Vertical-Objective-Based Ellipsometric Microscope for Real ...

Tribology Online, 7, 3 (2012) 139-146. ISSN 1881-2198

DOI 10.2474/trol.7.139

Copyright © 2012 Japanese Society of Tribologists 139

Article

Vertical-Objective-Based Ellipsometric Microscope for Real-Time Observation of nm-Thick Lubricant Films

Liu Qingqing1)*, Kenji Fukuzawa1), Yosuke Kajihara1), Hedong Zhang2) and Shintaro Itoh1)

1)Department of Micro-Nano Systems Engineering, Nagoya University

Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan 2)Department of Complex Systems Science, Nagoya University

Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan *Corresponding author: [email protected]

( Manuscript received 22 September 2011; accepted 2 December 2011; published 30 September 2012 )

( Presented at Symposium S5: Tribology in Information Storage Systems in the International Tribology Conference Hiroshima 2011 )

The vertical-objective-based ellipsometric microscope (VEM) is expected to be a useful method for clarifying the lubrication phenomena that uses thin liquid lubricants, especially the lubricant for hard disk drives (HDDs). Although the feasibility of VEM for thin lubricant films was confirmed, the designs for the optical system and image detection have not been established. In this report, the optical design of the VEM is presented, as well as the method of controlling the coherent noises and improving the thickness resolution is discussed. By our method, the thickness resolution of VEM can be improved to 0.4 nm, and the real-time observation of sub-nm-thick thin liquid lubricant films can also be achieved. Keywords: ellipsometry, lubricant film thickness, vertical-objective-based ellipsometric microscope, thickness resolution

1. Introduction

Thin lubricant films play an important role in the many micro/nano mechanical technologies, for example the lubrication for the hard disk drives (HDDs). High-density magnetic recording disk drives require the head-disk gap continuously decreasing to 2-3 nm, as well as the thickness of liquid lubricant films requires being 1-2 nm. Thus, controlling the dynamic distribution and behavior of the nm-thick liquid film is crucial to improve the recording density. Real-time observation of nm-thick thin lubricant films on magnetic disks with a sub-nanometer thickness resolution could provide a very useful method to clarify the dynamic behavior of molecularly thin lubricant films. Conventional methods, such as ellipsometer, atomic force microscope (AFM) or optical surface analyzer (OSA) require scanning mechanism and are not suitable for real-time observation [1,2]. Ellipsometric microscope (EM), which is based on elliposometry, is a good candidate because it does not require scanning mechanisms. In conventional EMs, the obliquely-set objective lens magnifies the sample and provides thickness distribution as a dark-bright contrast image on the CCD camera. This oblique observation causes a problem of narrow field of view for high lateral

resolution lenses, which causes a low spatial resolution of around 10 µm. To overcome this problem, the vertical-objective-based EMs (VEMs) were proposed [3,4]. Although the feasibility of VEM for thin lubricant films was confirmed [5], the designs for the optical system and image detection have not been established. Therefore, the thickness resolution was low, about 0.8 nm. In this paper, the design principle of the VEM, especially the methods for improvement of thickness resolution are presented.

2. Methods for improvement of thickness resolution

The schematic of VEM is shown in Fig. 1. Oblique illumination is necessary to get ellipsometric contrast in EMs. In our VEM, the objective lenses are set vertically and the off-axis light is focused onto the back focal plane of the objective lens to obtain the oblique illumination light. Here, we focused on the thickness resolution improvement. Higher signal-to-noise ratio (SNR) is required to improve the thickness resolution. In EMs, the signal depends on the light source power and ellipsometric contrast, and the noise includes shot noise and coherent noises. In this section, methods for signal enhancement and noise suppression to improve the thickness resolution are described.

Liu Qingqing, Kenji Fukuzawa, Yosuke Kajihara, Hedong Zhang and Shintaro Itoh

Japanese Society of Tribologists (http://www.tribology.jp/) Tribology Online, Vol. 7, No. 3 (2012) / 140

Fig. 1 Schematic of vertical-objective-based

ellipsometric microscope (VEM)

2.1. Improvement of ellipsometric contrast

2.1.1. Improvement of light source power High power light source can increase the light

intensity; however, the shot-noise is also increased. In light detectors, the signal is generally proportional to the light intensity whereas the noise is proportional to the square root of the light intensity for shot-noise dominant detectors. Therefore, the SNR is proportional to the square root of the light intensity [6]. Since a CCD camera is used as the light detector and the light intensity is rather large in the VEM, the above relation is valid. Therefore, the SNR of the VEM is expected to be proportional to the square root of the light intensity.

