Determining line edge roughness and line width roughness metrics

Abstract

Disclosed herein are techniques for determining line edge roughness and / or line width roughness metrics. In some embodiments, a method may involve obtaining a line pattern to be analyzed to determine the line edge roughness (LER) and / or the line width roughness (LWR) metrics. The method may further involve obtaining data points corresponding to one or more edges of the line pattern. The method may further involve determining the LER and / or the LWR metrics based at least in part on a spatial frequency analysis of the obtained data points.

Description

DETERMINING LINE EDGE ROUGHNESS AND LINE WIDTH ROUGHNESS METRICSINCORPORATION BY REFERENCE

[0000] A PCT Request Form is filed concurrently with this specification as part of the present application. Each application that the present application claims benefit of or priority to as identified in the concurrently filed PCT Request Form is incorporated by reference herein in its entirety and for all purposes.BACKGROUND

[0001] Metrics such as line edge roughness and / or line width roughness may be important for simulating process steps of a fabrication process. However, these metrics can be difficult to estimate, particularly after simulation of etch or deposition steps.

[0002] The background description provided herein is for the purposes of generally presenting the context of the disclosure. Work of the presently named inventors, to the extent it is described in this background section, as well as aspects of the description that may not otherwise qualify as prior art at the time of filing, are neither expressly nor impliedly admitted as prior art against the present disclosure.SUMMARY

[0003] Disclosed herein are systems, methods, and media for determining line edge roughness and line width roughness metrics. In some embodiments, a method for determining line edge roughness and / or line width roughness metrics comprises obtaining a line pattern to be analyzed to determine the line edge roughness (LER) and / or the line width roughness (LWR) metrics. The method may further comprise obtaining data points corresponding to one or more edges of the line pattern. The method may further comprise determining the LER and / or the LWR metrics based at least in part on a spatial frequency analysis of the obtained data points.

[0004] In some examples, obtaining the data points corresponding to the one or more edges of the line pattern comprises applying a mask to identify the one or more edges.

[0005] In some examples, the method may further comprise interpolating between the obtained data points prior to determining the LER and / or the LWR metrics.

[0006] In some examples, the method may further comprise determining a linear fit to the obtained data points; and rotating the obtained data points based on the linear fit such that the rotated data points have a modified linear fit having a slope and a y-intercept of 0, whereindetermining the LER and / or the LWR metrics is based on the rotated data points.

[0007] In some examples, the spatial frequency analysis comprises determining a correlation length of the obtained data points. In some examples, the correlation length is determined based on at least one of: a head-head correlation (HHC), a power spectra density (PSD), or an auto correlation curve (ACF).

[0008] In some examples, the LER and / or the LWR metrics comprise LWR metrics, and wherein the LWR metrics are determined based on the spatial frequency analysis of a distance between two opposing edges of the line pattern.

[0009] In some examples, the LER and / or the LWR metrics are utilized as a tunable parameter in a Design of Experiments (DoE) virtual fabrication environment.

[0010] In some examples, the line pattern is obtained via a user interface. In some examples, the LER and / or the LWR metrics are provided via the user interface.

[0011] According to some embodiments, a non-transitory computer-readable medium comprising computer-readable instructions is provided, that, when the computer-readable instructions are executed by one or more processors, cause the one or more processors to perform operations. The operations may comprise obtaining a line pattern to be analyzed to determine the line edge roughness (LER) and / or the line width roughness (LWR) metrics. The operations may further comprise obtaining data points corresponding to one or more edges of the line pattern. The operations may further comprise determining the LER and / or the LWR metrics based at least in part on a spatial frequency analysis of the obtained data points.

[0012] In some examples, obtaining the data points corresponding to the one or more edges of the line pattern comprises applying a mask to identify the one or more edges.

[0013] In some examples, the operations may further comprise interpolating between the obtained data points prior to determining the LER and / or the LWR metrics.

[0014] In some examples, the operations may further comprise determining a linear fit to the obtained data points; and rotating the obtained data points based on the linear fit such that the rotated data points have a modified linear fit having a slope and a y-intercept of 0, wherein determining the LER and / or the LWR metrics is based on the rotated data points.

[0015] In some examples, the spatial frequency analysis comprises determining a correlation length of the obtained data points. In some examples, the correlation length is determined based on at least one of: a head-head correlation (HHC). a power spectra density (PSD), or an auto correlation curve (ACF).

[0016] In some examples, the LER and / or the LWR metrics comprise LWR metrics, and wherein the LWR metrics are determined based on the spatial frequency analysis of a distance between two opposing edges of the line pattern.

[0017] In some examples, the LER and / or the LWR metrics are utilized as a tunable parameter in a Design of Experiments (DoE) virtual fabrication environment.

