The out-of-plane thermal conductivity of sputtered tungsten oxide thin films with thickness of 100 to ... accordingly an electrical resistance fluctuation of the metal.
Materials Transactions, Vol. 47, No. 8 (2006) pp. 1894 to 1897 #2006 The Japan Institute of Metals
Thermal Conductivity Measurement of Tungsten Oxide Nanoscale Thin Films Haitao Wang1 , Yibin Xu1 , Masahiro Goto2 , Yoshihisa Tanaka2 , Masayoshi Yamazaki1 , Akira Kasahara2 and Masahiro Tosa2 1 2
Materials Database Station, National Institute for Materials Science, Tokyo 153-0061, Japan Materials Engineering Laboratory, National Institute for Materials Science, Tsukuba 305-0047, Japan
The out-of-plane thermal conductivity of sputtered tungsten oxide thin films with thickness of 100 to 300 nm was measured by two omega method based on a new analytical model with consideration of the interfacial thermal resistance between the films and the substrate. The influence of the tungsten oxide structure on the thermal conductivity was studied. The result reveals that the tungsten oxide thin films made with 10% reactive gas of oxygen had a mixed phase of WO2 and WO3 , while those made with 100% oxygen were WO3 only. The thermal conductivity of WO3 thin films is 1.63 Wm1 K1 , and that of WO2 /WO3 films is 1.28 Wm1 K1 . The difference is explained by a higher thermal resistance at the interface of WO2 and WO3 crystals caused by the mismatch of phonon state. [doi:10.2320/matertrans.47.1894] (Received April 17, 2006; Accepted May 26, 2006; Published August 15, 2006) Keywords: tungsten oxide, thin film, nanoscale, thermal conductivity
1.
Introduction
Tungsten oxide thin films have been extensively researched because of their important applications for electrochromic device,1,2) gas sensor of NO2 , H2 S and NH3 ,3–5) and multi-layer optical disk6) etc. Thermal properties should be considered in these applications where the heat flow exists. However, few studies have been done. Kang7) has studied the thermal properties of the plasma-sprayed tungsten deposits. Tungsten powder was plasma-sprayed onto a graphite substrate in air, where argon gas was used as both the carrier and plasma gas. The tungsten was partially oxidized to tungsten oxide (WO3 ) during the plasma spraying to form a W/WO3 mixture. The thickness of the deposits was 0.8 mm. That paper reveals that the tungsten oxide and the lamellar structure with pores obviously reduce the thermal conductivity of the tungsten deposits. The thermal conductivity of the nano thin films is different from that of the bulk materials, and has strong size dependence. A three omega method has been developed by Cahill et al.8) to measure the thermal conductivity of the dielectric thin films. A stripe-shaped metal film is deposited on the dielectric thin film in order to serve simultaneously as a heater and as a thermometer. An ac electric current of angular frequency ! flows through the metal film and generates periodic Joule heating of frequency 2!, which induces a temperature fluctuation of the metal film surface, and accordingly an electrical resistance fluctuation of the metal film. This further leads to a voltage fluctuation of frequency 3! across the sample. Measuring the voltage fluctuation of frequency 3! can determine the thermal conductivity of the dielectric thin film. But this method has complex sample preparation that uses the lithography technique to deposit the metal film, because it is based on a two dimensional heat conduction model. Kato et al.9) have developed a two omega method to measure the thermal conductivity of the dielectric thin films. This method also deposits a stripe-shaped metal film on the dielectric thin film to serve as heater and thermometer, but uses thermoreflectance technique to measure the temperature fluctuation of the metal film surface, finally determines the thermal conductivity of the dielectric thin film. This method
has simple sample preparation, because it is based on a one dimensional heat conduction model. But the analytical model used by Kato did not consider the thermal resistances at the interface between the metal film and the dielectric thin film, and that between the dielectric thin film and the substrate. In fact, they measured the effective thermal conductivity of the dielectric thin film and the interfaces, and then calculate the thermal conductivity of the film using a series model. In this work, we modified the analytical model of 2! method by taking into account of the above thermal resistances in order to obtain more accurate measurement results of the thermal conductivity of the film. The out-ofplane thermal conductivity of the tungsten oxide thin films was measured by this model. And influence of the tungsten oxide structure on the thermal conductivity was researched. 2.
