Interfacial thermal resistance of Au/SiO 2 produced by sputtering method

High Temperatures-High Pressures, Vol. 37, pp. 31 39 Reprints available directly from the publisher Photocopying permitted by license only 2008 Old City Publishing, Inc. Published by license under the OCP Science imprint, a member of the Old City Publishing Group Interfacial thermal resistance of Au/SiO 2 produced by sputtering method Yibin Xu 1,, Masahiro Goto 2, Yoshihisa Tanaka 3, Miyoko Tanaka 4, Masato Shimono 5 and Masayoshi Yamazaki 1 1 Materials Database Station, National Institute for Materials Science, Tokyo 1530061, Japan 2 Materials Reliability Center, National Institute for Materials Science, Tsukuba 3050047, Japan 3 Composites and Coatings Center, National Institute for Materials Science, Tsukuba 3050047, Japan 4 High Voltage Electron Microscopy Station, National Institute for Materials Science, Tsukuba 3050047, Japan 5 Computational Materials Science Center, National Institute for Materials Science, Tsukuba 3050047, Japan Received: September 14, 2007. Revised: November 9, 2007. In Final Form: November 29, 2007. Interfacial thermal resistance between sputtered Au films and SiO 2 single crystal substrates produced under different sputtering conditions has been measured by 2 omega method, and compared with the calculation results of phonon acoustic mismatch model and phonon diffusion mismatch model. The interfacial thermal resistance shows strong dependence on the sputtering condition: increases with increasing of RF power, and decreases when heating the substrates above 200 C. The minimum interfacial thermal resistance obtained by the present experiment exhibits good agreement with the theoretical prediction. Keywords: Interfacial thermal resistance, Au/SiO 2 interface, 2ω method, thin film, sputter, acoustic mismatch model, diffusion mismatch model. 1 INTRODUCTION Interfacial thermal resistance is an indispensable parameter for the purpose of thermal design of electronic devices and prediction of the effective thermal conductivity of composite materials. To evaluate the interfacial thermal Corresponding author: E-mail: xu.yibin@nims.go.jp Paper presented at the 8 th Asian Thermophysical Properties Conference, August 21 24, 2007, Fukuoka, Japan. 31

32 Yibin Xu et al. resistance, two famous phonon models, acoustic mismatch model (AMM) and diffusion mismatch model (DMM) have been established on the basis of mechanisms of phonon reflection and diffuse scattering at the interface, respectively. As the materials are isotropic Debye solids, according to Swartz and Pohl [1], the interfacial thermal resistance can be written as: R = 1 π/2 c i,j 2 j 0 ω Debye i 0 α i,j (θ, ω) cos θ sin θdθ dn i,j (ω, T ) ω 2 dω dt (1) Where, c i,j is the phonon propagation velocity in side i for phonons with mode j; θ is the angle between the wave vector or the incident phonon and the normal to the interface; and ω is the phonon frequency. α i,j (θ, ω) is the transmission probability of phonons from side i, with mode j (longitudinal or transverse), and with a given energy ω; and N i,j (ω, T ) is the density of phonons with energy ω on side i with mode j at temperature T. For frequencies below the Debye cutoff frequencies ω Debye i, ω 2 N i,j (ω, T ) = 2π 2 ci,j 3 [exp( ω/k BT) 1] (2) In the acoustic mismatch model, phonons are treated as plane waves. When a wave is incident on the interface from side i = 1 with angle θ 0, the transmission probability for each mode is [2]: α 1,l (θ 0 ) = α 1,t1 (θ 0 ) = α 1,t2 (θ 0 ) = A 2 2l ρ 2 A 0l A 2l A 0t1 + cos θ 0 + cos θ 0 ρ 1 c 1l c 2l cos θ 2l 2 ρ 2 ρ 1 c 1t c 2l cos θ 2l A 2 2t1 ρ 2 A 0l A 2 2t1 ρ 2 A 0t1 ρ 1 c 1l c 2t cos θ 2t cos θ 0 (3) ρ 1 c 1t c 2t cos θ 2t cos θ 0 (4) 4u (1 + u) 2 (5) Where, j = l for longitudinal wave; j = t 1 for transverse wave with displacement vector in the plane of incidence; j = t 2 for a transverse wave with displacement vector perpendicular to the plane of incidence, and u = ρ 2 ρ 1 sin 2θ 2t sin 2θ 0. Here, ρ 1 and ρ 2 refer to the densities of side 1 and 2, A 0j is the amplitude of the incident wave with mode j, and A 2j is the amplitude of the transmitted mode j. θ 2j is the transmission angle of mode j. Finally, the incidence angle and transmission angles are related by the Snell s Law.

