Repair of lithography masks by simulating the photoresist thickness evolution.

Abstract

A system for repairing a mask design may develop a simulation-based model of layer thicknesses after one or more process steps that fabricate a feature on a sample, and develop a transformation model of the manufacturing process that emulates the simulation-based model and has a faster evaluation speed than the simulation-based model. An input to the transformation model includes an input mask design, and an output of the transformation model includes one or more output parameters related to manufacturing of the input mask design and one or more sensitivity metrics that represent the 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

[Technical Field]

[0001] FIELD OF THE DISCLOSURE The present disclosure relates generally to lithography mask designs, and more particularly to repairing lithography mask designs to mitigate stochastic defects. [Background technology]

[0002] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Patent 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.

[0003] The demand for reduced feature sizes in semiconductor devices results in tighter tolerances for lithographic printing processes. While minimum feature sizes can generally be reduced by scaling down the wavelength of light used in lithographic processes, it is often desirable to fabricate features near or below the traditional resolution limit at a particular wavelength. In this context, stochastic defects associated with various process randomness become increasingly problematic. Stochastic defects occurring during semiconductor manufacturing can be attributed to the inherent stochasticity of numerous physical phenomena that comprise the lithographic pattern transfer process, including, but not limited to, photon exposure and absorption, diffusion of photodecomposition products, spatial distribution of chemical reactants, and chemical reactions. In particular, stochasticity is distinct from uncertainty and is associated with random variations within the process. Typical approaches for characterizing stochastic wafer defects include top-down scanning electron microscopy (SEM)-based inspection, top-down simulation of after-develop inspection (ADI) and / or after-etch inspection (AEI) pattern edge placement and inspection. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] U.S. Patent Application Publication No. 2021 / 0263405 Summary of the Invention [Problem to be solved by the invention]

[0005] However, such techniques may be excessively time consuming and / or may not adequately measure parameters that result in defects in the manufactured samples, which may be of ultimate concern. Therefore, there is a need to develop systems and methods to address such defects. [Means for solving the problem]

[0006] A system is disclosed according to one or more exemplary embodiments. In one exemplary embodiment, the system includes a controller including one or more processors. In another exemplary embodiment, the controller develops a simulation-based model of layer thicknesses after one or more process steps that fabricate a feature on a sample, where the simulation-based model accepts an input mask design to be exposed on the sample and provides at least the layer thicknesses after the one or more process steps as an output. In another exemplary embodiment, the controller develops a transformation model of the 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 the inputs or outputs, where the input to the transformation model includes the input mask design, and the output of the transformation model includes one or more output parameters related to the fabrication of the input mask design and one or more sensitivity metrics representing the sensitivity of the one or more output parameters to variations in the input mask design. In another exemplary embodiment, the one or more output parameters include at least one of a layer thickness after one or more process steps or a probabilistic defect rate based on the layer thickness. In another exemplary embodiment, the controller receives a candidate mask design. In another exemplary embodiment, the controller generates a repaired mask design based on the transformation model and the candidate mask design.

[0007] A method is disclosed according to one or more exemplary embodiments. In one exemplary embodiment, the method includes developing a simulation-based model of layer thicknesses after one or more process steps for fabricating a feature on a sample, the simulation-based model accepting an input mask design to be exposed on the sample and providing at least layer thicknesses after the one or more process steps as an output. In another exemplary embodiment, the method includes developing a transformation model of the 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 the inputs or outputs, the input to the transformation model including the input mask design, and the output of the transformation model including one or more output parameters related to fabrication of the input mask design and one or more sensitivity metrics representing the sensitivity of the one or more output parameters to variations in the input mask design. In another exemplary embodiment, the one or more output parameters include at least one of a layer thickness after one or more process steps or a probabilistic defect rate based on the layer thickness. In another exemplary embodiment, the method includes receiving a candidate mask design. In another exemplary embodiment, the method includes generating a repaired mask design based on the transformation model and the candidate mask design.

[0008] A system is disclosed according to one or more exemplary embodiments. In one exemplary embodiment, the system includes a controller including one or more processors. In another exemplary embodiment, the controller develops a simulation-based model of layer thickness after one or more process steps that fabricate a feature on a sample, where inputs to the simulation-based model include 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, and an output of the simulation-based model includes at least the layer thickness after the one or more process steps. In another exemplary embodiment, the controller develops a transformation model of the 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 the 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 the output of the transformation model includes one or more output parameters associated with fabricating the input mask design using the one or more process steps and one or more sensitivity metrics representing the sensitivity of the one or more output parameters to the input to the transformation model. In another exemplary embodiment, the one or more output parameters include at least one of a layer thickness after the one or more process steps or a probabilistic defect rate based on the layer thickness. In another exemplary embodiment, the controller receives a candidate recipe including a candidate mask design and at least one of the one or more process parameters. In another exemplary embodiment, the controller generates a repaired recipe based on the transformation model and the candidate mask design.

[0009] It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not necessarily restrictive of 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.

[0010] The many advantages of the present disclosure may be better understood by those skilled in the art by reference to the following drawings. [Brief explanation of the drawings]

[0011] [Figure 1A] FIG. 1 is a block diagram of a system in accordance with one or more embodiments of the present disclosure. [Figure 1B] FIG. 1 is a conceptual diagram illustrating a lithography subsystem in accordance with one or more embodiments of the present disclosure. [Figure 1C] FIG. 1 is a conceptual diagram illustrating a characterization subsystem in accordance with one or more embodiments of the present disclosure. [Figure 2A] 1A-1C are top views of two mask designs in accordance with one or more embodiments of the present disclosure. [Figure 2B] 2B is a plot of the average resist edge position for six slices of both mask designs of FIG. 2A in accordance with one or more embodiments of the present disclosure. [Figure 2C] 2B is a plot of average resist height for six slices of the mask design of FIG. 2A in accordance with one or more embodiments of the present disclosure. [Figure 2D] 2B is a plot of probabilistic defect rates for six slices of the mask design of FIG. 2A in accordance with one or more embodiments of the present disclosure. [Figure 3A] 1 is a flow chart illustrating steps performed in a method for mask repair in accordance with one or more embodiments of the present disclosure. [Figure 3B] 3B is a flow chart illustrating additional steps of the method of FIG. 3A in accordance with one or more embodiments of the present disclosure. [Figure 4] FIG. 1 is a conceptual diagram of a transformation model tradeoff, in accordance with one or more embodiments of the present disclosure. [Figure 5] 1 is a simplified flow diagram illustrating mitigation of stochastic defects in accordance with one or more embodiments of the present disclosure. [Figure 6A] FIG. 10 is a simplified diagram of an inpainted mask shown in the form of update vectors on feature edges, in accordance with one or more embodiments of the present disclosure. [Figure 6B]FIG. 10 is a simplified diagram of an inpainted mask shown in the form of an update vector on a feature edge where only a subset of sample locations are inpainted, in accordance with one or more embodiments of the present disclosure. [Figure 7] FIG. 1 is a diagram of iterative mask repair of a region of interest (ROI), in accordance with one or more embodiments of the present disclosure. [Figure 8A] 1 is a simplified flow diagram illustrating training a machine learning model using a transformation model, in accordance with one or more embodiments of the present disclosure. [Figure 8B] 1 is a flow diagram illustrating a non-limiting example 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. [Figure 9A] 10 includes a series of plots illustrating additional non-limiting examples of repairing a mask, according to one or more embodiments of the present disclosure. [Figure 9B] 10 includes a series of plots illustrating additional non-limiting examples of repairing a mask, according to one or more embodiments of the present disclosure. [Figure 9C] 10 includes a series of plots illustrating additional non-limiting examples of repairing a mask, according to one or more embodiments of the present disclosure. [Figure 9D] 10 includes a series of plots illustrating additional non-limiting examples of repairing a mask, according to one or more embodiments of the present disclosure. [Figure 10] 1 is a simplified flow diagram illustrating mitigation of stochastic defects in accordance with one or more embodiments of the present disclosure. DETAILED DESCRIPTION OF THE INVENTION