Theoretical Model
Figure 1 illustrates the heat conduction model of the 2! method. The top layer is a metal film, the second layer is a dielectric thin film which thermal conductivity to be measured, and at the bottom is a substrate. When a heat flow passes through the metal film, an ac temperature gradient along the thickness of the film happens. Supposed that the substrate has an infinite thickness, but both the metal film and the dielectric thin film have finite thicknesses. The one-dimensional thermal conduction equations can be written as
Fig. 1 Sketch map of the modified theoretical model of two omega method.
Thermal Conductivity Measurement of Tungsten Oxide Nanoscale Thin Films
@Tm @2 Tm m ¼q @t @x2 @T f @2 T f ¼0 Cf f @t @x2 @Ts @2 Ts Cs s 2 ¼ 0 @t @x
Cm
x ¼ dm þ 0
ð1Þ
f ð2Þ
@T f 1 ðTm T f Þ ¼ Rm f @x
ð6Þ
x ¼ ðdm þ d f Þ 0 ð3Þ
f
3
Where, T is temperature, q heat per unit volume (Wm ), C heat capacity per unit volume (Jm3 K1 ) and thermal conductivity (Wm1 K1 ), Subscripts m, f and s refer to the metal film, the dielectric thin film and the substrate, respectively. With boundary conditions of x¼0 @Tm ¼0 @x x ¼ dm 0 @Tm 1 m ðTm T f Þ ¼ Rm f @x
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ð4Þ
@T f 1 ¼ ðT f Ts Þ R f s @x
ð7Þ
x ¼ ðdm þ d f Þ þ 0 s
@Ts 1 ðT f Ts Þ ¼ R f s @x
ð8Þ
Where, dm and d f are the thicknesses (m) of the metal film and the dielectric thin film respectively, Rm f is the interfacial thermal resistance between the metal film and the dielectric thin film (m2 KW1 ) and R f s that between the dielectric thin film and the substrate (m2 KW1 ). Solving above equations, we obtained.
ð5Þ
8 " !# 2 > > fkf m km > > ð1 þ iÞ f k f R f s 1 sinh½ð1 þ iÞkm dm 6 > > 6 > s ks fkf > 6 > !# ! > 6 " > > > 6 k k f f f f > > 6 ð1 þ iÞ f k f R f s 1 1þ e2ð1þiÞk f d f ð1 þ iÞ f k f R f s e2ð1þiÞk f d f > > 6 > s ks s ks > 6 < 6 q " !# TðmÞ ¼ 1þ6 f kf m km 6 i!Cm > > 6 ð1 þ iÞ f k f R f s þ 1 þ sinh½ð1 þ iÞkm dm > > 6 s ks fkf > > 6 þ" > !# ! > 6 > > 6 > fkf f kf > 6 2ð1þiÞk d f f > 1þ ð1 þ iÞ f k f R f s 1 e ð1 þ iÞ f k f R f s > 6 > > s ks s ks 4 > > > : ð1 þ iÞm km Rm f sinh½ð1 þ iÞkm dm cosh½ð1 þ iÞkm dm Where, TðmÞ is the temperature of the metal film surface (K), ! is the angular frequency (Hz) and k is the reciprocal pffiffiffiffiffiffi of thermal diffusion length (m1 ), which is equal to !C 2 . When km dm 1, k f d f 1 and Rm f 1, R f s 1, TðmÞ e 4 i fCf df pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ 1 qdm s Cs f 2s Cs ! 1 m Cm dm þ þ Rm f þ R f s ð10Þ 2 s Cs m In experiment TðmÞ and qdm are measured, and from eq. (10), we know that their ratio is proportional to !1=2 . If we plot TðmÞ=qdm versus !1=2 , the intercept In gives the sum of the last four terms of eq. (10), which is linearly relational to the thickness d f of the dielectric thin film. Then we conduct measurements for films with different thicknesses, and plot In versus d f , from the slope of the line, which C is given as ð1 fs Csf Þ 1f by eq. (10), and when the thermal conductivity s and heat capacity Cs of the substrate, and the heat capacity C f of the dielectric thin film are known, the thermal conductivity of the dielectric thin film f can be obtained. Further more, the intercept of In at d f ¼ 0 gives the sum of the interfacial thermal resistances Rm f , R f s and the
31 9 > > > 7 > > 7 > > > 7 > 7 > > > 7 > > 7 > > 7 > > 7 > 7 = 7 7 > ð9Þ 7 > > 7 > > 7 > > 7 > > 7 > > 7 > > 7 > > 5 > > > > ;
term of ð 12 ms CCms Þ dmm , when m , Cs and dm are known, the total interfacial thermal resistance Rm f þ R f s can be obtained. 3.
