Abstract

A common material for read–write sliders is a composite of alumina (Al2O3) and titanium carbide (TiC), with a grain size of the order of 1 μm. I derive the effective complex reflectivity of this material, using scalar diffraction theory and the known indices of refraction of Al2O3 and TiC. The effective reflectivity is a function of the relative surface area of the exposed TiC grains as well as of the numerical aperture of the collection optics. The theory resolves several known discrepancies between ellipsometry and reflectometry of Al2O3–TiC. The theory also predicts a systematic error in the phase shift on reflection calculation. These results are of considerable interest for surface shape metrology of the slider as well as for optical flying-height testing and control of pole-tip recession.

© 1998 Optical Society of America

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References

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  1. 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. Inf. Storage Syst. 4, 371–379 (1992); The same paper was presented at the American Society of Mechanical Engineers Winter Annual Meeting, Atlanta, Ga., 1991.
  2. D. M. Wood, N. W. Ashcroft, “Effective medium theory of optical properties of small particle composites,” Phil Mag. 35, 269–280 (1977).
    [CrossRef]
  3. G. A. Niklasson, C. G. Granqvist, O. Hunderi, “Effective medium models for the optical properties of inhomogeneous materials,” Appl. Opt. 20, 26–30 (1981).
    [CrossRef] [PubMed]
  4. C. Lacey, C. Durán, K. Womack, R. Simmons, “Optical measurement of flying height,” in Proceedings of the Future Dimensions in Storage Symposium (International Disk Drive Equipment and Materials Association, Santa Clara, Calif., 1997), pp. 81–88.
  5. R. Synowicki, “Difficulties associated with analysis of composite head structures using ellipsometry,” applications note (J. A. Woollam Company, Lincoln, Neb., 1997).
  6. R. M. A. Azzam, “Ellipsometry,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 27, p. 275.
  7. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), p. 40.
  8. H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, Boston, Mass., 1993), p. 28.
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 14.
  10. R. Smythe, L. Selberg, L. Deck, “Pole tip recession measurements of transducers on thin film sliders for rigid disk drives,” in Proceedings of the International Disk Conference in Tokyo, Japan (International Disk Drive Equipment and Materials Association, Santa Clara, Calif., 1992).
  11. E. W. Rogala, H. H. Barrett, “Phase-shifting interferometer/ellipsometer capable of measuring the complex index of refraction and the surface profile of a test surface,” J. Opt. Soc. Am. A 15, 538–548 (1998).
    [CrossRef]
  12. G. D. Feke, D. P. Snow, R. D. Grober, P. J. de Groot, L. Deck, “Interferometric back focal plane microellipsometry,” Appl. Opt. 37, 1796–1802 (1998).
    [CrossRef]
  13. W. Stone, “A proposed method for solving some problems in lubrication,” Commonw. Eng. 1921, 115–122.
  14. J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Devel. 18, 529–533 (1974).
    [CrossRef]
  15. 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]
  16. P. de Groot, “Optical gap measuring apparatus and method,” U.S. patent5,557,399 (17September1996).
  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. Carbon overcoats are crystalline thin films that have a columnar microstructure that can cause significant optical scatter. This additional light loss can be accommodated by an empirical measurement of the scatter-loss coefficient μ.
  19. An alternative approach is to correlate the reflectance of the slider to the index of refraction by using an empirically derived equation. See K. H. Womack, A. Butler, “Determining the complex refractive index phase offset in interferometric flying height testing,” U.S. patent5,781,299 (14July1998).

1998 (2)

1996 (1)

1994 (1)

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

1992 (1)

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. Inf. Storage Syst. 4, 371–379 (1992); The same paper was presented at the American Society of Mechanical Engineers Winter Annual Meeting, Atlanta, Ga., 1991.

1981 (1)

1977 (1)

D. M. Wood, N. W. Ashcroft, “Effective medium theory of optical properties of small particle composites,” Phil Mag. 35, 269–280 (1977).
[CrossRef]

1974 (1)

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

Ashcroft, N. W.

D. M. Wood, N. W. Ashcroft, “Effective medium theory of optical properties of small particle composites,” Phil Mag. 35, 269–280 (1977).
[CrossRef]

Azzam, R. M. A.

R. M. A. Azzam, “Ellipsometry,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 27, p. 275.

Barrett, H. H.

Biegen, J.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), p. 40.

Butler, A.

An alternative approach is to correlate the reflectance of the slider to the index of refraction by using an empirically derived equation. See K. H. Womack, A. Butler, “Determining the complex refractive index phase offset in interferometric flying height testing,” U.S. patent5,781,299 (14July1998).

de Groot, P.

de Groot, P. J.

Deck, L.

