Abstract: A method including obtaining (i) measurements of a parameter of the feature, (ii) data related to a process variable of a patterning process, (iii) a functional behavior of the parameter defined as a function of the process variable based on the measurements of the parameter and the data related to the process variable, (iv) measurements of a failure rate of the feature, and (v) a probability density function of the process variable for a setting of the process variable, converting the probability density function of the process variable to a probability density function of the parameter based on a conversion function, where the conversion function is determined based on the function of the process variable, and determining a parameter limit of the parameter based on the probability density function of the parameter and the measurements of the failure rate.

Abstract: A method including obtaining (i) measurements of a parameter of the feature, (ii) data related to a process variable of a patterning process, (iii) a functional behavior of the parameter defined as a function of the process variable based on the measurements of the parameter and the data related to the process variable, (iv) measurements of a failure rate of the feature, and (v) a probability density function of the process variable for a setting of the process variable, converting the probability density function of the process variable to a probability density function of the parameter based on a conversion function, where the conversion function is determined based on the function of the process variable, and determining a parameter limit of the parameter based on the probability density function of the parameter and the measurements of the failure rate.

Abstract: A process of selecting a measurement location, the process including: obtaining pattern data describing a pattern to be applied to substrates in a patterning process; obtaining a process characteristic measured during or following processing of a substrate, the process characteristic characterizing the processing of the substrate; determining a simulated result of the patterning process based on the pattern data and the process characteristic; and selecting a measurement location for the substrate based on the simulated result.

Abstract: A method and apparatus of detection, registration and quantification of an image is described. The method may include obtaining an image of a lithographically created structure, and applying a level set method to an object, representing the structure, of the image to create a mathematical representation of the structure. The method may include obtaining a first dataset representative of a reference image object of a structure at a nominal condition of a parameter, and obtaining second dataset representative of a template image object of the structure at a non-nominal condition of the parameter. The method may further include obtaining a deformation field representative of changes between the first dataset and the second dataset. The deformation field may be generated by transforming the second dataset to project the template image object onto the reference image object. A dependence relationship between the deformation field and change in the parameter may be obtained.

Abstract: A process of selecting a measurement location, the process including: obtaining pattern data describing a pattern to be applied to substrates in a patterning process; obtaining a process characteristic measured during or following processing of a substrate, the process characteristic characterizing the processing of the substrate; determining a simulated result of the patterning process based on the pattern data and the process characteristic; and selecting a measurement location for the substrate based on the simulated result.

Abstract: A method of topography determination, the method including: obtaining a first focus value derived from a computational lithography model modeling patterning of an unpatterned substrate or derived from measurements of a patterned layer on an unpatterned substrate; obtaining a second focus value derived from measurement of a substrate having a topography; and determining a value of the topography from the first and second focus values.

Abstract: Methods related to improving a simulation processes and solutions (e.g., retargeted patterns) associated with manufacturing of a chip. A method includes obtaining a plurality of dose-focus settings, and a reference distribution based on measured values of a characteristic of a printed pattern associated with each setting of the plurality of dose-focus settings. The method further includes, based on an adjustment model and the plurality of dose-focus settings, determining a probability density function (PDF) of the characteristic such that an error between the PDF and the reference distribution is reduced. The PDF can be a function of the adjustment model and variance associated with dose, the adjustment model being configured to change a proportion of non-linear dose sensitivity contribution to the PDF. A process window can be adjusted based on the determined PDF of the characteristic.

Abstract: Systems and methods for predicting substrate geometry associated with a patterning process are described. Input information including geometry information and/or process information for a pattern is received and, using a machine learning prediction model, multi-dimensional output substrate geometry is predicted. The multi-dimensional output information may include pattern probability images. A stochastic edge placement error band and/or a stochastic failure rate may be predicted. The input information can include simulated aerial images, simulated resist images, target substrate dimensions, and/or data from a lithography apparatus associated with device manufacturing. Different aerial images may correspond to different heights in resist layers associated with the patterning process, for example.

Abstract: Methods of identifying a hot spot from a design layout or of predicting whether a pattern in a design layout is defective, using a machine learning model. An example method disclosed herein includes obtaining sets of one or more characteristics of performance of hot spots, respectively, under a plurality of process conditions, respectively, in a device manufacturing process; determining, for each of the process conditions, for each of the hot spots, based on the one or more characteristics under that process condition, whether that hot spot is defective; obtaining a characteristic of each of the process conditions; obtaining a characteristic of each of the hot spots; and training a machine learning model using a training set including the characteristic of one of the process conditions, the characteristic of one of the hot spots, and whether that hot spot is defective under that process condition.

Abstract: Methods of identifying a hot spot from a design layout or of predicting whether a pattern in a design layout is defective, using a machine learning model. An example method disclosed herein includes obtaining sets of one or more characteristics of performance of hot spots, respectively, under a plurality of process conditions, respectively, in a device manufacturing process; determining, for each of the process conditions, for each of the hot spots, based on the one or more characteristics under that process condition, whether that hot spot is defective; obtaining a characteristic of each of the process conditions; obtaining a characteristic of each of the hot spots; and training a machine learning model using a training set including the characteristic of one of the process conditions, the characteristic of one of the hot spots, and whether that hot spot is defective under that process condition.