Experimental
The tungsten oxide thin films were prepared by a magnetron sputtering coating method with a tungsten target of 50 mm’ 5 mm, 99.99% purity. Glass (Corning 1737) 20 mm 10 mm 1 mm was used as substrate, maintaining at room temperature during the deposition. A distance between the substrate and the target is kept at 55 mm. Argon is used as carrier gas and oxygen as reactive gas. The impressed voltage is 100 W. Before the sputtering, the target was pre-sputtered for 15 min to clean the surface from any oxide layers. With different partial pressure ratios of reactive gas oxygen as 10 and 100%, two types of tungsten oxide thin films with the thicknesses of 100, 200 and 300 nm were deposited onto the glass substrates. The crystal structures of the films were analyzed by X-ray diffraction. Transmission spectra were used to analyze optical properties. A stripe-shaped gold film with 12.5 mm in length, 1.7 mm in width and 80 nm in thickness was
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H. Wang et al.
Fig. 2 Sample image of tungsten oxide thin films. (a) 10% oxygen (b) 100% oxygen.
(a)
(b)
Fig. 5 TðmÞ=qdm vs !1=2 plot for 100 nm tungsten oxide thin films of 10% oxygen. Fig. 3 Transmission spectrum of tungsten oxide thin films. (a) 10% oxygen (b) 100% oxygen.
Table 1 Thermophysical properties of substrate and films used in calculation.
Glass substrate (Corning 1737)
deposited on each of the tungsten oxide thin films by sputtering to serve as a heater in thermal conductivity measurement. The thermal conductivity was measured using a ULVAC-RIKO TCN-2!. The measurement was done at room temperature in a vacuum less than 2 102 Pa. An ac sinusoidal signal of 2.25 W power was applied across the gold film to supply heating. The ac frequency changed from 500 to 4000 Hz. The temperature at the surface of the gold film was measured by thermoreflactance method with a HeNe laser. 4.
Results and Discussion
The images of tungsten oxide thin films were shown in Fig. 2. The film of 10% oxygen shows dust color, and that of 100% oxygen shows transparent. As shown in Fig. 3, the film of 10% oxygen has almost no transmittance, and that of 100% oxygen has high transmittance in the range of visible light. Figure 4 shows the X-ray diffraction pattern of tungsten
Heat capacity, 106 Jm3 K1
2.46
1.22
WO3
—
2.2811Þ
Mixture phase of WO2 and WO3
—
2.54
Gold films (80 nm)
Fig. 4 X-ray diffraction pattern of tungsten oxide thin films of 10% oxygen and 100% oxygen.
Thermal conductivity, Wm1 K1
1789Þ
2.4911Þ
oxide thin films of 10% oxygen and 100% oxygen. The film of 10% oxygen shows two peaks at 2 ¼ 23 and 53 respectively, while the film of 100% oxygen shows a single broad peak at 23 . The peak of 53 belongs to trigonal WO2 (232), and the 23 peak probably belong to monoclinic WO3 (020) or trigonal WO2 (111). Considering that in 100% oxygen gas, the tungsten can be easily oxidized to a stable phase of tungsten oxide, and we thus think that the crystal structure of the film is monoclinic WO3 ; while, with 10% oxygen gas, the oxidation reaction is incomplete, therefore the film has a mixture phase of WO2 and WO3 . Using the Scherrer equation,10) from the width of the X-ray diffraction peaks the particle size of the film was estimated to be several nanometers. Figure 5 shows the plot of TðmÞ=qdm versus !1=2 for 100 nm tungsten oxide thin films of 10% oxygen. The values of the heat capacity and thermal conductivity used in calculation were listed in Table 1. The plot shows good linear relation in the frequency range from 500 to 4000 Hz. The measurements on the other samples exhibited similar results, which are not shown here. The measurement repeatability is less than 2%. The relation between In which is defined as In ð 12 m Cm dm s Cs Þ m and the thickness of the tungsten oxide thin films was shown in Fig. 6 with a linear fitting. The thermal conductivity of the tungsten oxide thin films was obtained from the slope of the lines. The parameters used to calculate the thermal conductivity were listed in Table 1. The heat capacity of mixture phase of WO2 and WO3 was calculated from the heat
Thermal Conductivity Measurement of Tungsten Oxide Nanoscale Thin Films
5.
