resistance of 1 Â°C/W, the total resistance is 2 Â°C/W. A common engineering design problem involves the selection of an appropriate sized heat sink for a given heat source. Working in units of thermal resistance greatly simplifies the design calcula
May 13, 2015 - cases, respectively. Our numerical method quantifies the role of electronic band structure and carrier scattering mechanisms. We have successfully demonstrated bipolar thermal conductivity reduction in doped semiconductors via electron
Aug 31, 2013 - ABSTRACT: Making and holding an artificial lipid bilayer horizontally in an aqueous solution within the microscopic working distance of â¼100 Î¼m are essential for simultaneous single molecule imaging and single ion- channel electrica
May 12, 2014 - Molecular dynamic simulations reveal that the ultrathin carbon nanotube (CNT) (2, 1) with a reconstructed structure ... phonon lifetimes strikingly decrease in CNT (2, 1), which result in the remarkable reduction of thermal conductivit
average of at least six measurements generally from between measurements five and ten. The average thermal conductivity values reported for each sample have typical standard devia- tions from 0.01 to 0.30 W mÐ1 KÐ1, with most less than. 0.10 W mÐ1
Jan 15, 2009 - Rawat, Vijay; Koh, Yee Kan; Cahill, David G.; and Sands, Timothy D., "Thermal conductivity of (Zr,W)N/ScN metal/semiconductor ... to the lattice component of the thermal conductivity of a Zr0.65Sc0.35N alloy film (5 W/m K). Alloying th
Measurement of thermal conductivity. Part A: P t Bar : â¢ Time domain ... thermal conductance from sidewalls to ambient. Modern application to suspended ... Schmidt et al., RSI 2008. â¢ Heat supplied by modulated pump beam (fundamental. Fourier com
between predictions from molecular dynamics simulations (a method valid at temperatures above the Debye temperature) ... A key feature of ionic materials is the presence of the long-range electrostatic interactions whose influence ... ranged and repr
Abstract. In recent years, many studies have been conducted regarding polymer nanocomposites, namely polymers doped with various forms of graphene. The impact toughness, tensile strength, and thermal conductivity of Polypropylene/ Graphene and. Polys
Feb 19, 2016 - To date, there is no experimental characterization of thermal conductivity of semiconductor polymeric individual nanowires embedded in a matrix. This work reports on scanning thermal microscopy measurements in a 3u configuration to det
May 2, 2011 - Qavg=50 mW, and has Tavg=7.6 K. Caution should be taken to minimize Tavg for low thermal conductivity samples by using low pump laser power or low duty-cycle periodic modulation that result in low Qavg. For the room temperature validati
NANOFLUID THERMAL CONDUCTIVITY-A REVIEW. Ravi Sankar.B. 1. , Nageswara Rao. D. 2. ,Srinivasa Rao.Ch. 3. 1. Lecturer, Mechanical Engg. Deptt., R.V.R&J.C. College of Engg., Guntur, A.P, India. 2. Vice-Chancellor, Centurion University, Odisa, India. 3.
