Microsystem Technologies

, Volume 18, Issue 9, pp 1283–1288

Ellipsometric measurement accuracy of ultrathin lubricant thickness on magnetic head slider


    • Data Storage Institute, Agent for Science, Technology and Research
  • M. S. Zhang
    • Data Storage Institute, Agent for Science, Technology and Research
  • M. C. Yang
    • WD Media (Singapore) Pte Ltd
  • R. Ji
    • Data Storage Institute, Agent for Science, Technology and Research
Technical Paper

DOI: 10.1007/s00542-012-1519-8

Cite this article as:
Zhao, J.M., Zhang, M.S., Yang, M.C. et al. Microsyst Technol (2012) 18: 1283. doi:10.1007/s00542-012-1519-8


The quantitative analysis of lubricant transferred from disk to slider is important in understanding the interaction in head-disk interface and designing a stable head-disk system. When applying ellipsometric technology to determine the lubricant thickness on slider, the measurement accuracy is of concern due to the location-to-location variations of slider optical constants. This paper carried out a systematic and quantitative study on how the variations of slider optical constants affect the measurement accuracy of lubricant thickness. In this study, the distribution of slider optical constant was obtained; a differential method was used to calculate the uncertainty in lubricant thickness and the calculated results were experimentally verified. The results show that for the state-of-art sliders, the uncertainty in lubricant thickness is about 20 % for below 2 nm thicknesses and less than 15 % for around 3 nm thicknesses when measured at 632.8 nm wavelength. The results of this study might be also useful for the other optical instruments used to determine the amount of the transferred lubricant.

1 Introduction

The continuing pursuit for higher magnetic recording areal density of hard disk drive (HDD) demands the smaller head-media spacing (HMS) (Ambeka and Bogy 2008). The lubricant transfer from the disk surface to a flying magnetic head slider (“slider” for short) increases with decreasing slider flying height. Transferred lubricant will affect HMS and deteriorate the slider flying stability, causing overall HDD reliability issues. The quantitative analysis of transferred lubricant is important in helping to understand the physical mechanism of interaction between lubricant and slider and design a stable head-disk interface system.

Nowadays, several nanometrological techniques have been applied to determine the lubricant amount or thickness on slider (Kim et al. 2009; Leavitt 1992; Yanagisawa et al. 2010; Chiba and Ogata 2008; Tani et al. 2011). These include time-of-flight secondary ion mass spectroscope (TOF–SIMS), X-ray photoelectron spectroscope (XPS), optical surface analyzer (OSA), interferometry and spectroscopic ellipsometry (SE). Of these techniques, TOF–SIMS, XPS and SE have spot sizes small enough to directly measure lubricant thickness on slider. TOF–SIMS and XPS must be performed under the ultra-high vacuum conditions which might cause the evaporation and/or redistribution of transferred lubricant, whereas SE enables a fast and non-destructive measurement under ambient environment. However, when applied to determine the lubricant thickness on slider, the measurement accuracy is of concern due to the location-to-location variations of slider optical constants (refractive index n and extinction coefficient k).

SE is not direct measurement technique, it is impossible to measure the optical constants and thickness of a given sample directly with light. Instead, it measures the change of polarization in light reflected from or tramsmitted through the given sample. The polarization change is described by an amplitude ratio tanΨ and phase difference Δ between light oriented in the p- and s- directions relative to the sample surface. These measured data must be modeled in order to determine the sample properties of interest (optical constants or thickness of the film). The model-generated data are then compared to the measured data while the sample properties are varied. Through specific regression analysis, the unknown sample properties whose response best match the measured data are found. Generally, an optical model consists of the optical constants of both substrate and sample layers as well as the thicknesses of sample layers, in which the substrate is treated as a special type of layer having 1 mm optical thickness and accurately known optical constants.

In SE measurement, the accuracy of an optical model usually contributes the significant accuracy to the measurement. In other word, if the optical model is not accurate, then its model fit result is not good and even might be completely wrong as through the original measured data are accurate and error free. To ensure the model accuracy, substrate optical constants used in the optical model should be the same as the measured ones for a given sample. For a case where substrate optical constants are not uniformly distributed, the location-to-location measurement should be applied, namely, before and after film deposition the same spot on the substrate will be measured and analyzed.

