Abstract: Methods, computer program products and apparatuses for optimizing design rules for producing a mask are disclosed, while keeping the optical conditions (including but not limited to illumination shape, projection optics numerical aperture (NA) etc.) fixed. A cross-correlation function is created by multiplying the diffraction order functions of the mask patterns with the eigenfunctions from singular value decomposition (SVD) of a TCC matrix. The diffraction order functions are calculated for the original design rule set, i.e., using the unperturbed condition. ILS is calculated at an edge of a calculated image of a critical polygon using the cross-correlation results and using translation properties of a Fourier transform. Once an optimum separation is calculated, it is incorporated into the design rule to optimize the mask layout for improved ILS throughout the mask.

Abstract: Methods, computer program products and apparatuses for optimizing design rules for producing a mask are disclosed, while keeping the optical conditions (including but not limited to illumination shape, projection optics numerical aperture (NA) etc.) fixed. A cross-correlation function is created by multiplying the diffraction order functions of the mask patterns with the eigenfunctions from singular value decomposition (SVD) of a TCC matrix. The diffraction order functions are calculated for the original design rule set, i.e., using the unperturbed condition. ILS is calculated at an edge of a calculated image of a critical polygon using the cross-correlation results and using translation properties of a Fourier transform. Once an optimum separation is calculated, it is incorporated into the design rule to optimize the mask layout for improved ILS throughout the mask.

Abstract: A method of decomposing a target pattern having features to be imaged on a substrate so as to allow said features to be imaged in a multi-exposure process. The method includes the steps of: segmenting a plurality of the features into a plurality of polygons; determining the image log slope (ILS) value for each of the plurality of polygons; determining the polygon having the minimum ILS value, and defining a mask containing the polygon; convolving the defined mask with an eigen function of a transmission cross coefficient so as to generate an interference map, where the transmission cross coefficient defines the illumination system to be utilized to image the target pattern; and, assigning a phase to the polygon based on the value of the interference map at a location corresponding to the polygon, where the phase defines which exposure in said multi-exposure process the polygon is assigned.

Abstract: Methods, computer program products and apparatuses for optimizing design rules for producing a mask are disclosed, while keeping the optical conditions (including but not limited to illumination shape, projection optics numerical aperture (NA) etc.) fixed. A cross-correlation function is created by multiplying the diffraction order functions of the mask patterns with the eigenfunctions from singular value decomposition (SVD) of a TCC matrix. The diffraction order functions are calculated for the original design rule set, i.e., using the unperturbed condition. ILS is calculated at an edge of a calculated image of a critical polygon using the cross-correlation results and using translation properties of a Fourier transform. The use of the calculated cross-correlation of the mask and the optical system, and the translation property of the Fourier transform for perturbing the design reduces the computation time needed for determining required changes in the design rules.

Abstract: A method for decomposing a target pattern containing features to be printed on a wafer into multiple patterns. The method includes the steps of segmenting the target pattern into a plurality of patches; identifying critical features within each patch which violate minimum spacing requirements; generating a critical group graph for each of the plurality of patches having critical features, where the critical group graph of a given patch defines a coloring scheme of the critical features within the given patch, and the critical group graph identifies critical features extending into adjacent patches to the given patch; generating a global critical group graph for the target pattern, where the global critical group graph includes the critical group graphs of each of the plurality of patches, and an identification of the features extending into adjacent patches; and coloring the target pattern based on the coloring scheme defined by the global critical group graph.

Abstract: The Hessian (second derivative) of the image log slope (ILS) can be quickly and accurately calculated without the need to use approximate methods from the gradient of the ILS with respect to mask transmission and source intensity. The Hessian has been traditionally calculated using a finite-difference approach. Calculating the Hessian through a finite-difference approach is slow and is an approximate method. The gradient of the ILS improves the speed of calculation of the Hessian, and thus accelerated SMO operation is realized. The results of ILS evaluation can be used in design for manufacturing (DFM) to suggest changes in the design rules to improve imaging. For a fixed illumination, this information can help remove forbidden pitches and help select design rules for 1-D and 2-D patterns on a mask design layout.

