- Email: [email protected]
polymer composite by laser flash analysis
International Journal of Heat and Mass Transfer 101 (2016) 470–475
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Thermal resistance measurement of 3D graphene foam/polymer composite by laser flash analysis Yun-Hong Zhao, Zhen-Kun Wu, Shu-Lin Bai ⇑ Department of Materials Science and Engineering, CAPT/HEDPS/LTCS, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Engineering, Peking University, Beijing 100871, China
a r t i c l e
i n f o
Article history: Received 2 November 2015 Received in revised form 17 March 2016 Accepted 13 May 2016 Available online 3 June 2016 Keywords: Graphene foam Thermal interface material (TIM) Thermal analysis Laser flash analysis (LFA)
a b s t r a c t In this work, three-dimensional graphene foam (GF)/polydimethylsiloxane (PDMS) composite was prepared and its thermal resistance in practical application was measured by laser flash analysis (LFA). Results show that the thermal resistance of GF/PDMS composite is as small as 14 mm2 K W1, which is only about 19% of that of commercial silver particles filled epoxy composite applied in the thermal management. In addition, the method of LFA used to measure thermal resistance is proved to be feasible and reliable by numerical simulation, which extends the functionality of LFA to meet a practical need. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Rapidly increasing power density of integrated circuit generates large amount of heat on chips, bringing about the hot-spot temperature rising. Due to the mismatch between chip and heat sink where thermal resistance is enormous, thermal interface materials (TIM) are developed to alleviate this issue [1]. Commercial TIM is mostly made of a polymeric matrix filled with thermally conductive fillers, such as thermally conductive greases, adhesive, pad, etc. The thermal resistance of commercial silver particles filled epoxy TIM is about 75 mm2 K W1 [2]. The past decade has witnessed the rapid development of carbon based TIM, particularly those based on carbon nanotubes (CNTs) and graphene. CNTs have long been thought as an ideal filler for TIM because of their extremely high intrinsic thermal conductivity (up to 6600 W m1 K1) [3–6]. However, composites fabricated with CNT additives show much worse results than expectation [7–10], which is partially attributed to the large interface thermal resistance across the nanotube-interface. In addition, their poor dispersion in polymer matrix also hinders the thermal conductivity enhancement. A promising approach is by using vertically aligned carbon nanotubes (VACNTs) instead of randomly dispersed ones. This method circumvented the dispersion issue to a large extent and the result was greatly improved [11–14]. ⇑ Corresponding author. Tel.: +86 10 6275 9379. E-mail address: [email protected] (S.-L. Bai). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.05.068 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
Graphene has attracted a lot of attention since its discovery due to its excellent electrical, mechanical and thermal properties [15–17]. Due to the superior thermal property, graphene based TIM has been investigated in the past decade [18–24]. As a twodimensional (2D) material, graphene is less vulnerable to the entanglement problem of one-dimensional (1D) CNTs. As a result, the thermal conductivity of graphene retains a large portion of its intrinsic value due to reduced internal phonon scattering. Cai et al. [25] reported a thermal conductivity of 370 W m1 K1 for supported CVD grown graphene. Randomly dispersing graphene layers into a polymeric matrix could get thermal conductivities of 5.1 and 6.44 W m1 K1 with a loading of 10 and 25 vol%, respectively [20,26], which are much higher than those reported CNT-based composites. However, they are still much below the expected value due to the interlayer contact thermal resistance. Different methods are designed to solve the problems caused by contact thermal resistance. Liang et al. [27] achieved a thermal conductivity of up to 112 W m1 K1 by vertically aligning functionalized multilayer graphene structure. As another special structure, three-dimensional (3D) graphene foam (GF) was grown by CVD method [28]. Its thermal conductivity reached 0.26–1.7 W m1 K1 at a solid concentration of 0.45 vol% [29]. The thermal interfacial resistance of GF at Si–Al interface is as low as 0.04 cm2 K W1 [30]. Previously our group has fabricated 3D GF/PDMS composite and achieved a thermal conductivity of 0.56 W m1 K1 at a small loading of 0.7 wt% [31].
Y.-H. Zhao et al. / International Journal of Heat and Mass Transfer 101 (2016) 470–475
For practical applications, contact thermal resistance plays an important role when samples are rigid. Generally, an intermediate TIM is adopted like soft indium between the substrate and sample in order to reduce the contact thermal resistance. Here we fabricated a 3D GF/PDMS TIM and applied it directly between two Cu pads without intermediate TIM. Meanwhile, a novel approach is designed to directly measure total thermal resistance, which is much more convenient compared with the steady-state method for thermal resistance measurement.