Au/SiO 2 Thermal Resistance 33 In the diffusion mismatch model, all phonons are assumed to be diffusely scattered at the interface. α i,j (ω) = j c 2 3 i,j i,j c 2 i,j (6) However some mismatches between the experimental data and the theoretical prediction at room temperature have been reported [1,3 5], and the influences of contamination [3] and roughness [4] on the interfacial thermal resistance have been observed. In our previous work [6], we measured the interfacial thermal resistances of Au/SiO 2 and Au/sapphire, however the data obtained with samples produced by different coating experiments showed large fluctuation, which implies strong influence of coating conditions on the interfacial thermal resistance. In this study, by using a new combinatorial sputtering equipment, we try to improve the preciseness of control of the coating experimental parameters and the reproducibility of samples, in order to investigate the dependency of the interfacial thermal resistance upon the coating conditions. 2 EXPERIMENTAL PROCEDURE 2.1 Sample preparation Au films were coated on SiO 2 substrates with a home-made combinatorial sputtering system [7,8]. Up to 14 substrates can be set at once on the sample stage and coated one by one continuously. For each sample, the sputtering parameters can be changed independently, while the other conditions, for example, the atmosphere inside the chamber can keep same for all samples. SiO 2 (quartz) single crystals 20 mm in length, 10 mm in width and 1 mm in thickness with two different cut directions were used as substrates. Before sputtering, the substrates were cleaned by supersonic cleaning in acetone for 15 minutes. The purity of Au target was 99.99%. Before deposition, the chamber was evacuated to 5 10 5 Pa. Ar with a purity of 99.999%, was used as sputtering gas, and the sputtering pressure was 0.4 Pa. The thickness of Au films was controlled to be 200 nm by adjusting the time of sputtering. The temperature of substrate and the RF power were changed as furnished in Table 1. Samples were sputtered under 6 different experimental conditions, and for each condition, 2 samples were produced, in order to confirm the reproducibility of experiments. 2.2 Observation of interfacial structure The structure of Au/SiO 2 interface was observed by a transmission electron electronic microscope JEM-2100F operated at acceleration voltage of 200 kv. The sample was processed using a JEM-9310FIB focused ion beam system.

34 Yibin Xu et al. Substrate Sputtering conditions Crystal Surface Substrate RF power No. orientation roughness temperature ( C) (W) 1 z-cut <1 nm 500 20 2 z-cut <1 nm 200 100 3 z-cut <1 nm 200 150 4 z-cut <1 nm 500 200 5 z-cut <1 nm 25 100 6 x-cut <1 nm 200 100 TABLE 1 Experimental conditions used to prepare the samples. FIGURE 1 Two-layered system in interfacial thermal resistance measurement by 2ω method. 2.3 Measurement of interfacial thermal resistance The interfacial thermal resistance was measured by 2ω method developed in our previous work [6] using a technique involving periodic Joule (ohmic) heating and thermo-reflectance. Comparing with the optical pulse heating and thermo-reflectance technique used by Cahill [9] and Shigesato [10], this method is featured by its simplicity in measurement principle and ease of technique. The specimen includes two layers as shown in Figure 1 and there are (i) a dielectric substrate with thermal conductivity λ s and heat capacity per unit volume C s, (ii) a metal film with thickness d m, thermal conductivity λ m and heat capacity per unit volume C m. The interfacial thermal resistance between the film and the substrate is noted as R. An alternating current q is supplied to the metal film, and the temperature at the film surface is measured by a thermo-reflectance method to be T(0). The heat conduction in the system can be treated as one-dimensional, and by solving the heat conduction equation T(0) can be obtained as T(0) = q iωc m 1 1 [ ] (1 + i)λ m k m R + λ mk m λ s k s sinh [(1 + i)k m d m ]+cosh [(1 + i)k m d m ] (7)

