Repair of lithographic masks by simulating photoresist thickness evolution

Abstract

A system for mask design repair may develop a simulation-based model of layer thickness after one or more process steps for manufacturing features on a sample, develop a transformation model of a manufacturing process that mimics the simulation-based model and has a faster evaluation speed than the simulation-based model, and develop a mask design repair model for the manufacturing process. And wherein an input to the transformation model includes an input mask design, and wherein an 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 describing sensitivity of the one or more output parameters to variations in the input mask design. The system may further receive a candidate mask design and generate a repaired mask design based on the transformation model and the candidate mask design.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

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

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

[0004] The demand for reducing feature sizes in semiconductor devices leads to tighter tolerances for photolithography processes. While the minimum feature size can be reduced generally by scaling down the wavelength of light used in the photolithography process, it is often desirable to fabricate features close to 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 occurring during semiconductor fabrication can be attributed to the inherent randomness of a large number of physical phenomena that make up the photolithography pattern transfer process, such as, but not limited to, photon exposure and absorption, photoproduct diffusion, chemical reactant spatial distribution, chemical reactions, or the like. Significantly, randomness is different from uncertainty and is related to random variations within the process. Typical methods for characterizing random wafer defects include top-down scanning electron microscopy (SEM)-based inspection, top-down simulation of post-development inspection (ADI) and / or post-etch inspection (AEI) pattern edge placement and their inspection. However, such techniques may be too time consuming and / or may not provide adequate measurements of parameters that lead to defect rates of fabricated samples, which may ultimately be of interest. Therefore, there is a need to develop systems and methods that address such deficiencies. Summary of the invention

[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 layer thickness after one or more process steps for manufacturing features on a sample, wherein the simulation-based model accepts 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. In another illustrative embodiment, the controller develops a transformation model of a manufacturing process, the transformation model mimicking the simulation-based model and having a faster evaluation speed than the simulation-based model for a selected range of at least one of input or output, wherein the input to the transformation model includes the input mask design, and wherein the output of the transformation model includes one or more output parameters associated with the manufacturing of the input mask design and one or more sensitivity metrics describing the 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 layer thickness after the one or more process steps or a random defect rate based on the layer thickness. 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 layer thickness after one or more process steps for fabricating features on a sample, wherein the simulation-based model accepts 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. In another illustrative embodiment, the method includes developing a transformation model of a fabrication process, the transformation model mimicking the simulation-based model and having a faster evaluation speed than the simulation-based model for a selected range of at least one of an input or an output, wherein the input to the transformation model includes the input mask design, and 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 describing the 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 layer thickness after the one or more process steps or a random defect rate based on the layer thickness. 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 designs.

[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 layer thickness after one or more process steps for fabricating features on a sample, wherein inputs to the simulation-based model include recipes defining an input mask design to be exposed on the sample and one or more process parameters associated with the one or more process steps, and wherein outputs of the simulation-based model include at least the layer thickness after the one or more process steps. In another illustrative embodiment, the controller develops a transformation model of a manufacturing process, the transformation model mimicking the simulation-based model and having a faster evaluation speed than the simulation-based model for a selected range of at least one of input or output, wherein the inputs to the transformation model include the input mask design and at least one of the one or more process parameters, and wherein the outputs of the transformation model include one or more output parameters associated with fabricating the input mask design with the one or more process steps and one or more sensitivity metrics describing the 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 layer thickness after the one or more process steps or a random defect rate based on the layer thickness. 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 repaired recipe based on the transformation model and the candidate mask design.

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

[0009] Those skilled in the art may better appreciate the numerous advantages of the present invention by referring to the accompanying drawings.

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

[0011] Figure 1B is a conceptual diagram illustrating a lithography subsystem according to one or more embodiments of the present invention.

[0012] Figure 1C is a conceptual diagram illustrating a characterization subsystem according to one or more embodiments of the invention.

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

[0014] Figure 2B According to one or more embodiments of the present invention Figure 2A Plot of the average resist edge position for six slices of two mask designs.

[0015] Figure 2C According to one or more embodiments of the present invention Figure 2A Plot of the average resist height for six slices of the mask design.

[0016] Figure 2D According to one or more embodiments of the present invention Figure 2A Plot of the random defect rate for six slices of the mask design.

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

[0018] Figure 3B The invention is described in one or more embodiments of the present invention. Figure 3A A flow chart of additional steps of the method.

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

[0020] Figure 5 is a simplified flow chart illustrating random defect mitigation in accordance with one or more embodiments of the present invention.

[0021] Fig. 6A is a simplified view of a patched mask shown in the form of update vectors on feature edges in accordance with one or more embodiments of the present invention.

[0022] Figure 6B is a simplified view of a patched mask shown in the form of update vectors on feature edges, where only a subset of sample locations are patched, in accordance with one or more embodiments of the present invention.

[0023] Figure 7 is an illustration of iterative mask inpainting in a region of interest (ROI) in accordance with one or more embodiments of the present invention.

[0024] Fig. 8A is a simplified flow chart illustrating the use of a transformation model to train a machine learning model according to one or more embodiments of the present invention.

[0025] Figure 8Bis a flow chart illustrating a non-limiting example of training a machine learning model based on training data generated by a transformation model according to one or more embodiments of the present invention.

[0026] Figures 9A to 9D Included is a series of plots illustrating additional non-limiting examples of patch masks in accordance with one or more embodiments of the present invention.

