Abstract: Scanner aberration impact modeling in a semiconductor manufacturing process, which may facilitate co-optimization of multiple scanners. Scanner aberration impact modeling may include executing a calibrated model and controlling a scanner based on output from the model. The model is configured to receive patterning system aberration data. The model is calibrated with patterning system aberration calibration data and corresponding patterning process impact calibration data. New pattering process impact data may be determined, based on the model, for the received patterning system aberration data. The model includes a hyperdimensional function configured to correlate the received patterning system aberration data with the new pattering process impact data.

Abstract: Methods for optimizing an aspect of a patterning process based on defects. For example, a method of source and mask optimization of a patterning process includes obtaining a location on a substrate having a threshold probability of having a defect; defining an defect ambit around the location to include a portion of a pattern on the substrate and one or more evaluation points associated with the portion of the pattern; determining a value of a first cost function based on a defect metric associated with the defect; determining a first guide function for the first cost function, wherein the first guide function is associated with a performance metric of the patterning process at the one or more evaluation locations within the defect ambit; and adjusting a source and/or a mask characteristic based on the value of the first cost function, and the first guide function.

Abstract: Methods for optimizing an aspect of a patterning process based on defects. For example, a method of source and mask optimization of a patterning process includes obtaining a location on a substrate having a threshold probability of having a defect; defining an defect ambit around the location to include a portion of a pattern on the substrate and one or more evaluation points associated with the portion of the pattern; determining a value of a first cost function based on a defect metric associated with the defect; determining a first guide function for the first cost function, wherein the first guide function is associated with a performance metric of the patterning process at the one or more evaluation locations within the defect ambit; and adjusting a source and/or a mask characteristic based on the value of the first cost function, and the first guide function.

Abstract: A method for determining a wavefront parameter of a patterning process. The method includes obtaining a reference performance (e.g., a contour, EPE, CD) of a reference apparatus (e.g., a scanner), a lens model for a patterning apparatus configured to convert a wavefront parameter of a wavefront to actuator movement, and a lens fingerprint of a tuning apparatus (e.g., a to-be-matched scanner). Further, the method involves determining the wavefront parameter (e.g., a wavefront parameter such as tilt, offset, etc.) based on the lens fingerprint of the tuning apparatus, the lens model, and a cost function, wherein the cost function is a difference between the reference performance and a tuning apparatus performance.

Abstract: A method for determining a patterning device pattern. The method includes obtaining (i) an initial patterning device pattern having at least one feature, and (ii) a desired feature size of the at least one feature, obtaining, based on a patterning process model, the initial patterning device pattern and a target pattern for a substrate, a difference value between a predicted pattern of the substrate image by the initial patterning device and the target pattern for the substrate, determining a penalty value related the manufacturability of the at least one feature, wherein the penalty value varies as a function of the size of the at least one feature, and determining the patterning device pattern based on the initial patterning device pattern and the desired feature size such that a sum of the difference value and the penalty value is reduced.

Abstract: A method including: obtaining a thin-mask transmission function of a patterning device and a M3D model for a lithographic process, wherein the thin-mask transmission function is a continuous transmission mask (CTM) and the M3D model at least represents a portion of M3D attributable to multiple edges of structures on the patterning device; determining a M3D mask transmission function of the patterning device by using the thin-mask transmission function and the M3D model; and determining an aerial image produced by the patterning device and the lithographic process, by using the M3D mask transmission function.

Abstract: A method to determine a curvilinear pattern of a patterning device that includes obtaining (i) an initial image of the patterning device corresponding to a target pattern to be printed on a substrate subjected to a patterning process, and (ii) a process model configured to predict a pattern on the substrate from the initial image, generating, by a hardware computer system, an enhanced image from the initial image, generating, by the hardware computer system, a level set image using the enhanced image, and iteratively determining, by the hardware computer system, a curvilinear pattern for the patterning device based on the level set image, the process model, and a cost function, where the cost function (e.g., EPE) determines a difference between a predicted pattern and the target pattern, where the difference is iteratively reduced.

Abstract: A method for determining a wavefront parameter of a patterning process. The method includes obtaining a reference performance (e.g., a contour, EPE, CD) of a reference apparatus (e.g., a scanner), a lens model for a patterning apparatus configured to convert a wavefront parameter of a wavefront to actuator movement, and a lens fingerprint of a tuning apparatus (e.g., a to-be-matched scanner). Further, the method involves determining the wavefront parameter (e.g., a wavefront parameter such as tilt, offset, etc.) based on the lens fingerprint of the tuning apparatus, the lens model, and a cost function, wherein the cost function is a difference between the reference performance and a tuning apparatus performance.

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 determining a wavefront parameter of a patterning process. The method includes obtaining a reference performance (e.g., a contour, EPE, CD) of a reference apparatus (e.g., a scanner), a lens model for a patterning apparatus configured to convert a wavefront parameter of a wavefront to actuator movement, and a lens fingerprint of a tuning apparatus (e.g., a to-be-matched scanner). Further, the method involves determining the wavefront parameter (e.g., a wavefront parameter such as tilt, offset, etc.) based on the lens fingerprint of the tuning apparatus, the lens model, and a cost function, wherein the cost function is a difference between the reference performance and a tuning apparatus performance.