Oct 21, 2016 - host lattice of MoS2 undergoes a phase transition from 2H to 1T phase19. The voltage dip at the initial stage of the discharge curve for bulk MoS2 sample is caused by the mass transport limitation of lithium ions. The voltage gradually
applications ranging from microelectronic devices to energy storage and energy conversion devices. Here, we report ultralow lattice thermal conductivities of solution-synthesized, single- crystalline all-inorganic halide perovskite nanowires composed
Downloaded 03 Apr 2012 to 184.108.40.206. Redistribution .... Sections 2.1 and 3.1 review steady-state techniques, and. Sections ... A "free-standing bridge" consists of a layer without a substrate or a layer- substrate composite for which Eq (3) was
Aug 25, 2011 - modulation frequency to measure MFPs, but this technique is limited by the modulation frequency . Here, we introduce a thermal conductivity spectroscopy technique which can measure MFP distributions over a wide range of length scal
Dec 31, 2016 - oils) are usually used as heat transfer fluids: in thermal engines (coolants ... alumina/water and copper oxide/water nanofluids are performed and ... Thus, we try in this work to answer the following fundamental ... In this case, the
Dec 14, 2010 - This thesis, âIn-Plane Thermal Conductivity Modeling of Carbon Filled Liquid. Crystal Polymer Based Resins,â is hereby approved in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE in the field of Chemical
For example, figure 1 shows a set of 1340 measurements for the conductivity of expanded polystyrene (EPS) at 10ÂºC, and dry and aged material. The key independent variable is density. Dispersion around the average conductivity is clearly seen in this
May 23, 2013 - The TEG efficiency can be broken into two terms: the limit- ing Carnot efficiency and the efficiency relative to Carnot called the reduced device efficiency (gr,d)6 g Â¼. DTTE. Th gr,d. (3). In the constant property model (CPM), a, q,
Big picture goals of our work: â Understand and push the limits of thermal conductivity in various classes of materials. â enhance thermal function in materials, e.g., abrupt changes in conductivity, actively controlled conduction, more efficient
Jun 15, 2012 - strated the use of TDTR for measuring the heat flow in non- conformal, porous solids as well as liquids,8â10 we show both experimentally, computationally, and theoretically the advantage of TDTR for measuring highly porous films due
May 29, 2013 - temperature thermal conductivity of Si/Ge cross-section modulated nanowires is almost three orders of magnitude lower than that of bulk Si.
received: 08 February 2016 accepted: 15 April 2016 Published: 04 May 2016
Superior thermal conductivity in suspended bilayer hexagonal boron nitride Chengru Wang1, Jie Guo1, Lan Dong1, Adili Aiyiti1, Xiangfan Xu1,2 & Baowen Li3 We reported the basal-plane thermal conductivity in exfoliated bilayer hexagonal boron nitride h-BN that was measured using suspended prepatterned microstructures. The h-BN sample suitable for thermal measurements was fabricated by dry-transfer method, whose sample quality, due to less polymer residues on surfaces, is believed to be superior to that of PMMA-mediated samples. The measured room temperature thermal conductivity is around 484 Wm−1K−1(+141 Wm−1K−1/ −24 Wm−1K−1) which exceeds that in bulk h-BN, providing experimental observation of the thicknessdependent thermal conductivity in suspended few-layer h-BN. Hexagonal boron nitride (h-BN), analogous to graphene, is an one-atomic layer two dimensional (2D) material with honeycomb structures in which equal Boron and Nitrogen atoms bond compartmentally by sp2 hybridization1. Due to their strong covalent bond between B-N and C-C atoms, h-BN and graphene hold similar structural and physical properties such as strong mechanical properties, high thermal stability and superior thermal conductivity2–10. Consequently, h-BN has been proposed to be potential as insulating and dielectric layer for graphene based electronics. Given their geometric similarity and atomic flat on surface, the carrier mobility in graphene/h-BN devices has been significantly improved by a factor of 20 at room temperature when comparing to that of graphene on amorphous SiO2 substrate and reaches an ultra high value of 1,000,000 cm2V−1s−1 at low temperature11–13. Furthermore, it’s important to note that thermal conductivity in bulk h-BN has been found to be as high as 390 Wm−1K−1, indicating a potential 2D material for efficient heat removal and conduction in further integration and miniaturization of the modern electronics14. Several theoretical calculations have suggested that room temperature thermal conductivity in single layer h-BN reaches 600Wm−1K−1 when considering the exact numerical solution of the Boltzmann transport equation, far exceeding that in bulk h-BN (~390 Wm−1K−1)14–17. This is reasonable as out-of-plane acoustic phonons are suppressed due to interlayer interaction, as already observed in graphene and graphite theoretically and experimentally9. However, recent experiments show that the highest thermal conductivity obtained is around 243 Wm−1K−1 in 9-layer h-BN by Raman method6 and around 360 Wm−1K−1 in 11-layer h-BN by microbridge device with built-in thermometers4, respectively. This is understandable that organic residues (e.g. PMMA) and functional groups which are introduced during PMMA-mediated wet-transfer process dominate thermal conduction in few-layer BN and reduce its value to below that of bulk h-BN4,18. Therefore, to study the intrinsic thermal conduction behavior in few-layer h-BN, a new transfer technique should be introduced to obtain high quality sample with as less residues as possible. Here we reported thermal conductivity measurement on suspended bilayer h-BN by using prepatterned microstructures with built-in platinum-resistive thermometers. A PMMA-free technique was used to fabricate suspended device suitable for thermal conduction measurement. This dry-transfer method guarantees cleaner surfaces of h-BN sample than that in PMMA-mediated method. Consequently, the measured room temperature thermal conductivity reaches a high value of 484 Wm−1K−1(+ 141 Wm−1K−1/− 24 Wm−1K−1), exceeding that in bulk hexagonal boron nitride, indicating h-BN as a potential 2D material for efficient heat removal and thermal management in integrated electronic circuit with further miniaturization.
Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, 200092 Shanghai, China. 2Institute of Advanced Studies, Tongji University, 200092 Shanghai, China. 3Department of Mechanical Engineering, University of Colorado Boulder, CO 80309-0427, USA. Correspondence and requests for materials should be addressed to X.X. (email: [email protected]) or B.L. (email: [email protected]) Scientific Reports | 6:25334 | DOI: 10.1038/srep25334
Figure 1. Details of the sample. (a) Optical image of exfoliated bilayer h-BN on PDMS. (b,c) Optical and Scanning Electron Microscope image of bilayer BN suspending on prepatterned devices; the rectangle in the center which bridging Heater and Sensor is the suspended h-BN sample with l = 3 μ m and w = 3.3 μ m. (d) Atomic Force Microscope on the edge of h-BN sample; the step of ~1 nm is the mark of bilayer h-BN. The scale bars are 10 μ m.
We employed the standard prepatterned microstructures for thermal measurements2,19–21, in which the two Pt/SiNx membranes, named Heater and Sensor in Fig. 1b, and their six supporting Pt/SiNx beams were released from silicon substrate by wet etching for 2.5 h to 3 h. The suspended prepatterned microstructure device was first placed in O2 plasma for 5 min to clean possible organic residue on top of Pt/SiNx membranes. At the mean time, few-layer h-BN was exfoliated from BN power by scotch tape method onto PDMS film, in which h-BN can been easily identified by different contrast under optical microscope (Fig. 1a). Subsequently, h-BN/PDMS was aligned under micro-manipulator upside down and attached onto the center of prepatterned microstructure. Due to the strong van der waals force/static electric force, the few-layer h-BN was left on Pt electrode after PDMS being peeled off. It is important to note this transfer process is challenging and the sample yield is only few hundred percents. Fortunately, a rectangular h-BN between two suspended membranes can be seen in Fig. 1b,c. The device was annealed at 225 °C in H2/Ar atmosphere for two hours to clean the possible residue on top and bottom sides of h-BN thin film before any thermal measurements. Raman spectroscopy is one of the most powerful and fastest methods to detect the number of layers in 2D materials such as graphene and MoS222–25. However, the Stokes shift of Raman peaks varies weekly between different h-BN layers, making it impossible to detect the thickness of h-BN samples by Raman method26. Hence,
Figure 2. Finite Element Simulations (COMSOL Multiphysics 5.2) of the temperature distributions in Sensor. (a) Temperature distribution of Sensor (left) and the whole suspended device (right) at T = 300 K. (b) Temperature profile crossing the Sensor (indicated by dashed line in (a)) at T = 300 K.