Slider material is a two-phase composite consisting of Al2O3 and TiC grains. The TiC grains are of random size, shape and separation at the order of micrometers, which makes slider optical constants vary with the measured locations and thus causes the variations in optical constants (Yuan et al. 2008). As stated above, the location-to-location measurement should be carried out for this case. However, the presence of positioning errors induced by the cycle of loading/unloading slider makes it very difficult to exactly get back to the original location before and after lubricant transfer, as a result, slider optical constants in the optical model might be not the same as the measured ones, thus causing the inaccurate result of determined lubricant thickness. There has not been a systematic and quantitative study on how the variation of slider optical constants affects the accuracy of the measured thickness. This paper presents a systematic and quantitative study on this problem. In this study, the statistical distribution of slider optical constants was obtained first. Then a differential method was described which was used to calculate the uncertainty (%) in lubricant thickness induced mainly by the variation of slider optical constants. The calculated results were finally verified experimentally. The results of this study might be also useful for the other optical instruments such as interferometry and reflectometry when they are used to determine the amount of the transferred lubricant (Tani et al. 2011).

2 Slider optical constants

Normally, sliders are coated with ~0.5 nm-thick amorphous-Si adhesive layer and ~1.5 nm-thick diamond-like carbon (DLC) layer orderly. We treat them as part of slider substrate and use a combined pseudo substrate approximation to simulate the DLC/a-Si/AlTiC structure. Ellipsometry is the only technology to uniquely determine the optical constants for slider substrate. The direct inversion of the measured ellipsometric Ψ and Δ can provide slider optical constants at each measurement wavelength. In this study, ellipsometry measurements were carried out over the spectral range of 360–800 nm using M-2000VF (J. A. Woollam Co., Inc. 2000) at an incident angle of 65° with 25 μm by 60 μm spot size. In total, 400 spots on slider row bars were measured. Figure 1 plots the n and k values of 400 testing spots at 632.8 nm wavelength. It can be seen that there are the scatters of both n and k values, n changes between 2.218 and 2.297 whereas k is between 0.404 and 0.466. The average n and k values of 400 spots are 2.256 and 0.428 with the corresponding standard deviations of 0.015 and 0.011 (resulting \( \delta \tilde{n} = \sqrt {\delta n^{2} + \delta k^{2} } \approx \, 0.0 1 9 \)) respectively. Figure 2 plots the n and k dispersions of two different spots. It shows that head slider optical constants vary with the measured location and wavelength. The variation in n is larger than k for this type slider under test.
Fig. 1

Scatter diagram of n and k values of 400 spots measured by ellipsometry at λ = 632.8 nm

Fig. 2

Dispersion of n and k values over spectral range of 375–725 nm for two different spots

3 Analysis of uncertainty in lubricant thickness

3.1 Calculation of uncertainty in lubricant thickness

In this study, the uncertainty in lubricant thickness was defined as the relative error (Δt/t) of the measured thickness (t) which was written as a percentage while the uncertainty in slider optical constants was referred to as the standard deviation of slider optical constant distribution. For an ambient-lubricant-slider substrate structure as shown in Fig. 3, ellipsometric parameters Ψ and Δ are expressed by
$$ \tan \Uppsi e^{j\Updelta } = \frac{{\tilde{r}_{p1} + \tilde{r}_{p2} e^{ - j\Upgamma } }}{{1 + \tilde{r}_{p1} \tilde{r}_{p2} e^{ - j\Upgamma } }} \times \frac{{1 + \tilde{r}_{s1} \tilde{r}_{s2} e^{ - j\Upgamma } }}{{\tilde{r}_{s1} + \tilde{r}_{s2} e^{ - j\Upgamma } }} .$$
Fig. 3

Schematic diagram of ambient-lubricant-slider geometry

where, \( \tilde{r}_{p1} \), \( \tilde{r}_{p2} \) and \( \tilde{r}_{s1} \), \( \tilde{r}_{s2} \) are the Fresnel reflection coefficients at the ambient-lubricant interface (denoted as the subscript 1) and lubricant-slider interface (denoted as the subscript 2) respectively for the p- and s- polarizations. Γ is the phase change which is induced by the film thickness when the reflected light traverses the film. They are described by
$$ r_{p1} = \frac{{n_{1}^{2} \cos \theta - n_{0} (n_{1}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} }}{{n_{1}^{2} \cos \theta + n_{0} (n_{1}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} }} $$
$$ r_{p2} = \frac{{n_{2}^{2} (n_{1}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} - n_{1} (n_{2}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} }}{{n_{2}^{2} (n_{1}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} + n_{1} (n_{2}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} }} $$
$$ r_{s1} = \frac{{n_{0}^{2} \cos \theta - (n_{1}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} }}{{n_{0}^{2} \cos \theta + (n_{1}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} }} $$
$$ r_{s2} = \frac{{(n_{1}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} - (n_{2}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} }}{{(n_{1}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} + (n_{2}^{2} - n_{0}^{2} \sin^{2} \theta )^{1/2} }} $$
$$ \Upgamma = (4\pi t/\lambda )(\tilde{n}_{1}^{2} - \tilde{n}_{0}^{2} \sin^{2} \theta )^{1/2}. $$