2.1.2. Improvement of ellipsometric contrast Since the thickness distribution is provided as a

dark-bright contrast image by using a CCD camera, the ellipsometric contrast may affect the thickness resolution. Therefore, the ellipsometric contrast ratio is discussed, which describes the dark-bright difference between the unlubricated and lubricated disks. The ellipsometric contrast ratio Cr here was defined by

d

dl

IIICr −

= (1)

where Il and Id are the signal intensities of lubricated and unlubricated disks, respectively.

The ellipsometric contrast depends on the incident angle θ because the contrast is determined by the complex reflectivity of the sample, which changes according to the incident angle. Moreover, the signal intensity of ellipsometric microscope I is generally given by [7]

Fig. 2 Reflection and transmission of a multilayer

structure plane

{ }APAArAr

IRI s

222

02

sin)2sin(cossin2cos2

+∆++

×=

(2)

where r is the amplitude ratio for p- and s-polarized lights, I0 is the intensity of incident light, and P and A is the angles of the polarizer and analyzer. r and ∆ depend on the incident angle θ. The contrast ratio can be calculated by using Eqs. (1) and (2).

In the VEM, the polarizer is adjusted so that the light signal I is proportional to the film thickness h in order to simplify conversion from the light intensity to the thickness [5]. We did a comparison of ellipsometric contrasts for different incident angles, when I was proportional to h by simulation. Here, Il and Id in Cr were obtained by using 2×2 matrix method [1]. When light incidents on the multilayer structure, the change of the reflected light can be decomposed into the effects of the propagation through the interface between different layers and the inside of a layer. Fig. 2 shows the layer model of a multilayer structure. Φ0 is the angle of incidence; Φj and Φm+1 are angles of refraction in the j-th layer and substrate, respectively. The complex refraction index of the j-th layer is Nj, and its thickness is dj. N0 and Nm+1 represent the complex refraction indices of the ambient and substrate, respectively. Using different 2×2 matrices I and L to describe the individual interface and layer of the entire stratified structure effects, the complex reflection coefficients defined by matrix S can be expressed as follows:

( ) )1(12121012221

1211+−=

= mmmjjj ILLILILI

SSSS

S KK

(3) For any two-media interface (ab), the interface matrix Iab is given as follows:

0 1 2

j

m

m+1

Φ0

Φj

Φm+1

LED

Speckle killer

Polarizer Compensator

Pinhole

Stage

A

Sample

EMCCD

Back focus plane

θ Substrate Lubricant

Objective lens

Incident light Reflective light

Objective lens

Analyzer



=

ababab

abababab ttr

trtI

/1///1

(4)

where rab and tab are the Fresnel reflection coefficients of the ab interface, respectively. The layer matrix L can be written by

=

− β

β

j

j

ee

L0

0

(5)

Here, β is the phase change that the multiply-reflected wave inside the film experiences as it traverses the film once from one boundary to the other, and is given by

φλ

πβ cos2 dN=

(6)

where λ is the wavelength of the light. For the purpose of ellipsometry, the

stratified-structure scattering matrix S have to be calculated for both polarizations parallel (p) and perpendicular (s) to plane of the incidence. Using Sp and Ss to represent these matrices for p- and s-polarizations and the p- and s-reflection coefficients are obtained by

p

pp S

SR

11

21= (7)

s

ss S

SR11

21= (8)

where Rp and Rs are the complex reflection coefficients of the p- and s-polarized lights. The ellipsometric parameters r and ∆ are given by

( )wpi

s

p

s

pi eRR

RR

er ϕϕ −∆ ⋅==⋅ (9)

So the signal intensity of ellipsometric microscope I can be provided by substituting r and ∆ to Eq. (2). By using Eq. (9), r and ∆ can be obtained from Rp and Rs calculated by the 2×2 matrix method.

Figure 3(a) shows the simulated relationships between ellipsometric contrast ratio Cr and film thickness h for different incident angles. The layer model consisted of air, lubricant film and magnetic disk as a substrate, whose refractive indices were 1, 1.3, and 2.35+3.93i, respectively. The air and disk were semi-infinitely thick. As shown in Fig. 3(a), the compensator and analyzer were set in extinction condition, which means the unlubricated disk has the minimum intensity, and the polarizer was adjusted so that the intensity was proportional to the thickness for

each incident angle. Fig. 3(b) shows the relationship between the contrast ratio and incident angle at a thickness of 2 nm. From these results, it is concluded that the incident angle affects the ellipsometric contrast ratio significantly, and it reaches the maximum when the incident angle θ is 60 deg.