2. Materials and experiments 2.1. Fabrication of 3D GF Ni foam (1.5 mm thick, 300 mesh) purchased from Shanghai Zhongwei Company was placed in a quartz tube of a CVD furnace (SGL-1200, Shanghai Daheng). It was heated to 1000 °C at a ramping rate of 16 °C/min in a mixed atmosphere (Ar: 500 s.c.c.m., H2: 200 s.c.c.m.) and kept for 5 min. Then CH4 (10 s.c.c.m.) was turned on for 5 min and shut off after the reaction. Finally the sample was cooled down to room temperature at a rapid rate of about 100 °C/min. Above process gave the Ni foam coated with graphene layers. Further treatment was undertaken to obtain freestanding 3D GF. First, the liquid of poly-methyl methacrylate (PMMA, Mw: 996,000; 4 wt% in ethyl lactate) was drop-coated onto the graphene surface covering Ni foams. A thin PMMA layer was formed after dried at 180 °C for 30 min. The sample was then immersed into a hydrochloric acid solution (HCl, 3 M) at 80 °C for 4 h, during which the Ni foam was etched away by the acid. After that the protective PMMA layer was completely dissolved in a hot acetone (55 °C for 30 min). The sample was fetched out and dried in air, leaving the freestanding graphene foam.
2.2. Fabrication of 3D GF/PDMS TIM GF was placed over a Cu pad (1 1 cm2, 1 mm thick, polished with #1000 sand papers), then dropped with liquid PDMS (uncured Sylgard 184, Dow Corning, base/curing agent = 10/1 in weight) and left static for 30 min, during which the bubbles were expelled. An identical Cu pad was then placed exactly on top of the mixture of GF and PDMS under a pressure of 1 MPa. The sample was cured at 80 °C for 4 h and has a thickness of about 25 lm. For comparison, pure PDMS TIM was prepared in the similar way. The only difference is that a piece of copper film with the thickness of 25 lm and with a central hole was put between Cu pads to shape PDMS.
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2.3. Characterization The morphology of freestanding 3D GF was observed by scanning electron microscope (SEM, S-4800, HITACHI). The microstructure of graphene sheet composing 3D GF was measured using transmission electron microscope (TEM, JEM-2100F, JEOL). A conductometer (DRL-III, Hunan Xiangyi Instruments Co. Ltd.) using heat flux method was used to supply a certain temperature field. An onset pressure of 0.3 MPa was applied to increase contact area between the sample and Cu blocks with the diameter of 30 mm. Before test, several droplets of silicone oil were painted on the cross surfaces of Cu blocks to reduce measurement error. The thermal transportation of studied materials was captured by thermal imager (SC7300M, Flir Systems USA). LFA is a non-contact transient thermal measurement method widely used for measuring the thermal diffusivities (a) of a wide range of materials (a ranging from 0.01 to 1000 mm2/s with a reproducibility of about ± 3%). Besides opaque solids, LFA was also developed to measure the thermal diffusivity of semitransparent materials and liquids [32,33]. Shen et al. [34] extended flash method to determine the containerless thermal diffusivity of levitated spherical specimen under high temperature. The thermal conductivity of samples can be derived through Eq. (1):
j ¼ q Cp a
ð1Þ
where q is the mass density and C p is the specific heat at constant pressure. In this work, the mass density of 3D GF/PDMS and pure PDMS is 0.983 and 0.975 g cm3, respectively. The specific heat of those is 1.44 and 1.48 J g1 K1, respectively. The diagram of LFA is shown in Fig. 1(a). A short laser pulse generated by a flash lamp hits the bottom surface of the sample. Both the intensity and the duration of the pulse (100, 400 and 1000 ls for LFA447) can be adjusted in accordance with measured sample. The laser pulse energy is absorbed at the surface. The temperature of the rear surface is real-time monitored with an infrared detector, according to which the thermal diffusivity can be derived. The analytical relation of the rear temperature and time (Fig. 1 (b)) follows Eq. (2), where d is the sample thickness, t 1=2 is the time for the rear surface to reach half of the maximum temperature rise [35].
a¼
2
1:37 d p2 t1=2
ð2Þ
Before measurements, both surfaces of the sandwiched sample were coated with a thin graphite layer to enhance the absorption (or emission) for a better signal-to-noise ratio. The sandwiched sample was placed in the machine chamber (LFA447, Netzsch) to
Fig. 1. Diagram of LFA method. (a) A sketch of data acquisition procedure and (b) profile of the obtained data (not to scale).
