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RETRACTED: Thermal transport across graphene-mediated multilayer tungsten nanostructures
International Journal of Heat and Mass Transfer 147 (2020) 118950
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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Thermal transport across graphene-mediated multilayer tungsten nanostructures Wenlong Bao a, Zhaoliang Wang a,⇑, Jie Zhu b a b
Thermal Engineering and Power Department, China University of Petroleum, Qingdao 266580, China Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education Dalian University of Technology, Dalian 116024, China
a r t i c l e
i n f o
Article history: Received 5 July 2019 Received in revised form 20 September 2019 Accepted 23 October 2019
Keywords: Two-color femtosecond laser pump-probe Interfacial thermal resistance Thermal conductivity Inelastic scattering
a b s t r a c t The thermal conductivity of monolayer graphene/b-phase tungsten (b-W) periodic stack nanostructure and the interfacial thermal resistance induced by graphene have been measured by a modified twocolor femtosecond laser pump-probe technique. The thickness of b-W films is 15, 30, 40 nm respectively, and the total thickness of periodic stack nanostructures is about 120 nm ignoring the thickness of graphene. The cross-plane thermal conductivity (k) of b-W film is determined as 7.58 W/m K which is two orders of magnitude smaller than that of a-phase bulk tungsten. The small value is attributed to the vacancies in b-W and the small grain size of b-W, which can suppress the mean free path of hot carriers. The cross-plane thermal conductivity of periodic stack nanostructure is smaller than the value of pure W film and gradually decreases with the increasing number of graphene layers. The interfacial thermal resistance between the monolayer graphene and the tungsten films ranges from 4 109 to 8.15 109 m2 K/W. The results predicted by the diffuse mismatch model are smaller than the experimental results, indicating that the phonon inelastic scattering plays an important role in the heat transport of W/graphene periodic stack nanostructure. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Graphene, a material with high electronic mobility [1–3] and thermal conductivity [4–8] has attracted great attention in the past few years. Owing to these special properties, graphene has been applied in various fields, such as phase change memory (PCM), radiation tolerance and so on. W/graphene structure has an important application in PCM. Generally, PCM is an information storage device that relies on the reversible phase transition of chalcogenide alloys between low-resistance crystalline and high-resistance amorphous phases. The energy efficiency of PCM devices can be improved by placing a single layer graphene at the interface between the phase-change material and the bottom electrode (W) heater [9]. The generated heat inside the active PCM volume can be confined with the assistance of the additional graphene interfacial thermal resistance (ITR). In addition, graphene could further enhance the PCM endurance by limiting atomic migration or material segregation at the bottom electrode interface [10]. Moreover, owing to the impermeability of graphene to helium gas [11] and its ability of absorbing the nearby crystalline defects [12], graphene has been considered as a promising material in ⇑ Corresponding author. E-mail address: [email protected] (Z. Wang). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118950 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
retarding the radiation damage. Tungsten (W) performs well under extreme conditions such as strong radiation and high temperature, and thus, it is considered to be a candidate for the plasma orientation component of the fusion reactor [13–15]. W/graphene periodic stack structures have been used to retard the radiation damage owing to these characteristics of W and graphene. As an antiradiation material, it should have significant radiation tolerance. Meanwhile, high thermal conductivity is necessary for prompt removal of heat from the core during nuclear reaction. Hence, thermal conductivity is also an important consideration for antiradiation materials and deserves further investigation [16]. Although there are some reports on the radiation tolerance ability of W/graphene periodic stack structures [17], the thermal transport mechanism of W/graphene periodic stack structures is rarely reported. Up to now, various measurement techniques have been developed to determine the thermal conductivity and ITR of nanomaterials and nanostructures [18], such as the 3x method [19], the Ttype method [20] and the transient thermoreflectance (TTR) methods including the frequency-domain thermoreflectance (FDTR) method [21,22] and the time-domain thermoreflectance (TDTR) method [23–25]. Chen et al. [19] measured the ITR between graphene and SiO2 which ranges from 5.6 109 to 1.2 108 m2 K/ W at room temperature by a differential 3x method. Mak et al.
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Nomenclature c d f H k Mi Qprobe Qpump R Rpump Rprobe Sx
vL vT
Y
specific heat capacity, J/m3 thickness of the materials, m heat flow, W/m2 response function of the sample in the frequency domain cross-plane thermal conductivity, W/m K transfer matrix single pulse energy of probe laser, J single pulse energy of pump laser, J thermal resistance, m2 K/W radius of pump laser, m radius of probe laser, m signal sensitivity the longitudinal wave velocity, m/s the transverse wave velocity, m/s lock-in amplifier signal
Greek letters b photothermal reflection coefficient, K1 b-W b-phase tungsten
[25] measured the ITR between the monolayer and multilayer graphene deposited on SiO2 substrates with an average value of 2.0 108 m2 K/W by an ultrafast optical pump pulse technique. Han et al. [21] reported the ITR between b-W and few-layered graphene as a maximum value of 1.2 108 m2 K/W. Koh et al. [26] reported the thermal conductance of 25 MW/m2 K for Au/Ti/graphene/SiO2 multilayer structure (the number of the graphene layers 1 n 10) by TDTR at room temperature, which is about a quarter of the thermal conductance of a Au/Ti/SiO2 interface. Guzman et al. [27] employed TDTR method on Al/graphene/SiO2 structures and the thermal conductance ranges from 15 to 60 MW/m2 K, which is about a half or a quarter of Al/SiO2 reference values. In most cases, the measured thermal transport across isolated interface between graphene and substrate is mainly attributed to phonon inelastic scattering, the surface morphology and significant mismatch of phonon spectrum [19,21,25,26] while the thermal transport in multilayer nanostructures may origin from other channels such as coherent and incoherent phonon scattering. In this paper, the thermal transport mechanism of W/graphene periodic stack nanostructures is investigated by a modified twocolor femtosecond laser pump-probe technique and the phonon dynamics. Firstly, a two-color femtosecond laser pump-probe system is modified and the signal sensitivity analysis is conducted. Secondly, the cross-plane thermal conductivity and ITR are measured for monolayer graphene/b-phase tungsten (b-W) periodic stack nanostructures with different layer number. Thirdly, the influence of coherent and incoherent phonon scattering on thermal transport is introduced to explain the suppressed cross-plane thermal conductivity of periodic stack nanostructures. Finally, the interfacial thermal resistance is predicted by the modified diffusive mismatch model (DMM), and the interfacial thermal transport is expressed by inelastic scattering.
