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J. Opt. Soc. Am. B / Vol. 20, No. 10 / October 2003
R. Rabady and I. Avrutsky
Reduced surface roughness of solid thin films prepared by alternating-bias, radio-frequency magnetron sputtering Rabi Rabady and Ivan Avrutsky Department of Electrical and Computer Engineering, Wayne State University, Detroit, Michigan 48202 Received November 21, 2002; revised manuscript received May 2, 2003 Surface roughness that is associated with thin-film deposition has a direct effect on the optical, electrical, and mechanical quality of solid-thin-film devices. The effect of using alternating bias during rf-magnetron sputtering of SiO2 on Si substrate was investigated, and it was proven experimentally that modulating the plasma flow by means of alternating bias produces more even deposition of the sputtered material. This effect was verified by analyzing the envelope of the reflection fringes that were recorded during the thin-film deposition process, and by observing the power reduction in the arc-shaped scattering that is associated with mode excitation of a rough-surface waveguide. © 2003 Optical Society of America OCIS codes: 240.6700, 240.5770, 310.1860, 350.5400.
1. INTRODUCTION
2. THEORY
Surface roughness that is associated with thin-film deposition has a direct effect on the performance of solid-thinfilm devices. For thin films that are prepared for optical waveguides, multilayer interference filters, and optical resonant filters, surface roughness becomes a significant issue. Using alternating bias during rf-magnetron sputtering can modulate the plasma flow of the sputtered material by modulating the sputtering energy resulting from the physical bombardment of the target by the argon ions. Modulating the plasma flow at a frequency that is comparable with the rate of depositing a single atomic layer can produce more even deposition of the sputtered material, and thus less surface roughness of the deposited film. One approach to a smoother film is described in Ref. 1, which proposes using rf bias at the substrate side to produce a more even deposition of material by increasing the mobility of the sputtered material at the moment of deposition. We propose in this paper using rf power at the target side and alternating bias at the substrate side to modulate the sputtering energy, which increases the mobility of material at the moment of deposition and produces the desired effect. To measure this effect we made use of the fact that the reflection (or transmission) interference fringes that result from changing the distance between two mirrors (the thickness of the growing thin film in our case) that form a Fabry–Perot resonator is a function not only of the wavelength of the light used and the optical constants of the resonator, but also of the optical quality (i.e., the surface roughness) of the mirrors. Before experimenting with different kinds of bias on the magnetron sputtering deposition and observing their effect on the film surface roughness, some review of the theory of reflection fringes produced from growing film will be presented in what follows.
In the absence of surface roughness, the reflection from a thin film of thickness L and refractive index N 1 ⫽ n 1 ⫹ jk 1 between a bulk substrate with refractive index N 2 and a superstrate with refractive index N 0 (Fig. 1) is given by a well-known formula2–4:
0740-3224/2003/102174-05$15.00
R⫽
兩 r 01兩 2 ⫹ 兩 r 12兩 2 ⫹ 2r 01r 12 cos 2 
1 ⫹ 兩 r 01兩 2 兩 r 12兩 2 ⫹ 2r 01r 12 cos 2 
,
(1)
where
⫽
2L
共 N 12 ⫺ sin2 兲 1/2,
N ⫽ n ⫹ jk,
⫽
␣ 4
;
(2)
and where is the incidence angle, r xy is the Fresnel reflection from the (x, y) interface (which depends on the incident angle and the light polarization), is the wavelength, and ␣ accounts for the film optical losses. While the film is growing, the extremes from Eq. (1) are located at L⫽
p 4
,
p ⫽ 1, 2, 3... ,
(3)
where odd (even) p corresponds to minima (maxima) locations when the substrate refractive index is higher than the film refractive index. The values of the extremes are given by © 2003 Optical Society of America
R. Rabady and I. Avrutsky
Fig. 1.
Vol. 20, No. 10 / October 2003 / J. Opt. Soc. Am. B
Rough-surface thin film on bulk substrate.
R max ⫽ R min ⫽
兩 r 01兩 2 ⫹ 兩 r 12兩 2 ⫹ 2r 01r 12
1 ⫹ 兩 r 01兩 2 兩 r 12兩 2 ⫹ 2r 01r 12 兩 r 01兩 2 ⫹ 兩 r 12兩 2 ⫺ 2r 01r 12
1 ⫹ 兩 r 01兩 2 兩 r 12兩 2 ⫺ 2r 01r 12
,
.
