METHOD FOR GENERATING A PLURALITY OF OPTIMIZED WAVEFRONTS FOR A MULTIPLE EXPOSURE LITHOGRAPHIC PROCESS

• US 20120077130A1
• Filed: 09/27/2010
• Published: 03/29/2012
• Est. Priority Date: 09/27/2010
• Status: Active Grant

• Current Assignee: GlobalFoundries, Inc.
• Original Assignee: International Business Machines Corporation
• Inventors: Bagheri, Saeed, Lai, Kafai, Melville, David O., Rosenbluth, Alan E., Tian, Kehan, Tirapu Azpiroz, Jaione
• Granted Patent: US 8,495,528 B2
• Time in Patent Office: Days
• US Class Current: 430/322
• 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: G03F 7/70466 Multiple exposures, e.g. combination of fine and coarse exposures, double patterning or multiple exposures for printing a single feature stitching G03F7/70475

Abstract

A simplified version of a multiexpose mask optimization problem is solved in order to find a compressed space in which to search for the solution to the full problem formulation. The simplification is to reduce the full problem to an unconstrained formulation. The full problem of minimizing dark region intensity while maintaining intensity above threshold at each bright point can be converted to the unconstrained problem of minimizing average dark region intensity per unit of average intensity in the bright regions. The extrema solutions to the simplified problem can be obtained for each source. This set of extrema solutions is then assessed to determine which features are predominantly printed by which source. A minimal set of extrema solutions serves as a space of reduced dimensionality within which to maximize the primary objective under constraints. The space typically has reduced dimensionality through selection of highest quality extrema solutions.

Claims

1. A method for generating a design for at least one mask for a lithographic process, said method comprising of:

selecting a set of bright evaluation points and a set of dark evaluation points in an exposure plane for a multiexposure lithographic process comprising a set of illumination sources and a set of basis components of candidate wavefronts for each source to be used in forming an image at said set of bright evaluation points and said set of dark evaluation points;

generating a set of relationships between intensities of said set of bright evaluation points and said set of dark evaluation points and weightings of said set of basis components of candidate wavefronts;

generating a primary objective function expressing a first merit quality for said intensities at said set of bright evaluation points and at said set of dark evaluation points and said weightings of said set of basis components, wherein constraint functions applied during said generating are functions of said weightings of said set of basis components of said candidate wavefronts;

transforming said primary objective function and said constraint functions into a secondary objective function that does not include constraints;

determining extrema solutions for said secondary objective function;

generating an expression of said primary objective function by employing said extrema solutions as a new set of basis components;

calculating an optimal wavefront by finding weights for said new set of basis components through minimizing said primary objective function; and

generating a design for at least one mask, wherein said at least one mask generates said optimal wavefront during exposure when illuminated by said illumination sources.

2. The method of claim 1, further comprising:

generating optimal new basis component weights that maximize said primary objective function under conditions of said constraint functions; and

adding said new set of basis components weighted by said optimal basis components weights to form said optimal wavefront.

3. The method of claim 1, wherein said generating of said set of relationships is effected by generating quadratic form matrices, wherein each of said quadratic form matrices is generated for an intensity at each bright evaluation point and each dark evaluation point in said exposure plane for each one of said set of illumination sources, wherein bases of said quadratic form matrices comprise said set of basis components of said candidate wavefronts.

5. The method of claim 4, wherein said determining of said extrema solutions is effected by generating joint eigenvectors of said averaged quadratic form matrices.

4. The method of claim 3, wherein said secondary objective function is formed by taking a ratio of an average of said quadratic form matrices for said bright intensity points to an average of said quadratic form matrices for said dark intensity points.

6. The method of claim 5, further comprising applying an initial set of ranking and exposure coverage criteria to eigenvalues of said averaged quadratic form matrices.

7. The method of claim 6, further comprising selecting a set of joint eigenvectors that has a highest overall ranking while achieving adequate exposure coverage of bright evaluation points.

8. The method of claim 7, further comprising modifying joint eigenvectors that are produced by all sources other than a source that has highest joint eigenvalues to include a worst-case intensity change that overlay errors among the multiple exposures can produce at evaluation points.

9. The method of claim 8, further comprising applying a second set of ranking and exposure coverage criteria to select a revised set of joint eigenvectors that has a highest overall ranking.

10. The method of claim 1, wherein said calculating of said optimal wavefront is effected by performing a pocket search.

11. The method of claim 10, wherein said performing of said pocket search includes:

solving an equi-brightness problem;

solving a maximum contrast problem; and

solving a maximum exposure latitude problem.

12. The method of claim 1, further comprising adding at least one solution to said extrema solutions, wherein said added at least one solution provides additional positive-valued amplitude at bright points at which preexisting extrema solutions cover with predominantly negative-valued amplitude.

13. The method of claim 1, further comprising expanding said extrema solutions so that bright points are covered by expanded extrema solutions without resorting to phase shift.

14. The method of claim 1, further comprising determining whether a subsequent pocket search needs to be accelerated.

15. The method of claim 14, further comprising:

forming multiple sets of sample points wherein said multiple sets correspond to the different exposures; and

reclassifying at least one bright point as dark points within each set.

16. A method of forming a lithographic pattern on a substrate, said method comprising:

selecting a set of bright evaluation points and a set of dark evaluation points in an exposure plane for a multiexposure lithographic process comprising a set of illumination sources and a set of basis components of candidate wavefronts for each source to be used in forming an image at said set of bright evaluation points and said set of dark evaluation points;

generating a set of relationships between intensities of said set of bright evaluation points and said set of dark evaluation points and weightings of said set of basis components of candidate wavefronts;

generating a primary objective function expressing a first merit quality for said intensities at said set of bright evaluation points and at said set of dark evaluation points and said weightings of said set of basis components, wherein constraint functions applied during said generating are functions of said weightings of said set of basis components of said candidate wavefronts;

transforming said primary objective function and said constraint functions into a secondary objective function that does not include constraints;

determining extrema solutions for said secondary objective function;

generating an expression of said primary objective function by employing said extrema solutions as a new set of basis components;

calculating an optimal wavefront by finding weights for said new set of basis components through minimizing said primary objective function;

generating a design for at least one mask, wherein said at least one mask generates said optimal wavefront during exposure when illuminated by said illumination sources; and

lithographically patterning a photoresist on a substrate, wherein said photoresist is patterned by employing multiple exposures in which at least two mask among said set of masks are employed.

17. The method of claim 16, further comprising:

generating optimal new basis components that maximize said primary objective function under conditions of said constraint functions; and

adding said new set of basis components weighted by said optimal joint eigenvector weights to form said optimal wavefront.

18. The method of claim 16, wherein said generating of said set of relationships is effected by generating quadratic form matrices, wherein each of said quadratic form matrices is generated for an intensity at each bright evaluation point and each dark evaluation point in said exposure plane for each one of said set of illumination sources, wherein bases of said quadratic form matrices comprise said set of basis components of said candidate wavefronts.

19. The method of claim 16, wherein said calculating of said optimal wavefront is effected by performing a pocket search.

20. The method of claim 16, further comprising adding at least one solution to said extrema solutions, wherein said added at least one solution provides additional positive-valued amplitude at bright points at which preexisting extrema solutions cover with predominantly negative-valued amplitude.