Abstract

Flying-height testers for rigid disk drives employ a transparent glass substrate in place of the magnetic disk and use optical interferometry to measure the flight properties of the read-write slider. Because of the material phase change on reflection, the effective optical constants n and k of the slider play an important role in the measurement. We describe an instrument that determines the optical constants simultaneously with flying height, using polarization interferometry. This in situ analysis of n and k obviates the need for independent ellipsometry, while avoiding the problematic retract calibration characteristic of traditional flying-height test equipment. The rms uncertainty for n and k are 0.04, resulting in height uncertainties that range from 3 nm for 250-nm flying heights down to 0.5 nm at contact. We verify these results by use of a variety of experimental techniques on both laboratory samples and actual read-write sliders.

© 1998 Optical Society of America

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  1. B. Bhushan, Tribology and Mechanics of Magnetic Storage Devices (Springer-Verlag, New York, 1990) pp. 765–797.
  2. W. Stone, “A proposed method for solving some problems in lubrication,” The Commonwealth Engineer (1November1921), pp. 115–122.
  3. J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Develop. 18, 529–533 (1974).
    [CrossRef]
  4. T. Ohkubo, J. Kishegami, “Accurate measurement of gas-lubricated slider bearing separation using laser interferometry,” Trans. ASME 110, 148–155 (1988).
    [CrossRef]
  5. C. Lacey, J. A. Adams, E. W. Ross, A. Cormier, “A new method for measuring flying height dynamically,” Proceedings of DiskCon ’92 (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1992), pp. 27–42.
  6. T. E. Erickson, J. P. Lauer, “Multiplexed laser interferometer for non-dispersed spectrum detection in a dynamic flying height tester,” U.S. patent5,673,110 (30September1997).
  7. P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
    [CrossRef] [PubMed]
  8. P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1997), pp. 89–94.
  9. P. de Groot, “Optical gap measuring apparatus and method,” U.S. patent5,557,399 (17September1996).
  10. F. Muranushi, K. Tanaka, Y. Takeuchi, “Estimation of zero-spacing error due to a phase shift of reflected light in measuring a magnetic head slider’s flying height by light interference,” Adv. Info. Storage Syst. 4, 371–379 (1992). The same paper was presented at the ASME Winter Annual Meeting, Atlanta, Ga., 1991.
  11. The calculations for Table 1 also appear in the paper “Interferometric measurement of disk/slider spacing: the effect of phase shift on reflection,” by C. Lacey, R. Shelor, A. Cormier, R. E. TalkeIEEE Trans. Magn. MAG-29, 3906–3910 (1993).
  12. M. Born, E. Wolf, Principles of Optics (Pergamon, New York) p. 40.
  13. Following Born and Wolf, we prefer to use the n + ik definition of the complex index, rather than the more common n - ik.
  14. P. de Groot, “Optical properties of alumina titanium carbide sliders used in rigid disk drives,” (submitted to Appl. Opt.).
  15. R. Pavlat, “Flying height measurement systems and slider absorption,” IDEMA Insight 7, 1 (1994).
  16. Y. Li, “Flying height measurement on Al2O3 film of a magnetic slider,” presented at the American Society of Mechanical Engineers Tribology Conference, paper 96-TRIB-61 (San Francisco, Calif., 13–17 October 1996).
  17. K. Lue, C. Lacey, F. E. Talke, “Measurement of flying height with carbon overcoated sliders,” IEEE Trans. Magn. 30, 4167–4169 (1994).
    [CrossRef]
  18. G. Sommargren, “Flying height and topography measuring interferometer,” U.S. patent5,218,424 (8June1993).
  19. Generally, it is not possible to calculate a film thickness as well as the optical constants from a single ellipsometric measurement; hence the need for three or more flying heights for proper n and k calibration. See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987), p. 317.
  20. P. de Groot, “Birefringence in rapidly-rotating glass disks,” J. Opt. Soc. Am. A 15, 1202–1211 (1998).
    [CrossRef]
  21. P. de Groot, “Method and apparatus for measuring and compensating birefringence in rotating disks,” U.S. patent5,644,562 (1July1997).
  22. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992) p. 680.
  23. Not everyone agrees that interference phase information is essential for n and k. K. H. Womack and A. Butler have proposed to calculate the two parameters n and k using only the intensity reflectivity at normal incidence, together with off-site characterization of the material. Their paper, entitled “In-situ n & k phase compensation in an interferometric flying height tester,” is available from Phase Metrics Corporation, 10260 Sorrento Valley Road, San Diego, Calif. 92121.
  24. P. de Groot, “Homodyne interferometric receiver and calibration method having improved accuracy and functionality,” U.S. patent5,663,793 (2September1997).
  25. C. P. Brophy, “Effect of intensity error correlation on the computed phase of phase-shifting interferometry,” J. Opt. Soc. Am. A 7, 537–541 (1990).
    [CrossRef]
  26. Another way to express the uncertainty in the optical constants would be to calculate the ratios Δk/k and Δn/n. However, this would create the misleading impression that the uncertainty improves for larger values of n and k. It would also create the false impression that measurement of k on a dielectric has an undefined uncertainty because the k is zero.
  27. P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecki, ed., Proc. SPIE2782, 47–57 (1996).
  28. C. Lacey, C. Durán, K. Womack, R. Simmons, “Optical measurement of flying height,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, San Diego, 1997), pp. 81–88.
  29. C. A. Durán, “Error analysis of a multiwavelength dynamic flying height tester,” IEEE Trans. Magn. 32, 3720–3723 (1996).
    [CrossRef]
  30. R. B. Edwards, “Three-color laser interferometer,” IBM Technical Disclosure Bulletin 16, 595–596 (1973).
  31. T. Fukuzawa, T. Hisano, T. Morita, K. Ikarugi, “Method and apparatus for measuring the flying height of a magnetic head above a disk surface at three wavelengths,” U.S. patent5,502,565 (26March1996).
  32. G. Sommargren, “Distance measuring interferometer and method of use,” U.S. patent4,606,638 (19August1986).
  33. C. Lacey, C. Duran, “Full surface detection of flying height with in-situ n & k measurement,” IDEMA Insight, 9(6), 1, 9 (1996).
  34. P. de Groot, J. Biegen, L. Deck, R. Smythe, “Calibration standard for optical gap measuring tools,” U.S. patent5,724,134 (3March1998).
  35. A similar arrangement for establishing known gaps for calibration appears in U.S. patent5,220,408 to M. Mager, entitled “Method and apparatus for calibration of optical flying-height testers” (15June1993).
  36. Our technique does require an estimated value for the scattered light loss, in the form of the μ factor. However, the effect of an incorrect μ on the ZSE is small. It serves primarily to simplify comparison of our technique with traditional ellipsometry.

