Cyclic error compensation in interferometry systems

• US 7,616,322 B2
• Filed: 08/03/2006
• Issued: 11/10/2009
• Est. Priority Date: 07/08/2002
• Status: Active Grant

• Current Assignee: Zygo Corporation (Ametek Incorporated)
• Original Assignee: Zygo Corporation (Ametek Incorporated)
• Inventors: Field, Alan H., Hill, Henry A., Demarest, Frank C.
• Primary Examiner(s): Connolly; Patrick J
• Application Number:
  US11/462,185
• Publication Number:
  US 20070008547A1
• Time in Patent Office: 1,195 Days
• Field of Search: 356/481, 356/482, 356/486, 356/487, 356/493, 356/498, 356/500, 356/517
• US Class Current: 356/500
• CPC Class Codes: G01B 9/02003 using beat frequencies
• CPC Class Codes: G01B 9/02007 Two or more frequencies or sources used for interferometric measurement using only beat G01B9/02003
• CPC Class Codes: G01B 9/0207 Error reduction by correction of the measurement signal based on independently determined error sources, e.g. using a reference interferometer
• CPC Class Codes: G01B 9/02084 Processing in the Fourier or frequency domain when not imaged in the frequency domain
• CPC Class Codes: G03F 7/70775 Position control, e.g. interferometers or encoders for determining the stage position

Abstract

An interference signal S(t) is provided from interference between two beams directed along different paths. The signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time. An error signal is provided to reduce errors in an estimate of {tilde over (L)}(t). The error signal is derived at least in part based on one or more collective properties of a distribution of multi-dimensional values. At least one of the multi-dimensional values in the distribution is generated from a plurality of samples of the signal S(t) (e.g., samples of the signal captured at different times).

Claims

1. A method comprising:

providing an interference signal S(t) from interference between two beams directed along different paths, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time; and

providing an error signal to reduce errors in an estimate of {tilde over (L)}(t), the error signal being derived at least in part based on one or more collective properties of a distribution of multi-dimensional values, at least one of the multi-dimensional values in the distribution being generated from a plurality of samples of the signal S(t);

wherein one of the paths is associated with a position of a reference object and the other path is associated with a position of a moveable measurement object;

wherein the position of the moveable object is controlled by a servo system having a bandwidth and f_S, the samples of the signal S(t) from which the multi-dimensional values are calculated correspond to sample times at which the velocity v of the moveable measurement object relative to the reference object divided by a wavelength λ

of the beams is less than ten times the bandwidth f_S; and

wherein the servo system controls the position of the measurement object based on the signal S(t) and the error signal.

2. The method of claim 1, wherein the two beams have different frequencies.

3. The method of claim 1, wherein providing the error signal comprises providing one or more coefficients representative of one or more errors that cause the signal S(t) to deviate from an ideal expression of the form A₁ cos(ω

_Rt+φ

(t)+ζ

₁), where A₁ and ζ

₁ are constants, ω

_R is an angular frequency difference between the two beams before being directed along the different paths, and φ

(t)=nk{tilde over (L)}(t), with k=2π

/λ and

λ

equal to a wavelength for the beams.

4. The method of claim 3, wherein the deviation can be expressed as

$\sum _{}$

m , p ⁢

⁢

A m , p ⁢

cos ⁡

( ω

R ⁢

t + m p ⁢

φ

⁡

( t ) + ζ

m , p ) ,

where p=1, 2, 3 . . . , and m is any integer not equal to p, and where the provided coefficients comprise information corresponding to at least some of A_m,p and ζ

_m,p.

5. The method of claim 3, wherein the coefficients are derived at least in part based on the one or more collective properties of the distribution of multi-dimensional values.

6. The method of claim 5, wherein the error signal is generated from the coefficients and one or more error basis functions derived at least in part from a plurality of samples of the signal S(t).

7. The method of claim 6, wherein each of the error basis functions is derived at least in part from a linear combination of samples of the signal S(t).

8. The method of claim 6, wherein each of the error basis functions corresponds to a function that includes one or more leading sinusoidal terms having a time-varying argument that corresponds to a time-varying argument of an error term that represents a portion of the deviation of S(t) from the ideal expression.

