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 modifying a photomask pattern, comprising:
providing an input file in a format selected from the group consisting of GDSII and Oasis, wherein the input file specifies a target pattern for a layer of an integrated circuit device and wherein the target pattern includes a plurality of enclosed regions;
storing a representation of the target pattern comprising a plurality of values, wherein
each value corresponds to a respective position over an area of the target pattern;
at least one of the values corresponds to a position within at least one of the enclosed regions of the target pattern;
at least one of the values corresponds to a position outside of the enclosed regions of the target pattern;
each value corresponding to a position within one of the enclosed regions of the target pattern is within a first range of values; and
each value corresponding to a position within one of the enclosed regions of the target pattern is within a second range of values, wherein the first range of values and the second range of values are non-overlapping;
determining a plurality of change values corresponding to each of the respective position over at least a portion of the area of the target pattern;
modifying the representation of the target pattern based on the plurality of change values; and
using the modified representation to provide an output file in a format selected from the group consisting of GDSII and Oasis, wherein the output file specifies a modified pattern different from the target pattern.
2. The method of claim 1 , wherein each of the first range of values is greater than a constant, and each of the second range of values is less than the constant.
3. The method of claim 2 , wherein the constant is zero.
4. The method of claim 1 , wherein each of the values corresponding to a position over at least a portion of the area of the target pattern represents a distance to a contour of at least one of the enclosed regions of the target pattern.
5. The method of claim 1 , wherein at least some of the values represent the position of a contour of at least one of the enclosed regions of the target pattern.
6. The method of claim 1 , wherein the step of determining a plurality of change values corresponding to each of the respective position over at least a portion of the area of the target pattern further comprises evaluating a forward model for the target pattern.
7. The method of claim 6 , wherein the step of determining a plurality of change values corresponding to each of the respective position over at least a portion of the area of the target pattern further comprises determining the plurality of change values based, at least in part, on a derivative of a forward model for the target pattern.
8. The method of claim 6 , wherein the step of determining a plurality of change values corresponding to each of the respective position over at least a portion of the area of the target pattern further comprises determining the plurality of change values based, at least in part, on a gradient of a forward model for the target pattern.
9. The method of claim 1 , wherein the values are the results of a level set function for the respective position over the area of the target pattern.
10. A method of modifying a photomask pattern, comprising:
providing an input file in a format selected from the group consisting of GDSII and Oasis, wherein the input file specifies a target pattern for a layer of an integrated circuit device and wherein the target pattern includes a plurality of enclosed regions;
storing a representation of the target pattern comprising a plurality of values, wherein
each value corresponds to a respective position over an area of the target pattern;
at least one of the values corresponds to a position within at least one of the enclosed regions of the target pattern;
at least one of the values corresponds to a position outside of the enclosed regions of the target pattern;
each value corresponding to a position within one of the enclosed regions of the target pattern is within a first range of values; and
each value corresponding to a position within one of the enclosed regions of the target pattern is within a second range of values, wherein the first range of values and the second range of values are non-overlapping;
iteratively determining a plurality of change values corresponding to each of the respective position over at least a portion of the area of the target pattern and modifying the representation of the target pattern based on the plurality of change values;
determining that a threshold has been met; and
using the modified representation to provide an output file in a format selected from the group consisting of GDSII and Oasis, wherein the output file specifies a modified pattern different from the target pattern.
11. The method of claim 10 , wherein the plurality of change values is determined based on a merit function.
12. The method of claim 11 , wherein the results of the merit function for the modified pattern are better than the results of the merit function for the target pattern.
13. The method of claim 10 , wherein each of the values corresponding to a position over at least a portion of the area of the target pattern represents a distance to a contour of at least one of the enclosed regions of the target pattern.
14. The method of claim 10 , wherein at least some of the values represent the position of a contour of at least one of the enclosed regions of the target pattern.
15. The method of claim 10 , wherein the values are the results of a level set function for the respective position over the area of the target pattern.
16. The method of claim 10 , wherein the first range includes a first plurality of values and the second range includes a second plurality of values.
17. The method of claim 16 , wherein there is at least one value between the first range and the second range.
18. The method of claim 17 , wherein the at least one value is zero.
19. The method of claim 17 , wherein the representation is stored as an array of the values corresponding to fixed points on a 2-dimensional grid over the area of the target pattern.
20. The method of claim 16 , wherein the change values represent a small change relative to the values stored in the representation.
21. The method of claim 10 , wherein the values correspond to a number of grid points, m, and the plurality of change values are an m dimensional vector, wherein the step of modifying the representation of the target pattern based on the plurality of change values further comprises adding the m dimensional vector to the representation.
22. The method of claim 10 , wherein the change values represent a small change relative to the values stored in the representation.