1998

1996

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
[CrossRef] [PubMed]

C. A. Durán, “Error analysis of a multiwavelength dynamic flying height tester,” IEEE Trans. Magn. 32, 3720–3723 (1996).
[CrossRef]

C. Lacey, C. Duran, “Full surface detection of flying height with in-situ n & k measurement,” IDEMA Insight, 9(6), 1, 9 (1996).

1994

R. Pavlat, “Flying height measurement systems and slider absorption,” IDEMA Insight 7, 1 (1994).

K. Lue, C. Lacey, F. E. Talke, “Measurement of flying height with carbon overcoated sliders,” IEEE Trans. Magn. 30, 4167–4169 (1994).
[CrossRef]

1993

The calculations for Table 1 also appear in the paper “Interferometric measurement of disk/slider spacing: the effect of phase shift on reflection,” by C. Lacey, R. Shelor, A. Cormier, R. E. TalkeIEEE Trans. Magn. MAG-29, 3906–3910 (1993).

1992

F. Muranushi, K. Tanaka, Y. Takeuchi, “Estimation of zero-spacing error due to a phase shift of reflected light in measuring a magnetic head slider’s flying height by light interference,” Adv. Info. Storage Syst. 4, 371–379 (1992). The same paper was presented at the ASME Winter Annual Meeting, Atlanta, Ga., 1991.

1990

1988

T. Ohkubo, J. Kishegami, “Accurate measurement of gas-lubricated slider bearing separation using laser interferometry,” Trans. ASME 110, 148–155 (1988).
[CrossRef]

1974

J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Develop. 18, 529–533 (1974).
[CrossRef]

1973

R. B. Edwards, “Three-color laser interferometer,” IBM Technical Disclosure Bulletin 16, 595–596 (1973).

Azzam, R. M. A.

