Method for time-evolving rectilinear contours representing photo masks
View Patent ↗Photomask patterns are represented using contours defined by level-set functions. Given target pattern, contours are optimized such that defined photomask, when used in photolithographic process, prints wafer pattern faithful to target pattern. Optimization utilizes “merit function” for encoding aspects of photolithographic process, preferences relating to resulting pattern (e.g. restriction to rectilinear patterns), robustness against process variations, as well as restrictions imposed relating to practical and economic manufacturability of photomasks.
1. A method of representing a photomask pattern that includes a number of different regions having different optical properties, the method comprising:
providing a function having input values corresponding to the area of the photomask and output values indicating the position of a contour of the photomask pattern, wherein the function results in at least three different output values over the area of the photomask; and
wherein the number of the different output values over the area of the photomask is greater than the number of the different regions having the different optical properties;
evaluating the function over at least a portion of the area of the photomask; and
storing the output values from the function in a data structure to represent the position of the contour of the pattern over the portion of the area of the photomask.
2. The method of claim 1 :
wherein the different regions of the photomask pattern include at least a first region and a second region and the boundary of the photomask pattern separates the first region from the second region; and
wherein the at least three output values of the function include a constant output value indicating the boundary of the photomask pattern, an output value in the first region that is greater than the constant output value, and an output value in the second region that is less than the constant output value.
3. The method of claim 2 , wherein the constant output value is zero.
4. The method of claim 2 , wherein the first region represents a type selected from the group consisting of a phase shift transmissive region, a non-phase shift transmissive region and a non-transmissive region.
5. The method of claim 4 , wherein the second region represents a different type selected from the group consisting of a phase shift transmissive region, a non-phase shift transmissive region and a non-transmissive region.
6. The method of claim 4 , wherein one of the first region and the second region represents a chrome region and the other of the first region and the second region represents a glass region.
7. The method of claim 1 , wherein the function is a level set function.
8. The method of claim 1 , wherein the function is a distance function.
9. The method of claim 1 , wherein the function is substantially continuous.
10. The method of claim 1 , wherein evaluating the function over at least a portion of the area of the photomask further comprises evaluating the function over a grid of m points across the portion of the area of the photomask.
11. The method of claim 1 , wherein the data structure is an array corresponding to a 2-dimensional grid across the portion of the area of the photomask.
12. The method of claim 1 , wherein storing the output values includes storing only selected output values based on a distance to the contour of the photomask pattern.
13. The method of claim 1 :
wherein the different regions of the photomask pattern include at least a first region and a second region; and
wherein the first region is transmissive and the second region is non-transmissive.
14. The method of claim 13 , wherein the function is a level set function.
15. The method of claim 13 , wherein the function is a distance function.
16. The method of claim 13 , wherein evaluating the function over at least a portion of the area of the photomask further comprises evaluating the function over a grid of m points across the portion of the area of the photomask.
17. The method of claim 13 , wherein the data structure corresponds to a 2-dimensional grid across the portion of the area of the photomask.
18. The method of claim 13 , wherein storing the output values includes storing only selected output values based on a distance to the contour of the photomask pattern.
19. The method of claim 13 , wherein storing the output values includes selectively storing only a portion of the output values.
20. The method of claim 13 , wherein the function is a distance function.
21. The method of claim 13 , wherein the data structure corresponds to a 2-dimensional grid across the portion of the area of the photomask.
22. The method of claim 21 , wherein the function is a distance function.