(4)
According to the scalar scattering theory presented by Carniglia,5,6 for a surface roughness of Gaussian distribution around zero mean level with a standard deviation (RMS value) given as ␦, the extreme values given by Eq. (4) can be modified to 2 冑R max ⫽ r 01 exp共 ⫺2k 2 ␦ 2 兲 ⫹ r 12共 1 ⫺ r 01 兲
⫻ exp关 ⫺2k 2 共 1 ⫺ n 兲 2 ␦ 2 ⫺ 2kL 兴 , 2 冑R min ⫽ r 01 exp共 ⫺2k 2 ␦ 2 兲 ⫺ r 12共 1 ⫺ r 01 兲
⫻ exp关 ⫺2k 2 共 1 ⫺ n 兲 2 ␦ 2 ⫺ 2kL 兴 ,
(5)
where k ⫽ 2 /. Equations (5) can be solved for and ␦, which results in
␦⫽
⫽
1 k
冑 冉冑 1 2
1 2kL
ln
再冋 ln
2r 01 R min ⫹
冑R max
2r 12共 1 ⫺ r 012 兲
冑R min ⫺ 冑R max
⫺ 共 1 ⫺ n 兲 2 ln
冉
册
冊
,
2r 01
冑R min ⫹ 冑R max
(6)
冊冎
.
(7)
Thus, by measuring R max and R min from the envelope of the reflection fringes graph and using r 01 that is found from the formula for Fresnel reflection, it would be possible to find the surface roughness RMS value and the optical losses of the deposited film.
when acquiring the data, where one data point was acquired every 400 msec and one data point was recorded after averaging all acquired data points for 38 s. Hardware integration was accomplished by connecting a shunt capacitance with the signal cable. This capacitance also filters out the high-frequency electromagnetic interference that is produced from the rf power source. A silica layer with n ⬍ 1.40 (the refractive index of the deposited silica depends on the density of the deposited film, and the density of the film depends in turn on the deposition rate and the amount of trapped gas molecules within the film) was deposited on a silicon (n ⫽ 3.88 ⫹ j0.02 ⬵ 3.88) substrate to exhibit high-amplitude modulation [i.e., high r12 in Eq. (1)] of the reflection fringes and thus provide more immunity against lowfrequency noise components that are not filtered out by averaging and integration. The deposition was performed starting at room temperature with a base pressure of the order of 10⫺7 Torr. The purity of the titanium target was 99.999%. The argon and oxygen gas flows were 5 and 30 SCCM (denotes cubic centimeters per minute at STP), respectively. Titanium was used as a target to deposit a titania–silica waveguide film on a BK7 glass substrate. The total chamber pressure during deposition was 15 mTorr, the distance between the target and the substrate was 15 cm, and the magnetron forward rf power was 200 W. The silicon substrate (2.5 cm ⫻ 2.5 cm) was cleaned in an ultrasonic bath with acetone, then methanol, and finally with distilled water just before deposition. A He-Ne stable laser of 632.8-nm wavelength and 1-mm-diameter beam was used for probing. Seven interference cycles were recorded, the first three cycles without any bias, then an alternating sinusoidal bias was applied of 10-V peak-to-peak amplitude and 2-Hz frequency for the next two cycles, and finally a forward DC bias of 10 V was applied for the last two cycles. The 2-Hz frequency is comparable to the rate of deposition of a single atomic layer of subnanometer thickness when a 3.8-nm/min deposition rate is realized with the deposition conditions described above. Figure 3(a) shows the entire set of the recorded reflection fringes. Zoomed-in pictures of the maxima and the minima are shown in Fig. 3(b) and 3(c), respectively. Applying different bias may produce different optical char-
3. EXPERIMENT AND RESULTS In this paper we report on a technique for high-resolution, real-time deposition monitoring that is based on recording the reflection intensity of a He-Ne laser beam that is striking the growing film at normal incidence as shown in Fig. 2. In the setup shown in Fig. 2 a high S/N ratio was achieved by applying different kinds of noise filtering. Hardware integration and software averaging procedures (low-pass noise filtering tools) were applied optimally to suppress noise and to facilitate soft integration of the reflection fringes curve. Software averaging was realized
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Fig. 2.
In situ, real-time optical monitoring setup.
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J. Opt. Soc. Am. B / Vol. 20, No. 10 / October 2003
R. Rabady and I. Avrutsky
and (7) to calculate the surface roughness RMS value and film absorption losses for the three cases. Fig. 5 shows these results and Table 1 summarizes all results. A clear response associated with applying different bias as shown in Fig. 3(b), Fig. 3(c), and Fig. 5(a), but not in Fig. 5(b) confirms the hypothesis and the theory that were used. The decrease of losses during deposition as shown in Fig. 5(b) can be attributed to a gradual cleaning of residual gases from the chamber environment. We chose to estimate the surface roughness RMS value and the optical
Fig. 4.
Fitting the first section where no bias was used.