Generally, it is not possible to calculate a film thickness as well as the optical constants from a single ellipsometric measurement; hence the need for three or more flying heights for proper n and k calibration. See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987), p. 317.

Bashara, N. M.

Generally, it is not possible to calculate a film thickness as well as the optical constants from a single ellipsometric measurement; hence the need for three or more flying heights for proper n and k calibration. See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987), p. 317.

Bhushan, B.

B. Bhushan, Tribology and Mechanics of Magnetic Storage Devices (Springer-Verlag, New York, 1990) pp. 765–797.

Biegen, J.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
[CrossRef] [PubMed]

P. de Groot, J. Biegen, L. Deck, R. Smythe, “Calibration standard for optical gap measuring tools,” U.S. patent5,724,134 (3March1998).

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecki, ed., Proc. SPIE2782, 47–57 (1996).

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1997), pp. 89–94.

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York) p. 40.

Brophy, C. P.

Cormier, A.

The calculations for Table 1 also appear in the paper “Interferometric measurement of disk/slider spacing: the effect of phase shift on reflection,” by C. Lacey, R. Shelor, A. Cormier, R. E. TalkeIEEE Trans. Magn. MAG-29, 3906–3910 (1993).

de Groot, P.

P. de Groot, “Birefringence in rapidly-rotating glass disks,” J. Opt. Soc. Am. A 15, 1202–1211 (1998).
[CrossRef]

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
[CrossRef] [PubMed]

P. de Groot, “Method and apparatus for measuring and compensating birefringence in rotating disks,” U.S. patent5,644,562 (1July1997).

P. de Groot, “Homodyne interferometric receiver and calibration method having improved accuracy and functionality,” U.S. patent5,663,793 (2September1997).

P. de Groot, J. Biegen, L. Deck, R. Smythe, “Calibration standard for optical gap measuring tools,” U.S. patent5,724,134 (3March1998).

P. de Groot, “Optical properties of alumina titanium carbide sliders used in rigid disk drives,” (submitted to Appl. Opt.).

P. de Groot, “Optical gap measuring apparatus and method,” U.S. patent5,557,399 (17September1996).

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1997), pp. 89–94.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecki, ed., Proc. SPIE2782, 47–57 (1996).

Deck, L.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
[CrossRef] [PubMed]

P. de Groot, J. Biegen, L. Deck, R. Smythe, “Calibration standard for optical gap measuring tools,” U.S. patent5,724,134 (3March1998).

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecki, ed., Proc. SPIE2782, 47–57 (1996).

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1997), pp. 89–94.

Dergevorkian, A.

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1997), pp. 89–94.

Duran, C.

C. Lacey, C. Duran, “Full surface detection of flying height with in-situ n & k measurement,” IDEMA Insight, 9(6), 1, 9 (1996).

Durán, C.

C. Lacey, C. Durán, K. Womack, R. Simmons, “Optical measurement of flying height,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, San Diego, 1997), pp. 81–88.

Durán, C. A.

C. A. Durán, “Error analysis of a multiwavelength dynamic flying height tester,” IEEE Trans. Magn. 32, 3720–3723 (1996).
[CrossRef]

Edwards, R. B.

R. B. Edwards, “Three-color laser interferometer,” IBM Technical Disclosure Bulletin 16, 595–596 (1973).

Erickson, T.

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1997), pp. 89–94.

Erickson, T. E.

T. E. Erickson, J. P. Lauer, “Multiplexed laser interferometer for non-dispersed spectrum detection in a dynamic flying height tester,” U.S. patent5,673,110 (30September1997).

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992) p. 680.

Fleischer, J. M.

J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Develop. 18, 529–533 (1974).
[CrossRef]

Fukuzawa, T.

T. Fukuzawa, T. Hisano, T. Morita, K. Ikarugi, “Method and apparatus for measuring the flying height of a magnetic head above a disk surface at three wavelengths,” U.S. patent5,502,565 (26March1996).

Hisano, T.

T. Fukuzawa, T. Hisano, T. Morita, K. Ikarugi, “Method and apparatus for measuring the flying height of a magnetic head above a disk surface at three wavelengths,” U.S. patent5,502,565 (26March1996).