2. Experiment condition and thermal modeling 2.1. Modified two-color femtosecond laser pump-probe technique The thermal transport mechanism of W/graphene periodic stack nanostructure is investigated by a modified two-color femtosecond laser pump-probe technique. This technology uses a pulsed laser to
D
rr rz h
x0 xs q s
thickness, m in-plane thermal conductivity, W/m K cross-plane thermal conductivity, W/m K temperature, K system modulation frequency, Hz laser pulse repetition frequency, Hz density, kg/m3 delay time, s
Subscripts 1 material 1 (tungsten) 2 material 2 (graphene) B lower surface of the structure j the jth polarization r in-plane direction T upper surface of the structure W tungsten z cross-plane direction
heat a metal sensing layer and monitor the surface temperature. Different from the way that the included angle between the pump and probe beams is usually set to 60° in a single-color system or 90° in a two-color system [28–30], both the pump and probe beams are collinearly irradiated on the sample at near-normal incidence. TDTR method is widely used to measure the thermal properties of bulk materials and nano-films [31,32]. In Fig. 1, the modified two-color femtosecond laser pump-probe system is based on a pulsed Ti: Sapphire which emits a train of 100 fs pulses at a repetition of 80 MHz. The center wavelength is 800 nm. Laser first passes through the optical isolator, and subsequently is divided into a pump laser and a probe laser via a 1/2 waveplate and a polarizing beam-splitter. The 1/2 waveplate can adjust the polarization direction of the linearly polarized laser, and the polarizing beam-splitter can separate the horizontally polarized and vertically polarized parts of the pulsed laser. The horizontally polarized laser can pass completely through the polarizing beamsplitter while the vertical polarized laser is completely reflected. A vertically polarized laser and a horizontally polarized laser are used as the pump laser and the probe laser, respectively. The pump laser passes a bismuth triborate (BIBO) crystal where it is frequency-doubled to 400 nm and then passes through an electro-optic modulator (EOM) where the laser intensity is loaded with a signal with a specific waveform. Pump laser at 800 nm can be completely filtered out by using the red filter. The two-color optical system can reduce the impact of the pump laser in the detection signal as much as possible. The probe laser passes through a mechanical delay stage that controls the time interval between the pump laser and the probe laser, thereby providing the resolution of the experimental system in the time domain. The pump beam and the probe beam are combined by a cold mirror, then they are focused on the sample surface by a 10 optical objective. The 1/e2 diameters of pump and probe beams are 40 lm and 20 lm, respectively. The reflected laser is detected by a high speed PIN photodiode with a rise time of 1 ns. Then, the effective signal is extracted by a radio-frequency lock-in amplifier. In addition, a blue filter is placed in front of the detector to eliminate blue light that scatters off the sample. A removable mirror can be placed in the probe path to reflect part of the light into a CCD camera, which can be used to view the sample in detail and accomplish the visualization of pump and probe spots.
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Fig. 1. An optical path schematic diagram of the two-color femtosecond laser pump-probe technique.
2.2. Thermal transport modeling
where RI is the ITR. Mathematically, multiple layers are handled by multiplying the matrices for individual layers together [33]:
Theoretically, the data detected by the lock-in amplifier can be expressed as [33]:
Zðx0 Þ ¼
1 bQ pump Q probe X
T2
Hðx0 þ mxs Þeimxs s
ð1Þ
m¼1
where Qpump and Qprobe are the single pulse energy of pump laser and probe laser respectively. T is the time interval between adjacent pulses, b is the photothermal reflection coefficient, H is the response function of the sample in the frequency domain, x0 and xs are the modulation frequency and repetition frequency of the pump laser, respectively. s is the delay time of the probe laser. The frequency response H(x) can be expressed as [33]:
HðxÞ ¼
1 2p
" 2 2 # þ1 k ðRpump þ R2probe Þ D dk kð Þexp C 8 0
Z
ð2Þ
where Rpump and Rprobe are the spot radius of the pump laser and the probe laser on the sample surface respectively. The coefficient –D/C can be calculated by the transfer matrix method. Transfer matrix method is used to calculate the heat transport process in multiple-layers sample. For a single layer structure in a multilayer parallel structure, the internal three-dimensional heat transport can be expressed in the frequency domain as [34]:
hB
"
¼
fB
sinhðqdÞ rz q
coshðqdÞ
rz qsinhðqdÞ coshðqdÞ
#
hT fT
ð3Þ
where h and f are the temperature and heat flow respectively. The subscripts T and B represent the upper and bottom surfaces of the structure respectively. d and rz are the thickness and the crossplane thermal conductivity, q2 can be expressed as:
q2 ¼
rr k2 þ qcix rz
ð4Þ
where rr and rz are the in-plane and cross-plane thermal conductivity, q and c are density and specific heat capacity, respectively. The ITR in a multilayer parallel structure can also be expressed in the form of the transfer formula:
hB fB
¼
1 RI 0
1
hT fT
ð5Þ
hB fB
¼ ðM n Mi Þ
hT
fT
¼
A
B
C
D
hT fT
ð6Þ
where Mi is the transfer matrix of the ith layer structure or interface. Under normal conditions, the heat flux of bottom surface fB equals 0. Since the substrate is usually thermally semi-infinite, the relationship between the temperature and heat flux of upper surface is given as follows [34].
hT D ¼ C fT
ð7Þ
The unknown thermal property parameters can be extracted by fitting the TDTR signal and theoretical model based on transform matrix method [34]. Finally, the cross-plane thermal conductivity (k) of W film, ITR of W/graphene interface and the variation of thermal conductivity with graphene layer number can be simultaneously determined. 2.3. Sample preparation In this paper, the samples are composed of the transferred graphene (trG) and deposited W films. The process includes sputtering tungsten and transferring graphene which is a periodic procedure. The W films are firstly sputtered on a silicon (Si) substrate by ultrahigh vacuum magnetron sputtering system (ULVAC, ACS-4000-C4) at room temperature. Then monolayer graphene is transferred onto the surface of the W films. By repeating the above process, the W/ trG multilayer film is obtained, as shown in Fig. 2. Monolayer graphene films are grown on one side of Cu foils by CVD (chemical vapor deposition). The PMMA (polymethyl methacrylate) layer is spin-coated on both sides of Cu foils and the graphene on the Cu foils is etched by oxygen plasma. Next, the Cu foil is etched by FeCl3 solution. The obtained PMMA/graphene which is floated on the surface of the FeCl3 solution is washed by deionized water. The cleaned PMMA/graphene is transferred onto the surface of W film. At last, the PMMA layer is dissolved by acetone and the W/trG multilayer films are obtained. The SEM imagines of multilayer nanostructures are shown in Fig. 3. Three graphene/W multilayer nanostructures with different thickness of W films are labeled as A, B, C. The period-thicknesses
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Fig. 2. Schematic diagram of tungsten–graphene multilayer system fabrication.
100 mm
100 mm
100 mm
100 mm
Fig. 3. SEM images of as-deposited multilayer nanostructures.
of W films are measured by SEM as 15, 30 and 40 nm respectively. Regardless of the graphene thickness, the total thickness of W/graphene periodic stack structure is about 120 nm. In order to study the influence of graphene interfaces on thermal transport, a pure W film with the thickness of 120 nm is prepared for comparison, which is labeled as D. 2.4. Signal sensitivity analysis It is important to quantify the sensitivity of the experiment to the target parameters. The sensitivity to the parameter x is defined as:
Sx ¼
dlnðYÞ dlnðxÞ
ð8Þ
where the sensitivity coefficient Sx represents the sensitivity of the lock-in amplifier signal Y to the unknown parameter x. Sensitivity analysis is necessary to obtain accurate results. The fitting error will be much smaller under higher sensitivity. In order to improve the sensitivity of the target parameters, the sample D is used as an example to analyze the factors that may affect the sensitivity during
the experiment which may be helpful to the preparation of the sample and the selection of experimental conditions. Fig. 4(a) shows the influence of the modulation frequency on the sensitivity of the phase signal. The modulation frequency of the pump laser in the femtosecond laser pump-probe experiment is usually set at 1–10 MHz. As shown in the figure, the sensitivity has the maximum value at 5 MHz, and the PIN photodiode used in Fig. 1 has the highest response signal at 5 MHz. Thus 5 MHz is used as the modulation frequency of the pump laser. Fig. 4(b) shows the influence of the thickness of Al transducer layer on the sensitivity of the phase signal. The sensitivity of thermal conductivity decreases with the increasing thickness of Al transducer. However, thicker Al layer is preferred to ensure that the Al layer completely absorbs the energy of the pump laser. Therefore, a 70 nm-thick Al transducer is selected in this work. Fig. 4(c) shows the sensitivity of the phase signal, as a function of pump-probe delay time, to the thermal conductivity of the multilayer structures and the top (RAl/W) and bottom (RW/Si) ITRs at the selected pump modulation frequency. As the figure shows, the model is an order of magnitude more sensitive to the thermal conductivity than to the interfacial resistance, which indicate the thermal conductivity has a greater influence on the phase signal.
