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Interfacial thermal resistance of Au/SiO
produced by sputtering method
Yibin Xu1,∗, Masahiro Goto2, Yoshihisa Tanaka3, Miyoko Tanaka4, Masato Shimono5and Masayoshi Yamazaki1
1Materials Database Station, National Institute for Materials Science, Tokyo 1530061, Japan 2Materials Reliability Center, National Institute for Materials Science, Tsukuba 3050047, Japan 3Composites and Coatings Center, National Institute for Materials Science, Tsukuba 3050047, Japan
4High Voltage Electron Microscopy Station, National Institute for Materials Science, Tsukuba 3050047, Japan
5Computational 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 SiO2single
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 sput-tering condition: increases with increasing of RF power, and decreases when heating the substrates above 200◦C. The minimum interfacial ther-mal resistance obtained by the present experiment exhibits good agreement with the theoretical prediction.
Keywords: Interfacial thermal resistance, Au/SiO2interface, 2ωmethod, thin film, sputter, acoustic mismatch model, diffusion mismatch model.
Interfacial thermal resistance is an indispensable parameter for the purpose of thermal design of electronic devices and prediction of the effective ther-mal conductivity of composite materials. To evaluate the interfacial therther-mal
∗Corresponding author: E-mail: firstname.lastname@example.org
†Paper presented at the 8thAsian Thermophysical Properties Conference, August 21–24, 2007, Fukuoka, Japan.
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 , the interfacial thermal resistance can be written as:
R= 1 2 j ci,j π/2 0 ωDebye i 0
dNi,j(ω, T )
(1) Where,ci,jis the phonon propagation velocity in sideifor phonons with mode j;θis the angle between the wave vector or the incident phonon and the normal to the interface; andωis the phonon frequency.αi,j(θ, ω)is the transmission
probability of phonons from sidei, with modej (longitudinal or transverse), and with a given energyω; andNi,j(ω, T )is the density of phonons with
energyωon sideiwith modej at temperatureT. For frequencies below the Debye cutoff frequenciesωDebyei ,
Ni,j(ω, T )= ω
In the acoustic mismatch model, phonons are treated as plane waves. When a wave is incident on the interface from sidei=1 with angleθ0, the transmission
probability for each mode is :
α1,l(θ0)= A2l A0l 2ρ2 ρ1 c1l c2l cosθ2l cosθ0 + A2t1 A0l 2ρ2 ρ1 c1l c2t cosθ2t cosθ0 (3) α1,t1(θ0)= A2l A0t1 2ρ2 ρ1 c1t c2l cosθ2l cosθ0 +A2t1 A0t1 2ρ2 ρ1 c1t c2t cosθ2t cosθ0 (4) α1,t2(θ0)= 4u (1+u)2 (5)
Where,j = l for longitudinal wave; j = t1for transverse wave with
dis-placement vector in the plane of incidence;j =t2for a transverse wave with
displacement vector perpendicular to the plane of incidence, and
Here,ρ1andρ2refer to the densities of side 1 and 2,A0j is the amplitude of
the incident wave with modej, andA2j is the amplitude of the transmitted
modej.θ2jis the transmission angle of modej. Finally, the incidence angle
In the diffusion mismatch model, all phonons are assumed to be diffusely scattered at the interface.
αi,j(ω)= jc− 2 3−i,j i,jc− 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  and roughness  on the interfacial thermal resistance have been observed. In our previous work , we measured the interfacial thermal resistances of Au/SiO2and Au/sapphire, however the data obtained
with samples produced by different coating experiments showed large fluctu-ation, 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 SiO2substrates with a home-made combinatorial
sput-tering 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 parame-ters can be changed independently, while the other conditions, for example, the atmosphere inside the chamber can keep same for all samples. SiO2(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 5×10−5Pa. 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/SiO2 interface was observed by a transmission
elec-tron elecelec-tronic microscope JEM-2100F operated at acceleration voltage of 200 kV. The sample was processed using a JEM-9310FIB focused ion beam system.
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.
Two-layered system in interfacial thermal resistance measurement by 2ωmethod.
