Abstract: A patterning process modeling method includes determining, with a front end of a process model, a function associated with process physics and/or chemistry of an operation within a patterning process flow; and determining, with a back end of the process model, a predicted wafer geometry. The back end includes a volumetric representation of a target area on the wafer. The predicted wafer geometry is determined by applying the function from the front end to manipulate the volumetric representation of the wafer. The volumetric representation of the wafer may be generated using volumetric dynamic B-trees. The volumetric representation of the wafer may be manipulated using a level set method. The function associated with the process physics and/or chemistry of the operation within the patterning process flow may be a velocity/speed function. Incoming flux on a modeled surface of the wafer may be determined using ray tracing.

Abstract: A method involving determining an etch bias for a pattern to be etched using an etch step of a patterning process based on an etch bias model, the etch bias model including a formula having a variable associated with a spatial property of the pattern or with an etch plasma species concentration of the etch step, and including a mathematical term including a natural exponential function to the power of a parameter that is fitted or based on an etch time of the etch step; and adjusting the patterning process based on the determined etch bias.

Abstract: A method for determining a likelihood that an assist feature of a mask pattern will print on a substrate. The method includes obtaining (i) a plurality of images of a pattern printed on a substrate and (ii) variance data the plurality of images of the pattern; determining, based on the variance data, a model configured to generate variance data associated with the mask pattern; and determining, based on model-generated variance data for a given mask pattern and a resist image or etch image associated with the given mask pattern, the likelihood that an assist feature of the given mask pattern will be printed on the substrate. The likelihood can be applied to adjust one or more parameters related to a patterning process or a patterning apparatus to reduce the likelihood that the assist feature will print on the substrate.

Abstract: A method including performing a simulation to evaluate a plurality of metrology targets and/or a plurality of metrology recipes used to measure a metrology target, identifying one or more metrology targets and/or metrology recipes from the evaluated plurality of metrology targets and/or metrology recipes, receiving measurement data of the one or more identified metrology targets and/or metrology recipes, and using the measurement data to tune a metrology target parameter or metrology recipe parameter.

Abstract: A method involving determining an etch bias for a pattern to be etched using an etch step of a patterning process based on an etch bias model, the etch bias model including a formula having a variable associated with a spatial property of the pattern or with an etch plasma species concentration of the etch step, and including a mathematical term including a natural exponential function to the power of a parameter that is fitted or based on an etch time of the etch step; and adjusting the patterning process based on the determined etch bias.

Abstract: Methods of constructing a process model for simulating a characteristic of a product of lithography from patterns produced under different processing conditions. The methods use a deviation between the variation of the simulated characteristic and the variation of the measured characteristic to adjust a parameter of the process model.

Abstract: A method including performing a simulation to evaluate a plurality of metrology targets and/or a plurality of metrology recipes used to measure a metrology target, identifying one or more metrology targets and/or metrology recipes from the evaluated plurality of metrology targets and/or metrology recipes, receiving measurement data of the one or more identified metrology targets and/or metrology recipes, and using the measurement data to tune a metrology target parameter or metrology recipe parameter.

Abstract: A method for determining measurement data of a printed pattern on a substrate. The method involves obtaining (i) images of the substrate including a printed pattern corresponding to a reference pattern, (ii) an averaged image of the images, and (iii) a composite contour based on the averaged image. Further, the composite contour is aligned with respect to a reference contour of the reference pattern and contours are extracted from the images based on both the aligned composite contour and the output of die-to-database alignment of the composite contour. Further, the method determines a plurality of pattern measurements based on the contours and the measurement data corresponding to the printed patterns based on the plurality of the pattern measurements. Further, the method determines a one or more process variations such as stochastic variation, inter-die variation, intra-die variation and/or total variation.

Abstract: A method for training a machine learning model to generate a predicted measured image, the method including obtaining (a) an input target image associated with a reference design pattern, and (b) a reference measured image associated with a specified design pattern printed on a substrate, wherein the input target image and the reference measured image are non-aligned images; and training, by a hardware computer system and using the input target image, the machine learning model to generate a predicted measured image.

Abstract: A method for evaluating images of a printed pattern. The method includes obtaining a first averaged image of the printed pattern, where the first averaged image is generated by averaging raw images of the printed pattern. The method also includes identifying one or more features of the first averaged image. The method further includes evaluating the first averaged image, using an image quality classification model and based at least on the one or more features. The evaluating includes determining, by the image quality classification model, whether the first averaged image satisfies a metric.