2.2. Suppression of noise In the VEM, the shot and coherent noises are

dominant. As mentioned before, the shot noise increases with the light intensity increasing, however it does not decrease the SNR, because the signal increases more rapidly than the noise when the light intensity increases. Therefore, the coherent noises should be suppressed.

Coherence noises appear as dark-bright fringe images in VEM. Coherence is a property of waves that enables interference, which includes temporal and spatial coherence. When we discuss the coherent noises, the temporal coherent noise and spatial coherent noise must be expressed, separately.

2.2.1. Suppression of temporal coherence noises Temporal coherence is the property that the phase

difference between the lights emitted at different times does not change with time. If the coherent lights passing through the different distance paths arrive at the same point, interference fringes are generated there. Temporal coherence is usually characterized by coherent length. Coherence length lc is the maximum optical path difference when coherence can occur. It is given by

λλ∆

=2

cl (10)

where λ and ∆λ are the wavelength and width of the wavelength of the light source, respectively. The smaller ∆λ is, and the temporal coherence noises occur more clearly. For the coherence length is larger than 100 m of the He-Ne lasers with ∆λ of 10-6~10-9 nm, and the lasers cause the temporal coherence. To decrease the temporal coherent noise, the large wavelength width light source is necessary. In VEM, the temporal coherence is mainly caused by the reflection in the optical devices, so when the minimum of the distance between two optical devices is larger than lc, the temporal coherent noise can be reduced. In VEM, the objective lenses have the smallest distance of 1 mm order, so the light source with lc smaller than 1 mm is needed.

2.2.2. Suppression of spatial coherence noises Spatial coherence describes is the property that the

phase difference between the lights emitted at different position does not change with time. Usually, distant points have poorer phase correlation. Therefore, the larger light source can decrease the spatial coherent noise. In the VEM, as shown in Fig. 1, the area of light source was adjusted by setting the pinhole behind the light source and the light passing through the pinhole



(a)

0

0.1

0.2

0.3

0 2 4 6 8 10

Film thickness h , nm

Ellip

som

etric

con

trast

ratio

Cr,

a.u

. 0 deg40deg50deg60deg70deg

(b)

0

0.02

0.04

0.06

0.08

0.1

0 10 20 30 40 50 60 70 80

Incident angle θ , deg

Ellip

som

etric

con

trast

ratio

Cr,

a.u

.

Fig. 3 Simulated relationship between ellipsometric contrast ratio Cr and thickness h for different incident angles: (a) relationship between the contrast ratio and thickness after adjustment of polarizer angle so that the intensity is proportional to the thickness for each incident angle for different incident angles; (b) relationship for incident angle θ and contrast ratio Cr of 2 nm-thick film

was converted to the parallel beam by the collimation lens. The coherence is evaluated by the degree of coherence |µ12|, which corresponds to the visibility of interference fringes. The lights are coherent when |µ12| = 1, and incoherent when |µ12| = 0. The average degree of coherence between the light passing through the center of the optical axis and all the lights passing through the pinhole is given by [8]

rdrr

fR

rfRJ

a

a

∫

=0

1

212 2

2221

λπ

λπ

ππ

µ

(11)

where a, R and f are the radius of the pinhole, radius and focal length of the collimation lens, respectively. J1(x) is

0

0.2

0.4

0.6

0.8

1

0 50 100 150 200 250 300 350 400

Pinhole diameter a , µm

Ave

rage

deg

ree

ofco

here

nce

<|µ

12|>

, a.u

.

Fig. 4 calculated relationship between the pinhole

diameter a and the average degree of coherence <|µ12|>

the first Bessel function of the first kind. Fig. 4 shows the calculated relationship between the pinhole diameter a and the average degree of coherence <|µ12|>. Here, R = 27 mm, f = 60 mm, and λ = 512 nm, which are the values in the experimental setup. The estimation indicates that the larger pinhole decreases the degree of coherence. The degree of coherence decreases down to 1/10 at about a diameter of 28 µm and 1/100 at 100 µm. This means suppression of the spatial coherence noise requires the pinhole diameter of larger than around 100 µm.

