Effect of Contact Pressure on the Performance of Carbon Nanotube Arrays Thermal Interface Material

Vertically aligned carbon nanotube (CNT) arrays are promising candidates for advanced thermal interface materials (TIMs) since they possess high mechanical compliance and high intrinsic thermal conductivity. Some of the previous works indicate that the CNT arrays in direct dry contact with the target surface possess low contact thermal conductance, which is the dominant thermal resistance. Using a phase sensitive transient thermo-reflectance (PSTTR) technique, we measure the thermal conductance between CNT arrays and copper (Cu) surfaces under different pressures. The experiments demonstrated that the contact force is one of the crucial factors for optimizing the thermal performance of CNT array-based TIMs. The experimental results suggest that the Cu-CNT arrays’ contact thermal conductance has a strong dependence on the surface deformation and has an order of magnitude rise as the contact pressure increases from 0.05 to 0.15 MPa. However, further increase of the contact pressure beyond 0.15 MPa has little effect on the contact thermal resistance. This work could provide guidelines to determine the minimum requirement of packaging pressure on CNT TIMs.


Introduction
With rapidly increasing power densities in electronic devices, thermal management is becoming a crucial issue in maintaining the reliability and performance. Inadequate power dissipation will raise the device temperature and shorten device lifetime. One way to improve the heat dispassion of devices is to find ultrahigh thermal conductivity materials for chips and heat sinks. Recently, Hu et al. synthesized semiconductor boron arsenide single crystals without detectable defects and with a thermal conductivity of 1300 W/mK at room temperature [1]. The graphite flakes-metal composites, reported by J. Narciso et al., possess a thermal conductivity between 294-390 W/mK, and are excellent materials for heat sinks [2]. However, with the further decrease of the thermal resistance of heat sinks, the thermal contact resistance between the chips and heat sinks due to the microscale surface roughness at the interface has become critical. A lot of effort has been put into searching for advanced thermal interface materials (TIMs) to enhance thermal conduction between chips and heat sinks. TIMs are used to replace the microscopic asperities between contact surfaces which contribute to the prominent thermal resistance [3]. Vertically aligned carbon nanotube (CNT) arrays are promising candidates for advanced TIMs since they possess high mechanical compliance [4][5][6][7][8] and high thermal conductivity at room temperature range [9][10][11][12][13]. 3 of 10 in Figure 1a [20]. A 20-nm buffer layer of aluminium oxide (Al 2 O 3 ) and a 1-nm layer of Fe were subsequently deposited onto the Si substrate by sputtering (Kurt J. Lesker. LAB 18, Jefferson Hills, PA, USA) and thermal evaporation (VNANO, Beijing, China, VZZ-300). The CVD process was done under an argon (Ar) and hydrogen (H 2 ) environment with ethylene (C 2 H 4 ) as feedstock in a tube furnace (KEJING, Hefei, China, OTF-1200X). A mixture of Ar (120 sccm), H 2 (80 sccm), and a small amount of water vapor (~100 ppm) was supplied into the reaction tube while the tube was heated to 750 • C. Once the furnace reached the target temperature, C 2 H 4 gas with a flow rate of 80 sccm was introduced into the gas stream to start the growth process. The growth time was controlled to be 10 to 15 min. Then the supply of C 2 H 4 , H 2 and water vapor was terminated and the sample was cooled down to room temperature in an Ar environment. By changing the time of the flow of ethylene, CNT arrays with lengths of 200 and 500 µm were obtained, respectively. It has been shown that both the contact conductance and the effective thermal conductivity have direct relationship with volume fraction of CNT arrays [21]. In this work, the array volume fraction of the CNT arrays was controlled to be around 1.8% which was determined by the ratio of the array mass density to the individual CNT mass density [22], 2.1 g/cm 3 . Scanning electron microscopy (SEM) (Hatachi, Tokyo, Japan, SU8220) image ( Figure 1b) at 3 KV voltage shows the morphology of the upper surface of CNT arrays. The diameter of individual carbon nanotubes are 10 to 20 nanometers. The mechanical behaviors of the prepared CNT arrays were studied with an electronic compression testing machine (REGER, Shenzhen, China, RGM-6005T). The compression head was set to retreat at a speed of 5 mm/min. And an atomic force microscopy (AFM) (Bruker, Billerica, MA, USA, Demension Icon) was used to characterize the roughness of the upper surface of the CNT both before and after the pressing. Hills, PA, USA) and thermal evaporation (VNANO, Beijing, China, VZZ-300). The CVD process was done under an argon (Ar) and hydrogen (H2) environment with ethylene (C2H4) as feedstock in a tube furnace (KEJING, Hefei, China, OTF-1200X). A mixture of Ar (120 sccm), H2 (80 sccm), and a small amount of water vapor (~100 ppm) was supplied into the reaction tube while the tube was heated to 750 °C . Once the furnace reached the target temperature, C2H4 gas with a flow rate of 80 sccm was introduced into the gas stream to start the growth process. The growth time was controlled to be 10 to 15 min. Then the supply of C2H4, H2 and water vapor was terminated and the sample was cooled down to room temperature in an Ar environment. By changing the time of the flow of ethylene, CNT arrays with lengths of 200 and 500 μm were obtained, respectively. It has been shown that both the contact conductance and the effective thermal conductivity have direct relationship with volume fraction of CNT arrays [21]. In this work, the array volume fraction of the CNT arrays was controlled to be around 1.8% which was determined by the ratio of the array mass density to the individual CNT mass density [22], 2.1 g/cm 3