W. Bao et al. / International Journal of Heat and Mass Transfer 147 (2020) 118950
5
Fig. 4. Influence of physical properties on phase signal sensitivity.
3. Result and analysis 3.1. Results measured by modified TDTR method Fig. 5 shows the experimental data of phase at different time and the optimal fitting curve. The parameters used in the multilayer thermal model are listed in Table 1. The thermal conductivity of Si is measured by a separate sample (Al/Si) and the thermal conductivity of Al is the bulk thermal conductivity. The thermal conductivities of sample A, B, C and D are measured as 1.7, 2.14, 2.49, 7.58 W/m K, respectively. The dotted line in Fig. 5 presents the influence of the altered thermal conductivity (±20%) on the optimal fitting curve. According to the experimental results, the thermal conductivity of W film with thickness of 120 nm is only 7.58 W/m K which is remarkably smaller than that of bulk a-phase W (174 W/m K). The reason is that the W atoms are stacked together by vacuum magnetron sputtering and the nanostructure is not annealed in order to prevent the chemical reaction between W and graphene. Therefore, the b-phase W appears. In Fig. 6, it could be verified that there are a large number of vacancies, which may trigger the scattering of electrons and phonons with these vacancies. The energy carriers scattered at the grain boundaries and within the grains may hinder thermal transport through the nanostructure and this hindrance is directly related to the grain size which locally reduces the mean free path (MFP) of these energy carriers and hence the thermal conductivity decreases. Also, Hao et al. [38] reported that the grain size in a-W is much larger than b-W (by a factor of 2–4). Grain boundary density is closely related to grain size. The smaller
Fig. 5. Experiment data and the best-fitting curves.
the grain size is, the larger the grain boundary density is. And large grain boundary density may lead to a decrease in the MFP of energy carriers, resulting in a smaller thermal conductivity of b-W. The variation of thermal conductivity of graphene/W periodic stack nanostructure with the number of graphene layers is shown in Fig. 7. The uncertainty in the measured thermal conductivity is mainly attributed to the experimental noise in the phase data,
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Table 1 The parameters in the multilayer thermal model. Materials
Thickness (nm)
Volumetric heat capacity (J/m3 K)
Thermal conductivity (W/m K)
Al W [35] Graphene [4–8,36] Si [37]
70 – 0.3
2.42 106 2.55 106 1.38 106
237 – 100–3000
–
1.6 106
142
where d and k are the total thickness and the thermal conductivity of the W/graphene stack nanostructure, dW and kb-W are the thickness and thermal conductivity of b-W film, dgraphene and kgraphene are the thickness and thermal conductivity of monolayer graphene, respectively. n is the number of graphene layers. RW/graphene is the ITR of the monolayer graphene/W interface. Based on the thermal transport model by Eqs. (1)–(7), it is rather difficult to isolate the intrinsic thermal conductivity of W films with different thickness from the effective thermal conductivity of the W/graphene stack nanostructure. Thus, the thermal conductivity of the other W films is approximated by the thermal conductivity of 120 nm W film. Therefore, the ITR calculated by Eq. (9) is slightly larger than the true value, but these values are on the same order. As is shown in Fig. 8, the value of RW/graphene can be obtained and its value varies from 4 109 to 8.15 109 m2 K/W. The measured ITR is similar to that measured by Han et al., which is 0.1–11.9 109m2 K/W [21]. The total ITR (Rtotal) induced by graphene can be calculated as [24].
Rtotal ¼ 2nRW=graphene Fig. 6. SEM image of W films at different length scale.
uncertainty in the controlled parameters and the systematic errors [39]. Before the experiment, an Al/Si standard sample is used to correct the system, so we do not consider the effect of any systematic errors. The method reported by Schmidt et al. is used to determine the uncertainty [39], and the error bar is shown in Fig. 7. When the number of graphene layers is small, the thermal conductivity of W/graphene stacks nanostructure decreases sharply with the increase of the number of graphene layers while the thermal conductivity levels off with larger number of graphene layers. The factor leading to this result may be that the ITR induced by graphene layer hinders the thermal transport through the multilayer nanostructure more significantly when the number of graphene layers is small. The ITR between monolayer graphene and W film can be calculated by Eq. (9) [40].
dgraphene d dW ¼ ðn þ 1Þ þ 2nRW=graphene þ n k kb - W kgraphene
ð9Þ
Fig. 7. Dependence of thermal conductivity with number of graphene layers.
ð10Þ
Based on Eq. (10), Rtotal of sample A (n = 7), B (n = 3) and C (n = 2) can be obtained as 5.6 108, 4.1 108 and 3.3 108 m2 K/W, respectively. This indicates that ITR induced by graphene indeed hinders thermal transport. As phonon boundary scattering plays an important role, it leads to the reduced thermal conductivity of W/graphene stack structure with the increasing number of graphene layers. In such monolayer graphene/W multilayer nanostructures, the phonon transport process can be described by particle-like incoherent phonons and wave-like coherent phonons. The influence of coherent and incoherent phonons on thermal conductivity is important for understanding heat conduction in multilayer nanostructures [41]. For the incoherent phonon scattering such as phonon-boundary scattering, phonon-vacancy scattering and Umklapp phonon-phonon scattering, the phonons lose their phase. Most methods of reducing thermal conductivity are realized by shortening the MFP of phonons according to incoherent scattering mechanism [42–44]. In contrast to incoherent scattering, for the coherent scattering, the phase is preserved and wave interference of phonons appears, serving as a new approach for manipulating
Fig. 8. Dependence of ITR with number of graphene layers.
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the heat flow. In order to maintain the phase of coherent phonons, phonons scatter specularly at the surface boundaries or the interface of nanostructures. Therefore, nanoscale periodicity and relatively smooth interfaces are preferred to realize the wave-like coherent phonons. The above dependence of the thermal conductivity and ITR with the number of the graphene layers is attributed to the incoherentphonon-dominated heat conduction neat the interfaces. In this incoherent regime, phonon-boundaries scattering dominates the thermal transport by dramatically suppressing the MFP of phonons. No or few phonon interferences can occur due to the limited number of interfaces [45]. In addition, the phonon dispersion forms mini-band owing to band folding along the cross-plane axis, which decreases the overall group velocity of phonons of high-frequency phonon modes [46–48]. Thermal conductivity decreases with increasing interface scattering and decreasing group velocity of phonons. In addition, as is shown in Fig. 8, the value of RW/graphene for sample A (n = 7) is determined as 4 109 m2 K/W, which is much smaller than 6.83 109 m2 K/W for sample B and 8.25 109 m2 K/W for sample C. The deviations are attributed to the enhancement of inelastic scattering at the interfaces with the increasing interface density. The inelastic scattering provides extra channels for phonons to transport across the interface [49]. Moreover, the measured values of ITR are relatively smaller compared with the previously reported values of metal/graphene interfaces. Koh et al. [26] reported the thermal conductance of Au/Ti/graphene/SiO2 interfaces (graphene layers 1 6 n 6 10) is 25 MW/m2 K, which is about a quarter of the thermal conductance of Au/Ti/ SiO2 interface. This result is caused by the interfacial thermal resistance of Au/Ti/graphene and graphene/SiO2. Huang et al. [23] compared the interfacial thermal conductance of Al/transferred graphene (trG)/Cu and Al/grown graphene (grG)/Cu. In the experiment, the thermal conductance of Al/rG/Cu interfaces is about 20 MW/m2 K, which is about 35% lower than that of Al/grG/Cu interfaces (31 MW/m2 K). These results show that trG and Cu have a larger degree of lattice mismatch and phonons are the main heat carries across the metal and graphene interfaces. One possible reason for the small value of ITR is that graphene structural damage provides additional channels of heat transport for electrons. The recent work by Huang et al. can explain this phenomenon. Huang et al. [24] reported the thermal conductance of Pd/transferred graphene (trG)/Pd which is prepared by either thermal evaporation or radio-frequency magnetron sputtering. The reported interfacial thermal conductances of Pd/trG/Pd interfaces are 42 MW/m2 K and 300 MW/m2 K, respectively. The enhancement of thermal conductance was attributed to an extra channel of heat transport by electrons via atomic-scale pinholes formed in the graphene during the magnetron sputtering process.