9. The method of claim 1, wherein the multi-dimensional values comprise two-dimensional values.

10. The method of claim 9, wherein the one or more collective properties comprise one or more properties associated with a curve fit to at least some of the two-dimensional values in the distribution.

11. The method of claim 10, wherein the one or more properties associated with the curve comprise values interpolated from the curve.

12. The method of claim 10, wherein the curve comprises an ellipse.

13. The method of claim 12, wherein the one or more properties associated with the curve comprise one or more of a center location, an ellipticity, and an angle of a major or minor axis.

14. The method of claim 9, wherein each of the two-dimensional values is represented as a complex number.

15. The method of claim 14, wherein the complex number comprises a linear combination of samples of the signal S(t).

16. The method of claim 15, wherein the linear combination comprises a transform signal D_q (t₁) based on values of the signal S(t), for a frequency value determined by q, updated at a time t₁.

17. The method of claim 16, wherein the transform signal D_q (t₁) comprises a sample of a discrete Fourier transform of the signal S(t).

18. The method of claim 17, wherein

$D_q$

( t 1 ) = ∑

n = 0 N - 1 ⁢

⁢

W n ⁢

S ⁡

( n ⁢

⁢

τ

+ t 1 ) ⁢

exp ⁢

{ - j ( 2 ⁢

π

( n - N - 1 2 ) ⁢

q ⁢

/ ⁢

N ) } ,

where τ

=1/f_S, and W_n is a window function centered at

$n=\frac{N-1}{2}.$

19. The method of claim 14, wherein the complex number is represented as a phase and a magnitude.

20. The method of claim 19, wherein at least two phases associated with respective values in the distribution are separated from each other by at least 90 degrees.

21. The method of claim 19, wherein the spacing between the phases of the values in the distribution varies by less than 20%.

22. The method of claim 1, wherein the one or more collective properties of the distribution of multi-dimensional values comprise a statistical average derived from the multi-dimensional values in the distribution.

23. The method of claim 1, the distribution of multi-dimensional values includes at least 20 values.

24. The method of claim 1, wherein reducing errors in the estimate of {tilde over (L)}(t) comprises deriving the estimate of {tilde over (L)}(t) from a difference between the error signal and a discrete Fourier transform of samples of S(t).

25. The method of claim 1, further comprising directing the two beams along the different paths and measuring the interference signal S(t).

26. The method of claim 25, wherein at least one of the beams is directed to reflect from a movable measurement object before producing the interference signal S(t).

27. The method of claim 26, wherein the beam directed to reflect from the movable measurement object reflects from the measurement object multiple times before producing the interference signal S(t).

28. The method of claim 26, wherein the beams are directed to reflect from different locations of the movable measurement object before producing the interference signal S(t).

29. The method of claim 1, wherein the errors correspond to spurious beam paths.

30. A lithography method for use in fabricating integrated circuits on a wafer, the method comprising:

supporting the wafer on a moveable stage;

imaging spatially patterned radiation onto the wafer;

adjusting the position of the stage; and

monitoring the position of the stage using an interferometry system, wherein monitoring the position of the stage comprises reducing errors in an estimate of a physical path difference associated with a position of a measurement object associated with the stage using the method of claim 1.

31. A method for fabricating integrated circuits, the method comprising:

applying a resist to a wafer;

forming a pattern of a mask in the resist by exposing the wafer to radiation using the lithography method of claim 30; and

producing an integrated circuit from the wafer.

32. A lithography method for use in the fabrication of integrated circuits, the method comprising:

directing input radiation through a mask to produce spatially patterned radiation;

positioning the mask relative to the input radiation;

monitoring the position of the mask relative to the input radiation using an interferometry system, wherein monitoring the position of the mask comprises reducing errors in an estimate of a physical path difference associated with the position of the mask using the method of claim 1; and

imaging the spatially patterned radiation onto a wafer.

33. A method for fabricating integrated circuits, the method comprising:

applying a resist to a wafer;

forming a pattern of a mask in the resist by exposing the wafer to radiation using the lithography method of claim 32; and

producing an integrated circuit from the wafer.