Abstract: A method of decomposing a target pattern having features to be imaged on a substrate so as to allow said features to be imaged in a multi-exposure process. The method includes the steps of: (a) dividing a plurality of the features into a plurality of segments; (b) determining the image log slope (ILS) value for each of the plurality of segments; (c) determining the value of the gradient of the image log slope (ILS) value for each of the plurality of segments; and (d) assigning a phase or color to the segments based on the values of the gradient of the image log slope of each of the plurality of segments.

Abstract: A method of decomposing a target pattern containing features to be imaged onto a substrate into a plurality of exposure patterns for use in a multi-exposure process. The method includes dividing the target pattern into fragments; associating the fragments with an exposure pattern; associating the fragments with image log slope (ILS) evaluation points; and maximizing ILS values. Maximizing the ILS values further includes calculating ILS values at the ILS evaluation points; determining a minimum ILS value; calculating changes in the ILS values as a result of associating fragments with a different exposure pattern; determining a maximum change of the ILS values; and associating fragments associated with the maximum change with a different exposure pattern.

Abstract: A method of decomposing a target pattern having features to be imaged on a substrate so as to allow said features to be imaged in a multi-exposure process. The method includes the steps of: segmenting a plurality of the features into a plurality of polygons; determining the image log slope (ILS) value for each of the plurality of polygons; determining the polygon having the minimum ILS value, and defining a mask containing the polygon; convolving the defined mask with an eigen function of a transmission cross coefficient so as to generate an interference map, where the transmission cross coefficient defines the illumination system to be utilized to image the target pattern; and, assigning a phase to the polygon based on the value of the interference map at a location corresponding to the polygon, where the phase defines which exposure in said multi-exposure process the polygon is assigned.

Abstract: A method of decomposing a target pattern having features to be imaged on a substrate so as to allow said features to be imaged in a multi-exposure process. The method includes the steps of: (a) segmenting a plurality of the features into a plurality of polygons; (b) determining the image log slope (ILS) value for each of the plurality of polygons; (c) determining the polygon having the minimum ILS value, and defining a mask containing the polygon; (d) convolving the mask defined in step (c) with an eigen function of a transmission cross coefficient so as to generate an interference map, where the transmission cross coefficient defines the illumination system to be utilized to image the target pattern; and (e) assigning a phase to the polygon based on the value of the interference map at a location corresponding to the polygon, where the phase defines which exposure in said multiexposure process the polygon is assigned.

Abstract: Methods, computer program products and apparatuses for optimizing design rules for producing a mask are disclosed, while keeping the optical conditions (including but not limited to illumination shape, projection optics numerical aperture (NA) etc.) fixed. A cross-correlation function is created by multiplying the diffraction order functions of the mask patterns with the eigenfunctions from singular value decomposition (SVD) of a TCC matrix. The diffraction order functions are calculated for the original design rule set, i.e., using the unperturbed condition. ILS is calculated at an edge of a calculated image of a critical polygon using the cross-correlation results and using translation properties of a Fourier transform. The use of the calculated cross-correlation of the mask and the optical system, and the translation property of the Fourier transform for perturbing the design reduces the computation time needed for determining required changes in the design rules.

Abstract: A method of decomposing a target pattern containing features to be imaged onto a substrate into a plurality of exposure patterns for use in a multi-exposure process. The method includes dividing the target pattern into fragments; associating the fragments with an exposure pattern; associating the fragments with image log slope (ILS) evaluation points; and maximizing ILS values. Maximizing the ILS values further includes calculating ILS values at the ILS evaluation points; determining a minimum ILS value; calculating changes in the ILS values as a result of associating fragments with a different exposure pattern; determining a maximum change of the ILS values; and associating fragments associated with the maximum change with a different exposure pattern.

