Methods for modeling of a design in reticle enhancement technology

1. A method for reticle enhancement technology (RET) for a lithographic imaging system, the method comprising:

representing a target wafer pattern or a predicted wafer pattern as a smooth function captured as a function sample array (FSA), wherein the FSA is an array of sampled values of the smooth function, which is a continuous differentiable function;

providing a continuous tone mask (CTM), wherein the CTM is used to produce the predicted wafer pattern, the predicted wafer pattern spanning an entire design area; and

calculating the predicted wafer pattern from the CTM, wherein the calculating comprises:

calculating a cost, the cost being based on comparing the predicted wafer pattern to the target wafer pattern, wherein the cost is represented as a third smooth function; and updating the CTM, using the cost.

2. The method of claim 1 , further comprising:

determining the CTM, wherein the CTM captures values of a continuously varying amplitude transmission coefficient map.

3. The method of claim 1 , wherein the FSA is band limited to a spatial frequency cutoff of a substrate lithography system and is sampled on a grid that meets a Nyquist criterion.

4. The method of claim 1 , further comprising inputting a target geometry, wherein the FSA for the target wafer pattern is generated from the input target geometry.

5. A method for reticle enhancement technology (RET) for a lithographic imaging system, the method comprising:

representing a target wafer pattern or a predicted wafer pattern as a smooth function captured as a function sample array (FSA), wherein the FSA is an array of sampled values of the smooth function, which is a continuous differentiable function;

providing a continuous tone mask (CTM), wherein the CTM is used to produce the predicted wafer pattern, the predicted wafer pattern spanning an entire design area; and

representing the CTM as a second smooth function captured as a second function sample array (FSA) wherein the second FSA is an array of sampled values of the second smooth function, which is a continuous differentiable function.

6. A method for reticle enhancement technology (RET) for a lithographic imaging system, the method comprising:

representing a target wafer pattern or a predicted wafer pattern as a smooth function captured as a function sample array (FSA), wherein the FSA is an array of sampled values of the smooth function, which is a continuous differentiable function; and

providing a continuous tone mask (CTM), wherein the CTM is used to produce the predicted wafer pattern, the predicted wafer pattern spanning an entire design area;

wherein the FSA for the target wafer pattern or the predicted wafer pattern has a plurality of grid points, and the grid points are spaced at a grid pitch, wherein the grid pitch is set at a transition distance less than a lithographic imaging resolution of the lithographic imaging system.

7. The method of claim 1 , wherein the calculating further comprises:

calculating a derivative data, the derivative data being based on comparing the predicted wafer pattern to the target wafer pattern.

8. The method of claim 1 , further comprising iterating the CTM for the entire design area until the CTM meets criteria towards producing the target wafer pattern.

9. The method of claim 8 , wherein the calculating is performed on a computing platform comprising a plurality of computing nodes having an aggregate total memory of all computing nodes of the computing platform, wherein the aggregate total memory holds the target wafer pattern and the CTM of the entire design area throughout all iterations.

10. The method of claim 8 , further comprising:

dividing the entire design area into a plurality of tiles,

wherein the iterating comprises calculating the predicted wafer pattern for a subset of the plurality of tiles;

wherein all tiles in the subset are calculated before the next iteration.

11. The method of claim 10 , wherein each tile in the subset of the plurality of tiles has a halo region surrounding the tile, wherein the calculating for each tile includes its halo region, and wherein each iteration further comprises:

updating the CTM for an individual tile in the subset of tiles, after calculating the predicted wafer pattern for the individual tile; and

using the updated CTM for the individual tile to update the halo regions of tiles that neighbor the individual tile.

12. The method of claim 11 , wherein the halo region has a thickness surrounding the tile that is 1.5 to 4 times a lithographic imaging proximity range cutoff of a substrate lithography system for the RET.

13. The method of claim 10 , wherein the calculating of a tile in the subset of the plurality of tiles is performed on a computing node accelerated by a graphical processing unit.

14. The method of claim 5 , further comprising determining the CTM, wherein the CTM captures values of a continuously varying amplitude transmission coefficient map.

15. The method of claim 5 , wherein the FSA is band limited to a spatial frequency cutoff of a substrate lithography system and is sampled on a grid that meets a Nyquist criterion.

16. The method of claim 5 , further comprising inputting a target geometry, wherein the FSA for the target wafer pattern is generated from the input target geometry.

17. The method of claim 6 , further comprising determining the CTM, wherein the CTM captures values of a continuously varying amplitude transmission coefficient map.