Optimization of lithographic process based on bandwidth and speckle

1 . A method for improving a lithographic process of imaging a portion of a design layout onto a substrate using a lithographic apparatus, the method comprising:

computing, by a hardware computer system, a multi-variable cost function, the multi-variable cost function being a function of: (i) a plurality of design variables that affect characteristics of the lithographic process and (ii) a radiation bandwidth of a radiation source of the lithographic apparatus; and

reconfiguring, by the hardware computer system, one or more of the characteristics of the lithographic process by adjusting one or more of the design variables to reduce or minimize a speckle characteristic associated with the radiation generation by the radiation source, while maintaining an image contrast associated with the lithographic process within a desired range, wherein the speckle characteristic is reduced by increase of the radiation bandwidth.

2 . The method of claim 1 , wherein the speckle characteristic is a metric associated with a speckle produced by mutual interference of a set of coherent wavefronts of the radiation source, the speckle indicative of local dose variations.

3 . The method of claim 1 , wherein the speckle characteristic is a speckle contrast associated with the radiation generated by the radiation source.

4 . The method of claim 3 , wherein the speckle contrast associated with the radiation is characterized by contribution from both spatial coherence and temporal coherence, and reduction of the speckle contrast comprises reducing temporal coherence and/or spatial coherence.

5 . The method of claim 1 , wherein the characteristics comprises one or more selected from:

the image contrast of an image produced during the lithographic process;

a process window of the lithographic process;

an illumination characteristic;

a performance indicator associated with the lithographic process; or

the speckle characteristic and a range of bandwidth of the radiation source.

6 . The method of claim 1 , wherein reconfiguring the one or more of the characteristics of the lithographic process comprises:

performing, via one or more process models associated with the lithographic process, an illumination optimization using the multi-variate cost function; or

performing, via one or more process models associated with the lithographic process, an illumination mask co-optimization using the multi-variate cost function.

7 . The method of claim 1 , wherein the radiation bandwidth is a full width at half maximum (FWHM) bandwidth.

8 . The method of claim 1 , wherein the radiation bandwidth is an E95 bandwidth.

9 . The method of claim 1 , wherein the radiation bandwidth is increased to a value greater than a minimum that hardware of the radiation source allows.

10 . The method of claim 1 , wherein reconfiguring the one or more of the characteristics of the lithographic process maintains the image contrast associated with the portion of the design layout within a desired range of best image contrast.

11 . The method of claim 1 , wherein reconfiguring the one or more of the characteristics of the lithographic process increases latitude of at least one of the design variables.

12 . The method of claim 1 , wherein reconfiguring the one or more of the characteristics of the lithographic process optimizes the radiation bandwidth of the radiation source.

13 . The method of claim 1 , wherein reconfiguring the one or more of the characteristics of the lithographic process comprises:

(i) performing a simulation using the one or more design variables with one or more process models associated with the lithographic process;

(ii) computing the multi-variate cost function using values of the design variables and simulation results; and

(iii) perturbing the one or more design variables and performing steps (i)-(iii) using the perturbed one or more design variables.

14 . The method of claim 1 , wherein the cost function is based on one or more selected from: edge placement error, pattern placement error, critical dimension (CD), a local CD uniformity as a function of the speckle characteristic, resist contour distance, worst defect size, best focus shift, or mask rule check.

15 . A non-transitory computer-readable medium comprising instructions stored therein that, when executed by one or more processors, are configured to cause the one or more processors to at least:

compute a multi-variable cost function, the multi-variable cost function being a function of: (i) a plurality of design variables that affect characteristics of a lithographic process of imaging a portion of a design layout onto a substrate using a lithographic apparatus and (ii) a radiation bandwidth of a radiation source of the lithographic apparatus; and

reconfigure one or more of the characteristics of the lithographic process by adjusting one or more of the design variables to reduce or minimize a speckle characteristic associated with the radiation generation by the radiation source, while maintaining an image contrast associated with the lithographic process within a desired range, the speckle characteristic is reduced by increase of the radiation bandwidth.

16 . The non-transitory computer-readable medium of claim 15 , wherein the speckle characteristic is a metric associated with a speckle produced by mutual interference of a set of coherent wavefronts of the radiation source or the speckle characteristic is a speckle contrast associated with the radiation generated by the radiation source.

17 . A method comprising:

computing, by a hardware computer system, a multi-variable cost function, the multi-variable cost function being a function of: (i) a plurality of design variables that affect characteristics of a lithographic process of imaging a portion of a design layout onto a substrate using a lithographic apparatus and (ii) a radiation bandwidth of a radiation source of the lithographic apparatus; and

determining, by the hardware computer system, an optimal radiation bandwidth to improve the lithographic process by adjusting one or more design variables until a termination condition is satisfied, the termination condition including a speckle characteristic being within a speckle specification associated with the radiation generation by the radiation source, while maintaining an image contrast associated with the lithographic process within a desired range, the speckle characteristic being reduced by increase of the radiation bandwidth.

18 . The method of claim 17 , wherein the speckle characteristic is a metric associated with a speckle produced by mutual interference of a set of coherent wavefronts of the radiation source, the speckle indicative of local dose variations.

19 . The method of claim 17 , wherein the speckle characteristic is a speckle contrast associated with the radiation generated by the radiation source, and wherein the speckle contrast is caused to reduce or minimize during determination of the optimal bandwidth.

20 . A non-transitory computer-readable medium comprising instructions stored therein that, when executed by one or more processors, are configured to cause the one or more processors to at least:

compute a multi-variable cost function, the multi-variable cost function being a function of: (i) a plurality of design variables that affect characteristics of a lithographic process of imaging a portion of a design layout onto a substrate using a lithographic apparatus and (ii) a radiation bandwidth of a radiation source of the lithographic apparatus; and

determine an optimal radiation bandwidth to improve the lithographic process by adjusting one or more design variables until a termination condition is satisfied, the termination condition including a speckle characteristic being within a speckle specification associated with the radiation generation by the radiation source, while maintaining an image contrast associated with the lithographic process within a desired range, the speckle characteristic being reduced by increase of the radiation bandwidth.