Accurate determination of anisotropic thermal conductivity for ultrathin composite film

Qiu-Hao Zhu(朱秋毫) Jing-Song Peng(彭景凇) Xiao Guo(郭潇) Ru-Xuan Zhang(张如轩)Lei Jiang(江雷) Qun-Feng Cheng(程群峰) and Wen-Jie Liang(梁文杰)

1Beijing National Center for Condensed Matter Physics,Beijing Key Laboratory for Nanomaterials and Nanodevices,Institute of Physics,Chinese Academy of Sciences(CAS),Beijing 100190,China

2CAS Center of Excellence in Topological Quantum Computation and School of Physical Sciences,University of Chinese Academy of Sciences,Beijing 100190,China

3School of Chemistry,Key Laboratory of Bio-inspired Smart Interfacial Science and Technology of Ministry of Education,Beijing Advanced Innovation Center for Biomedical Engineering,Beihang University,Beijing 100191,China

4Songshan Lake Materials Laboratory,Dongguan 523808,China

Keywords: ultrathin,composite film,thermal conductivity,anisotropic ratio

1. Introduction

With the further miniaturization of transistors, more and more devices are integrated into a single integrated circuit chip.Owing to the consequent large power density,local overheating becomes a great challenge if the heat dissipation capability is poor. High temperature will severely degrade the system performance because of thermal fluctuation effects, and also cause a great many of irreversible damages to the inner devices and sensing units, thus accelerating their aging processes. Thus, efficient thermal management is of great importance in the field of chip manufacturing and packaging.[1,2]Films with highly anisotropic thermal conductivity whose inplane thermal conductivity (λx) is substantially higher than the cross-plane one (λz),[3,4]capable of in-plane rapid Joule heat diffusion and out-of-plane thermal heat blocking,have attracted extensive research interest in the past few decades.[5,6]It is a promising way to realize high-performance on-chip systems with a long-duration stability by directionally accelerating heat transfer that depositing such films on chip surface within a limited space,which have the capacity to conduct heat from local overheating spots, ensuring that the other internal structures are not susceptive to adjacent thermal fields. Hence,the exploration of ultrathin (＜10 μm) thermal management films is of great value for the applications in some specific size-confined environments. However, the accurate determination of thermal conductivity for ultrathin composite film is still a pending issue due to its ultrathin nature and small thermal conductance;hence,now there are no reports on ultrathin(micron-sized) composite films for efficient thermal management.

Usually, in-plane and cross-plane thermal conductivityλxandλzof thick composite film are determined by using laser flash techniques by heating the films in the center with a laser pulse and measuring its in-/cross-plane thermal response (surface temperatures) at the edge/rear with an infrared detector.[7–10]However, this method is in question for the thermal property measurement of ultrathin composite films.[11]For cross-plane measurements,on the one hand,ultrathin film reaches a thermal equilibrium state in the crossplane direction within a very short time, and visible temperature difference could be hardly obtained. Hence, fitted and extracted thermal diffusivity is unreliable. On the other hand,the laser penetration depth is comparable or larger in ultrathin films, making the adopted 1D cross-plane heat diffusion model invalid. As for in-plane measurements, the direct contact of sample holder’s cap mask to film surface dramatically affects the in-plane thermal transport process from the laserheated spot to the detector-sensed one for ultrathin composite with small thermal conductance, raising the measurement error. Some other typical measurement methods,including Raman method,[12,13]3ωmethod,[14,15]and suspension bridge method,[16,17]are also proposed to detect thin film in-plane thermal conductivity. Nevertheless, the small laser penetration depth,unmatched heat penetration depth or large thermal contact resistance drastically rigidify the boundary conditions,limiting their practical applications in our micron-sized ultrathin composite film measurements.

To accurately determinate the highly anisotropic thermal conductivity of ultrathin composite film with a thickness less than 10 μm, we develop a hybrid method combining the 1D steady-state heat conduction approach and the 3ωmethod in this work. We carry out measurements based on a montmorillonite/reduced graphene oxide(MMT/rGO)composite system, and the measurement accuracy is verified by control experiments. A more reliableλxresult of～3.99 W·m-1·K-1is obtained through the modified 1D steady-state means by effectively eliminating the influence from background heat dissipation and contact thermal resistance. On the other hand, a reducedλzvalue of～0.066 W·m-1·K-1and a high anisotropic ratio of～60.5 are discovered for composite films by using the 3ωmethod through avoiding the laser penetration effects.As-measured composite thermal conductivity is independent of film thickness from 0.2 μm to 2 μm, further attesting the feasibility of our measurement method.