2.3 Measurement of interfacial thermal resistance
The interfacial thermal resistance was measured by 2ωmethod developed in our previous work  using a technique involving periodic Joule (ohmic) heating and thermo-reflectance. Comparing with the optical pulse heating and thermo-reflectance technique used by Cahill  and Shigesato , 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 conductivityλs and heat capacity per unit
volumeCs, (ii) a metal film with thicknessdm, thermal conductivityλmand
heat capacity per unit volumeCm. The interfacial thermal resistance between
the film and the substrate is noted asR. An alternating currentq is supplied to the metal film, and the temperature at the film surface is measured by a thermo-reflectance method to beT (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 iωCm 1− 1
(1+i)λmkmR+λλmskkms sinh[(1+i)kmdm] +cosh[(1+i)kmdm]
where km= ωCm 2λm and ks = ωCs 2λs .
ωis the frequency of the heating current. When the conditionkmdm 1 is
satisfied by adjustingωanddm, we get
T (0) qdm ≈ e−iπ4 √ λsCs ω−12 +R+ 1 2 − λmCm λsCs dm λm. (8)
The first term on the right-hand side of Equation (8) is proportional toω−1/2
and the second and third terms are independent on it. The plot ofT (0)/qdmvs.
ω−1/2gives 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 termRcan be obtained.
The measurement was done with a ULVAC-RIKO TCN-2ωapparatus at room temperature in a vacuum less than 2×10−2Pa. 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 SiO2 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 SiO2was calculated using
Equations (1) to (6), with the sound velocities and densities of Au and SiO2
shown in Table 2.
3 RESULTS AND DISCUSSION
The TEM images of Au/SiO2 interface observed in the sample deposited
with RF power of 100 W and substrate temperature of 200◦C were shown in
conductivity, capacity, Sound velocity Density (Wm−1K−1) (106Jm−3K−1) ct (m/s) cl(m/s) (Mgm−3)
Au film 178  2.49  1290  3390  2.65  SiO2 z-cut 10.4  1.98  4660  6310  19.32 
x-cut 6.21  1.98 
Thermal conductivity, heat capacity, and phonon propagation velocity of Au and SiO2
TEM images of Au/SiO2interface.
Interf acial ther mal resistance (m 2KW -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 60 80 100 120 140 160 180 RF Power (W) 200 220 experimental data calculated using AMM model calculated using DMM model
Interfacial thermal resistance of Au/SiO2measured with different samples and calculated using acoustic mismatch model and diffusion mismatch model.
Figure 2. As the single crystalline SiO2substrate 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/SiO2interface is nearly a
flat plane. In Figure 2(b), we can observe more clearly the crystallization of Au on the surface of SiO2.
The measurement and calculation results of interfacial thermal resistance were shown in Figure 3. The measured interfacial thermal resistance dispersed in a range from 1.8×10−8to 6.2×10−8m2KW−1. In Figure 3, except the
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 sub-strate higher than 200◦C, because when raising the temperature of substrate from 200◦C to 500◦C, we did not observed significant changes in the interfa-cial thermal resistance. In Figure 3, the interfainterfa-cial 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, dif-ference the in crystalline direction of SiO2did 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 10−9m2KW−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/SiO2 interfacial thermal resistance is
2.08×10−8m2KW−1 using phonon acoustic mismatch model and 1.48× 10−8m2KW−1 using phonon diffusion mismatch model. The two lowest experimental interfacial thermal resistances 1.8×10−8m2KW−1and 2.33× 10−8m2KW−1obtained with RF power of 20 W and substrate temperature of 500◦C, and RF power of 100 W and substrate temperature of 200◦C respec-tively, 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.  reported an increase in interfacial thermal resistance resulting from contamination at the Au/sapphire interface. In this work, the decrease in Au/SiO2 interfacial thermal resistance with the increase of
sub-stance temperature is probably due to the same effect. At room temperature, the contamination like water and organic substance may resident on the sur-face 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 , we might suppose such a possibility that a very thin layer of SiO2single crystal at the surface of substrate has transformed to amorphous
silica during the sputtering process by argon ion bombardment, and the thick-ness 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/silica interface, the amorphous silica layer and the amorphous-silca/SiO2-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
velocity of 3764 m/s for amorphous silica , the thermal resistance for both of the two interfaces can be calculated 1.06× 10−8m2KW−1 and 1.02×10−9m2KW−1, respectively. Using 1.38 WK−1m−1 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.
One of the difficulties to determine interfacial thermal resistance is that the interfacial thermal resistance is a subject to change depending on the manu-facturing method and conditions. In this work, we proved such dependence. The experimental results of Au/SiO2 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.
A part of this work was financially supported by the Budget for Nuclear Research of the Ministry of Education, Culture, Sports, Science and Technol-ogy, 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 Devel-opment Organization (NEDO) of Japan.
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