Determining source patterns for use in photolithography
View Patent ↗Embodiments of a computer system, a process, a computer-program product (i.e., software), and a data structure or a file for use with the computer system are described. These embodiments may be used to determine or generate source patterns that define illumination patterns on photo-masks during a photolithographic process. Moreover, a given source pattern may be determined concurrently with an associated mask pattern (to which a given photo-mask corresponds) or sequentially (i.e., either the given source pattern may be determined before the associated mask pattern or vice versa.). During the determining, the given source pattern may be represented using one or more level-set functions. Additionally, the source pattern may be determined using an Inverse Lithography (ILT) calculation.
1. A computer-implemented method for determining a source pattern to illuminate a photo-mask during a photolithographic process, comprising:
determining a first function representing a first source pattern, a cardinality of the first function, including values of the first function greater than a number of distinct types of regions in the source pattern, and a domain of the first function including input values of the first function corresponding to a first plane of the first source pattern;
using the computer, generating a second function based, at least in part, on the first function, the second function representing a second source pattern, the first function providing a representation of the first source pattern and the second function providing a representation of the second source pattern;
determining the second source pattern by evaluating the second function within a domain of the second function, the domain of the second function including input values of the second function; and
determining a resulting source pattern based on the determined second source pattern, the resulting source pattern placed between a light source and a photo-mask to illuminate the photo-mask in a photolithographic process.
2. The method of claim 1 , wherein the number of distinct types of regions of the first source pattern is 2.
3. The method of claim 1 , wherein the number of distinct types of regions of the first source pattern is greater than 2.
4. The method of claim 3 , wherein the distinct types of regions of the first source pattern include at least one translucent region.
5. The method of claim 1 , wherein the distinct types of regions of the first source pattern include at least one polarized region.
6. The method of claim 1 , wherein the first function includes a level-set function.
7. The method of claim 1 , wherein the first function is a distance function in which a value of the first function corresponds to a distance from a nearest contour in the first plane of the first source pattern; and
wherein the nearest contour separates a first distinct type of region in the source pattern from a second distinct type of region in the source pattern.
8. The method of claim 1 , wherein the generating involves determining a gradient of a cost function.
9. The method of claim 8 , wherein the gradient corresponds to a Frechet derivative of the cost function.
10. The method of claim 8 , wherein the gradient is a closed-form expression.
11. The method of claim 8 , wherein the gradient is determined without calculating the cost function.
12. The method of claim 8 , wherein the cost function corresponds to a difference of a target pattern and an aerial image at an image plane of an optical system in the photolithographic process;
wherein the aerial image is associated with the first source pattern and a mask pattern corresponding to the photo-mask.
13. The method of claim 12 , wherein the target pattern corresponds to a distorted version of a circuit pattern that is to be printed at the image plane.
14. The method of claim 13 , wherein the distortion involves convolving a Gaussian function with the circuit pattern.
15. The method of claim 12 , wherein the cost function includes a 2-norm of the difference.
16. The method of claim 1 , further comprising calculating the second source pattern by evaluating the second function in a second plane, which can be the first plane.
17. The method of claim 1 , further comprising determining a mask pattern corresponding to the photo-mask concurrently with determining of the source pattern.
18. The method of claim 1 , further comprising determining a mask pattern corresponding to the photo-mask separately from determining of the source pattern.
19. The method of claim 1 , further comprising determining the first source pattern on a pixel-by-pixel basis based at least on metrics associated with the photolithographic process prior to determining the first function.
20. The method of claim 19 , wherein a given metric includes a contrast of a gradient of an aerial image at an image plane of an optical system in the photolithographic process;
wherein the aerial image is associated with a given pixel in the first source pattern and a mask pattern corresponding to the photo-mask.
21. The method of claim 20 , wherein determining the first source pattern involves comparing the metrics with a predetermined threshold; and
wherein a given pixel has a finite transmittance if the given metric associated with the given pixel exceeds the predetermined threshold.
22. The method of claim 20 , further comprising refining the determined first source pattern based at least on interactions between pixels.
23. A computer-program product for use in conjunction with a computer system, the computer-program product comprising a non-transitory computer-readable storage medium and a computer-program mechanism embedded therein for determining a source pattern to illuminate a photo-mask during a photolithographic process, the computer-program mechanism including:
instructions for determining a first function representing a first source pattern, a cardinality of the first function including values of the first function greater than a number of distinct types of regions in the source pattern, and a domain of the first function including input values of the first function corresponding to a first plane of the first source pattern;
instructions for generating a second function based, at least in part, on the first function, the second function representing a second source pattern, the first function providing a representation of the first source pattern and the second function providing a representation of the second source pattern;
instructions for determining the second source pattern by evaluating the second function within a domain of the second function, the domain of the second function including input values of the second function; and
instructions for determining a resulting source pattern based on the determined second source pattern, the resulting source pattern placed between a light source and a photo-mask to illuminate the photo-mask in a photolithographic process.
24. A computer system, comprising:
a processor;
a memory; and
a program module for determining a source pattern to illuminate a photo-mask during a photolithographic process, the program module stored in the memory and configured to be executed by the processor, the program module including:
instructions for determining a first function representing a first source pattern, a cardinality of the first function, including values of the first function greater than a number of distinct types of regions in the source pattern, and a domain of the first function, including input values of the first function, corresponding to a first plane of the first source pattern; and
instructions for generating a second function based, at least in part, on the first function, the second function representing a second source pattern, the first function providing a representation of the first source pattern and the second function providing a representation of the second source pattern;
instructions for determining the second source pattern by evaluating the second function within a domain of the second function, the domain of the second function including input values of the second function; and
instructions for determining a resulting source pattern based on the determined second source pattern, the resulting source pattern placed between a light source and a photo-mask to illuminate the photo-mask in a photolithographic process.
25. The method of claim 1 , wherein the resulting source pattern is the second source pattern.