Thermal Properties of Two Dimensional Layered Materials

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1 Thermal Properties of Two Dimensional Layered Materials Yuxi Wang, Ning Xu, Deyu Li, and Jia Zhu* The rise of graphene has motivated intensive investigation into other twodimensional layered materials (2DLMs). In addition to their superior optical, electrical, and mechanical properties, 2DLMs have also demonstrated intriguing thermal properties, the understanding of which is not only fundamentally important but also critical to enabling widespread applications in electronics, optoelectronics, and energy conversion and storage devices. Here, we review recent progress in the thermal transport of 2DLMs. Indeed, due to unique and diversified two dimensional crystal structures and the contribution of different phonon modes to thermal transport, while the family of 2DLMs share common thermal properties, such as layer-dependent thermal conductivity, each member also has unique features related to thermal transport. Ultimately, the unusual and rich thermal properties of two-dimensional materials can lay a solid foundation for understanding new phonon transport physics and potentially lead to novel applications in various emerging fields. 1. Introduction All 2DLMs share several common features. For example, the intra-layer bonds are typically covalent, whereas the layers are coupled by van der Waals bonds. [1 3] The term 2DLMs typically refers to a single layer of these materials, although it has also been commonly used for membranes of a few layers. 2DLMs have gained an overwhelming interest since the discovery of single-layer graphene in 2004 by Novoselov and Geim. [4] The exciting research findings on graphene [5 7] promoted the discovery of various other atomically thick 2DLMs with high crystal quality. Figure 1a f shows the schematic structures of several typical 2DLMs: graphene, h-bn, SnSe, MoS 2, black phosphorous (BP) and Bi 2 Te 3, respectively. Because of the relatively weak van der Waals bonds between different layers, methods such as mechanical exfoliation [1,4,8 11] and liquidphase exfoliation [12 16] have been developed to obtain atomically thick 2DLMs. While the size of 2DLMs from exfoliation is usually quite limited, chemical vapor deposition (CVD) [17 21] can Y. Wang, N. Xu, Prof. J. Zhu National Laboratory of Solid State Microstructures College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures Nanjing University Nanjing , China jiazhu@nju.edu.cn Prof. D. Li Department of Mechanical Engineering Vanderbilt University Nashville, TN 37212, USA DOI: /adfm grow wafer-scale 2DLMs on substrates. Furthermore, the development of effective transfer techniques [22 29] has paved the road for the fabrication of various devices to explore the properties and applications of 2DLMs. Over the past decade, 2DLMs have been employed as novel building blocks for constructing various electronic, optoelectronic, and energy conversion and storage devices. The push for widespread applications of 2DLMs calls for a comprehensive understanding of the heat flow physics of 2DLMs and their contacts with the substrate, as it is directly related to energy consumption, heat dissipation, energy conversion, and thermal management at a device or system level. [30 32] From a fundamental perspective, the advances in both synthesis methods of high quality 2DLMs and thermal transport measurements of low dimensional materials build an ideal playground to explore thermal transport in 2DLMs. Therefore, thermal transport in 2DLMs such as few-layer graphene, [29,33 37] h-bn, [38 40] MoS 2, [41 43] BP, [44 46] and Bi 2 Te 3, [47] has been intensively investigated over the past few years. Different from the classical size effect (reduced thermal conductivity relative to bulk value) commonly observed in other low dimensional systems such as various nanowires, [48 51] superlattices [52 55] and nanocomposites, [56] 2DLMs with covalent intra-layer bonds and van der Waals layer-to-layer interactions demonstrate interesting thermal properties, such as high inplane thermal conductivities and the relatively low out-of-plane values. In addition, each different member of 2DLMs also has unique thermal properties fundamentally linked to their crystal structures, which will be discussed in this review. In this feature article, we focus on the progress of the measurements of thermal transport in 2DLMs. For more information about the synthesis, transfer and characterization of 2DLMs, and the modeling of phonon transport in 2D materials, [2,3,57 59] we refer to other excellent review papers. First, we will discuss various thermal