Method For Forming Arbitrary Lithographic Wavefronts Using Standard Mask Technology

• US 20100281449A1
• Filed: 04/29/2009
• Published: 11/04/2010
• Est. Priority Date: 04/29/2009
• Status: Active Grant

• Current Assignee: Siemens Industry Software Limited (Siemens AG)
• Original Assignee: International Business Machines Corporation
• Inventors: Tirapu-Azpiroz, Jaione, RosenBluth, Alan E.
• Granted Patent: US 8,108,802 B2
• Time in Patent Office: Days
• US Class Current: 716/53
• CPC Class Codes: G03F 1/36 Masks having proximity correction features; Preparation thereof, e.g. optical proximity correction [OPC] design processes
• 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

Abstract

A desired set of diffracted waves using mask features whose transmissions are chosen from a set of supported values are generated. A representation of the mask as a set of polygonal elements is created. Constraints which require that the ratio of the spatial frequencies in the representation take on the amplitude ratios of the desired set of diffracted waves are defined. An optimization algorithm is used to adjust the transmission discontinuities at the edges of the polygons to substantial equality with the discontinuity values allowed by the set of supported transmissions while maintaining the constraints.

Claims

1. A method for generating a desired set of diffracted waves using features of a lithographic mask for which a set of supported transmissions are chosen from a set of supported values, by the steps of:

creating at a computer a representation of the mask as a set of polygonal elements,

defining constraints for the computer which require that the ratio of spatial frequencies in the representation take on amplitude ratios of the desired set of diffracted waves, and

using an optimization algorithm stored in a memory of the computer to adjust transmission discontinuities at edges of the polygonal elements to substantial equality with discontinuity values allowed by the set of supported transmissions while maintaining the constraints.

2. The method of claim 1 where the optimization algorithm comprises iterated steps, the iterated steps comprising:

forming a 3D topographical representation from the polygonal elements, and

simulating it with a full-3D Maxwell solver to calculate a Fourier transform of the transmission discontinuities at the edges of the polygonal elements.

3. The method of claim 2 where the iterated steps further comprise:

calculating at the computer a compensating adjustment that cancels deviations of the Fourier transforms of the transmission discontinuities at the edges of the polygonal elements from the required spatial frequency ratios.

4. The method of claim 3 where the iterated steps further comprise:

forming at the computer an adjusted set of Fourier orders using the compensated edge Fourier transforms calculated in the previous step and use them to generate with thin-mask wavefront engineering a new set of iterated polygonal elements.

5. The method of claim 4, where the optimization algorithm further comprises terminating the iterations when the Fourier transform of the 3D topographical representation of the iterated polygonal elements substantially reproduces the amplitude ratios of the desired set of diffracted waves.

6. The method of claim 1 where one or more transmission discontinuities are driven to substantial equality with an allowed value by:

forming the 3D topographical representation of the polygonal elements,

calculating the transmission discontinuity at the edges of the polygonal elements, and

adding features to the mask whose in-quadrature transmission component substantially cancels the in-quadrature component of the transmission discontinuities at edges of the polygonal elements.

7. The method of claim 1 where one or more transmission discontinuities are driven to substantial equality with an allowed value by:

giving the desired ratios of spatial frequencies complex values that provide the image with a desired behavior through focus,

forming the 3D topographical representation of the polygon elements,

calculating the transmission discontinuity at the edges of the polygonal elements, and

adding features to the mask whose quadrature transmission component combined with the quadrature component of the transmission discontinuities at the edges of the polygonal elements provides the in-quadrature part of the complex values of the desired spatial frequency ratios.

8. A memory storing a program of computer readable instructions executable by a processor to perform actions directed to generating a desired set of diffracted waves using features of a lithographic mask for which a set of supported transmissions are chosen from a set of supported values, the actions comprising:

creating a representation of the mask as a set of polygonal elements,

defining constraints which require that the ratio of the spatial frequencies in the representation take on the amplitude ratios of the desired set of diffracted waves, and

using an optimization algorithm to adjust transmission discontinuities at edges of the polygonal elements to substantial equality with the discontinuity values allowed by the set of supported transmissions while maintaining the constraints.

9. The memory of claim 8 where the optimization algorithm comprises iterated steps, the iterated steps comprising:

forming a 3D topographical representation from the polygonal elements, and simulating it with a full-3D Maxwell solver to calculate a Fourier transform of the transmission discontinuities at the edges of the polygonal elements.

10. The memory of claim 9 where the iterated steps further comprise:

calculating a compensating adjustment that cancels the deviations of the Fourier transforms of the transmission discontinuities at the edges of the polygonal elements from the required spatial frequency ratios.

11. The memory of claim 10 where the iterated steps further comprise:

forming an adjusted set of Fourier orders using the compensated edge Fourier transforms calculated in the previous step and use them to generate with thin-mask wavefront engineering a new set of iterated polygonal elements.

12. The memory of claim 11, where the optimization algorithm further comprises terminating the iterations when the Fourier transform of the 3D topographical representation of the iterated polygonal elements substantially reproduces the amplitude ratios of the desired set of diffracted waves.

13. The memory of claim 8 where one or more transmission discontinuities are driven to substantial equality with an allowed value by:

forming the 3D topographical representation of the polygonal elements,

calculating the transmission discontinuity at the edges of the polygonal elements, and

adding features to the mask whose in-quadrature transmission component substantially cancels the in-quadrature component of the transmission discontinuities at edges of the polygonal elements.

14. The memory of claim 8 where one or more transmission discontinuities are driven to substantial equality with an allowed value by:

giving the desired ratios of spatial frequencies complex values that provide the image with a desired behavior through focus,

forming the 3D topographical representation of the polygon elements,

calculating the transmission discontinuity at the edges of the polygonal elements, and

adding features to the mask whose quadrature transmission component combined with the quadrature component of the transmission discontinuities at the edges of the polygonal elements provides the in-quadrature part of the complex values of the desired spatial frequency ratios.