2. Results and discussion

2.1. Material characterization

The multi-layered composite film to be tested is synthesized through layer-by-layer filtration with a mixture of MMT and rGO layers(in Fig.1(a)). Total thickness of ultrathin hybrid film, ranging from～0.2 μm to 2 μm, is related to the deposition cycle (n, 1–10). A typical cross-sectional scanning electron microscopy(SEM)image of the film(Fig.1(b))shows that the MMT/rGO layers are stacked along the crossplane direction,corresponding with our measurement requirements for highly-anisotropic thermal conductive material.The x-ray diffraction (XRD) patterns show the crystallographic structure of the as-prepared composite as shown in Fig. 1(c),where five distinct peaks exist in the spectra. An evident diffraction peak centered at 6.7°possesses a high intensity,corresponding to(001)plane for MMT in the composite. Two small high-order peaks detected at 13.4°and 19.7°, corresponding to(002)and(020)planes of MMT,further attest its short-range order nature. Thed-spacing value for MMT(001)plane is～13.18 ˚A in the stack composite,similar to the value reported previously.[18]Two characteristic peaks at 26.6°and 44.7°(Fig. 1(c)) are from (002) plane and 2D (10) plane of rGO layer. The calculatedd-spacing value of～3.35 ˚A for 26.6°peak matches ideally with that of graphite (002)plane.[19,20]We see no other impurity phases from our XRD patterns, indicating that the composite only consists of MMT and rGO.

Fig.1. (a)Schematic illustration for film composition and measured film thickness. (b)Cross-sectional SEM image of(MMT/rGO)15 composite film,and(c)XRD pattern of the film.

2.2. In-plane thermal conductivity measurement

We adopt an improved 1D steady-state heat conduction method,i.e.using a four-probe configuration under a highvacuum condition to measureλxat room temperature, which is a more essential and reliable method.[21,22]The steady-state measurement system (Fig. 2(a)) is carried out in a probe station’s vacuum chamber. A heat flow is generated by a suspended resistive heater at the hot junction, passes through a narrow and long strip composite sample (cut from the MMT/rGO composite film)and is absorbed by a copper block at the clod junction. Two thermocouples are connected with a hot end and a cold end respectively to measure the corresponding hot-/cold-junction temperatureThandTc. Our sample strips are suspended and glued with silver paste between the two junctions. Strip length(l)and width(w)are～2 mm and～1 mm, respectively, and its thickness (h) is variable in our experiments. To minimize the influence of inevitable background heat losses, including the radiation and the heat flow from supporting structures, thermal conductance of ten composite strips is measured together to enhance thermal conductance signal. At the same time,hot junction is completely supported by the pull of thin insulated constantan wires.

Fig.2. (a)A schematic illustration for modified four-probe setup. (b)Temperature differences between two junctions as a function of heating power for samples with various values of deposition cycle n,with inset showing actual measurement setup.(c)Measured total thermal resistance as a function of sample strip length. (d)Measured IR signal intensity versus time for(MMT/rGO)5 composite by laser flash technique.

Figure 2(b)shows the in-plane thermal conductance measurement results for composite strips with different values ofn. The background heat dissipation is also exhibited. Note that the background signal is obtained when no sample is suspended on the two junctions, and it is completely determined by heat leakages through the thermocouples and conduction wires together with radiation heat loss. It is found that the temperature difference between two junctions(ΔT=Th-Tc)shows an approximately linear dependence on the heating power,and there appear obvious ΔTdifferences between various samples. The film thermal conductance (G) can be determined by the difference between the reciprocals of fitted slopes for the tested structure and the background. According to the relationshipλx=Gl/wh,the values of the in-plane thermal conductivityλxare obtained to be 4.04, 4.00, 4.07,and 3.84 W·m-1·K-1for strip samples with a deposition cycle of 3, 6, 8, and 10, respectively. Hence, it shows thatλxremains constant when the sample thickness changes,indicating the accuracy and reliability of the measurement. To estimate the thermal contact resistances at hot junction and cold junction and to guarantee our thermal measurement accuracy,the thermal resistances of samples are repeatedly measured for strips with the same thickness(～2 μm)and different lengths.As illustrated in Fig. 2(c), there exists an approximately linear relationship between the measured total thermal resistance and the strip length for multiple measurements, and the linear fitting result passes through the origin within an allowed error range. Thus,it indicates that the total thermal contact resistance is negligible and has little influence on the measured values ofλx.