Abstract: A method for determining a patterning device pattern. The method includes obtaining (i) an initial patterning device pattern having at least one feature, and (ii) a desired feature size of the at least one feature, obtaining, based on a patterning process model, the initial patterning device pattern and a target pattern for a substrate, a difference value between a predicted pattern of the substrate image by the initial patterning device and the target pattern for the substrate, determining a penalty value related the manufacturability of the at least one feature, wherein the penalty value varies as a function of the size of the at least one feature, and determining the patterning device pattern based on the initial patterning device pattern and the desired feature size such that a sum of the difference value and the penalty value is reduced.

Abstract: A method including: determining a first simulated partial image formed, by a lithographic projection apparatus, from a first radiation portion propagating along a first group of one or more directions; determining a second simulated partial image formed, by the lithographic projection apparatus, from a second radiation portion propagating along a second group of one or more directions; and determining an image by incoherently adding the first partial image and the second partial image, wherein the first group of one or more directions and the second group of one or more directions are different.

Abstract: A method including: obtaining a thin-mask transmission function of a patterning device and a M3D model for a lithographic process, wherein the thin-mask transmission function is a continuous transmission mask (CTM) and the M3D model at least represents a portion of M3D attributable to multiple edges of structures on the patterning device; determining a M3D mask transmission function of the patterning device by using the thin-mask transmission function and the M3D model; and determining an aerial image produced by the patterning device and the lithographic process, by using the M3D mask transmission function.

Abstract: A method to determine a curvilinear pattern of a patterning device that includes obtaining (i) an initial image of the patterning device corresponding to a target pattern to be printed on a substrate subjected to a patterning process, and (ii) a process model configured to predict a pattern on the substrate from the initial image, generating, by a hardware computer system, an enhanced image from the initial image, generating, by the hardware computer system, a level set image using the enhanced image, and iteratively determining, by the hardware computer system, a curvilinear pattern for the patterning device based on the level set image, the process model, and a cost function, where the cost function (e.g., EPE) determines a difference between a predicted pattern and the target pattern, where the difference is iteratively reduced.

Abstract: A method to determine a curvilinear pattern of a patterning device that includes obtaining (i) an initial image of the patterning device corresponding to a target pattern to be printed on a substrate subjected to a patterning process, and (ii) a process model configured to predict a pattern on the substrate from the initial image, generating, by a hardware computer system, an enhanced image from the initial image, generating, by the hardware computer system, a level set image using the enhanced image, and iteratively determining, by the hardware computer system, a curvilinear pattern for the patterning device based on the level set image, the process model, and a cost function, where the cost function (e.g., EPE) determines a difference between a predicted pattern and the target pattern, where the difference is iteratively reduced.

Abstract: A method to improve a lithographic process for imaging a portion of a design layout onto a substrate using a lithographic projection apparatus having an illuminator and projection optics, the method including: computing a multi-variable cost function of a plurality of design variables that are characteristics of the lithographic process, at least some of the design variables being characteristics of the illumination produced by the illuminator and of the design layout, wherein the multi-variable cost function is a function of a three-dimensional resist profile on the substrate, or a three-dimensional radiation field projected from the projection optics, or both; and reconfiguring one or more characteristics of the lithographic process by adjusting the design variables until a predefined termination condition is satisfied.

Abstract: A method including: obtaining a thin-mask transmission function of a patterning device and a M3D model for a lithographic process, wherein the thin-mask transmission function represents a continuous transmission mask and the M3D model at least represents a portion of M3D attributable to multiple edges of structures on the patterning device; determining a M3D mask transmission function of the patterning device by using the thin-mask transmission function and the M3D model; and determining an aerial image produced by the patterning device and the lithographic process, by using the M3D mask transmission function.

Abstract: A method to determine a mask pattern for a patterning device. The method includes obtaining a target pattern to be printed on a substrate, an initial continuous tone image corresponding to the target pattern, a binarization function (e.g., a sigmoid, an arctan, a step function, etc.) configured to transform the initial continuous tone image, and a process model configured to predict a pattern on the substrate from an output of the binarization function; and generating a binarized image having a mask pattern corresponding to the initial continuous tone image by iteratively updating the initial continuous tone image based on a cost function such that the cost function is reduced. The cost function (e.g., EPE) determines a difference between a predicted pattern determined by the process model and the target pattern.

Abstract: A method for improving a lithographic process for imaging a portion of a design layout onto a substrate using a lithographic projection apparatus, the method including: calculating a discrete pupil profile based on a desired pupil profile; selecting a discrete change to the discrete pupil profile; and applying the selected discrete change to the discrete pupil profile. The methods according to various embodiments disclosed herein may reduce the computational cost of discrete optimization from O(an) to O(n) wherein a is constant and n is the number of knobs that can generate discrete change in the pupil profile.

Abstract: A method to improve a lithographic process for imaging a portion of a design layout onto a substrate using a lithographic projection apparatus having an illumination system and projection optics, the method including: obtaining an illumination source shape and a mask defocus value; optimizing a dose of the lithographic process; and optimizing the portion of the design layout for each of a plurality of slit positions of the illumination source.