Au/SiO 2 Thermal Resistance 35 where ωc m ωc s k m = and k s =. 2λ m 2λ s ω is the frequency of the heating current. When the condition k m d m 1is satisfied by adjusting ω and d m,weget T(0) qd m e i π ( 4 ω 1 1 2 + R + λs C s 2 λ mc m λ s C s ) dm λ m. (8) The first term on the right-hand side of Equation (8) is proportional to ω 1/2 and the second and third terms are independent on it. The plot of T(0)/qd m vs. ω 1/2 gives a straight line with a intercept equaling to the sum of the second and third terms. If the thickness of the metal film, the specific heat and thermal conductivity of the metal film and substrate are known, the second term R can be obtained. The measurement was done with a ULVAC-RIKO TCN-2ω apparatus at room temperature in a vacuum less than 2 10 2 Pa. The frequency of heating currents was changed to 500, 1000, 2000 and 4000 Hz, and the power was kept 2.25 W. For each sample, the interfacial thermal resistance was measured at two or three different locations. The heat capacities and thermal conductivities of Au films and SiO 2 substrates used to determine the interfacial thermal resistances were listed in Table 2 [11 13]. 2.4 Calculation of interfacial thermal resistance The interfacial thermal resistance between Au and SiO 2 was calculated using Equations (1) to (6), with the sound velocities and densities of Au and SiO 2 shown in Table 2. 3 RESULTS AND DISCUSSION The TEM images of Au/SiO 2 interface observed in the sample deposited with RF power of 100 W and substrate temperature of 200 C were shown in Thermal Heat conductivity, capacity, Sound velocity Density (Wm 1 K 1 ) (10 6 Jm 3 K 1 ) c t (m/s) c l (m/s) (Mgm 3 ) Au film 178 [11] 2.49 [12] 1290 [1] 3390 [1] 2.65 [13] SiO 2 z-cut 10.4 [12] 1.98 [12] 4660 [13] 6310 [13] 19.32 [13] x-cut 6.21 [12] 1.98 [12] TABLE 2 Thermal conductivity, heat capacity, and phonon propagation velocity of Au and SiO 2 used in calculation.

36 Yibin Xu et al. FIGURE 2 TEM images of Au/SiO 2 interface. Interfacial thermal resistance (m 2 KW -1 ) 5.0x10-8 4.0x10-8 3.0x10-8 2.0x10-8 1.0x10-8 0.0 0 20 40 deposite at 25 C x _ cut SiO 2 experimental data calculated using AMM model calculated using DMM model 60 80 100 120 140 160 180 200 220 RF Power (W) FIGURE 3 Interfacial thermal resistance of Au/SiO 2 measured with different samples and calculated using acoustic mismatch model and diffusion mismatch model. Figure 2. As the single crystalline SiO 2 substrate has transitioned to amorphous during the FIB processing unfortunately, only the fine structure of Au can be observed. Figure 2(a) shows that the Au film is polycrystalline including grains with different crystalline orientations, and the Au/SiO 2 interface is nearly a flat plane. In Figure 2(b), we can observe more clearly the crystallization of Au on the surface of SiO 2. The measurement and calculation results of interfacial thermal resistance were shown in Figure 3. The measured interfacial thermal resistance dispersed in a range from 1.8 10 8 to 6.2 10 8 m 2 KW 1. In Figure 3, except the