[0027] Fig.10 is a simplified flow chart illustrating random defect mitigation in accordance with one or more embodiments of the present invention. DETAILED DESCRIPTION

[0028] Reference will now be made in detail to the disclosed subject matter illustrated in the accompanying drawings. The present invention has been particularly shown and described with respect to specific embodiments and specific features thereof. The embodiments described herein should be regarded as illustrative and not restrictive. It should be readily apparent to those skilled in the art that various changes and modifications in form and details may be made without departing from the spirit and scope of the present invention.

[0029] Embodiments of the present invention relate to systems and methods for providing remedial mask pattern design changes that attempt to mitigate or control random wafer defects within acceptable tolerances. For example, embodiments of the present invention may evaluate the sensitivity of an input mask design to random defects and provide remedial changes to the input mask design to reduce the sensitivity to such random defects. Significantly, the systems and methods disclosed herein may provide remedial changes to masks that have undergone other modifications (such as, but not limited to, optical proximity correction (OPC) changes) to facilitate accurate manufacturing according to the intended design. It should be noted that OPC and other techniques may be prone to errors when based on "rule-based" or other "compact" modeling techniques that may include approximate estimates to provide full-chip evaluations with high throughput. However, the systems and methods disclosed herein may be combined with more accurate and potentially more computationally rigorous modeling to provide superior random defect mitigation and can provide acceptable throughput. In addition, the repair process can be flexibly applied to the entire design (e.g., the entire chip) or in a calibrated manner to specific areas of concern and / or areas most susceptible to random defects of concern.

[0030] Techniques for measuring and controlling semiconductor manufacturing in the presence of random defects are generally described in U.S. Pat. No. 10,474,042, issued on Nov. 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 the photolithographic pattern transfer process (e.g., but not limited to, photon exposure and absorption, photoproduct diffusion, chemical reactant spatial distribution, or chemical reaction). In this way, when nominally identical structures are manufactured under nominally identical conditions (e.g., 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 on a sample across multiple wafers), randomly occurring manufacturing defects may occur with a specific probability.

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

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

[0033] The transformation model and associated sensitivity metrics may be utilized in various ways to provide corrective mask design changes that mitigate random defects within the spirit and scope of the present invention.

[0034] In some embodiments, the transformation model evaluates the 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.), as well as 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 may provide a measure of the sensitivity of the candidate mask design to the output parameter, either individually or in combination. If the output parameter is unacceptable (e.g., outside a selected tolerance), the candidate mask design is updated based on the sensitivity metric. This process may be iterated as needed to provide a patched mask design that meets the selected tolerance. It should be noted that within the spirit and scope of the present invention, the mask design may be provided in various forms (e.g., but not limited to, a binary representation, a polygonal representation, a distance field representation, or a level set representation). In a general sense, the mask design may be represented by any parameter for which a sensitivity metric may 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 patching. For example, a machine learning model can be developed to generate a patched mask design from an input mask design, wherein the machine learning model is trained based at least in part on the training data generated by the transformation model. As an illustration, the transformation model can evaluate the patched mask design by generating output parameters and associated sensitivity metrics. In addition, in the case where the patched mask design provided by the machine learning model does not meet the application tolerance, the sensitivity metrics 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 invention are directed to providing corrective modifications to additional aspects of a manufacturing recipe, such as, but not limited to, properties of the illumination used during lithography (e.g., source distribution, wavelength, polarization, angle of incidence, or the like) or properties of the sample (e.g., thickness of a handle layer, thickness of a photoresist, or the like). In this way, such recipe parameters may be adjusted in addition to and / or in lieu of mask design to reduce the probability of random defects during manufacturing.

[0037] Reference Figures 1A to 10 , in accordance with one or more embodiments of the present invention, systems and methods for providing corrective mask design changes to mitigate random defects are described in more detail.

[0038] Figure 1A1 is a block diagram of a system 100 according to one or more embodiments of the present invention. In some embodiments, the system 100 includes a lithography subsystem 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 subsystem 102 can operate by illuminating the mask 106 and projecting an image of the mask 106 onto the sample 104.

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

[0040] In some embodiments, the system 100 includes a characterization subsystem 108 configured to generate one or more measurements of the mask 106 and / or the sample 104 having features associated with the mask 106 through photolithographic exposure and potentially additional processing steps. The characterization subsystem 108 may 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). In addition, the characterization subsystem 108 or any portion thereof may be characterized as an inspection tool and / or metrology. In this manner, the characterization subsystem 108 may perform various functions, including, but not limited to, identifying defects in the mask 106 or performing one or more measurements of a portion of the mask (e.g., a critical dimension (CD) measurement, a feature thickness measurement, a film thickness measurement, a composition measurement, an edge position measurement, 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 may be communicatively coupled with any component of the system 100 to provide one-way communication and / or two-way communication. In this manner, the controller 110 may perform (e.g., via one or more processors 112) any of the various process steps described throughout the present invention, such as, but not limited to, developing a simulation-based model of a manufacturing process, developing a transformation model that mimics the simulation-based model for a selected input space and provides a sensitivity metric that describes the sensitivity of one or more output parameters to variations of the mask, receiving a candidate mask design, or generating a patched mask design based on iteratively updating the candidate mask design using a transformation model.

