Optimized correction of wafer thermal deformations in a lithographic process

1. A method of correcting thermally-induced field deformations of a lithographically exposed substrate, comprising:

exposing a pattern onto a plurality of fields of a substrate in accordance with pre-specified exposure information including at least one of exposure energy information, exposure time information, exposure field position information, exposure field sequencing information, and exposure field deformation information;

measuring attributes of said fields to assess deformation of said fields induced by thermal effects of said exposing;

determining corrective information based on said measured attributes;

adjusting said pre-specified exposure information deformation effects based on said corrective information, to compensate for the thermally-induced field deformations;

providing a model to predict thermally-induced field deformation information; and

modifying said pre-specified exposure information prior to exposing, based on said predicted thermally-induced deformation information wherein said predicted thermally-induced field deformation includes predicting deformation effects of selected points within each of said fields based on a global expansion model.

2. The method of claim 1 , wherein said predictive model is based on:

[

dx

]

p

=

[

x

r

w

·

N

i

N

tot

·

dx

max

]

;

and

[

dy

]

p

=

[

y

r

w

·

N

i

N

tot

·

dy

max

]

;

where

dx p : represents the predicted deformation along the x axis;

dx max : represents the predicted total deformation of the wafer substrate W in the x direction after the last target field has been exposed;

x: represents the x coordinate of a point on the wafer substrate W;

r w : represents the radius of the wafer substrate W;

N i : represents the current target field index number;

N tot : represents the total number of target fields;

dy p : represents the predicted deformation along the y axis;

dy max : represents the predicted total deformation of the wafer substrate W in the y direction after the last target field has been exposed; and

y: represents the y coordinate of a point on the wafer substrate W.

3. The method of claim 2 , wherein said adjusting said pre-specified exposure information includes adjusting said exposure field sequencing information based on said predicted thermally-induced field deformation information.

4. A method of correcting thermally-induced field deformations of a lithographically exposed substrate, comprising:

exposing a pattern onto a plurality of fields of a substrate in accordance with pre-specified exposure information including at least one of exposure energy information, exposure time information, exposure field position information, exposure field sequencing information, and exposure field deformation information;

measuring attributes of said fields to assess deformation of said fields induced by thermal effects of said exposing;

determining corrective information based on said measured attributes;

adjusting said pre-specified exposure information deformation effects based on said corrective information, to compensate for the thermally-induced field deformations;

providing a model to predict thermally-induced field deformation information; and

modifying said pre-specified exposure information prior to exposing, based on said predicted thermally-induced deformation information wherein said thermally-induced field deformation includes predicting deformation effects of selected points within each of said fields based on a time-decay characteristic as energy is transported across the wafer.

5. The method of claim 4 , wherein said predictive model is based on:

dx p =Σ i T i x D i x ; and

dy p =Σ i T i y D i y ; where

T

i

=

ⅇ

-

t

-

t

i

τ

⁢

:

represents thermal effects of exposing one of said target fields C i which will decay in time as energy is transported across said substrate in either the x or y direction;

τ: represents the time sensitivity constant which depends on the thermal properties of the lithographic exposure components;

D i =ke −| r i − r |/χ : represents effects induced by a distance r i between said exposed target field C i and target field to be currently exposed in either the x or y direction;

χ: represents the spatial thermal properties of the lithographic exposure components;

k: represents a proportionality constant which depends on thermal properties of the lithographic exposure components;

dx p : represents predicted deformation along the x axis; and

dy p : represents predicted deformation along the y axis.

6. The method of claim 5 , wherein said adjusting said pre-specified exposure information includes adjusting said exposure field sequencing information based on said predicted thermally-induced field deformation information.

7. A method of correcting thermally-induced field deformations of a lithographically exposed substrate, comprising:

exposing a pattern onto a plurality of fields of a substrate in accordance with pre-specified exposure information at least one of exposure energy information, exposure time information, exposure field position information, exposure field sequencing information, and exposure field deformation information;

measuring attributes of said fields to assess deformation of said fields induced by thermal effects of said exposing;

determining corrective information based on said measured attributes;

adjusting said pre-specified exposure information, based on said corrective information, to compensate for the thermally-induced field deformations;

measuring temperature variations on surface of said substrate prior to exposing; and

generating a deformation map based on said measured substrate temperature variations.