34. A lithography method for fabricating integrated circuits on a wafer, the method comprising:

positioning a first component of a lithography system relative to a second component of a lithography system to expose the wafer to spatially patterned radiation; and

monitoring the position of the first component relative to the second component using an interferometry system, wherein monitoring the position of the first component comprises reducing errors in an estimate of a physical path difference associated with a position of a measurement object associated with the first component using the method of claim 1.

35. A method for fabricating integrated circuits, the method comprising:

applying a resist to a wafer;

forming a pattern of a mask in the resist by exposing the wafer to radiation using the lithography method of claim 34; and

producing an integrated circuit from the wafer.

36. A method for fabricating a lithography mask, the method comprising:

directing a write beam to a substrate to pattern the substrate;

positioning the substrate relative to the write beam; and

monitoring the position of the substrate relative to the write beam using an interferometry system, wherein monitoring the position of the substrate comprises reducing errors in an estimate of a physical path difference associated with a position of a measurement object associated with the substrate using the method of claim 1.

37. A computer readable medium storing instructions that cause a processor to perform the method of claim 1.

38. An apparatus comprising:

an interferometry system, which during operation directs two beams along different paths and provides an interference signal S(t) from interference between the two beams, wherein the signal S(t) is indicative of changes in an optical path difference n{tilde over (L)}(t) between the different paths, where n is an average refractive index along the different paths, {tilde over (L)}(t) is a total physical path difference between the different paths, and t is time; and

an electronic processor, which during operation receives the interference signal S(t) from the interferometry system and provides an error signal to reduce errors in an estimate of {tilde over (L)}(t), the error signal being derived at least in part based on one or more collective properties of a distribution of multi-dimensional values, at least one of the multi-dimensional values in the distribution being generated from a plurality of samples of the signal;

wherein one of the paths is associated with a position of a reference object and the other path is associated with a position of a moveable measurement object;

wherein the position of the moveable object is controlled by a servo system having a bandwidth f_S, and the samples of the signal S(t) from which the multi-dimensional values are calculated correspond to sample times at which the velocity v of the moveable measurement object relative to the reference object divided by a wavelength λ

of the beams is less than ten times the bandwidth f_S; and

wherein the servo system controls the position of the measurement object based on the signal S(t) and the error signal S(t).

39. A lithography system for use in fabricating integrated circuits on a wafer, the system comprising:

a stage for supporting the wafer;

an illumination system for imaging spatially patterned radiation onto the wafer;

a positioning system for adjusting the position of the stage relative to the imaged radiation; and

the apparatus of claim 38 for monitoring the position of the wafer relative to the imaged radiation.

40. A method for fabricating integrated circuits, the method comprising:

applying a resist to a wafer;

forming a pattern of a mask in the resist by exposing the wafer to radiation using the lithography system of claim 39; and

producing an integrated circuit from the wafer.

41. A lithography system for use in fabricating integrated circuits on a wafer, the system comprising:

a stage for supporting the wafer; and

an illumination system including a radiation source, a mask, a positioning system, a lens assembly, and the apparatus of claim 38, wherein during operation the source directs radiation through the mask to produce spatially patterned radiation, the positioning system adjusts the position of the mask relative to the radiation from the source, the lens assembly images the spatially patterned radiation onto the wafer, and the apparatus monitors the position of the mask relative to the radiation from the source.

42. A method for fabricating integrated circuits, the method comprising:

applying a resist to a wafer;

forming a pattern of a mask in the resist by exposing the wafer to radiation using the lithography system of claim 41; and

producing an integrated circuit from the wafer.

43. A beam writing system for use in fabricating a lithography mask, the system comprising:

a source providing a write beam to pattern a substrate;

a stage supporting the substrate;

a beam directing assembly for delivering the write beam to the substrate;

a positioning system for positioning the stage and beam directing assembly relative one another; and

the apparatus of claim 38 for monitoring the position of the stage relative to the beam directing assembly.

44. A method for fabricating a lithography mask comprising:

directing a beam to a substrate using the beam writing system of claim 43;

varying the intensity or the position of the beam at the substrate to form a pattern in the substrate; and

forming the lithography mask from the patterned substrate.