[0018] In some examples, the line pattern is obtained via a user interface. In some examples, the LER and / or the LWR metrics are provided via the user interface.BRIEF DESCRIPTION OF THE DRAWINGS

[0019] FIG. 1 is a flowchart of an example process for determining line edge roughness and / or line width roughness metrics in accordance with some embodiments.

[0020] FIG. 2 is a diagram depicting example techniques for extracting data points associated with a line edge in accordance with some embodiments.

[0021] FIG. 3 depicts an example of data points associated with a line edge in accordance with some embodiments.

[0022] FIG. 4A is a diagram depicting example techniques for rotating data points associated with a line edge in accordance with some embodiments.

[0023] FIGS. 4B and 4C are diagrams depicting example techniques for extracting data points associated with a line width in accordance with some embodiments.

[0024] FIG. 5 depicts example graphs for determining a correlation length associated with a line edge roughness in accordance with some embodiments.

[0025] FIG. 6 is a flowchart of an example process for determining line edge roughness and / or line width roughness metrics in accordance with some embodiments.

[0026] FIG. 7 presents an example computer system that may be employed to implement certain embodiments described herein.DETAILED DESCRIPTION

[0027] In the following description, numerous specific details are set forth to provide a thorough understanding of the presented embodiments. The disclosed embodiments may be practiced without some or all of these specific details. In other instances, w ell-known process operations have not been described in detail to not unnecessarily obscure the disclosed embodiments. While the disclosed embodiments will be described in conjunction with the specificembodiments, it will be understood that it is not intended to limit the disclosed embodiments.

[0028] Line edge roughness (LER) and / or line width roughness (LWR) metrics may be useful for characterizing process steps. In some cases, process steps may be simulated using a virtual fabrication engine or simulation package. However, it can be difficult to determine LER and / or LWR metrics associated with such virtual processing steps. It may be particularly difficult to determine LER and / or LWR metrics after virtual deposition and / or etching steps.

[0029] Disclosed herein are techniques for determining LER and / or LWR metrics. In some embodiments, the techniques disclosed herein may involve obtaining a line pattern to be analyzed. In some embodiments, the line pattern may be one that is fabricated after one or more process steps (which may be virtual process steps), such as one or more deposition and / or etching steps. In some embodiments, the line pattern may be obtained using virtual metrology' techniques within a virtual fabrication environment. Data points associated with one or more edges of the line pattern may be obtained. For example, the data points may be obtained by applying a mask to the line pattern and / or using edge detection techniques to extract data points associated with the one or more edges of the line pattern. Note that, in instances in which LER metrics are to be determined, the data points may be associated with a single edge of the line pattern. In instances in which LWR metrics are to be determined, the data points may include a first set of data points associated with a first edge of the line pattern and a second set of data points associated with a second edge of the line pattern opposing the first edge. Based on the obtained data points, the LER and / or the LWR metrics may be determined. For example, the LER and / or the LWR metrics may be determined based on a spatial frequency analysis of the obtained data points. The spatial frequency analysis may indicate a degree of smoothness of the line edge and / or a degree of smoothness of a width of the line pattern across the length of the line pattern.

[0030] In some embodiments, the LER and / or the LWR metrics may be utilized within a virtual fabrication environment. For example, the LER and / or the LWR metrics may be provided to a user to indicate characteristics of a simulation of a process step or a sequence of process steps. As another example, in some embodiments, the LER and / or the LWR metrics may be utilized as a tunable parameter within a Design of Experiments (DoE) setup in the virtual fabrication environment. As used herein, DoE refers to a statistical technique that allows for multiple input factors (e g., process parameters associated with a fabrication process) to be manipulated and determining their effect on a desired output, such as a desired wafer fabrication characteristics. As described herein, the LER and / or the LWR metrics may be utilized within the DoE to identify modifications to one or more process parameter values to,e.g., obtain target LER and / or LWR metrics. For example, the target LER and / or LWR metrics may be related to a fabrication specification.

[0031] Note that, although the line patterns described herein are generally described as being obtained from virtual metrology and the LER and / or LWR metrics are generally described as being obtained after simulations of process steps, in some implementations, line patterns may be obtained from metrology conducted after physical performance of one or more physical fabrication steps.