[0012] Reference will now be made in detail to the disclosed subject matter, as illustrated in the accompanying drawings. The present disclosure has been shown and described in detail with respect to certain embodiments and specific features thereof. The embodiments disclosed herein are to be considered illustrative and not limiting. It will be readily apparent to those skilled in the art that various changes and modifications in form and detail can be made therein without departing from the spirit and scope of the disclosure.

[0013] Embodiments of the present disclosure are directed to systems and methods that provide remedial mask pattern design modifications that attempt to mitigate or control stochastic wafer defects within acceptable error ranges. For example, embodiments of the present disclosure may evaluate an input mask design for sensitivity to stochastic defects and make remedial modifications to the input mask design to reduce its sensitivity to such stochastic defects. In particular, the systems and methods disclosed herein may make remedial modifications to a mask that has already undergone other modifications, such as, but not limited to, optical proximity correction (OPC) modifications, to facilitate accurate manufacturing according to the intended design. It is noted that OPC and other techniques can be error-prone when based on "rule-based" or otherwise "compact" modeling techniques that may include approximations for high-throughput whole-chip evaluation. However, the systems and methods disclosed herein may incorporate more accurate and potentially more computationally rigorous modeling to provide superior mitigation of stochastic defects while also providing acceptable throughput. Furthermore, the repair process can be flexibly applied to the entire design (eg, the entire chip) or in a targeted manner to certain target areas and / or target areas most susceptible to stochastic defects.

[0014] Techniques for measuring and controlling semiconductor manufacturing in the presence of stochastic 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. Stochastic defects can result from the inherent stochasticity of numerous physical phenomena that comprise the lithographic pattern transfer process, such as, but not limited to, photon exposure and absorption, diffusion of photodecomposition products, spatial distribution of chemical reactants, or chemical reactions. As such, stochastically occurring manufacturing defects may occur with some probability when nominally identical structures are manufactured under nominally identical conditions, such as, but not limited to, multiple locations within a field, predetermined locations across multiple fields on a single wafer, or predetermined locations on a sample across multiple wafers.

[0015] In some embodiments, an accurate simulation-based model (e.g., a physics-based model) is first generated that predicts sample layer thickness after one or more process steps (e.g., lithography, etching, polishing, etc.), thereby enabling an accurate understanding of stochastic defectivity. For example, the simulation-based model may predict the thickness of a photoresist layer after lithography exposure (e.g., after a development step). As another example, the simulation-based model may predict the thickness of a process layer after an etching and / or polishing step. Furthermore, the simulation-based model may incorporate the effects of stochastic variations and / or variations in process parameters that may 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, etc.

[0016] A transformation model can then be developed that reproduces the results of the simulation model for selected input and / or output spaces while providing faster evaluation speeds (e.g., faster computation times) than the simulation-based model. For example, the transformation model may emulate the simulation-based model for selected ranges of inputs (e.g., a range of inputs, such as, but not limited to, mask design and / or manufacturing process parameters) and / or outputs (e.g., a range of outputs, such as, but not limited to, mask design corrections, relatively reduced pixel densities associated with mask design corrections, and / or process parameters) within acceptable error ranges while providing faster evaluation speeds (e.g., faster computation times) than the simulation-based model. The transformation model may be, but is not necessarily, a machine learning model. In a general sense, the transformation model can be tuned to balance input space coverage, speed, and accuracy for a given application. The transformation model may further provide mathematical differentiability so that the transformation model may provide a direct and efficient estimate of the sensitivity of a particular mask design (or variants thereof) to output parameters of interest, such as, but not limited to, stochastic defect rates. Such sensitivity estimates may be provided in the form of sensitivity metrics (e.g., analytical model gradients, etc.) and may be used to provide remedial design changes to improve mask performance.

[0017] The transformation models and associated sensitivity metrics may be utilized in a variety of ways within the spirit and scope of the present disclosure to provide remedial mask design modifications that mitigate stochastic defects.

[0018] In some embodiments, the transformation model evaluates candidate mask designs and provides outputs in the form of output parameters of interest (e.g., probabilistic defect rate, resist edge placement error, distance field violations, mask rule check violations, etc.) and sensitivity metrics characterizing the sensitivity of the candidate mask design to the output parameters. In the case of multiple output parameters, the sensitivity metrics may provide measures of the sensitivity of the candidate mask design to the output parameters individually or in combination. If the output parameters are unacceptable (e.g., outside a selected tolerance), the candidate mask design is updated based on the sensitivity metrics. This process may be repeated as necessary to provide a repaired mask design that meets the selected tolerance. It should be noted that the mask design may be provided in various formats within the spirit and scope of the present disclosure, such as, 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 through any parameters for which a sensitivity metric can be generated using the transformation model.

[0019] In some embodiments, the transformation model is used to provide training data for a machine learning model for mask repair. For example, a machine learning model may be developed to generate a repaired mask design from an input mask design, and the machine learning model is trained based at least in part on the training data generated by the transformation model. Illustratively, the transformation model may evaluate the repaired mask design by generating output parameters and associated sensitivity metrics. Furthermore, if the repaired mask design provided by the machine learning model does not meet applicable error tolerances, the sensitivity metrics from the transformation model may be used to train the machine learning model (e.g., weights within the machine learning model).

[0020] Additional embodiments of the present disclosure are directed to making corrective modifications to additional aspects of the manufacturing recipe, such as, but not limited to, properties of the illumination used during lithography (e.g., source distribution, wavelength, polarization, angle of incidence, etc.) or properties of the sample (e.g., process layer thickness, photoresist thickness, etc.) In this manner, such recipe parameters may be adjusted in addition to and / or instead of mask design to reduce the probability of stochastic defects during manufacturing.