Ikarugi, K.

T. Fukuzawa, T. Hisano, T. Morita, K. Ikarugi, “Method and apparatus for measuring the flying height of a magnetic head above a disk surface at three wavelengths,” U.S. patent5,502,565 (26March1996).

Kishegami, J.

T. Ohkubo, J. Kishegami, “Accurate measurement of gas-lubricated slider bearing separation using laser interferometry,” Trans. ASME 110, 148–155 (1988).
[CrossRef]

Lacey, C.

C. Lacey, C. Duran, “Full surface detection of flying height with in-situ n & k measurement,” IDEMA Insight, 9(6), 1, 9 (1996).

K. Lue, C. Lacey, F. E. Talke, “Measurement of flying height with carbon overcoated sliders,” IEEE Trans. Magn. 30, 4167–4169 (1994).
[CrossRef]

The calculations for Table 1 also appear in the paper “Interferometric measurement of disk/slider spacing: the effect of phase shift on reflection,” by C. Lacey, R. Shelor, A. Cormier, R. E. TalkeIEEE Trans. Magn. MAG-29, 3906–3910 (1993).

C. Lacey, C. Durán, K. Womack, R. Simmons, “Optical measurement of flying height,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, San Diego, 1997), pp. 81–88.

Lauer, J. P.

T. E. Erickson, J. P. Lauer, “Multiplexed laser interferometer for non-dispersed spectrum detection in a dynamic flying height tester,” U.S. patent5,673,110 (30September1997).

Lin, C.

J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Develop. 18, 529–533 (1974).
[CrossRef]

Lue, K.

K. Lue, C. Lacey, F. E. Talke, “Measurement of flying height with carbon overcoated sliders,” IEEE Trans. Magn. 30, 4167–4169 (1994).
[CrossRef]

Mager, M.

A similar arrangement for establishing known gaps for calibration appears in U.S. patent5,220,408 to M. Mager, entitled “Method and apparatus for calibration of optical flying-height testers” (15June1993).

Morace, J.

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1997), pp. 89–94.

Morita, T.

T. Fukuzawa, T. Hisano, T. Morita, K. Ikarugi, “Method and apparatus for measuring the flying height of a magnetic head above a disk surface at three wavelengths,” U.S. patent5,502,565 (26March1996).

Muranushi, F.

F. Muranushi, K. Tanaka, Y. Takeuchi, “Estimation of zero-spacing error due to a phase shift of reflected light in measuring a magnetic head slider’s flying height by light interference,” Adv. Info. Storage Syst. 4, 371–379 (1992). The same paper was presented at the ASME Winter Annual Meeting, Atlanta, Ga., 1991.

Ohkubo, T.

T. Ohkubo, J. Kishegami, “Accurate measurement of gas-lubricated slider bearing separation using laser interferometry,” Trans. ASME 110, 148–155 (1988).
[CrossRef]

Pavlat, R.

R. Pavlat, “Flying height measurement systems and slider absorption,” IDEMA Insight 7, 1 (1994).

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1997), pp. 89–94.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992) p. 680.

Shelor, R.

The calculations for Table 1 also appear in the paper “Interferometric measurement of disk/slider spacing: the effect of phase shift on reflection,” by C. Lacey, R. Shelor, A. Cormier, R. E. TalkeIEEE Trans. Magn. MAG-29, 3906–3910 (1993).

Simmons, R.

C. Lacey, C. Durán, K. Womack, R. Simmons, “Optical measurement of flying height,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, San Diego, 1997), pp. 81–88.

Smythe, R.

P. de Groot, J. Biegen, L. Deck, R. Smythe, “Calibration standard for optical gap measuring tools,” U.S. patent5,724,134 (3March1998).

Sommargren, G.

G. Sommargren, “Distance measuring interferometer and method of use,” U.S. patent4,606,638 (19August1986).

G. Sommargren, “Flying height and topography measuring interferometer,” U.S. patent5,218,424 (8June1993).

Soobitsky, J.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Polarization interferometer for measuring the flying height of magnetic read-write heads,” Opt. Lett. 21, 441–443 (1996).
[CrossRef] [PubMed]

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecki, ed., Proc. SPIE2782, 47–57 (1996).

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1997), pp. 89–94.

Stone, W.