Abstract: A method for generating modified contours and/or generating metrology gauges based on the modified contours. A method of generating metrology gauges for measuring a physical characteristic of a structure on a substrate includes obtaining (i) measured data associated with the physical characteristic of the structure printed on the substrate, and (ii) at least portion of a simulated contour of the structure, the at least a portion of the simulated contour being associated with the measured data; modifying, based on the measured data, the at least a portion of the simulated contour of the structure; and generating the metrology gauges on or adjacent to the modified at least a portion of the simulated contour, the metrology gauges being placed to measure the physical characteristic of the simulated contour of the structure.

Abstract: A method for training a machine learning model configured to predict values of a physical characteristic associated with a substrate and for use in adjusting a patterning process. The method involves obtaining a reference image; determining a first set of model parameter values of the machine learning model such that a first cost function is reduced from an initial value of the cost function obtained using an initial set of model parameter values, where the first cost function is a difference between the reference image and an image generated via the machine learning model; and training, using the first set of model parameter values, the machine learning model such that a combination of the first cost function and a second cost function is iteratively reduced, the second cost function representing a difference between measured values and predicted values.

Abstract: A patterning process modeling method includes determining, with a front end of a process model, a function associated with process physics and/or chemistry of an operation within a patterning process flow; and determining, with a back end of the process model, a predicted wafer geometry. The back end includes a volumetric representation of a target area on the wafer. The predicted wafer geometry is determined by applying the function from the front end to manipulate the volumetric representation of the wafer. The volumetric representation of the wafer may be generated using volumetric dynamic B-trees. The volumetric representation of the wafer may be manipulated using a level set method. The function associated with the process physics and/or chemistry of the operation within the patterning process flow may be a velocity/speed function. Incoming flux on a modeled surface of the wafer may be determined using ray tracing.

Abstract: A method for training a patterning process model, the patterning process model configured to predict a pattern that will be formed by a patterning process. The method involves obtaining an image data associated with a desired pattern, a measured pattern of the substrate, a first model including a first set of parameters, and a machine learning model including a second set of parameters; and iteratively determining values of the first set of parameters and the second set of parameters to train the patterning process model. An iteration involves executing, using the image data, the first model and the machine learning model to cooperatively predict a printed pattern of the substrate; and modifying the values of the first set of parameters and the second set of parameters such that a difference between the measured pattern and the predicted pattern is reduced.

Abstract: A method for determining measurement data of a printed pattern on a substrate. The method involves obtaining (i) images of the substrate including a printed pattern corresponding to a reference pattern, (ii) an averaged image of the images, and (iii) a composite contour based on the averaged image. Further, the composite contour is aligned with respect to a reference contour of the reference pattern and contours are extracted from the images based on both the aligned composite contour and the output of die-to-database alignment of the composite contour. Further, the method determines a plurality of pattern measurements based on the contours and the measurement data corresponding to the printed patterns based on the plurality of the pattern measurements. Further, the method determines a one or more process variations such as stochastic variation, inter-die variation, intra-die variation and/or total variation.

Abstract: A process to model post-exposure effects in patterning processes, the process including: obtaining values based on measurements of structures formed on one or more substrates by a post-exposure process and values of a pair of process parameters by which process conditions were varied; modeling, by a processor system, as a surface, correlation between the values based on measurements of the structures and the values of the pair of process parameters; and storing the model in memory.

Abstract: Methods of determining, and using, a process model that is a machine learning model. The process model is trained partially based on simulation or based on a non-machine learning model. The training data may include inputs obtained from a design layout, patterning process measurements, and image measurements.

Abstract: A method for improving a process model for a patterning process, the method including obtaining a) a measured contour from an image capture device, and b) a simulated contour generated from a simulation of the process model. The method also includes aligning the measured contour with the simulated contour by determining an offset between the measured contour and the simulated contour. The process model is calibrated to reduce a difference, computed based on the determined offset, between the simulated contour and the measured contour.

Abstract: A method including: obtaining a relationship between a performance indicator of a substrate measurement recipe and a parameter of the substrate measurement recipe; deriving a range of the parameter from the relationship, wherein absolute values of the performance indicator satisfy a first condition or a magnitude of variation of the performance indicator satisfies a second condition, when the first parameter is in the range; selecting a substrate measurement recipe that has the parameter in the range; and inspecting a substrate with the selected substrate measurement recipe.

Abstract: Methods of determining, and using, a patterning process model that is a machine learning model. The process model is trained partially based on simulation or based on a non-machine learning model. The training data may include inputs obtained from a design layout, patterning process measurements, and image measurements.