R xD;j
11!2 ¼ R xD;j 0
0
hxv 2;j D2;j ðxÞfdx R xD;j hxv 2;j D2;j ðxÞfdx 0
hxv 1;j D1;j ðxÞfdx þ
ð12Þ
In our implementation, the Debye-like dispersion relation for the tungsten is used. The density of states is given by [51]
DðxÞ ¼
x2 2p 2 v 2
ð13Þ
On the graphene side, the approach of Duda et al. [52] is employed. A two-dimensional density of states is given by
D2D ðxÞ ¼
x
2pv 2
ð14Þ
Kumatsu [53] gives the dispersion relation of the graphene acoustic branch which can predict the thermal conductivity and specific heat of graphene accurately. The dispersion relation of graphene is given as follows
x1 ¼ vL qa
ð15Þ
x2 ¼ vT qa
ð16Þ
x3 ¼ dq2a
ð17Þ
where the longitudinal wave velocity vL is 20100 m/s, the transverse wave velocity vT is 12300 m/s, d = 6.11 107 m2/s, and qa is the in-plane wave vector, qa,max = 1.55 1010 m1. The experimental results and the result predicted by DMM are shown in Fig. 9. For the convenience of the comparison with the data in the references, the vertical axis is expressed in terms of thermal conductance (ITR1). The measured interfacial thermal conductance is slightly underestimated by Eq. (11). One possible explanation for the underestimated results by DMM model is the inelastic scattering. The inelastic scattering provides extra channels for phonon to transport across the interface. Electrons and phonons in tungsten can exchange energy with phonons in graphene by inelastic scattering, which would enhance the thermal transport. Moreover, the phonons thermalized by inelastic scattering may increase the population of phonon modes with high transmissivity [49]. Another explanation is the possible damage formed in graphene during the sputtering process because of bombardment of carbon atoms by tungsten atoms. Similar damages were observed in graphene after deposition of oxides and nitrides by
3.2. ITR prediction by DMM In order to explain the experimental results, the DMM is used. The most basic assumption in the DMM is that all phonon scattering is diffuse scattering. The ITR is given by [50]
ITR ¼
" #1 3 Z xD;j 1X @f 11!2 hxv 1;j D1;j ðxÞ dx 4 j 0 @T e
ð11Þ
where j is polarization, 11!2 is the phonon transmissivity from is the reduced material 1 (tungsten) to material 2 (graphene), h Planck’s constant, x is the phonon angular frequency, v1,j is the phonon group velocity in the direction of transport, D1,j (x) is the density of states and f is the Bose-Einstein distribution function. For the DMM, the transmissivity is given by
Fig. 9. ITR1 versus the radio of Debye temperature of the metal and graphene.
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magnetron sputtering [54]. Due to the partial removal of carbon atoms, electrons can transmit directly from the top tungsten film to the bottom tungsten film, and thus the thermal resistance could be suppressed due to the additional heat transfer channels of the electrons [23,24]. All of the above factors may lead to the thermal transport underestimated by the DMM. 4. Conclusion The two-color femtosecond laser pump-probe technique is used to measure the thermal conductivity of graphene/W periodic stack nanostructures and the ITR which is induced by graphene. The interfaces induced by graphene may change the thermal conductivity of tungsten. The value of total thermal resistance caused by W/graphene interfaces is determined as 3.3 108– 5.6 108 m2 K/W. As the number of graphene layers increases, the effective thermal conductivity of the stacked nanostructure tends to decrease and the influence of incoherent phonon transport has been discussed. The DMM model is used to predict the ITR between tungsten film and graphene. Inelastic scattering is the key factor leading to a slightly underestimated value. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements We acknowledge funding supports from the National Natural Science Foundation of China under Grant No. 51876223. Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118950. References [1] Q. Zhou, J. Zheng, S. Onishi, Graphene electrostatic microphone and ultrasonic radio, Proc. Natl. Acad. Sci. U. S. A. 112 (29) (2015) 8942–8946. [2] I.N. Kholmanov, C.W. Magnuson, A.E. Aliev, Improved electrical conductivity of graphene films integrated with metal nanowires, Nano Lett. 12 (11) (2012) 5679–5683. [3] Y. Fan, L. Wang, J. Li, Preparation and electrical properties of graphene nanosheet/Al2O3 composites, Carbon 48 (6) (2010) 1743–1749. [4] G. Xin, T. Yao, H. Sun, Highly thermally conductive and mechanically strong graphene fibers, Science 46 (50) (2016) 1083–1087. [5] A.A. Balandin, S. Ghosh, W.Z. Bao, et al., Superior thermal conductivity of single-layer graphene, Nano Lett. 8 (3) (2008) 902–907. [6] W. Jang, Z. Chen, W. Bao, Thickness-dependent thermal conductivity of encased graphene and ultrathin graphite, Nano Lett. 10 (10) (2010) 3909– 3913. [7] A.A. Balandin, Nanophononics: phonon engineering in nanostructures and nanodevices, J. Nanosci. Nanotechnol. 5 (7) (2005) 1015–1022. [8] A.A. Balandin, D.L. Nika, Phononics in low-dimensional materials, Mater. Today 15 (6) (2012) 266–275. [9] L. Chen, R. Xue, S. Chen, Heat confinement of phase-change memory using graphene, IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, 29th May–1st Jun, 2017, San Diego, CA, USA, 2017. [10] C. Ahn, S.W. Fong, Y. Kim, et al., Energy-efficient phase-change memory with graphene as a thermal barrier, Nano Lett. 15 (10) (2015) 6809–6814. [11] J.S. Bunch, S.S. Verbridge, J.S. Alden, et al., Impermeable atomic membranes from graphene sheets, Nano Lett. 8 (8) (2008) 2458–2462. [12] Y. Kim, J. Baek, S. Kim, et al., Radiation resistant vanadium-graphene nanolayered composite, Sci. Rep. 6 (2016) 24785. [13] A. Hasegawa, M. Fukuda, K. Yabuuchi, et al., Neutron irradiation effects on the microstructural development of tungsten and tungsten alloys, J. Nucl. Mater. 471 (2016) 175–183. [14] Y. Gao, T. Yang, J. Xue, et al., Radiation tolerance of Cu/W multilayered nanocomposites, J. Nucl. Mater. 413 (1) (2011) 11–15. [15] M. Callisti, M. Karlik, T. Polcar, Bubbles formation in helium ion irradiated Cu/ W multilayer nanocomposites: effects on structure and mechanical properties, J. Nucl. Mater. 473 (2016) 18–27.