[0021] 1A-10, systems and methods for providing remedial mask design modifications to mitigate stochastic defects will be described in greater detail in accordance with one or more embodiments of the present disclosure.

[0022] 1A is 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 subsystem 102 that lithographically prints one or more patterns on a sample 104 based on a mask 106 (e.g., a lithography mask, a pattern mask, a reticle, etc.). For example, the lithography subsystem 102 may operate by illuminating the mask 106 and projecting an image of the mask 106 onto the sample 104.

[0023] Lithography subsystem 102 may include any type of lithographic printing tool known in the art, including, but not limited to, a scanner or a stepper. Furthermore, lithography subsystem 102 may utilize any type of illumination. For example, lithography subsystem 102 may utilize extreme ultraviolet (EUV) illumination and thus may be characterized as an EUV lithography subsystem.

[0024] 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 lithographic 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, etc.), 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, etc.). Additionally, 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 portions of the mask (e.g., critical dimension (CD) measurement, feature thickness measurement, film thickness measurement, composition measurement, edge position measurement, etc.).

[0025] In some embodiments, system 100 includes a controller 110. In some embodiments, controller 110 includes one or more processors 112 configured to execute program instructions maintained in memory 114 (e.g., a memory device). Controller 110 may be communicatively coupled to any component of system 100 to provide unidirectional and / or bidirectional communication. In this manner, controller 110 may perform (e.g., via one or more processors 112) any of the various process steps described throughout this disclosure, such as, but not limited to, developing a simulation-based model of a manufacturing process, developing a transformation model that emulates the simulation-based model for a selected input space and provides sensitivity metrics representing the sensitivity of one or more output parameters to mask deformations, receiving a candidate mask design, or generating a repaired mask design based on iteratively updating the candidate mask design using the transformation model.

[0026] 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 comprise a desktop computer, a mainframe computer system, a workstation, an image computer, a parallel processor, or any other computer system (e.g., a networked computer) configured to execute programs configured to operate the system 100 described throughout this disclosure. It is further recognized that the term “processor” may be broadly defined to encompass any device having one or more processing elements that executes program instructions from non-transitory memory 114. Furthermore, the steps described throughout this disclosure may be performed by a single controller 110, or alternatively, by multiple controllers. Additionally, the controller 110 may include one or more controllers housed within a common housing or within multiple housings. As such, any controller or combination of controllers may be packaged separately as a module suitable for integration into the system 100.

[0027] The memory 114 may include any storage medium known in the art suitable for storing program instructions executable by the associated one or more processors 112. For example, the memory 114 may include a non-transitory memory medium. As another example, the memory 114 may include, but is not limited to, read-only memory, random-access memory, magnetic or optical memory devices (e.g., disks), magnetic tape, solid-state drives, etc. It is further noted that the memory 114 may be contained within a common controller housing with the one or more processors 112. In some embodiments, the memory 114 may be located remotely relative to the physical location of the one or more processors 112 and the controller 110. For example, one or more processors 112 of the controller 110 may access a remote memory (e.g., a server) accessible through a network (e.g., the Internet, an intranet, etc.). Therefore, the above description should not be construed as a limitation on the present invention, but merely as an example.

[0028] Mask design repair is described in further detail in Figures 2-10. Typical approaches to stochastic defect control focus on modeling the placement of photoresist (e.g., resist) edges or some intermediate metric, such as an aerial image (e.g., continuous or thresholded, typically contoured to approximate the resist edge). An edge in such techniques is typically defined as a boundary separating a resist region from an aerial region, and defects are typically defined to be at locations where the edge crosses or tends to cross. For example, typical approaches to stochastic defect control are described in U.S. Pat. No. 11,126,090, issued September 21, 2021, entitled "Model for calculating a stochastic variation in an arbitrary pattern"; Spence, Chris, "Full-chip lithography simulation and design analysis: how OPC is changing IC design," Emerging Lithographic Technologies IX. Vol. 5751. 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.SPIE, 2006; Linyong Pang 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 Azat Latypov et al., "Gaussian random field EUV stochastic models, their generalizations and lithographically meaningful stochastic metrics," Extreme Ultraviolet (EUV) Lithography XII, Vol. 11609, SPIE, 2021, all of which are incorporated herein by reference in their entireties.

[0029] However, it is contemplated herein that stochastic defectivity may be more directly and accurately estimated based on the local resist thickness of a region of interest on a sample (e.g., a wafer) rather than through edge location. This is in part because edge location inherently encodes an approximate form of resist thickness. Furthermore, existing techniques may not be well-suited for relatively rare stochastic errors. The advantages of probabilistic defect characterization based on local resist thickness are discussed in U.S. Patent Application Publication No. 2022 / 0129775, published April 28, 2022, entitled "Prediction and metrology of stochastic photoresist thickness defects," 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), the entire contents of which are incorporated herein by reference.

[0030] By way of example, FIGS. 2A-2D show a series of plots illustrating the probabilistic defect rate for two mask designs that provide similar edge positions but result in different local resist thicknesses and different error rates, in accordance with one or more embodiments of the present disclosure. FIG. 2A is a top view of the two mask designs (labeled "Mask 1" and "Mask 2"), in accordance with one or more embodiments of the present disclosure. FIG. 2B is a plot of the average resist edge position (EP) for six slices (p1-P6) of both mask designs in FIG. 2A, in accordance with one or more embodiments of the present disclosure. FIG. 2C is a plot of the average resist height (RH) for six slices of the mask design of FIG. 2A, in accordance with one or more embodiments of the present disclosure. FIG. 2D is a plot of the probabilistic defect rate (DR) for six slices of the mask design of FIG. 2A, in accordance with one or more embodiments of the present disclosure.

[0031] As shown in Figures 2A-2D, both mask designs result in substantially the same edge positions when fabricated on sample 104 (see, e.g., Figures 2A and 2B). However, the mask designs exhibit significant deviations in both the average resist height and the stochastic defect rate at certain locations. For example, both the average resist height data (see, e.g., Figure 2C) and the stochastic defect rate (see, e.g., Figure 2D) for the two mask designs exhibit significant deviations for slices p1, p4, and p6. Thus, resist height is a more accurate predictor of stochastic defect rate than resist edge position.

[0032] 3A is a flow diagram illustrating steps performed in a method 300 for mask repair in accordance with one or more embodiments of the present disclosure. Applicant states that the embodiments and enabling techniques described herein above in the context of system 100 should be construed to extend 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 is further noted that method 300 is not limited by the architecture of system 100.