measurement methods for 2DLMs, introducing the unique advantages and limitations of each measurement scheme, particularly when measuring 2DLMs. Then, we will summarize common and unique thermal transport properties in several 2DLMs, and present potential correlations between thermal transport properties and crystal structures. Finally, based on the advantages of thermal properties in 2DLMs, such as number of layer-dependent and anisotropic thermal conductivities, we will present several potential applications taking advantage of these unique thermal properties. It is extremely attractive that 2DLMs may have potential advantages in both heat dissipation and thermal insulation, (1 of 17) wileyonlinelibrary.com 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

2 which make them promising for applications including device thermal management and thermoelectric energy conversion. During the preparation and review process of this work, we have become aware of a review article on a similar topic from the perspective of heat transfer. [59] 2. Thermal Measurement for 2DLMs The exploration of thermal transport in 2DLMs would not be possible without the recent progress in thermal transport measurement techniques. In the past two decades, various techniques have been developed to measure thermal conductivity of thin films. For example, the well-known 3ω-method, [60,61] which uses microfabricated metal lines for both joule heating and resistance thermometry, can measure thermal conductivities in both the in-plane and the cross-plane directions for thin films and superlattice structures. Also, developments in time-domain thermoreflectance (TDTR) technique [62,63] has allowed precise measurement of the thermal conductivity of thin films and the thermal conductance at interfaces. However, owing to the fact that both the 3ω and TDTR methods are mainly for cross-plane thermal transport measurements and require a metal line/film as a transducer, they have not been widely used for investigating the intrinsic in-plane thermal transport properties of atomically thin 2DLMs. [64] Indeed, it has been rather challenging to experimentally explore thermal transport in 2DLMs due to several practical difficulties, such as sample preparation and clean transfer without residues. To date, two approaches, the suspended micro-bridge and optothermal Raman techniques, have been successfully employed to measure in-plane thermal transport in 2DLMs. As the measurement principles and the details of these methods have been reviewed elsewhere, [65] we only provide a brief illustration of these measurement methods here and focus mainly on the development and limitations of these techniques for 2DLMs Suspended Micro-Bridge Method The micro-bridge method was first developed to measure the thermal conductivity of individual carbon nanotubes. [66] It was then used to measure the thermal conductivities of various nanowires/nanotubes/nanoribbons [67 69] and thin films, [70 72] and was most recently extended to measure the thermal conductivities of 2DLMs, [42,44,47] such as graphene, [29,73] Bi 2 Te 3, and MoS 2. In addition to thermal conductivity measurement with a steady-state temperature difference established across the two ends of the sample, the micro-bridge method, in principle, also has the capability to simultaneously measure the Seebeck coefficient and the electrical conductivity. For example, by using an improved device with four-probe electrical measurement, ZT values of 1D [74] and 2D [44,47] materials have been reported. Figure 2a shows the schematic of the thermal measurement set-up (top) and thermal resistance circuit (bottom) for the micro-bridge method. The suspended device for the measurement consists of two adjacent SiN x membranes supported by several long SiN x beams with Pt resistance heaters/thermometers fabricated on them. To measure the thermal conductance Yuxi Wang received his bachelor degree at the College of Engineering and Applied Sciences of Nanjing University, June His research interests focus on nanoscale thermal transport and the synthesis of lowdimensional thermoelectric materials. Dr. Deyu Li is a professor in the Mechanical Engineering Department at Vanderbilt University. He received his Ph.D. degree from the University of California, Berkeley, and his research interests include nanoscale thermal transport and micro/ nanofluidics. Jia Zhu is a Professor at College of Engineering and Applied Sciences, Nanjing University, China (since September 2013). He obtained his Ph.D. from Stanford University and then worked as a postdoctoral fellow at University of California, Berkeley, and Lawrence Berkeley National