[0042] The one or more processors 112 of the controller 110 may include any processing element known in the art. In this sense, the one or more processors 112 may include any microprocessor-type device configured to execute algorithms and / or instructions. In some embodiments, the one or more processors 112 may be composed of the following: a desktop computer, a large computer system, a workstation, an image computer, a parallel processor, or any other computer system (e.g., a networked computer) configured to execute a program configured to operate the system 100, as described in various places of the present invention. It should be further recognized that the term "processor" can be broadly defined as covering any device having one or more processing elements that execute program instructions from a non-temporary memory 114. In addition, the steps described in various places of the present invention may be implemented by a single controller 110 or alternatively multiple controllers. In addition, the controller 110 may include one or more controllers housed in a common housing or in multiple housings. In this way, any controller or controller combination can be individually packaged as a module suitable for integration into the system 100.

[0043] The memory 114 may include any storage medium known in the art that is suitable for storing program instructions that can be executed by the associated one or more processors 112. For example, the memory 114 may include a non-transitory storage medium. By way of another example, the memory 114 may include, but is not limited to, a read-only memory, a random access memory, a magnetic or optical storage device (e.g., a disk), a tape, a solid-state drive, and the like. It should be further noted that the memory 114 may be housed in a common controller housing with the one or more processors 112. In some embodiments, the memory 114 may 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 may access a remote memory (e.g., a server) that is accessible via a network (e.g., the Internet, an intranet, and the like). Therefore, the above description should not be construed as a limitation of the present invention, but is merely illustrative.

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

[0045] However, it is contemplated herein that random defect rates may be estimated more directly and accurately based on local resist thickness at a region of interest on a sample (e.g., a wafer) rather than by edge location. This is in part because edge location by definition encodes an approximate form of resist thickness. Furthermore, prior art techniques may not be suitable for relatively rare random errors. The 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, & MOEMS 10.3 (2011): 033019-033019); and Mack, Chris A., John J. Biafore, and Mark D. Smith, “Stochastic exposure kinetics of extreme ultraviolet photoresists: simulation study” (Journal of Micro / Nanolithography, MEMS, & MOEMS 10.3 (2011): 033019-033019). D. Smith., “Stochastic exposure kinetics of extreme ultraviolet photoresists: Trapping model” (Journal of Vacuum Science & Technology B 31.6 (2013)); all references are incorporated herein by reference in their entirety.

[0046] As an illustration, Figures 2A to 2D Depicted is a series of plots demonstrating random defect rates for two mask designs that provide similar edge locations, but different local resist thicknesses and different error rates, in accordance with one or more embodiments of the present invention. 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 invention. Figure 2B According to one or more embodiments of the present invention Figure 2A Plot of the average resist edge position (EP) for six slices (p1 to p6) of two mask designs. Figure 2CAccording to one or more embodiments of the present invention Figure 2A Plot of the average resist height (RH) of six slices for the mask design of FIG. Figure 2D According to one or more embodiments of the present invention Figure 2A Plot of the random defect rate (DR) of six slices of the mask design.

[0047] As Figures 2A to 2D As shown, when fabricated on sample 104, the two mask designs provide substantially the same edge positions (see, for example, Figure 2A and 2B ). However, the mask designs show substantial deviations in both average resist height and random defect rate in certain locations. For example, for slices p1, p4, and p6, the average resist height data for two mask designs (see, e.g., Figure 2C ) and random defect rates (see, for example, Figure 2D ) both show substantial deviation. In this way, resist height is a more accurate predictor of random defectivity than resist edge position.

[0048] Figure 3A 300 is a flow chart illustrating steps performed in a method 300 for mask repair according to one or more embodiments of the present invention. Applicants mention that the embodiments and implementation techniques previously described herein in the context of system 100 should be interpreted as extending to method 300. For example, one or more processors 112 of system 100 may execute program instructions that cause one or more processors 112 to perform any of the various steps of method 300. However, it should be further noted that method 300 is not limited to the architecture of system 100.

[0049] In some embodiments, 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 sample 104. As an illustration, the simulation-based model may provide a distribution of sample layer thickness that varies as a function of location across sample 104 or a portion thereof. The distribution of sample layer thickness may be expressed as a single output value per location on sample 104 or a probability distribution of thickness per location on sample 104.

[0050] Step 302 may describe features on sample 104 after any number of process steps. For example, features on sample 104 (e.g., on a particular layer of sample 104) may be fabricated using process steps such as, but not limited to, deposition of one or more layers (e.g., a handle layer and / or a photoresist layer), photolithographic exposure of a pattern from mask 106, post-exposure baking, etching, ion implantation (e.g., doping), metallization oxidation, polishing, or the like. Furthermore, such steps may be repeated multiple times to build a semiconductor device. In some embodiments, the simulation-based model of step 302 provides a photoresist thickness after the photolithographic exposure process, which may be similar to the photoresist thickness that may be measured in a post-development inspection (ADI) step. The simulation-based model may model any type of commercial or custom photoresist, including, but not limited to, positive-tone-develop chemically amplified resist (PTD CAR), negative tone developing (NTD) resist, or metal oxide (MOx) resist. In some embodiments, the simulation-based model of step 302 provides a seasoning layer thickness after an etching step, which may be similar to a seasoning layer thickness that may be measured in a post-etch inspection (AEI) step. In addition, the simulation-based model of step 302 may 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 may include developing a simulation-based model of sample layer thickness using any suitable technique. Input parameters to the simulation-based model may include, but are not limited to, the 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 may 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 temperature, or the like. As used herein, an input space defines a range of various input parameters that may 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 the lithographic exposure of the mask 106 using techniques such as, but not limited to, rigorous coupled wave analysis (RCWA), finite difference time domain (FDTD) analysis, finite element method (FEM) analysis, moment method analysis, surface integral techniques, or volume integral techniques. In this way, 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), a physics-based simulator sold by KLA Corporation, can be used to simulate photoresist thickness. Physics-based simulations of photoresist thickness are generally described in the above-referenced and fully incorporated herein by reference entitled "Prediction and metrology of stochastic photoresist thickness defects" and in U.S. Patent Publication No. 2022 / 0129775 published on April 28, 2022.

