system of claim 9, wherein the selected sensitivity threshold corresponds to a selected percentage of locations having a highest sensitivity based on the one or more sensitivity metrics.

11. The system of claim 8, wherein generating the update vectors for at least some edges in the candidate mask design based on the one or more sensitivity metrics comprises: generating the update vectors for at least some edges in the candidate mask design based on the one or more sensitivity metrics corresponding to one or more regions of interest.

12. The system of claim 8, wherein the candidate mask design and the patched mask design are represented by a polygonal representation defining a set of polygons, wherein updating the candidate mask design with the update vectors comprises: updating the set of polygons in the candidate mask design with the update vectors using a gradient descent optimizer.

13. The system of claim 8, wherein the candidate mask design and the patched mask design are represented by a level set representation, wherein updating the candidate mask design with the update vectors comprises: updating the candidate mask design with the update vectors using a velocity field controlled to obey conditions in at least one of a level set or fast marching technique.

14. The system of claim 1, wherein generating the patched mask design based on the transformation model and the candidate mask design comprises: training a machine learning model with training data generated by the transformation model; and generating the patched mask design with the machine learning model.

15. The system of claim 1, wherein the one or more output parameters comprise: two or more output parameters, wherein the one or more sensitivity metrics comprise: two sensitivity metrics each associated with a different one of the two or more output parameters.

16. The system of claim 1, wherein the one or more output parameters comprise: two or more output parameters, wherein at least one of the one or more sensitivity metrics comprises: a combined sensitivity metric associated with a combination of at least two of the two or more output parameters.

17. The system of claim 1, wherein the one or more output parameters comprise: the layer thickness, the random defect rate based on the layer thickness, and an edge placement error.

18. The system of claim 1, wherein the one or more output parameters comprise: the random defect rate based on the layer thickness.

19. The system of claim 1, wherein the one or more output parameters comprise: the random defect rate based on the layer thickness, and an edge placement error.

20. The system of claim 1, further comprising: a lithography subsystem configured to pattern expose one or more samples based on the patched mask design.

21. A method comprising: developing a simulation-based model of a layer thickness after one or more process steps for manufacturing features on a sample, wherein the simulation-based model takes an input mask design to be exposed on the sample and provides at least the layer thickness after the one or more process steps as an output; developing a transformation model of a manufacturing process that mimics the simulation-based model and has a faster evaluation speed than the simulation-based model for a selected range of at least one of inputs or outputs, wherein the inputs to the transformation model include the input mask design, wherein the outputs of the transformation model include one or more output parameters associated with manufacturing of the input mask design and one or more sensitivity metrics that describe sensitivity of the one or more output parameters to variations of the input mask design, wherein the one or more output parameters include at least one of the layer thickness after the one or more process steps or a random defect rate based on the layer thickness; receiving a candidate mask design; and generating a patched mask design based on the transformation model and the candidate mask design.

22. The method of claim 21, further comprising: a lithography subsystem configured to pattern expose one or more samples based on the patched mask design.

23. A system comprising: a controller including one or more processors configured to execute program instructions to cause the one or more processors to: develop a simulation-based model of a layer thickness after one or more process steps for manufacturing features on a sample, wherein inputs to the simulation-based model include a recipe that defines an input mask design to be exposed on the sample and one or more process parameters associated with the one or more process steps, wherein outputs of the simulation-based model include at least the layer thickness after the one or more process steps; ​ developing a transformation model of a manufacturing process that mimics the simulation-based model and has a faster evaluation speed than the simulation-based model for a selected range of at least one of inputs or outputs, wherein the inputs to the transformation model include at least one of the input mask design and the one or more process parameters, wherein the outputs of the transformation model include one or more output parameters associated with manufacturing the input mask design with the one or more process steps and one or more sensitivity metrics that describe a sensitivity of the one or more output parameters to the inputs to the transformation model, wherein the one or more output parameters include at least one of the layer thickness after the one or more process steps or a random defect rate based on the layer thickness; receiving a candidate recipe that includes a candidate mask design and the at least one of the one or more process parameters; and generating a patched recipe based on the transformation model and the candidate mask design.

24. The system of claim 23, wherein the layer thickness comprises: at least one of a thickness of a photoresist layer after a lithography process step or a thickness of a treatment layer after an etching step.

25. The system of claim 23, wherein at least one of the simulation-based model or the transformation model provides at least one of the layer thickness or a probability of the layer thickness in the presence of process variations.

26. The system of claim 23, wherein the candidate mask design and patched mask design are represented by at least one of a binary representation, a polygon representation, a distance field representation, or a level set representation.

27. The system of claim 23, wherein generating the patched recipe based on the transformation model and the candidate mask design comprises: generating an update to the candidate recipe that includes at least one of an update vector to the candidate mask design or an update to the at least one of the one or more process parameters; and updating the candidate recipe with the update to generate the patched recipe.

28. The system of claim 23, wherein generating a patched mask design based on the transformation model and the candidate mask design comprises: training a machine learning model with training data generated by the transformation model; and generating the patched recipe with the machine learning model.

29. The system of claim 23, wherein the one or more output parameters comprise: the layer thickness, the random defect rate based on the layer thickness, and an edge placement error.

30. The system of claim 23, wherein the one or more output parameters comprise: the random defect rate based on the layer thickness.

31. The system of claim 23, wherein the one or more output parameters comprise: the random defect rate based on the layer thickness, and an edge placement error.

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