Here \( \tilde{n}_{0} \), \( \tilde{n}_{1} \), \( \tilde{n}_{2} \) are the optical constants of the ambient, lubricant film and substrate, respectively, θ is the incident angle, λ is the optical wavelength and t is the film thickness (J. A. Woollam Co., Inc. 2000; Tompkins and McGahan 1999).

When lubricant film is very thin, the film optical constants are always taken to be constant and its uncertainty is negligible, only the film thickness is to be determined. For this reason, ellipsomtric parameter Ψ and Δ can be written as the functions of slider optical constant \( \tilde{n}_{2} \), incident angle θ and film thickness t:
$$ \Uppsi = \Uppsi (\tilde{n}_{2} ,\theta ,t) $$
$$ \Updelta = \Updelta (\tilde{n}_{2} ,\theta ,t).$$
If \( \tilde{n}_{2} \) is known, t can be determined from the measured Ψ and Δ with either Eq. (7) or (8). Furthermore, by expanding these equations in a Taylor series and considering the first-order items, the effect of small experimental uncertainties in Ψ, Δ, θ and the structural uncertainty in \( \tilde{n}_{2} \) on the uncertainty in the thickness t can be calculated from
$$ (\delta t)_{RMS} = \left[ {(A\delta \Uppsi )^{2} + (B\delta \theta )^{2} + (C\delta \tilde{n}_{2} )^{2} } \right]^{1/2} $$
$$ (\delta t)_{RMS} = \left[ {\left( {D\delta \Updelta } \right)^{2} + \left( {E\delta \theta } \right)^{2} + \left( {F\delta \tilde{n}_{2} } \right)^{2} } \right]^{1/2}. $$
Where, (δt)RMS is the root mean square uncertainty in t, δΨ, δΔ, δθ and \( \delta \tilde{n}_{2} \)are the uncertainties in Ψ, Δ, θ and \( \tilde{n}_{2} \)whose values are given and they are independent random deviations from their corresponding values. \( \tilde{n}_{2} \) is the measured value of slider optical constants. As Eqs. (9) and (10) give the two independent determinations for δt, the smaller of two calculated values was used. The coefficients A through F are shown in Table 1.
Table 1

The coefficients A through F

\( A = \left| {{{\partial \Uppsi } \mathord{\left/ {\vphantom {{\partial \Uppsi } {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}}} \right|^{ - 1} \)

\( B = \left| {{{\partial \Uppsi } \mathord{\left/ {\vphantom {{\partial \Uppsi } {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}}} \right|^{ - 1} \left| {{{\partial \Uppsi } \mathord{\left/ {\vphantom {{\partial \Uppsi } {\partial \theta }}} \right. \kern-\nulldelimiterspace} {\partial \theta }}} \right| \)

\( C = \left| {{{\partial \Uppsi } \mathord{\left/ {\vphantom {{\partial \Uppsi } {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}}} \right|^{ - 1} \left| {{{\partial \Uppsi } \mathord{\left/ {\vphantom {{\partial \Uppsi } {\partial \tilde{n}_{2} }}} \right. \kern-\nulldelimiterspace} {\partial \tilde{n}_{2} }}} \right| \)

\( D = \left| {{{\partial \Updelta } \mathord{\left/ {\vphantom {{\partial \Updelta } {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}}} \right|^{ - 1} \)

\( E = \left| {{{\partial \Updelta } \mathord{\left/ {\vphantom {{\partial \Updelta } {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}}} \right|^{ - 1} \left| {{{\partial \Updelta } \mathord{\left/ {\vphantom {{\partial \Updelta } {\partial \theta }}} \right. \kern-\nulldelimiterspace} {\partial \theta }}} \right| \)

