Characterization and compensation of non-cyclic errors in interferometry systems

• US 20030174341A1
• Filed: 02/12/2003
• Published: 09/18/2003
• Est. Priority Date: 02/12/2002
• Status: Active Grant

• Current Assignee: Zygo Corporation (Ametek Incorporated)
• Original Assignee: Zygo Corporation (Ametek Incorporated)
• Inventors: Hill, Henry A.
• Granted Patent: US 6,956,655 B2
• Time in Patent Office: Days
• US Class Current: 356/498
• CPC Class Codes: G01B 2290/60 Reference interferometer, i.e. additional interferometer not interacting with object
• CPC Class Codes: G01B 2290/70 Using polarization in the interferometer
• CPC Class Codes: G01B 9/02019 contacting different points on same face of object
• CPC Class Codes: G01B 9/02059 Reducing effect of parasitic reflections, e.g. cyclic errors

Abstract

Systems and methods for characterizing and compensating non-cyclic errors in interferometers and interferometer components are disclosed.

Claims

1. A method comprising:

providing a test interferometer which during operation directs two beams along different paths and then combines them to produce an output beam, wherein the output beam comprises information about an optical path length difference between the two beams,

wherein imperfections in the test interferometer cause a measurable interferometric test phase derived from the output beam to deviate from the expression Φ

=pknL, where p is an integer, k is the wavenumber of the output beam, and nL corresponds to the optical path length difference, wherein the deviation comprises a non-cyclic error term that varies in a nonperiodic way on the optical path length difference;

using the test interferometer to measure the test phase as a function of a test parameter that causes the optical path length difference to vary;

comparing the measured test phase to another expression indicative of the optical path length difference; and

determining a representation indicative of the non-cyclic error term for the test interferometer based on the comparison.

2. The method of claim 1, wherein during operation at least one of the two beams contacts a measurement object and the test parameter is a distance between the test interferometer and the measurement object.

3. The method of claim 1, wherein during operation at least one of the two beams contacts a measurement object and the test parameter is an angular orientation of the measurement object with respect to the interferometer.

4. The method of claim 1, wherein the interferometer derives the two beams from an input beam and the test parameter is a propagation direction of the input beam.

5. The method of claim 2, wherein measuring the test phase as a function of the test parameter comprises scanning the position of the measurement object with respect to the test interferometer.

6. The method of claim 5, wherein the other expression indicative of the optical path length difference is based on a reference phase that is monitored as a function of the test parameter simultaneously to measuring the test phase.

7. The method of claim 6, wherein the reference phase is monitored using a reference interferometer, which during operation directs a first reference interferometer beam to contact the measurement object at least once.

8. The method of claim 7, wherein imperfections in the reference interferometer are sufficiently small so that a non-cyclic error contribution to the reference phase due to the imperfections is negligible compared to the non-cyclic error term of the test interferometer.

9. The method of claim 7, wherein the reference interferometer is positioned sufficiently close to the measurement object so that a non-cyclic error contribution to the reference phase due to imperfections in the reference interferometer is negligible compared to the non-cyclic error term of the test interferometer.

10. The method of claim 9, further comprising adjusting the position of the reference interferometer with respect to the measurement object to maintain the reference interferometer sufficiently close to the measurement object so that the non-cyclic error contribution to the reference phase is negligible compared to the non-cyclic error term of the test interferometer for a range of the test parameter greater than a maximum distance between the measurement object and the reference interferometer.

11. The method of claim 6, wherein the non-cyclic error term is determined from a deviation of a sum of the test phase and the reference phase from a constant value.

12. The method of claim 3, wherein measuring the test phase as a function of the test parameter comprises rotating the measurement object about a pivot axis to vary the angular orientation of the measurement object with respect to the test interferometer.

13. The method of claim 12, further comprising adjusting the position of the pivot axis and determining the representation for different pivot axis positions.

14. The method of claim 12, wherein the other expression indicative of the optical path length difference comprises a mathematical formula relating the orientation of the measurement object to the optical path length difference.

15. The method of claim 14, wherein determining the representation indicative of the non-cyclic error term comprises fitting a polynomial to the measured test phase as a function of the test parameter.

16. The method of claim 15, wherein the non-cyclic error term is determined from a cubic coefficient of the fitted polynomial.

17. The method of claim 16, wherein the non-cyclic error term is also determined from quartic or quartic and higher order coefficients of the fitted polynomial.

18. The method of claim 12, further comprising fitting a polynomial to the measured test phase as a function of the test parameter and determining a point on an axis of the test interferometer from the fitted polynomial.

19. The method of claim 18, wherein the point on the test interferometer axis is determined from a point at which the first derivative of the fitted polynomial with respect to the test parameter is zero.

20. The method of claim 4, wherein measuring the test phase as a function of the test parameter comprises scanning the input beam propagation direction with respect to the test interferometer.

21. The method of claim 20, wherein scanning the input beam propagation direction comprises directing the input beam to contact a beam steering element prior to the test interferometer and scanning the orientation of the beam steering element with respect to the test interferometer.

22. The method of claim 21, wherein the other expression indicative of the optical path length difference is based on a reference phase that is monitored as a function of the orientation of the beam steering element simultaneous to measuring the test phase.

23. The method of claim 20, wherein the reference phase is monitored using a reference interferometer that directs a beam to contact the beam steering element and combines that beam with another beam to produce a reference output beam.

24. The method of claim 23, wherein the reference phase comprises information indicative of the orientation of the beam steering element.

