Method and system for reconstructing aberrated image profiles through simulation
AssigneeNikon Precision Inc.
InventorSteven Slonaker
Life of this patent
Estimating the term…
Abstract
A system and method of calculating estimated image profiles. The system and method includes providing lens characteristic data and performing simulation calculations for various levels of aberration components using the lens characteristic data. A response surface functional relation is built between selected variables of the lens characteristics, in particular the lens aberration components, and the Image Profile using the simulation calculations. Evaluation is then performed on the arbitrary specified aberration values of a lens in relation to the response surface functional relations to provide a calculated estimate of the Image Profile for the specified aberration values. A machine readable medium and exposure apparatus are also provided.
Claims48
A method of calculating estimated image profiles,
- comprising the steps of:
- providing imaging configuration characteristic data;
- performing simulation calculations for various levels of aberration components using the imaging configuration characteristic data;
- building response surface functional relations between variables of lens characteristics and an image profile of interest using the simulation calculations;
- and
- evaluating specified aberration values of a lens in relation to the response surface functional relations to provide an estimate of the image profile in a presence of specified aberration(s).
A method of calculating estimated image profiles, comprising the steps of:
- performing simulation calculations for various levels of aberration components using image configuration characteristic data;
- building response surface functional relations between variables of the image configuration characteristics and the image profile of interest using the simulation calculations as data input to be fit using:
- Ispx(x)=b0+b1x+b2x2+b3x3+ . . . +bnxn
- where Ispx indicates aerial image intensity or amplitude at a simulation pixel (spx) and x indicates defocus;
- and
- expressing a change of the coefficients b0 . . . bn described by an order fitting function as:
- b
- i
-
- (
- with_aberration
- )
- =
-
- b
- i
-
- (
- w
- /
- o_aberration
- )
- +
- ∑
- j
- =
- 2
- Zn
-
-
- Δ
-
-
- b
- i
-
- (
- cj
- )
- =
-
- b
- i
-
- (
- w
- /
- o_aberration
- )
- +
- ∑
- j
- =
- 2
- Zn
-
-
- φ
- 0
-
- (
- i
- ,
- j
- )
- +
- φ
- 1
-
- (
- i
- ,
- j
- )
-
- c
- j
- +
- φ
- 2
- (
- i
- ,
- j
- )
-
- c
- j
- 2
- +
-
- φ
- 3
-
- (
- i
- ,
- j
- )
-
- c
- j
- 3
- +
- …
- +
- φ
- n
-
- (
- i
- ,
- j
- )
-
- c
- j
- n
- wherein
- bi(with aberration) and bi(w/o aberration) represents the coefficients b0 . . . bn influenced by lens aberrations and the coefficients b0 . . . bn without aberrations, respectively,
- Δbi indicates the change in coefficients and it is expressed by an nth order fitting function of jth Zernike coefficient cj;
- and
- Ø0(ij) . . . Øn(ij) are the coefficients of the fitting function;
- and
- summing an impact from at least one of all new specified aberration coefficients and combinations of aberration coefficients from the built response surface functional relations to provide lens adjustment data.
An exposure apparatus, comprising:
- an illumination system that projects radiant energy through a mask pattern on a reticle R that is supported by and scanned using a wafer positioning stage;
- at least one linear motor that positions the wafer positioning stage;
- a system for providing optimal image profiling, including:
- means for providing image configuration characteristic data;
- means for performing simulation calculations for various levels of aberration components using the image configuration characteristic data;
- means for building response surface functional relations between variables of lens characteristics associated with the image configuration characteristic data using the simulation calculations;
- and
- means for evaluating specified aberration values of a lens in relation to the response surface functional relations to provide image profile estimates for the specified aberration values.
A system for providing optimal image profiles through the optimization of specified aberration components, according to their associated impact upon image profile, comprising:
- means for performing simulation calculations for various levels of aberration components using characteristic data;
- means for building response surface functional relations between variables of lens characteristics using the simulation calculations;
- means for evaluating specified aberration values of a lens in relation to the response surface functional relations to provide image profile estimates for the specified aberration values;
- and
- means for applying the aberrated image profile estimates in an optimization calculation method which judges image profile information against defined criteria as part of a lens adjustment optimization calculation
A machine readable medium containing code for adjusting a lens, comprising at least one module for:
- performing simulation calculations for various levels of aberration components using characteristic data;
- building response surface functional relations between variables of lens characteristics using the simulation calculations;
- and
- evaluating specified aberration values of a lens in relation to the response surface functional relations to provide image profile estimates for the specified aberration values.
Dependencies are inferred from the claim text.