Mask fabrication effects in three-dimensional mask simulations using feature images
Feature images representing a layout geometry of a lithographic mask are received. Mask function (MF) contributions from individual feature images are calculated by convolving the feature image with a corresponding three-dimensional mask (M3D) filter. The M3D filters represent an electromagnetic scattering effect of that feature image. At least one M3D filter also accounts for effects arising from a fabrication process for the lithographic mask.
1 . A method comprising:
receiving feature images that are images representing geometric features present in a layout geometry of a lithographic mask;
calculating, by a processor device, a mask function (MF) contribution from the feature images by convolving each feature image with a corresponding three-dimensional mask (M3D) filter; wherein the M3D filter represents an electromagnetic scattering effect of that feature image, and at least one M3D filter is a mask-corrected M3D filter that also accounts for effects arising from a mask fabrication process for the lithographic mask by applying a spatial shift, an additive constant or a multiplicative constant to an uncorrected version of the M 3 D filter.
2 . The method of claim 1 wherein the mask-corrected M3D filter includes a parameter for the spatial shift, additive constant or multiplicative constant and the parameter of the mask-corrected M3D filter is tuned based on a measurement of a wafer fabricated using a lithographic mask that was fabricated using the mask fabrication process.
3 . The method of claim 2 wherein the mask-corrected M3D filter is an area filter, and the parameter for the area filter is the additive constant or the multiplicative constant.
4 . The method of claim 2 wherein the mask-corrected M3D filter is a single-edge filter, and the parameter for the single-edge filter is the spatial shift.
5 . The method of claim 2 wherein the mask-corrected M3D filter is an edge-to-edge filter, and the parameter for the edge-to-edge filter is the spatial shift.
6 . The method of claim 1 further comprising:
determining a mask function for the lithographic mask based on a combination of the calculated MF contributions;
using the mask function to estimate a result comprising an aerial image or a printed mask pattern produced by the lithographic mask; and
applying a mask correction to a design of the lithographic mask based on the estimated result; wherein the mask correction comprises at least one of optical proximity correction, sub-resolution assist features, phase shifting masks, and inverse lithography techniques.
7 . A non-transitory computer readable medium comprising stored instructions, which when executed by a processor device, cause the processor device to:
access uncorrected versions of mask 3D (M3D) filters corresponding to feature images; wherein the feature images are images that represent geometric features present in layout geometries of lithographic masks, and the uncorrected versions of the M3D filters represent an electromagnetic scattering effect of the feature images; and
modifying, by a processor device, the uncorrected versions of the M3D filters to produce mask-corrected M3D filters that account for effects arising from the mask fabrication process for the lithographic mask by applying spatial shifts, additive constants and/or multiplicative constants to the uncorrected versions of the M3D filters.
8 . The non-transitory computer readable medium of claim 7 wherein modifying the uncorrected versions of the M3D filters comprises:
accessing measurements of wafers fabricated using lithographic masks that were fabricated using the mask fabrication process; and
modifying the uncorrected versions of the M3D filters based on the measurements of wafers.
9 . The non-transitory computer readable medium of claim 8 wherein modifying the uncorrected versions of the M3D filters comprises: modifying the uncorrected versions of the M3D filters based on matching (a) results predicted by a simulation of wafers using candidate mask-corrected M3D filters; and (b) the measurements of wafers.
10 . The non-transitory computer readable medium of claim 7 wherein modifying the uncorrected versions of the M3D filters comprises: modifying the uncorrected versions of the M3D filters based on matching (a) results predicted by a simulation of wafers using candidate mask-corrected M3D filters; and (b) results predicted by a simulation of wafers in which models for wafer structures include fabrication effects arising from the mask fabrication process.
11 . The non-transitory computer readable medium of claim 7 wherein the lithographic mask includes a feature with a sidewall, the feature images representing the mask feature include a single-edge image and/or a multi-edge image, and modifying the uncorrected versions of the M3D filters comprises shifting the uncorrected versions of the M3D filter(s) for those feature image(s) to account for variation in an angle of the sidewall.
12 . The non-transitory computer readable medium of claim 7 wherein the lithographic mask includes a film stack, the feature images representing the film stack include a single-edge image and/or a multi-edge image, and modifying the uncorrected versions of the M3D filters comprises shifting the uncorrected versions of the M3D filter(s) for those feature image(s) to account for variation in thickness of the film stack.
13 . The non-transitory computer readable medium of claim 7 wherein the lithographic mask includes an absorber characterized by an index of refraction and a dielectric constant, the feature images representing the absorber include a single-edge image and/or a multi-edge image, and modifying the uncorrected versions of the M3D filters comprises shifting the uncorrected versions of the M3D filter(s) for those feature image(s) to account for variation in the index of refraction or dielectric constant.
14 . The non-transitory computer readable medium of claim 7 wherein the feature images include a single-edge image and/or a multi-edge image, and modifying the uncorrected versions of the M3D filters comprises applying a feature-dependent shifting to the uncorrected versions of the M3D filter(s) for those feature image(s) to account for short range proximity effects in the fabrication process for the lithographic mask.
15 . A system comprising:
a computer readable storage medium storing instructions and a library containing predefined feature images and corresponding precalculated mask 3D (M3D) filters; wherein the feature images are images that represent geometric features present in layout geometries of lithographic masks, the M3D filter represents an electromagnetic scattering effect of that feature image and at least one M3D filter is a mask-corrected M3D filter that also accounts for effects arising from a mask fabrication process for the lithographic mask by applying a spatial shift, an additive constant or a multiplicative constant to an uncorrected version of the M3D filter; 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 a layout geometry of a lithographic mask into a plurality of feature images based on the predefined feature images contained in the library;
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; and
combine the calculated MF contributions to determine a mask function for the lithographic mask.
16 . The system of claim 15 further comprising: applying the mask function as input to an Abbe imaging model or Hopkins imaging model.
17 . The system of claim 15 wherein the layout geometry comprises a layout geometry for an entire integrated circuit die.
18 . The system of claim 15 wherein a source illumination of the lithographic mask is an extreme ultraviolet (EUV) or deep ultraviolet (DUV) illumination.
19 . The system of claim 15 wherein the layout geometry comprises a plurality of shapes, and the feature images representing each shape include not more than area images, single-edge images, and two-edge images.