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: (a) segmenting a plurality of the features into a plurality of polygons; (b) determining the image log slope (ILS) value for each of the plurality of polygons; (c) determining the polygon having the minimum ILS value, and defining a mask containing the polygon; (d) convolving the mask defined in step (c) 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 (e) 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 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, said method comprising the steps of:
(a) segmenting a plurality of said features into a plurality of polygons;
(b) determining the image log slope (ILS) value for each of said plurality of polygons;
(c) determining the polygon having the minimum ILS value, and defining a mask containing said polygon;
(d) convolving said mask defined in step (c) with an eigen function of a transmission cross coefficient so as to generate a first interference map, said transmission cross coefficient defining an illumination system; and
(e) assigning a phase to said polygons based on the value of the first interference map at a location respectively corresponding to said polygons, said phase defining which exposure in said multi-exposure process said polygons are assigned.
2. The method of decomposing a target pattern according to claim 1 , further comprising the steps of:
(f) selecting another polygon, and defining a mask containing said polygon;
(g) convolving said mask defined in step (f) with said eigen function of said transmission cross coefficient so as to generate a second interference map;
(h) generate a total interference map by combining said first interference map and said second interference map; and
(i) assigning a phase to said polygons based on the value of the total interference map at a location respectively corresponding to said polygons, said phase defining which exposure in said multi-exposure process said polygons are assigned;
wherein said steps (f)-(i) are repeated until all polygons have been processed.
3. The method of decomposing a target pattern according to claim 2 , wherein step (f) comprises ranking the polygons utilizing a cost function, and the polygon having the highest cost function is selected as the next polygon for processing.
4. The method of decomposing a target pattern according to claim 2 , wherein said polygons are assigned either a first phase or a second phase, said polygons assigned said first phase are to be imaged in a first exposure process and said polygons assigned said second phase are to be imaged in a second exposure process.
5. The method of decomposing a target pattern according to claim 4 , wherein each polygon having a positive value in the corresponding location of the total interference map is assigned said first phase, and each polygon having a negative value in the corresponding location of the total interference map is assigned said second phase.
6. The method of decomposing a target pattern according to claim 2 , wherein a single feature contained in said target pattern can be decomposed into multiple segments which are assigned different phases and which are to be imaged in different exposure processes.
7. A mask formed utilizing the method of claim 1 .
8. A computer program product for controlling a computer comprising a recording medium readable by the computer, means recorded on the recording medium for directing the computer to decompose 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 process comprising the steps of:
(a) segmenting a plurality of said features into a plurality of polygons;
(b) determining the image log slope (ILS) value for each of said plurality of polygons;
(c) determining the polygon having the minimum ILS value, and defining a mask containing said polygon;
(d) convolving said mask defined in step (c) with an eigen function of a transmission cross coefficient so as to generate a first interference map, said transmission cross coefficient defining an illumination system; and
(e) assigning a phase to said polygons based on the value of the first interference map at a location respectively corresponding to said polygons, said phase defining which exposure in said multi-exposure process said polygons are assigned.
9. The computer program product of claim 8 , wherein said process further comprising the steps of:
(f) selecting another polygon, and defining a mask containing said polygon;
(g) convolving said mask defined in step (f) with said eigen function of said transmission cross coefficient so as to generate a second interference map;
(h) generate a total interference map by combining said first interference map and said second interference map; and
(i) assigning a phase to said polygons based on the value of the total interference map at a location respectively corresponding to said polygons, said phase defining which exposure in said multi-exposure process said polygons are assigned;
wherein said steps (f)-(i) are repeated until all polygons have been processed.
10. The computer program product of claim 9 , wherein step (f) comprises ranking the polygons utilizing a cost function, and the polygon having the highest cost function is selected as the next polygon for processing.
11. The computer program product of claim 9 , wherein said polygons are assigned either a first phase or a second phase, said polygons assigned said first phase are to be imaged in a first exposure process and said polygons assigned said second phase are to be imaged in a second exposure process.
12. The computer program product of claim 11 , wherein each polygon having a positive value in the corresponding location of the total interference map is assigned said first phase, and each polygon having a negative value in the corresponding location of the total interference map is assigned said second phase.
13. The computer program product of claim 9 , wherein a single feature contained in said target pattern can be decomposed into multiple segments which are assigned different phases and which are to be imaged in different exposure processes.
14. A device manufacturing method comprising the steps of:
(a) providing a substrate that is at least partially covered by a layer of radiation-sensitive material;
(b) providing a projection beam of radiation using an imaging system;
(c) using a pattern on a mask to endow the projection beam with a pattern in its cross-section;
(d) projecting the patterned beam of radiation onto a target portion of the layer of radiation-sensitive material,
wherein, in step (c), said mask is formed by a method comprising the steps of:
(e) segmenting a plurality of said features into a plurality of polygons;
(f) determining the image log slope (ILS) value for each of said plurality of polygons;
(g) determining the polygon having the minimum ILS value, and defining a mask containing said polygon;
(h) convolving said mask defined in step (g) with an eigen function of a transmission cross coefficient so as to generate a first interference map, said transmission cross coefficient defining an illumination system; and
(i) assigning a phase to said polygons based on the value of the first interference map at a location respectively corresponding to said polygons, said phase defining which exposure in said multi-exposure process said polygons are assigned.