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Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Thermal transport across graphene-mediated multilayer tungsten nanostructures Wenlong Bao a, Zhaoliang Wang a,⇑, Jie Zhu b a b
Thermal Engineering and Power Department, China University of Petroleum, Qingdao 266580, China Key Laboratory of Ocean Energy Utilization and Energy Conservation of Ministry of Education Dalian University of Technology, Dalian 116024, China
a r t i c l e
i n f o
Article history: Received 5 July 2019 Received in revised form 20 September 2019 Accepted 23 October 2019
Keywords: Two-color femtosecond laser pump-probe Interfacial thermal resistance Thermal conductivity Inelastic scattering
a b s t r a c t The thermal conductivity of monolayer graphene/b-phase tungsten (b-W) periodic stack nanostructure and the interfacial thermal resistance induced by graphene have been measured by a modified twocolor femtosecond laser pump-probe technique. The thickness of b-W films is 15, 30, 40 nm respectively, and the total thickness of periodic stack nanostructures is about 120 nm ignoring the thickness of graphene. The cross-plane thermal conductivity (k) of b-W film is determined as 7.58 W/m K which is two orders of magnitude smaller than that of a-phase bulk tungsten. The small value is attributed to the vacancies in b-W and the small grain size of b-W, which can suppress the mean free path of hot carriers. The cross-plane thermal conductivity of periodic stack nanostructure is smaller than the value of pure W film and gradually decreases with the increasing number of graphene layers. The interfacial thermal resistance between the monolayer graphene and the tungsten films ranges from 4 109 to 8.15 109 m2 K/W. The results predicted by the diffuse mismatch model are smaller than the experimental results, indicating that the phonon inelastic scattering plays an important role in the heat transport of W/graphene periodic stack nanostructure. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Graphene, a material with high electronic mobility [1–3] and thermal conductivity [4–8] has attracted great attention in the past few years. Owing to these special properties, graphene has been applied in various fields, such as phase change memory (PCM), radiation tolerance and so on. W/graphene structure has an important application in PCM. Generally, PCM is an information storage device that relies on the reversible phase transition of chalcogenide alloys between low-resistance crystalline and high-resistance amorphous phases. The energy efficiency of PCM devices can be improved by placing a single layer graphene at the interface between the phase-change material and the bottom electrode (W) heater [9]. The generated heat inside the active PCM volume can be confined with the assistance of the additional graphene interfacial thermal resistance (ITR). In addition, graphene could further enhance the PCM endurance by limiting atomic migration or material segregation at the bottom electrode interface [10]. Moreover, owing to the impermeability of graphene to helium gas [11] and its ability of absorbing the nearby crystalline defects [12], graphene has been considered as a promising material in ⇑ Corresponding author. E-mail address: [email protected] (Z. Wang). https://doi.org/10.1016/j.ijheatmasstransfer.2019.118950 0017-9310/Ó 2019 Elsevier Ltd. All rights reserved.
retarding the radiation damage. Tungsten (W) performs well under extreme conditions such as strong radiation and high temperature, and thus, it is considered to be a candidate for the plasma orientation component of the fusion reactor [13–15]. W/graphene periodic stack structures have been used to retard the radiation damage owing to these characteristics of W and graphene. As an antiradiation material, it should have significant radiation tolerance. Meanwhile, high thermal conductivity is necessary for prompt removal of heat from the core during nuclear reaction. Hence, thermal conductivity is also an important consideration for antiradiation materials and deserves further investigation [16]. Although there are some reports on the radiation tolerance ability of W/graphene periodic stack structures [17], the thermal transport mechanism of W/graphene periodic stack structures is rarely reported. Up to now, various measurement techniques have been developed to determine the thermal conductivity and ITR of nanomaterials and nanostructures [18], such as the 3x method [19], the Ttype method [20] and the transient thermoreflectance (TTR) methods including the frequency-domain thermoreflectance (FDTR) method [21,22] and the time-domain thermoreflectance (TDTR) method [23–25]. Chen et al. [19] measured the ITR between graphene and SiO2 which ranges from 5.6 109 to 1.2 108 m2 K/ W at room temperature by a differential 3x method. Mak et al.
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W. Bao et al. / International Journal of Heat and Mass Transfer 147 (2020) 118950
Nomenclature c d f H k Mi Qprobe Qpump R Rpump Rprobe Sx
vL vT
Y
specific heat capacity, J/m3 thickness of the materials, m heat flow, W/m2 response function of the sample in the frequency domain cross-plane thermal conductivity, W/m K transfer matrix single pulse energy of probe laser, J single pulse energy of pump laser, J thermal resistance, m2 K/W radius of pump laser, m radius of probe laser, m signal sensitivity the longitudinal wave velocity, m/s the transverse wave velocity, m/s lock-in amplifier signal
Greek letters b photothermal reflection coefficient, K1 b-W b-phase tungsten
[25] measured the ITR between the monolayer and multilayer graphene deposited on SiO2 substrates with an average value of 2.0 108 m2 K/W by an ultrafast optical pump pulse technique. Han et al. [21] reported the ITR between b-W and few-layered graphene as a maximum value of 1.2 108 m2 K/W. Koh et al. [26] reported the thermal conductance of 25 MW/m2 K for Au/Ti/graphene/SiO2 multilayer structure (the number of the graphene layers 1 n 10) by TDTR at room temperature, which is about a quarter of the thermal conductance of a Au/Ti/SiO2 interface. Guzman et al. [27] employed TDTR method on Al/graphene/SiO2 structures and the thermal conductance ranges from 15 to 60 MW/m2 K, which is about a half or a quarter of Al/SiO2 reference values. In most cases, the measured thermal transport across isolated interface between graphene and substrate is mainly attributed to phonon inelastic scattering, the surface morphology and significant mismatch of phonon spectrum [19,21,25,26] while the thermal transport in multilayer nanostructures may origin from other channels such as coherent and incoherent phonon scattering. In this paper, the thermal transport mechanism of W/graphene periodic stack nanostructures is investigated by a modified twocolor femtosecond laser pump-probe technique and the phonon dynamics. Firstly, a two-color femtosecond laser pump-probe system is modified and the signal sensitivity analysis is conducted. Secondly, the cross-plane thermal conductivity and ITR are measured for monolayer graphene/b-phase tungsten (b-W) periodic stack nanostructures with different layer number. Thirdly, the influence of coherent and incoherent phonon scattering on thermal transport is introduced to explain the suppressed cross-plane thermal conductivity of periodic stack nanostructures. Finally, the interfacial thermal resistance is predicted by the modified diffusive mismatch model (DMM), and the interfacial thermal transport is expressed by inelastic scattering.