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Conclusions
A new analytical model of measuring thermal conductivity of thin film with 2! method has been built with consideration of the interfacial thermal resistances among the films and the substrate. The new model was used to measure the out-ofplane thermal conductivity of the tungsten oxide nanoscale thin films. The thin films show a lower thermal conductivity than the bulks, and the thermal conductivity of films with a mixture phase of WO2 and WO3 is even lower than that of WO3 only. Acknowledgements
Fig. 6 In vs d f plot for tungsten oxide thin films on glass substrate.
capacities of WO2 12) and WO3 11) using the law of mixture and assuming the volume fraction of every phase was 50%. The obtained thermal conductivity of the tungsten oxide thin film of 10% oxygen is 1.28 Wm1 K1 , and that of 100% oxygen is 1.63 Wm1 K1 . The intercept of the lines gives the total interfacial thermal resistance of Rm f þ R f s , which is nearly 31 m2 KW1 for both 10% and 100% oxygen films. The films of 10% oxygen have a lower thermal conductivity than those of 100% oxygen. It can be explained by the mismatch of phonon state between the WO2 and WO3 phases. When a phonon with vibration frequency !1 incidents at the crystal boundary, it may transmit into the other side only when the same phonon frequency exists in the other side, otherwise it will be reflected or scattered back. If the crystal structures of the two sides are same, i.e. the phonon states are same, all phonons have a possibility to transmit the boundary; however, if the crystal structures are different, phonons with some frequencies are not allowed to go to the other side because of the mismatch of the frequency, therefore causes a lower thermal conductance at the boundary.
The authors would like to thank Prof. Hatta of Fukui University of Technology and Dr. Kato of ULVAC-RIKO Inc. for their kind advices in theoretical deducing. This study was financially supported by the Budget for Nuclear Research of the Ministry of Education, Culture, Sports, Science and Technology, based on the screening and counseling by the Atomic Energy Commission. REFERENCES 1) P. V. Ashrit, G. Bader and Vo-Van Truong: Thin Solid Films 320 (1998) 324–328. 2) O. Bohnke, C. Bohnke, A. Donnadieu and D. Davazoglou: J. Appl. Electrochem. 18 (1998) 447–452. 3) C. Cantaalini, H. T. Sun, M. Faccio, M. Pelino, S. Santucci, L. Lozzi and M. Passacantando: Sensors Actuators B 31 (1996) 81–87. 4) A. Agrawal and H. Habibi: Thin Solid Films 169 (1989) 257–270. 5) H. Meixner, J. Gerblinger, U. Lampe and M. Fleischer: Sensors Actuators B 23 (1995) 119–125. 6) K. Kojima and M. Terao: Jpn. J. Appl. Phys. 43 (2004) 7058–7064. 7) H. K. Kang: Journal of Nuclear Materials 335 (2004) 1–4. 8) D. G. Cahill: J. Vac. Sci. Technol. A 7 (1989) 1259–1266. 9) R. Kato and I. Hatta: Int. J. Thermophys. 179 (2005) 179–190. 10) M. Chakrabarti, S. Dutta, S. Chattapadhyay, A. Sarkar, D. Sanyal and A. Chakrabarti: Nanotechnology 15 (2004) 1792–1796. 11) Japan Society of Thermophysical Properties, Thermophysical Properties Handbook (Yokendo, Tokyo, 1990). 12) Engineering Chemistry, CAS Scientific Database, www.sdb.ac.cn, CAS Number: 12036-22-5.