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

[0054] However, it is further contemplated herein that this technique may require a large number of samples to adequately characterize relatively rare random defects (e.g., defects having a part per million or part per billion defect rate). In addition, the run time of this model may be relatively slow. Therefore, it may be undesirable or impractical to rely solely on this simulation-based model to characterize random defect rates.

[0055] In some embodiments, method 300 includes a step 304 of developing a transformation model of a manufacturing process that mimics a simulation-based model and has a faster evaluation speed than the simulation-based model for a selected range of inputs and / or outputs. The transformation model may accept an input mask design, input parameters within at least a portion of the input space of the simulation-based model (e.g., as fixed or floating parameters), output one or more output parameters associated with the manufacture of the input mask design, and output one or more sensitivity metrics describing the sensitivity of the one or more output parameters to variations in the input mask design. The output parameters provided by the transformation model may 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. In addition, the transformation model may incorporate or otherwise account for variations in process parameters that may occur naturally during manufacturing (e.g., process variations). For example, the transformation model may provide probabilities for any output parameter (e.g., sample layer thicknesses or the like) based on known or expected variations in process parameters and / or random processes. In this manner, the transformation model may be adapted to characterize the robustness of a mask design to process variations.

[0056] Step 304 may include developing a transformation model of at least the sample layer thickness using any suitable technique. In some embodiments, a machine learning technique is used to generate the transformation model. In this way, the transformation model may be a trained machine learning model. This machine learning model may be trained using any suitable training data. For example, simulation data and / or metrology data from training samples made with different variations of input parameters may be used to train this machine learning model. The metrology data may be generated using any suitable characterization subsystem 108 (e.g., but not limited to, a scanning electron microscope (SEM) tool, a transmission electron microscope tool (TEM), an x-ray tool, or the like). In addition, this machine learning model may be combined with 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, machine learning is further combined with 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 speeds than the simulation-based model for at least a subset of the input space and / or output space of the simulation-based model. In this way, the development and utilization of the transformation model can provide increased throughput relative to the simulation-based model while maintaining performance tolerances 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 the size of the input space (e.g., the size of the input parameter range for which the transformation model mimics the simulation-based model within an acceptable tolerance). The use of a machine learning model for photoresist thickness that mimics a simulation-based model 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 is incorporated herein by reference in its entirety.

[0058] Figure 4 4 is a conceptual illustration of the tradeoffs of a transformation model according to one or more embodiments of the present invention. Plot 402 is a conceptual illustration of the speed of a transformation model as a function of the covered input space of a simulation-based model. Plot 404 is a conceptual illustration of the accuracy of a transformation model as a function of the speed of the transformation model. As illustrated, the speed of a transformation model may generally decrease as the covered input space increases. Furthermore, the accuracy of a transformation model may generally decrease as the speed increases. However, there may be situations where a transformation model provides sufficient accuracy (e.g., within a selected tolerance) within a suitable subset of the input space of a simulation-based model while also providing a substantial speed enhancement relative to a simulation-based model.

[0059] In some embodiments, the transformation model further provides mathematical differentiability. For example, the transformation model may generate a sensitivity metric associated with an estimate of the sensitivity of any of the output parameters to changes in the process parameters of interest. Any suitable sensitivity metric may be generated, such as, but not limited to, an analytical model gradient. The analytical model gradient is generally described in: Griewank, Andreas., "Who invented the reverse differential mode (Who invented thereverse mode of differentiation)" (Documenta Mathematica, Extra Volume ISMP 389400 (2012)); and Baydin, Atilim Gunes, et al., "Automatic differentiation in machine learning: a survey" (Journal of Machine Learning Research 18 (2018): 1-43); the two documents are incorporated herein by reference in their entirety.

[0060] In addition, the transformation model may provide a sensitivity metric for each output parameter (e.g., local photoresist thickness, random defect rate based on photoresist thickness, or the like) alone to selected input parameters or a sensitivity metric for a combination of output parameters. As an illustration, the sensitivity metric may provide an indication of how sensitive the local photoresist thickness and / or random defect rate (e.g., output parameters of the transformation model) of a particular candidate mask design is to variations in process parameters. In other words, the sensitivity metric may provide an indication of how deviations in process parameters occurring during manufacturing may affect the photoresist thickness and / or random defect rate. It is contemplated herein that this information may be utilized to make corrective design changes 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 may 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. Furthermore, the patched mask design may be provided as a complete design or an update vector describing a modification to the candidate mask design.

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

[0063] Figure 3B is a flow chart illustrating the sub-steps of step 308 of generating a patched mask design in accordance with one or more embodiments of the present invention.