2. Experiment condition and thermal modeling 2.1. Modified two-color femtosecond laser pump-probe technique The thermal transport mechanism of W/graphene periodic stack nanostructure is investigated by a modified two-color femtosecond laser pump-probe technique. This technology uses a pulsed laser to
D
rr rz h
x0 xs q s
thickness, m in-plane thermal conductivity, W/m K cross-plane thermal conductivity, W/m K temperature, K system modulation frequency, Hz laser pulse repetition frequency, Hz density, kg/m3 delay time, s
Subscripts 1 material 1 (tungsten) 2 material 2 (graphene) B lower surface of the structure j the jth polarization r in-plane direction T upper surface of the structure W tungsten z cross-plane direction
heat a metal sensing layer and monitor the surface temperature. Different from the way that the included angle between the pump and probe beams is usually set to 60° in a single-color system or 90° in a two-color system [28–30], both the pump and probe beams are collinearly irradiated on the sample at near-normal incidence. TDTR method is widely used to measure the thermal properties of bulk materials and nano-films [31,32]. In Fig. 1, the modified two-color femtosecond laser pump-probe system is based on a pulsed Ti: Sapphire which emits a train of 100 fs pulses at a repetition of 80 MHz. The center wavelength is 800 nm. Laser first passes through the optical isolator, and subsequently is divided into a pump laser and a probe laser via a 1/2 waveplate and a polarizing beam-splitter. The 1/2 waveplate can adjust the polarization direction of the linearly polarized laser, and the polarizing beam-splitter can separate the horizontally polarized and vertically polarized parts of the pulsed laser. The horizontally polarized laser can pass completely through the polarizing beamsplitter while the vertical polarized laser is completely reflected. A vertically polarized laser and a horizontally polarized laser are used as the pump laser and the probe laser, respectively. The pump laser passes a bismuth triborate (BIBO) crystal where it is frequency-doubled to 400 nm and then passes through an electro-optic modulator (EOM) where the laser intensity is loaded with a signal with a specific waveform. Pump laser at 800 nm can be completely filtered out by using the red filter. The two-color optical system can reduce the impact of the pump laser in the detection signal as much as possible. The probe laser passes through a mechanical delay stage that controls the time interval between the pump laser and the probe laser, thereby providing the resolution of the experimental system in the time domain. The pump beam and the probe beam are combined by a cold mirror, then they are focused on the sample surface by a 10 optical objective. The 1/e2 diameters of pump and probe beams are 40 lm and 20 lm, respectively. The reflected laser is detected by a high speed PIN photodiode with a rise time of 1 ns. Then, the effective signal is extracted by a radio-frequency lock-in amplifier. In addition, a blue filter is placed in front of the detector to eliminate blue light that scatters off the sample. A removable mirror can be placed in the probe path to reflect part of the light into a CCD camera, which can be used to view the sample in detail and accomplish the visualization of pump and probe spots.
3
W. Bao et al. / International Journal of Heat and Mass Transfer 147 (2020) 118950
Fig. 1. An optical path schematic diagram of the two-color femtosecond laser pump-probe technique.
2.2. Thermal transport modeling
where RI is the ITR. Mathematically, multiple layers are handled by multiplying the matrices for individual layers together [33]:
Theoretically, the data detected by the lock-in amplifier can be expressed as [33]:
Zðx0 Þ ¼
1 bQ pump Q probe X
T2
Hðx0 þ mxs Þeimxs s
ð1Þ
m¼1
where Qpump and Qprobe are the single pulse energy of pump laser and probe laser respectively. T is the time interval between adjacent pulses, b is the photothermal reflection coefficient, H is the response function of the sample in the frequency domain, x0 and xs are the modulation frequency and repetition frequency of the pump laser, respectively. s is the delay time of the probe laser. The frequency response H(x) can be expressed as [33]:
HðxÞ ¼
1 2p
" 2 2 # þ1 k ðRpump þ R2probe Þ D dk kð Þexp C 8 0
Z
ð2Þ
where Rpump and Rprobe are the spot radius of the pump laser and the probe laser on the sample surface respectively. The coefficient –D/C can be calculated by the transfer matrix method. Transfer matrix method is used to calculate the heat transport process in multiple-layers sample. For a single layer structure in a multilayer parallel structure, the internal three-dimensional heat transport can be expressed in the frequency domain as [34]:
hB
"
¼
fB
sinhðqdÞ rz q
coshðqdÞ
rz qsinhðqdÞ coshðqdÞ
#
hT fT
ð3Þ
where h and f are the temperature and heat flow respectively. The subscripts T and B represent the upper and bottom surfaces of the structure respectively. d and rz are the thickness and the crossplane thermal conductivity, q2 can be expressed as:
q2 ¼
rr k2 þ qcix rz
ð4Þ
where rr and rz are the in-plane and cross-plane thermal conductivity, q and c are density and specific heat capacity, respectively. The ITR in a multilayer parallel structure can also be expressed in the form of the transfer formula:
hB fB
¼
1 RI 0
1
hT fT
ð5Þ
hB fB
¼ ðM n Mi Þ
hT
fT
¼
A
B
C
D
hT fT
ð6Þ
where Mi is the transfer matrix of the ith layer structure or interface. Under normal conditions, the heat flux of bottom surface fB equals 0. Since the substrate is usually thermally semi-infinite, the relationship between the temperature and heat flux of upper surface is given as follows [34].
hT D ¼ C fT
ð7Þ
The unknown thermal property parameters can be extracted by fitting the TDTR signal and theoretical model based on transform matrix method [34]. Finally, the cross-plane thermal conductivity (k) of W film, ITR of W/graphene interface and the variation of thermal conductivity with graphene layer number can be simultaneously determined. 2.3. Sample preparation In this paper, the samples are composed of the transferred graphene (trG) and deposited W films. The process includes sputtering tungsten and transferring graphene which is a periodic procedure. The W films are firstly sputtered on a silicon (Si) substrate by ultrahigh vacuum magnetron sputtering system (ULVAC, ACS-4000-C4) at room temperature. Then monolayer graphene is transferred onto the surface of the W films. By repeating the above process, the W/ trG multilayer film is obtained, as shown in Fig. 2. Monolayer graphene films are grown on one side of Cu foils by CVD (chemical vapor deposition). The PMMA (polymethyl methacrylate) layer is spin-coated on both sides of Cu foils and the graphene on the Cu foils is etched by oxygen plasma. Next, the Cu foil is etched by FeCl3 solution. The obtained PMMA/graphene which is floated on the surface of the FeCl3 solution is washed by deionized water. The cleaned PMMA/graphene is transferred onto the surface of W film. At last, the PMMA layer is dissolved by acetone and the W/trG multilayer films are obtained. The SEM imagines of multilayer nanostructures are shown in Fig. 3. Three graphene/W multilayer nanostructures with different thickness of W films are labeled as A, B, C. The period-thicknesses
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W. Bao et al. / International Journal of Heat and Mass Transfer 147 (2020) 118950
Fig. 2. Schematic diagram of tungsten–graphene multilayer system fabrication.
100 mm
100 mm
100 mm
100 mm
Fig. 3. SEM images of as-deposited multilayer nanostructures.
of W films are measured by SEM as 15, 30 and 40 nm respectively. Regardless of the graphene thickness, the total thickness of W/graphene periodic stack structure is about 120 nm. In order to study the influence of graphene interfaces on thermal transport, a pure W film with the thickness of 120 nm is prepared for comparison, which is labeled as D. 2.4. Signal sensitivity analysis It is important to quantify the sensitivity of the experiment to the target parameters. The sensitivity to the parameter x is defined as:
Sx ¼
dlnðYÞ dlnðxÞ
ð8Þ
where the sensitivity coefficient Sx represents the sensitivity of the lock-in amplifier signal Y to the unknown parameter x. Sensitivity analysis is necessary to obtain accurate results. The fitting error will be much smaller under higher sensitivity. In order to improve the sensitivity of the target parameters, the sample D is used as an example to analyze the factors that may affect the sensitivity during
the experiment which may be helpful to the preparation of the sample and the selection of experimental conditions. Fig. 4(a) shows the influence of the modulation frequency on the sensitivity of the phase signal. The modulation frequency of the pump laser in the femtosecond laser pump-probe experiment is usually set at 1–10 MHz. As shown in the figure, the sensitivity has the maximum value at 5 MHz, and the PIN photodiode used in Fig. 1 has the highest response signal at 5 MHz. Thus 5 MHz is used as the modulation frequency of the pump laser. Fig. 4(b) shows the influence of the thickness of Al transducer layer on the sensitivity of the phase signal. The sensitivity of thermal conductivity decreases with the increasing thickness of Al transducer. However, thicker Al layer is preferred to ensure that the Al layer completely absorbs the energy of the pump laser. Therefore, a 70 nm-thick Al transducer is selected in this work. Fig. 4(c) shows the sensitivity of the phase signal, as a function of pump-probe delay time, to the thermal conductivity of the multilayer structures and the top (RAl/W) and bottom (RW/Si) ITRs at the selected pump modulation frequency. As the figure shows, the model is an order of magnitude more sensitive to the thermal conductivity than to the interfacial resistance, which indicate the thermal conductivity has a greater influence on the phase signal.