Thermal Measurement Setup
The heat transfer properties of Cu/CNT interface were measured using phase sensitive transient thermo-reflectance (PSTTR) method [15,23]. Similar to time-domain thermo-reflectance (TDTR), [24,25] PSTTR is an optical method based on the thermal reflectance effect. Instead of using a femtosecond laser as heating source, it uses a modulated continuous wave laser to provide heat flux at sample surfaces. The modulation frequency is kept at the kHz range to ensure the penetration of the

Thermal Measurement Setup
The heat transfer properties of Cu/CNT interface were measured using phase sensitive transient thermo-reflectance (PSTTR) method [15,23]. Similar to time-domain thermo-reflectance (TDTR), [24,25] PSTTR is an optical method based on the thermal reflectance effect. Instead of using a femto-second laser as heating source, it uses a modulated continuous wave laser to provide heat flux at sample surfaces. The modulation frequency is kept at the kHz range to ensure the penetration of the heat wave through the several microns thick copper layer and few hundred microns thick CNT array in sequence. The experimental apparatus is illustrated in Figure 2a.
in sequence. The experimental apparatus is illustrated in Figure 2a.
The sample was heated by a diode laser (RPMC, O'Fallen, MO, USA, LDX-3315-808 with nominal wavelength of 808 nm and maximum output power ~1 W) with intensity sinusoidally modulated at frequency ω. Taking into account the factors of thermal penetration depth and signal to noise ratio, the modulation frequency ω was set within 3000-6000 Hz range and controlled by a function generator. Figure 2b shows the sample configuration for thermal characterization. A piece of glass was sequentially deposited with 10 nm chromium (Cr) as adhesion promoter and 100 nm gold (Au) for its high thermo-reflectance coefficient at the probe laser wavelength (632.8 nm). Then a five-micron thickness of copper was deposited onto the Au side of the glass wafer by thermal evaporation. The CNT array on the silicon substrate was adhered to the Cu side of the glass wafer with a controlled pressure by a load cell.