[0033] In some embodiments, the method 300 includes developing 302 a simulation-based model of sample layer thickness after one or more process steps that fabricate features on the sample 104. By way of example, the simulation-based model may provide a distribution of sample layer thickness as a function of position across the sample 104 or a portion thereof. The distribution of sample layer thickness may be expressed as either a single output value for each position on the sample 104 or a probability distribution of thickness for each position on the sample 104.

[0034] Step 302 may represent features on the sample 104 after any number of process steps. For example, features on the sample 104 (e.g., on a particular layer of the sample 104) may be fabricated using process steps such as, but not limited to, deposition of one or more layers (e.g., process layers and / or photoresist layers), lithographic exposure of a pattern from a mask 106, post-exposure bake, etching, ion implantation (e.g., doping), metallization oxidation, polishing, etc. 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 lithographic exposure process, which may be similar to that which may be measured in a post-development inspection (ADI) step. The simulation-based model may model any type of commercially available or custom photoresist, including, but not limited to, a positive-tone developed chemically amplified resist (PTD CAR), a negative-tone developed (NTD) resist, or a metal oxide (MOx) resist. In some embodiments, the simulation-based model of step 302 provides a process layer thickness after the etching step, which may be similar to what may be measured in an after-etch inspection (AEI) step. Additionally, the simulation-based model of step 302 may provide various additional outputs, such as, but not limited to, edge placement, line edge roughness (LER), or critical dimension uniformity (CDU) after any process step.

[0035] 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, etc.), 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, etc.), focus position, development time, post-exposure bake temperature, etc. As used herein, input space defines the range of various input parameters that may be utilized by the model.

[0036] In some embodiments, the simulation-based model includes modeling of the optical interaction of light with the sample 104 during 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 analysis, surface integral techniques, or volume integral techniques. In this manner, the simulation-based model may be characterized as a physics-based model. In some embodiments, the photoresist thickness may be simulated using a simulator such as, but not limited to, PROLITH (Positive Resist Optical Lithography). PROLITH is a physics-based simulator sold by KLA Corporation. Physics-based simulation of photoresist thickness is generally described in the above-referenced U.S. Patent Application Publication No. 2022 / 0129775, published April 28, 2022, entitled "Prediction and metrology of stochastic photoresist thickness defects," which is incorporated herein by reference in its entirety.

[0037] It is contemplated herein that the simulation-based model developed in step 302 may be suitable for characterizing stochastic defects during a manufacturing process. For example, a Monte Carlo method may be utilized to randomly sample a stochastic process (e.g., photon absorption, etc.) by applying the simulation-based model multiple times. In this case, the output of the simulation may provide a probability distribution of an output parameter (e.g., local photoresist thickness). Such a technique may, in theory, result in accurate characterization of a wide range of process steps over a wide range of conditions. Furthermore, the simulation-based model may incorporate or otherwise account for variations in process parameters (e.g., process variation) that may naturally occur during manufacturing. For example, the simulation-based model may provide a probability of any output parameter (e.g., sample layer thickness, etc.) based on known or expected variations in the process parameters and / or the stochastic process.

[0038] However, it is further contemplated herein that such techniques may require an enormous 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). Furthermore, the execution time of such models may be relatively slow. As a result, relying solely on such simulation-based models to characterize stochastic defect rates may be undesirable or impractical.

[0039] In some embodiments, method 300 includes step 304 of developing a transformation model of the manufacturing process that emulates 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 transformation model may 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, and output one or more output parameters related to the manufacturing of the input mask design and one or more sensitivity metrics that represent 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 layer thicknesses and / or process layer thicknesses) or stochastic defect rates based on the sample layer thicknesses. Furthermore, the transformation model may incorporate or otherwise take into account variations in process parameters (e.g., process variations) that may naturally occur during manufacturing. For example, the transformation model may provide a probability of any output parameter (e.g., sample layer thickness, etc.) based on known or expected variations in process parameters and / or stochastic processes. In this manner, the transformation model may be suitable for characterizing the robustness of a mask design to process variations.

[0040] Step 304 may include developing a transformation model of at least the sample layer thickness using any suitable technique. In some embodiments, the transformation model is generated using machine learning techniques. As such, the transformation model may be a trained machine learning model. Such a machine learning model may be trained using any suitable training data. For example, such a machine learning model may be trained using simulation data and / or metrology data from training samples manufactured with various variations of input parameters. The metrology data may be generated using any suitable characterization subsystem 108, such as, but not limited to, a scanning electron microscope (SEM) tool, a transmission electron microscope (TEM) tool, an x-ray tool, or the like. Furthermore, such a machine learning model may incorporate any type of supervised machine learning model, such as, but not limited to, a general linear model, a neural network, a Bayesian inference network, 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.

[0041] In some embodiments, the conversion model is designed to provide faster evaluation speeds than the simulation-based model for at least a subset of the input and / or output space of the simulation-based model. In this manner, development and utilization of the conversion model may provide increased throughput relative to the simulation-based model while maintaining performance tolerances for at least a subset of the input space. In a general sense, the conversion model may be tunable to provide a desired tradeoff between accuracy, speed (e.g., evaluation speed), and size of the input space (e.g., the size of the input parameter range over which the conversion model emulates the simulation-based model within acceptable error). The use of machine learning models for photoresist thickness that emulate simulation-based models is generally described in the above-referenced U.S. Patent Application Publication No. 2022 / 0129775, published April 28, 2022, entitled "Prediction and Metrology of Stochastic Photoresist Thickness Defects," which is incorporated herein by reference in its entirety.

[0042] 4 is a conceptual illustration of a transformation model tradeoff, in accordance with one or more embodiments of the present disclosure. Plot 402 is a conceptual illustration of the transformation model's speed as a function of the covered input space of the simulation-based model. Plot 404 is a conceptual illustration of the transformation model's accuracy as a function of the transformation model's speed. As shown, the transformation model's speed may generally decrease as the covered input space increases. Furthermore, the transformation model's accuracy may generally decrease as the speed increases. However, there may be conditions under which the transformation model provides sufficient accuracy (e.g., within a selected error tolerance) over a reasonable subset of the simulation-based model's input space, while also providing a significant speed improvement compared to the simulation-based model.

[0043] In some embodiments, the transformation model further provides mathematical differentiability. For example, the transformation model may generate a sensitivity metric related to an estimate of the sensitivity of any output parameter to variations in the process parameter of interest. Any suitable sensitivity metric may be generated, such as, but not limited to, analytical model gradients. Analytical model gradients are generally described in Griewank, Andreas, "Who invented the reverse 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 Marchine Learning Research 18 (2018):1-43, both of which are incorporated herein by reference in their entireties.

[0044] Additionally, the transformation model may provide sensitivity metrics for each output parameter (e.g., local photoresist thickness, stochastic defect rate based on photoresist thickness, etc.) relative to select input parameters only, or for combinations of output parameters. By way of example, the sensitivity metric may provide an indication of how sensitive the local photoresist thickness and / or stochastic 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 much deviations in process parameters occurring during manufacturing can affect the photoresist thickness and / or stochastic defect rate. It is contemplated herein that such information may be utilized to make corrective design changes to reduce the design's sensitivity to these process variations.