W. Bao et al. / International Journal of Heat and Mass Transfer 147 (2020) 118950
5
Fig. 4. Influence of physical properties on phase signal sensitivity.
3. Result and analysis 3.1. Results measured by modified TDTR method Fig. 5 shows the experimental data of phase at different time and the optimal fitting curve. The parameters used in the multilayer thermal model are listed in Table 1. The thermal conductivity of Si is measured by a separate sample (Al/Si) and the thermal conductivity of Al is the bulk thermal conductivity. The thermal conductivities of sample A, B, C and D are measured as 1.7, 2.14, 2.49, 7.58 W/m K, respectively. The dotted line in Fig. 5 presents the influence of the altered thermal conductivity (±20%) on the optimal fitting curve. According to the experimental results, the thermal conductivity of W film with thickness of 120 nm is only 7.58 W/m K which is remarkably smaller than that of bulk a-phase W (174 W/m K). The reason is that the W atoms are stacked together by vacuum magnetron sputtering and the nanostructure is not annealed in order to prevent the chemical reaction between W and graphene. Therefore, the b-phase W appears. In Fig. 6, it could be verified that there are a large number of vacancies, which may trigger the scattering of electrons and phonons with these vacancies. The energy carriers scattered at the grain boundaries and within the grains may hinder thermal transport through the nanostructure and this hindrance is directly related to the grain size which locally reduces the mean free path (MFP) of these energy carriers and hence the thermal conductivity decreases. Also, Hao et al. [38] reported that the grain size in a-W is much larger than b-W (by a factor of 2–4). Grain boundary density is closely related to grain size. The smaller
Fig. 5. Experiment data and the best-fitting curves.
the grain size is, the larger the grain boundary density is. And large grain boundary density may lead to a decrease in the MFP of energy carriers, resulting in a smaller thermal conductivity of b-W. The variation of thermal conductivity of graphene/W periodic stack nanostructure with the number of graphene layers is shown in Fig. 7. The uncertainty in the measured thermal conductivity is mainly attributed to the experimental noise in the phase data,
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W. Bao et al. / International Journal of Heat and Mass Transfer 147 (2020) 118950
Table 1 The parameters in the multilayer thermal model. Materials
Thickness (nm)
Volumetric heat capacity (J/m3 K)
Thermal conductivity (W/m K)
Al W [35] Graphene [4–8,36] Si [37]
70 – 0.3
2.42 106 2.55 106 1.38 106
237 – 100–3000
–
1.6 106
142
where d and k are the total thickness and the thermal conductivity of the W/graphene stack nanostructure, dW and kb-W are the thickness and thermal conductivity of b-W film, dgraphene and kgraphene are the thickness and thermal conductivity of monolayer graphene, respectively. n is the number of graphene layers. RW/graphene is the ITR of the monolayer graphene/W interface. Based on the thermal transport model by Eqs. (1)–(7), it is rather difficult to isolate the intrinsic thermal conductivity of W films with different thickness from the effective thermal conductivity of the W/graphene stack nanostructure. Thus, the thermal conductivity of the other W films is approximated by the thermal conductivity of 120 nm W film. Therefore, the ITR calculated by Eq. (9) is slightly larger than the true value, but these values are on the same order. As is shown in Fig. 8, the value of RW/graphene can be obtained and its value varies from 4 109 to 8.15 109 m2 K/W. The measured ITR is similar to that measured by Han et al., which is 0.1–11.9 109m2 K/W [21]. The total ITR (Rtotal) induced by graphene can be calculated as [24].
Rtotal ¼ 2nRW=graphene Fig. 6. SEM image of W films at different length scale.
uncertainty in the controlled parameters and the systematic errors [39]. Before the experiment, an Al/Si standard sample is used to correct the system, so we do not consider the effect of any systematic errors. The method reported by Schmidt et al. is used to determine the uncertainty [39], and the error bar is shown in Fig. 7. When the number of graphene layers is small, the thermal conductivity of W/graphene stacks nanostructure decreases sharply with the increase of the number of graphene layers while the thermal conductivity levels off with larger number of graphene layers. The factor leading to this result may be that the ITR induced by graphene layer hinders the thermal transport through the multilayer nanostructure more significantly when the number of graphene layers is small. The ITR between monolayer graphene and W film can be calculated by Eq. (9) [40].
dgraphene d dW ¼ ðn þ 1Þ þ 2nRW=graphene þ n k kb - W kgraphene
ð9Þ
Fig. 7. Dependence of thermal conductivity with number of graphene layers.
ð10Þ
Based on Eq. (10), Rtotal of sample A (n = 7), B (n = 3) and C (n = 2) can be obtained as 5.6 108, 4.1 108 and 3.3 108 m2 K/W, respectively. This indicates that ITR induced by graphene indeed hinders thermal transport. As phonon boundary scattering plays an important role, it leads to the reduced thermal conductivity of W/graphene stack structure with the increasing number of graphene layers. In such monolayer graphene/W multilayer nanostructures, the phonon transport process can be described by particle-like incoherent phonons and wave-like coherent phonons. The influence of coherent and incoherent phonons on thermal conductivity is important for understanding heat conduction in multilayer nanostructures [41]. For the incoherent phonon scattering such as phonon-boundary scattering, phonon-vacancy scattering and Umklapp phonon-phonon scattering, the phonons lose their phase. Most methods of reducing thermal conductivity are realized by shortening the MFP of phonons according to incoherent scattering mechanism [42–44]. In contrast to incoherent scattering, for the coherent scattering, the phase is preserved and wave interference of phonons appears, serving as a new approach for manipulating
Fig. 8. Dependence of ITR with number of graphene layers.
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W. Bao et al. / International Journal of Heat and Mass Transfer 147 (2020) 118950
the heat flow. In order to maintain the phase of coherent phonons, phonons scatter specularly at the surface boundaries or the interface of nanostructures. Therefore, nanoscale periodicity and relatively smooth interfaces are preferred to realize the wave-like coherent phonons. The above dependence of the thermal conductivity and ITR with the number of the graphene layers is attributed to the incoherentphonon-dominated heat conduction neat the interfaces. In this incoherent regime, phonon-boundaries scattering dominates the thermal transport by dramatically suppressing the MFP of phonons. No or few phonon interferences can occur due to the limited number of interfaces [45]. In addition, the phonon dispersion forms mini-band owing to band folding along the cross-plane axis, which decreases the overall group velocity of phonons of high-frequency phonon modes [46–48]. Thermal conductivity decreases with increasing interface scattering and decreasing group velocity of phonons. In addition, as is shown in Fig. 8, the value of RW/graphene for sample A (n = 7) is determined as 4 109 m2 K/W, which is much smaller than 6.83 109 m2 K/W for sample B and 8.25 109 m2 K/W for sample C. The deviations are attributed to the enhancement of inelastic scattering at the interfaces with the increasing interface density. The inelastic scattering provides extra channels for phonons to transport across the interface [49]. Moreover, the measured values of ITR are relatively smaller compared with the previously reported values of metal/graphene interfaces. Koh et al. [26] reported the thermal conductance of Au/Ti/graphene/SiO2 interfaces (graphene layers 1 6 n 6 10) is 25 MW/m2 K, which is about a quarter of the thermal conductance of Au/Ti/ SiO2 interface. This result is caused by the interfacial thermal resistance of Au/Ti/graphene and graphene/SiO2. Huang et al. [23] compared the interfacial thermal conductance of Al/transferred graphene (trG)/Cu and Al/grown graphene (grG)/Cu. In the experiment, the thermal conductance of Al/rG/Cu interfaces is about 20 MW/m2 K, which is about 35% lower than that of Al/grG/Cu interfaces (31 MW/m2 K). These results show that trG and Cu have a larger degree of lattice mismatch and phonons are the main heat carries across the metal and graphene interfaces. One possible reason for the small value of ITR is that graphene structural damage provides additional channels of heat transport for electrons. The recent work by Huang et al. can explain this phenomenon. Huang et al. [24] reported the thermal conductance of Pd/transferred graphene (trG)/Pd which is prepared by either thermal evaporation or radio-frequency magnetron sputtering. The reported interfacial thermal conductances of Pd/trG/Pd interfaces are 42 MW/m2 K and 300 MW/m2 K, respectively. The enhancement of thermal conductance was attributed to an extra channel of heat transport by electrons via atomic-scale pinholes formed in the graphene during the magnetron sputtering process.
