Method of modeling a mask by taking into account of mask pattern edge interaction

1. A method, comprising:

receiving a mask layout that includes one or more non-Manhattan patterns, wherein the one or more non-Manhattan patterns includes two or more curvilinear edges, wherein the mask layout includes a plurality of pixels, and wherein a subset of the pixels are edge pixels that are located on the two or more curvilinear edges;

applying an interaction-free mask model to the mask layout;

applying an edge interaction model to at least the one or more non-Manhattan patterns of the mask layout, the edge interaction model describing an influence exerted on each of the plurality of pixels due to a plurality of combinations of the edge pixels of the two or more curvilinear edges interacting with one another;

applying a thin mask model to the mask layout; and

determining a near field based on the applying of the interaction-free mask model, the applying of the edge interaction model, and the applying of the thin mask model.

2. The method of claim 1 , further comprising: identifying the edge pixels by taking a normal vector of each of a plurality of segments of the two or more curvilinear edges.

3. The method of claim 1 , wherein the applying the edge interaction model comprises:

dividing the mask layout into a plurality of tiles;

computing an edge interaction correction for each of the tiles; and

determining a total edge interaction correction for an entirety of the mask layout by combining the edge interaction correction from each of the tiles.

4. The method of claim 3 , wherein:

the computing the edge interaction correction comprises computing a plurality of kernels; and

the kernels each describe a correction field at an influenced pixel due to an interaction between two or more of the edge pixels.

5. The method of claim 4 , wherein the computing the plurality of kernels comprises computing each of the kernels as a function of: a location of the influenced pixel, a respective location of each of the two or more of the edge pixels, and a respective orientation angle associated with each of the two or more of the edge pixels.

6. The method of claim 3 , wherein the dividing comprises: adding a margin of interaction length to each of the tiles.

7. The method of claim 1 , wherein the one or more non-Manhattan patterns have angles other than 0 degrees, 90 degrees, 180 degrees, or 270 degrees.

8. The method of claim 1 , wherein the two or more curvilinear edges interacting with one another are located within a predefined proximity to one another.

9. The method of claim 1 , further comprising: processing the mask layout, wherein the applying of the interaction-free mask model, the applying of the edge interaction model, and the applying of the thin mask model are performed to the processed mask layout.

10. The method of claim 9 , wherein the processing the mask layout comprises performing rasterization or anti-aliasing filtering to the mask layout.

11. The method of claim 1 , wherein the thin mask model contains binary modeling of patterns on the mask layout.

12. The method of claim 1 , further comprising:

applying an optical model to the near field to obtain an aerial image on a wafer; and

applying a resist model to the aerial image to obtain a final resist image on the wafer.

13. A method, comprising:

receiving a mask layout, the mask layout including one or more non-Manhattan patterns that each have two or more curvilinear edge segments, wherein the mask layout includes a plurality of pixels;

identifying, from the plurality of pixels, a plurality of edge pixels that are located on the two or more curvilinear edge segments, wherein the identifying comprise taking a normal vector of each of the two or more curvilinear edge segments;

applying an interaction-free mask model to the received mask layout;

generating an edge interaction model with a set of pre-selected mask layout samples, wherein the generating comprises determining an influence exerted to each of the plurality of pixels of the mask layout samples by a plurality of combinations of the edge pixels;

applying the edge interaction model to at least the one or more non-Manhattan patterns of the received mask layout;

applying a thin mask model to the received mask layout; and

determining a near field of the received mask layout based on the applying of the interaction-free mask model, the applying of the edge interaction model, and the applying of the thin mask model.

14. The method of claim 13 , wherein the generating the edge interaction model comprises:

dividing the mask layout samples into a plurality of tiles;

computing an edge interaction field for each of the tiles by computing a plurality of kernels, wherein the kernels each describe a correction field at an influenced pixel due to an interaction between two or more of the edge pixels; and

determining one or more edge interaction kernels for a tile.

15. The method of claim 14 , wherein the computing the plurality of kernels comprises computing each of the kernels as a function of: a location of the influenced pixel, a respective location of each of the two or more of the edge pixels, and a respective orientation angle associated with each of the two or more of the edge pixels.

16. The method of claim 14 , wherein the dividing comprises: adding a margin of interaction length to each of the tiles.

17. The method of claim 13 , further comprising:

processing the received mask layout at least in part by performing rasterization or anti-aliasing filtering to the received mask layout, wherein the applying of the interaction-free mask model, the applying of the edge interaction model, and the applying of the thin mask model are performed to the processed received mask layout;

applying an optical model to the near field to obtain an aerial image of the received mask layout on a wafer; and

applying a resist model to the aerial image to obtain a final resist image on the wafer.

18. A method, comprising:

receiving a mask layout, the mask layout including one or more non-Manhattan patterns that each have two or more curvilinear edges, wherein the mask layout includes a plurality of pixels;

processing the received mask layout, including identifying a plurality of edge pixels that are located on the two or more curvilinear edges, wherein the identifying includes taking a normal vector of each of a plurality of segments of the two or more curvilinear edges;

applying an interaction-free mask model to the processed received mask layout;

generating an edge interaction model with a set of pre-selected mask layout samples, wherein the generating comprises computing a plurality of kernels that each describe a correction field at an influenced pixel of the plurality of pixels due to an interaction between a plurality of different combinations of the edge pixels;

applying the edge interaction model to the one or more non-Manhattan patterns of the processed received mask layout;

applying a thin mask model to the processed received mask layout;

determining a near field of the received mask layout based on the applying of the interaction-free mask model, the applying of the edge interaction model, and the applying of the thin mask model;

applying an optical model to the near field to obtain an aerial image of the received mask layout on a wafer; and

applying a resist model to the aerial image to obtain a final resist image on the wafer.

19. The method of claim 18 , wherein the generating the edge interaction model comprises:

dividing the mask layout samples into a plurality of tiles, the tiles each being surrounded by a margin of interaction length; and

determining the edge interaction model for a tile.

20. The method of claim 18 , wherein the computing the plurality of kernels comprises computing each of the kernels as a function of: a location of the influenced pixel, a respective location of each of the different combinations of the edge pixels, and a respective orientation angle associated with each of the different combinations of the edge pixels.