[0045] In some embodiments, method 300 includes receiving 306 a candidate mask design. In some embodiments, method 300 includes generating 308 a repaired mask design based on the transformation model. The candidate mask design and / or the repaired 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 repaired mask design may be provided as a complete design or as an update vector representing modifications to the candidate mask design.

[0046] It is contemplated herein that step 308 may utilize the transformation model in a variety of ways to generate a repaired mask design. In any event, the repaired mask design may result in a reduced stochastic defect rate and may be robust to process variations (e.g., as characterized by the transformation model).

[0047] FIG. 3B is a flow diagram illustrating substeps of step 308 of generating a repaired mask design in accordance with one or more embodiments of the present disclosure.

[0048] In some embodiments, step 308 includes step 310 of utilizing the candidate mask design as an input mask design for the transformation model to generate one or more output parameters and one or more sensitivity metrics for 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 does not meet an applicable tolerance (e.g., within a selected tolerance). For example, step 312 may 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).

[0049] In some embodiments, steps 310 and 312 are repeated as necessary until a repaired mask design is produced that meets applicable tolerances. Any applicable tolerances may be considered, such as, but not limited to, tolerances related to stochastic defect rates.

[0050] 5 is a simplified flow diagram illustrating stochastic defect mitigation in accordance with one or more embodiments of the present disclosure. In particular, FIG. 5 illustrates a process in which a candidate mask design 500-C (e.g., the design of candidate mask design 500-C) is provided as input to a transformation model 502 (e.g., generated in step 304) along with additional process parameters 504 of interest. 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, a stochastic defect rate based at least in part on the local photoresist thickness, edge placement error, LER, CDU, distance field violations, or mask rule check parameters. The transformation model 502 may also generate (e.g., in step 310) sensitivity metrics 508 related to any of the output parameters 506, either singly or in one or more combinations.

[0051] 5 further illustrates determining (e.g., as part of step 312) whether applicable tolerances are met (e.g., box 510). If the tolerances are met, a repaired mask design 500-R (e.g., a design of repaired mask design 500-R) is provided. If not, the design is updated (e.g., box 512) to generate an updated candidate mask design 500-C. This process may be repeated as necessary until the applicable tolerances are met (e.g., satisfied). Any applicable tolerances may be considered, such as, but not limited to, tolerances related to probabilistic defect rates.

[0052] 6A-8B, non-limiting variations of the method 300 (and the flow diagram of FIG. 5) are described.

[0053] Method 300 (e.g., step 308) may apply the correction or repair to the entire candidate mask design 500-C or to a portion of candidate mask design 500-C. For example, applying the correction to a portion of candidate mask design 500-C rather than the entire candidate mask design 500-C may reduce computational speed. If only a portion of candidate mask design 500-C is to be corrected, the portion may be determined using any suitable technique.

[0054] In some embodiments, regions of interest (ROIs) may be selected (either globally or for specific iterations) for repair 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 stochastic defects. In another example, the ROIs may correspond to features or sample locations that are particularly important to device performance.

[0055] In some embodiments, the portions of the candidate mask design 500-C selected for repair are selected based on filtering (e.g., before updating the candidate mask design 500-C). For example, the transformation model output parameters 506 may identify one or more areas on the sample 104 as potentially problematic based on the current candidate mask design 500-C. For example, the transformation model output parameters 506 may predict one or more hot spots as having a relatively high probability of stochastic defects when manufactured using the candidate mask design 500-C. It may be possible to mitigate such problematic areas through multiple adjustments to various portions of the candidate mask design 500-C (e.g., multiple different combinations of adjustments to different edge locations). However, it may not be desirable to incorporate all identified potential adjustments to the candidate mask design 500-C. For example, some adjustments may be redundant. As another example, some adjustments may repair identified problematic areas but adversely affect different areas. Thus, 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 example, a selected percentage of positions (e.g., the top X% of positions, where X may be any selected value such as, but not limited to, 10%) for adjustments having sensitivity metrics 508 exhibiting the highest sensitivity to output parameters 506 may be selected for repair. As another example, positions having sensitivity metrics above a selected threshold (e.g., defining the magnitude of sensitivity) may be selected for repair. Furthermore, filtering conditions may be individually adjusted for each iteration, dynamically or based on predefined rules. By way of example, it may be desirable to gradually decrease the number and / or magnitude of corrections to candidate mask design 500-C over successive iterations to promote convergence to a robust design.

[0056] 6A and 6B illustrate repair on a selected portion of the sample 104. In FIGS. 6A and 6B, the transformation model 502 provides output parameters 506, including the stochastic defect rate and edge placement error in the photoresist (e.g., after lithography exposure). FIG. 6A is a simplified diagram of a repaired mask design 500-R shown in the form of update vectors on feature edges generated through multiple iterations of step 308, in accordance with one or more embodiments of the present disclosure. For example, various arrows indicate the direction and magnitude of edge position 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 may vary across the sample 104 and between different iterations. FIG. 6B is a simplified diagram of a repaired mask design 500-R shown in the form of update vectors on feature edges through multiple iterations of step 308, in which only a subset of sample locations are repaired, in accordance with one or more embodiments of the present disclosure. For example, FIG. 6B is substantially similar to FIG. 6A, except that it includes only updates related to a portion of the sample 104. The locations shown may be selected based on an ROI definition, filtering, or any other suitable technique. In particular, Figure 6B is generated based on filtering a set of potential modifications to candidate mask design 500-C based on sensitivity metric 508 to include a selected percentage of modifications that result in the highest sensitivity to output parameter 506.

[0057] 7 is a diagram of iterative mask repair in a ROI 702 using method 300, in accordance with one or more embodiments of the present disclosure. In FIG. 7, transformation model 502 provides output parameters 506, including a stochastic defect rate within ROI 702, a stochastic defect rate outside ROI 702, and an edge placement error in the photoresist (e.g., after lithography exposure).

[0058] In particular, FIG. 7 shows a diagram of an initial candidate mask design 500-C (e.g., candidate mask design 500-C before repair), two provisional masks associated with the iteration of step 308, and a final repaired mask design 500-R. Thus, the two provisional masks represent both the repaired mask design 500-R from one iteration and the candidate mask design 500-C for a subsequent iteration. Additionally, FIG. 7 shows an arrow 704 indicating a repair modification (e.g., performed in box 512 of FIG. 5) to the illustrated candidate mask design 500-C. For reference, the initial design is also shown in dashed lines so that the impact of design changes across various iterations can be visualized.

