A mask data generation method including: calculating first evaluation value of projection image based on first mask data in which first value or second value different from first value is set for each of a plurality of unit elements that constitute 2-dimensional grid; generating second mask data by changing value of first unit element to which first value is set to second value and by changing value of second unit element which is disposed close to first unit element on 2-dimensional grid and to which second value is set to first value, among the plurality of unit elements included in the first mask data; calculating second evaluation value of projection image based on the second mask data; and comparing the first evaluation value and the second evaluation value and selecting either the first mask data or the second mask data as output mask data based on the comparison result.

A mask data generation method including: calculating first evaluation value of projection image based on first mask data in which first value or second value different from first value is set for each of a plurality of unit elements that constitute 2-dimensional grid; generating second mask data by changing value of first unit element to which first value is set to second value and by changing value of second unit element which is disposed close to first unit element on 2-dimensional grid and to which second value is set to first value, among the plurality of unit elements included in the first mask data; calculating second evaluation value of projection image based on the second mask data; and comparing the first evaluation value and the second evaluation value and selecting either the first mask data or the second mask data as output mask data based on the comparison result.

Aspects of the invention include systems and methods configured to provide hierarchical circuit designs that makes use of a color decomposition of library cells having boundary-aware color selection. A non-limiting example computer-implemented method includes placing a plurality of shapes within a hierarchical level of a chip design. The plurality of shapes can include a top boundary shape, a bottom boundary shape, one or more center boundary shapes, and one or more internal shapes. A hierarchical hand-off region is constructed by pinning the top boundary shape to a first mask, pinning the bottom boundary shape to a second mask, and pinning the one or more center boundary shapes to a same mask. The same mask is selected from one of the first mask and the second mask.

Aspects of the invention include systems and methods configured to provide hierarchical circuit designs that makes use of a color decomposition of library cells having boundary-aware color selection. A non-limiting example computer-implemented method includes placing a plurality of shapes within a hierarchical level of a chip design. The plurality of shapes can include a top boundary shape, a bottom boundary shape, one or more center boundary shapes, and one or more internal shapes. A hierarchical hand-off region is constructed by pinning the top boundary shape to a first mask, pinning the bottom boundary shape to a second mask, and pinning the one or more center boundary shapes to a same mask. The same mask is selected from one of the first mask and the second mask.

A process of overlay offset measurement includes providing a substrate; forming a first pattern layer with a predetermined first pattern on the substrate; forming a first photoresist layer on the substrate and the first pattern layer; forming a second photoresist layer on the first photoresist layer; forming a second pattern layer with a predetermined second pattern on the second photoresist layer; patterning the second photoresist layer to form a trench having a predetermined third pattern being substantially aligned with the predetermined first pattern of the first pattern layer; and performing overlay offset measurement according to the second pattern layer and the trench.

A process of overlay offset measurement includes providing a substrate; forming a first pattern layer with a predetermined first pattern on the substrate; forming a first photoresist layer on the substrate and the first pattern layer; forming a second photoresist layer on the first photoresist layer; forming a second pattern layer with a predetermined second pattern on the second photoresist layer; patterning the second photoresist layer to form a trench having a predetermined third pattern being substantially aligned with the predetermined first pattern of the first pattern layer; and performing overlay offset measurement according to the second pattern layer and the trench.

According to one embodiment, a pattern inspection method includes detecting a region of a photomask having a pattern that differs from a corresponding design, acquiring an exposure focus shift information including an exposure focus shift amount of a portion of a substrate corresponding to the detected region of the photomask. The exposure focus shift amount for the detected region is acquired from the exposure focus shift information, and then a pass/fail determination for the detected region is performed based on an estimated pattern to be formed on the substrate.

A method of determining a mask pattern for a target pattern to be printed on a substrate. The method includes partitioning a portion of a design layout including the target pattern into a plurality of cells with reference to a given location on the target pattern; assigning a plurality of variables within a particular cell of the plurality of cells, the particular cell including the target pattern or a portion thereof; and determining, based on values of the plurality of variables, the mask pattern for the target pattern such that a performance metric of a patterning process utilizing the mask pattern is within a desired performance range.

A method of determining a mask pattern for a target pattern to be printed on a substrate. The method includes partitioning a portion of a design layout including the target pattern into a plurality of cells with reference to a given location on the target pattern; assigning a plurality of variables within a particular cell of the plurality of cells, the particular cell including the target pattern or a portion thereof; and determining, based on values of the plurality of variables, the mask pattern for the target pattern such that a performance metric of a patterning process utilizing the mask pattern is within a desired performance range.

A method of manufacturing a semiconductor device includes forming M_1st segments in a first metallization layer including: forming first and second M_1st segments for which corresponding long axes extend in a first direction and are substantially collinear, the first and second M_1st segments being free from another instance of M_1st segment being between the first and second M_1st segments; and (A) where the first and second M_1st segments are designated for corresponding voltage values having a difference equal to or less than a reference value, separating the first and second M_1st segments by a first gap; or (B) where the first and second M_1st segments are designated for corresponding voltage values having a difference greater than the reference value, separating the first and second M_1st segments by a second gap, a second size of the second gap being greater than a first size of the first gap.