Method of modeling a mask having patterns with arbitrary angles

1. A method, comprising:

receiving a mask layout;

generating a two-dimensional kernel based on a set of pre-selected mask layout samples;

applying the two-dimensional kernel to the mask layout to obtain a correction field for the mask layout, wherein the applying the two-dimensional kernel includes:

building an orientation map for the mask layout, the orientation map including an orientation angle φ for each edge segment of an edge of the mask layout, and

applying the two-dimensional kernel to the edge according to the orientation map;

determining a near field of the mask layout based at least in part on the correction field;

evaluating a simulated device layout based on the near field of the mask layout against a design rule;

refining the mask layout based on the evaluation; and

fabricating a wafer using a mask with the refined mask layout.

2. The method of claim 1 , wherein the mask layout contains a non-Manhattan pattern, and wherein the generating, the applying the two-dimensional kernel to the mask layout, the determining, and the evaluating are performed using the non-Manhattan pattern with a mask design system that is configured to manipulate an integrated circuit design layout according to a variety of design rules, wherein the variety of design rules includes the design rule.

3. The method of claim 1 , wherein the two-dimensional kernel is described using polar coordinates.

4. The method of claim 2 , wherein the building the orientation map for the mask layout includes identifying the edge by taking a gradient of the non-Manhattan pattern; and building the orientation map by determining the orientation angle φ of each edge segment according to a normal vector of the edge segment.

5. The method of claim 4 , wherein the applying the two-dimensional kernel according to the orientation map includes rotating the two-dimensional kernel according to the orientation angle for the edge segment; and applying the rotated two-dimensional kernel to the edge segment.

6. The method of claim 1 , further comprising: processing the mask layout, wherein the two-dimensional kernel is applied to the processed mask layout.

7. The method of claim 1 , further comprising: applying a thin mask model to the mask layout, and wherein the near field is determined as a function of the correction field of the mask layout having the thin mask model applied thereon.

8. The method of claim 1 , wherein the generating the two-dimensional kernel includes generating the two-dimensional kernel f(r, θ) as a function of a radial coordinate r and an angular coordinate θ, and as a sum of a plurality of components including at least h 0 (r) and h 1 (r) e iθ , and

wherein the applying the two-dimensional kernel includes, for each edge segment having the orientation angle φ, applying a rotated two-dimensional kernel, the rotated two-dimensional kernel including the two-dimensional kernel f (r, θ) convolved with a function of the orientation angle φ and including at least h 0 (r) and h 1 (r) e iθ e −iφ .

9. The method of claim 1 , wherein the generating further includes:

building a set of orientation maps, each associated with one sample of the set of pre-selected mask layout sample;

applying a thin mask model to a first sample of the set of pre-selected mask layout samples to obtain a thin mask near field;

computing a rigorous near field of the first sample;

computing a difference between the rigorous near field and the thin mask near field; and

regressing the difference against the set of orientation maps.

10. A method, comprising:

receiving a mask layout, the mask layout containing a non-Manhattan pattern;

processing the mask layout;

generating a two-dimensional kernel based on a set of processed pre-selected mask layout samples, wherein the two-dimensional kernels each have a respective rotational symmetry;

applying the two-dimensional kernel to an edge segment of the non-Manhattan pattern having an orientation angle φ to obtain a correction field for the non-Manhattan pattern represented by a modified kernel, wherein the modified kernel includes e −iφ ; and

determining a near field of the non-Manhattan pattern based at least in part on the correction field;

obtaining a final resist image of the non-Manhattan pattern based on the near field;

evaluating the final resist image against a design rule;

refining the mask layout based on the evaluation; and

fabricating a wafer using a mask with the refined mask layout.

11. The method of claim 10 , wherein the applying the two-dimensional kernel comprises identifying the edge segment of the non-Manhattan pattern by taking a gradient of the non-Manhattan pattern and identifying the orientation angle φ according to a normal vector of the edge segment.

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

13. The method of claim 10 , further comprising: applying a thin mask model to the mask layout, the thin mask model containing a binary modeling of the non-Manhattan pattern, wherein the near field is determined by combining the correction field and the mask layout having the thin mask model applied thereon.

14. The method of claim 10 , wherein the two-dimensional kernel includes components each having a rotational symmetry, wherein the generating includes building a pattern edge by taking a gradient of each of the set of processed pre-selected mask layout samples, and building an orientation map using a normal vector of a segment of the pattern edge.

15. The method of claim 14 , wherein each of the components is a function independent of the normal vector.

16. The method of claim 10 , wherein the two-dimensional kernel includes components h 0 (r) and h 1 (r) e iθ , wherein r is a radial coordinate, and θ is an angular coordinate, and wherein the correction field includes h 0 (r) and h 1 (r) e iθ e −iθ .

17. A method, comprising:

generating a two-dimensional kernel, wherein the generating includes:

receiving a processed pre-selected mark layout sample having a first non-Manhattan pattern;

identifying a first set of edges of the first non-Manhattan pattern and an orientation angle for each of the first set;

generating the two-dimensional kernel as a first function independent of the orientation angle for the each of the first set;

receiving a mask layout, the mask layout containing a second non-Manhattan pattern;

processing the mask layout;

identifying a second set of edges of the second non-Manhattan pattern and an orientation angle for each of the second set;

applying the two-dimensional kernel to each of the second set by convolving the two-dimensional kernel with a second function of the orientation angle for the each of the second set to obtain a correction field for the second non-Manhattan pattern;

applying a thin mask model to the second non-Manhattan pattern, the thin mask model containing a binary modeling of the second non-Manhattan pattern;

determining a near field of the second non-Manhattan pattern by applying the correction field to the second non-Manhattan pattern having the thin mask model applied thereon;

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

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

evaluating the final resist image against a design rule;

refining the mask layout based on the evaluation; and

fabricating a wafer using a mask with the refined mask layout.

18. The method of claim 17 , wherein the first function includes a plurality of components, each having a respective rotational symmetry and each being independent of the orientation angle for the each of the first set.

19. The method of claim 17 , wherein the two-dimensional kernel includes components h 0 (r) and h 1 (r) e iθ , wherein r is a radial coordinate, and θ is an angular coordinate, and wherein the correction field includes h 0 (r) and h 1 (r) e iθ e −iφ .

20. The method of claim 17 ,

wherein the generating the two-dimensional kernel as the first function includes generating components h 0 (r) and h 1 (r) e iθ , r being a radial coordinate, and θ being an angular coordinate, and

wherein the applying the two-dimensional kernel includes, for each edge segment having an orientation angle φ, applying a rotated two-dimensional kernel, the rotated two-dimensional kernel includes h 0 (r) and h 1 (r) e iθ e −iφ .