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run the test. The data of the rear surface signal was stored and exported to a self-developed analysis program. For comparison, the thermal resistance of 3D GF/PDMS TIM was also tested with steady-state method (DRL-III, Hunan Xiangyi Instruments Co. Ltd.). 3. Results and discussion 3.1. Morphology of 3D GF/PDMS TIM The microstructure of freestanding 3D GF is shown in Fig. 2 (a) and (b). The interconnected structure of Ni foam was well maintained after the Ni etching and PMMA dissolving process. The width of GF arms is about 50 lm and the diameter of cell is about 400 lm. In Fig. 2(b), some crevices are seen on GF arms, which shows the hollow structure of GF arms. The TEM image in Fig. 2(c) clearly shows a multilayer structure with about 7 layers of graphene sheet (GS) composing 3D GF. 3.2. Sandwich model Fig. 3. Illustration of the measurement method.
3.2.1. Analysis of sandwich model Here we designed a sandwiched model based on the prototype of LFA447 to test its feasibility for practical applications. The TIM was sandwiched between two smooth Cu pads illustrated in Fig. 3. For the derivation of Eq. (2), five assumptions are proposed: (1) The heat conduction is one directional; (2) The duration of the laser pulse is negligible compared with the characteristic time t 1=2 and the energy absorption occurs instantaneously; (3) The penetration depth of the laser pulse is negligible; (4) The properties of samples are independent of temperature. (5) The TIM is taken as a non-dimensional resistive layer because of its small thickness (25 lm). As a result, we can derive the thermal resistance based on these five reasonable assumptions. The heat transfer equation inside the copper pads is:
@Tðx; tÞ @ 2 Tðx; tÞ ¼ aCu @t @x2
ð3Þ
in which aCu is the thermal diffusivity of Cu, T is temperature and x is the distance from the bottom surface. Adiabatic boundary is chosen because of the short duration that can be told from the temperature curve. So at the two surfaces, the boundary condition is:
jCu
@Tðx; tÞ @Tðx; tÞ ¼ jCu ¼0 @x x¼d @x x¼d
where
jCu is the thermal conductivity of Cu.
ð4Þ
Energy conservation should be maintained across the interface:
Q ¼ jCu
@Tðx; tÞ @Tðx; tÞ ¼ j Cu @x x¼0þ @x x¼0
Rt Q ¼ Rt
jCu
@Tðx; tÞ ¼ Tðx; tÞ Tðx; tÞ þ @x x¼0 x¼0 x¼0
ð5Þ
ð6Þ
in which Rt is the total thermal resistance and Q is the heat flux. The initial condition is set to be:
Tðx; tÞ ¼
T 0 ; ðd < x < d þ lÞ 0; ðd þ l < x < dÞ
ð7Þ
in which l is the as-conceived thin absorption layer and T 0 is an initial temperature. 3.2.2. Feasibility of sandwich model Fig. 4 shows the results of our numerical simulation with the model described previously, in which the red diamonds represent the data directly obtained from the machine. It is clear that the simulated curves have the same variation tendency with the experimental data. The thermal resistance lies in between 10 to 18 mm2 K W1, in which 14 mm2 K W1 gives the smallest deviation. This means that the thermal resistance of 3D GF/PDMS TIM is about 14 mm2 K W1. This result is slightly better than most of the CNTs and VACNTs based TIM (ranging from 5.2 to 43 mm2 K W1), comparable to that of commercial thermal greases and is
Fig. 2. (a) and (b) Low and high magnification SEM images of freestanding 3D GF. (c) TEM image showing a multilayer structure of GS composing 3D GF.
Y.-H. Zhao et al. / International Journal of Heat and Mass Transfer 101 (2016) 470–475
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shown in Fig. 5(b). The curves of temperature drop across the interface of samples and Cu blocks was plotted in Fig. 5(c), by which the temperature difference (DT) across the interface was obtained. Finally, the measured thermal resistance of the package (Rname package ) was obtained as below:
Rname package ¼
DT Q
ð8Þ
where Q is the heat flow recorded by the device (values given in Fig. 5(c)). The thermal resistance of 3D GF/PDMS TIM (Rt) could be calculated as below:
Rt
GF=PDMSTIM
¼ Rpackage ¼
Fig. 4. Comparing curves to estimate the thermal resistance of 3D GF/PDMS TIM (four solid curves simulated with Rc ranging from 10 to 18 mm2 K W1 and red diamonds obtained from LFA447).