[0064] In some embodiments, step 308 includes step 310 of utilizing the candidate mask design as an input mask design of the transformation model to generate one or more output parameters and one or more sensitivity metrics of the candidate mask design. 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 application tolerances (e.g., within selected tolerances). For example, step 312 may include updating the design of mask 106 based on the sensitivity metrics so 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 produced that meets application tolerances.Any application tolerance may be considered, such as, but not limited to, tolerance-dependent random defect rates.

[0066] Figure 5 is a simplified flow chart illustrating random defect mitigation according to one or more embodiments of the present invention. Specifically, Figure 5 A process is depicted in which a candidate mask design 500-C (e.g., a design of the candidate mask design 500-C) is provided as input to a transformation model 502 (e.g., as generated in step 304) along with additional process parameters of interest 504. For example, the process parameters 504 may include values ​​and / or ranges of the process parameters 504 within the input space covered by the transformation model 502. The transformation model 502 may then generate (e.g., in step 310) any number of output parameters 506, such as, but not limited to, local photoresist thickness, random defect rate based at least in part on the local photoresist thickness, edge placement error, LER, CDU, distance field violation, or mask rule check parameters. The transformation model 502 may also generate (e.g., in step 310) sensitivity metrics 508 associated with any output parameter 506, either alone or in one or more combinations.

[0067] Figure 5Further illustrating whether an application tolerance is met (e.g., block 510) is determined (e.g., as part of step 312). If the tolerance is met, then a 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 may be repeated as necessary until the application tolerance is met (e.g., satisfied). Any application tolerance may be considered, such as, but not limited to, a tolerance-dependent random defect rate.

[0068] Reference Figures 6A to 8B , describing method 300 (and Figure 5 Non-limiting variations of the flowchart in FIG.

[0069] Method 300 (e.g., step 308) can apply corrections or repairs to the entire candidate mask design 500-C or a portion of the candidate mask design 500-C. For example, applying corrections to a portion of the candidate mask design 500-C rather than the entire candidate mask design 500-C can reduce computational speed. In the case where only a portion of the candidate mask design 500-C is corrected, the portion may be determined using any suitable technique.

[0070] In some embodiments, regions of interest (ROIs) may be selected for repair (either overall or for a specific iteration) using method 300. These ROIs may be selected using any criteria. For example, the ROIs may correspond to features or sample locations that are prone to random defects. In another example, the ROIs may correspond to features or sample locations that are particularly critical to device performance.

[0071] In some embodiments, the portion of the candidate mask design 500-C selected for repair is selected based on the screening (e.g., before updating the candidate mask design 500-C). For example, the output parameters 506 of the transformation model may identify one or more areas on the sample 104 as potentially problematic based on the current candidate mask design 500-C. For example, when manufacturing using the candidate mask design 500-C, the output parameters 506 of the transformation model may predict one or more hot spots as having a relatively high probability of random defects. Such problematic areas may 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 may not be desirable to incorporate all identified potential adjustments into the candidate mask design 500-C. For example, some adjustments may be redundant. As another example, some adjustments may repair the identified problematic areas but may adversely affect different areas. Therefore, in some embodiments, only a subset of the potential adjustments to the candidate mask design 500-C are implemented in a particular iteration. As an illustration, a selected percentage of positions for adjustment having sensitivity metrics 508 indicating the highest sensitivity to output parameter 506 may be selected for patching (e.g., the top X% of positions, where X may be any selected value, such as, but not limited to, 10%). As another illustration, positions having sensitivity metrics exceeding a selected threshold (e.g., defining a magnitude of sensitivity) may be selected for patching. Furthermore, the filter criteria may be adjusted individually for each iteration, either dynamically or based on predefined rules. As an illustration, it may be desirable to gradually reduce the number and / or magnitude of corrections to candidate mask design 500-C within successive iterations to facilitate convergence to a robust design.

[0072] Fig. 6A and 6B A patching of a selected portion of the sample 104 is illustrated. Fig. 6A and 6B , transformation model 502 provides output parameters 506 including random defect rate and edge placement error in the photoresist (eg, after lithographic exposure). Fig. 6A 308 in accordance with one or more embodiments of the present invention. For example, the various arrows indicate the direction and magnitude of the edge position modification identified for adjustment in a particular iteration. As illustrated, the magnitude and / or direction of the update vectors in the patched mask design 500-R may vary across the sample 104 and between different iterations. Figure 6B is a simplified view of a patched mask design 500-R shown in the form of update vectors on feature edges through multiple iterations of step 308, wherein only a subset of sample locations are patched, according to one or more embodiments of the present invention. Figure 6B Roughly similar to Fig. 6A , except that it includes updates associated with only a portion of sample 104, where the displayed locations may be selected based on defining an ROI, filtering, or any other suitable technique. In particular, Figure 6B is generated based on screening a set of potential modifications to candidate mask design 500 -C based on sensitivity metric 508 to include a selected percentage of modifications that provide the highest sensitivity to output parameter 506 .

[0073] Figure 7 7 is an illustration of iterative mask patching performed in ROI 702 using method 300 according to one or more embodiments of the present invention. Figure 7 , the transformation model 502 provides output parameters 506 including the random defect rate within the ROI 702, the random defect rate outside the ROI 702, and the edge placement error in the photoresist (eg, after lithographic exposure).