Atomic Force Microscope was used and a clear step of around 1 nm was obtained on edge, indicating two atomic layers in the fabricated h-BN sample (Fig. 1d). We followed the same approach employed by Xu et al. to measure the thermal conductivity of the suspended device2. The device was loaded in Variable Temperature Instrument with vacuum better than 1 × 10−4 pa and an in-situ anneal was carried out at T = 450 K for 2 hours to remove possible residual gas and water molecule. The total measured thermal conductance of h-BN sample (σs) and the six supporting Pt/SiNx beams (σb) follows21: σb =
Qh + Q s ∆T h + ∆T s
σs = σb
∆T s ∆T h − ∆T s
where Qh and Qs are the Joule heating power on the Heater and one supporting Pt/SiNx beam, respectively. Δ Th and Δ Ts, corresponding to resistance changes Δ Rh and Δ Rs, are the temperature rise on Heater and Sensor, respectively. In previous studies, a uniform temperature distribution was assumed and the average temperature rise Δ Th (Δ Ts) in Heater (Sensor) was used instead of the real temperature rise Δ TR,h (Δ TR,s) at the joint part of sample and Heater (Sensor). This assumption is valid when thermal conductance is low, e.g. σs < 0.1σb. However for high thermal conductance sample when Δ Th is comparable to Δ Ts, according to equation (2), a tiny inaccuracy in measuring Δ Th (Δ Ts) will result in significant changes in final σs. As such, the Finite Element Simulations (COMSOL Multiphysics 5.2, License No: 9400382) was carried out to simulate the temperature distribution in the suspended membranes, Heater and Sensor, at each temperature we measured. Figure 2 shows the simulating results at T = 300 K. In this simulation, thermal conductivity of Pt can be obtained from the Weidemann-Franz law, thermal conductance of SiNx beam was determined by subtracting the thermal conductance contribution of Pt from the measured Pt/SiNx beams σb and its thermal conductivity is calculated to be around 5.8 Wm−1K−1. The Δ TR,h (Δ TR,s) was obtained by adjusting the averaged temperature of Heater (Sensor) membrane bounded by dash-dot rectangle to be consistent with the measured temperature rise Δ Th (Δ Ts). Figure 2b illustrates the temperature profile cross the platform with Δ TR,s determined to be 5.344 K, comparing to Δ Th = 6.822 K and Δ Ts = 5.245 K. The final thermal conductivity of h-BN sample varies 8% and 7.2% at T = 300 K and T = 80 K respectively after the Finite Element Simulations. Generally speaking, the total measured thermal resistance R = 1/σs consistent of the contributions from suspended region of h-BN sample, RBN, and the contacting area between h-BN sample and Pt electrode, Rc, i.e.
Figure 3. Thermal conductivity of the measured bilayer h-BN. (a) Thermal conductivity with respect to temperature. The diamonds, pentagons, squares and triangles represent thermal conductivity of single layer h-BN (theory)15, high-quality bulk h-BN (experiment)14, 11-layers suspended h-BN and 5-layers suspended hBN (experiment)4, respectively. (b) Layer-dependent thermal conductivity. The left diagonal and right diagonal represent thermal conductivity of high-quality14 and low-quality28 bulk h-BN (experiment), respectively. R = RBN + 2Rc. The thermal contact resistance Rc can be calculated using interfacial thermal resistance (Rint). The two have been shown to be related as18 κ Aw w Rc = c tanh κ R AR c int int
where κc is thermal conductivity of supported bilayer h-BN (we assume κc equal to κ in suspended bilayer h-BN), A is the cross section area between h-BN sample and electrode, w is the sample width, lc is the contact length, Rint is the interfacial thermal resistance per unit area between BN and Pt electrode. We have not found Rint of clean h-BN and Pt interface and the samples in reference have PMMA residues on bottom and top h-BN surface4, therefore Rint of clean graphene and metal interface was used here. Based on the Rint data on available literature for graphene measured by the same prepatterned microstructure method, we used the data of Rint from the length dependent measurement of suspended single layer graphene with two ends encased by Au and Pt electrode2. If this Rint is used, the obtained 2Rc/RBN ratio reaches 29.1% and 34.1% at T = 300 K and T = 60 K, respectively. Figure 3a shows the final thermal conductivity κ of biyaler h-BN with respect to temperature. κ is calculated from κ = σl/(wh), where l = 3 μ m is the suspended length, w = 3.3 μ m is suspended width, h = 0.666 nm is the thickness of bilayer h-BN as suggested14,27, σ is the obtained thermal conductance after the Finite Element