Application of FreeForm MRC to SRAF optimization based on ILT mask optimization

1. A method of extracting shapes from a pixelated SRAF bitmap image of pixels for mask making, the method comprising:

receiving the pixelated SRAF bitmap image of pixels, each pixel having a respective brightness value;

selecting a ridge point in the pixelated SRAF bitmap image, the ridge point being one of the pixels and selected based on the respective brightness value of the one of the pixels;

for each pixel of at least some of the pixels, determining a respective arrival time at the pixel, the respective arrival time being based on a respective brightness value of the pixel and a Mask Rule Check (MRC) rule; and

determining a mask shape using the arrival times of the at least some of the pixels.

2. The method of claim 1 , wherein receiving the pixelated SRAF bitmap image of pixels comprises:

receiving a mask image from a design pattern comprising design shapes;

simulating the mask image to generate a bitmap image; and

generating the pixelated SRAF bitmap image by removing the design shapes from the bitmap image.

3. The method of claim 1 , wherein determining the mask shape using the arrival times of the at least some of the pixels comprises selecting first boundary pixels for a first mask shape, the first boundary pixels corresponding to pixels having arrival times that are less than a first target arrival time.

4. The method of claim 3 , further comprising:

selecting second boundary pixels for a second mask shape, the second boundary pixels corresponding to pixels having arrival times that are less than a second target arrival time; and

selecting, as the mask shape, the one of the first mask shape or the second mask shape corresponding to a smaller Edge Placement Error (ERE).

5. The method of claim 1 , further comprising modifying the mask shape to resolve MRC rules violations.

6. The method of claim 5 , wherein modifying the mask shape to resolve MRC rules violations comprises modifying the mask shape based on an internal pixel query and the MRC rules.

7. The method of claim 5 , wherein modifying the mask shape to resolve MRC rules violations comprises modifying the mask shape based on an external pixel query and the MRC rules.

8. An apparatus for determining sub-resolution assist features (SRAFs) for mask making, the apparatus comprising:

a processor; and

a memory storing instructions executable by the processor to at least:

receive a pixelated SRAF bitmap image of pixels, each pixel having a respective brightness value;

determine, using a fast marching method (FMM), arrival times for at least some of the pixels, the FMM using a speed function that is based on a Mask Rule Check (MRC); and

determine a SRAF shape using the arrival times of the at least some of the pixels.

9. The apparatus of claim 8 , wherein the instructions to cause the processor to receive the pixelated SRAF bitmap image comprises instructions to cause the processor to:

generate a mask image from a design pattern comprising design shapes;

simulate the mask image to generate a bitmap image; and

generate the pixelated SRAF bitmap image by removing the design shapes from the bitmap image.

10. The apparatus of claim 8 , wherein the instructions to cause the processor to determine the SRAF shape using the arrival times of the at least some of the pixels comprises instructions to cause the processor to select first boundary pixels for a first SRAF shape, the first boundary pixels corresponding to pixels having arrival times that are less than a first target arrival time.

11. The apparatus of claim 10 , wherein the instructions further comprise instructions to cause the processor to:

select second boundary pixels for a second SRAF shape, the second boundary pixels corresponding to pixels having arrival times that are less than a second target arrival time; and

select, as the SRAF shape, the one of the first SRAF shape and the second SRAF shape corresponding to a smaller Edge Placement Error (EPE).

12. The apparatus of claim 8 , wherein the instructions further comprise instructions to cause the processor to modify the SRAF shape to resolve MRC rules violations.

13. The apparatus of claim 12 , wherein the instructions to cause the processor to modify the SRAF shape to resolve MRC rules violations comprises instructions to cause the processor to modify the SRAF shape based on an internal pixel query and the MRC rules.

14. The apparatus of claim 12 , wherein the instructions to cause the processor to modify the SRAF shape to resolve MRC rules violations comprises instructions to cause the processor modify the SRAF shape based on an external pixel query and the MRC rules.

15. A method for extracting shapes from a pixelated SRAF bitmap image of pixels for mask making, the method comprising:

receiving the pixelated SRAF bitmap image of pixels, each pixel having a respective brightness value;

calculating a speed image, for use with a fast marching method, with mask-manufacturing (MRC) rules, the speed image being based on pixel brightness values;

generating an arrival time map using the fast marching method;

determining a binary SRAF image using the arrival time map; and

resolving MRC rule violations in the binary SRAF image.

16. The method of claim 15 , wherein resolving MRC rule violations in the binary SR AF image comprises:

resolving the MRC rule violations using an internal pixel query; and

resolving the MRC rule violations using an external pixel query.

17. The method of claim 15 , wherein determining a binary SRAF image using the arrival time map comprises:

generating a first binary SRAF image based on a first arrival time;

generating a second binary SRAF image based on a second arrival time; and

selecting, as the binary SRAF image, the first binary SRAF image or the second binary SRAF image resulting in a smaller Edge Placement Error (EPE).

18. The method of claim 15 , wherein the binary SRAF image comprises a first shape and a second shape, and wherein resolving MRC rule violations in the binary SRAF image comprises modifying the first shape and the second shape to resolve a MRC rule violation.

19. The method of claim 15 , wherein the binary SRAF image comprises a shape, and wherein resolving MRC rule violations in the binary SRAF image comprises removing the shape to resolve a MRC rule violation.

20. The method of claim 15 , wherein the MRC rules comprise a maximum shape edge size, and wherein generating the arrival time map using the fast marching method comprises:

calculating a distance from a pixel that is a ridge point to another pixel; and

setting the arrival time of the other pixel to a large value based on a comparison of the distance to the maximum shape size.