Measurement Principle
The heating laser beam passed through the glass plate and was focused onto the Cr/Au layer with beam size around 1 mm × 2 mm as shown in Figure 2b. The oscillating heat flux propagated through the sample causing temperature oscillation at the Cr/Au surface at same frequency. Due to the thermo-reflectance effect, the reflectivity of Au surface oscillates accordingly. A He-Ne laser (CNI Laser, Changchun, China, 633 nm, 5 mW) beam with constant intensity was concentrically focused on to the Cr/Au layer with beam size around 100 μm in radius as a probe beam. The intensity of reflected probe beam was therefore modulated by the temperature at Au surface. A photo detector captured the reflected probe beam, and the signal was sent to a lock-in amplifier (Stanford Research Systems, Sunnyvale, CA, USA, SR850) to extract the intensity oscillation at frequency ω. The thermal impedance of the sample caused a phase lag of the temperature oscillation compared with the heating signal. Therefore, by analyzing the phase lags according to modulation frequencies, thermal properties of the sample could be determined.
The conduction of heat within the samples can be simplified as one-dimensional heat transfer, since the heating area on the Cr/Au surface was much larger than the probe beam size and penetration depth of the heat wave. Therefore, a three layer 1-D transient heat conduction model was constructed to obtain the thermal properties according to the sample structure in Figure 2b. The governing equation [26] and their boundary conditions are The sample was heated by a diode laser (RPMC, O'Fallen, MO, USA, LDX-3315-808 with nominal wavelength of 808 nm and maximum output power~1 W) with intensity sinusoidally modulated at frequency ω. Taking into account the factors of thermal penetration depth and signal to noise ratio, the modulation frequency ω was set within 3000-6000 Hz range and controlled by a function generator. Figure 2b shows the sample configuration for thermal characterization. A piece of glass was sequentially deposited with 10 nm chromium (Cr) as adhesion promoter and 100 nm gold (Au) for its high thermo-reflectance coefficient at the probe laser wavelength (632.8 nm). Then a five-micron thickness of copper was deposited onto the Au side of the glass wafer by thermal evaporation. The CNT array on the silicon substrate was adhered to the Cu side of the glass wafer with a controlled pressure by a load cell.

Measurement Principle
The heating laser beam passed through the glass plate and was focused onto the Cr/Au layer with beam size around 1 mm × 2 mm as shown in Figure 2b. The oscillating heat flux propagated through the sample causing temperature oscillation at the Cr/Au surface at same frequency. Due to the thermo-reflectance effect, the reflectivity of Au surface oscillates accordingly. A He-Ne laser (CNI Laser, Changchun, China, 633 nm, 5 mW) beam with constant intensity was concentrically focused on to the Cr/Au layer with beam size around 100 µm in radius as a probe beam. The intensity of reflected probe beam was therefore modulated by the temperature at Au surface. A photo detector captured the reflected probe beam, and the signal was sent to a lock-in amplifier (Stanford Research Systems, Sunnyvale, CA, USA, SR850) to extract the intensity oscillation at frequency ω. The thermal impedance of the sample caused a phase lag of the temperature oscillation compared with the heating signal. Therefore, by analyzing the phase lags according to modulation frequencies, thermal properties of the sample could be determined.
The conduction of heat within the samples can be simplified as one-dimensional heat transfer, since the heating area on the Cr/Au surface was much larger than the probe beam size and penetration depth of the heat wave. Therefore, a three layer 1-D transient heat conduction model was constructed to obtain the thermal properties according to the sample structure in Figure 2b. The governing equation [26] and their boundary conditions are where: j represents the j th layer (1 = glass, 2 = copper, 3 = CNTs, 4 = silicon), α is the thermal diffusivity, T is the temperature, k is cross-plane effective thermal conductivity, ω is the frequency of pump laser, h is the interface thermal conductance.

