Methods and system for lithography process window simulation
View Patent ↗A method of efficient simulating imaging performance of a lithographic process utilized to image a target design having a plurality of features. The method includes the steps of determining a function for generating a simulated image, where the function accounts for process variations associated with the lithographic process; and generating the simulated image utilizing the function, where the simulated image represents the imaging result of the target design for the lithographic process. In one given embodiment, the function for simulating the aerial images with focus and dose (exposure) variation is defined as: I ( x,f ,1+ε)= I 0 ( x )+└ε· I 0 ( x )+(1+ε)· a ( x )·( f−f 0 )+(1+ε)· b ( x )·( f−f 0 ) 2 ┘ where I O represents image intensity at nominal focus and exposure, f O represents nominal focus, f and ε represent an actual focus-exposure level at which the simulated image is calculated, and parameters “a” and “b” represent first order and second order derivative images with respect to focus change.
1. A computer-implemented method of simulating imaging performance of a lithographic process utilized to image a target design having a plurality of features, said method comprising:
determining, using a computer, a function for generating a simulated image, said function having one or more variables accounting for process window variations from a nominal process condition associated with said lithographic process; and
generating, using the computer, said simulated image utilizing said function; said simulated image representing an imaging result of said target design for said lithographic process.
2. The computer-implemented method of simulating imaging performance of a lithographic process according to claim 1 , wherein said function includes a polynomial function of the process window variations, and said process window variations include variations in at least one of focus and exposure dose.
3. The computer-implemented method of simulating imaging performance of a lithographic process according to claim 2 , wherein said process window variations further include variations in optical settings including at least one of numerical aperture and sigma.
4. The computer-implemented method of simulating imaging performance of a lithographic process according to claim 2 , wherein said function is defined as:
I ( x,f, 1+ε)= I 0 ( x )+[ε· I 0 ( x )+(1+ε)· a ( x )·( f−f 0 )+(1+ε)· b ( x )·( f−f 0 ) 2 ]
where I represents image intensity at actual focus and exposure, I 0 represents image intensity at nominal focus and exposure, x is a point at which the image intensity is determined, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent first order and second order derivative images with respect to focus change.
5. The computer-implemented method of simulating imaging performance of a lithographic process according to claim 2 , wherein said function is defined as: I ( x,f, 1+ε)= I 0 ( x )+[ε· I 0 ( x )+(1+ε)· a ( x )·( f−f 0 )+(1+ε)· b ( x )·( f−f 0 ) 2 ]
where I represents image intensity at actual focus and exposure, I 0 represents image intensity at nominal focus and exposure, x is a point at which the image intensity is determined, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent best fit of a series of aerial images at different focuses.
6. The computer-implemented method of simulating imaging performance of a lithographic process according to claim 2 , wherein said function is defined as:
I ( x,f, 1+ε)= I 0 ( x )+[· I 0 ( x )+(1+ε)· a ( x )·( f−f 0 )+(1+ε)· b ( x )·( f−f 0 ) 2 ]
where I represents image intensity at actual focus and exposure, I 0 represents image intensity at nominal focus and exposure x is a point at which the image intensity is determined, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent the aerial images computed from Transmission Cross Coefficients (TCCs) A and B which are linear combinations of a series of TCCs at different focuses.
7. The computer-implemented method of simulating imaging performance of a lithographic process according to claim 2 , wherein said function is defined as:
I ( x,f, 1+ε)= I 0 ( x )+[ε· I 0 ( x )+(1+ε)· a ( x )·( f−f 0 )+(1+ε)· b ( x )·( f−f 0 ) 2 ]
where I represents image intensity at actual focus and exposure, I 0 represents image intensity at nominal focus and exposure x is a point at which the image intensity is determined, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent the aerial images computed from Transmission Cross Coefficients (TCCs) A and B which are first order and second order derivative TCCs with respect to focus change.
8. The computer-implemented method of simulating imaging performance of a lithographic process according to claim 1 , wherein said simulated image corresponds to a resist image.
9. The computer-implemented method of simulating imaging performance of a lithographic process according to claim 8 , wherein said function for simulating said resist image is defined as:
R=R 0 +ε·P{I 0 }+(1+ε)·( f−f 0 )· P{a }+(1+ε)·( f−f 0 ) 2 ·P{b}
where R represents image intensity at actual focus and exposure, R 0 represents image intensity at nominal focus and exposure, I 0 represents nominal aerial image, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent first order and second order derivative aerial images with respect to focus change, P{ } denotes the functional action of applying a filter as a resist model.
10. A computer-implemented method of estimating feature edge shift or critical dimension (CD) change due to process window parameter variation of a lithographic process, said method comprising the steps of:
determining, using a computer, a function for generating a simulated image, said function having one or more variables accounting for process window variations from a nominal process condition associated with said lithographic process; and
generating, using the computer, said simulated image utilizing said function; said simulated image representing an imaging result of said target design for said lithographic process; and
estimating, using the computer, said feature edge shift or CD change by analyzing said simulated image.