Lab. His current research focuses on the development of nanomaterials-based energy conversion and storage, including solar steam generations, solar cells, and nanoscale heat transfer. of the suspended sample, the basic principle is to induce a temperature difference between the two membranes by means of joule heating (Q tot ) in the Pt resistor on one side. The dissipated Q tot leads to temperature increases of ΔT h on the heating membrane, and ΔT s on the sensing membrane due to the heat transferred through the sample. All the heat eventually is transferred to the environment through the SiN x beams. By analyzing the thermal resistance circuit and determining the amount of heat (Q 2 ) conducted through the sample, the relationship between the joule heating and thermal conductance can be written as Qtot = Gb( Th + Ts) (1) Q2 = Gs( Th Ts) = Gb Ts (2) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com (2 of 17)

3 Figure 1. Schematic of 2DLMs: a) graphene, b) h-bn, c) SnSe, d) black phosphorous, e) MoS 2, f) Bi 2 Te 3. where G s and G b are the conductance of the sample and the five SiN x beams, respectively. Although the suspended micro-bridge method provides a powerful platform for measuring the in-plane thermal conductivity of 2DLMs, one big challenge particularly related to the application of this method to 2DLMs is clean transfer of the sample. One effective approach to transfer low dimensional materials (such as nanowires or nanotubes) involves manipulation with a sharp probe tip to pick up the nanostructure and lay it down, bridging the two suspended membranes. However, it has been found that picking up 2DLMs with thickness less than 50 nm is rather challenging due to limitations in the sharpness of probe tips and the mechanical properties of 2DLMs. [44] In 2DLMs studies, the polymer-assisted transfer process has been developed and widely used for transferring 2DLMs. However, this transfer process could possibly cause damage to suspended devices and could leave a polymer residue on the sample. Because of the extremely large surface-area-to-volume ratios of 2DLMs, the polymer residue may cause a significant decrease in the measured thermal conductivity from additional scattering events. [75] Another challenge to extracting the intrinsic thermal conductance of 2DLMs from the measurement results is correctly accounting for the thermal interface conductance G c = 1/R c between the suspended membranes and the 2DLMs. A common treatment for the thermal interface resistance R c has been reported in several works, [40,70] R c = kaw c tan h R w kar int c int l c 1 where k c is the thermal conductivity of supported sample, A is the cross section, w is the sample width, l c is the contact length, and R int is the interfacial thermal resistance per unit area between sample and suspended membrane. Because of the limited availability of accurate R int data in the literature, it is rather challenging to evaluate R c for various 2DLMs. Therefore, a lot of research is still needed for the accurate determination of the thermal contact resistance. (3) 2.2. Optothermal Raman Technique Another commonly used approach to measure the thermal conductivity of 2DLMs is the optothermal Raman technique. As a direct relationship can be built to associate Raman signals with the temperature [33] and/or thickness [76,77] of 2DLMs, Raman spectra can serve as an effective thermometer for measuring the thermal conductivity of 2DLMs. This noncontact thermal measurement was first applied to single-layer graphene in [33] Several results have been reported in other atomically thin 2DLMs, including MoS 2, [41,43] BN, [39] and black phosphorus. [46] In a typical configuration for optothermal Raman measurement (Figure 2b), the sample is suspended over a hole or a trench. The supported part is connected to the heat sink that is maintained at a constant temperature during the experiment. A laser light of a desirable wavelength is focused on the middle part of the sample, inducing a temperature gradient and heat flow. When the temperature difference is determined with the Raman shift at different temperatures, the in-plane thermal conductivity of samples can be measured. Different laser powers are commonly used to induce the temperature change ΔT in the sample. Under the assumption that heat propagates in a radial wave, the thermal conductivity can be expressed as follows: 1 P k = 2π h T where h is the thickness of the sample and ΔP = P 2 P 1 is the power difference. Details about the measurement process [33] and a comprehensive analysis regarding the thermal transport of the supported part on the substrate can be found in the published report. [35] Even though the optothermal Raman technique has achieved great success in thermal measurements of 2DLMs, several uncertainties, which originate from measuring the temperature-dependent peak frequency shift and the optical absorption coefficient, could lead to significant measurement errors. Obviously, it will be difficult for 2DLMs or other material systems (4) (3 of 17) wileyonlinelibrary.com 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