Results and Discussion
The thermal circuit of the system is shown in Figure 3a. The heat flux from the laser can be divided into two components, a steady state part and an oscillatory or AC part given as Qe −iωt . The phase lag of the temperature oscillation at the Au/Cr-coated surface of the glass is analytically solved as a function of the driving frequency to fit with the measured phase response. The contact conductance between Cr/Au coated glass and the Cu film is set to be 10 9 W/m 2 ·K according to the measured metal/metal thermal contact conductance [27]. The penetration depth of a thermal wave in CNT is about a few hundred microns at our measurement frequency domain. The contact conductance between CNT arrays and the silicon substance is set to be 10 6 W/m 2 ·K according to previous reports [15]. The volumetric heat capacity of the CNT arrays, C CNTs , is equal to the mass density times the heat capacity of the individual MWCNT, 700 J/kg·K [28].
The measured phase responses (various points) of the samples with 500 µm high CNT arrays versus excitation frequency are shown in Figure 3b. Five hundred phase data are obtained for each frequency point, and the error bar is the standard deviation of these data. The best-fit solutions are calculated by MATLAB models. The experimental results are then fitted to theoretical model (solid lines in Figure 3b) using a best fit scenario to extract the contact thermal conductance at Cu/CNT arrays interface (h Cu-CNTs ) and the effective thermal conductivity of CNT arrays (k CNTs ). The error bars of h Cu-CNTs and k CNTs came from the fitting of the experimental data varying according to the standard deviation of the measurements (the error bar in Figure 3b). The fitted value of k CNTs is around 18 ± 6 W/m·K. Considering an array volume fraction of 1.8% of the MWCNTs, the effective thermal conductivity of the MWCNT array qualitatively matches with the previous measurement of an individual MWCNT, 650-3000 W/mK [13,29]. The thermal conductance at interface for various contact force are listed in Table 1, and plotted in Figure 3c which shows three distinct stages along the loading process. In the initial stage at pressure below 0.1 MPa, h Cu-CNTs increases slowly with the contact force. Then as contact pressure keeps increasing, there is a sharp rise in h Cu-CNTs . In the final plateau, contact pressure has almost no influence on h Cu-CNTs .   The fact that the thermal contact conductance has a strong dependence on contact force reveals that the morphology and the roughness at the contact surfaces impair the effective contact between CNT arrays and target surfaces significantly. The top surface of CNT array is examined under an AFM scanner before and after compression testing with 0.5 MPa pressure, and a decrease of the arithmetical mean roughness (Ra) from 197 to 136 nm is observed (Figure 4a,b). If considering that the deformation of the top of the CNT is not completely plastically deformed, the actual roughness will be lower in the loaded state. The Ra roughness of the evaporated Cu top surface is 5.67 nm (Figure 4c). Figure 1b shows that on the top surface of CNT arrays, the nanotubes form an entangling surface layer like a canopy as a result of van der Waals interactions. As depicted in Figure 5a, a CNT that is directly facing a cavity (shown in red) cannot make contact due to restriction force from adjacent tubes (shown in blue). And those tubes that are not in direct contact to the mating surfaces cannot participate in heat conduction. Hence, the CNT/Cu interface shows a poor thermal contact at the beginning stage.  The fact that the thermal contact conductance has a strong dependence on contact force reveals that the morphology and the roughness at the contact surfaces impair the effective contact between CNT arrays and target surfaces significantly. The top surface of CNT array is examined under an AFM scanner before and after compression testing with 0.5 MPa pressure, and a decrease of the arithmetical mean roughness (Ra) from 197 to 136 nm is observed (Figure 4a,b). If considering that the deformation of the top of the CNT is not completely plastically deformed, the actual roughness will be lower in the loaded state. The Ra roughness of the evaporated Cu top surface is 5.67 nm (Figure 4c). Figure 1b shows that on the top surface of CNT arrays, the nanotubes form an entangling surface layer like a canopy as a result of van der Waals interactions. As depicted in Figure 5a, a CNT that is directly facing a cavity (shown in red) cannot make contact due to restriction force from adjacent tubes (shown  The slowly increased thermal contact at the initial stage distinguishes CNT/Cu interfaces from general dry contact surfaces as they usually experience immediate increase with contact force. The behavior is due to the unique mechanical response of CNT arrays under pressure. Figure 3d shows the stress (the applied force divided by the array's area) versus strain (the compressed distance relative to the array's thickness) curves for the CNT arrays under compression. The compression process is generally including an initial elastic region, a buckling region marked by a plateau and a final densification, which is consistent with previous research [19]. SEM images (Figure 5e-h) illustrate that CNT arrays form sequential buckling-like folds, which emanates from the bottom and propagates toward the top. The average buckling wavelength is around 2 μm. Previous study has revealed that the sequence of bottom-to-top buckling was driven by the relative local density [30]. As can be evaluated from the level of the stresses, the slowly increasing stage shown in Figure 3c corresponds to the buckling region in Figure 3d. As can be seen, the pressure mainly contributes to the buckling rather than the deformation of the top surface of CNT arrays at this stage as illustrated in Figure 5a,b and therefore, does not improve the thermal contact at interface significantly.