8. The method of claim 7 , further including modifying said pre-specified exposure information, prior to exposing, based on said deformation map.

9. The method of claim 8 , wherein said temperature variation measurement includes thermographic imaging.

10. The method of claim 7 , wherein said deformation map is characterized by:

[

dx

]

p

=

[

c

⁢

x

i

r

w

⁢

1

N

i

⁢

∑

k

⁢

(

T

k

-

T

nom

)

]

;

[

dy

]

p

=

[

c

⁢

y

i

r

w

⁢

1

N

i

⁢

∑

k

⁢

(

T

k

-

T

nom

)

]

;

where

dx p : represents the predicted deformation along the x axis;

x i : represents the x coordinate of field i;

c: represents a proportionality constant (thermal expansion coefficient);

N i : represents the number of fields taken into account in the summation;

k: sums over the relevant fields, along the connection line between the wafer centre and field i;

T k : represents the measured temperature of field k;

T nom : represents the nominal temperature for which the machine is set up;

y i : represents the y coordinate of field i; and

dy p : represents the predicted deformation along the y axis.

11. The method of claim 8 , wherein said adjusting said pre-specified exposure information includes adjusting said modified pre-specified exposure information, after said exposing, based on deformation offset information determined by said corrective information.

12. A method of correcting thermally-induced field deformations of a lithographically exposed substrate, comprising:

providing a model to predict deformation of a plurality of fields of a substrate induced by thermal effects of exposing;

modifying exposure information used to configure the exposure of said fields of said substrate based on said predicted thermally-induced deformation information;

exposing a pattern onto said fields of said substrate in accordance with said modified exposure information;

measuring attributes of said fields to assess deformation of said fields induced by thermal effects of said exposing;

determining corrective information based on said measured attributes; and

adjusting said modified exposure information, based on said corrective information, to compensate for the thermally-induced field deformations, wherein said predicted thermally-induced field deformation information includes predicting deformation effects of selected points within each of said fields based on a global expansion model.

13. The method of claim 12 , wherein said predictive model is based on:

[

dx

]

p

=

[

x

r

w

·

N

i

N

tot

·

dx

max

]

;

and

[

dy

]

p

=

[

y

r

w

·

N

i

N

tot

·

dy

max

]

;

where

dx p : represents the predicted deformation along the x axis;

dx max : represents the predicted total deformation of the wafer substrate W in the x direction after the last target field has been exposed;

x: represents the x coordinate of a point on the wafer substrate W;

r w : represents the radius of the wafer substrate W;

N i : represents the current target field index number;

N tot : represents the total number of target fields;

dy p : represents the predicted deformation along the y axis;

dy max : represents the predicted total deformation of the wafer substrate W in the y direction after the last target field has been exposed; and

y: represents the y coordinate of a point on the wafer substrate W.

14. The method of claim 13 , wherein said adjusting said pre-specified exposure information includes adjusting said exposure field sequencing information based on said predicted thermally-induced field deformation information.

15. A method of correcting thermally-induced field deformations of a lithographically exposed substrate, comprising:

providing a model to predict deformation of a plurality of fields of a substrate induced by thermal effects of exposing;

modifying exposure information used to configure the exposure of said fields of said substrate based on said predicted thermally-induced deformation information;

exposing a pattern onto said fields of said substrate in accordance with said modified exposure information;

measuring attributes of said fields to assess deformation of said fields induced by thermal effects of said exposing;

determining corrective information based on said measured attributes; and

adjusting said modified exposure information, based on said corrective information, to compensate for the thermally-induced field deformations, wherein said thermally-induced field deformation information includes predicting deformation effects of selected points within each of said fields based on a time-decaying characteristic as energy is transported across said wafer.

16. The method of claim 15 , wherein said predictive model is based on:

dx p =Σ i T i x D i x ; and

dy p =Σ i T i y D i y ; where

T

i

=

ⅇ

-

t

-

t

i

τ

:

represents thermal effects of exposing one of said target fields C i which will decay in time as energy is transported across said substrate in either the x or y direction;

τ: represents the time sensitivity constant which depends on the thermal properties of the lithographic exposure components;

D i =ke −| r i − r |/χ : represents effects induced by a distance r i between said exposed target field C i and target field to be currently exposed in either the x or y direction;

χ: represents the spatial thermal properties of the lithographic exposure components;

k: represents a proportionality constant which depends on thermal properties of the lithographic exposure components;

dx p : represents predicted deformation along the x axis; and

dy p : represents predicted deformation along the y axis.

