Abstract: An etch bias direction is determined based on a curvature of a contour in a substrate pattern. The etch bias direction is configured to be used to enhance an accuracy of a semiconductor patterning process relative to prior patterning processes. In some embodiments, a representation of the substrate pattern is received, which includes the contour in the substrate pattern. The curvature of the contour of the substrate pattern is determined, and an etch bias direction is determined based on the curvature by considering curvatures of adjacent contour portions. A simulation model is used to determine an etch effect based on the etch bias direction for an etching process on the substrate pattern.

Abstract: Machine learning models can be trained to predict imaging characteristics with respect to variation in a pattern on a wafer resulting from a patterning process. However, due to low pattern coverage provided by limited wafer data used for training, machine learning models tend to overfit, and predictions from the machine learning models deviate from physical trends that characterize the pattern on the wafer and/or the patterning process with respect to the pattern variation. To enhance pattern coverage, training data is augmented with pattern data that conforms to a certain expected physical trend, and applies to new patterns not covered by previously measured wafer data.

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 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 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 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 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 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 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.