25. The method of claim 24, wherein a non-cyclic error term for the reference interferometer is small compared to that of the test interferometer.

26. The method of claim 24, wherein a non-cyclic error term for the reference interferometer is known and the reference phase is compensated for contributions from the reference interferometer non-cyclic error term.

27. The method of claim 20, wherein the test interferometer separates the input beam into two component beams that exit the interferometer along parallel paths whose separation depends on the input beam propagation direction.

28. The method of claim 1, wherein the test interferometer comprises a single pass interferometer.

29. The method of claim 1, wherein the interferometer comprises a multiple pass interferometer.

30. The method of claim 29, wherein the multiple pass interferometer is a high-stability plane mirror interferometer.

31. The method of claim 1, wherein the interferometer comprises an angular displacement interferometer.

32. The method of claim 1, wherein the interferometer comprises a dynamic beam steering element.

33. The method of claim 1, wherein the interferometer comprises a passive zero shear interferometer.

34. The method of claim 1, wherein the representation correlates a value for the non-cyclic error term as a function of at least one correlation parameter that depends on the optical path length difference.

35. The method of claim 34, wherein the correlation parameter is the test parameter.

36. The method of claim 35, wherein the representation is a lookup table.

37. The method of claim 35, wherein the representation is an algebraic expression parameterized by the correlation parameter.

38. An apparatus comprising:

a test interferometer which during operation directs two beams along different paths and then combines them to produce an output beam, wherein the output beam comprises information about an optical path length difference between the two beams,

wherein imperfections in the interferometer causes a measurable interferometric phase derived from the output beam to deviate from the expression Φ

=pknL, where p is an integer, k is the wavenumber of the output beam, and nL corresponds to the optical path length difference, wherein the deviation comprises a non-cyclic error term that varies in a nonperiodic way on the optical path length difference; and

an electronic storage medium providing a representation indicative of the non-cyclic error term for the test interferometer.

39. The apparatus of claim 38, further comprising an electronic controller configured to couple to the electronic storage medium, wherein during operation the electronic controller corrects the output of the test interferometer based on the representation in the electronic storage medium.

40. The apparatus of claim 38, wherein the representation comprises information about a deviation of the measured phase from Φ

=pknL as a function of a distance between the test interferometer and a measurement object.

41. The apparatus of claim 38, wherein the representation comprises information about a deviation of the measured phase from Φ

=pknL as a function of an orientation of a measurement object with respect to the test interferometer.

42. The apparatus of claim 41, wherein the representation comprises information about a deviation of the measured phase from Φ

=pknL as a function of a position of an axis about which the orientation of the measurement object pivots.

43. The apparatus of claim 38, wherein during operation the test interferometer derives the two beams from an input beam and the representation comprises information about a deviation of the measured phase from Φ

=pknL as a function of the propagation direction of the input beam.

44. The apparatus of claim 38, wherein the interferometer is a single pass interferometer.

45. The apparatus of claim 38, wherein the interferometer is a multiple pass interferometer.

46. The apparatus of claim 38, wherein the multiple pass interferometer is a high-stability plane mirror interferometer.

47. The apparatus of claim 38, wherein the interferometer is an angular displacement interferometer.

48. The apparatus of claim 38, wherein the interferometer comprises a dynamic beam steering element.

49. The apparatus of claim 38, wherein the interferometer is a passive zero shear interferometer.

50. 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.

51. 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 interferometry system monitors the position of the mask relative to the radiation from the source.

52. 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.

60. A method for fabricating integrated circuits, the method comprising using the lithography system of claim 50.

61. A method for fabricating integrated circuits, the method comprising using the lithography system of claim 51.

53. An interferometry method comprising:

positioning a test interferometer relative to a measurement object, wherein during operation of the test interferometer directs two beams along different paths and then combines them to produce an output beam, wherein at least one of the beams contacts the measurement object and the output beam comprises information about an optical path length difference between the two beams,

wherein imperfections in the interferometer causes a measurable interferometric phase derived from the output beam to deviate from the expression Φ

=pknL, where p is an integer, k is the wavenumber of the output beam, and nL corresponds to the optical path length difference, wherein the deviation comprises a non-cyclic error term that varies in a nonperiodic way on the optical path length difference;

correcting the measured phase based on a representation indicative of the non-cyclic error term for the test interferometer; and

monitoring the position of the measurement object based on the corrected phase.

54. 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 the method of claim 53.

55. A lithography method for use in the fabrication of integrated circuits 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 the method of claim 53;

and

imaging the spatially patterned radiation onto a wafer.

56. A lithography method for fabricating integrated circuits on a wafer 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 the method of claim 53.

57. A method for fabricating integrated circuits, the method comprising the lithography method of claim 54.

58. A method for fabricating integrated circuits, the method comprising the lithography method of claim 55.

59. A method for fabricating integrated circuits, the method comprising the lithography method of claim 56.

62. 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 the interferometry method of claim 53.

63. The method of claim 53, wherein the measurement object is mounted on a movable stage and the method further comprises:

adjusting the location of the movable stage to position an alignment artifact on the stage coincident with a rotation axis of the stage;

monitoring the output beam phase as a function of the orientation of the movable stage about the axis; and

calibrating the test interferometer based on the monitored phase.

64. The method of claim 63, wherein calibrating the test interferometer comprises fitting a polynomial to the monitored phase.

65. The method of claim 64, wherein the polynomial is a quadratic.

66. The method of claim 64, wherein the test interferometer is calibrated based on coefficients of the fitted polynomial.