only about 19% of that of commercial silver particles filled epoxy TIM [2,12–14,36,37]. Our method was also verified with an infrared thermometry method described elsewhere [30,38,39]. Briefly, the sample was sandwiched between a heating source and a cooling source with constant temperature as shown in Fig. 5(a). The system was left to equilibrium and an infrared thermometer was used to monitor the temperature across from the side view. The temperature field of a small rectangular area near the interface was captured as
GF=PDMSTIM Rpackage
RCuCu RbulkCu RbulkCu RCuCu RCu package RbulkCu
ð9Þ
where RCuCu is the thermal interfacial resistance between the Cu block and Cu disk, and RbulkCu is the thermal resistance of bulk Cu, which can be directly calculated from its thermal conductivity (jCu ) and thickness (t Cu ) as below:
RbulkCu ¼
t Cu
jCu
¼
1ðmmÞ 400 103 ðW mm1 K1 Þ
¼ 2:5ðmm2 K W1 Þ
ð10Þ
Fig. 5(d) shows the thermal resistance of studied materials. The thermal resistance of 3D GF/PDMS TIM was measured to be 13–22 mm2 K W1 with the steady-state method. The value is very close to that obtained with our model. What’s more, it takes much shorter time for our method since it does not need to wait for the
Fig. 5. (a) Schematic of thermal resistance measurement. (b) Thermographic images of the samples pressed between copper blocks. (c) Plots of the temperature drop across the interface of samples and copper blocks. (Inset: the heat flow Q) (d) Thermal resistance of 3D GF/PDMS TIM and pure PDMS TIM.
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equilibrium of the system. Thus we can conclude that our model is feasible and practical for the measurement of thermal resistance of TIM. 3.2.3. Stability and reliability of sandwich model The stability of our model is also justified. As the thermal interface resistance is much larger than that of pure Cu, the exact thermal conductivity of Cu will not interfere as long as it is large enough. This is also supported by simulations as shown in Fig. 6, in which the thermal conductivity of Cu was set to 250, 300, 350 and 400 W m1 K1 respectively, and no significant deviation was obtained from the results. This phenomenon offers a convenient choice of substrates as long as its thermal conductivity is large enough. Besides, the reliability of our codes was also checked. The iteration time was increased from 3000 to 30,000, while the simulated curves are identical to each other (Fig. 7). It thus indicates that our model is convergent and reliable for usage. 3.3. Comparison between PDMS and 3D GF/PDMS TIM The thermal resistance of 3D GF/PDMS TIM was calculated to be 14 mm2 W K1 with our model. As a comparison, the pure PDMS TIM shows a much higher value of 60 mm2 W K1 as shown in
Fig. 8. Stability test of 3D GF/PDMS TIM and pure PDMS TIM. The curves are simulated with Rc = 14 and 60 mm2 K W1, respectively, and the diamonds represent the data obtained from LFA447.
Fig. 8. Due to the high thermal conductivity of graphene and interconnected structure of GF, the thermal interface is greatly improved with the addition of small loading of 3D GF. It indicates that our 3D GF/PDMS TIM is of great potential to be used in real applications.
4. Conclusions
Fig. 6. Stability test with different thermal conductivity of Cu.