[0032] It should be noted that one or more operations or functions described herein may be performed within a virtual fabrication environment. A virtual fabrication environment for a semiconductor device structure offers a platform for performing semiconductor process development at a lower cost and higher speed than is possible with conventional trial-and-error physical experimentation. In contrast to conventional computer-aided design (CAD) and technology-CAD (TCAD) environments, a virtual fabrication environment is capable of virtually modeling an integrated process flow and predicting the complete 3D structures of all devices and circuits that comprise a full technology suite. Virtual fabrication can be described in its most simple form as combining a description of an integrated process sequence with a subject design, in the form of 2D design data (masks or layout), and producing a 3D structural model that is predictive of the result expected from a real / physical fabrication run. A 3D structural model includes the geometrically accurate 3D shapes of multiple layers of materials, implants, diffusions, etc. that comprise a chip or a portion of a chip. Virtual fabrication is done in way that is primarily geometric, however the geometry involved is instructed by the physics of the fabrication processes. By performing the modeling at the structural level of abstraction (rather than physics-based simulations), construction of the structural models can be dramatically accelerated, enabling full technology modeling, at a circuit-level area scale. The use of a virtual fabrication environment thus provides fast verification of process assumptions, and visualization of the complex interrelationship between the integrated process sequence and the 2D design data. In some cases, a virtual fabrication environment may be configured to provide one or more virtual metrology measurement steps, which allow virtual metrology7measurement data to be collected from modeled structures. The virtual metrology data may then be exported (e.g., to a data analysis tool, saved in a file or other document, etc.) and / or displayed to a user (e.g., such that the user can modify process steps based on the virtual metrology). In some embodiments, the techniques disclosed herein for determining LER and / or LWR metrics may be used in conjunction with virtual metrology performed on a modeled structure, e.g.. to provide estimates or virtual measurements of LER and / or LWR. Insome embodiments, the LER and / or LWR metrics may be used as part of a Design of Experiments (DoE) engine utilized by the virtual fabrication environment to optimally select experimental virtual process parameter values to efficiently identify optimal process parameter values that, e.g., meet a target specification.

[0033] In some embodiments, a virtual fabrication environment may utilize a 3D modeling engine which represents an underlying structural model in the form of voxels. Voxels are essentially 3D pixels. Each voxel is a cube of the same size, and may contain one or more materials, or no materials. Most of the operations performed by the 3D modeling engine in the embodiment are voxel modeling operations. Modeling operations based on a digital voxel representation may be more robust than corresponding operations in a conventional analog solid modeling kernel. However, it should be understood that, in some embodiments, nonvoxel based modeling methods may be used in conjunction with the techniques disclosed herein.

[0034] FIG. 1 is a flowchart of an example process 100 for determining LER and / or LWR metrics in accordance with some embodiments. In some implementations, blocks of process 100 may be implemented by one or more processors and / or controllers of a computing device, which may be a laptop computer, a desktop computer, a server, a computing device of a cloud system, or the like. In some embodiments, blocks of process 100 may be executed in an order other than what is show n in FIG. 1. In some embodiments, two or more blocks of process 100 may be executed substantially in parallel. In some embodiments, one or more blocks of process 100 may be omitted.

[0035] Process 100 can begin at 102 by identifying a line pattern to be analyzed to determine LER and / or LWR metrics. For example, in some embodiments, the line pattern may be obtained from a portion of a simulation of a fabrication process that is simulated using a process simulation software package or other virtual fabrication engine. As a more particular example, in some embodiments, the line pattern may be obtained using virtual metrology techniques of the simulation. As another example, in some embodiments, the line pattern may be associated with a physical fabrication process and may be obtained using various metrology techniques.

[0036] At 104. process 100 can apply a mask to the line of the line pattern to identify one or more edges of the pattern. Note that, in instances in which an LER metric is to be obtained, the mask may identify one edge of the pattern for which the LER metric is to be determined. In instances in which an LWR metric is to be obtained, the mask may identify two approximately parallel edges of the line pattern that delineate the opposing sides, where the space between the two opposing sides corresponds to the line width associated with the LWRmetric. By way of example, referring to FIG. 2, line patterns 202 and 204 are illustrated. Mask 206 is used to extract edge 208 associated with line pattern 204.

[0037] Referring back to process 100, at 106, process 100 can obtain data points corresponding to the one or more edges of the pattern. By way of example, referring to FIG. 2, data points 210 correspond to data points associated with edge 108 of line pattern 204. In some embodiments, the data points may be obtained using edge detection or other techniques applied to an edge obtained using the mask. In some embodiments, process 100 can perform data cleaning by, e g., removing outlier data points. For example, in some embodiments, process 100 can identify outlier data points by identifying data points that are more than a threshold distance from other data points, by using a clustering analysis, or the like.

[0038] At 108, process 100 can optionally interpolate between data points of the obtained data points. For example, in some embodiments, process 100 can use any suitable interpolation technique (e.g.. linear interpolation) to identify one or more interpolated data points between two of the obtained data points. In some embodiments, interpolation may be performed such that a minimum number of data points are associated with a given edge and / or such that a distance between any two data points is less than a predetermined threshold. FIG. 3 illustrates an example of data points after interpolation has been performed.

[0039] At 110, process 100 can determine a linear fit to the data points. In some embodiments, the linear fit may include determining a slope and / or a y-intercept associated with the data points. The linear fit may be determined using linear regression techniques. In instances in which LWR metrics are to be determined, a linear fit may be determined for both edges of the line pattern.