\( F = \left| {{{\partial \Updelta } \mathord{\left/ {\vphantom {{\partial \Updelta } {\partial t}}} \right. \kern-\nulldelimiterspace} {\partial t}}} \right|^{ - 1} \left| {{{\partial \Updelta } \mathord{\left/ {\vphantom {{\partial \Updelta } {\partial \tilde{n}_{2} }}} \right. \kern-\nulldelimiterspace} {\partial \tilde{n}_{2} }}} \right| \)

3.2 Analysis and discussion

We first used the above analysis method to calculate the effect of wavelength on the uncertainty in lubricant thickness due to the wavelength-dependent nature of slider optical constants. During calculating, we found that \( \delta \tilde{n}_{2} \)was more than tenfold larger than δΨ, δΔ, δθ, it contributed the most to the overall uncertainty in lubricant thickness. Figure 4 plots the uncertainty in lubricant thickness as a function of wavelengths for various lubricant thicknesses under some given conditions. It is clear that the uncertainty in lubricant thickness follows the similar trend over the spectral region for all the thicknesses. It rapidly increases in the spectral region of 380–520 nm and starts to slowly grow from 520 nm wavelength, and then turns to slightly decrease from 580 nm wavelength. The uncertainty can be greatly reduced if the short wavelength is used for below 2 nm thickness. e.g., it falls from 35 to 20 % as the wavelength decreases from 520 to 400 nm for 1 nm thickness. Furthermore, it can be also observed that the uncertainty in lubricant thickness is highly depends on the thickness. The uncertainty tends to significantly decrease as the thickness becomes thicker. e.g., at 520 nm wavelength, the uncertainty drops from 35 to 17 % as thickness increases from 1 nm to 2 nm. It further falls to <5 % when the thickness gets to 5 nm.
Fig. 4

Thickness uncertainty as function of wavelength for case of δΨ = δθ = 0.01°, θ = 65°, \( \tilde{n}_{0} \) = 1, \( \tilde{n}_{1} \) = 1.3, and δ\( \tilde{n}_{2} \) = 0.02

In a similar manner, we also calculated the uncertainty in lubricant thickness as a function of uncertainty in slider optical constants. Figure 5 displays the uncertainty in thickness versus the uncertainty in slider optical constants for various lubricant thicknesses corresponding to λ = 632.8 nm. It can be seen that the uncertainty in thickness is approximately linearly proportional to the uncertainty in slider optical constants for all the thicknesses. The larger the uncertainty in slider optical constants, the larger the uncertainty in lubricant thickness. This is very pronounced for some cases where the thicknesses are below 2 nm. e.g., for 1 nm thickness, the uncertainty in thickness drops by 17 % whereas it dips only 1.7 % for 5 nm thickness when the uncertainty in slider optical constants decreases from 0.025 to 0.015. On the other hand, Fig. 5 also reveals the same phenomenon as observed in Fig. 3 that the effect of uncertainty in slider optical constants diminishes with increasing the lubricant thickness. e.g., ~3 nm lubricant film on the slider with the uncertainty of ~0.02 in optical constants could be measured with the more than 85 % accuracy.
Fig. 5

Thickness uncertainty as for case of δΨ = δ∆ = δθ = 0.01°, θ = 65°, \( \tilde{n}_{0} \) = 1, \( \tilde{n}_{1} \) = 1.3, and λ = 632.8 nm

4 Experimental study

To verify the results of above theoretical analysis, we carried out the ellipsometry measurement and XPS measurement. As non-optical metrology tool, XPS is widely used for accurately measuring the lubricant thickness and also for calibrating ellipsometry (Leavitt 1992). In this study, it served with the assumed real thickness in order to evaluate the uncertainty in thickness measured by ellipsometry.

4.1 Samples

The sliders used in the experimental study were from the same batch as the mapping of slider optical constants in Sect. 2. To facilitate the verification purpose, two uniform lubricant films were prepared by dip-coating technique. Two slider row bars under test were immersed in a 0.1 % solution of Z-DOL4000 in Vertrel XF and pulled out at different speeds, respectively. The dwell time was approximately 7 min for each dip-coating process.