Simulations. The plus error bars (i.e. 29.1% at T = 300 K and 34.1% at T = 60 K) are resulted from the uncertainty in determining the contact resistance 2Rc as mentioned above in this manuscript. The measured thermal conductivity increases with temperature and shows a broad plateau/peak when T > 250 K due to the Umklapp phonon scattering process dominating the thermal conduction at higher temperature. The plateau/peak value reaches as high as 484 Wm−1K−1(+ 141 Wm−1K−1/− 24 Wm−1K−1), exceeding that in bulk h-BN14,28. Meanwhile, the plateau/peak at higher temperature when comparing with that in bulk h-BN single crystal suggests that the extrinsic scattering such as contact, defect and grain size dominance the intrinsic phonon-phonon scattering process at higher temperature. At lower temperature, the thermal conductivity decreases rapidly with its value below that of bulk h-BN when T < 200 K. This is probably due to the contact29, relatively smaller grain size28, or possible tiny residue4 but non-negligible effect on thermal conductivity. Nevertheless, the obtained thermal conductivity is larger than that in 5-layer and 11-layer exfoliated h-BN measured by modified prepatterned microstructure method (Fig. 3a), and that in 9-layer CVD h-BN measured by Raman method, suggesting that sample prepared by dry-transfer method holds cleaner surfaces and superior sample quality when comparing to that prepared by PMMA-mediated transfer method4,6,18.
Thickness-dependent behavior on basal-plane thermal conductivity of 2D materials is an important topic in thermal transport properties in low dimensional materials and gained intense attractions in last decade. Both theory and experiment suggested that basal-plane thermal conductivity in clean few-layer graphene decreases with increasing layers due to the enhancement of phonon scattering between layers30–33. On the other hand, the question on thickness-dependent basal-plane thermal conductivity in MoS2 is still under debate34,35, as MoS2 has much stronger bond between different layers. Due to the geometric similarity, few-layer h-BN has been suggested to have the same thickness dependence similar to graphene16, yet not observed experimentally. Figure 3b shows the thermal conductivity with respect to layers. At T = 300 K, the observed thermal conductivity is larger than that in Scientific Reports | 6:25334 | DOI: 10.1038/srep25334
www.nature.com/scientificreports/ bulk h-BN but smaller than that in single layer h-BN by theoretical calculation, indicating a thickness-dependent thermal conductivity in few-layer h-BN. It is importing to note that thermal conductivity of supported or encased few-layer graphene and h-BN decrease with decreased thickness with the value below that of its bulk counterpart36. These two different trends with respect to thickness is understandable as the interaction between graphene (h-BN) and substrate materials can also enhance the phonon scatterings in the graphene (h-BN) layers. Interestingly, the polymer residues on graphene (h-BN) surfaces can also increase the phonon scattering, resulting in opposite trend of the thickness-dependent thermal conductivity. In Fig. 3b, the previously measured thermal conductivity in 5-layer and 11-layer h-BN with PMMA residue has lower value than that in bulk h-BN. It is worth noting that directly comparison of the results from this study and reference 4 is unfair due to the length-dependent thermal conductivity in two-dimensional materials, which has been predicted theoretically33,37–40 and later confirmed by experiment2. However, when comparing the result of sample in this study (with length of 3 μ m and width of 3.3 μ m) and that of 12-layers sample in reference 4 (with length of 3 μ m and width of 9 μ m), the thermal conductivity in former sample is much larger than that in latter sample with polymer residues on surface, no mention about the slightly width dependent2,40. This result provides further evidence that the sample prepared by dry-transfer method has much cleaner surfaces than that obtained by PMMA-mediated method. In summary, we observed a thickness-dependent thermal conductivity in bilayer h-BN with the room temperature value reach as high as 484 Wm−1K−1(+ 141 Wm−1K−1/− 24 Wm−1K−1), exceeding that in bulk h-BN. Our thermal conduction measurement indicates that the PMMA-free dry-transfer method preserves relatively higher sample quality with less residues on surfaces, providing a brand-new and reliable technique for transferring 2D materials onto suspended prepatterned microstructures suitable for thermal measurements.