In summary, we prove that the CVD grown 3D GF/PDMS composite is able to be directly used as TIM. Its thermal resistance is as small as 14 mm2 K W1, comparable to those of commercial products. What’s more, we developed a convenient approach for measuring the thermal resistance. This transient method is easy to operate, and takes less than 10 min for sample preparation and measurement. The data analysis procedure will take less than 5 min to run. As a result, it saves much time compared with the steady-state method that generally consumes a lot of time for equilibrium. In addition, the non-contact attribute will avoid contamination to the equipment. In our model, the TIM is so thin that it can be taken as a pure resistance layer for convenience. However, this sandwich model is also easily developed to accommodate the measurement for samples with finite thickness. Firstly, the thermal conductivity of TIM sample is measured. Then, the contact resistance of thick TIM can be derived with a modified model using the same boundary and initial conditions. Acknowledgements The authors would like to thank the support by the National Natural Science Foundation of China (NSFC) and the National Natural Science Foundation of China and the Research Grants Council of Hong Kong (NSFC-RGC) Joint Research Scheme (Nos. 11272008, 11361161001, 11202005 and CUHK450/13). References
Fig. 7. Stability test with iteration numbers from 3000 to 30,000.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Thermal resistance measurement of 3D graphene foam/polymer composite by laser flash analysis Yun-Hong Zhao, Zhen-Kun Wu, Shu-Lin Bai ⇑ Department of Materials Science and Engineering, CAPT/HEDPS/LTCS, Key Laboratory of Polymer Chemistry and Physics of Ministry of Education, College of Engineering, Peking University, Beijing 100871, China
a r t i c l e
i n f o
Article history: Received 2 November 2015 Received in revised form 17 March 2016 Accepted 13 May 2016 Available online 3 June 2016 Keywords: Graphene foam Thermal interface material (TIM) Thermal analysis Laser flash analysis (LFA)
a b s t r a c t In this work, three-dimensional graphene foam (GF)/polydimethylsiloxane (PDMS) composite was prepared and its thermal resistance in practical application was measured by laser flash analysis (LFA). Results show that the thermal resistance of GF/PDMS composite is as small as 14 mm2 K W1, which is only about 19% of that of commercial silver particles filled epoxy composite applied in the thermal management. In addition, the method of LFA used to measure thermal resistance is proved to be feasible and reliable by numerical simulation, which extends the functionality of LFA to meet a practical need. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Rapidly increasing power density of integrated circuit generates large amount of heat on chips, bringing about the hot-spot temperature rising. Due to the mismatch between chip and heat sink where thermal resistance is enormous, thermal interface materials (TIM) are developed to alleviate this issue [1]. Commercial TIM is mostly made of a polymeric matrix filled with thermally conductive fillers, such as thermally conductive greases, adhesive, pad, etc. The thermal resistance of commercial silver particles filled epoxy TIM is about 75 mm2 K W1 [2]. The past decade has witnessed the rapid development of carbon based TIM, particularly those based on carbon nanotubes (CNTs) and graphene. CNTs have long been thought as an ideal filler for TIM because of their extremely high intrinsic thermal conductivity (up to 6600 W m1 K1) [3–6]. However, composites fabricated with CNT additives show much worse results than expectation [7–10], which is partially attributed to the large interface thermal resistance across the nanotube-interface. In addition, their poor dispersion in polymer matrix also hinders the thermal conductivity enhancement. A promising approach is by using vertically aligned carbon nanotubes (VACNTs) instead of randomly dispersed ones. This method circumvented the dispersion issue to a large extent and the result was greatly improved [11–14]. ⇑ Corresponding author. Tel.: +86 10 6275 9379. E-mail address: [email protected] (S.-L. Bai). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.05.068 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.
Graphene has attracted a lot of attention since its discovery due to its excellent electrical, mechanical and thermal properties [15–17]. Due to the superior thermal property, graphene based TIM has been investigated in the past decade [18–24]. As a twodimensional (2D) material, graphene is less vulnerable to the entanglement problem of one-dimensional (1D) CNTs. As a result, the thermal conductivity of graphene retains a large portion of its intrinsic value due to reduced internal phonon scattering. Cai et al. [25] reported a thermal conductivity of 370 W m1 K1 for supported CVD grown graphene. Randomly dispersing graphene layers into a polymeric matrix could get thermal conductivities of 5.1 and 6.44 W m1 K1 with a loading of 10 and 25 vol%, respectively [20,26], which are much higher than those reported CNT-based composites. However, they are still much below the expected value due to the interlayer contact thermal resistance. Different methods are designed to solve the problems caused by contact thermal resistance. Liang et al. [27] achieved a thermal conductivity of up to 112 W m1 K1 by vertically aligning functionalized multilayer graphene structure. As another special structure, three-dimensional (3D) graphene foam (GF) was grown by CVD method [28]. Its thermal conductivity reached 0.26–1.7 W m1 K1 at a solid concentration of 0.45 vol% [29]. The thermal interfacial resistance of GF at Si–Al interface is as low as 0.04 cm2 K W1 [30]. Previously our group has fabricated 3D GF/PDMS composite and achieved a thermal conductivity of 0.56 W m1 K1 at a small loading of 0.7 wt% [31].
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For practical applications, contact thermal resistance plays an important role when samples are rigid. Generally, an intermediate TIM is adopted like soft indium between the substrate and sample in order to reduce the contact thermal resistance. Here we fabricated a 3D GF/PDMS TIM and applied it directly between two Cu pads without intermediate TIM. Meanwhile, a novel approach is designed to directly measure total thermal resistance, which is much more convenient compared with the steady-state method for thermal resistance measurement.
