2010 Black Engineering Building, Department of Mechanical Engineering. Iowa State University, Ames, IA, 50011

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1 Interface Energy Couplng between -tungsten Nanoflm and Few-layered Graphene Meng Han a, Pengyu Yuan a, Jng Lu a, Shuyao S b, Xaolong Zhao b, Yanan Yue c, Xnwe Wang a,*, Xangheng Xao b,* a 2010 Black Engneerng Buldng, Department of Mechancal Engneerng Iowa State Unversty, Ames, IA, b Department of Physcs and Key Laboratory of Artfcal Mcro- and Nano-structures of Mnstry of Educaton, Hube Nuclear Sold Physcs Key Laboratory and Center for Ion Beam Applcaton, Wuhan Unversty, Wuhan , P. R. Chna c School of Power and Mechancal Engneerng, Wuhan Unversty, Wuhan, Hube , P. R. Chna * Correspondng authors. XW: xwang3@astate.edu; XX: xxh@whu.edu.cn 1

2 S1. Structure nformaton of the samples prepared and measured n the present work Table 1. Index and geometres of all samples Sngle W flm thckness n the multlayered sample 15 nm 30 nm 40 nm Multlayered W/Graphene flm Multlayered W flm and the layer number Sngle-layered W flm and the thckness A1: 3[W+G]+W a1 (4) Aa1 (74 nm) A2: 5 [W+G]+W a2 (6) Aa2 (110 nm) A3: 7 [W+G]+W a3 (8) Aa3 (138 nm) B1: 3 [W+G]+W b1 (4) Bb1 (128 nm) B2: 5 [W+G]+W b2 (6) Bb2 (190 nm) B3: 7 [W+G]+W b3 (8) Bb3 (247 nm) D1: 3 [W+G]+W d1 (4) Dd1 (167 nm) D2: 5 [W+G]+W d2 (6) Dd2 (252 nm) D3: 7 [W+G]+W d3 (8) Dd3 (344 nm) 7[W+G] means 7 cycles of tungsten+graphene layer. 2

3 S2. Experment setup and the physcal model The noncontact PT technque 1-3 s used to characterze the thermal transport propertes of a multlayer structure n the cross-plane drecton. A modulated laser beam s used to rradate the flm surface whch serves as a heat source and leads to a perodcal temperature varaton at the flm surface. Ths temperature varaton s strongly affected by the thermal conducton of the sample and s sensed by detectng the surface thermal radaton. As the thermal radaton s from the sample surface, we beleve the detecton can accurately reflect the real temperature varatons of the sample surface. The phase shft of radaton to the laser beam s used to characterze the nterface energy couplng propertes of the samples. Fgure 1 (a) shows the expermental setup and how t s operated. A contnuous nfrared laser s modulated by a functon generator and then s drected and focused on the sample. The sample s heated to dfferent temperatures by the laser beam under dfferent modulaton frequences. In ths experment, the modulated laser beam s 600 mw, whch assures suffcently hgh radaton sgnal from the surface whle prevents hgh temperature rse that may damage the sample or sgnfcantly change the sample s thermophyscal propertes. The laser beam has a Gaussan dstrbuton n space and the spot sze s mm n our experment. As the dmenson of the laser spot s much larger than the thermal dffuson length n the lateral drecton of the sample, the Gaussan dstrbuton has neglgble nfluence on the measured phase shft sgnal. The thermal radaton sgnal s drected to an nfrared detector whch has a Ge wndow n front to flter out the reflecton sgnal of the laser beam and only allows the thermal radaton sgnal to pass. The radaton sgnals are then pre-amplfed and measured by a lock-n amplfer and the phase shft wthn a large laser frequency range s obtaned for further data processng. 3

4 In ths experment, the modulaton frequences of the laser beam range from 600 Hz to 20 khz, under whch the thermal dffuson depth wthn one perod heatng s much smaller than the dmensons of the heatng spot. Thus, the thermal transport process nduced by the laser beam can be smplfed to a one-dmensonal cross-plane heat transfer model. Fgure 1 (b) shows the cross-sectonal vew of the one-dmensonal multlayer model. Layers from 1 to N are the sample layers between the substrate (layer 0) and the ar (layer N+1). The governng equaton for a multlayer one-dmensonal thermal conducton problem n layer can be expressed as 4 : 2 N 1 I0 2 m m x t 2k m 1 exp L e 1e. (1) xl jt Here L l l 1 s the thckness of layer. Other thermophyscal propertes of layer are thermal conductvty k, specfc heat c p, and optcal absorpton coeffcent β. T Tamb s the temperature rse of layer whle T amb s the ambent temperature. ω s the angular frequency (2πf). The soluton to equaton 1 conssts of a transent component θ,t, a steady DC component s, and a steady AC component s,. In ths experment, only the steady AC component s, s measured. The general soluton to ths part follow the below form 4 : xl xl xl jt e e e e s, In the above equaton, E 2 2 G G 2 N NI0 kn, and GN 1 0. s defned as. (2) wth I0 N G exp m 1 ml m 1 j a for N 2k wth j 1., The coeffcent and can be determned by usng the nterfacal condtons at x l as: 1 E U V 1 E 1, (3) 4