1. Alem, N. et al. Atomically thin hexagonal boron nitride probed by ultrahigh-resolution transmission electron microscopy. Phys. Rev. B 80, 155425 (2009). 2. Xu, X. et al. Length-dependent thermal conductivity in suspended single layer graphene. Nat. Comm. 5, 3689 (2014). 3. Butler, S. Z. et al. Progress, Challenges, and Opportunities in Two-Dimensional Materials Beyond Graphene. ACS Nano 7, 2898–2926 (2013). 4. Jo, I. et al. Thermal conductivity and phonon transport in suspended few-layer hexagonal boron nitride. Nano Lett. 13, 550–554 (2013). 5. Xu, M., Liang, T., Shi, M. & Chen, H. Graphene-like two-dimensional materials. Chem. Rev. 113, 3766–3798 (2013). 6. Zhou, H. et al. High thermal conductivity of suspended few-layer hexagonal boron nitride sheets. Nano Research 7, 1232–1240 (2014). 7. Balandin, A. A. et al. Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902–907 (2008). 8. Balandin, A. A. Thermal properties of graphene and nanostructured carbon materials. Nat. Mater. 10, 569–581 (2011). 9. Ghosh, S. et al. Dimensional crossover of thermal transport in few-layer graphene. Nat. Mater. 9, 555–558 (2010). 10. Chen, S. et al. Thermal conductivity of isotopically modified graphene. Nat. Mater. 11, 203–207 (2012). 11. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 5, 722–726 (2010). 12. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013). 13. Wang, L. et al. One-Dimensional Electrical Contact to a Two-Dimensional Material. Science 342, 614–617 (2013). 14. Sichel, E. K., Miller, R. E., Abrahams, M. S. & Buiocchi, C. J. Heat capacity and thermal conductivity of hexagonal pyrolytic boron nitride. Phys. Rev. B 13, 4607–4611 (1976). 15. Lindsay, L. & Broido, D. A. Enhanced thermal conductivity and isotope effect in single-layer hexagonal boron nitride. Phys. Rev. B 84, 155421 (2011). 16. Lindsay, L. & Broido, D. A. Theory of thermal transport in multilayer hexagonal boron nitride and nanotubes. Phys. Rev. B 85, 035436 (2012). 17. Cepellotti, A. et al. Phonon hydrodynamics in two-dimensional materials. Nat. Comm. 6, 6400 (2014). 18. Pettes, M. T., Jo, I., Yao, Z. & Shi, L. Influence of polymeric residue on the thermal conductivity of suspended bilayer graphene. Nano Lett. 11, 1195–1200 (2011). 19. Shi, L. et al. Measuring thermal and thermoelectric properties of one-dimensional nanostructures using a microfabricated device J. Heat Transfer. 125, 881–888 (2003). 20. Wang, Z. et al. Thermal transport in suspended and supported few-layer graphene. Nano Lett. 11, 113–118 (2011). 21. Kim, P., Shi, L., Majumdar, A. & McEuen, P. L. Thermal transport measurements of individual multiwalled nanotubes. Phys. Rev. Lett. 87, 215502 (2001). 22. Ferrari, A. C. et al. Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 97, 187401 (2006). 23. Graf, D. et al. Spatially resolved Raman spectroscopy of single-and few-layer graphene. Nano Lett. 7, 238–242 (2007). 24. Gupta, A., Chen, G., Joshi, P., Tadigadapa, S. & Eklund, P. C. Raman scattering from high-frequency phonons in supported n-graphene layer films. Nano Lett. 6, 2667–2673 (2006). 25. Lee, C. et al. Anomalous lattice vibrations of single-and few-layer MoS2. ACS Nano 4, 2695–2700 (2010). 26. Gorbachev, R. V. et al. Hunting for monolayer boron nitride: optical and Raman signatures. Small 7, 465–468 (2011). 