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 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 mask pattern to be used on a photo-mask in a photolithographic process, wherein the photo-mask has a plurality of distinct types of regions having distinct optical properties, the computer-program mechanism including:
instructions for providing a first mask pattern that includes a plurality of distinct types of regions corresponding to the distinct types of regions of the photo-mask;
instructions for calculating a gradient of a function, wherein the function depends on the first mask pattern and an estimate of a wafer pattern that results from the photolithographic process utilizing at least a portion of the first mask pattern, and wherein the gradient is calculated in accordance with a formula obtained by taking a derivative of the function; and
instructions for generating a second mask pattern based, at least in part, on the gradient of the function.
2. The computer-program product of claim 1 , wherein the gradient corresponds to a Frechet derivative.
3. The computer-program product of claim 1 , wherein the gradient is a closed-form expression.
4. The computer-program product of claim 1 , wherein the gradient is calculated without determining the function.
5. The computer-program product of claim 1 , wherein the output of the function further depends on at least a portion of a target pattern that is to be printed by the photo-mask during the photolithographic process.
6. The computer-program product of claim 5 , wherein another target pattern is modified to produce the target pattern.
7. The computer-program product of claim 5 , wherein the computer-program mechanism further includes instructions for converting a document that includes a polygon-based representation of the target pattern into the target pattern.
8. The computer-program product of claim 5 , wherein the computer-program mechanism further includes instructions for converting a document that includes an edge-based representation of the target pattern into the target pattern.
9. The computer-program product of claim 1 , wherein the function depends, at least in part, on a model of the photolithographic process, wherein the model includes a resist model.
10. The computer-program product of claim 1 , wherein the generating involves:
modifying a first representation of the first mask pattern to produce a second representation of the second mask pattern in accordance with the gradient; and
extracting a second mask pattern from the second representation.
11. The computer-program product of claim 10 , wherein the second mask pattern is piece-wise rectilinear.
12. The computer-program product of claim 10 , wherein the first representation is a distance function in which a value of the first representation corresponds to a distance from a nearest contour in a plane of the first mask pattern.
13. The computer-program product of claim 12 , wherein the first representation has a pre-determined value on a contour in the plane.
14. The computer-program product of claim 13 , wherein the computer-program mechanism further includes instructions for adjusting the second representation such that it is a distance function in which a value of the second representation corresponds to a distance from a nearest contour in a plane of the second mask pattern.
15. The computer-program product of claim 1 , wherein the computer-program mechanism further includes instructions for combining the second mask pattern with a third mask pattern, wherein the third mask pattern is determined in accordance with pre-determined optical-proximity-correction rules.
16. The computer-program product of claim 1 , wherein the function is a merit function that assigns different relative weights to different regions of the first mask pattern.
17. The computer-program product of claim 1 , wherein the function is a merit function that includes estimate of a process window corresponding to the photolithographic process.
18. The computer-program product of claim 1 , wherein the function is a merit function that includes a model of the photolithographic process that includes out-of-focus conditions.
19. The computer-program product of claim 1 , wherein the function is a merit function that indicates a degree of desirability of the first mask pattern.
20. A computer system, comprising:
at least one processor;
at least one memory; and
at least one program module, the program module stored in the memory and configured to be executed by the processor, wherein at least the program module is for determining a mask pattern to be used on a photo-mask in a photolithographic process, and wherein the photo-mask has a plurality of distinct types of regions having distinct optical properties, at least the program module including:
instructions for providing a first mask pattern that includes a plurality of distinct types of regions corresponding to the distinct types of regions of the photo-mask;
instructions for calculating a gradient of a function, wherein the function depends on the first mask pattern and an estimate of a wafer pattern that results from the photolithographic process utilizing at least a portion of the first mask pattern, and wherein the gradient is calculated in accordance with a formula obtained by taking a derivative of the function; and
instructions for generating a second mask pattern based, at least in part, on the gradient of the function.
21. A computer system, comprising:
means for computing;
means for storing; and
at least one program module mechanism, the program module mechanism stored in at least the means for storing and configured to be executed by at least the means for computing, wherein at least the program module is for determining a mask pattern to be used on a photo-mask in a photolithographic process, and wherein the photo-mask has a plurality of distinct types of regions having distinct optical properties, at least the program module including:
instructions for providing a first mask pattern that includes a plurality of distinct types of regions corresponding to the distinct types of regions of the photo-mask;
instructions for calculating a gradient of a function, wherein the function depends on the first mask pattern and an estimate of a wafer pattern that results from the photolithographic process utilizing at least a portion of the first mask pattern, and wherein the gradient is calculated in accordance with a formula obtained by taking a derivative of the function; and
instructions for generating a second mask pattern based, at least in part, on the gradient of the function.