Abstract: A method of decomposing a target pattern having features to be imaged on a substrate so as to allow said features to be imaged in a multi-exposure process. The method includes the steps of: (a) dividing a plurality of the features into a plurality of segments; (b) determining the image log slope (ILS) value for each of the plurality of segments; (c) determining the value of the gradient of the image log slope (ILS) value for each of the plurality of segments; and (d) assigning a phase or color to the segments based on the values of the gradient of the image log slope of each of the plurality of segments.

Abstract: Disclosed concepts include a method of optimizing an illumination profile of a pattern to be formed in a surface of a substrate. Illumination is optimized by defining a transmission cross coefficient (“TCC”) function determined in accordance with an illumination pupil and a projection pupil corresponding to an illuminator, representing at least one resolvable feature of a mask to be printed on the substrate by at least one impulse function, and creating an interference map of a predetermined order based on the at least one impulse function and the TCC function, wherein the interference map represents the at least one resolvable feature to be printed on the substrate and areas of destructive interference.

Abstract: A method of transferring an image of a pattern layout onto a surface of a substrate including selecting a first illumination profile for a first area of the pattern layout and a second illumination profile for a second area of the pattern layout; switching illumination profile during transfer of the image of the pattern layout such that the first area of the pattern layout is illuminated with the first illumination profile and the second area is illuminated with the second illumination profile; and projecting an image of the illuminated first and second areas onto the surface of the substrate.

Abstract: A method of decomposing a target pattern having features to be imaged on a substrate so as to allow said features to be imaged in a multi-exposure process. The method includes the steps of: (a) segmenting a plurality of the features into a plurality of polygons; (b) determining the image log slope (ILS) value for each of the plurality of polygons; (c) determining the polygon having the minimum ILS value, and defining a mask containing the polygon; (d) convolving the mask defined in step (c) with an eigen function of a transmission cross coefficient so as to generate an interference map, where the transmission cross coefficient defines the illumination system to be utilized to image the target pattern; and (e) assigning a phase to the polygon based on the value of the interference map at a location corresponding to the polygon, where the phase defines which exposure in said multiexposure process the polygon is assigned.

Abstract: Disclosed concepts include a method of, and program product for, optimizing an illumination profile of a pattern to be formed in a surface of a substrate relative to a given mask. Steps include mathematically representing resolvable feature(s) from the given mask, generating an interference map representation from the previous step, modifying the interference map representation to maximize intensity corresponding to the resolvable features, and determining assist feature size(s) such that intensity side lobes do not print.

Abstract: A method of decomposing a target pattern having features to be imaged on a substrate so as to allow said features to be imaged in a multi-exposure process. The method includes the steps of: (a) segmenting a plurality of the features into a plurality of polygons; (b) determining the image log slope (ILS) value for each of the plurality of polygons; (c) determining the polygon having the minimum ILS value, and defining a mask containing the polygon; (d) convolving the mask defined in step (c) with an eigen function of a transmission cross coefficient so as to generate an interference map, where the transmission cross coefficient defines the illumination system to be utilized to image the target pattern; and (e) assigning a phase to the polygon based on the value of the interference map at a location corresponding to the polygon, where the phase defines which exposure in said multi-exposure process the polygon is assigned.

Abstract: An apparatus and method for providing a variable illumination field for use in lithographic imaging for semiconductor manufacturing includes providing a an illumination system including a variable optical element having an array of addressable elements, each addressable element constructed and arranged to have a variable transmittance.

Abstract: A method of decomposing a target pattern having features to be imaged on a substrate so as to allow said features to be imaged in a multi-exposure process. The method includes the steps of: (a) segmenting a plurality of the features into a plurality of polygons; (b) determining the image log slope (ILS) value for each of the plurality of polygons; (c) determining the polygon having the minimum ILS value, and defining a mask containing the polygon; (d) convolving the mask defined in step (c) with an eigen function of a transmission cross coefficient so as to generate an interference map, where the transmission cross coefficient defines the illumination system to be utilized to image the target pattern; and (e) assigning a phase to the polygon based on the value of the interference map at a location corresponding to the polygon, where the phase defines which exposure in said multi-exposure process the polygon is assigned.