Fast freeform source and mask co-optimization method
The present disclosure relates to lithographic apparatuses and processes, and more particularly to tools for optimizing illumination sources and masks for use in lithographic apparatuses and processes. According to certain aspects, the present disclosure significantly speeds up the convergence of the optimization by allowing direct computation of gradient of the cost function. According to other aspects, the present disclosure allows for simultaneous optimization of both source and mask, thereby significantly speeding the overall convergence. According to still further aspects, the present disclosure allows for free-form optimization, without the constraints required by conventional optimization techniques.
1. A method for configuring a lithographic process, the method comprising:
obtaining respective computerized descriptions of an illumination and a patterning device pattern for the lithographic process, wherein the patterning device pattern is to be imaged onto a substrate by the lithographic process using the illumination and wherein the illumination is a free form discretized as a plurality of radiation intensity pixels and the patterning device pattern is represented as a plurality of pixels;
iteratively adjusting, by a computer system, intensity values of the plurality of radiation intensity pixels among a range of three of more values and values of the plurality of patterning device pattern pixels among a range of three or more values, until an imaging response is suitably configured with respect to both the illumination and the pattern; and
producing electronic data of respective configurations of the illumination and the patterning device pattern for which the imaging response is suitably configured to configure an aspect of the lithographic process, where the electronic data is used to setup and/or modify an aspect of the lithographic process and/or used to create and/or modify a physical object or apparatus for use in the lithographic process.
2. The method of claim 1 , wherein the iteratively adjusting comprises iteratively converging a cost function, wherein the cost function comprises a function of both the illumination and the patterning device pattern.
3. The method of claim 2 , wherein the cost function is formulated in terms of one of the following: worst case edge placement error (EPE) over a given process window, EPE least square function, EPE least p-norm function, inverse normalized image log slope (NILS) p-norm function, contour integral image slope, edge image value least square, edge image p-norm, or image log slope p-norm.
4. The method of claim 1 , wherein the adjusting comprises using a gradient of the imaging response with respect to the illumination and the patterning device pattern.
5. The method of claim 4 , wherein the imaging response is suitably configured when a gradient of the imaging response with respect to both the illumination and the pattern is essentially zero.
6. The method of claim 1 , wherein the imaging response comprises one or more selected from: an edge placement error (EPE), an image log slope, an inverse image log slope, and/or a contour integral of an image log slope.
7. The method of claim 1 , further comprising modifying the computerized description of the patterning device pattern from an unconstrained continuous transmission pattern to a modified pattern constrained by a manufacturability factor.
8. The method of claim 7 , wherein the modified pattern comprises a fixed transmission value.
9. The method of claim 1 , further comprising modifying the computerized description of the illumination from a free-form illumination to a modified illumination constrained by a manufacturability factor.
10. The method of claim 1 , wherein the method is accelerated by performing a first co-optimization without constraints followed by performing a second co-optimization with constraints.
11. A method comprising:
receiving electronic descriptions of an illumination and a patterning device pattern, the patterning device pattern to be imaged by a lithographic process using the illumination;
forming a cost function as a function of both the illumination and the patterning device pattern; and
until the illumination and patterning device pattern are suitably configured for a desired process window of the lithographic process, selectively repeating:
evaluating, by a hardware computer system, the cost function,
calculating, by the hardware computer system, a gradient of the cost function, and
reconfiguring, by the hardware computer system, the illumination and patterning device pattern descriptions based on the calculated gradient; and
producing electronic data of respective configurations of the illumination and the patterning device pattern to configure an aspect of the lithographic process, where the electronic data is used to setup and/or modify an aspect of the lithographic process and/or used to create and/or modify a physical object or apparatus for use in the lithographic process.
12. The method of claim 11 , wherein the illumination and patterning device pattern are suitably configured when the calculated gradient has a value of zero.
13. The method of claim 11 , further comprising characterizing the illumination as independent illumination points.
14. The method of claim 11 , further comprising characterizing the patterning device pattern as diffraction elements in a spatial frequency domain.
15. The method of claim 11 , wherein reconfiguring the patterning device pattern description includes:
using optical proximity correction;
placing sub-resolution assist features; and
re-characterizing the reconfigured patterning device pattern description.
16. The method of claim 11 , wherein the cost function is formulated in terms of worst case edge placement error over a given process window.
17. The method of claim 11 , wherein the cost function F is expressed as:
F
=
∑
pw
∑
x
w
(
pw
,
x
)
[
I
pw
(
x
)
-
I
th
]
p
∇
I
pw
p
,
p
∈
N
,
wherein I pw (x) denotes aerial image intensity at process window condition pw at evaluation point x, wherein I th denotes a threshold for an aerial image contour, wherein ∥∇I pw ∥ represents a slope of an aerial image, wherein w(pw,x) is a weighting function, and wherein p is a positive integer.
18. A non-transitory computer readable medium having instructions recorded thereon, the instructions, when executed by a computer, configured to at least:
obtain respective computerized descriptions of an illumination and a patterning device pattern for a lithographic process, wherein the patterning device pattern is to be imaged onto a substrate by the lithographic process using the illumination and wherein the illumination is a free form discretized as a plurality of radiation intensity pixels and the patterning device pattern is represented as a plurality of pixels;
iteratively adjust intensity values of the plurality of radiation intensity pixels among a range of three of more values and values of the plurality of patterning device pattern pixels among a range of three or more values, until an imaging response is suitably configured with respect to both the illumination and the pattern; and
produce electronic data of respective configurations of the illumination and the patterning device pattern for which the imaging response is suitably configured to configure an aspect of the lithographic process, where the electronic data is used to setup and/or modify an aspect of the lithographic process and/or used to create and/or modify a physical object or apparatus for use in the lithographic process.
19. The non-transitory computer readable medium of claim 18 , wherein the instruction configured to iteratively adjust are further configured to iteratively converge a cost function, wherein the cost function comprises a function of both the illumination and the patterning device pattern.
20. The non-transitory computer readable medium of claim 18 , wherein the adjustment comprises use of a gradient of the imaging response with respect to the illumination and the patterning device pattern.
21. The non-transitory computer readable medium of claim 20 , wherein the imaging response is suitably configured when a gradient of the imaging response with respect to both the illumination and the pattern is essentially zero.
22. The non-transitory computer readable medium of claim 18 , wherein the imaging response comprises one or more selected from: an edge placement error (EPE), an image log slope, an inverse image log slope, and/or a contour integral of an image log slope.
23. A non-transitory computer readable medium having instructions recorded thereon, the instructions, when executed by a computer, configured to at least:
receive electronic descriptions of an illumination and a patterning device pattern, the patterning device pattern to be imaged by a lithographic process using the illumination;
form a cost function as a function of both the illumination and the patterning device pattern; and
until the illumination and patterning device pattern are suitably configured for a desired process window of the lithographic process, selectively repeat:
evaluation of the cost function,
calculation of a gradient of the cost function, and
reconfiguration of the illumination and patterning device pattern descriptions based on the calculated gradient; and
produce electronic data of respective configurations of the illumination and the patterning device pattern to configure an aspect of the lithographic process, where the electronic data is used to setup and/or modify an aspect of the lithographic process and/or used to create and/or modify a physical object or apparatus for use in the lithographic process.