11. The computer-implemented method of estimating feature edge shift or CD change due to process window parameter variation of a lithographic process according to claim 10 , wherein said function accounts for variations in focus and dose, said function being defined as:
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where ΔEP is the edge shift or change in edge placement, S represents resist image slope at nominal focus and exposure, I 0 represents nominal aerial image, x i is a point at which the image intensity is determined, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent first order and second order derivative aerial images with respect to focus change, P{ } denotes a functional action of applying a filter as the resist model.
12. A computer program product having a non-transitory computer readable medium bearing a computer program for simulating imaging performance of a lithographic process utilized to image a target design having a plurality of features, the computer program, when executed, causing a computer to perform the steps of:
determining a function for generating a simulated image, said function having one or more variables accounting for process window variations from a nominal process condition associated with said lithographic process; and
generating said simulated image utilizing said function; said simulated image representing the imaging result of said target design for said lithographic process.
13. The computer program product of claim 12 , wherein said function, includes a polynomial function of the process window variations, and said process window variations include variations in at least one of focus and exposure dose.
14. The computer program product of claim 13 , wherein said process window variations further include variations in optical settings including at least one of numerical aperture and sigma.
15. The computer program product according to claim 12 , wherein said function for generating simulated images is defined as:
I ( x,f, 1+ε)== I 0 ( x )+[ε· I 0 ( x )+(1+ε)· a ( x )·( f−f 0 )+(1+ε)· b ( x )·( f−f 0 ) 2 ]
where I represents image intensity at actual focus and exposure, I 0 represents image intensity at nominal focus and exposure, x is a point at which the image intensity is determined, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent first order and second order derivative images with respect to focus change.
16. The computer program product according to claim 15 , wherein said simulated image corresponds to a resist image.
17. The computer program product according to claim 16 , wherein said function for simulating said resist image is defined as:
R=R 0 +ε·P{I 0 }+(1+ε)·( f−f 0 )· P{a}+ (1+ε)·( f−f 0 ) 2 ·P{b}
where R represents image intensity at actual focus and exposure, R 0 represents image intensity at nominal focus and exposure, I 0 represents nominal aerial image, f o represents nominal focus, f and c represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent first order and second order derivative aerial images with respect to focus change, P{ } denotes the functional action of applying a filter as a resist model.
18. The computer program product according to claim 12 , wherein said function for generating simulated images is defined as:
I ( x,f, 1+ε)== I 0 ( x )+[ε· I 0 ( x )+(1+ε)· a ( x )·( f−f 0 )+(1+ε)· b ( x )·( f−f 0 ) 2 ]
where I represents image intensity at actual focus and exposure, I 0 represents image intensity at nominal focus and exposure x is a point at which the image intensity is determined, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent best fit of a series of aerial images at different focuses.
19. The computer program product according to claim 12 , wherein said function for generating simulated images is defined as:
I ( x,f, 1+ε)= I 0 ( x )+[ε· I 0 ( x )+(1+ε)· a ( x )·( f−f 0 )+(1+ε)· b ( x )·( f−f 0 ) 2 ]
where I represents image intensity at actual focus and exposure, I 0 represents image intensity at nominal focus and exposure, x is a point at which the image intensity is determined, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent the aerial images computed from Transmission Cross Coefficients (TCCs) A and B which are linear combinations of a series of TCCs at different focuses.
20. The computer program product according to claim 12 , wherein said function for generating simulated images is defined as:
I ( x,f, 1+ε)= I 0 ( x )+[ε· I 0 ( x )+(1+ε)· a ( x )·( f−f 0 )+(1+ε)· b ( x )·( f−f 0 ) 2 ]
where I represents image intensity at actual focus and exposure, I 0 represents image intensity at nominal focus and exposure, x is a point at which the image intensity is determined, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent the aerial images computed from Transmission Cross Coefficients (TCCs) A and B which are first order and second order derivative TCCs with respect to focus change.
21. A computer program product having a non-transitory computer readable medium bearing a computer program for estimating feature edge shift or critical dimension (CD) change due to process window parameter variation of a lithographic process, the computer program, when executed, causing a computer to perform the steps of:
determining a function for generating a simulated image, said function having one or more variables accounting for process window variations from a nominal process condition associated with said lithographic process;
generating said simulated image utilizing said function; said simulated image representing an imaging result of a target design for said lithographic process; and
estimating said feature edge shift or CD change by analyzing said simulated image.
22. The computer program product according to claim 21 , wherein said function accounts for variations in focus and dose, said function being defined as:
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where ΔEP is the edge shift or change in edge placement, S represents resist image slope at nominal focus and exposure, I 0 represents nominal aerial image, x i is a point at which the image intensity is determined, f 0 represents nominal focus, f and ε represent an actual focus and exposure level at which the simulated image is calculated, and parameters “a” and “b” represent first order and second order derivative aerial images with respect to focus change, P{ } denotes a functional action of applying a filter as the resist model.