4.2 Ellipsometry measurement

Ellipsomertric measurement was carried out using the same experimental setup as used in Sect. 2. Before and after lubricant deposition, the ellipsometric Ψ and Δ were acquired from the same 15 marked locations along each row bar, respectively. With an optical model as shown in Fig. 6, the lubricant thickness was calculated through the model fit to the measured Ψ and Δ. Figure 6 illustrates a typical best-fit result for ~2.5 nm lubricant film on the slider row bar.
Fig. 6

Generated and experimental Ψ and Δ data from lubricant film on slider row bar. Generated data were calculated from best-fit Cauchy model

4.3 XPS measurement

Shortly after ellipsometric measurement, the XPS data were obtained from 5 spots along each sample surface using PHI Quantera SXM Scanning X-ray Microprobe with a monochromatic Al Ka source. The system was operated at 15 kV, 25 W and pass energy of 55 eV. The lubricant thickness was calculated based on the ratio of C1s peak from the lubricant (C–F peak) and the slider (C–C/C–H peak) after the correction of the overlap of the C–C/C–H peak from lubricant. The resulting average values of the lubricant thicknesses of two samples were 1.89 and 2.97 nm with the standard deviations of 0.09 and 0.08 nm, respectively. Figure 7 displays the measured XPS data of one of them.
Fig. 7

XPS spectrum of C1 s photoemission peaks for 5 spots on slider row bar, shown for 1.89 nm average thickness of lubricant film

4.4 Analysis and discussion

Figure 8 plots the measured thickness of each individual spot measured by ellipsometry against the corresponding average thickness obtained by XPS. The uncertainty in measured thickness were calculated by
Fig. 8

Comparison of XPS and ellipsometric measurement for lubricant thickness on slider

$$ \delta {\text{t}}(\% ) = {{\sqrt {\frac{{\sum\nolimits_{{{\text{i}} = 1}}^{\text{n}} {({\text{t}}_{{{\text{i\_ellip}}}} - {\bar{\text{t}}}_{\text{xps}} )^{2} } }}{\text{n}}} } \mathord{\left/ {\vphantom {{\sqrt {\frac{{\sum\limits_{{{\text{i}} = 1}}^{\text{n}} {({\text{t}}_{{{\text{i\_ellip}}}} - {\bar{\text{t}}}_{\text{xps}} )^{2} } }}{\text{n}}} } {{\bar{\text{t}}}_{\text{xps}} }}} \right. \kern-\nulldelimiterspace} {{\bar{\text{t}}}_{\text{xps}} }} \times 100\,\% $$

Here, n is the total number of measured spots in ellipsometry measurement, ti_ellip is the ith thickness of the film measured by ellipsometry, and \( \bar{t}_{xps} \) is the average thickness of the film obtained by XPS. It is clear from Fig. 8 that the thicknesses measured by ellipsometry randomly distribute around the ones measured by XPS with different deviations. This is attributed to the location-to-location variations in slider optical constants. It can be also seen that the uncertainty in experimental thickness reduces with increasing the thickness, which is in a good agreement with the result of theoretic analysis as shown in Fig. 5. Furthermore, the experimentally measured uncertainty in lubricant thickness is 23.9 % for 1.89 nm thickness and 13.9 % for 2.97 nm thickness. As mentioned before, the slider row bar under study had the uncertainty in optical constants of ~0.019. Correspondingly, the theoretically calculated uncertainty is 15.2 % for 1.9 nm thickness and 7.3 % for 3.0 nm thickness, respectively. Obviously, the overall experimental values are larger than the theoretical values. It is reasonable because in addition to the measurement random errors, the optical model induced further systematic errors such as neglecting the roughness of slider surface.

5 Conclusion

The measurement accuracy of lubricant thickness on slider was investigated theoretically and experimentally. Based on those results, we conclude:
  1. 1.

    The uncertainty in lubricant thickness is approximately proportional to the uncertainty in slider optical constants. It is very pronounced for below 2 nm thickness. Controlling the variation of slider optical constants is critical for ellipsometric measurement.

  2. 2.

    The uncertainty in lubricant thickness also depends on measurement wavelength. It is up to maximum at around 580 nm wavelength whereas it goes down to the minimum at around 400 nm wavelength in the spectral range of 380–640 nm. Using the short wavelength can improve the measurement accuracy.

  3. 3.

    The uncertainty in lubricant thickness is related to the thickness itself. For the state-of-art sliders, it falls from 35 to 5 % as thickness increases from 1 to 5 nm at 632.8 nm wavelength and it is <15 % as thickness is ~3 nm.

  4. 4.

    The theoretical results are in the agreement with the experimental results.


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