[0040] At 112, process 100 can optionally rotate the data based on the intercept and slope of the linear fit to the data points. For example, process 100 can rotate the data points such that the linear fit of the rotated data points has a slope of 0. In implementations in which LWR metrics are to be determined, process 100 can rotate the data points such that the linear fit of data points corresponding to both edges of the line pattern have a slope of 0.

[0041] FIG. 4A illustrates an example of rotating data points associated with an edge of a line pattern in accordance with some embodiments. As illustrated, graph 402 depicts a linear fit 404 to a set of data points 406 associated with a line edge. Note that linear fit 404 has a nonzero slope. Graph 408 illustrates rotated data points 410. Rotated data points 410 correspond to set of data points 406 which have been rotated to reverse the slope of linear fit 404 such that a line fit to rotated data points 410 would have a slope of 0. In some embodiments, the rotated data points may additionally or alternatively be translated such that the rotated data points havea y-intercept of 0.

[0042] FIG. 4B illustrates an example of rotating data points associated with two edges of a line pattern, e.g., for determining LWR metrics. As illustrated, graph 420 depicts data points associated with two opposing edges of a line pattern. Graph 422 depicts the data points associated with the two opposing edges rotated such that the slope of the rotated data points associated with each edge is approximately 0. e.g., such that a linear fit to the data points of each edge has a slope of 0.

[0043] Referring back to FIG. 1, in instances in which LWR metrics are to be determined, process 100 can use the data points (and optionally, the rotated data points) to determine a width between the two opposing edges of the line pattern. For example, process 100 can determine the width by subtracting the y-coordinate value of the rotated data points associated with the lower opposing edge of the line pattern from the y-coordinate value of the rotated data points associated with the upper opposing edge of the line pattern to obtain the width for a given x-coordinate. FIG. 4C illustrates an example of a width of a line pattern in accordance with some embodiments.

[0044] At 114, process 100 can determine the LER and / or LWR metrics based on an analysis of the data points. For example, in some embodiments, the LER and / or the LWR metrics may be determined based at least in part on a spatial frequency analysis of the data points. Note that, in instances in which LWR metrics are determined, spatial frequency analysis may be performed on data points that indicate a width (e g., at different x-coordinate values) of a line pattern. In some embodiments, the spatial frequency analysis may involve determining a correlation length of the data points. As used herein, a correlation length may indicate a smoothness of the edge of a line pattern (e.g.. in instances in which LER metrics are determined) and / or a smoothness of a width of the line pattern (e.g., in instances in which LWR metrics are determined). In some implementations, the correlation length may be determined using at least one of: a head-head correlation (HHC), a power spectra density (PSD), or an auto correlation curve (ACF).

[0045] FIG. 5 illustrates the use of HHC, PSD, and ACF to determine correlation length based on rotated data points 502 associated with an edge of a line pattern. Graph 504 illustrates the HHC as a function of x-coordinate of the rotated data points. As illustrated, the correlation length may be determined based on a value at which the HHC exceeds a predetermined standard deviation threshold. Graph 506 illustrates the PSD as a function of spatial frequency f Graph 508 illustrates the correlation A of an ACF function as a function of x-coordinate of the rotated points. It should be understood that in some embodiments, HHC, PSD, and / orACF may be applied to data points representing a width between two opposing edges of a line pattern to determine correlation length associated with the line width (e.g., to determine LWR metrics). In some cases, the correlation length extracted from an HHC curve may be more stable than the correlation length extracted from the ACF and PSD curves.

[0046] Referring back to FIG. 1, in some embodiments, the LER and / or LWR metrics may additionally or alternatively include other statistical metrics associated with the data points (and / or the rotated data points). For example, the other statistical metncs may include a mean value of the data points, a standard deviation of the data points, and / or a range of the data points. For example, in some embodiments, data points of a line pattern associated with a larger range value and / or a large standard deviation value may indicate a higher roughness of the line pattern relative to a line pattern with a smaller range value and / or a smaller standard deviation.

[0047] In some embodiments, the LER metrics and / or the LWR metrics may be presented to the user, e.g., via a user interface. For example, such a user interface may be associated with a virtual fabrication environment in which the user can modify various process parameters. In such examples, the user may utilize the presented LER metrics and / or LWR metrics to modify process parameters, e.g., in order to achieve more optimal LER and / or LWR values. Additionally or alternatively, in some embodiments, the LER metrics and / or the LWR metrics may be utilized as part of a DoE where the LER and / or the LWR metrics may be used as tunable parameters to select potential experimental values of various process parameters.

[0048] In some embodiments, the techniques disclosed herein may identify a line pattern to be analyzed to determine LER and / or LWR metrics. The techniques may then determine LER and / or LWR metrics based at least in part on a spatial frequency analysis of the obtained data points. FIG. 6 is a flowchart of an example process 600 for determining LER and / or LWR metrics based on a spatial frequency analysis in accordance with some embodiments. In some implementations, blocks of process 600 may be implemented by one or more processors and / or controllers of a computing device, which may be a laptop computer, a desktop computer, a server, a computing device of a cloud system, or the like. In some embodiments, blocks of process 600 may be executed in an order other than what is shown in FIG. 6. In some embodiments, two or more blocks of process 600 may be executed substantially in parallel. In some embodiments, one or more blocks of process 600 may be omitted.

