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Nuclear Instruments and Methods in Physics Research B 206 (2003) 842­845 www.elsevier.com/locate/nimb

Modeling of surface smoothing process by cluster ion beam irradiation
A. Nakai
c

a,* ,
a

T. Aoki

a,b

, T. Seki

a,b

, J. Matsuo a, G.H. Takaoka a, I. Yamada

b,c

Ion Beam Engineering Experimental Laboratory, Kyoto University, Sakyo, Kyoto 606-8501, Japan b Collaborative Research Center for Cluster Ion Beam Process Technology, Japan Laboratory of Advanced Science and Technology, Himeji Institute of Technology, 3-1-2, Kohto, Kamigori-cho, Ako, Hyogo 678-1205, Japan

Abstract Smoothing effect is one of the advantages of cluster ion beam. It is important to estimate an ion dose to achieve required surface smoothness. The smoothing rate with cluster ion beam depends on surface profiles. In this work, modeling of surface smoothing process with cluster ion beams was examined. Ar cluster ions with an energy of 20 keV was irradiated on rough Si Surface. Fast Fourier transform was applied to atomic force microscope data of 100 á 100 lm2 , and power spectra were calculated. Smoothing rate depends on the wave number as well as the ion dose. Relationship between smoothing rate and wave number was derived. The surface smoothing process was modeled with the use of the wave number dependence of the smoothing rate. The calculated and the experimental surface profiles are in good agreements. ñ 2003 Elsevier Science B.V. All rights reserved.
PACS: 79.20.Rf.; 79.20.Ap Keywords: Cluster; Surface; Smoothing; Ion beam processing

1. Introduction Cluster ion beam has a lot of advantages for material processes [1]. Especially, smoothing process is one of the promising technology to be utilized for industrial applications. There are many reports on surface smoothing effect with cluster ion beam. Cluster ion beam smoothes the various

* Corresponding author. Tel.: +81-75-753-4994; fax: +81-75751-6774. E-mail address: atsuko@nishiki.kuee.kyoto-u.ac.jp (A. Nakai).

materials; not only metal [2] but also hard materials such like diamond [3,4]. Small scratches on surfaces also removed. Smoothing effect depends on the surface morphology [5]. It is very difficult to predict process parameters to realize desired smoothness for complex surface profiles. It is important to estimate an ion dose to achieve required surface smoothness to utilize cluster ion beams to industrial processes. In this work, the relation between smoothing process and surface profiles was studied. Fast Fourier transform (FFT) was applied to atomic force microscope (AFM) data measured for rough Si surface irradiated with Ar cluster ion beam, in

0168-583X/03/$ - see front matter ñ 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0168-583X(03)00875-9


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order to reveal relation between surface morphology and smoothing rate with cluster ion beam. As a result, it was revealed that smoothing rate depends on both the ion dose and the wavelength, which is the period of roughness. The smoothing process was modeled by means of smoothing rate dependence on wave number, the inverse number of wavelength. Simulated results with our smoothing model were compared with experimental data.
Fig. 1. AFM images of Si surfaces (100 á 100 lm2 ).

2. Experimental Cluster ion beam equipment was constituted by nozzle, skimmer, ionization unit, and target. Neutral cluster beam was formed with high pressure in the nozzle made of glass. Cluster gone out from the nozzle passed through the skimmer, and were ionized by electron impact in ionization unit. Electrons emitted from hot W filament, and bombarded neutral cluster beam. Cluster ions were accelerated between ionization unit and target. With this equipment, Ar cluster ion beam was irradiated on the backside Si(0 0 1) wafer at dose of 1 á 1017 , 3 á 1017 and 1 á 1018 ions/cm2 . The inlet gas pressure was about 4000 Torr. The distribution of cluster size was 1000­10,000 and the average of cluster size was about 2000 atoms/ion. The ionization voltage was set to 500 V, and the ionization current was 400 mA. The total acceleration voltage was 20 kV. 100 á 100 lm2 and 10 á 10 lm2 surface images were measured by AFM. The resolution of AFM was 256 á 256 (65,536 pixels). Before irradiation, root-mean-square (RMS) of 100 á 100 lm2 was 177.7 nm.

In order to clarify length and smoothing applied to these AFM applied to remove function is

the relation between waverate, 2-dimension FFT was data. Window function was aliasing. Applied window

W Ïi; j÷ ¼ 1½1 þ cosfÏ2pi÷=ÏL þ 1÷g 4 á½1 þ cosfÏ2pj÷=ÏL þ 1÷g; Ï1÷ where i and j means coordinate of AFM data, and L means the number of measurement point for each axis by AFM. Fig. 2 shows average power spectra of 100 á 100 lm2 AFM data. Wave number [N ] means the inverse number of wavelength. As the ion dose increases, total intensity decreases. RMS can be calculated by

Wavelength [µm]
20 1011 1010 10 6.6 5
Before 1e17 3e17 1e18

4
Irradiation ions/cm 2 ions/cm 2 ions/cm2

3.3

3. Results and discussion
Intensity

Fig. 1(a) and (b) are AFM images of the nonirradiated Si surface and the irradiated with 1 á 1018 ions/cm2 Ar cluster ion beam. After 1 á 1018 ions/cm2 irradiation, RMS decreased so far as 107.9 nm. From these AFM images, it is clear that the roughness of short period was removed, but the roughness of long period still remained.