2. Materials and experiments 2.1. Fabrication of 3D GF Ni foam (1.5 mm thick, 300 mesh) purchased from Shanghai Zhongwei Company was placed in a quartz tube of a CVD furnace (SGL-1200, Shanghai Daheng). It was heated to 1000 °C at a ramping rate of 16 °C/min in a mixed atmosphere (Ar: 500 s.c.c.m., H2: 200 s.c.c.m.) and kept for 5 min. Then CH4 (10 s.c.c.m.) was turned on for 5 min and shut off after the reaction. Finally the sample was cooled down to room temperature at a rapid rate of about 100 °C/min. Above process gave the Ni foam coated with graphene layers. Further treatment was undertaken to obtain freestanding 3D GF. First, the liquid of poly-methyl methacrylate (PMMA, Mw: 996,000; 4 wt% in ethyl lactate) was drop-coated onto the graphene surface covering Ni foams. A thin PMMA layer was formed after dried at 180 °C for 30 min. The sample was then immersed into a hydrochloric acid solution (HCl, 3 M) at 80 °C for 4 h, during which the Ni foam was etched away by the acid. After that the protective PMMA layer was completely dissolved in a hot acetone (55 °C for 30 min). The sample was fetched out and dried in air, leaving the freestanding graphene foam.
2.2. Fabrication of 3D GF/PDMS TIM GF was placed over a Cu pad (1 1 cm2, 1 mm thick, polished with #1000 sand papers), then dropped with liquid PDMS (uncured Sylgard 184, Dow Corning, base/curing agent = 10/1 in weight) and left static for 30 min, during which the bubbles were expelled. An identical Cu pad was then placed exactly on top of the mixture of GF and PDMS under a pressure of 1 MPa. The sample was cured at 80 °C for 4 h and has a thickness of about 25 lm. For comparison, pure PDMS TIM was prepared in the similar way. The only difference is that a piece of copper film with the thickness of 25 lm and with a central hole was put between Cu pads to shape PDMS.
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2.3. Characterization The morphology of freestanding 3D GF was observed by scanning electron microscope (SEM, S-4800, HITACHI). The microstructure of graphene sheet composing 3D GF was measured using transmission electron microscope (TEM, JEM-2100F, JEOL). A conductometer (DRL-III, Hunan Xiangyi Instruments Co. Ltd.) using heat flux method was used to supply a certain temperature field. An onset pressure of 0.3 MPa was applied to increase contact area between the sample and Cu blocks with the diameter of 30 mm. Before test, several droplets of silicone oil were painted on the cross surfaces of Cu blocks to reduce measurement error. The thermal transportation of studied materials was captured by thermal imager (SC7300M, Flir Systems USA). LFA is a non-contact transient thermal measurement method widely used for measuring the thermal diffusivities (a) of a wide range of materials (a ranging from 0.01 to 1000 mm2/s with a reproducibility of about ± 3%). Besides opaque solids, LFA was also developed to measure the thermal diffusivity of semitransparent materials and liquids [32,33]. Shen et al. [34] extended flash method to determine the containerless thermal diffusivity of levitated spherical specimen under high temperature. The thermal conductivity of samples can be derived through Eq. (1):
j ¼ q Cp a
ð1Þ
where q is the mass density and C p is the specific heat at constant pressure. In this work, the mass density of 3D GF/PDMS and pure PDMS is 0.983 and 0.975 g cm3, respectively. The specific heat of those is 1.44 and 1.48 J g1 K1, respectively. The diagram of LFA is shown in Fig. 1(a). A short laser pulse generated by a flash lamp hits the bottom surface of the sample. Both the intensity and the duration of the pulse (100, 400 and 1000 ls for LFA447) can be adjusted in accordance with measured sample. The laser pulse energy is absorbed at the surface. The temperature of the rear surface is real-time monitored with an infrared detector, according to which the thermal diffusivity can be derived. The analytical relation of the rear temperature and time (Fig. 1 (b)) follows Eq. (2), where d is the sample thickness, t 1=2 is the time for the rear surface to reach half of the maximum temperature rise [35].
a¼
2
1:37 d p2 t1=2
ð2Þ
Before measurements, both surfaces of the sandwiched sample were coated with a thin graphite layer to enhance the absorption (or emission) for a better signal-to-noise ratio. The sandwiched sample was placed in the machine chamber (LFA447, Netzsch) to
Fig. 1. Diagram of LFA method. (a) A sketch of data acquisition procedure and (b) profile of the obtained data (not to scale).