[0059] 7, the determination of whether the design as a whole meets the selected tolerance (e.g., box 510 of FIG. 5) is based at least in part on the ROI 702 (e.g., the probabilistic defect rate within the ROI 702). In particular, the method 300 may continue to iterate until the locations within the ROI 702 meet the selected tolerance. In some embodiments, the method 300 may additionally iterate until the locations outside the ROI 702 meet the additional tolerance. The additional tolerance may be different from the tolerance for the area within the ROI 702. Additionally, it should be noted that the filtering techniques described herein (e.g., with respect to FIGS. 6A-6B) may also be applied to limit the repair correction based on any of the output parameters 506.

[0060] Referring again generally to FIGS. 3 and 5 , step 312 (e.g., box 512) of updating candidate mask design 500-C may be adapted to the manner in which the design is represented. For example, step 312 (e.g., box 512) of updating candidate mask design 500-C may include updating mask polygons, which may correspond to the feature design directly or as parameters of distance field and / or level set techniques. Furthermore, updating mask polygons is not limited to modifying existing polygons but may also include adding new polygons and / or removing existing polygons. Any type of update or optimization technique may be utilized, including but not limited to gradient descent optimization techniques. As another example, step 312 (e.g., box 512) of updating candidate mask design 500-C may include updating parameters of the distance field and / or level set as used to represent the design. In some embodiments, step 312 (e.g., box 512) of updating candidate mask design 500-C may further control and / or manage parameters related to the manner in which the design is represented. For example, step 312 (e.g., box 512) of updating candidate mask design 500-C may further control and / or manage the velocity field to comply with Courant-Friedrichs-Lewy (CFL) conditions, etc., when using level set or fast marching techniques.

[0061] In some embodiments, method 300 (e.g., step 308) may generate repaired mask design 500-R in two or more stages with different tolerance conditions, and steps 310 and 312 may be repeated as necessary to achieve the relevant tolerance conditions.

[0062] For example, the flow of FIG. 5 may be first executed in a first stage to generate a first repaired mask design 500-R of an initial candidate mask design 500-C. Subsequently, the flow of FIG. 5 may be executed a second time in a second stage, in which 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. Illustratively, the output parameters 506 of the first stage may include a probabilistic defect rate within one or more ROIs (e.g., as exemplarily shown in FIG. 7 ), a probabilistic defect rate outside one or more ROIs, and an edge placement error. Updates (e.g., box 512) to the candidate mask design 500-C may then be performed for the entire sample 104, only the ROIs, or the set of filtered positions described above. The output parameters 506 of the second stage may then further include mask rule check violations. It is believed herein that such a two-stage operation may result in efficient repair during the first stage without expending computational resources and associated time on mask rule check violations until a certain level of performance is reached in the first stage. The second stage may then perform any additional corrections as needed to avoid mask rule check violations. Note, however, that this example is provided for illustrative purposes only and should not be construed as limiting. In a general sense, a multi-stage implementation may enable correction of a mask based on multiple combinations of output parameters in a controlled and efficient manner.

[0063] 8A and 8B, in some embodiments, the transformation model 502 (e.g., generated in step 304) may be used to train a machine learning model (e.g., an inverse machine learning model) to directly generate a repaired mask design 500-R from the candidate mask design 500-C.

[0064] FIG. 8A is a simplified flow diagram illustrating training a machine learning model 802 using a transformation model 502, in accordance with one or more embodiments of the present disclosure.

[0065] In some embodiments, the machine learning model 802 generates a repaired mask design 500-R from the input candidate mask design 500-C. This repaired mask design 500-R may then be provided as input to the transformation model 502 (e.g., generated in step 304), which may provide the output parameters 506 and the sensitivity metric 508. Further, in some embodiments, the sensitivity metric 508 includes the sensitivity of the machine learning weights of the machine learning model 802 to the output parameters 506. In this manner, the sensitivity metric 508 may characterize the sensitivity of the machine learning model 802 to the output parameters 506 (e.g., stochastic defect rate, etc.). If the repaired mask design 500-R from the machine learning model 802 does not meet a selected applicable error tolerance, the machine learning model 802 may be updated based on the sensitivity metric 508 (box 804). Further, this process may be repeated until the repaired mask design 500-R generated by the machine learning model 802 meets (e.g., satisfies) the applicable error tolerance.

[0066] 8B is a flow diagram illustrating a non-limiting example of training a machine learning model 802 based on training data generated by the transformation model 502, according to one or more embodiments of the present disclosure. Note that FIG. 8B illustrates a particularly non-limiting case in which the output parameters 506-T include local resist thickness and resist edge placement values.

[0067] In some embodiments, the transformation model 502 generates output parameters 506-T based on multiple input candidate mask designs 500-T as training data. For example, the input candidate mask designs 500-T may be manufactured using known variations of process parameters (e.g., within the covered input space). Once trained, the machine learning model 802 may directly generate the repaired mask design 500-R based on any suitable input, including, but not limited to, the input candidate mask designs 500-C or the desired values of the output parameters shown in FIG. 8B.

[0068] 9A-9D, which include a series of plots illustrating additional non-limiting examples of repairing a mask design 500 using method 300 in accordance with one or more embodiments of the present disclosure. Each of FIGS. 9A-9D includes a simplified top-view image labeled "Mask Design" showing a candidate mask design 500-C and a repaired mask design 500-R generated using the systems and methods disclosed herein. Each of FIGS. 9A-9D further includes a simplified top-view image of a sample 104 having predicted features of an exposed photoresist layer fabricated based on the associated mask design 500. Note that predicted features associated with different mask designs 500 are overlaid to illustrate the differences. Each of FIGS. 9A-9D further includes a plot of the probabilistic defect rate (DR) for the associated mask design 500. Additionally, FIGS. 9A-9C illustrate a configuration providing repair based on a single ROI 900, while FIG. 9D illustrates a configuration providing repair based on multiple ROIs 900. In either case, method 300 results in a substantial reduction in the probability of stochastic defects. Additionally, in each case, the stochastic defect rate of the associated repaired mask design 500-R is less than the applicable error tolerance (e.g., as indicated by dashed line 902).

[0069] 10 , mitigating stochastic defects through modifications to process parameters instead of, or in addition to, the design of the mask 106 is described in accordance with one or more embodiments of the present disclosure. It is contemplated herein that the defect rate (e.g., stochastic defect rate) can be affected 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, etc. Accordingly, process parameters may be adjusted in addition to, or instead of, the mask design to mitigate stochastic defects.