[0074] Specifically, Figure 7 A diagram depicting an initial candidate mask design 500-C (e.g., pre-patch candidate mask design 500-C), two interim masks associated with an iteration of step 308, and a final patched mask design 500-R. In this manner, the two interim masks represent both the patched mask design 500-R from one iteration and the candidate mask design 500-C of a subsequent iteration. In addition, Figure 7 Depicts a patch modification to the candidate mask design 500-C shown (e.g., in Figure 5 512 of FIG. 5 ). For reference, the initial design is also shown as a dashed line so that the impact of design changes within each iteration can be visualized.

[0075] exist Figure 7 In the process presented in , decisions about whether the design as a whole meets the selected tolerances (e.g. Figure 5 702 (e.g., the random defect rate within the ROI 702). In particular, the method 300 may continue to iterate until the location within the ROI 702 meets the selected tolerance. In some embodiments, the method 300 may further iterate until the location outside the ROI 702 meets an additional tolerance, which may be different from the tolerance for the area within the ROI 702. In addition, it should be noted that the above-described methods previously described herein (e.g., with respect to Figures 6A to 6B ) describes a screening technique to limit remedial corrections based on any of the output parameters 506.

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

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

[0078] For example, you can execute the first Figure 5 The process in the embodiment of the present invention is repeated to generate the first patched mask design 500-R of the initial candidate mask design 500-C. Subsequently, the second step may be performed in the second stage. Figure 5 , wherein the first repaired mask design 500-R is provided as a candidate mask design 500-C for the second stage to generate a second (e.g., final) repaired mask design 500-R. As an illustration, the output parameters 506 of the first stage may include random defect rates within one or more ROIs (e.g., Figure 7), random defect rates outside one or more ROIs, and edge placement errors. Then, an update to the candidate mask design 500-C may be performed for the entire sample 104, just the ROI, or for a set of screened locations as described above (e.g., block 512). Then, the output parameters 506 in the second stage may further include mask rule check violations. It is contemplated herein that this one two-stage operation may provide efficient repair 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 may make any additional modifications as needed to avoid mask rule check violations. However, it should be noted that this example is provided for illustration only and should not be construed as limiting. In a general sense, a multi-stage implementation may allow mask correction based on multiple combinations of output parameters in a controlled and efficient manner.

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

[0080] Fig. 8A is a simplified flow chart illustrating the use of the transformation model 502 to train the machine learning model 802 according to one or more embodiments of the present invention.

[0081] In some embodiments, the machine learning model 802 generates a patched mask design 500-R from the input candidate mask design 500-C. This patched mask design 500-R may then be provided as input to the transformation model 502 (e.g., generated in step 304), which may provide output parameters 506 and 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 may characterize the sensitivity of the machine learning model 802 to the output parameters 506 (e.g., random defect rate or the like). If the patched mask design 500-R from the machine learning model 802 does not meet the selected application tolerance, the machine learning model 802 may be updated (block 804) based on the sensitivity metrics 508. Further, this process may be repeated until the patched mask design 500-R generated by the machine learning model 802 meets (e.g., satisfies) the application tolerance.

[0082] Figure 8B 8 is a flowchart illustrating a non-limiting example of training a machine learning model 802 based on training data generated by a transformation model 502 according to one or more embodiments of the present invention. It should be noted that Figure 8B A specific non-limiting case is described where 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 based on a plurality of input candidate mask designs 500-T as training data. For example, the input candidate mask designs 500-T may be manufactured with known variations of process parameters (e.g., within the covered input space). After training, the machine learning model 802 may be trained based on any suitable input (including but not limited to the input candidate mask designs 500-C or such). Figure 8B ) directly produces the repaired mask design 500-R.

[0084] Reference Figures 9A to 9D , Figures 9A to 9D Included is a series of plots illustrating additional non-limiting examples of using method 300 to repair a mask design 500 in accordance with one or more embodiments of the present invention. Figures 9A to 9D Each of includes a simplified top view image labeled "MASK DESIGN" that depicts a candidate mask design 500-C and a repaired mask design 500-R generated using the systems and methods disclosed herein. Figures 9A to 9D Each of 500 further includes an image of a simplified top view of sample 104 having predicted features in an exposed photoresist layer fabricated based on the associated mask design 500. It should be noted that the predicted features associated with different mask designs 500 are superimposed to illustrate the differences. Figures 9A to 9D Each of further includes a plot of the random defect rate (DR) of the associated mask design 500. In addition, Figures 9A to 9C Depicting a configuration for providing patching based on a single ROI 900, while Fig.9D Depicted are configurations that provide repairs based on multiple ROIs 900. In each case, 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 an applied tolerance (eg, illustrated as dashed line 902).

[0085] Reference Fig.10 , according to one or more embodiments of the present invention, random defects are mitigated by modification of process parameters in place of or in addition to the design of mask 106. It is contemplated herein that defect rates (e.g., random defect rates) may be affected not only by the design of mask 106 used for photolithography, but also by various process parameters (e.g., but not limited to, dose, focus position, illumination numerical aperture, illumination source shape, post-exposure bake temperature, development time, or the like). Therefore, process parameters may be adjusted in addition to or in place of mask design to mitigate random defects.