[0049] Process 600 can begin at 602 by identifying a line of a pattern to be analyzed to determine LER and / or LWR metrics. For example, in some embodiments, the line pattern may be obtained from a portion of a simulation of a fabrication process that is simulated using a processsimulation software package. As a more particular example, in some embodiments, the line pattern may be obtained using virtual metrology techniques of the simulation. As another example, in some embodiments, the line pattern may be associated with a physical fabrication process and may be obtained using various metrology techniques.

[0050] At 604, process 600 can obtain data points corresponding to the one or more edges of the line patern. For example, in an instance in which LER metrics are to be determined, the data points may correspond to one edge of the line patern. As another example, in an instance in which LWR metrics are to be determined, the data points may correspond to two opposing edges of the line pattern. In some embodiments, the data points may be obtained by applying a mask to the line patern and / or performing edge detection techniques to extract the one or more edges of the line patern.

[0051] In some embodiments, the obtained data points may be manipulated. For example, in some embodiments, outlier data points may be removed. As another example, in some embodiments, interpolation may be performed between the obtained data points to, e.g., increase a spatial resolution of the data points. As yet another example, in some embodiments, the data points may be rotated and / or translated. As a more particular example, in some embodiments, data points representing a line edge may be rotated such that a linear fit to the rotated data points has a slope of approximately 0. As another more particular example, in some embodiments, data points representing a line edge may be translated such that a linear fit to the rotated data points has a y -intercept of approximately 0. In instances in which the data points correspond to two opposing edges of a line patern, a width between the two opposing edges may be determined by, e.g., determining a distance between linear fits to data points representing each edge. Note that, in instances in which data points corresponding to two opposing edges of a line patern are utilized (e.g., to determine LWR metrics), translation and / or rotation of the data points may be performed before or after the width between the two opposing edges is determined.

[0052] At 606, process 600 can determine the LER and / or the LWR metrics based at least in part on a spatial frequency analysis of the obtained data points. For example, in some embodiments, the spatial frequency analysis may involve determining a correlation length associated with the data points, where the correlation length is indicative of a smoothness of the data points. Note that, in instances in which LER metrics are determined, the spatial frequency analysis may be applied to data points representing the edge of the line patern. In instances in which LWR metrics are determined, the spatial frequency analysis may be applied to data points representing a width between two opposing edges of the line patern across a length of the linepattern.

[0053] As described above, in some embodiments, the LER metrics and / or the LWR metrics may be presented to the user, e.g., via a user interface. For example, such a user interface may be associated with a virtual fabrication environment in which the user can modify various process parameters. In such examples, the user may utilize the presented LER metrics and / or LWR metrics to modify process parameters, e.g., in order to achieve more optimal LER and / or LWR values. Additionally or alternatively, in some embodiments, the LER metrics and / or the LWR metrics may be utilized as part of a DoE where the LER and / or the LWR metrics may be used as tunable parameters to select potential experimental values of various process parameters.CONTEXT FOR DISCLOSED COMPUTATIONAL EMBODIMENTS

[0054] Systems including fabrication tools as described herein may include logic for determining line edge roughness and / or line width roughness metrics.

[0055] The analysis logic may be designed and implemented in any of various ways. For example, the logic can be implemented in hardware and / or software. Examples are presented in the controller section herein. Hardware-implemented control logic may be provided in any of a variety of forms, including hard coded logic in digital signal processors, applicationspecific integrated circuits, and other devices that have algorithms implemented as hardware. Analysis logic may also be implemented as software or firmware instructions configured to be executed on a general-purpose processor. System control software may be provided by “programming” in a computer readable programming language.

[0056] The computer program code for controlling processes in a process sequence can be written in any conventional computer readable programming language: for example, assembly language, C, C++, Pascal, Fortran, Python, or others. Compiled object code or script is executed by the processor to perform the tasks identified in the program. Also as indicated, the program code may be hard coded.

[0057] Integrated circuits used in logic may include chips in the form of firmware that store program instructions, digital signal processors (DSPs), chips defined as application specific integrated circuits (ASICs), and / or one or more microprocessors, or microcontrollers that execute program instructions (e.g., software). Program instructions may be instructions communicated in the form of various individual settings (or program files), defining operational parameters for carrying out a particular analysis or image analysis application.

[0058] Figure 7 is a block diagram of an example of the computing device 700 suitable for usein implementing some embodiments of the present disclosure. For example, device 700 may be suitable for implementing some or all functions for determining LER and / or LWR metrics as described herein.