[0070] In some embodiments, a manufacturing process is governed or otherwise described by a recipe, which may include parameters describing various aspects of the sample 104 being manufactured and / or the process tools (lithography tools, etching tools, polishing tools, etc.) used in any process step. As such, a recipe may include process parameters 504 associated with any process step. For example, a recipe may include process parameters 504 associated with the sample 104 in any process step, including, but not limited to, a film thickness to be deposited or a composition of the film to be deposited. As another example, a recipe may include the design of a mask 106 used in a lithography step. As another example, a recipe may include process parameters 504 for a lithography step, such as, but not limited to, a irradiance dose, an illumination wavelength, an illumination polarization, an illumination source shape, an exposure time, or a focus position of the sample 104. As another example, a recipe may include process parameters 504 associated with an etching step, including, but not limited to, an etchant composition or an etching duration. As another example, a recipe may include process parameters 504 associated with a post-exposure bake step, including, but not limited to, a bake temperature or duration.

[0071] In some embodiments, remedial corrections (e.g., updates) may be made to any aspect of a recipe to mitigate stochastic defects (e.g., reduce the stochastic defect rate) based on transformation model 502. Thus, the teachings of the present disclosure related to providing remedial corrections to mask design 500 may be extended to providing remedial corrections to recipes that more generally describe one or more process steps.

[0072] For example, any component of the recipe may be iteratively modified (e.g., updated) based on the transformation model 502. FIG. 10 is a simplified flow diagram illustrating mitigation of stochastic defects in accordance with one or more embodiments of the present disclosure. Note that FIG. 10 is substantially similar to FIG. 5, except that box 512 in FIG. 5, which refers to updating the mask design 500, is replaced with box 1002, which refers to updating a recipe describing a manufacturing process. As shown in 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 applicable tolerances, any aspect of the recipe may be updated (box 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 the applicable tolerances, a repaired mask design 500-R and / or repaired process parameters 504-R (e.g., a repaired recipe more generally) may be provided as output.

[0073] 8A-8B 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 candidate process parameters 504-C and generate a repaired mask design 500-R and / or repaired process parameters 504-R based on training data including the associated process parameters. Thus, FIG. 8B can be extended to include process parameters 504 in the training data set and provide an associated output.

[0074] 1A-1C, additional aspects of system 100 will be described in more detail in accordance with one or more embodiments of the present disclosure.

[0075] 1B is a conceptual diagram illustrating a lithography subsystem 102 in accordance with one or more embodiments of the present disclosure. In some embodiments, the lithography subsystem 102 includes an illumination source 116 configured to generate one or more illumination beams 118. The illumination beam 118 may include one or more selected wavelengths of light, including but not limited to EUV light. For example, at least a portion of the spectrum of the illumination beam 118 may include a wavelength such as, but not limited to, 13.5 nm. 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.

[0076] In some embodiments, the illumination source 116 includes an extreme ultraviolet illumination source 116. For example, the EUV illumination source 116 may include a broadband plasma (BBP) illumination source. In this regard, the illumination beam 118 may include radiation emitted by a plasma. For example, the BBP illumination source 116 may, but need not, include one or more pump sources (e.g., one or more lasers) configured to focus illumination into a volume of gas and cause the gas to absorb energy to generate or maintain a plasma suitable for emitting radiation. Furthermore, at least a portion of the plasma radiation may be utilized as the illumination beam 118. In some embodiments, the illumination source 116 may include one or more lasers capable of emitting radiation at one or more selected wavelengths.

[0077] In some embodiments, the illumination source 116 directs an illumination beam 118 toward 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 elements, etc. Furthermore, the illumination optics 122 may include any reflective optical element 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, etc.), such as, but not limited to, a flat mirror or a curved mirror (e.g., an elliptical mirror, a parabolic mirror, etc.).

[0078] 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 angles of incidence (e.g., the 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.

[0079] In some embodiments, the lithography subsystem 102 includes a mask support device 124. The mask support device 124 may be configured to secure the mask 106.

[0080] 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 the surface of the sample 104 disposed on the sample stage 128. For example, the set of projection optics 126 may be configured to project the image of the mask 106 onto the resist layer 130 on the sample 104 to generate (e.g., expose) 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 drive or position the mask 106. For example, the mask support device 124 may drive the mask 106 to a selected position with respect to the projection optics 126 of the lithography subsystem 102.

[0081] The mask 106 may be utilized (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 in the resist layer 130 of the sample 104. As another example, the mask 106 may be a negative mask (e.g., a dark-field mask) in which the pattern elements of the mask 106 form negatively printed pattern elements (e.g., gaps, spaces, etc.) in the resist layer 130 of the sample 104.

[0082] As used throughout this disclosure, the term "sample" generally refers to a substrate (e.g., a wafer) formed from 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. A sample may include one or more layers. For example, such layers may include, but are not limited to, resist, dielectric material, conductive material, and semiconductive material. Many 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 may be formed. One or more layers formed on a sample may be patterned or unpatterned. For example, a sample may include multiple dies, each having repeatable patterned features. The formation and processing of such layers of material may ultimately result in a completed device. Many different types of devices may be formed on a sample, and the term sample, as used herein, is intended to encompass samples on which any type of device known in the art is fabricated. Furthermore, for purposes of this disclosure, the terms sample and wafer should be interpreted interchangeably. Additionally, for the purposes of this disclosure, the terms patterning device, pattern mask, mask, and reticle should be considered interchangeable.

[0083] 1C is a conceptual diagram illustrating the characterization subsystem 108, in accordance with one or more embodiments of the present disclosure. Note that FIG. 1C illustrates the characterization subsystem 108 as an optical system. However, this is merely exemplary and not limiting. Rather, the characterization subsystem 108 may be included and / or configured as a particle beam system (e.g., an electron beam system, an ion beam system, etc.) or an x-ray system (e.g., including an optical configuration suitable for light in the x-ray spectral region).

[0084] In some embodiments, the characterization subsystem 108 includes an illumination source 132 for generating an illumination beam 134. The illumination beam 134 may include one or more selected wavelengths of light, including, but not limited to, ultraviolet (UV), visible, or infrared (IR) light. It is noted herein that the characterization subsystem 108 may include any type of characterization subsystem 108 known in the art without limiting the scope of the present disclosure. For example, although not shown in FIG. 1C , the characterization subsystem 108 may include an extreme ultraviolet (EUV) characterization subsystem, a deep ultraviolet (DUV) characterization subsystem, etc., without departing from the scope of the present disclosure.

[0085] In some embodiments, the illumination source 132 directs the illumination beam 134 toward the sample 104 via an illumination path 136. The illumination path 136 may include one or more lenses 138. Additionally, the illumination path 136 may 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 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.

[0086] 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 may include multiple optical elements 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 blocks, or one or more beam splitters.

[0087] For example, the detector 146 may receive an image of the sample 104 provided by elements in the collection path 148 (e.g., the objective lens 144, the one or more lenses 150, etc.). As another example, the detector 146 may receive radiation reflected or scattered from the sample 104 (e.g., by specular reflection, diffuse reflection, etc.). As another example, the detector 146 may receive radiation generated by the sample (e.g., emission associated with absorption of the illumination beam 134, etc.). It is further 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), etc.

