Abstract: A method of determining a relationship between a stochastic variation of a characteristic of an aerial image or a resist image and one or more design variables, the method including: measuring values of the characteristic from a plurality of aerial images and/or resist images for each of a plurality of sets of values of the design variables; determining a value of the stochastic variation, for each of the plurality of sets of values of the design variables, from a distribution of the values of the characteristic for that set of values of the design variables; and determining the relationship by fitting one or more parameters from the values of the stochastic variation and the plurality of sets of values of the design variables.

Abstract: A method of determining a failure model of a resist process of a patterning process. The method includes obtaining (i) measured data of a pattern failure (e.g., failure rate) related to a feature printed on a substrate based on a range of values of dose, and (ii) image intensity values for the feature via simulating a process model using the range of the dose values; and determining, via fitting the measured data of the pattern failure to a product of the dose values and the image intensity values, a failure model to model a stochastic behavior of spatial fluctuations in the resist and optionally predict failure of the feature (e.g., hole closing).

Abstract: A method of determining a relationship between a stochastic variation of a characteristic of an aerial image or a resist image and one or more design variables, the method including: measuring values of the characteristic from a plurality of aerial images and/or resist images for each of a plurality of sets of values of the design variables; determining a value of the stochastic variation, for each of the plurality of sets of values of the design variables, from a distribution of the values of the characteristic for that set of values of the design variables; and determining the relationship by fitting one or more parameters from the values of the stochastic variation and the plurality of sets of values of the design variables.

Abstract: A method of determining a failure model of a resist process of a patterning process. The method includes obtaining (i) measured data of a pattern failure (e.g., failure rate) related to a feature printed on a substrate based on a range of values of dose, and (ii) image intensity values for the feature via simulating a process model using the range of the dose values; and determining, via fitting the measured data of the pattern failure to a product of the dose values and the image intensity values, a failure model to model a stochastic behavior of spatial fluctuations in the resist and optionally predict failure of the feature (e.g., hole closing).

Abstract: A method of determining a relationship between a stochastic variation of a characteristic of an aerial image or a resist image and one or more design variables, the method including: measuring values of the characteristic from a plurality of aerial images and/or resist images for each of a plurality of sets of values of the design variables; determining a value of the stochastic variation, for each of the plurality of sets of values of the design variables, from a distribution of the values of the characteristic for that set of values of the design variables; and determining the relationship by fitting one or more parameters from the values of the stochastic variation and the plurality of sets of values of the design variables.

Abstract: A method including obtaining a selected component of optical aberration of or for a lithography apparatus, under a processing condition; computing an approximate of a cost function, based on the selected component; and producing an adjustment of the lithography apparatus or a patterning process that uses the lithography apparatus, based on the approximate of the cost function.

Abstract: A method including: obtaining a resist process dose sensitivity value for a patterning process; applying the resist process dose sensitivity value to a stochastic model providing values of a stochastic variable as a function of resist process dose sensitivity to obtain a value of the stochastic variable; and designing or modifying a parameter of the patterning process based on the stochastic variable value.

Abstract: A method of determining a relationship between a stochastic variation of a characteristic of an aerial image or a resist image and one or more design variables, the method including: measuring values of the characteristic from a plurality of aerial images and/or resist images for each of a plurality of sets of values of the design variables; determining a value of the stochastic variation, for each of the plurality of sets of values of the design variables, from a distribution of the values of the characteristic for that set of values of the design variables; and determining the relationship by fitting one or more parameters from the values of the stochastic variation and the plurality of sets of values of the design variables.

Abstract: A method of determining a relationship between a stochastic variation of a characteristic of an aerial image or a resist image and one or more design variables, the method including: measuring values of the characteristic from a plurality of aerial images and/or resist images for each of a plurality of sets of values of the one or more design variables; determining a value of the stochastic variation, for each of the plurality of sets of values of the one or more design variables, from a distribution of the values of the characteristic for that set of values of the one or more design variables; and determining the relationship by fitting one or more parameters from the values of the stochastic variation and the plurality of sets of values of the one or more design variables.

Abstract: A method including obtaining a selected component of optical aberration of or for a lithography apparatus, under a processing condition; computing an approximate of a cost function, based on the selected component; and producing an adjustment of the lithography apparatus or a patterning process that uses the lithography apparatus, based on the approximate of the cost function.