Height of CNT Array Parameters Values
The buckling process ends roughly at 0.1 MPa stress level (Figure 3d), and a sharp increase of the thermal conductance at CNT/Cu interface is observed simultaneously (Figure 3c), since the top  The slowly increased thermal contact at the initial stage distinguishes CNT/Cu interfaces from general dry contact surfaces as they usually experience immediate increase with contact force. The behavior is due to the unique mechanical response of CNT arrays under pressure. Figure 3d shows the stress (the applied force divided by the array's area) versus strain (the compressed distance relative to the array's thickness) curves for the CNT arrays under compression. The compression process is generally including an initial elastic region, a buckling region marked by a plateau and a final densification, which is consistent with previous research [19]. SEM images (Figure 5e-h) illustrate that CNT arrays form sequential buckling-like folds, which emanates from the bottom and propagates toward the top. The average buckling wavelength is around 2 μm. Previous study has revealed that the sequence of bottom-to-top buckling was driven by the relative local density [30]. As can be evaluated from the level of the stresses, the slowly increasing stage shown in Figure 3c corresponds to the buckling region in Figure 3d. As can be seen, the pressure mainly contributes to the buckling rather than the deformation of the top surface of CNT arrays at this stage as illustrated in Figure 5a,b and therefore, does not improve the thermal contact at interface significantly.
The buckling process ends roughly at 0.1 MPa stress level (Figure 3d), and a sharp increase of the thermal conductance at CNT/Cu interface is observed simultaneously (Figure 3c), since the top The slowly increased thermal contact at the initial stage distinguishes CNT/Cu interfaces from general dry contact surfaces as they usually experience immediate increase with contact force. The behavior is due to the unique mechanical response of CNT arrays under pressure. Figure 3d shows the stress (the applied force divided by the array's area) versus strain (the compressed distance relative to the array's thickness) curves for the CNT arrays under compression. The compression process is generally including an initial elastic region, a buckling region marked by a plateau and a final densification, which is consistent with previous research [19]. SEM images (Figure 5e-h) illustrate that CNT arrays form sequential buckling-like folds, which emanates from the bottom and propagates toward the top. The average buckling wavelength is around 2 µm. Previous study has revealed that the sequence of bottom-to-top buckling was driven by the relative local density [30]. As can be evaluated from the level of the stresses, the slowly increasing stage shown in Figure 3c corresponds to the buckling region in Figure 3d. As can be seen, the pressure mainly contributes to the buckling rather than the deformation of the top surface of CNT arrays at this stage as illustrated in Figure 5a,b and therefore, does not improve the thermal contact at interface significantly.
The buckling process ends roughly at 0.1 MPa stress level (Figure 3d), and a sharp increase of the thermal conductance at CNT/Cu interface is observed simultaneously (Figure 3c), since the top surface of the CNT array starts to experience large deformation and comply with the roughness at interface (Figure 5c,d). CNT arrays with heights of 200 µm and 500 µm have shown a similar surging trend. However, for 500 µm CNT array, the pressure needed to complete the buckling process would be larger than 200 µm one, as shown in the stress-strain curve. In other words, longer CNT arrays require a higher pressure to enter the stage of rapid rise. In the final plateau, the value of h Cu-CNTs tends to be stable owing to the fact that all the deformations have been completed in this phase. Therefore, the pressure at the inflection point of the second and the third stage may be considered to be an optimum packaging pressure.

Conclusions
In this work, we investigated the effect of contact pressure on the performance of carbon nanotube arrays thermal interface material. CNT arrays with two different heights were both measured for contact thermal conductance by phase sensitive transient thermo-reflectance method under different loads. The entanglement of the upper surface of the CNT array weakens its contact with the target surface, which can be notably alleviated by raising the contact pressure. In addition, the experimental results indicate that the buckling of the CNT arrays defers the improvement of thermal contact at interface with contact pressure, and the deformation of the upper surface of CNT arrays mainly occurred at the end of the buckling process. As the contact force increases from 0.1 to 0.15 MPa, h Cu-CNTs enhances sharply. Worth mentioning, however, is that h Cu-CNTs tends to level off after 0.15 MPa, which should be the optimal pressure applied during the packaging of the electronic components for the studied CNT arrays. However, it should be noted that the height and density of the CNT arrays could affect their mechanical response under compression significantly, and thus the optimal packaging pressure is sensitive to the arrays that are in use. Moreover, the roughness of target surface is also an important factor at thermal interface, thus the effect of contact pressure of a thermal interface with various roughness should also be studied carefully.