[0059] Computing device 700 may include a bus 702 that directly or indirectly couples the following devices: memory 704, one or more central processing units (CPUs) 706, one or more graphics processing units (GPUs) 708, a communication interface 710, input / output (I / O) ports 712, input / output components 714, a power supply 716, and one or more presentation components 718 (e.g., display(s)). In addition to CPU 706 and GPU 708, computing device 700 may include additional logic devices that are not shown in Figure 7, such as but not limited to an image signal processor (ISP), a digital signal processor (DSP), an ASIC, an FPGA, or the like.

[0060] Although the various blocks of Figure 7 are shown as connected via the bus 702 with lines, this is not intended to be limiting and is for clarity only. For example, in some embodiments, a presentation component 718, such as a display device, may be considered an I / O component 714 (e.g., if the display is a touch screen). As another example, CPUs 706 and / or GPUs 708 may include memory (e.g., the memory 704 may be representative of a storage device in addition to the memory of the GPUs 708, the CPUs 706, and / or other components). In other words, the computing device of Figure 7 is merely illustrative. Distinction is not made between such categories as “workstation,” “server,” “laptop,” “desktop,” “tablet,” “client device,” “mobile device,” “hand-held device,” “electronic control unit (ECU),” “virtual reality system,” and / or other device or system types, as all are contemplated within the scope of the computing device of Figure 7.

[0061] Bus 702 may represent one or more busses, such as an address bus, a data bus, a control bus, or a combination thereof. The bus 702 may include one or more bus types, such as an industry standard architecture (ISA) bus, an extended industry standard architecture (EISA) bus, a video electronics standards association (VESA) bus, a peripheral component interconnect (PCI) bus, a peripheral component interconnect express (PCIe) bus, and / or another type of bus.

[0062] Memory 704 may include any of a variety of computer-readable media. The computer- readable media may be any available media that can be accessed by the computing device 700. The computer-readable media may include both volatile and nonvolatile media, and removable and non-removable media. By way of example, and not limitation, the computer-readable media may comprise computer-storage media and / or communication media.

[0063] The computer-storage media may include both volatile and nonvolatile media and / orremovable and non-removable media implemented in any method or technology for storage of information such as computer-readable instructions, data structures, program modules, and / or other data types. For example, memoiy 704 may store computer-readable instructions (e.g., that represent a program(s) and / or a program element(s), such as an operating system. Computer-storage media may include, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by computing device 700. As used herein, computer storage media does not comprise signals per se.

[0064] The communication media may embody computer-readable instructions, data structures, program modules, and / or other data types in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media. The term “modulated data signal” may refer to a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, the communication media may include wired media such as a wired network or direct-wired connection, and wireless media such as acoustic, RF, infrared and other wireless media. Combinations of any of the above should also be included within the scope of computer- readable media.

[0065] CPU(s) 706 may be configured to execute the computer-readable instructions to control one or more components of the computing device 700 to perform one or more of the methods and / or processes described herein. CPU(s) 706 may each include one or more cores (e.g., one, two, four, eight, twenty-eight, seventy-two, etc.) that are capable of handling a multitude of software threads simultaneously. CPU(s) 706 may include any type of processor and may include different types of processors depending on the type of computing device 700 implemented (e.g., processors with fewer cores for mobile devices and processors with more cores for servers). For example, depending on the type of computing device 700, the processor may be an ARM processor implemented using Reduced Instruction Set Computing (RISC) or an x86 processor implemented using Complex Instruction Set Computing (CISC). Computing device 700 may include one or more CPUs 906 in addition to one or more microprocessors or supplementary co-processors, such as math co-processors.

[0066] GPU(s) 708 may be used by computing device 700 to render graphics (e.g., 3D graphics).GPU(s) 708 may include many (e.g., tens, hundreds, or thousands) of cores that are capable of handling many software threads simultaneously. GPU(s) 708 may generate pixel data foroutput images in response to rendering commands (e.g., rendering commands from CPU(s) 706 received via a host interface). GPU(s) 708 may include graphics memory, such as display memory, for storing pixel data. The display memory may be included as part of memory 704. GPU(s) 708 may include two or more GPUs operating in parallel (e.g., via a link). When combined, each GPU 708 can generate pixel data for different portions of an output image or for different output images (e.g., a first GPU for a first image and a second GPU for a second image). Each GPU can include its own memory or can share memoiy with other GPUs.

[0067] In examples where the computing device 700 does not include the GPU(s) 708, the CPU(s) 706 may be used to render graphics.

[0068] Communication interface 710 may include one or more receivers, transmitters, and / or transceivers that enable computing device 700 to communicate with other computing devices via an electronic communication network, included wired and / or wireless communications. Communication interface 710 may include components and functionality to enable communication over any of a number of different networks, such as wireless networks (e.g., Wi-Fi, Z-Wave, Bluetooth, Bluetooth LE, ZigBee, etc.), wired networks (e.g., communicating over Ethernet), low-power wide-area networks (e.g., LoRaWAN, SigFox, etc.), and / or the internet.