[0088] Additionally, in some embodiments, the characterization subsystem 108 includes a translation stage 152 for fixing and positioning the sample 104 .

[0089] The subject matter described herein may depict different components contained within or connected to other components. It should be understood that such illustrated architectures are merely exemplary, and that in fact many other architectures may be implemented that 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. Thus, any two components herein that are combined to achieve a particular functionality may be viewed as being "associated" with one another such that the desired functionality is achieved, regardless of the architecture or intermediate components. Similarly, any two components so associated may also be viewed as being "connected" or "coupled" to one another to achieve the desired functionality. Any two components that can be so associated may also be viewed as being "couplable" to one another to achieve the desired functionality. Specific examples of components that can be coupled include, but are not limited to, components that are physically interacting and / or physically interacting, and / or components that are wirelessly interacting and / or wirelessly interacting, and / or components that can logically interact and / or logically interacting.

[0090] It is believed that the present disclosure and many of its attendant advantages will be understood from the foregoing description. It will be apparent that various changes may be made in the form, construction, and arrangement of the elements without departing from the disclosed subject matter or sacrificing all of its specific advantages. The forms described are illustrative only, and it is the intent of the appended claims to embrace and include such modifications. It is further to be understood that the present invention is defined by the appended claims.

Claims

1. 1. A system comprising: a controller including one or more processors configured to execute program instructions, the program instructions causing the one or more processors to: developing a simulation-based model of layer thicknesses after one or more process steps that fabricate features on a sample, the simulation-based model accepting an input mask design to be exposed on the sample and providing as an output at least the layer thicknesses after the one or more process steps; developing a transformation model of the 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, wherein the input to the transformation model includes the input mask design, and the output of the transformation model includes one or more output parameters related to manufacturing of the input mask design and one or more sensitivity metrics representing sensitivities of the one or more output parameters to variations in the input mask design, the one or more output parameters including at least one of the layer thickness after the one or more process steps or a probabilistic defect rate based on the layer thickness; receiving a candidate mask design; generating a repaired mask design based on the transformation model and the candidate mask designs; A system characterized by executing the above.

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

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

4. 10. The system of claim 1, wherein the candidate mask designs and the repaired mask designs are represented by at least one of a binary representation, a polygonal representation, a distance field representation, or a level set representation.

5. 2. The system of claim 1, wherein generating the repaired 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; updating the candidate mask design with the update vector to provide the repaired mask design; A system comprising:

6. 2. The system of claim 1, wherein generating the repaired mask design based on the transformation model and the candidate mask designs comprises: utilizing the candidate mask design as the input mask design of the transformation model to generate the one or more output parameters and the one or more sensitivity metrics for the candidate mask design; updating the candidate mask design based on the one or more sensitivity metrics when the candidate mask design does not meet the one or more applicable tolerances to provide the repaired mask design; and repeatedly executing the above steps.

7. 7. The system of claim 6, wherein the one or more adaptive tolerances are: A system comprising a random defect rate tolerance.

8. 7. The system of claim 6, wherein updating the candidate mask design based on the one or more sensitivity metrics when the candidate mask design does not meet the applicable error tolerance comprises: generating update vectors for at least some edges in the candidate mask design based on the one or more sensitivity metrics; updating the candidate mask design with the update vector to generate the repaired mask design; A system comprising:

9. 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 does not meet the applicable error tolerance comprises: and filtering the update vectors to include only a subset of the update vectors having sensitivities above a sensitivity threshold selected based on the one or more sensitivity metrics before updating the candidate mask designs with the update vectors to generate the repaired mask designs.

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

11. 9. 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. 9. The system of claim 8, wherein the candidate mask design and the repaired mask design are represented by polygonal representations defining a set of polygons, and updating the candidate mask design with the update vector comprises: updating the set of polygons in the candidate mask design with the update vector using a gradient descent optimizer.

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

14. 2. The system of claim 1, wherein generating the repaired 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; generating the repaired mask design with the machine learning model; and A system comprising:

15. 2. The system of claim 1, wherein the one or more output parameters are: two or more output parameters, wherein the one or more sensitivity metrics are:

1. A system comprising two or more output parameters, including two sensitivity metrics, each related to a different one of the two or more output parameters.

16. 2. The system of claim 1, wherein the one or more output parameters are: Two or more output parameters, wherein at least one of the one or more sensitivity metrics is:

10. A system comprising two or more output parameters, the system comprising a combined sensitivity metric associated with a combination of at least two of the two or more output parameters.

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

18. 2. The system of claim 1, wherein the one or more output parameters are: the probabilistic defect rate being based on the layer thickness.

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

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

21. 1. A method comprising: developing a simulation-based model of layer thicknesses after one or more process steps that fabricate features on a sample, the simulation-based model accepting an input mask design to be exposed on the sample and providing as an output at least the layer thicknesses after the one or more process steps; developing a transformation model of the 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, wherein the input to the transformation model includes the input mask design, and the output of the transformation model includes one or more output parameters related to manufacturing of the input mask design and one or more sensitivity metrics representing sensitivities of the one or more output parameters to variations in the input mask design, the one or more output parameters including at least one of the layer thickness after the one or more process steps or a probabilistic defect rate based on the layer thickness; receiving a candidate mask design; generating a repaired mask design based on the transformation model and the candidate mask designs; A method comprising:

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

23. 1. A system comprising: a controller including one or more processors configured to execute program instructions, the program instructions causing the one or more processors to: developing a simulation-based model of a layer thickness after one or more process steps that fabricate a feature on a sample, wherein inputs to the simulation-based model include 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, and an output of the simulation-based model includes at least the layer thickness after the one or more process steps; developing a transformation model of the 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, wherein the input to the transformation model includes at least one of the input mask design and the one or more process parameters, and the output of the transformation model includes one or more output parameters related to manufacturing of the input mask design using the one or more process steps and one or more sensitivity metrics representing sensitivities of the one or more output parameters to the input 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 probabilistic defect rate based on the layer thickness; receiving a candidate recipe including a candidate mask design and the at least one of the one or more process parameters; generating a repaired recipe based on the transformation model and the candidate mask designs; A system characterized by executing the above.

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

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

26. 24. The system of claim 23, wherein the candidate mask designs and the repaired 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. 24. The system of claim 23, wherein generating the repaired recipe based on the transformation model and the candidate mask designs comprises: generating updates to the candidate recipe, the updates including at least one of an update vector for the candidate mask design or an update to the at least one of the one or more process parameters; updating the candidate recipe with the updates to generate the repaired recipe; A system comprising:

28. 24. The system of claim 23, wherein generating the repaired 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; generating the repaired recipe with the machine learning model; A system comprising:

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

30. 24. The system of claim 23, wherein the one or more output parameters are: the probabilistic defect rate being based on the layer thickness.

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

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