3. Experiments

3.1. Setup of VEM Our VEM is shown in Fig. 1, a commercial inverted

microscope was modified and an objective lens with a numerical aperture (NA) of 0.95 was used. High power green LED (output power = 26 mw, λ = 512 nm, ∆λ = 35 nm, and lc is about 7.5 µm) was used as the light source to decrease the temporal coherent noise. lc was much smaller than distance between the optical devices. This can suppress the temporal coherence as explained in Section 2.2. A bundle-fiber-based device, called speckle killer, was set to reduce the spatial coherent noise after the light source. Since the speckle killer expands the size of the light source, the range of incident angles would also be increased. The ellipsometric contrast changes due to the incident angles. Thus, to control the range of incident angles, a pinhole behind the light source was added, which was also critical to improve the thickness resolution. The light reflected from the sample was imaged through the objective and imaging lenses onto a highly sensitive electron multiplying CCD camera with an area of 8×8 mm2, and 160×160 µm2 field of view, as well. Adjusting the polarizer angle so that the intensity difference Il-Id was approximately proportional to the thickness h, Il-Id = ah, and the thickness could be converted from intensity directly.

As described in Section 2, the incident angle and pinhole size affect the signal and noise ratio, the influences of incident angle and pinhole size were investigated.

(b)



(a)

0

2000

4000

6000

8000

10000

0 2 4 6 8 10Film thickness h , nm

Inte

nsity

diff

eren

ce I

-Id

,a.

u.

incident angle 70degincident angle 60degincident angle 50degincident angle 40degincident angle 00deg

(b)

0

0.1

0.2

0.3

0.4

0 10 20 30 40 50 60 70 80Incident angle θ , deg

Ellip

som

etric

con

trast

ratio

Cr,

a.u

.

20µm-pinhole100µm-pinhole200µm-pinhole400µm-pinhole1mm-pinholenon-pinhole

Fig. 5 Experimental relationships between intensity

and thickness: (a) Il-Id is proportional to h for different incident angles when the diameter of pinhole is 400 µm; (b) ellipsometric contrast ratio of 2.7 nm-thick lubricant image for different pinhole sizes at different incident angles

3.2. Experiment samples For thickness resolution measurement, magnetic

disks with lubricants were used as the sample substrate. The test lubricants were polar and nonpolar perfluoropolyether (PFPE) lubricants (Fomblin Zdol4000 and Z03, Solvay Solexis) with molecular weight of about 4000 g/mol, which were applied onto the disk by a dip method [5]. The lubricants are widely used in HDDs, and the refractive indices are almost same for these lubricants of n = 1.3. The nonpolar lubricant is stable on magnetic disks whereas the polar one at a thickness of around 6 nm is unstable and ‘dewet’ the disk. The thickness of the film was measured with a commercial ellipsometer.

For the noise comparison experiments, the 1951-USAF-resolution-test-chart was used. The 1951-USAF-resolution-test-chart is a kind of resolution test pattern, which was set by US Air Force in 1951. It has variously-sized patterns made of a metal film on a glass substrate, and is widely used for testing the lateral resolving power of optical systems.

Fig. 6 Noise images for different pinhole diameters

4. Results and discussion

4.1. Improvement of ellipsometric contrast For our setup, the incident angle as well as the

pinhole size may affect the ellipsometric contrast, so we compared the ellipsometric contrast ratio Cr of lubricated and unlubricated regions on the disk at different incident angles when using different pinholes. A 2.7 nm-thick lubricant film was applied on the magnetic disk. The polarizer, compensator and analyzer were set so that the intensity was proportional to the thickness for each incident angle, as shown in Fig. 5(a). The relationship between the contrast ratio and incident angle is shown in Fig. 5(b). The contrast ratio reached the maximum at the incident angle θ of about 60 deg for all the pinholes, which well matched the theoretical results as shown in Fig. 3(b). For different pinholes, the ellipsometric contrast ratio changed not much except for 1-mm-diameter pinhole and non-pinhole conditions, and the contrast ratio decreased significantly at the last two conditions. According to the theory, the contrast ratio changes depending on the incident angle, when the incident angle is about 60 deg, it reaches the maximum. The larger pinhole causes the larger range of the incident angles. The contrast ratio Cr is smaller because it is averaged over the larger ranges. In the experiment, some other factors may affect the result, for example, the noise influence. When the pinhole is small, such as 20, 100 and 200-µm-diameter pinholes, the noises may

d: 20 µm

d: 100 µm d: 200 µm

d: 400 µm

d: 1 mm d: Non-pinhole

Table 1 Light intensity I and standard deviation σ of the test pattern image for 400-µm-diameter pinhole condition

Incident angle θ, deg

Light intensity I

Standard deviation σ

0 6995 218 40 7075 226 50 7090 230 60 7088 222 70 7069 219



be too large to make the Cr distortion. Therefore, the difference of Cr is not clear for the small pinholes, whereas, clear for 1-mm-diameter pinhole and non-pinhole conditions, due to the smaller noises.

