Fast and accurate method to simulate intermediate range flare effects
View Patent ↗A method is provided for modeling lithographic processes in the design of photomasks for the manufacture of semiconductor integrated circuits, and more particularly for simulating intermediate range flare effects. For a region of influence (ROI) from first ROI 1 of about 5λ/NA to distance ROI 2 when the point spread function has a slope that is slowly varying according to a predetermined criterion, then mask shapes at least within the distance range from ROI 1 to ROI 2 are smoothed prior to computing the SOCS convolutions. The method provides a fast method for simulating intermediate range flare effects with sufficient accuracy.
1. A method of designing a lithographic mask including the use of a lithographic process model for simulating an image formed by illumination of the lithographic mask in a lithographic system, the method comprising:
determining a first region of influence (ROI 1 ) around a point of interest on a mask design, such that mask features within said first ROI 1 will contribute a relatively large amount of flare energy at said point of interest;
determining a second region of influence (ROI 2 ) around said point of interest, such that mask features outside of said ROI 2 will contributed a relatively small amount of flare energy at said point of interest in accordance with a predetermined criterion, such that the region between ROI 1 and ROI 2 comprises an intermediate region of influence (intermediate ROI);
identifying an initial mask polygon shape having a first plurality of vertices located within the intermediate ROI;
smoothing said initial mask polygon shape to form a smoothed mask polygon shape that has fewer vertices within the intermediate ROI than said first plurality of vertices;
determining, by using a computer, a smoothed flare contribution at said point of interest from said vertices of said smoothed mask polygon within the intermediate ROI; and
determining an image at the point of interest comprising using said smoothed flare contribution in the lithographic process model rather than a flare contribution from said initial mask polygon shape;
wherein said predetermined criterion comprises a slope cutoff for determining when a slope of a point spread function of the lithographic system is close to zero.
2. The method according to claim 1 , wherein said ROI 1 has an outer boundary at a distance of about 5λ/NA around the point of interest, where λ is the wavelength of the illumination energy and NA is the numerical aperture of the lithographic system.
3. The method according to claim 1 , wherein the point spread function (h) [h({right arrow over (r)}−{right arrow over (r)} Avg )] is a function of distance [({right arrow over (r)}−{right arrow over (r)} Avg )] from a point of interest ({right arrow over (r)}), and the point spread function has the form h∝K/({right arrow over (r)}−{right arrow over (r)}′) γ , where K is a constant, {right arrow over (r)} is a point of interest, {right arrow over (r)} first dummy distance variable in the optical coordinate system from the point of interest {right arrow over (r)}, and γ is the flare kernel parameter and is experimentally determined, and wherein the slope of the point spread function is given by
∂
h
(
r
→
-
r
→
Avg
)
∂
r
→
,
where
r
→
Avg
=
r
→
′
+
r
→
′′
2
,
and {right arrow over (r)}″ is a second dummy distance variable in the optical coordinate system from the point of interest {right arrow over (r)}.
4. The method according to claim 1 , wherein said intermediate ROI is further divided into a plurality of sub-intermediate ROIs, and wherein a different amount of smoothing is performed in at least one of said plurality of sub-intermediate ROIs than in another of said plurality of sub-intermediate ROIs.
5. The method according to claim 4 , wherein the amount of smoothing in a sub-intermediate ROI depends on the proximity of said sub-intermediate ROI to said point of interest.
6. The method according to claim 1 , wherein said smoothing is performed by a sequential grow and shrink operation or a low-pass filtering in a spatial frequency domain.
7. The method according to claim 1 , wherein in said step of determining an image at the point of interest comprises determining a flare contribution from within said first ROI 1 using mask features within said first ROI 1 that are not smoothed.
8. The method according to claim 1 , wherein in said step of determining an image at the point of interest comprises determining a flare contribution from mask features located beyond said second ROI 2 using a density mapping approach.
9. The method according to claim 1 , wherein said image is provided for use in an optical proximity correction methodology or in a mask verification methodology.
10. A computer program product comprising a computer readable storage device having a computer readable program embodied in said medium, for designing a lithographic mask, including a lithographic process model for simulating an image formed by illumination of the lithographic mask in a lithographic system wherein the computer readable program when executed on a computer causes the computer to perform the steps of:
determining a first region of influence (ROI 1 ) around a point of interest on the mask design, such that mask features within said first ROI 1 will contribute a relatively large amount of flare energy at said point of interest;
determining a second region of influence (ROI 2 ) around said point of interest, such that mask features outside of said ROI 2 will contributed a relatively small amount of flare energy at said point of interest in accordance with a predetermined criterion, such that the region between ROI 1 and ROI 2 comprises an intermediate region of influence (intermediate ROI);
identifying an initial mask polygon shape having a first plurality of vertices located within the intermediate ROI; and
smoothing said initial mask polygon shape to form a smoothed mask polygon shape that has fewer vertices within the intermediate ROI than said first plurality of vertices;
determining a smoothed flare contribution at said point of interest from said vertices of said smoothed mask polygon within the intermediate ROI;
determining an image at the point of interest comprising using said smoothed flare contribution in the lithographic process model rather than a flare contribution from said initial mask polygon shape; and
wherein said predetermined criterion comprises a slope cutoff for determining when a slope of a point spread function of the lithographic system is close to zero.
11. The computer program product according to claim 10 , wherein said ROI 1 has an outer boundary at a distance of about 5λ/NA around the point of interest, where λ is the wavelength of the illumination energy and NA is the numerical aperture of the lithographic system.
12. The computer program product according to claim 10 , wherein the point spread function (h)[h({right arrow over (r)}−{right arrow over (r)} Avg )] is a function of distance [{right arrow over (r)}−{right arrow over (r)} Avg ] from a point of interest ({right arrow over (r)}), and the point spread function has the form h∝K/({right arrow over (r)}−{right arrow over (r)}′) γ , where K is a constant, {right arrow over (r)} is a point of interest, {right arrow over (r)}′ is a first dummy distance variable in the optical coordinate system from the point of interest {right arrow over (r)}, and γ is the flare kernel parameter and is experimentally determined, and wherein the slope of the point spread function is given by
∂
h
(
r
→
-
r
→
Avg
)
∂
r
→
,
where
r
→
Avg
=
r
→
′
+
r
→
′′
2
,
and where {right arrow over (r)}″ is a second dummy distance variable in the optical coordinate system from the point of interest {right arrow over (r)}.
13. The computer program product according to claim 10 , wherein said intermediate ROI is further divided into a plurality of sub-intermediate ROIs, and wherein a different amount of smoothing is performed in at least one of said plurality of sub-intermediate ROIs than in another of said plurality of sub-intermediate ROIs.
14. The computer program product according to claim 13 , wherein the amount of smoothing in a sub-intermediate ROI depends on the proximity of said sub-intermediate ROI to said point of interest.
15. The computer program product according to claim 10 , wherein said smoothing is performed by a sequential grow and shrink operation or a low-pass filtering in a spatial frequency domain.
16. The computer program product according to claim 10 , wherein in said step of determining an image at the point of interest comprises determining a flare contribution from within said first ROI 1 using mask features within said first ROI 1 that are not smoothed.
17. The computer program product according to claim 10 , wherein in said step of determining an image at the point of interest comprises determining a flare contribution from mask features located beyond said second ROI 2 using a density mapping approach.
18. The computer program product according to claim 10 , wherein said image is provided for use in an optical proximity correction methodology or in a mask verification methodology.