Mask corner rounding effects in three-dimensional mask simulations using feature images
A layout geometry of a lithographic mask is received. The layout geometry includes at least one shape having one or more rounded corners. The layout geometry is partitioned into a plurality of feature images, for example as selected from a library. The feature images include at least one mask corner rounding (MCR)-corrected feature image that accounts for the rounded corners of the shape. The feature images have corresponding mask 3D (M3D) filters, which represent the electromagnetic scattering effect of that feature image for a given source illumination. The mask function contribution from each of the feature images is calculated by convolving the feature image with its corresponding M3D filter. The mask function contributions are combined to determine a mask function for the mask illuminated by the source illumination.
1 . A method comprising:
receiving a layout geometry of a lithographic mask, the layout geometry including at least one shape having one or more rounded corners;
partitioning, by one or more processors, the layout geometry into a plurality of feature images; wherein the feature images comprise at least one mask corner rounding (MCR)-corrected feature image that accounts for the rounded corners of the shape, and the MCR-corrected feature image is a sum of a polygon-based feature image for the shape plus an image that accounts for the rounded corners of the shape;
calculating a mask function (MF) contribution from each of the plurality of feature images by convolving the feature image with a corresponding mask 3D (M3D) filter; wherein the M3D filter corresponding to each feature image represents an electromagnetic scattering effect of that feature image, and the M3D filter for the MCR-corrected feature image is the same as an M3D filter for the corresponding polygon-based feature image; and
determining a mask function for the lithographic mask based on a combination of the calculated MF contributions.
2 . The method of claim 1 wherein a correction for the at least one polygon-based feature image is parameterized by an angle of the rounded corners and a curvature of the rounded corners.
3 . The method of claim 1 wherein a correction for the at least one polygon-based feature images is determined by a rigorous electromagnetic simulation of the scattering effects of mask structures based on the feature image with rounded corners illuminated by a source illumination.
4 . The method of claim 1 wherein partitioning the layout geometry into a plurality of feature images comprises:
partitioning the layout geometry into a plurality of polygon-based feature images; and
for at least one shape with rounded corners, correcting all of the polygon-based feature images for that shape to produce MCR-corrected feature images for that shape.
5 . The method of claim 4 wherein the feature images for that shape consist of an area image, one or more single-edge images, and multiple multi-edge images.
6 . The method of claim 1 further comprising:
applying the mask function as input to an Abbe imaging model or Hopkins imaging model.
7 . The method of claim 1 wherein the layout geometry comprises a layout geometry for an entire chip.
8 . The method of claim 1 wherein a source illumination of the lithographic mask is an extreme ultraviolet (EUV) or deep ultraviolet (DUV) illumination.
9 . A system comprising:
a computer readable storage medium storing instructions and a library containing predefined feature images and corresponding precalculated mask 3D (M3D) filters; and
a processor device, coupled with the computer readable storage medium and to execute the instructions, the instructions when executed cause the processor device to:
partition shapes of a layout geometry of a lithographic mask into a plurality of feature images based on the predefined feature images contained in the library, the plurality of feature images including at least one MCR-corrected feature image, wherein the MCR-corrected feature image is a sum of a polygon-based feature image for the shape plus an image that accounts for rounded corners of the shape;
calculate mask function (MF) contributions from each of the plurality of feature images by convolving the feature image with the corresponding M3D filter from the library, wherein the M3D filter for the MCR-corrected feature image is the same as an M3D filter for the corresponding polygon-based feature image; and
combine the calculated MF contributions to determine a mask function for the lithographic mask.
10 . The system of claim 9 wherein the feature images are contained in one or more lookup tables, and partitioning the layout geometry and calculating the MF contributions comprises:
selecting feature images and corresponding M3D filters from the lookup tables.
11 . The system of claim 9 wherein the predefined feature images in the library comprise feature images that account for rounded inner corners, rounded outer corners, different angles of rounded corners, and different curvatures of the rounded corners.
12 . The system of claim 9 wherein the predefined feature images in the library comprise an area image, one or more single-edge images, and multiple multi-edge images that are based on sharp corners; and an area image, one or more single-edge images, and multiple multi-edge images that account for rounded corners.
13 . A non-transitory computer readable medium comprising stored instructions, which when executed by a processor device, cause the processor device to:
receive a layout geometry of a lithographic mask, the layout geometry including at least one shape having one or more rounded corners;
partition the layout geometry into a plurality of feature images, wherein the plurality of feature images comprise at least one feature image that accounts for the rounded corners of the shape, and the MCR-corrected feature image is a sum of a polygon-based feature image for the shape plus an image that accounts for the rounded corners of the shape;
calculate a mask function (MF) contribution from each of the plurality of feature images by convolving the feature image with a corresponding mask 3D (M3D) filter, wherein the M3D filter corresponding to each feature image represents an electromagnetic scattering effect of that feature image, and the M3D filter for the MCR-corrected feature image is the same as an M3D filter for the corresponding polygon-based feature image; and
determine a mask function for the lithographic mask based on a combination of the calculated MF contributions.
14 . The computer readable medium of claim 13 wherein partitioning the layout geometry and calculating the mask function (MF) contribution are based on a library of predefined feature images and corresponding precalculated mask 3D (M3D) filters.
15 . The computer readable medium of claim 13 wherein the plurality of feature images comprise an area image, one or more single-edge images, and multiple multi-edge images.