W. Stone, “A proposed method for solving some problems in lubrication,” The Commonwealth Engineer (1November1921), pp. 115–122.

Takeuchi, Y.

F. Muranushi, K. Tanaka, Y. Takeuchi, “Estimation of zero-spacing error due to a phase shift of reflected light in measuring a magnetic head slider’s flying height by light interference,” Adv. Info. Storage Syst. 4, 371–379 (1992). The same paper was presented at the ASME Winter Annual Meeting, Atlanta, Ga., 1991.

Talke, F. E.

K. Lue, C. Lacey, F. E. Talke, “Measurement of flying height with carbon overcoated sliders,” IEEE Trans. Magn. 30, 4167–4169 (1994).
[CrossRef]

Talke, R. E.

The calculations for Table 1 also appear in the paper “Interferometric measurement of disk/slider spacing: the effect of phase shift on reflection,” by C. Lacey, R. Shelor, A. Cormier, R. E. TalkeIEEE Trans. Magn. MAG-29, 3906–3910 (1993).

Tanaka, K.

F. Muranushi, K. Tanaka, Y. Takeuchi, “Estimation of zero-spacing error due to a phase shift of reflected light in measuring a magnetic head slider’s flying height by light interference,” Adv. Info. Storage Syst. 4, 371–379 (1992). The same paper was presented at the ASME Winter Annual Meeting, Atlanta, Ga., 1991.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992) p. 680.

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992) p. 680.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York) p. 40.

Womack, K.

C. Lacey, C. Durán, K. Womack, R. Simmons, “Optical measurement of flying height,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, San Diego, 1997), pp. 81–88.

Adv. Info. Storage Syst.

F. Muranushi, K. Tanaka, Y. Takeuchi, “Estimation of zero-spacing error due to a phase shift of reflected light in measuring a magnetic head slider’s flying height by light interference,” Adv. Info. Storage Syst. 4, 371–379 (1992). The same paper was presented at the ASME Winter Annual Meeting, Atlanta, Ga., 1991.

IBM J. Res. Develop.

J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Develop. 18, 529–533 (1974).
[CrossRef]

IBM Technical Disclosure Bulletin

R. B. Edwards, “Three-color laser interferometer,” IBM Technical Disclosure Bulletin 16, 595–596 (1973).

IDEMA Insight

C. Lacey, C. Duran, “Full surface detection of flying height with in-situ n & k measurement,” IDEMA Insight, 9(6), 1, 9 (1996).

R. Pavlat, “Flying height measurement systems and slider absorption,” IDEMA Insight 7, 1 (1994).

IEEE Trans. Magn.

The calculations for Table 1 also appear in the paper “Interferometric measurement of disk/slider spacing: the effect of phase shift on reflection,” by C. Lacey, R. Shelor, A. Cormier, R. E. TalkeIEEE Trans. Magn. MAG-29, 3906–3910 (1993).

K. Lue, C. Lacey, F. E. Talke, “Measurement of flying height with carbon overcoated sliders,” IEEE Trans. Magn. 30, 4167–4169 (1994).
[CrossRef]

C. A. Durán, “Error analysis of a multiwavelength dynamic flying height tester,” IEEE Trans. Magn. 32, 3720–3723 (1996).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Trans. ASME

T. Ohkubo, J. Kishegami, “Accurate measurement of gas-lubricated slider bearing separation using laser interferometry,” Trans. ASME 110, 148–155 (1988).
[CrossRef]

Other

C. Lacey, J. A. Adams, E. W. Ross, A. Cormier, “A new method for measuring flying height dynamically,” Proceedings of DiskCon ’92 (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1992), pp. 27–42.

T. E. Erickson, J. P. Lauer, “Multiplexed laser interferometer for non-dispersed spectrum detection in a dynamic flying height tester,” U.S. patent5,673,110 (30September1997).

P. de Groot, “Method and apparatus for measuring and compensating birefringence in rotating disks,” U.S. patent5,644,562 (1July1997).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992) p. 680.

Not everyone agrees that interference phase information is essential for n and k. K. H. Womack and A. Butler have proposed to calculate the two parameters n and k using only the intensity reflectivity at normal incidence, together with off-site characterization of the material. Their paper, entitled “In-situ n & k phase compensation in an interferometric flying height tester,” is available from Phase Metrics Corporation, 10260 Sorrento Valley Road, San Diego, Calif. 92121.