Fig. 3. Reflection interference fringes: (a) Whole; (b) zoom in on interference fringes maxima; (c) zoom in on interference fringes minima.
acteristics of the deposited film. So, to have an accurate and detailed characterization of the deposition rate and the real refractive index of the film during the three periods—no bias, alternating bias, and direct bias—each part of the graph was fitted with respect to its own deposition rate and real refractive index. Figure 4 shows the results for the fitting of the first period (i.e., the first three cycles in Fig. 3(a) when no bias was applied). Additional independent fittings were performed for the other two periods (i.e., alternating bias and forward direct bias). The data extracted from the three fits were applied to Eqs. (6)
Fig. 5. (a) Surface roughness RMS value evolution; (b) extinction coefficient evolution.
R. Rabady and I. Avrutsky
Vol. 20, No. 10 / October 2003 / J. Opt. Soc. Am. B
Table 1. Summary of Results Surface Experimental Deposition Rate Real Refractive Roughness RMS Condition (nm/min) Index (nm) Without bias AC bias DC bias
3.84 3.79 3.79
1.348 1.360 1.352
0.088 0.079 0.085
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tive refractive index. The efficiency of the outcoupling depends mainly on the grating depth, which is closely related to the surface roughness RMS value. The waveguide excitation condition is given by: n* ⫽ m
⌳
⫾ sin ,
(8)
where n * is the waveguide effective refractive index, is the wavelength of the laser beam used for mode excitation, ⌳ is the grating period, is the incident angle for mode excitation, and m is the order of diffraction. The arc-shaped-scattering power shown in Fig. 6(a) and Fig. 6(b) is attributed to a mode excitation of a roughsurface waveguide. The higher scattering power shown in Fig. 6(a) is attributed to relatively higher surface roughness, which is associated with a waveguide that was prepared without applying any bias. On the other hand, Fig. 6(b) is associated with a mode excitation of a waveguide that was prepared by applying alternating bias. The surface roughness can be modeled by a random collection of gratings, thus higher surface roughness represents deeper gratings with higher scattering (outcoupling) power.
4. CONCLUSIONS
Fig. 6. Arc-shaped scattered power that is associated with waveguide mode excitation: (a) Waveguide was deposited without bias; (b) waveguide was deposited with alternating bias.
losses after fitting and not to include them as fitting parameters because of the dynamic nature of these parameters during deposition, and with the aim of achieving a reliable fitting by not overloading the fitting with parameters that have minor effect on the reflection fringes graph. The reduction in film surface roughness as a result of applying alternating bias during deposition was also verified by observing the power reduction of the arc-shaped scattering that is associated with the mode excitation of a relatively rough-surface waveguide.7–9 Figure 6 shows the arc-shaped scattering for a titania–silica waveguide that was deposited on BK7 glass substrate without applying any bias (left), and when applying a 2-Hz with 20-V peak-to-peak, sinusoidal, alternating bias (right). The reduction of the scattered power for the waveguide that was prepared using alternating bias during deposition is attributed to reducing the surface roughness. To understand this relation between the scattered power and the surface roughness, we consider the surface roughness as a random collection of gratings with different periods, orientations, and depths that can be modeled mathematically by a Fourier transformation of the surface topography. The grating outcouples the confined energy from the waveguide in a certain spatial direction that depends on the grating period, wavelength, and waveguide effec-
Modulating plasma deposition by applying alternating bias at a frequency that is comparable with the rate of deposition of a single atomic layer is expected to cut some of the surface roughness by increasing the mobility of the material plasma at the moment of deposition, thus providing a more even deposition of the sputtered material. This was confirmed when analyzing the reflection fringes that were recorded during deposition and observing the arc-shaped-scattering power reduction when applying alternating bias during deposition. This technique is quite affordable for industrial application to produce the high surface quality that is required for many applications, such as planar waveguides for integrated optics, multilayer mirrors, and thin-film devices. The smoothness of the loss curve in Fig. 5(b) but not the surface roughness curve in Fig. 5(a), combined with results shown in Fig. 6, confirms the analysis and the reasoning. We also conclude that the alternating bias affects the optical and physical properties of the deposited film by reducing the deposition rate (i.e., film thickness) and increasing the real refractive index of the film (see Table 1). This is not surprising since applying alternating bias is expected to produce more dense films by providing more even deposition of the material and by reducing the chances of gas molecules being trapped within the film. Corresponding author R. Rabady may be reached by e-mail to
[email protected].
REFERENCES 1.
2. 3.
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J. Opt. Soc. Am. B / Vol. 20, No. 10 / October 2003 O. Auciello and A. R. Krauss, In Situ Real-Time Characterization Of Thin Films (Wiley, New York, 2001). C. K. Carniglia, ‘‘Scalar scattering theory for multiplayer optical coatings,’’ Opt. Eng. 18, 104–115 (1979). J. M. Bennett and L. Mattsson, Introduction To Surface Roughness And Scattering 2nd ed. (Optical Society of America, Washington, D.C., 1999). R. W. Wood, ‘‘On a remarkable case of uneven distribution
R. Rabady and I. Avrutsky
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