4 significant challenge to accurately extracting the thermal conductivities of the suspended 2DLMs, k s. To overcome this issue, Cai et al. [35] carried out a Raman measurement on both the suspended and supported part of graphene samples and directly determined both g c and k s. The thermal conductivity of the suspended graphene was extracted by combining the heat conductance equations on both the suspended part and the supported part with proper boundary conditions. Despite of these measurement uncertainties, the convenient sample fabrication and measurement processes make the optothermal Raman measurement a favorable option for investigating thermal transport in 2DLMs. While these two approaches (the suspended micro-bridge and optothermal Raman techniques) have been widely employed to measure in-plane thermal transport in 2DLM, the limitations of each measurement technique, as discussed above, call for the development of new techniques with high measurement accuracy in the future. One notable example is the introduction of an electron beam as the heating source into the micro-bridge method, which, by putting the whole set-up into an electron microscope, could help to simultaneously measure the intrinsic thermal conductivity of sample and the thermal contact resistance. [73] 3. Thermal Properties in 2DLMs 3.1. Graphene Figure 2. Schematic of thermal conductivity measurement technique for 2DLMs. a) Schematic set-up of the micro-bridge method consists of heating and sensing membranes (up) and corresponding thermal resistance circuit (bottom). b) Optothermal Raman technique with laser focused on the suspended sample. The red arrow represents the heat flow. with weak Raman intensity and weak temperature dependence to be measured by this technique. Moreover, the heat power that the sample absorbs from the laser beam should be determined carefully. Based on equation (4), the thermal conductivity is directly related to the absorbed heat power (P). The amount of absorption depends on the wavelength of the laser beam used, as materials typically have a wavelength-dependent absorption coefficient. As an example, due to the different optical absorption and sample quality in different experiments, quite scattered data have been reported for the thermal conductivity of graphene by this technique. [33,78] Similar to the micro-bridge method, interfacial thermal conductance between 2D sample and substrate, g c, poses a As the first discovered and most explored 2D material, the thermal transport properties of single layer and few-layer graphene have been extensively investigated and reviewed. [79 83] Balandin et al. [33] first reported a measurement of the thermal conductivity of a single layer graphene suspended over a trench using an optothermal Raman technique. They used a 488 nm wavelength laser as the optical heat source and extracted the optical absorption coefficient from the Raman intensity of highly oriented bulk pyrolytic graphite (HOPG) samples. With the G Raman peak as the thermometer, they extracted a thermal conductivity of 5300 W m 1 K 1, which is much higher than the value in HOPG and diamond. However, later on, a much lower thermal conductivity (630 W m 1 K 1 ) [84] was measured with an absorption of 2.3% based on the optical transmission and reflection measurement. By taking into account the thermal conductivity of the supported part and the contact resistance, Cai et al. [35] reported a value of 2500 (+1100/ 1050) W m 1 K 1 around 350 K for the suspended graphene. Experiments conducted on exfoliated graphene supported on SiN x [73] or silicon dioxide [36] yielded values of 1250 W m 1 K 1 and 600 W m 1 K 1 for 3-layer and monolayer samples, respectively, which are still very high and thus promising for heat dissipation in nanoelectronics. Additionally, various other aspects related to thermal transport of graphene, such as dimensionality cross-over, [34,85] the effect of isotopic modification, [86] impurity deposition, [87] chemical functionalization, [88,89] and length dependent properties [29,90,91] have been studied, which provide deep physical understanding on this unique system WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com (4 of 17)