4.2. Suppression of noise We also compared the noise level at different incident

angles with different pinholes. The relationship between noise and incident angle is shown in Table 1. We used the standard deviation of the light intensity of the image to describe the noise level. In this experiment, the 400-µm-diameter pinhole was used, and a 1951-USAF-resolution-test-chart was used as the sample. The laser power was adjusted so that the light intensities on the CCD were equal for the different pinholes. Table 1 indicates that the incident angle has no effect on the noise. The result shows that pinhole size affects the noises rather than incident angle. Fig. 6 shows the noises on test pattern for different pinhole diameters when the incident angle was 60 deg. The coherent noises, which appeared as interference fringes, were clearly observed when the diameter of pinhole was 20 µm. The pinhole larger reduced the coherent noises, which corresponded to the theory as shown in Fig. 4. However another noise was observed, which was considered to be caused by the pinhole camera effect. Since the speckle killer is composed by a bundle of optical fibers, light rays from the fiber bundle pass through the small pinhole behind the speckle killer may form an image of the fiber bundle, which was a noise image. When the diameter of pinhole was larger than 400 µm, the pinhole-camera-image was obscure; because the larger pinhole made the lights from different parts of the light source coincide, and the images became uniform.

4.3. Thickness resolution When a thin film with a uniform thickness is

observed, the light intensity of the image should be uniform. However, in practice, due to the noise of the imaging system, the intensity on CCD was not uniform, which caused the error of thickness analysis for VEM. In the measurement, the polarizer angle was adjusted so that the light intensity I was proportional to the thickness h, which is shown in Fig. 5(a). Using the difference of the light intensities between the lubricated and unlubricated disks Il-Id to express the signal S, as well as the standard deviation of the light intensity of lubricated disk image σ to describe the noise N, the signal-to-noise ratio (SNR) is given by

Fig. 7 Thickness resolution for different pinholes (θ

= 60 deg)

σdl IISNR −

= (12)

If the thickness resolution hm is defined as the thickness when SNR = 1,

SNRhhm = (13)

As the incident angle has no effect on the noise N, and the ellipsometric contrast ratio reaches the maximum when the incident angle θ is 60 deg, we compared the thickness resolutions of different pinholes when the incident angle θ is 60 deg. The results are shown in Fig. 7. The sample was disk with 2.7 nm-thick lubricant films, and the intensity Id was adjusted as a fixed value so that the effect of shot noise on standard deviation can be omitted. The results indicate that the pinhole is larger from 20 µm pinhole to 400 µm pinhole, the thickness resolution becomes better, due to the noise decreasing, and the thickness resolution reaches the maximum when pinhole diameter is 400 µm and keep fair for pinhole diameter of 1 mm and non-pinhole. 400-µm-diameter pinhole was chosen rather than 1 mm and non-pinhole, so that the much more parallel light could be obtained. Then increasing the input light intensity to the maximum, signal Il-Id was improved by 1.33 times, as well as the noise σ was increased by 1.17 times, which is about the square root of the signal magnification. And the SNR was increased from 5.6 to 6.3, and the thickness resolution was improved to about 0.4 nm, shown in Table 2. This improvement matched that theory predicted as explained in Section 2.1.

Thus, by choosing 400-µm-diameter pinhole and incident angle of 60 deg can get the higher ellipsometric contrast ratio, as well as obtain higher thickness resolution. The thickness resolution can be improved from 0.8 nm to 0.4 nm by this method5).

In addition, the magnetic disks have some fluctuations of the refractive index n and extinction coefficient k, and those effects on the thickness measurement should be discussed. In this experiment,

0

1

2

3

1 2 3 4 5 6

Pinhole diameter, µm

Thic

knes

s re

solu

tion

hm,

nm

20 100 200 400 1000 5000

Table 2 Thickness resolution for increasing the light intensity, h = 2.7 nm, θ = 60 deg

Il Id σ SNR hm, nmBefore increasing

11066 8637 437 5.56 0.49

After increasing

15513 12281 514 6.29 0.43



(a) t = 0 s (b) t = 30 s

(c) t = 1 min (d) t = 1 min 30 s

Fig. 8 Dewetting image of 6.6 nm-thick film at different times. Images were taken at 0 s, 30 s, 1 min, and 1 min 30 s after the start of the observation

Fig. 9 Magnified image of the upper right rectangle

framed in Fig. 8 (a)

we obtained the thickness resolution of 0.4 nm using 2.7 nm-thick lubricant film, which means the noise was about 15% of the signal. And we used an ellipsometer to measure the n and k of the samples, the fluctuations defined as standard deviation were about 0.01 for both n and k for 80 sampling points, which means the fluctuations of n and k were less than 1%. Although the VEM and ellipsometer have different lateral resolutions, the noise level is much higher than the n and k errors. Therefore, we might consider that the noise caused by the optical system was much larger than the n and k fluctuations.