27. Paszkowicz, W., Pelka, J. B., Knapp, M., Szyszko, T. & Podsiadlo, S. Lattice parameters and anisotropic thermal expansion of hexagonal boron nitride in the 10–297.5 K temperature range. Appl. Phys. A 75, 431–435 (2002). 28. Duclaux, L., Nysten, B. & Issi, J. P. Structure and low-tempearture thermal conductivity of pyrolytic boron nitride. Phys. Rev. B 46, 3362–3367 (1992). 29. Wang, J., Zhu, L., Chen, J., Li, B. & Thong, J. T. L. Suppressing thermal conductivity of suspended tri-layer graphene by gold deposition. Adv. Mater. 25, 6884–6888 (2013). 30. Wei, Z., Ni, Z., Bi, K., Chen, M. & Chen, Y. In-plane lattice thermal conductivities of multilayer graphene films. Carbon 49, 2653–2658 (2011). 31. Zhong, W.-R., Zhang, M.-P., Ai, B.-Q. & Zheng, D.-Q. Chirality and thickness-dependent thermal conductivity of few-layer graphene: A molecular dynamics study. Appl. Phys. Lett. 98, 113107 (2011). 32. Nika, D. L. & Balandin, A. A. Two-dimensional phonon transport in graphene. J. Phys.: Condens. Matter 24, 233203 (2012). 33. Lindsay, L., Broido, D. A. & Mingo, N. Flexural phonons and thermal transport in multilayer graphene and graphite. Phys. Rev. B 83, 235428 (2011). 34. Jo, I., Pettes, M. T., Ou, E., Wu, W. & Shi, L. Basal-plane thermal conductivity of few-layer molybdenum disulfide. Appl. Phys. Lett. 104, 201902 (2014). 35. Ding, Z., Jiang, J.-W., Pei, Q.-X. & Zhang, Y.-W. In-plane and cross-plane thermal conductivities of molybdenum disulfide. Nanotechnol. 26, 065703 (2015).
www.nature.com/scientificreports/ 36. Jang, W., Chen, Z., Bao, W., Lau, C. N. & Dames, C. Thickness-Dependent Thermal Conductivity of Encased Graphene and Ultrathin Graphite. Nano Lett. 10, 3909–3913 (2010). 37. Nika, D., Askerov, A. & Balandin, A. Anomalous size dependence of the thermal conductivity of graphene ribbons. Nano Lett. 12, 3238–3244 (2012). 38. Nika, D. L., Pokatilov, E. P., Askerov, A. S. & Balandin, A. A. Phonon thermal conduction in graphene: Role of Umklapp and edge roughness scattering. Phys. Rev. B 79, 155413 (2009). 39. Nika, D. L., Pokatilov, E. P. & Balandin, A. A. Theoretical description of thermal transport in graphene: The issues of phonon cut-off frequencies and polarization branches. Phys. Status Solidi B 248, 2609 (2011). 40. Bae, M. H. et al. Ballistic to diffusive crossover of heat flow in graphene ribbons. Nat. Comm. 4, 1734 (2013).
This work was supported by National Natural Science Foundation of China (No. 11304227 & No. 11334007) and by the Fundamental Research Funds for the Central Universities (No. 2013KJ024).
C.W. carried out the sample fabrications and thermal measurements, J.G. contributed to the COMSOL simulations, L.D., A.A. and X.X. helped with the measurement system setup, X.X. wrote the main manuscript text, X.X. and B.L. supervised the project. All the authors contributed to interpret the results and review the manuscript.
Competing financial interests: The authors declare no competing financial interests. How to cite this article: Wang, C. et al. Superior thermal conductivity in suspended bilayer hexagonal boron nitride. Sci. Rep. 6, 25334; doi: 10.1038/srep25334 (2016). This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/