109 108 107 0

5

10

15

20

25

30

Wave number (N )
Fig. 2. Power spectra of 100 á 100 lm2 AFM data.


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A. Nakai et al. / Nucl. Instr. and Meth. in Phys. Res. B 206 (2003) 842­845

RMS ¼

1 n

qffiffiffiffiffiffiffiffiffiffi X I;

Ï 2÷

Wavelength [ µm]
1012 1011 1010 10 5 3.3 2.5 2 1.7 1. 4
Bef ore Calculated 1e17 Calculated 3e17 Calculated 1e18 1e17 (Experimental) 3e17 (Experimental) 1e18 (Experimental)

where n means the number of total pixels of AFM and I means intensity of each 2-dimension wave number. Decrease of total intensity means decrease of RMS in Eq. (2). The relationship between intensity and the ion dose was analyzed from Fig. 2. The intensity of each wave number seems to decrease exponentially as the ion dose. On the assumption that smoothing rate depends on both the ion dose and the wave number, the intensity after cluster ion beam irradiation is given by I ÏN ; D÷ ¼ I0 ÏN ÷ expÏcÏN ÷D÷; Ï 3÷ where I0 means the intensity before irradiation, D means the ion dose, and cÏN ÷ means smoothing rate dependence on wave number. Fig. 3 shows smoothing rate for each wave number from 0 to 25. Smoothing rate was calculated with the intensity of non-irradiated, 1 á 1017 and 3 á 1017 ions/cm2 irradiated power spectra. The inclination of the intensity against the ion dose was defined as smoothing rate. This graph shows that smoothing rate (c) can be approximated by linear equation of wave number (N ) cÏN ÷ ¼ þ5:34 á 10
þ19

Int ensity

109 108 107 106 105 0 10 20 30

40

50

60

70

Wavenumber (N)
Fig. 4. Comparison for experimental and simulated spectra.

N × 2:46 á 10

þ18

:

Ï 4÷

In Fig. 3, smoothing rate at wave number less than 4 is positive value, which means intensity increases as the ion dose increases. This was due to the

Fig. 3. Approximation of smoothing rate.

window function used in FFT. Intensity of very small wave number is in accurate in FFT calculation. If the surface larger than 100 á 100 lm2 (for example, 1 á 1 mm2 ) was analyzed, these intensity will decrease as the ion dose. Accordingly, smoothing rate at wave number less than 4 should be ignored. In the region of N 6 3, c was set to 0. Using Eqs. (3) and (4), it is possible to calculate power spectrum for desired ion dose. Fig. 4 shows a comparison of experimental and calculated spectra. In large wave number region, calculated intensity doesnót match well to experimental value. This is due to noise or inaccuracy in AFM measurement. These are ignored, because there has little influence on RMS in Eq. (2). Experimental and calculated intensity show good agreements for small wave numbers. With Eqs. (3) and (4), surface images at any ion dose can be obtained by inverse-FFT from calculated power spectra. Fig. 5 shows the comparison of experimental and simulated surface. Simulated surface was calculated from power spectrum with ion dose 1 á 1018 ions/cm2 shown in Fig. 4. These AFM images showed good agreements in surface morphology as well as surface roughness. For quantitative analysis, RMS in 10 á 10 lm2 area was calculated. As mention above, FFT has little precision in the small wave number region. In order to discuss reliability of this model, simulated RMS was calculated from Eq. (2) with the sum of intensity over wave number 10 instead of total


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spectra with that smoothing model (Fig. 4). This model gives good tendencies of surface smoothness irradiated with cluster ion beam.

4. Conclusions FFT analysis reveals that the larger wave number roughness decreases rapidly. The smoothing process was modeled with smoothing rate dependence on both the ion dose and the wave number of roughness. With this model, experimental and simulated surface morphology and RMS of roughness showed good agreements. This model makes possible to calculate surface morphology of any ion dose without experiment.

Fig. 5. 1 á 1018 ions/cm2 irradiated surface.

120 100 80
10 â10µm2 RMS (Experiment al) Simulated RMS

RMS [ nm]

60 40 20 0 0 2 4
17

Acknowledgement This work is supported by New Energy and Industrial Technology Development Organization (NEDO).
6
2

8

10

Do se [ â 10 ions/cm ]
Fig. 6. Dose dependency for 10 á 10 lm2 roughness.

References
[1] I. Yamada, J. Matsuo, Z. Insepov, T. Aoki, T. Seki, N. Toyoda, Nucl. Instr. and Meth. B 164­165 (2000) 944. [2] H. Kitani, N. Toyoda, J. Matsuo, I. Yamada, Nucl. Instr. and Meth. B 121 (1997) 491. [3] A. Yoshida, M. Deguchi, M. Kitabatake, T. Hirao, J. Matsuo, N. Toyoda, I. Yamada, Nucl. Instr. and Meth. B 112 (1996) 249. [4] N. Toyoda, N. Hagiwara, J. Matsuo, I. Yamada, Nucl. Instr. and Meth. B 148 (1999) 639. [5] N. Toyoda, N. Hagiwara, J. Matsuo, I. Yamada, Nucl. Instr. and Meth. B 161­163 (2000) 984.

intensity, because it was expected that this calculated RMS is equal to 10 á 10 lm2 RMS. Fig. 6 shows the relation between RMS and the ion dose. Solid line (experimental) means 10 á 10 lm2 RMS measured by AFM. RMS decreased as the ion dose increased. Dotted line (simulated) means RMS calculated from simulated power