As stated above,the conventional laser flash technique is not suitable for measuring the thermal conductances of ultrathin films. To the best of our knowledge,the film thickness of the thinnest composite that was measured by using this technique is on the order of 10 μm to 100 μm.[23–27]For comparison, we also try to estimate in-plane thermal conductivity of ultrathin(～1 μm)(MMT/rGO)5film by using the laser flash technique. Not surprisingly,either the signal is too small to be detected, or laser irradiation creates local heating and makes visual damage to the thin samples. One of such measurement results is shown in Fig. 2(d). The in-plane thermal diffusion coefficient and thermal conductivity of the extracted composite are 177.0±14.7 mm2·s-1and～442.5 W·m-1·K-1, respectively,even greatly exceeding the reported values of pure rGO materials,[4]indicating the large potential measurement errors for in-plane thermal measurements of thin composites.This may be due to the inevitable large thermal leakage induced by laser flash measurement setup, where the cap mask of sample holder closely contacts the film surface as shown in the inset.

It is noted that although the sample will keep a better balance assisted by supporting the hot junction with a nylon wire(see the inset of Fig.3(a)),the background thermal conductance reaches up to 3.72 mW·K-1for the heat dissipation in such a steady-state measurement setup (see Fig. 3(a)). On this occasion, the ultrathin composite-caused small temperature change cannot be distinguished from the background signals. This phenomenon can be explained by simple heat transfer analyses. It is well established from 1D Fourier heat transfer equation that heat flow ˙Qis related to thermal conductive material cross-sectional areaAand temperature gradient. For the nylon wire-supported measurement setup, the total heat flow is determined by the heat flow through sample ˙QS, the heat flow through nylon wires ˙QNand the heat flow related to background leakage factors ˙QB(including conduction wiresrelevant or thermocouples-correlated conduction heat flows and also the radiation heat flow),following the relationship

for measurement setups respectively with nylon wire supported and with hot junctions suspended. Owing to the ultrathin sample nature,the nylon wire-induced heat flow portion is far larger than the sample-induced one,and thus scarcely any valid sample heat flow can be extracted from the obtained data when the hot junction is supported.

Fig.3. Accuracy analyses for modified in-plane thermal conductivity measurement approach, showing (a) as-measured temperature variation results for the (MMT/rGO)10 composite from conventional steady-state measurement and(b)temperature differences between two junctions as a function of the heating power for different numbers of platinum wires. The solid line represents linear fitting results. The insets schematically illustrate the measurement setups with nylon wire-supported and suspended hot junctions,respectively.

Therefore,we,for the sake of measurement accuracy,determine to suspend the hot junction and the resulting background heat dissipation is reduced by an order of magnitude.To verify the measurement reliability, we use the modified method to measure the values ofλxfor different numbers of commercial platinum wires with diameters～20 μm, whose thermal conductance is comparable to that of our tested ultrathin composite film. The measurement results are shown in Fig. 3(b), and the background heat dissipation is also exhibited here. The calculatedλxis 67.6±6.7 W·m-1·K-1, corresponding with its standard value ofλx(72 W·m-1·K-1). It is worth mentioning that there is a～2%size distribution error(2%in length and 2‰in cross-sectional area)between the purchased platinum wires, resulting in large measurement errors. On the other hand,the material property deviation from standard counterparts is also a main cause forλxdifferent from standard result. This result further demonstrates the feasibility of this modified 1D steady-state heat conduction method to accurately determine the thermal conductivity of the materials with small thermal conductances.

2.3. Cross-plane thermal conductivity measurement

A modified 3ωmethod[28,29]is utilized to measure the cross-plane thermal conductivity(see Fig.4(a)). The 10-mmdiameter composites are attached to a silicon substrate and a four-probe gold wire is patterned by using shadow mask and thermally evaporated on the composite film surface to form a 3ωtesting structure. The main conducting path has a physical dimension of 1400 μm/30 μm as determined by gold wire length/width(see Fig.4(b)). The SR830 lock-in amplifier provides an AC heating current for the gold wire and measures high-order harmonic voltage signals of the same wire to reflect thermal properties of composite film underneath it. A steady AC currentIωwith frequencyωis generated in the lock-in amplifier via the internal oscillator andV-to-Iconvertor,passing through two probes of the gold wire. The conducting gold wire is heated,and an oscillating heat flow enters into composite film. Depending on how fast heat enters into the film, an oscillating temperature ΔT2ωtogether with an oscillating electrical resistance can be measured on the wire via the other two voltage probes at an oscillation frequency of 2ω. The voltage oscillationV3ωis eventually realized by combining the heatinduced resistanceR2ωwith the current signalIω,and it is then detected with the lock-in amplifier on the same voltage probes to further extract the composite and substrate thermal properties. To ensure the measurement accuracy,a precise resistance box is connected in series into the circuit, and the intrinsic high-order harmonic noise is offset through a differential circuit. The supplied power remains constant for per unit wire length.

Fig. 4. (a) Schematic diagram of employed 3ω testing setup, (b) optical microscopy image for as-fabricated 3ω gold structure, (c) input frequency-dependent temperature oscillations for samples with various deposition cycles, and (d) enlarged view of temperature oscillation properties for substrate(n=0)and MMT/rGO/substrate(n=1).