G. D. Feke, D. P. Snow, R. D. Grober, P. J. de Groot, L. Deck, “Interferometric back focal plane microellipsometry,” Appl. Opt. 37, 1796–1802 (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]

R. Smythe, L. Selberg, L. Deck, “Pole tip recession measurements of transducers on thin film sliders for rigid disk drives,” in Proceedings of the International Disk Conference in Tokyo, Japan (International Disk Drive Equipment and Materials Association, Santa Clara, Calif., 1992).

Durán, C.

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

Feke, G. D.

Fleischer, J. M.

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

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 14.

Granqvist, C. G.

Grober, R. D.

Hunderi, O.

Lacey, C.

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

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

Lin, C.

J. M. Fleischer, C. Lin, “Infrared laser interferometer for measuring air-bearing separation,” IBM J. Res. Devel. 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]

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. Inf. Storage Syst. 4, 371–379 (1992); The same paper was presented at the American Society of Mechanical Engineers Winter Annual Meeting, Atlanta, Ga., 1991.

Niklasson, G. A.

Rogala, E. W.

Selberg, L.

R. Smythe, L. Selberg, L. Deck, “Pole tip recession measurements of transducers on thin film sliders for rigid disk drives,” in Proceedings of the International Disk Conference in Tokyo, Japan (International Disk Drive Equipment and Materials Association, Santa Clara, Calif., 1992).

Simmons, R.

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

Smythe, R.

R. Smythe, L. Selberg, L. Deck, “Pole tip recession measurements of transducers on thin film sliders for rigid disk drives,” in Proceedings of the International Disk Conference in Tokyo, Japan (International Disk Drive Equipment and Materials Association, Santa Clara, Calif., 1992).

Snow, D. P.

Soobitsky, J.

Stone, W.

W. Stone, “A proposed method for solving some problems in lubrication,” Commonw. Eng. 1921, 115–122.

Synowicki, R.

R. Synowicki, “Difficulties associated with analysis of composite head structures using ellipsometry,” applications note (J. A. Woollam Company, Lincoln, Neb., 1997).

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. Inf. Storage Syst. 4, 371–379 (1992); The same paper was presented at the American Society of Mechanical Engineers 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]

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. Inf. Storage Syst. 4, 371–379 (1992); The same paper was presented at the American Society of Mechanical Engineers Winter Annual Meeting, Atlanta, Ga., 1991.

Tompkins, H. G.

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, Boston, Mass., 1993), p. 28.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), p. 40.

Womack, K.

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

Womack, K. H.

An alternative approach is to correlate the reflectance of the slider to the index of refraction by using an empirically derived equation. See K. H. Womack, A. Butler, “Determining the complex refractive index phase offset in interferometric flying height testing,” U.S. patent5,781,299 (14July1998).

Wood, D. M.

D. M. Wood, N. W. Ashcroft, “Effective medium theory of optical properties of small particle composites,” Phil Mag. 35, 269–280 (1977).
[CrossRef]

Adv. Inf. Storage Syst. (1)

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. Inf. Storage Syst. 4, 371–379 (1992); The same paper was presented at the American Society of Mechanical Engineers Winter Annual Meeting, Atlanta, Ga., 1991.

Appl. Opt. (2)

Commonw. Eng. (1)

W. Stone, “A proposed method for solving some problems in lubrication,” Commonw. Eng. 1921, 115–122.

IBM J. Res. Devel. (1)

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

IEEE Trans. Magn. (1)

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

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Phil Mag. (1)

D. M. Wood, N. W. Ashcroft, “Effective medium theory of optical properties of small particle composites,” Phil Mag. 35, 269–280 (1977).
[CrossRef]

Other (10)

Carbon overcoats are crystalline thin films that have a columnar microstructure that can cause significant optical scatter. This additional light loss can be accommodated by an empirical measurement of the scatter-loss coefficient μ.

An alternative approach is to correlate the reflectance of the slider to the index of refraction by using an empirically derived equation. See K. H. Womack, A. Butler, “Determining the complex refractive index phase offset in interferometric flying height testing,” U.S. patent5,781,299 (14July1998).

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

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

R. Synowicki, “Difficulties associated with analysis of composite head structures using ellipsometry,” applications note (J. A. Woollam Company, Lincoln, Neb., 1997).

R. M. A. Azzam, “Ellipsometry,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, Chap. 27, p. 275.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1987), p. 40.

H. G. Tompkins, A User’s Guide to Ellipsometry (Academic, Boston, Mass., 1993), p. 28.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 14.

R. Smythe, L. Selberg, L. Deck, “Pole tip recession measurements of transducers on thin film sliders for rigid disk drives,” in Proceedings of the International Disk Conference in Tokyo, Japan (International Disk Drive Equipment and Materials Association, Santa Clara, Calif., 1992).

