METHOD AND SYSTEM FOR COMPUTING FOURIER SERIES COEFFICIENTS FOR MASK LAYOUTS USING FFT

• US 20130152025A1
• Filed: 02/12/2013
• Published: 06/13/2013
• Est. Priority Date: 04/30/2010
• Status: Active Grant

• Current Assignee: GlobalFoundries, Inc.
• Original Assignee: International Business Machines Corporation
• Inventors: HURLEY, Paul T., KRYSZCZUK, Krzysztof, SCHEIBLER, Robin, SCHIPANI, Davide
• Granted Patent: US 8,739,081 B2
• Time in Patent Office: Days
• US Class Current: 716/51
• CPC Class Codes: G03F 1/70 Adapting basic layout or design of masks to lithographic process requirements, e.g., second iteration correction of mask patterns for imaging
• CPC Class Codes: G06F 30/392 Floor-planning or layout, e.g. partitioning or placement

Abstract

A method and system for computing Fourier coefficients for a Fourier representation of a mask transmission function for a lithography mask. The method includes: sampling a polygon of a mask pattern of the lithography mask to obtain an indicator function which defines the polygon, performing a Fourier Transform on the indicator function to obtain preliminary Fourier coefficients, and scaling the Fourier coefficients for the Fourier representation of the mask transmission function, where at least one of the steps is carried out using a computer device.

Claims

1. A method for computing Fourier coefficients for a Fourier representation of a mask transmission function for a print simulation of a lithography mask used in a manufacture of lithography masks, the lithography masks having use in a manufacture of integrated circuits, the method comprising the steps of:

sampling at least one polygon of a mask pattern of the lithography mask to obtain an indicator function defining the at least one polygon using a number of pixels;

performing a Fourier Transform on the indicator function to obtain preliminary Fourier coefficients; and

scaling, using a computer device, the preliminary Fourier coefficients to obtain the Fourier coefficients for the Fourier representation of the mask transmission function,

wherein the mask pattern comprises at least one tile, wherein the tile comprises the at least one polygon.

2. The method according to claim 1, such that the at least one polygon is fully contained in the at least one tile, wherein a pixel size is defined as a pixel size in at least one dimension.

3. The method according to claim 2, wherein the pixel size in the at least one dimension is obtained as a greatest common divider of a tile size in the at least one dimension and a coordinates of vertices of the at least one polygon in the at least one dimension.

4. The method according to claim 1, wherein a pixel size in at least one dimension is obtained as a greatest common divider of a tile size in the at least one dimension and coordinates of vertices of the at least one polygon in at least one dimension.

5. The method according to claim 1, wherein the Fourier Transform is a Fast Fourier Transform.

6. The method according to claim 1, wherein the Fourier Transform is a Discrete Fourier Transform.

7. The method according to claim 1, wherein the sampling utilizes a minimal number of pixels possible.

8. The method according to claim 1, further comprising the step of using an obtained Fourier coefficients to obtain a print simulation of the lithography mask.

9. The method according to claim 1, further comprising the step of using an obtained Fourier coefficients for manufacture of at least one of integrated circuits and lithography masks.

10. The method according to claim 1, wherein the indicator function represents the at least one polygon by a function of coordinates within the tile, wherein the indicator function defines whether a point is within the at least one polygon, wherein each the coordinate corresponds to a pixel having a pixel size in at least one dimension.

11. The method according to claim 10, wherein the step of scaling the preliminary Fourier coefficients is performed by multiplying the preliminary Fourier coefficients by scaling factors to obtain the Fourier coefficients for the Fourier representation of the mask transmission function, wherein the scaling factors are determined according to a scaling factor function depending on the coordinates.

12. The method according to claim 11, wherein the scaling factors are provided using a lookup table.

13. A system for computing Fourier coefficients for a Fourier representation of a mask transmission function for a lithography mask, comprising:

means for sampling at least one polygon of a mask pattern of the lithography mask to obtain an indicator function defining the at least one polygon using a number of pixels;

a computer device including means for performing a Fourier Transform operation on the indicator function to obtain preliminary Fourier coefficients; and

means for scaling the preliminary Fourier coefficients to obtain the Fourier coefficients for the Fourier representation of the mask transmission function,

wherein the mask pattern comprises at least one tile, wherein the tile comprises the at least one polygon.

14. The system according to claim 13, such that the at least one polygon is fully contained in the at least one tile, wherein a pixel size is defined as a pixel size in at least one dimension.

15. The system according to claim 14, wherein the pixel size in the at least one dimension is obtained as a greatest common divider of a tile size in the at least one dimension and coordinates of vertices of the at least one polygon in the at least one dimension.

16. The system according to claim 13, wherein a pixel size in at least one dimension is obtained as a greatest common divider of a tile size in the at least one dimension and coordinates of vertices of the at least one polygon in at least one dimension.

17. The system according to claim 13, wherein the Fourier Transform is a Fast Fourier Transform.

18. The system according to claim 13, wherein the sampling utilizes a minimal number of pixels possible.

19. A method for computing Fourier coefficients for a Fourier representation of a mask transmission function for a print simulation of a lithography mask used in a manufacture of lithography masks, the lithography masks having use in a manufacture of integrated circuits, the method comprising the steps of:

sampling at least one polygon of a mask pattern of the lithography mask to obtain an indicator function defining the at least one polygon using a number of pixels;

performing a Fourier Transform on the indicator function to obtain preliminary Fourier coefficients; and

scaling, using a computer device, the preliminary Fourier coefficients to obtain the Fourier coefficients for the Fourier representation of the mask transmission function,

wherein the mask pattern comprises at least one tile, wherein the tile comprises the at least one polygon.

using the Fourier coefficients to obtain a print simulation of the lithography mask; and

using the print simulation for a manufacture of at least one of integrated circuit and lithography mask.

20. The method according to claim 19, such that the at least one polygon is fully contained in the at least one tile, wherein a pixel size is defined as a pixel size in at least one dimension.