Mask design method, program, and mask design system
A method, an article of manufacture, and a system for designing a mask. The method for designing a mask is implemented by a computer device having a memory, a processor device communicatively coupled to the memory, and a module configured to carry out the method including the steps of: generating an optical domain representation from a design pattern and an imaging light; and optimizing the optical domain representation under a constraint that values of negative excursions at predetermined evaluation points must be greater than or equal to predetermined negative threshold values assigned to the predetermined evaluation points; where: the optical domain representation is a variable representation of a wavefront; the imaging light is light that is transmitted through the mask; the negative excursions are in an object domain representation of the optical domain representation; and the predetermined evaluation points are in the object domain representation.
1. A method for manufacturing a mask comprising the steps of:
generating an optical domain representation from a design pattern and an imaging light; and
optimizing said optical domain representation under a constraint that values of negative excursions at predetermined evaluation points must be greater than or equal to predetermined negative threshold values assigned to said predetermined evaluation points;
wherein:
said optical domain representation is a variable representation of a wavefront;
said imaging light is light that is transmitted through said mask;
said negative excursions are in an object domain representation of said optical domain representation;
said predetermined evaluation points are in said object domain representation;
said predetermined negative threshold values are determined as a function of distances from a feature edge of said mask;
outside of the feature, said function specifies that a negative threshold value for a first distance is smaller than a negative threshold value for a second distance that is larger than the first distance; and
at least one of the steps is carried out by a computing device.
2. The method according to claim 1 , wherein said optical domain representation is a pupil domain representation that is band-limited.
3. The method according to claim 1 , wherein:
said optical domain representation is an object domain representation; and
said constraint is applied to a band-limited component of said optical domain representation.
4. The method according to claim 3 , wherein:
said constraint is applied to an object domain representation of said optical domain representation; and
said object domain representation is band-limited using a filter.
5. The method according to claim 1 , wherein:
said optical domain representation is an object domain representation; and
said constraint is applied to non-limited amplitudes of said object domain representation.
6. The method according to claim 1 , wherein said negative threshold values are assigned to said evaluation points based on distances from a center of a local design pattern.
7. The method according to claim 1 , wherein said predetermined evaluation points provide a linear constraint during the optimization.
8. The method according to claim 1 , comprising a step of:
filtering a pupil domain representation of said wavefront with a circular band-limit.
9. A non-transitory article of manufacture tangibly embodying computer readable instructions which, when implemented, cause a computer device to carry out a method for designing a mask, the method comprising the steps of:
generating an optical domain representation from a design pattern and an imaging light; and
optimizing said optical domain representation under a constraint that values of negative excursions at predetermined evaluation points be greater than or equal to predetermined negative threshold values assigned to said predetermined evaluation points;
wherein:
said optical domain representation is a variable representation of a wavefront;
said imaging light is light that is transmitted through said mask;
said negative excursions are in an object domain representation of said optical domain representation;
said predetermined evaluation points are in said object domain representation;
said predetermined negative threshold values are determined as a function of distances from a feature edge of said mask; and
outside of the feature, said function specifies that a negative threshold value for a first distance is smaller than a negative threshold value for a second distance that is larger than the first distance.
10. The article of manufacture according to claim 9 , wherein said optical domain representation is a pupil domain representation that is band-limited.
11. The article of manufacture according to claim 9 , wherein
said optical domain representation is an object domain representation; and
said constraint is applied to a band-limited component of said optical domain representation.
12. The article of manufacture according to claim 9 , wherein:
said constraint is applied to an object domain representation of said optical domain representation; and
said object domain representation is band-limited using a filter.
13. The article of manufacture according to claim 9 , wherein:
said optical domain representation is an object domain representation; and
said constraint is applied to non-limited amplitudes of said object domain representation.
14. The article of manufacture according to claim 9 , wherein said negative threshold values are assigned to said evaluation points based on distances from a center of a local design pattern.
15. The article of manufacture according to claim 9 , wherein said optimization step is iterated by using variables in a pupil domain expression while allowing an amount of negative excursions in said object domain representation.
16. The article of manufacture according to claim 9 , comprising a step of:
filtering a pupil domain representation of said wavefront with a circular band-limit.
17. A system for designing a mask, comprising:
a memory;
a processor device communicatively coupled to said memory;
a module for designing said mask, communicatively coupled to said memory and said processor device;
a generator for generating an optical domain representation of a wavefront from a design pattern and an imaging light; and
an optimizer for optimizing said optical domain representation under a constraint that values of negative excursions at predetermined evaluation points be greater than or equal to predetermined negative threshold values assigned to said predetermined evaluation points;
wherein:
said optical domain representation is a variable representation of a wavefront;
said imaging light is light that is transmitted through said mask;
said negative excursions are in an object domain representation of said optical domain representation;
said predetermined evaluation points are in said object domain representation;
said predetermined negative threshold values are determined as a function of distances from a feature edge of said mask; and
outside of the feature, said function specifies that a negative threshold value for a first distance is smaller than a negative threshold value for a second distance that is larger than the first distance.
18. The system according to claim 17 , wherein said optical domain representation is pupil domain representation that is band-limited.
19. The system according to claim 17 , wherein:
said optical domain representation is an object domain representation; and
said constraint is applied to a band-limited component of said optical domain representation.
20. The system according to claim 17 , wherein:
said constraint is applied to an object domain representation of said optical domain representation; and
said object domain representation is band-limited using a filter.