[0069] I / O ports 712 may enable the computing device 700 to be logically coupled to other devices including I / O components 714, presentation component(s) 718, and / or other components, some of which may be built in to (e.g., integrated in) computing device 700. Illustrative I / O components 714 include a microphone, mouse, keyboard, joystick, track pad, satellite dish, scanner, printer, wireless device, etc. I / O components 714 may provide a natural user interface (NUI) that processes air gestures, voice, or other physiological inputs generated by a user. In some instances, inputs may be transmitted to an appropriate network element for further processing. An NUI may implement any combination of speech recognition, stylus recognition, facial recognition, biometric recognition, gesture recognition both on screen and adjacent to the screen, air gestures, head and eye tracking, and touch recognition (as described in more detail below) associated with a display of computing device 700. Computing device 700 may be include depth cameras, such as stereoscopic camera systems, infrared camera systems, RGB camera systems, touchscreen technology, and combinations of these, for gesture detection and recognition. Additionally, computing device 700 may include accelerometers or gyroscopes (e.g., as part of an inertia measurement unit (IMU)) that enable detection of motion. In some examples, the output of the accelerometers or gyroscopes may be used by computing device 700 to render immersive augmented reality or virtual reality.[0070| Power supply 716 may include a hard-wired power supply, a battery power supply, or a combination thereof. Power supply 716 may provide power to computing device 700 to enable the components of computing device 700 to operate.

[0071] Presentation component(s) 718 may include a display (e.g., a monitor, a touch screen, a television screen, a heads-up-display (HUD), other display types, or a combination thereof), speakers, and / or other presentation components. Presentation component(s) 718 may receive data from other components (e.g., GPU(s) 708, CPU(s) 706, etc.), and output the data (e.g., as an image, video, sound, etc.).

[0072] The disclosure may be described in the general context of computer code or machine- useable instructions, including computer-executable instructions such as program modules, being executed by a computer or other machine, such as a personal data assistant or other handheld device. Generally, program modules including routines, programs, objects, components, data structures, etc., refer to code that perform particular tasks or implement particular abstract data types. The disclosure may be practiced in a variety of system configurations, including hand-held devices, consumer electronics, general-purpose computers, more specialty computing devices, etc. The disclosure may also be practiced in distributed computing environments where tasks are performed by remote-processing devices that are linked through a communications network.Additional Considerations

[0073] As used in this specification and appended claims, the singular forms “a”, “an”, and “the” include plural referents unless the content and context dictates otherwise. For example, reference to “a cell” includes a combination of two or more such cells. Unless indicated otherwise, an “or” conjunction is used in its correct sense as a Boolean logical operator, encompassing both the selection of features in the alternative (A or B, where the selection of A is mutually exclusive from B) and the selection of features in conjunction (A or B, where both A and B are selected).

[0074] It is to be understood that the phrases “for each <item> of the one or more <items>,” “each <item> of the one or more <items>,” or the like, if used herein, are inclusive of both a single-item group and multiple-item groups, i.e., the phrase “for ... each” is used in the sense that it is used in programming languages to refer to each item of whatever population of items is referenced. For example, if the population of items referenced is a single item, then “each” would refer to only that single item (despite the fact that dictionary definitions of “each” frequently define the term to refer to “every one of two or more things”) and would not imply that there must be at least two of those items. Similarly, the term “set” or “subset” should notbe viewed, in itself, as necessarily encompassing a plurality of items — it will be understood that a set or a subset can encompass only one member or multiple members (unless the context indicates otherwise).

[0075] The use, if any, of ordinal indicators, e.g., (a), (b), (c). . . or the like, in this disclosure and claims is to be understood as not conveying any particular order or sequence, except to the extent that such an order or sequence is explicitly indicated. For example, if there are three steps labeled (i), (ii), and (iii), it is to be understood that these steps may be performed in any order (or even concurrently, if not otherwise contraindicated) unless indicated otherwise. For example, if step (ii) involves the handling of an element that is created in step (i), then step (ii) may be viewed as happening at some point after step (i). Similarly, if step (i) involves the handling of an element that is created in step (ii), the reverse is to be understood. It is also to be understood that use of the ordinal indicator “first” herein, e.g., “a first item,” should not be read as suggesting, implicitly or inherently, that there is necessarily a “second” instance, e.g., “a second item.”

[0076] Various computational elements including processors, memory, instructions, routines, models, or other components may be described or claimed as “configured to” perform a task or tasks. In such contexts, the phrase “configured to” is used to connote structure by indicating that the component includes structure (e.g., stored instructions, circuitry, etc.) that performs the task or tasks during operation. As such, the unit / circuit / component can be said to be configured to perform the task even when the specified component is not necessarily currently operational (e.g., is not on).

