Method, program product and apparatus for model based geometry decomposition for use in a multiple exposure process
A method of decomposing a target pattern having features to be imaged on a substrate so as to allow said features to be imaged in a multi-exposure process. The method includes the steps of: segmenting a plurality of the features into a plurality of polygons; determining the image log slope (ILS) value for each of the plurality of polygons; determining the polygon having the minimum ILS value, and defining a mask containing the polygon; convolving the defined mask with an eigen function of a transmission cross coefficient so as to generate an interference map, where the transmission cross coefficient defines the illumination system to be utilized to image the target pattern; and, assigning a phase to the polygon based on the value of the interference map at a location corresponding to the polygon, where the phase defines which exposure in said multi-exposure process the polygon is assigned.
1. A computer-implemented method of decomposing a target pattern having features to be imaged on a substrate so as to allow the features to be imaged in a multi-exposure process, the method comprising the steps of:
(a) segmenting a plurality of the features into a plurality of polygons;
(b) generating, using a computer, a first interference map corresponding to the target pattern using a first one of the plurality of polygons and a function representing an illumination system for the multi-exposure process;
(c) generating, using the computer, a second interference map corresponding to the target pattern using a second one of the plurality of polygons and the function representing the illumination system for the multi-exposure process;
(d) combining the first and second interference maps to obtain a total interference map corresponding to the target pattern; and
(e) assigning a phase to the plurality of polygons based on values of the total interference map at locations respectively corresponding to the polygons, the phase defining which exposure in the multi-exposure process the polygons are assigned.
2. The method of claim 1 , further comprising iteratively performing steps (c) and (d) for all of the plurality of polygons such that the total interference map is a combination of all of the interference maps generated for all of the plurality of polygons.
3. The method of claim 1 , wherein the step of generating the first interference map includes:
defining a mask containing the first polygon; and
convolving the mask with the function representing the illumination system for the multi-exposure process.
4. The method of claim 3 , wherein the function representing the illumination system of the multi-exposure process comprises a transmission cross coefficient.
5. The method of claim 4 , wherein the transmission cross coefficient is orthogonalized into a set of eigen functions, wherein only one or more of the set of eigen functions are used to generate the first interference map.
6. The method of claim 5 , wherein the one or more eigen functions are one of the set of eigen functions having the highest eigen value.
7. The method of claim 1 , wherein the function representing the illumination system of the multi-exposure process comprises a transmission cross coefficient.
8. The method of claim 7 , wherein the transmission cross coefficient is orthogonalized into a set of eigen functions, wherein only one or more of the set of eigen functions are used to generate the first and second interference maps.
9. The method of claim 8 , wherein the one or more eigen functions are one of the set of eigen functions having the highest eigen value.
10. A mask formed utilizing the method of claim 1 .
11. A computer program product for controlling a computer comprising a non-transitory recording medium readable by the computer, means recorded on the recording medium for directing the computer to perform a method for decomposing a target pattern having features to be imaged on a substrate so as to allow the features to be imaged in a multi-exposure process, the method comprising the steps of:
(a) segmenting a plurality of the features into a plurality of polygons;
(b) generating a first interference map corresponding to the target pattern using a first one of the plurality of polygons and a function representing an illumination system for the multi-exposure process;
(c) generating a second interference map corresponding to the target pattern using a second one of the plurality of polygons and the function representing the illumination system for the multi-exposure process;
(d) combining the first and second interference maps to obtain a total interference map corresponding to the target pattern; and
(e) assigning a phase to the plurality of polygons based on values of the total interference map at locations respectively corresponding to the polygons, the phase defining which exposure in the multi-exposure process the polygons are assigned.
12. The computer program product according to claim 11 , further comprising iteratively performing steps (c) and (d) for all of the plurality of polygons such that the total interference map is a combination of all of the interference maps generated for all of the plurality of polygons.
13. The computer program product according to claim 11 , wherein the step of generating the first interference map includes:
defining a mask containing the first polygon; and
convolving the mask with the function representing the illumination system for the multi-exposure process.
14. The computer program product according to claim 13 , wherein the function representing the illumination system of the multi-exposure process comprises a transmission cross coefficient.
15. The computer program product according to claim 14 , wherein the transmission cross coefficient is orthogonalized into a set of eigen functions, wherein only one or more of the set of eigen functions are used to generate the first interference map.
16. The computer program product according to claim 15 , wherein the one or more eigen functions are one of the set of eigen functions having the highest eigen value.
17. The computer program product according to claim 11 , wherein the function representing the illumination system of the multi-exposure process comprises a transmission cross coefficient.
18. The computer program product according to claim 17 , wherein the transmission cross coefficient is orthogonalized into a set of eigen functions, wherein only one or more of the set of eigen functions are used to generate the first and second interference maps.
19. The computer program product according to claim 18 , wherein the one or more eigen functions are one of the set of eigen functions having the highest eigen value.