Mask pattern generation based on fast marching method

1. A method for determining a binary mask pattern from a pixelated mask pattern, the method comprising:

determining, by a hardware processor and based on a fast marching method (FMM), arrival values for pixels of a portion of the pixelated mask pattern;

determining the binary mask pattern based on the arrival values determined based on the FMM; and

updating at least one of the arrival values based on a comparison between a design pattern corresponding to the pixelated mask pattern and a substrate pattern simulated based on the binary mask pattern.

2. The method of claim 1 , wherein the comparison between the design pattern and the substrate pattern further comprises determining an evaluation value based on at least one selected from: an edge placement error (EPE) of the substrate pattern, a nominal process window condition, a mask error enhancement factor (MEEF), and/or a side-lobe printing indication value indicative of a possibility of side-lobe printing in the substrate pattern.

3. The method of claim 2 , wherein updating the at least one of the arrival values based on the comparison between the design pattern corresponding to the pixelated mask pattern and the substrate pattern simulated based on the binary mask pattern further comprises:

based on a determination that the evaluation value is greater than or equal to a predetermined threshold, updating the at least one of the arrival values; and

based on a determination that the evaluation value is smaller than the predetermined threshold, outputting the binary mask pattern for mask making.

4. The method of claim 1 , wherein determining the arrival values for the pixels of the portion of the pixelated mask pattern further comprises:

determining a ridge point as the brightest pixel of the portion or the darkest pixel of the portion;

determining speed values associated with the pixels of the portion based on image characteristics of the pixels of the portion and distances between the ridge point and the pixels of the portion; and

determining the arrival values based on the speed values and the distances.

5. The method of claim 4 , wherein the image characteristics comprise at least one selected from: brightness values of the pixels, intensities of the pixels, colors of the pixels, and/or image gradients associated with the pixels, wherein the image gradients are indicative of changes associated with the pixels in at least one selected from: of the brightness values of the pixels, the intensities of the pixels, and the colors of the pixels.

6. The method of claim 1 , wherein determining the binary mask pattern based on the arrival values further comprises determining a segment of the binary mask pattern as pixels of the portion having the same predetermined value of the arrival values.

7. The method of claim 1 , wherein the binary mask pattern comprises a curve-linear pattern.

8. The method of claim 1 , wherein the binary mask pattern comprises at least one selected from: a main pattern and/or a sub-resolution assistant feature (SRAF).

9. The method of claim 1 , further comprising determining, using inverse lithography technology (ILT), the pixelated mask pattern based on the design pattern.

10. An apparatus for determining a binary mask pattern from a pixelated mask pattern, the apparatus comprising:

a processor; and

a memory coupled to the processor, the memory storing instructions which when executed by the processor become operational with the processor to at least:

determine, based on a fast marching method (FMM), arrival values for pixels of a portion of the pixelated mask pattern;

determine the binary mask pattern based on the arrival values determined based on the FMM; and

update at least one of the arrival values based on a comparison between a design pattern corresponding to the pixelated mask pattern and a substrate pattern simulated based on the binary mask pattern.

11. The apparatus of claim 10 , wherein the comparison between the design pattern and the substrate pattern further comprises determination of an evaluation value based on at least one selected from: an edge placement error (EPE) between the design pattern and the substrate pattern, a nominal process window condition, a mask error enhancement factor (MEEF), and/or a side-lobe printing indication value indicative of a possibility of side-lobe printing in the substrate pattern.

12. The apparatus of claim 11 , wherein the memory comprising the instructions operational with the processor to update the at least one of the arrival values further comprises instructions which when executed by the processor become operational with the processor to:

based on a determination that the evaluation value is greater than or equal to a predetermined threshold, update the at least one of the arrival values; and

based on a determination that the evaluation value is smaller than the predetermined threshold, output the binary mask pattern for mask making.

13. The apparatus of claim 10 , wherein the memory comprising the instructions operational with the processor to determine the arrival values for the pixels of the portion of the pixelated mask pattern further comprises instructions which when executed by the processor become operational with the processor to:

determine a ridge point as the brightest pixel of the portion or the darkest pixel of the portion;

determine speed values associated with the pixels of the portion based on image characteristics of the pixels of the portion and distances between the ridge point and the pixels of the portion; and

determine the arrival values based on the speed values and the distances.

14. The apparatus of claim 13 , wherein the image characteristics comprise at least one selected from: brightness values of the pixels, intensities of the pixels, colors of the pixels, and/or image gradients associated with the pixels, wherein the image gradients are indicative of changes associated with the pixels in at least one selected from: the brightness values of the pixels, the intensities of the pixels, and/or the colors of the pixels.

15. The apparatus of claim 10 , wherein the memory comprising the instructions operational with the processor to determine the binary mask pattern based on the arrival values further comprises instructions which when executed by the processor become operational with the processor to determine a segment of the binary mask pattern as pixels of the portion having the same predetermined value of the arrival values.

16. The apparatus of claim 10 , wherein the binary mask pattern comprises at least one selected from: a main pattern and/or a sub-resolution assistant feature (SRAF), and wherein the at least one selected from: the main pattern and/or the SRAF comprises a curve-linear pattern.

17. A non-transitory computer-readable storage medium, comprising instructions for determining a binary mask pattern from a pixelated mask pattern, which instructions when executed by a processor become operational with the processor to at least:

determine, based on a fast marching method (FMM), arrival values for pixels of a portion of the pixelated mask pattern;

determine the binary mask pattern based on the arrival values determined based on the FMM; and

update at least one of the arrival values based on a comparison between a design pattern corresponding to the pixelated mask pattern and a substrate pattern simulated based on the binary mask pattern.

18. The non-transitory computer-readable storage medium of claim 17 , wherein the instructions operational with the processor to update the at least one of the arrival values further comprise instructions which when executed by the processor become operational with the processor to:

based on a determination that an evaluation value is greater than or equal to a predetermined threshold, update the at least one of the arrival values, wherein the evaluation value is determined based on at least one selected from: an edge placement error (EPE) between the design pattern and the substrate pattern, a nominal process window condition, a mask error enhancement factor (MEEF), and/or a side-lobe printing indication value indicative of a possibility of side-lobe printing in the substrate pattern; and

based on a determination that the evaluation value is smaller than the predetermined threshold, output the binary mask pattern for mask making.

19. The non-transitory computer-readable storage medium of claim 17 , wherein the instructions operational with the processor to determine the arrival values for the pixels of the portion of the pixelated mask pattern further comprise instructions which when executed by the processor become operational with the processor to:

determine a ridge point as the brightest pixel of the portion or the darkest pixel of the portion;

determine speed values associated with the pixels of the portion based on image characteristics of the pixels of the portion and distances between the ridge point and the pixels of the portion, wherein the image characteristics comprise at least one selected from: brightness values of the pixels, intensities of the pixels, colors of the pixels, and/or image gradients associated with the pixels, wherein the image gradients are indicative of changes associated with the pixels in at least one selected from: the brightness values of the pixels, the intensities of the pixels, and/or the colors of the pixels; and

determine the arrival values based on the speed values and the distances.

20. The non-transitory computer-readable storage medium of claim 17 , wherein the instructions operational with the processor to determine the binary mask pattern based on the arrival values further comprise instructions which when executed by the processor become operational with the processor to determine a segment of the binary mask pattern as pixels of the portion having the same predetermined value of the arrival values.