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

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

[0088] For example, any component of the recipe may be iteratively modified (eg, updated) based on the transformation model 502 . Fig.10 is a simplified flow chart illustrating random defect mitigation according to one or more embodiments of the present invention. It should be noted that Fig.10 Roughly similar to Figure 5 , just means to update the mask design 500 Figure 5 Except that the box 512 of FIG. 1 is replaced by the box 1002 representing updating the recipe describing the manufacturing process. Fig.10 , the transformation model 502 may accept any process parameters 504 (e.g., candidate process parameters 504-C) and a mask design 500 (e.g., candidate mask design 500-C) as inputs and provide output parameters 506 and associated sensitivity metrics 508. If the output parameters 506 are not within application tolerances, any aspect of the recipe may be updated (block 1002), including only the mask design 500, only any process parameters 504, and / or a combination of the mask design 500 and any process parameters 504. If the output parameters 506 are within application tolerances, a repaired mask design 500-R and / or repaired process parameters 504-R (e.g., more generally, a repaired recipe) may 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 including relevant process parameters. Thus, Figure 8B This can be extended to include process parameters 504 in the training data set and provide associated outputs.

[0090] Now generally refer to Figures 1A to 1C , additional aspects of system 100 are described in greater detail according to one or more embodiments of the present invention.

[0091] Figure 1B 1 is a conceptual diagram illustrating a lithography subsystem 102 according to one or more embodiments of the present invention. In some embodiments, the lithography subsystem 102 includes an illumination source 116 configured to generate one or more illumination beams 118. The illumination beams 118 may 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 may include wavelengths such as but not limited to 13.5 nm or the like. EUV-based lithography is generally described in U.S. Pat. No. 8,916,831, issued Dec. 23, 2014, which is incorporated herein by reference in its entirety.

[0092] In some embodiments, the illumination source 116 comprises an extreme ultraviolet illumination source 116. For example, the EUV illumination source 116 may comprise a broadband plasma (BBP) illumination source. In this regard, the illumination beam 118 may comprise radiation emitted by the plasma. For example, the BBP illumination source 116 may comprise, but is not required to comprise, one or more pump sources (e.g., one or more lasers) configured to focus illumination into a volume of a gas, causing the gas to absorb energy to create or maintain a plasma suitable for emitting radiation. Furthermore, at least a portion of the plasma radiation may be used as the illumination beam 118. In some embodiments, the illumination source 116 may comprise one or more lasers capable of emitting radiation at one or more selected wavelengths.

[0093] In some embodiments, the illumination source 116 directs an illumination beam 118 to the mask 106 via an illumination path 120. The illumination path 120 may include one or more illumination optics 122 suitable for directing, focusing, and / or shaping the illumination beam 118 onto the mask 106. For example, the illumination optics 122 may include one or more lenses, one or more focusing components, or the like. Furthermore, the illumination optics 122 may 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 may 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, a plane mirror or a curved mirror (e.g., an elliptical mirror, a parabolic mirror, or the like).

[0094] The illumination optics 122 may further include one or more additional illumination path components suitable for shaping the illumination beam 118 and / or controlling the range of incidence angles (e.g., illumination pupil distribution) of the illumination beam 118 on the mask 106. For example, the illumination path components may 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 subsystem 102 includes a mask support device 124. The mask support device 124 can be configured to hold the mask 106.

[0096] In some embodiments, the lithography subsystem 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 a sample 104 disposed on a sample stage 128. For example, the set of projection optics 126 may be configured to project the 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 may be configured to actuate or position the mask 106. For example, the mask support device 124 may actuate the mask 106 to a selected position relative to the projection optics 126 of the lithography subsystem 102.

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

[0098] As used throughout the present invention, the term "sample" generally refers to a substrate (e.g., a wafer or the like) formed of a semiconductor or non-semiconductor material. For example, the semiconductor or non-semiconductor material may include, but is not limited to, single crystal silicon, gallium arsenide, and indium phosphide. The sample may include one or more layers. For example, such layers may include, but are not limited to, resists, dielectric materials, conductive materials, and semiconductive materials. Many different types of such layers are known in the art, and the term sample as used herein is intended to cover samples on which all types of such layers can be formed. One or more layers formed on the sample may be patterned or unpatterned. For example, the sample may include a plurality of dies, each of which has repeatable patterned features. The formation and processing of such material layers may ultimately lead to finished devices. Many different types of devices may be formed on the sample, and the term sample as used herein is intended to cover samples on which any type of device known in the art is manufactured. In addition, for the purposes of the present invention, the terms sample and wafer should be interpreted as interchangeable. Additionally, for the purposes of the present invention, the terms patterning device, pattern mask, mask, and reticle should be interpreted as interchangeable.

[0099] Figure 1C 1 is a conceptual diagram illustrating the characterization subsystem 108 according to one or more embodiments of the present invention. It should be noted that Figure 1C Characterization subsystem 108 is depicted as an optical system. However, this is illustrative only and not limiting. In practice, characterization subsystem 108 may 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 for generating an illumination beam 134. The illumination beam 134 may include light of one or more selected wavelengths, including but not limited to ultraviolet (UV) radiation, visible radiation, or infrared (IR) radiation. It should be noted herein that without limiting the scope of the present invention, the characterization subsystem 108 may include any type of characterization subsystem 108 known in the art. For example, although Figure 1C Not depicted, but without departing from the scope of the present invention, the characterization subsystem 108 may 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 an illumination beam 134 to the sample 104 via an illumination path 136. The illumination path 136 may include one or more lenses 138. In addition, the illumination path 136 may include one or more additional optical components 140 suitable for modifying and / or adjusting the illumination beam 134. For example, the one or more optical components 140 may 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 emitted from the sample 104 through a collection path 148. The collection path 148 may include a plurality of optical components to direct and / or modify the illumination collected by the objective 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 detector 146 may receive an image of the sample 104 provided by a component in the light collection path 148 (e.g., the objective 144, the one or more lenses 150, or the like). By another example, the detector 146 may receive radiation reflected or scattered (e.g., via specular reflection, diffuse reflection, and the like) from the sample 104. By another example, the detector 146 may receive radiation generated by the sample (e.g., luminescence associated with absorption of the illumination beam 134, and the like). Furthermore, it should be noted herein that the one or more detectors 146 may include any optical detector known in the art suitable for measuring illumination received from the sample 104. For example, the detector 146 may include, but is 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 for securing and positioning the sample 104 .