Figures 4(c) and 4(d) show the gold wire’s temperature oscillations against input current’s frequency for samples with diverse deposition cycles. Experimental data are plotted in dots in different colors. Thermal characteristics of our samples can be extracted from the linear-region results based on an established approximate model,[30,31]where the slope reflects the substrate thermal properties while the temperature oscillation difference is related to compositeλz. It is observed that the ΔT2ω-logarithmic input frequency dependency deviates from the linear relationship in the high-frequency region,and this is a result of the gradually reduced thermal penetration depth approaching the film thickness. On the other hand,a similar phenomenon takes place in the low-frequency region due to the limited silicon substrate thickness. Furthermore, the linear-region slopes are all constant for tested composites with diverse values ofn, meaning the fixed substrate thermal properties and further attesting our measurement accuracy. The calculated values ofλzare 0.060, 0.066,0.072, 0.069, 0.073, 0.058 W·m-1·K-1for composite films with deposition cycles of 1, 2, 3, 4, 6, and 8, respectively,while the silicon substrate possesses a typical conductivity value of 129.3 W·m-1·K-1. For comparison, we also measure the value ofλzfor pure rGO thin film and MMT thin film(thickness＜1 μm)by using the same method. The obtained room-temperatureλzvalue is 0.117±0.016 W·m-1·K-1for rGO and 0.160±0.022 W·m-1·K-1for MMT,consistent with the results reported previously.[4,32]Thus the measurement result accuracy and reliability are verified. Besides, we measure the values ofλzof commercial SiO2/Si wafers with diverse SiO2thickness values of 300 nm and 500 nm, and the derived values ofλzare 130.43±6.52 W·m-1·K-1and 1.47±0.12 W·m-1·K-1for silicon substrate and oxide layer,respectively.These results also coincide well with the reported values.[31]

2.4. Thermal conductivity feature analysis

Thickness-related composite in-/cross-plane thermal conductivities are plotted in Fig.5,whereλxandλzvalues are denoted by using solid squares and solid circles, respectively.λxandλzare kept constant (3.99±0.20 W·m-1·K-1and 0.066±0.004 W·m-1·K-1) for composite films with various thickness values (i.e., various values of deposition cyclen),meaning that the measuredλxandλzvalues have very high accuracy. We also obtain the value ofλx,442.5 W·m-1·K-1,by using the laser flash method in Fig. 2(a). Apparently,significant difference can be seen between the two methods,showing that for determining the ultrathin composite filmλx,the 1D steady-state heat conduction method is more accurate and effective than the laser flash method. These results also show that the composite films have a highly-anisotropic thermal conductivity, with an anisotropic ratioλx/λzbeing up to～60.5 and independent ofn. The obtained anisotropic ratio also has a high accuracy because the cross-plane thermal conductivity and the in-plane thermal conductivity measuring methods are both reliable. In view of the lack of reports on the thermal properties of ultrathin (＜10 μm) composite films due to the difficulties in accurately evaluating their temperature variations, we compare our measurement results with those reported previously on thick composite counterparts with a thickness ranging from 10 μm to 10 mm. It is discovered that the measured value ofλx(～3.99 W·m-1·K-1)is a common result for graphene/rGO-contained composite film,[26,33,34]and the high anisotropic ratio (～60.5) is also similar to that of MXene/MMT film,[24]demonstrating that this proposed hybrid measuring method, instead of conventional laser flash technique, is greatly effective to accurately determine the anisotropic thermal counductivities of ultrathin composite films.

3. Conclusions

In summary, we developed a hybrid method of determining ultrathin composite thermal conductivity , where a modified 1D steady-state heat conduction approach and a 3ωmethod are adopted to accurately assess itsλxvalue andλzvalue, respectively. The obtained value ofλxandλzare～3.99 W·m-1·K-1and～0.066 W·m-1·K-1, respectively,meaning the high anisotropic ratio of 60.5 for the tested ultrathin composite films. The thermal conductivity result is thickness-independent and close to that of reported thick composite counterpart, suggesting that the proposed method possesses a higher measurement accuracy than conventional techniques. This work presents a powerful guidance to measure the thermal properties of ultrathin composites,paving the way for developing the high-performance material towards efficient thermal management.

Acknowledgements

Project supported by the National Basic Research Program of China (Grant No. 2016YFA0200800), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant Nos. XDB30000000 and XDB07030100),the Sinopec Innovation Scheme (A-527), the National Key Research and Development Program of China (Grant No. 2021YFA0715700), and the National Science Fund for Distinguished Young Scholars,China(Grant No.52125302).