[0077] The components used with the “configured to” language may refer to hardware — for example, circuits, memory storing program instructions executable to implement the operation, etc. Additionally, “configured to” can refer to generic structure (e.g., generic circuitry) that is manipulated by software and / or firmware (e.g., an FPGA or a general-purpose processor executing software) to operate in manner that is capable of performing the recited task(s). Additionally, “configured to” can refer to one or more memories or memory elements storing computer executable instructions for performing the recited task(s). Such memory elements may include memory on a computer chip having processing logic. In some contexts, “configured to” may also include adapting a manufacturing process (e.g., a semiconductor fabrication facility) to fabricate devices (e.g., integrated circuits) that are adapted to implement or perform one or more tasks.

[0078] Although the foregoing embodiments have been described in some detail for purposes of clarity of understanding, it will be apparent that certain changes and modifications may bepracticed within the scope of the appended claims. It should be noted that there are many alternative ways of implementing the processes, systems, and apparatus of the present embodiments. Accordingly, the present embodiments are to be considered as illustrative and not restrictive, and the embodiments are not to be limited to the details given herein.

Claims

CLAIMSWhat is claimed is:

1. A method for determining line edge roughness and / or line width roughness metrics, the method comprising: obtaining a line pattern to be analyzed to determine the line edge roughness (LER) and / or the line width roughness (LWR) metrics; obtaining data points corresponding to one or more edges of the line pattern; determining the LER and / or the LWR metrics based at least in part on a spatial frequency analysis of the obtained data points.

2. The method of claim 1, wherein obtaining the data points corresponding to the one or more edges of the line pattern comprises applying a mask to identify the one or more edges.

3. The method of claim 1. further comprising interpolating between the obtained data points prior to determining the LER and / or the LWR metrics.

4. The method of claim 1, further comprising: determining a linear fit to the obtained data points; and rotating the obtained data points based on the linear fit such that the rotated data points have a modified linear fit having a slope and ay-intercept of 0, wherein determining the LER and / or the LWR metrics is based on the rotated data points.

5. The method of any one of claims 1-4, wherein the spatial frequency analysis comprises determining a correlation length of the obtained data points.

6. The method of claim 5. wherein the correlation length is determined based on at least one of: a head-head correlation (HHC), a power spectra density (PSD), or an auto correlation curve (ACF).

7. The method of any one of claims 1-5, wherein the LER and / or the LWR metrics comprise LWR metrics, and wherein the LWR metrics are determined based on the spatial frequency analysis of a distance between two opposing edges of the line pattern.

8. The method of any one of claims 1-5, wherein the LER and / or the LWR metrics are utilized as a tunable parameter in a Design of Experiments (DoE) virtual fabrication environment.

9. The method of any one of claims 1-5, wherein the line pattern is obtained via a user interface.

10. The method of claim 9, wherein the LER and / or the LWR metrics are provided via the user interface.

11. A non-transitory computer-readable medium comprising computer-readable instructions that, when executed by one or more processors, cause the one or more processors to perform operations comprising: obtaining a line pattern to be analyzed to determine the line edge roughness (LER) and / or the line width roughness (LWR) metrics; obtain data points corresponding to one or more edges of the line pattern; determining the LER and / or the LWR metrics based at least in part on a spatial frequency analysis of the obtained data points.

12. The non-transitory computer-readable medium of claim 11, wherein obtaining the data points corresponding to the one or more edges of the line pattern comprises applying a mask to identify the one or more edges.

13. The non-transitory computer-readable medium of claim 11, wherein the operations further comprise interpolating between the obtained data points prior to determining the LER and / or the LWR metrics.

14. The non-transitory computer-readable medium of claim 11, wherein the operations further comprise: determining a linear fit to the obtained data points; and rotating the obtained data points based on the linear fit such that the rotated data points have a modified linear fit having a slope and ay-intercept of 0, wherein determining the LER and / or the LWR metrics is based on the rotated data points.

15. The non-transitory computer-readable medium of any one of claims 11-14, wherein the spatial frequency analysis comprises determining a correlation length of the obtained data points.

16. The non-transitory computer-readable medium of claim 15, wherein the correlation length is determined based on at least one of: a head-head correlation (HHC). a power spectra density (PSD), or an auto correlation curve (ACF).

17. The non-transitory computer-readable medium of any one of claims 11-15, wherein the LER and / or the LWR metrics comprise LWR metrics, and wherein the LWR metrics are determined based on the spatial frequency analysis of a distance between two opposing edges of the line pattern.

18. The non-transitory computer-readable medium of any one of claims 11-15, wherein the LER and / or the LWR metrics are utilized as a tunable parameter in a Design of Experiments (DoE) virtual fabrication environment.

19. The non-transitory computer-readable medium of any one of claims 11-15, wherein the line pattern is obtained via a user interface.

20. The non-transitory computer-readable medium of claim 19, wherein the LER and / or the LWR metrics are provided via the user interface.

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