An optical proximity correction method includes designing a mask design. The designing of the mask design includes setting a reference point of the mask design, calculating a plurality of chief ray angles of a plurality of points of interest on the mask design, respectively, each of the plurality of points of interest having a corresponding distance from the reference point, finding, among the plurality of points of interest, a first point of interest having a maximum chief ray angle among the plurality of chief ray angles, a distance of the first point of interest from the reference point being set as a deteriorated distance, and compensating for distortion of an image to be transferred from a pattern located at the deteriorated distance from the reference point of the mask design.

A layout modification method for fabricating a semiconductor device is provided. The layout modification method includes calculating uniformity of critical dimensions of first and second portions in a patterned layer by using a layout for an exposure manufacturing process to produce the semiconductor device. A width of the first and second portions equals a penumbra size of the exposure manufacturing process. The penumbra size is utilized to indicate which area of the patterned layer is affected by light leakage exposure from another exposure manufacturing process. The layout modification method further includes compensating non-uniformity of the first and second portions of the patterned layer according to the uniformity of critical dimensions to generate a modified layout. The first portion is divided into a plurality of first sub-portions. The second portion is divided into a plurality of second sub-portions. Each second sub-portion is surrounded by two of the first sub-portions.

A layout modification method for fabricating a semiconductor device is provided. The layout modification method includes calculating uniformity of critical dimensions of first and second portions in a patterned layer by using a layout for an exposure manufacturing process to produce the semiconductor device. A width of the first and second portions equals a penumbra size of the exposure manufacturing process. The penumbra size is utilized to indicate which area of the patterned layer is affected by light leakage exposure from another exposure manufacturing process. The layout modification method further includes compensating non-uniformity of the first and second portions of the patterned layer according to the uniformity of critical dimensions to generate a modified layout. The first portion is divided into a plurality of first sub-portions. The second portion is divided into a plurality of second sub-portions. Each second sub-portion is surrounded by two of the first sub-portions.

In a method of manufacturing a photo mask used in a semiconductor manufacturing process, a mask pattern layout in which a plurality of patterns are arranged is acquired. The plurality of patterns are converted into a graph having nodes and links. It is determined whether the nodes are colorable by N colors without causing adjacent nodes connected by a link to be colored by a same color, where N is an integer equal to or more than 3. When it is determined that the nodes are colorable by N colors, the nodes are colored with the N colors. The plurality of patterns are classified into N groups based on the N colored nodes. The N groups are assigned to N photo masks. N data sets for the N photo masks are output.

In a method of manufacturing a photo mask used in a semiconductor manufacturing process, a mask pattern layout in which a plurality of patterns are arranged is acquired. The plurality of patterns are converted into a graph having nodes and links. It is determined whether the nodes are colorable by N colors without causing adjacent nodes connected by a link to be colored by a same color, where N is an integer equal to or more than 3. When it is determined that the nodes are colorable by N colors, the nodes are colored with the N colors. The plurality of patterns are classified into N groups based on the N colored nodes. The N groups are assigned to N photo masks. N data sets for the N photo masks are output.

A method includes determining topographic information of a substrate for use in a lithographic imaging system, determining or estimating, based on the topographic information, imaging error information for a plurality of points in an image field of the lithographic imaging system, adapting a design for a patterning device based on the imaging error information. In an embodiment, a plurality of locations for metrology targets is optimized based on imaging error information for a plurality of points in an image field of a lithographic imaging system, wherein the optimizing involves minimizing a cost function that describes the imaging error information. In an embodiment, locations are weighted based on differences in imaging requirements across the image field.

A design method of a metal mask, a manufacturing method of the metal mask and a computer-readable storage medium are provided. The design method of a metal mask includes: calculating amounts of deformations of the metal mask in two directions perpendicular to each other based on a stretching force of the metal mask in use and deformation properties of the metal mask in the two directions; and compensating the deformations of the metal mask in the two directions by compensation amounts for the deformations, which are identical and opposite to the amounts of the deformations of the metal mask in the two directions, respectively.

A design method of a metal mask, a manufacturing method of the metal mask and a computer-readable storage medium are provided. The design method of a metal mask includes: calculating amounts of deformations of the metal mask in two directions perpendicular to each other based on a stretching force of the metal mask in use and deformation properties of the metal mask in the two directions; and compensating the deformations of the metal mask in the two directions by compensation amounts for the deformations, which are identical and opposite to the amounts of the deformations of the metal mask in the two directions, respectively.

A method for determining an etch profile is described. The method includes determining a masking layer profile. Loading information can be determined. The loading information indicates dependence of an etch rate for the masking layer profile on a quantity and pattern of material being etched. Flux information can be determined. The flux information indicates dependence of the etch rate on an intensity and a spread angle of radiation incident on the masking layer profile. Re-deposition information can be determined. The re-deposition information indicates dependence of the etch rate on an amount of material removed from the masking layer profile that is re-deposited back on the masking layer profile. An output etch profile for the layer of the wafer is determined based on the loading information, the flux information, and/or the re-deposition information.

A method for determining an etch profile is described. The method includes determining a masking layer profile. Loading information can be determined. The loading information indicates dependence of an etch rate for the masking layer profile on a quantity and pattern of material being etched. Flux information can be determined. The flux information indicates dependence of the etch rate on an intensity and a spread angle of radiation incident on the masking layer profile. Re-deposition information can be determined. The re-deposition information indicates dependence of the etch rate on an amount of material removed from the masking layer profile that is re-deposited back on the masking layer profile. An output etch profile for the layer of the wafer is determined based on the loading information, the flux information, and/or the re-deposition information.