P. de Groot, “Homodyne interferometric receiver and calibration method having improved accuracy and functionality,” U.S. patent5,663,793 (2September1997).

Another way to express the uncertainty in the optical constants would be to calculate the ratios Δk/k and Δn/n. However, this would create the misleading impression that the uncertainty improves for larger values of n and k. It would also create the false impression that measurement of k on a dielectric has an undefined uncertainty because the k is zero.

P. de Groot, L. Deck, J. Soobitsky, J. Biegen, “Optical flying-height testing of magnetic read-write heads,” in Lasers, Optics, and Vision for Productivity in Manufacturing I, C. Gorecki, ed., Proc. SPIE2782, 47–57 (1996).

C. Lacey, C. Durán, K. Womack, R. Simmons, “Optical measurement of flying height,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, San Diego, 1997), pp. 81–88.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York) p. 40.

Following Born and Wolf, we prefer to use the n + ik definition of the complex index, rather than the more common n - ik.

P. de Groot, “Optical properties of alumina titanium carbide sliders used in rigid disk drives,” (submitted to Appl. Opt.).

Y. Li, “Flying height measurement on Al2O3 film of a magnetic slider,” presented at the American Society of Mechanical Engineers Tribology Conference, paper 96-TRIB-61 (San Francisco, Calif., 13–17 October 1996).

P. de Groot, J. Biegen, L. Deck, A. Dergevorkian, T. Erickson, J. Morace, R. Pavlat, J. Soobitsky, “Polarization interferometer for flying height testing,” in Proceedings of Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Sunnyvale, Calif., 1997), pp. 89–94.

P. de Groot, “Optical gap measuring apparatus and method,” U.S. patent5,557,399 (17September1996).

T. Fukuzawa, T. Hisano, T. Morita, K. Ikarugi, “Method and apparatus for measuring the flying height of a magnetic head above a disk surface at three wavelengths,” U.S. patent5,502,565 (26March1996).

G. Sommargren, “Distance measuring interferometer and method of use,” U.S. patent4,606,638 (19August1986).

G. Sommargren, “Flying height and topography measuring interferometer,” U.S. patent5,218,424 (8June1993).

Generally, it is not possible to calculate a film thickness as well as the optical constants from a single ellipsometric measurement; hence the need for three or more flying heights for proper n and k calibration. See, for example, R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (Elsevier, Amsterdam, 1987), p. 317.

B. Bhushan, Tribology and Mechanics of Magnetic Storage Devices (Springer-Verlag, New York, 1990) pp. 765–797.

W. Stone, “A proposed method for solving some problems in lubrication,” The Commonwealth Engineer (1November1921), pp. 115–122.

P. de Groot, J. Biegen, L. Deck, R. Smythe, “Calibration standard for optical gap measuring tools,” U.S. patent5,724,134 (3March1998).

A similar arrangement for establishing known gaps for calibration appears in U.S. patent5,220,408 to M. Mager, entitled “Method and apparatus for calibration of optical flying-height testers” (15June1993).

Our technique does require an estimated value for the scattered light loss, in the form of the μ factor. However, the effect of an incorrect μ on the ZSE is small. It serves primarily to simplify comparison of our technique with traditional ellipsometry.

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Figures (12)

Fig. 1
Fig. 1

Polarization interferometer for flying-height testing of magnetic read-write sliders. A rotating glass substrate takes the place of the magnetic disk to facilitate optical inspection of the gap. The receiver measures the polarization-dependent complex reflectivity of the slider–glass interface. The source is a 3-mW, 670-nm laser diode.

Fig. 2
Fig. 2

Comparison of theoretical (solid circle) and experimental intensity and phase data. The arrow indicates the direction of increasing flying height, starting from contact. The experimental data were acquired (at several different locations on the ABS) by use of polarization interferometry of a read-write slider in steady flight.

Fig. 3
Fig. 3

Calculation of the uncertainty Δn with the sensitivity of the merit function M to variations in n.

Fig. 4
Fig. 4

Theoretical estimate of flying-height errors in polarization interferometry. These data correspond to a rms uncertainty in both n and k of 0.04.