Abstract: A method including: obtaining a resist process dose sensitivity value for a patterning process; applying the resist process dose sensitivity value to a stochastic model providing values of a stochastic variable as a function of resist process dose sensitivity to obtain a value of the stochastic variable; and designing or modifying a parameter of the patterning process based on the stochastic variable value.

Abstract: Disclosed herein is a computer-implemented method for improving a lithographic process for imaging a portion of a design layout onto a substrate using a lithographic projection apparatus, the method comprising defining a multi-variable cost function, the multi-variable cost function being a function of a stochastic effect of the lithographic process.

Abstract: An illumination system is disclosed having a polarization member that includes first and second polarization modifiers movable into at least partial intersection with a radiation beam such that the respective polarization modifier applies a modified polarization to at least part of the beam. The illumination system further includes an array of individually controllable reflective elements positioned to receive the radiation beam after it has passed the polarization member, and a controller configured to control movement of the first and second polarization modifiers such that the first and second polarization modifiers intersect with different portions of the radiation beam.

Abstract: A method for configuring an illumination source of a lithographic apparatus, the method including dividing the illumination source into pixel groups, each pixel group including one or more illumination source points in a pupil plane of the illumination source; changing a polarization state of each pixel group and determining an incremental effect on each of the plurality of critical dimensions resulting from the change of polarization state; calculating a first plurality of sensitivity coefficients for each of the plurality of critical dimensions using the determined incremental effects; selecting an initial illumination source; iteratively calculating a lithographic metric as a result of a change of polarization state using the calculated first plurality of sensitivity coefficients, the change of the polarization state of the pixel group in the initial illumination source creating a modified illumination source; and adjusting the initial illumination source based on the iterative results of calculations.

Abstract: A method of determining a relationship between a stochastic variation of a characteristic of an aerial image or a resist image and one or more design variables, the method including: measuring values of the characteristic from a plurality of aerial images and/or resist images for each of a plurality of sets of values of the one or more design variables; determining a value of the stochastic variation, for each of the plurality of sets of values of the one or more design variables, from a distribution of the values of the characteristic for that set of values of the one or more design variables; and determining the relationship by fitting one or more parameters from the values of the stochastic variation and the plurality of sets of values of the one or more design variables.

Abstract: Disclosed herein is a computer-implemented method for improving a lithographic process for imaging a portion of a design layout onto a substrate using a lithographic projection apparatus, the method comprising defining a multi-variable cost function, the multi-variable cost function being a function of a stochastic effect of the lithographic process.

Abstract: Disclosed herein is a computer-implemented method for improving a lithographic process for imaging a portion of a design layout onto a substrate using a lithographic projection apparatus, the method comprising defining a multi-variable cost function, the multi-variable cost function being a function of a stochastic effect of the lithographic process.

Abstract: An illumination system is disclosed having a polarization member that includes first and second polarization modifiers movable into at least partial intersection with a radiation beam such that the respective polarization modifier applies a modified polarization to at least part of the beam. The illumination system further includes an array of individually controllable reflective elements positioned to receive the radiation beam after it has passed the polarization member, and a controller configured to control movement of the first and second polarization modifiers such that the first and second polarization modifiers intersect with different portions of the radiation beam.

Abstract: An illumination system is disclosed having a polarization member that includes first and second polarization modifiers movable into at least partial intersection with a radiation beam such that the respective polarization modifier applies a modified polarization to at least part of the beam. The illumination system further includes an array of individually controllable reflective elements positioned to receive the radiation beam after it has passed the polarization member, and a controller configured to control movement of the first and second polarization modifiers such that the first and second polarization modifiers intersect with different portions of the radiation beam.

Abstract: Improved low k1 lithographic imaging is disclosed by optimizing or improving an illumination polarization condition. The polarization condition may be a pre-defined spatially varying polarization, or a spatially customized local polarization of bright illumination points based on tracking a value of a desired lithographic response. Several non-traditional polarization conditions, e.g., TM/TE polarization (with or without a central TM region), diagonal polarization, and Y+X polarization (typically for dark field illumination) are disclosed, that offer substantial imaging advantages for specific lithographic problems, especially at low k1 values. The initial polarization definition may be limited to specific fixed polarization angles.