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run the test. The data of the rear surface signal was stored and exported to a self-developed analysis program. For comparison, the thermal resistance of 3D GF/PDMS TIM was also tested with steady-state method (DRL-III, Hunan Xiangyi Instruments Co. Ltd.). 3. Results and discussion 3.1. Morphology of 3D GF/PDMS TIM The microstructure of freestanding 3D GF is shown in Fig. 2 (a) and (b). The interconnected structure of Ni foam was well maintained after the Ni etching and PMMA dissolving process. The width of GF arms is about 50 lm and the diameter of cell is about 400 lm. In Fig. 2(b), some crevices are seen on GF arms, which shows the hollow structure of GF arms. The TEM image in Fig. 2(c) clearly shows a multilayer structure with about 7 layers of graphene sheet (GS) composing 3D GF. 3.2. Sandwich model Fig. 3. Illustration of the measurement method.
3.2.1. Analysis of sandwich model Here we designed a sandwiched model based on the prototype of LFA447 to test its feasibility for practical applications. The TIM was sandwiched between two smooth Cu pads illustrated in Fig. 3. For the derivation of Eq. (2), five assumptions are proposed: (1) The heat conduction is one directional; (2) The duration of the laser pulse is negligible compared with the characteristic time t 1=2 and the energy absorption occurs instantaneously; (3) The penetration depth of the laser pulse is negligible; (4) The properties of samples are independent of temperature. (5) The TIM is taken as a non-dimensional resistive layer because of its small thickness (25 lm). As a result, we can derive the thermal resistance based on these five reasonable assumptions. The heat transfer equation inside the copper pads is:
@Tðx; tÞ @ 2 Tðx; tÞ ¼ aCu @t @x2
ð3Þ
in which aCu is the thermal diffusivity of Cu, T is temperature and x is the distance from the bottom surface. Adiabatic boundary is chosen because of the short duration that can be told from the temperature curve. So at the two surfaces, the boundary condition is:
jCu
@Tðx; tÞ @Tðx; tÞ ¼ jCu ¼0 @x x¼d @x x¼d
where
jCu is the thermal conductivity of Cu.
ð4Þ
Energy conservation should be maintained across the interface:
Q ¼ jCu
@Tðx; tÞ @Tðx; tÞ ¼ j Cu @x x¼0þ @x x¼0
Rt Q ¼ Rt
jCu
@Tðx; tÞ ¼ Tðx; tÞ Tðx; tÞ þ @x x¼0 x¼0 x¼0
ð5Þ
ð6Þ
in which Rt is the total thermal resistance and Q is the heat flux. The initial condition is set to be:
Tðx; tÞ ¼
T 0 ; ðd < x < d þ lÞ 0; ðd þ l < x < dÞ
ð7Þ
in which l is the as-conceived thin absorption layer and T 0 is an initial temperature. 3.2.2. Feasibility of sandwich model Fig. 4 shows the results of our numerical simulation with the model described previously, in which the red diamonds represent the data directly obtained from the machine. It is clear that the simulated curves have the same variation tendency with the experimental data. The thermal resistance lies in between 10 to 18 mm2 K W1, in which 14 mm2 K W1 gives the smallest deviation. This means that the thermal resistance of 3D GF/PDMS TIM is about 14 mm2 K W1. This result is slightly better than most of the CNTs and VACNTs based TIM (ranging from 5.2 to 43 mm2 K W1), comparable to that of commercial thermal greases and is
Fig. 2. (a) and (b) Low and high magnification SEM images of freestanding 3D GF. (c) TEM image showing a multilayer structure of GS composing 3D GF.
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shown in Fig. 5(b). The curves of temperature drop across the interface of samples and Cu blocks was plotted in Fig. 5(c), by which the temperature difference (DT) across the interface was obtained. Finally, the measured thermal resistance of the package (Rname package ) was obtained as below:
Rname package ¼
DT Q
ð8Þ
where Q is the heat flow recorded by the device (values given in Fig. 5(c)). The thermal resistance of 3D GF/PDMS TIM (Rt) could be calculated as below:
Rt
GF=PDMSTIM
¼ Rpackage ¼
Fig. 4. Comparing curves to estimate the thermal resistance of 3D GF/PDMS TIM (four solid curves simulated with Rc ranging from 10 to 18 mm2 K W1 and red diamonds obtained from LFA447).