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Figures (12)

Fig. 1
Fig. 1

Microscope image of a polished Al2O3–TiC surface. The image width is 25 μm.

Fig. 2
Fig. 2

Null ellipsometer using a 633-nm He–Ne laser.

Fig. 3
Fig. 3

Simple model of composite Al2O3–TiC that comprises stripes of TiC embedded in Al2O3.

Fig. 4
Fig. 4

Predicted effective n and k values as a function of the TiC composition ε, according to the SD model in the low-N.A. limit.

Fig. 5
Fig. 5

Comparison of experimental and theoretical variation of measured n and k with incident angle for Al2O3–TiC. The experimental data are from Ref. 4. For a true homogeneous material, n and k would be constant.

Fig. 6
Fig. 6

Comparison of the predicted intensity reflectivities R for the n-and-k model and for the SD model. The SD model predicts a 20% relative intensity difference at normal incidence, confirming the experimental results in Table 1.

Fig. 7
Fig. 7

Theoretical PCOR. The SD model predicts a PCOR at normal incidence that is 4° lower than the value calculated with the effective n and k.

Fig. 8
Fig. 8

Theoretical s-polarization PCOR and intensity reflectivity with the constant μ = 9.5% and δ = 3.8° offsets, as a function of the TiC composition ε at an incident angle of 50°. The μ and δ make it possible to continue to use n and k to map changes in Al2O3–TiC composition.

Fig. 9
Fig. 9

Theoretical s-polarization PCOR and intensity reflectivity at normal incidence as a function of a variable refractive index for TiC. The n and k results include the constant offsets μ N = 10% and δ N = 4.2°. The TiC composition ε is fixed at 30%.

Fig. 10
Fig. 10

Simple model of Al2O3–TiC with a DLC coating and a SiO2 adhesion layer.

Fig. 11
Fig. 11

PCOR at normal incidence and at an incident angle ϕ of 50° for the n-and-k and the SD models, for variable DLC thickness. For a fixed relative TiC composition, ε = 20%. The ellipsometry for n and k in both cases is calculated at 50°. The n-and-k model prediction includes the offsets δ = -3.8° and δ N = -4.2°.

Fig. 12
Fig. 12

Intensity reflectivity at normal incidence for variable DLC thickness for a nominal scatter-loss coefficient μ N = 10%. The ellipsometry for n and k is calculated at a 50° incident angle, and the TiC composition is ε = 20%. The large divergence forces a reduction of the μ N factor from 10% to a compromise value of 5%.

Tables (4)

Tables Icon

Table 1 Normal-Incidence Intensity Reflectivity R0 and 50° s-Polarization Intensity Reflectivity Rs for Four Al2O3–TiC Samples

Tables Icon

Table 2 Predicted Optical Constants When Only the TiC Surface Composition ε is Used as a Variable Parameter

Tables Icon

Table 3 Predicted Intensity Reflectivities and Effective Optical Constants of an Al2O3-TiC Sample Known to Have 6 nm of DLC over a 2-nm SiO2 Adhesion Layer

Tables Icon

Table 4 Observed TiC Surface Composition When Conventional Microscopy is Used Compared with the ε Found by Optimizing for Best Match to the Effective n and k

Equations (21)

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E s , p = r s , p E s , p ,
v = n + ik .
A = r A + Δ rA G ,
A G = comb x / D rect x / ε D ,
comb a = m = -   δ a - m ,
rect a = 1 | a | 1 / 2 0 | a | > 1 / 2 ,
U = r A δ f + ε Δ r   comb Df / λ sin π ε Df / λ π ε Df / λ .
r ˜ = r A + ε r T - r A .
R ˜ = | r ˜ | 2 ,
α ˜ = arctan Im r ˜ Re r ˜ .
I ˜ = | r ref   exp i θ + r ˜ | 2 ,
I ˜ = R ref + R ˜ + 2 R ref R ˜ cos θ - α ref - α ˜ ,
R ˆ = R A + ε R T - R A .
R ˆ - R ˜ = ε 1 - ε | r T - r A | 2 .
I ˆ = R ref + R ˆ + 2 R ref R ˜ cos θ - α ref - α ˜ .
r = 1 - μ r   exp i δ ,
Γ r 1 ,   r 2 ,   ϕ ,   h ,   v = r 1 + r 2 exp ikhv   cos ϕ 1 + r 1 r 2 exp ikhv   cos ϕ .
z A , T = Γ r C ,   z A , T   ϕ C ,   h C ,   v C ,
z A , T = Γ r S ,   r A , T ,   ϕ S ,   h S ,   v S
sin ϕ C = sin ϕ v C ,
sin ϕ S = sin ϕ v S .

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