Fig. 5
Fig. 5

Uncertainty in n and k as a function of the calibration height range. The calculation assumes phase and intensity measurements over a range of evenly spaced flying heights, with the lowest flying height at 75 nm. The calibration height range is the difference between the highest and the lowest flying height.

Fig. 6
Fig. 6

Minimum calibration range to maintain a rms uncertainty for n and k below 0.05.

Fig. 7
Fig. 7

Comparison of the minimum calibration range for a 3-λ intensity tester (upper curve) with that of a polarization interferometer (lower curve). The 3-λ curve is the minimum range needed to normalize experimental intensity data at 436-, 548-, and 580-nm wavelengths. As flying heights decrease, it becomes increasingly attractive to use polarization interferometry because of its relative ease of calibration.

Fig. 8
Fig. 8

Data acquisition by use of ABS scanning. The single-point measurement beam moves from point to point on the ABS, acquiring data at different heights for the n and k calibration.

Fig. 9
Fig. 9

Cross section of a cylindrical surface fit of height data obtained when the slider ABS is scanned as shown in Fig. 8. The obvious curvature is referred to as the ABS crown and is generated by polishing the slider on a spherical lap. The surface fit permits extrapolation to the read-write element of the slider.

Fig. 10
Fig. 10

Gap standard for verifying the accuracy of polarization interferometry. The glass has a 20-m radius of curvature, and when placed in contact with the flat SiC substrate, provides a well-controlled range of gaps. The contact region is a small circular area of low reflectivity.

Fig. 11
Fig. 11

Polarization interferometry data for the gap standard shown in Fig. 10 with a SiC substrate. The contact region between -1 and +1 mm has an average measured gap of 0.5 nm. The increasing heights to either side of the contact region are caused by the 20-m radius of curvature of the glass.

Fig. 12
Fig. 12

Contact region of the gap standard shown in Fig. 10 for a flat substrate made of carbon-coated Al2O3-TiC. For this sample of common slider material, the in situ n and k analysis reduces the ZSE to less than 1 nm.

Tables (4)

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Table 1 Theoretical Zero-Spacing Error Δh Attributable to the Material Phase Change on Reflection of Al2O3-TiC at Three Different Wavelengths

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Table 2 Intensity Reflectivity of Four Al2O3-TiC Samples at a Wavelength of 633 nm Compared with the Theoretical Predictions with n and k

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Table 3 Experimental Determination of the Optical Constants of SiC at a Wavelength of 670 nm by Polarization Interferometry with 16 Different Sensors a

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Table 4 Dynamic Repeatability of Calibration for an Al2O3-TiC Slider with ABS Scanning

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

r s = tan ϕ - ϕ ¯ tan ϕ + ϕ ¯ ,
r p = - sin ϕ - ϕ ¯ sin ϕ + ϕ ¯ .
ñ   sin ϕ ¯ = sin ϕ ,
ñ = n + ik
R = ñ - 1 ñ + 1 2 .
E = E s E p .
E r = SE ,
S = z s 0 0 z p ,
z s , p β = r s , p + r s , p   exp i β 1 + r s , p r s , p   exp i β ,
β = 2 kh   cos ϕ ,
r s , p = 1 - μ r s , p ,
I = | E s r | 2 + | E p r | 2 ,
θ = arg E s r - arg E p r .
I = I + 0.1 , Ω = - I   sin θ , Π = - I   cos θ .
I m = I AD / I 0 ,
I 0 = I s bak / R s ,
χ ˆ i 2 h = 1 2 Π i m - Π h σ Π 2 + Ω i m - Ω h σ Ω 2 ,
M = 1 ν i = 0 N - 1 χ ˆ min 2 i ,
σ I 2 = I σ 2 ,
σ θ 2 = σ 2 / I .
σ Ω 2 = σ θ 2 Π 2 + σ I / I 2 Ω 2 , σ Π 2 = σ θ 2 Ω 2 + σ I / I 2 Π 2 .
σ Ω 2 = σ Π 2 = I σ 2 .
M = 1 ν σ 2 i = 0 N - 1 χ min 2 i ,
χ i 2 h = Π i m - Π h 2 + Ω i m - Ω h 2 2 I h .
Δ h = 1 2 Δ h n 2 + Δ h k 2 1 / 2 .

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