17. The method of claim 16 , wherein said adjusting said pre-specified exposure information includes adjusting said exposure field sequencing information based on said predicted thermally-induced field deformation information.

18. A method of correcting thermally-induced field deformations of a lithographically exposed substrate, comprising:

measuring temperature variations on surface of a substrate containing a plurality of fields to be exposed;

generating a deformation map based on said measured substrate temperature variations;

modifying exposure information used to configure the exposure of said fields of said substrate based on said deformation map;

exposing a pattern onto said fields in accordance with said modified exposure information;

measuring attributes of said fields to assess deformation of said fields induced by thermal effects of said exposing;

determining corrective information based on said measured attributes; and

adjusting said modified exposure information, based on said corrective information, to compensate for the thermally-induced field deformations, wherein said temperature variation measurement includes thermographic imaging.

19. A method of correcting thermally-induced field deformations of a lithographically exposed substrate, comprising:

measuring temperature variations on surface of a substrate containing a plurality of fields to be exposed;

generating a deformation map based on said measured substrate temperature variations;

modifying exposure information used to configure the exposure of said fields of said substrate based on said deformation map;

exposing a pattern onto said fields in accordance with said modified exposure information;

measuring attributes of said fields to assess deformation of said fields induced by thermal effects of said exposing;

determining corrective information based on said measured attributes; and

adjusting said modified exposure information, based on said corrective information wherein said deformation map is characterized by:

[

dx

]

p

=

[

c

⁢

⁢

x

i

r

w

⁢

1

N

i

⁢

∑

k

⁢

(

T

k

-

T

nom

)

]

;

⁢

[

dy

]

p

=

[

c

⁢

⁢

y

i

r

w

⁢

1

N

i

⁢

∑

k

⁢

(

T

k

-

T

nom

)

]

;

where

dx p : represents the predicted deformation along the x axis;

x i : represents the x coordinate of field i;

c: represents a proportionality constant (thermal expansion coefficient);

N i : represents the number of fields taken into account in the summation;

k: sums over the relevant fields, along the connection line between the wafer centre and field i;

T k : represents the measured temperature of field k;

T nom : represents the nominal temperature for which the machine is set up;

y i : represents the y coordinate of field i; and

dy p : represents the predicted deformation along the y axis.

20. The method of claim 19 , wherein said adjusting said pre-specified exposure information includes adjusting said modified pre-specified exposure information, after said exposing, based on deformation offset information determined by said corrective information.

21. A method of correcting thermally-induced field deformations of substrates exposed by a lithographic apparatus, said method comprising:

determining corrective information based on exposed target fields of at least one prior substrate;

applying said corrective information to exposure information; and

exposing target fields of subsequent substrates in accordance with said exposure information having applied corrective information, wherein said determining corrective information includes exposing a pattern onto a plurality of said target fields of said at least one prior substrate and measuring attributes of said target fields of said at least one prior substrate to assess deformation induced by thermal effects of said exposing and wherein said determining corrective information includes deriving a thermal corrective model characterized by:

Δ

⁢

r

_

≈

∑

i

⁢

T

i

⁢

D

i

;

where

T

i

=

T

i

⁡

(

t

,

t

i

,

C

_

)

;

and

D

i

=

D

i

⁡

(

r

_

,

r

_

i

,

G

_

)

wherein T i represents thermal effects of exposing a target field C i , t is a current time, t i is time of exposing target field C i , and C =(c 1 ,c 2 , . . . , c n ) represents a vector of calibrated parameters that correspond to thermal properties of the lithographic exposure components with respect to time; and

wherein D i represents effects induced by a distance between the exposed target field C i and the target field to be currently exposed, r is a point of a wafer substrate W currently being exposed, r i is a point on target field C i , and G =(g 1 ,g 2 , . . . ,g m ) represents a vector of calibrated parameters that corresponds to thermal properties of the lithographic exposure components with respect to distance.