R xD;j
11!2 ¼ R xD;j 0
0
hxv 2;j D2;j ðxÞfdx R xD;j hxv 2;j D2;j ðxÞfdx 0
hxv 1;j D1;j ðxÞfdx þ
ð12Þ
In our implementation, the Debye-like dispersion relation for the tungsten is used. The density of states is given by [51]
DðxÞ ¼
x2 2p 2 v 2
ð13Þ
On the graphene side, the approach of Duda et al. [52] is employed. A two-dimensional density of states is given by
D2D ðxÞ ¼
x
2pv 2
ð14Þ
Kumatsu [53] gives the dispersion relation of the graphene acoustic branch which can predict the thermal conductivity and specific heat of graphene accurately. The dispersion relation of graphene is given as follows
x1 ¼ vL qa
ð15Þ
x2 ¼ vT qa
ð16Þ
x3 ¼ dq2a
ð17Þ
where the longitudinal wave velocity vL is 20100 m/s, the transverse wave velocity vT is 12300 m/s, d = 6.11 107 m2/s, and qa is the in-plane wave vector, qa,max = 1.55 1010 m1. The experimental results and the result predicted by DMM are shown in Fig. 9. For the convenience of the comparison with the data in the references, the vertical axis is expressed in terms of thermal conductance (ITR1). The measured interfacial thermal conductance is slightly underestimated by Eq. (11). One possible explanation for the underestimated results by DMM model is the inelastic scattering. The inelastic scattering provides extra channels for phonon to transport across the interface. Electrons and phonons in tungsten can exchange energy with phonons in graphene by inelastic scattering, which would enhance the thermal transport. Moreover, the phonons thermalized by inelastic scattering may increase the population of phonon modes with high transmissivity [49]. Another explanation is the possible damage formed in graphene during the sputtering process because of bombardment of carbon atoms by tungsten atoms. Similar damages were observed in graphene after deposition of oxides and nitrides by
3.2. ITR prediction by DMM In order to explain the experimental results, the DMM is used. The most basic assumption in the DMM is that all phonon scattering is diffuse scattering. The ITR is given by [50]
ITR ¼
" #1 3 Z xD;j 1X @f 11!2 hxv 1;j D1;j ðxÞ dx 4 j 0 @T e
ð11Þ
where j is polarization, 11!2 is the phonon transmissivity from is the reduced material 1 (tungsten) to material 2 (graphene), h Planck’s constant, x is the phonon angular frequency, v1,j is the phonon group velocity in the direction of transport, D1,j (x) is the density of states and f is the Bose-Einstein distribution function. For the DMM, the transmissivity is given by
Fig. 9. ITR1 versus the radio of Debye temperature of the metal and graphene.
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magnetron sputtering [54]. Due to the partial removal of carbon atoms, electrons can transmit directly from the top tungsten film to the bottom tungsten film, and thus the thermal resistance could be suppressed due to the additional heat transfer channels of the electrons [23,24]. All of the above factors may lead to the thermal transport underestimated by the DMM. 4. Conclusion The two-color femtosecond laser pump-probe technique is used to measure the thermal conductivity of graphene/W periodic stack nanostructures and the ITR which is induced by graphene. The interfaces induced by graphene may change the thermal conductivity of tungsten. The value of total thermal resistance caused by W/graphene interfaces is determined as 3.3 108– 5.6 108 m2 K/W. As the number of graphene layers increases, the effective thermal conductivity of the stacked nanostructure tends to decrease and the influence of incoherent phonon transport has been discussed. The DMM model is used to predict the ITR between tungsten film and graphene. Inelastic scattering is the key factor leading to a slightly underestimated value. Declaration of Competing Interest The authors declared that there is no conflict of interest. Acknowledgements We acknowledge funding supports from the National Natural Science Foundation of China under Grant No. 51876223. Appendix A. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijheatmasstransfer.2019.118950. References [1] Q. Zhou, J. Zheng, S. Onishi, Graphene electrostatic microphone and ultrasonic radio, Proc. Natl. Acad. Sci. U. S. A. 112 (29) (2015) 8942–8946. [2] I.N. Kholmanov, C.W. Magnuson, A.E. Aliev, Improved electrical conductivity of graphene films integrated with metal nanowires, Nano Lett. 12 (11) (2012) 5679–5683. [3] Y. Fan, L. Wang, J. Li, Preparation and electrical properties of graphene nanosheet/Al2O3 composites, Carbon 48 (6) (2010) 1743–1749. [4] G. Xin, T. Yao, H. Sun, Highly thermally conductive and mechanically strong graphene fibers, Science 46 (50) (2016) 1083–1087. [5] A.A. Balandin, S. Ghosh, W.Z. Bao, et al., Superior thermal conductivity of single-layer graphene, Nano Lett. 8 (3) (2008) 902–907. [6] W. Jang, Z. Chen, W. Bao, Thickness-dependent thermal conductivity of encased graphene and ultrathin graphite, Nano Lett. 10 (10) (2010) 3909– 3913. [7] A.A. Balandin, Nanophononics: phonon engineering in nanostructures and nanodevices, J. Nanosci. Nanotechnol. 5 (7) (2005) 1015–1022. [8] A.A. Balandin, D.L. Nika, Phononics in low-dimensional materials, Mater. Today 15 (6) (2012) 266–275. [9] L. Chen, R. Xue, S. Chen, Heat confinement of phase-change memory using graphene, IEEE Intersociety Conference on Thermal and Thermomechanical Phenomena in Electronic Systems, 29th May–1st Jun, 2017, San Diego, CA, USA, 2017. [10] C. Ahn, S.W. Fong, Y. Kim, et al., Energy-efficient phase-change memory with graphene as a thermal barrier, Nano Lett. 15 (10) (2015) 6809–6814. [11] J.S. Bunch, S.S. Verbridge, J.S. Alden, et al., Impermeable atomic membranes from graphene sheets, Nano Lett. 8 (8) (2008) 2458–2462. [12] Y. Kim, J. Baek, S. Kim, et al., Radiation resistant vanadium-graphene nanolayered composite, Sci. Rep. 6 (2016) 24785. [13] A. Hasegawa, M. Fukuda, K. Yabuuchi, et al., Neutron irradiation effects on the microstructural development of tungsten and tungsten alloys, J. Nucl. Mater. 471 (2016) 175–183. [14] Y. Gao, T. Yang, J. Xue, et al., Radiation tolerance of Cu/W multilayered nanocomposites, J. Nucl. Mater. 413 (1) (2011) 11–15. [15] M. Callisti, M. Karlik, T. Polcar, Bubbles formation in helium ion irradiated Cu/ W multilayer nanocomposites: effects on structure and mechanical properties, J. Nucl. Mater. 473 (2016) 18–27.
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