[0105] The objects described herein sometimes illustrate different components contained in or connected to other components. It should be understood that such depicted architectures are exemplary only, and in fact many other architectures that realize the same functionality can be implemented. In a conceptual sense, any component arrangement for realizing the same functionality is effectively "associated" so as to realize the desired functionality. Therefore, any two components combined to realize a specific functionality herein can be considered to be "associated" with each other so as to realize the desired functionality, without considering the architecture or intermediate components. Similarly, any two components so associated can also be considered to be "connected" or "coupled" to realize the desired functionality, and any two components that can be so associated can also be considered to be "coupleable" to realize the desired functionality. Specific examples that can be coupled include but are not limited to physically interactable and / or physically interactive components, and / or wirelessly interactive and / or wirelessly interactive components, and / or logically interactive and / or logically interactive components.

[0106] It is believed that the present invention and its many attendant advantages will be understood from the foregoing description, and it will be appreciated that various changes may be made in the form, construction and arrangement of components without departing from the disclosed object or sacrificing all of its material advantages. The forms described are merely illustrative, and the appended claims are intended to cover and encompass such changes. Furthermore, it should be understood that the present invention is defined by the appended claims.

Claims

1. A system comprising: A controller comprising one or more processors configured to execute program instructions causing the one or more processors to: developing a simulation-based model of layer thickness after one or more process steps for fabricating features on a sample, wherein the simulation-based model accepts an input mask design to be exposed on the sample and provides as output 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 input to the transformation model comprises the input mask design, wherein the output of the transformation model comprises one or more output parameters associated with manufacturing of the input mask design and one or more sensitivity metrics describing sensitivity of the one or more output parameters to variations of the input mask design, wherein the one or more output parameters comprises 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 A patched mask design is generated based on the transformation model and the candidate mask designs.

2. The system of claim 1, wherein the layer thickness comprises: At least one of the thickness of the photoresist layer after a photolithography process step or the thickness of the seasoning 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 layer thickness or a probability of the layer thickness 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 polygonal 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 The candidate mask design is updated with the update vector 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 met: utilizing the candidate mask design as the input mask design for the transformation model to generate the one or more output parameters and the one or more sensitivity metrics of the candidate mask design; and The candidate mask design is updated based on the one or more sensitivity metrics to provide the repaired 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 include: Tolerance for random defect rate.

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 The candidate mask design is updated with the update vector to produce 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: Prior to updating the candidate mask design with the update vectors to generate the patched mask design, the update vectors are screened based on the one or more sensitivity metrics to include only a subset of the update vectors having sensitivities above a selected sensitivity threshold.

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: The update vectors for at least some edges in the candidate mask designs are generated 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 vector comprises: A gradient descent optimizer is used to update the set of polygons in the candidate mask design with the update vector.

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 vector comprises: The candidate mask design is updated with the update vector using a velocity field controlled to obey the conditions of 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 using training data generated by the transformation model; and The patched mask design is generated using the machine learning model.

15. The system of claim 1, wherein the one or more output parameters include: two or more output parameters, wherein the one or more sensitivity metrics include: Two sensitivity metrics are 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 include: 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 include: The layer thickness, the random defect rate based on the layer thickness, and the edge placement error.

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

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

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

21. A method comprising: developing a simulation-based model of layer thickness after one or more process steps for fabricating features on a sample, wherein the simulation-based model accepts an input mask design to be exposed on the sample and provides as output 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 input to the transformation model comprises the input mask design, wherein the output of the transformation model comprises one or more output parameters associated with manufacturing of the input mask design and one or more sensitivity metrics describing sensitivity of the one or more output parameters to variations of the input mask design, wherein the one or more output parameters comprises 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 A patched mask design is generated based on the transformation model and the candidate mask designs.

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

23. A system comprising: A controller comprising one or more processors configured to execute program instructions causing the one or more processors to: developing a simulation-based model of layer thickness after one or more process steps for fabricating features on a sample, wherein an input to the simulation-based model comprises a recipe defining 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 an output of the simulation-based model comprises 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 the input mask design and at least one of the one or more process parameters, wherein the outputs of the transformation model include one or more output parameters associated with fabricating the input mask design with the one or more process steps and one or more sensitivity metrics describing 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 comprising a candidate mask design and the at least one of the one or more process parameters; and A patched recipe is generated based on the transformation model and the candidate mask designs.

24. The system of claim 23, wherein the layer thickness comprises: At least one of the thickness of the photoresist layer after a photolithography process step or the thickness of the seasoning 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 designs and patched mask designs are represented by at least one of a binary representation, a polygonal 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 of at least one of the update vectors including the candidate mask design or an update to the at least one of the one or more process parameters; and The candidate recipe is updated with the update to produce 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 using training data generated by the transformation model; and The repaired recipe is generated using the machine learning model.

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

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

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

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