4.4. Real-time visualization of thin lubricant film Figure 8 shows the dewetting images of the 6.6

nm-thick polar lubricant film on magnetic disk observed in real time by our VEM. These images were taken at 0 s, 30 s, 1 min, and 1 min 30 s after the start of the observation. The lubricant on the disk was unstable and

0

2

4

6

8

10

0 20 40 60 80

Posation x , µm

Film

thic

knes

s h

, nm

Fig. 10 Cross-sectional view on line L in Fig. 9

spontaneously dewetted the disk. Fig. 9 is the magnified image of the upper right rectangle framed in Fig. 8(a). A big black hole can be found in Fig. 9. The film thickness is proportional to the light intensity when the thickness is from 0 to about 30 nm. As for thicker films, the relationship between the film thickness and light intensity is a periodic function due to the optical interference. Therefore the black hole is considered to be a big droplet with much larger thickness. Fig. 10 shows a cross-sectional view at line L in Fig. 9, and the position of arrows A and B correspond to those in Fig. 9, respectively. From the observation by our VEM, small holes (arrow A and B in Fig. 9) were found over the film surface, which could not be found in the previous experiment [5]. As the thickness of the flat region of the lubricant was about 6.6 nm, the depth of the small holes were about 1.5 nm measured from the flat film surface. This demonstrates that our VEM can observe the temporal change of the nm-thick lubricant film, at a higher thickness resolution. The film on the right side, which is the edge of the illumination field, appeared to be thinner than that on the left side, due to the ununiformity of the light source intensity. And this may be reduced by the adjustment of the light source in further experiment.

5. Summary

The method to improve the thickness resolution was presented by analyzing the effects of incident angle and pinhole size on the signal-to-noise ratio. Both the incident angle and pinhole size affect the ellipsometric contrast, significantly, as well as the pinhole size may determine the noise level. Thus, by choosing the optimum pinhole size and incident angle (400-µm-diameter pinhole and 60-deg-incident angle in this setup), the thickness resolution was improved to 0.4 nm. In addition, the dewetting process observation demonstrated the real-time visualization of nm-thick thin liquid lubricant films.

0nm

15nm

40µm

L

B

20µm

A

A B



Acknowledgements

This work was supported in part by SENTAN, the Japan Science Technology Agency (JST), and the Storage Research Consortium.

References

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[2] Meeks, S. W., Weresin, W. E. and Rosen, H. J., “Optical Surface Analysis of the Head-Disk-Interface of Thin Film Disks,” ASME J. Tribol., 117, 1995, 112-118.

[3] Linke, F. and Merkel, R., “Quantitative Ellipsometric Microscopy at the Silicon-Air Interface,” Rev. Sci. Instrum., 76, 6, 2005, 3701-1-3701-10.

[4] Fukuzawa, K., Yoshida, T., Itoh, S. and Zhang, H., “Motion Picture Imaging of a Nanometer-Thick

Liquid Film Dewetting by Ellipsometric Microscopy with a Sub-µm Lateral Resolution,” Langmuir, 24, 20, 2008, 11645-11650.

[5] Qingqing, L., Fukuzawa, K., Kajihara, Y., Zhang, H. and Itoh, S., “Development of Ellipsometric Microscope for High-Resolution Observation of Nanometer-Thick Lubricant Films,” Tribology Online, 6, 6, 2011, 251-256.

[6] Horowitz, P. and Winfield H., “The Art of Electronics,” 2nd edition. Cambridge University Press, Cambridge, 1989, 431.

[7] Fukuzawa, K., Noda, T. and Mitsuya, Y., “Direct Visualization of Molecularly Thin Lubricant Films on Magnetic Disks with a Digitally Enhanced Ellipsometric Microscope,” IEEE Trans. Magn., 39, 2, 2003, 898-902.

[8] Born, M. and Wolf, E., “Principles of Optics,” Pergamon Press, Oxford, 1980, 505-511.

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