5 where U s the nterfacal transmsson matrx of heat and V s the absorpton matrx of lght from layer 1to and they can be expressed as: U 1 u11, u12, 1 v11, v12, ; V 2 u21, u 22, 2 v21, v. (4) 22, u1 n, 1k 1 1 k k 1 1 R, 1 exp 1 l 1l, n1,2, (5a) u2 n, 1 k 1 1 k k 1 1 R, 1 exp 1 l 1l, n1,2, (5b) n1, 1, n 1,2, (5c) and vn2, 1 k 1 1 k k 1 1 R, 1 exp 1 l 1l, n1,2. (5d) R,+1 s the thermal contact resstance between layer and +1. Detals of the parameters are provded n Ref. 4. From the above soluton, the phase shft between thermal radaton of the sample surface and the rradatng laser beam can be derved. Then the least square method s used to determne unknown thermophyscal propertes of the sample. Notce that, the optcal absorpton depth (τ opt ) s a key parameter n the PT measurement and the fttng process. In ths work, τ opt s taken as 22.8 nm for the β-w flms. Ths value s larger than the thckness of top layers of several samples. The second or thrd layers may absorb laser energy. Ths has also been taken nto full consderaton by gven τ opt of these layers n the fttng program. 5

6 (a) (b) Fg. 1 (a) Schematc of the photothermal expermental setup. (b) Schematc of an N-layer sample to show a multlayered model used n the data processng. 6

7 S3. Schematc and experment setup of the four-probe method Fgure 2(a) shows the schematc of the four-probe method. The two out probes (probes 1 and 4) are fed wth a DC current whle the voltage s measured from the two nner probes (probes 2 and 3). Fgure 2(b) shows the experment setup of the four-probe method n our lab. The four probes are fxed on the 3D mcrostage whch makes the contact between probes and the sample much flexble. The orange wres are connected wth a DC current source and multmeter whle the copper pece below the four pns represents the samples that are measured n our experment. (a) (b) Fg. 2 (a) Schematc of the four-probe method for measurng the n-plane electrcal conductvty of flms. (b) Expermental setup of the four-probe measurement n our lab. 7

8 S4. Measurement results through the four-probe method Table 2. In-plane electrcal conductvty and thermal conductvty of sngle-layered β-w Samples V/I (A) F 1 σ ( 10 5 Ω -1 m -1 ) ρ (µω cm) k (Wm -1 K -1 ) Aa Aa Aa Bb Bb Bb Dd Dd Dd

9 Table 3. In-plane electrcal conductvty and thermal conductvty of multlayered β-w samples V/I (A) F 1 σ ( 10 5 Ω -1 m -1 ) ρ (µω cm) k (Wm -1 K -1 ) a a a b b b d d d

10 Table 4. In-plane electrcal conductvty and thermal conductvty of multlayered β-w/g samples V/I (A) F 1 σ ( 10 5 Ω -1 m -1 ) ρ (µω cm) k (Wm -1 K -1 ) A A A B B B D D D

11 S5. Atomc-force mcroscopy (AFM) characterzaton of the transferred graphene Fgure 3 shows the AFM mage of the transferred graphene on β-w flm from whch we can see several wnkles appear n the graphene sheet. Fg. 3 AFM mage of the transferred graphene on β-w flm 11

12 References 1 Wang, X. W., Zhong, Z. R. & Xu, J. Noncontact thermal characterzaton of multwall carbon nanotubes. J. Appl. Phys. 97, , (2005). 2 Chen, X. W., He, Y. P., Zhao, Y. P. & Wang, X. W. Thermophyscal propertes of hydrogenated vanadum-doped magnesum porous nanostructures. Nanot 21, , (2010). 3 Wang, T. et al. Effect of zrconum(iv) propoxde concentraton on the thermophyscal propertes of hybrd organc-norganc flms. J. Appl. Phys. 104, , (2008). 4 Hu, H. P., Wang, X. W. & Xu, X. F. Generalzed theory of the photoacoustc effect n a multlayer materal. J. Appl. Phys. 86, , (1999). 12

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