only about 19% of that of commercial silver particles filled epoxy TIM [2,12–14,36,37]. Our method was also verified with an infrared thermometry method described elsewhere [30,38,39]. Briefly, the sample was sandwiched between a heating source and a cooling source with constant temperature as shown in Fig. 5(a). The system was left to equilibrium and an infrared thermometer was used to monitor the temperature across from the side view. The temperature field of a small rectangular area near the interface was captured as
GF=PDMSTIM Rpackage
RCuCu RbulkCu RbulkCu RCuCu RCu package RbulkCu
ð9Þ
where RCuCu is the thermal interfacial resistance between the Cu block and Cu disk, and RbulkCu is the thermal resistance of bulk Cu, which can be directly calculated from its thermal conductivity (jCu ) and thickness (t Cu ) as below:
RbulkCu ¼
t Cu
jCu
¼
1ðmmÞ 400 103 ðW mm1 K1 Þ
¼ 2:5ðmm2 K W1 Þ
ð10Þ
Fig. 5(d) shows the thermal resistance of studied materials. The thermal resistance of 3D GF/PDMS TIM was measured to be 13–22 mm2 K W1 with the steady-state method. The value is very close to that obtained with our model. What’s more, it takes much shorter time for our method since it does not need to wait for the
Fig. 5. (a) Schematic of thermal resistance measurement. (b) Thermographic images of the samples pressed between copper blocks. (c) Plots of the temperature drop across the interface of samples and copper blocks. (Inset: the heat flow Q) (d) Thermal resistance of 3D GF/PDMS TIM and pure PDMS TIM.
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equilibrium of the system. Thus we can conclude that our model is feasible and practical for the measurement of thermal resistance of TIM. 3.2.3. Stability and reliability of sandwich model The stability of our model is also justified. As the thermal interface resistance is much larger than that of pure Cu, the exact thermal conductivity of Cu will not interfere as long as it is large enough. This is also supported by simulations as shown in Fig. 6, in which the thermal conductivity of Cu was set to 250, 300, 350 and 400 W m1 K1 respectively, and no significant deviation was obtained from the results. This phenomenon offers a convenient choice of substrates as long as its thermal conductivity is large enough. Besides, the reliability of our codes was also checked. The iteration time was increased from 3000 to 30,000, while the simulated curves are identical to each other (Fig. 7). It thus indicates that our model is convergent and reliable for usage. 3.3. Comparison between PDMS and 3D GF/PDMS TIM The thermal resistance of 3D GF/PDMS TIM was calculated to be 14 mm2 W K1 with our model. As a comparison, the pure PDMS TIM shows a much higher value of 60 mm2 W K1 as shown in
Fig. 8. Stability test of 3D GF/PDMS TIM and pure PDMS TIM. The curves are simulated with Rc = 14 and 60 mm2 K W1, respectively, and the diamonds represent the data obtained from LFA447.
Fig. 8. Due to the high thermal conductivity of graphene and interconnected structure of GF, the thermal interface is greatly improved with the addition of small loading of 3D GF. It indicates that our 3D GF/PDMS TIM is of great potential to be used in real applications.
4. Conclusions
Fig. 6. Stability test with different thermal conductivity of Cu.
In summary, we prove that the CVD grown 3D GF/PDMS composite is able to be directly used as TIM. Its thermal resistance is as small as 14 mm2 K W1, comparable to those of commercial products. What’s more, we developed a convenient approach for measuring the thermal resistance. This transient method is easy to operate, and takes less than 10 min for sample preparation and measurement. The data analysis procedure will take less than 5 min to run. As a result, it saves much time compared with the steady-state method that generally consumes a lot of time for equilibrium. In addition, the non-contact attribute will avoid contamination to the equipment. In our model, the TIM is so thin that it can be taken as a pure resistance layer for convenience. However, this sandwich model is also easily developed to accommodate the measurement for samples with finite thickness. Firstly, the thermal conductivity of TIM sample is measured. Then, the contact resistance of thick TIM can be derived with a modified model using the same boundary and initial conditions. Acknowledgements The authors would like to thank the support by the National Natural Science Foundation of China (NSFC) and the National Natural Science Foundation of China and the Research Grants Council of Hong Kong (NSFC-RGC) Joint Research Scheme (Nos. 11272008, 11361161001, 11202005 and CUHK450/13). References
Fig. 7. Stability test with iteration numbers from 3000 to 30,000.
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