Au/SiO 2 Thermal Resistance 37 conditions indicated in the graph, all samples are deposited on z-cut substrates heated to above 200 C. Here we do not distinguish the temperature of substrate higher than 200 C, because when raising the temperature of substrate from 200 Cto500 C, we did not observed significant changes in the interfacial thermal resistance. In Figure 3, the interfacial thermal resistance shows an increasing trend with the increase of RF power, while the uncertainty of data becomes large due to the deviation of data measured at different locations. The sample deposited at room temperature has an interfacial thermal resistance twice that of the sample deposited at 200 C. The interfacial thermal resistances of the samples with x-cut substrate is similar to that of with z-cut substrate, difference the in crystalline direction of SiO 2 did not result in obvious difference in the interfacial thermal resistance. The thermal resistance of the Au films in our experiments was in a grade of 10 9 m 2 KW 1, therefore, although the thermal conductivity of Au films probably changed also for different coating conditions, it would not be possible to affect the results so much. The difference observed should be due to the change in interfacial thermal resistance. The calculated value of Au/SiO 2 interfacial thermal resistance is 2.08 10 8 m 2 KW 1 using phonon acoustic mismatch model and 1.48 10 8 m 2 KW 1 using phonon diffusion mismatch model. The two lowest experimental interfacial thermal resistances 1.8 10 8 m 2 KW 1 and 2.33 10 8 m 2 KW 1 obtained with RF power of 20 W and substrate temperature of 500 C, and RF power of 100 W and substrate temperature of 200 C respectively, are reasonably agreed with the theoretical predictions; nevertheless the data measured with sample sputtered with higher RF power or at room temperature are higher. Stoner et al. [3] reported an increase in interfacial thermal resistance resulting from contamination at the Au/sapphire interface. In this work, the decrease in Au/SiO 2 interfacial thermal resistance with the increase of substance temperature is probably due to the same effect. At room temperature, the contamination like water and organic substance may resident on the surface of substrates; by heating the substrates to above 200 C, the contamination can be removed and a cleaner interface can be obtained. The reason of interfacial thermal resistance increasing with enhancement of RF power is still not clear. Since quartz single crystal has been known to be instable and have an inclination to transformation to amorphous phase under pressure [14], we might suppose such a possibility that a very thin layer of SiO 2 single crystal at the surface of substrate has transformed to amorphous silica during the sputtering process by argon ion bombardment, and the thickness of the glassy layer will increase with the increase of sputtering power. In this case, the interfacial thermal resistance comes from three aspects: the Au/amorphous-silica interface, the amorphous silica layer and the amorphoussilca/sio 2 -single-crystal interface. We can use the phonon diffusion mismatch model to estimate the thermal resistance of the two interfaces. Using density of 2.2 Mgm 3, longitudinal sound velocity of 5968 m/s and transverse sound

38 Yibin Xu et al. velocity of 3764 m/s for amorphous silica [15], the thermal resistance for both of the two interfaces can be calculated 1.06 10 8 m 2 KW 1 and 1.02 10 9 m 2 KW 1, respectively. Using 1.38 WK 1 m 1 [10] as the thermal conductivity of amorphous silica, we can derive the thickness of the amorphous silica layer to be about 5, 10, 15 and 20 nm for RF power of 20, 100, 150 and 200 W respectively, according to the measurement results as shown in Figure 3. 4 CONCLUSION One of the difficulties to determine interfacial thermal resistance is that the interfacial thermal resistance is a subject to change depending on the manufacturing method and conditions. In this work, we proved such dependence. The experimental results of Au/SiO 2 interfacial thermal resistance show a strong dependence on sputtering conditions, and have very high probability to be higher than the theoretical values predicted by phonon acoustic mismatch model and diffusion mismatch model. There are many considerable factors which may result in the extra thermal resistance, such as impurity, roughness, a glassy layer, etc. so, further study is necessary to prove these suppositions. ACKNOWLEDGMENTS A part of this work was financially supported by the Budget for Nuclear Research of the Ministry of Education, Culture, Sports, Science and Technology, based on screening and counseling by the Atomic Energy Commission. And a part of this study was supported by Industrial Technology Research Grant Program in 2006 from New Energy and Industrial Technology Development Organization (NEDO) of Japan. REFERENCES [1] Swartz E. T. and Pohl R. O. Rev. Mod. Phys. 61 (1989), 605. [2] Cheeke J. D. N., Ettinger H. and Hebral B. Can. J. Phys. 54 (1976), 1749. [3] Stoner R. J. and Maris H. J. Phys. Rev. B. 48 (1993), 16373. [4] Swartz E. T. and Pohl R. O. Appl. Phys. Lett. 51 (1987), 2200. [5] Cahill D. G., Gord W. K., Goodson K. E., Mahan G. D., Majumdar A., Maris H. J., Merlin R. and Phillpot S. R. J. Appl. Phys. 93 (2003), 793. [6] Xu Y., Wang H., Tanaka Y., Shimono M. and Yamazaki M. Mater Trans. 48 (2007), 148. [7] Goto M., Kasahara A. and Tosa M. Appl. Surf. Sci. 252 (2006), 2482. [8] Goto M., Kasahara A. and Tosa M. Vacuum. 80 (2006), 740. [9] Cahill D. Rev. Sci. Instrum. 75 (2004), 5119. [10] Aoyama H., Yagi T., Taketoshi N., Baba T., Miyamura A., Sato Y. and Shigesato Y. Proceedings of the Asian Thermophysical Properties Conference. 21 24 August, 2007, Fukuoka, Japan. Paper No. 116.

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