Abstract: A method for training a machine learning model configured to predict a substrate image corresponding to a printed pattern of a substrate as measured via a metrology tool. The method involves obtaining a training data set including (i) metrology data of the metrology tool used to measure the printed pattern of the substrate, and (ii) a representation of a mask pattern employed for imaging the printed pattern on the substrate; and training, based on the training data set, a machine learning model to predict the substrate image of the substrate as measured by the metrology tool such that a cost function is improved, wherein the cost function includes a relationship between the predicted substrate image and the metrology data.

Abstract: A defect prediction method for a device manufacturing process involving processing a pattern onto a substrate, the method comprising: identifying a processing window limiting pattern (PWLP) from the pattern; determining a processing parameter under which the PWLP is processed; and determining or predicting, using the processing parameter, existence, probability of existence, a characteristic, or a combination thereof, of a defect produced from the PWLP with the device manufacturing process.

Abstract: A defect prediction method for a device manufacturing process involving processing a pattern onto a substrate, the method comprising: identifying a processing window limiting pattern (PWLP) from the pattern; determining a processing parameter under which the PWLP is processed; and determining or predicting, using the processing parameter, existence, probability of existence, a characteristic, or a combination thereof, of a defect produced from the PWLP with the device manufacturing process.

Abstract: A method and apparatus of detection, registration and quantification of an image is described. The method may include obtaining an image of a lithographically created structure, and applying a level set method to an object, representing the structure, of the image to create a mathematical representation of the structure. The method may include obtaining a first dataset representative of a reference image object of a structure at a nominal condition of a parameter, and obtaining second dataset representative of a template image object of the structure at a non-nominal condition of the parameter. The method may further include obtaining a deformation field representative of changes between the first dataset and the second dataset. The deformation field may be generated by transforming the second dataset to project the template image object onto the reference image object. A dependence relationship between the deformation field and change in the parameter may be obtained.

Abstract: A method including obtaining (i) measurements of a parameter of the feature, (ii) data related to a process variable of a patterning process, (iii) a functional behavior of the parameter defined as a function of the process variable based on the measurements of the parameter and the data related to the process variable, (iv) measurements of a failure rate of the feature, and (v) a probability density function of the process variable for a setting of the process variable, converting the probability density function of the process variable to a probability density function of the parameter based on a conversion function, where the conversion function is determined based on the function of the process variable, and determining a parameter limit of the parameter based on the probability density function of the parameter and the measurements of the failure rate.

Abstract: A method and apparatus of detection, registration and quantification of an image is described. The method may include obtaining an image of a lithographically created structure, and applying a level set method to an object, representing the structure, of the image to create a mathematical representation of the structure. The method may include obtaining a first dataset representative of a reference image object of a structure at a nominal condition of a parameter, and obtaining second dataset representative of a template image object of the structure at a non-nominal condition of the parameter. The method may further include obtaining a deformation field representative of changes between the first dataset and the second dataset. The deformation field may be generated by transforming the second dataset to project the template image object onto the reference image object. A dependence relationship between the deformation field and change in the parameter may be obtained.

Abstract: A method is proposed involving obtaining data regarding an expected focus offset during a patterning process due to topography of a region of a substrate surface. A modification of, e.g., a transmission or reflection of a region of a patterning device associated with the region of the substrate surface is determined based on the data. Using the patterning device modified according the determined modification during the patterning process mitigates an impact of the substrate topography on a parameter of the patterning process.

Abstract: A defect prediction method for a device manufacturing process involving processing one or more patterns onto a substrate, the method including: determining values of one or more processing parameters under which the one or more patterns are processed; and determining or predicting, using the values of the one or more processing parameters, an existence, a probability of existence, a characteristic, and/or a combination selected from the foregoing, of a defect resulting from production of the one or more patterns with the device manufacturing process.

Abstract: A method for correcting metrology data of a patterning process. The method includes obtaining (i) metrology data of a substrate subjected to the patterning process and (ii) a quality metric (e.g., a focus index) that quantifies a quality of the metrology data of the substrate; establishing a correlation between the quality metric and the metrology data; and determining a correction to the metrology data based on the correlation between the quality metric and the metrology data.

Abstract: A method including obtaining (i) measurements of a parameter of the feature, (ii) data related to a process variable of a patterning process, (iii) a functional behavior of the parameter defined as a function of the process variable based on the measurements of the parameter and the data related to the process variable, (iv) measurements of a failure rate of the feature, and (v) a probability density function of the process variable for a setting of the process variable, converting the probability density function of the process variable to a probability density function of the parameter based on a conversion function, where the conversion function is determined based on the function of the process variable, and determining a parameter limit of the parameter based on the probability density function of the parameter and the measurements of the failure rate.