Method for Time-Evolving Rectilinear Contours Representing Photo Masks

• US 20070198966A1
• Filed: 10/16/2006
• Published: 08/23/2007
• Est. Priority Date: 04/06/2003
• Status: Active Grant

• Current Assignee: Dino Technology Acquisition LLC
• Original Assignee: Luminescent Technologies, Inc. (KLA Corporation)
• Inventors: Osher, Stanley, Abrams, Daniel, Peng, Danping
• Granted Patent: US 7,441,227 B2
• Time in Patent Office: Days
• US Class Current: 716/54
• CPC Class Codes: G03F 1/36 Masks having proximity correction features; Preparation thereof, e.g. optical proximity correction [OPC] design processes

Abstract

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.

Claims

1. A method of representing a photomask pattern comprising:

providing a function having input values corresponding to an area of a 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;

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 photomask pattern comprises at least two regions representing portions of the photomask having different optical properties, including 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 further comprises storing only selected output values based on a distance from the corresponding point to the boundary of the photomask pattern.

13. A method of generating a photomask pattern, comprising:

providing an initial photomask pattern;

selecting an initial function representing the initial photomask pattern, wherein the function has at least three different output values; and

iteratively evolving the initial function to generate a modified function representing a modified photomask pattern, wherein the modified function has at least three different output values.

14. The method of claim 13, wherein the initial function is a level set function and the modified function is a level set function.

15. The method of claim 14, wherein the modified function is rectilinear.

16. The method of claim 13, wherein the initial function is a distance function.

17. The method of claim 13, wherein the output values from the initial function represent the distance to a boundary of the initial photomask pattern.

18. The method of claim 17, further comprising re-distancing the modified function.

19. The method of claim 13, wherein iteratively evolving the initial function further comprises adding a change function to the initial function over the same domain as the initial function.

20. The method of claim 19, further comprising creating a rectilinear projection of the sum of the change function and the initial function.

21. The method of claim 13, wherein iteratively evolving the initial function further comprises modifying the initial function based at least in part upon the gradient of a merit function.

22. The method of claim 13, wherein iteratively evolving the initial function further comprises modifying the initial function based at least in part upon a derivative of a merit function.

23. The method of claim 13, wherein iteratively evolving the initial function further comprises modifying the initial function based at least in part upon the frechet derivative of a merit function.

24. The method of claim 13, wherein iteratively evolving the initial function further comprises solving a differential equation.

25. A method of generating a photomask pattern, comprising:

providing an initial pattern;

selecting an initial function representing the initial pattern; and

time-evolving the initial function in a series of iterations, wherein;

each iteration has an input function and an output function modified from the input function;

the initial function is used as the input function for the initial iteration; and

the modified output function for each iteration is determined based, at least in part, upon the output function from the previous iteration and an aspect of a Hamiltonian function.

26. The method of claim 25, wherein the aspect of the Hamiltonian function is a derivative of the Hamiltonian function.

27. The method of claim 25, wherein the aspect of the Hamilton is a gradient of the Hamiltonian function.

28. The method of claim 25, further comprising:

determining whether to stop iterating based upon the evaluation of a condition; and

upon meeting the condition, using the output function from the last iteration to form the photomask pattern.

29. The method of claim 25, further comprising:

determining whether to stop iterating based, at least in part, upon the number of iterations that have been performed.

30. The method of claim 25, further comprising:

determining whether to stop iterating based, at least in part, upon the amount of change in the Hamiltonian function resulting from the current iteration.

31. The method of claim 25, further comprising:

determining whether to stop iterating based, at least in part, upon the amount of change in the respective input function resulting from the current iteration.

32. A method of generating a photomask pattern, comprising:

using a function to represent a pattern;

evolving the function to form a modified curvilinear function representing a modified pattern;

projecting the modified curvilinear function onto a rectilinear pattern; and

using the rectilinear pattern to generate the photomask pattern.

33. A method of generating a photomask pattern, comprising:

using a set of m points to represent an area of the photomask pattern; and

associating a respective value with each of the m points, wherein the respective value for each of the m point represents the location of a boundary of the photomask pattern.

34. The method of claim 33, wherein the respective value at each point represents the distance from the point to the boundary of the photomask pattern.

35. The method of claim 33, wherein at least some of the values associated with the m points are used as inputs to a merit function.

36. The method of claim 33, wherein the set of m points is a grid over the area of the photomask pattern and wherein the values associated with the m points specify a location for the boundary of the photomask pattern between the points on the grid.

37. The method of claim 33, wherein the set of m points is a grid over the area of the photomask pattern and wherein the values associated with the m points specify a location for the boundary of the photomask pattern at a resolution higher than the resolution of the grid.

38. The method of claim 35, wherein the merit function is based, at least in part, on a forward model of a wafer pattern formed from a photomask having the photomask pattern.

39. A method of manufacturing a photomask, comprising:

providing an initial pattern;

modeling the initial pattern using an initial function;

evolving the initial function through a series of iterations, wherein;

each iteration has an input function and an output function that is modified from the input function;

the initial function is used as the input function for the first iteration; and

each output function has at least three different output values, wherein a first range of the output values represents a first region of the photomask and a second range of the output values represents a second region of the photomask;

selecting an output function resulting from one of the iterations; and

fabricating a photomask having a first optical property in a first area of the photomask corresponding to the first region defined by the selected output function and a second optical property in a second area of the photomask corresponding to the second region defined by the selected output function.

40. The method of claim 39, wherein the first area of the photomask is chrome.