22. A method of correcting thermally-induced field deformations of substrates exposed by a lithographic apparatus, said method comprising:

determining corrective information based on exposed target fields of at least one prior substrate;

applying said corrective information to exposure information; and

exposing target fields of subsequent substrates in accordance with said exposure information having applied corrective information, wherein said determining corrective information includes exposing a pattern onto a plurality of said target fields of said at least one prior substrate and measuring attributes of said target fields of said at least one prior substrate to assess deformation induced by thermal effects of said exposing and said determining corrective information includes employing a predictive model characterized by:

[

dx

]

p

=

[

x

r

w

·

N

i

N

tot

·

dx

max

]

;

and

⁢

[

dy

]

p

=

[

y

r

w

·

N

i

N

tot

·

dy

max

]

;

where

dx p : represents the predicted deformation along the x axis;

dx max : represents the predicted total deformation of the wafer substrate W in the x direction after the last target field has been exposed;

x: represents the x coordinate of a point on the wafer substrate W;

r w : represents the radius of the wafer substrate W;

N i : represents the current target field index number;

N tot : represents the total number of target fields;

dy p : represents the predicted deformation along the y axis;

dy max : represents the predicted total deformation of the wafer substrate W in the y direction after the last target field has been exposed; and

y: represents the y coordinate of a point on the wafer substrate W.

23. A method of correcting thermally-induced field deformations of substrates exposed by a lithographic apparatus, said method comprising:

determining corrective information based on exposed target fields of at least one prior substrate;

applying said corrective information to exposure information; and exposing target fields of subsequent substrates in accordance with said exposure information having applied corrective information, wherein said determining corrective information includes exposing a pattern onto a plurality of said target fields of said at least one prior substrate and measuring attributes of said target fields of said at least one prior substrate to assess deformation induced by thermal effects of said exposing and said determining corrective information includes employing a predictive model characterized by:

dx p =Σ i T i x D i x ; and

dy p =Σ i T i y D i y ; where

T

i

=

ⅇ

-

t

-

t

i

τ

:

represents thermal effects of exposing one of said target fields C i which will decay in time as energy is transported across said substrate in either the x or y direction;

τ: represents the time sensitivity constant which depends on the thermal properties of the lithographic exposure components;

D i =ke −| r i − r |/χ : represents effects induced by a distance r i between said exposed target field C i and target field to be currently exposed in either the x or y direction;

χ: represents the spatial thermal properties of the lithographic exposure components;

k: represents a proportionality constant which depends on thermal properties of the lithographic exposure components;

dx p : represents predicted deformation along the x axis; and

dy p : represents predicted deformation along the y axis.

24. A method of correcting thermally-induced field deformations of substrates exposed by a lithographic apparatus, said method comprising:

determining corrective information based on exposed target fields of at least one prior substrate;

applying said corrective information to exposure information; and

exposing target fields of subsequent substrates in accordance with said exposure information having applied corrective information, wherein said determining corrective information includes exposing a pattern onto a plurality of said target fields of said at least one prior substrate and measuring attributes of said target fields of said at least one prior substrate to assess deformation induced by thermal effects of said exposing and said determining corrective information comprises:

measuring temperature variations on surface of said at least one prior substrate, and

generating a deformation map based on said measured substrate temperature variations,

wherein said deformation map is characterized by:

[

dx

]

p

=

[

c

⁢

⁢

x

i

r

w

⁢

1

N

i

⁢

∑

k

⁢

(

T

k

-

T

nom

)

]

;

⁢

[

dy

]

p

=

[

c

⁢

⁢

y

i

r

w

⁢

1

N

i

⁢

∑

k

⁢

(

T

k

-

T

nom

)

]

;

where

dx p : represents the predicted deformation along the x axis;

x i : represents the x coordinate of field i;

c: represents a proportionality constant (thermal expansion coefficient);

N i : represents the number of fields taken into account in the summation;

k: sums over the relevant fields, along the connection line between the wafer centre and field i;

T k : represents the measured temperature of field k;

T nom : represents the nominal temperature for which the machine is set up;

y i : represents the y coordinate of field i; and

dy p : represents the predicted deformation along the y axis.