5 Figure 3. Structure characterization of h-bn: a) Top view of single-layer h-bn. b) High resolution transmission electron microscope and Selected area electron diffraction pattern image (inset). Reproduced with permission. [38] Copyright 2013, American Chemical Society. c,d) Temperature-dependent Raman shift of 9L h-bn. Reproduced with permission. [39] Copyright 2014, Springer Science and Business Media Boron Nitride Figure 3a shows a top-view of the sp 2 -bonded h-bn structure, which is comprised of alternating boron and nitrogen atoms in a honeycomb arrangement, instead of only carbon atoms as in graphene. The atomically thin h-bn, which has unique properties and applications, [92] can also be exfoliated from h-bn bulk crystal using the conventional process for obtaining 2DLMs. As a typical 2D material, the layered and honeycombed structure was revealed in the high resolution transmission electron microscopy (HRTEM) image and the selected area electron diffraction (SAED) pattern (Figure 3b). Because it is atomically planar and electrically insulating, h-bn has been used as a dielectric substrate in high performance graphene-based heterostructures. [93,94] With the reported high thermal conductivity in bulk BN [95] /BN nanotubes [96] and the requirement for heat dissipation in nano-devices, the thermal conductivity of atomically thin h-bn has been explored in recent years, as shown in Figure 4. Compared to graphene, there are much less experimental data for the thermal conductivity of few-layer h-bn. 5-Layer and 11-layer mechanically exfoliated h-bn have been measured using a novel suspended micro-bridge device with U-shaped resistance thermometers. [38] Through careful estimation of the contact thermal conductance, the room temperature thermal conductivity of 11-layer h-bn was found to be 360 W m 1 K 1, close to the reported basal-plane value for bulk samples, while the 5-layer h-bn has a lower value compared with the 11-layer sample, which was attributed to the polymer residue on the thinner sample. Another result was reported using the optothermal Raman technique for 9-layer h-bn prepared by a LPCVD method. [39] Figure 3c,d show the temperaturedependent Raman spectra of that 9-layer h-bn from 298 K to 448 K. The Raman shift of E 2g peak used as the thermometer decreases with increasing temperature, giving a firstorder temperature coefficient of χ = cm 1 K 1. The calculated thermal conductivity is in the range from 227 to 280 W m 1 K 1 at room temperature, which is comparable to Thermal conductivity(wm -1 K -1 ) Lindsay et al. 1L Jo et al. 5L Jo et al. 11L Sichel et al. Bulk Zhou et al. 9L Chang et al. BNNT Wang et al. bilayer Temperature(K) Figure 4. Temperature-dependent thermal conductivity of few layer h-bn reported by Lindsay et al., [97] Jo et al., [38] Sichel et al., [95] Chang et al., [96] Zhou et al., [39] and Wang et al. [40] (5 of 17) wileyonlinelibrary.com 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

6 the data reported for 5-layer h-bn. [38] Using a PDMS-assisted dry-transfer method to prepare h-bn sample on the suspended micro-bridge device yielded cleaner surface than the previous PMMA-assisted method, which led to a thermal conductivity of 484 W m 1 K 1[40] for suspended bilayer h-bn at room temperature. This value is higher than that of bulk h-bn [95] but still lower than the theoretically predicted single layer h-bn, [97] indicating a thickness-dependent property consistent with previous theoretical results. [98] Although the reported experimental data have not provided obvious layer- or thickness-dependent thermal conductivity in h-bn, theoretical calculations revealed that it should have the similar trend as graphene. [98] The discrepancy between experiments and theoretical studies can be attributed to several different reasons. First of all, different crystal quality can be produced by different synthesis methods. In addition, the polymer-assisted transfer method could leave polymer residue on the sample, as mentioned above. In fact, amorphous poly mer residue has been observed at the edge of the sample in the HRTEM (Figure 3b). Theoretical analysis with the phonon Boltzmann transport equation shows that the contamination may induce additional phonon scattering, and hence reduce the thermal conductivity. The effects become even more obvious at lower temperature (Figure 4) due to the longer phonon mean free path (MFP) for the 5L and 11L h-bn. A similar influence of the polymer residue on thermal conductivity has also been discussed in details for bilayer graphene. [75] 3.3. Transition Metal Dichalcogenides (TMDs) Unlike graphene and h-bn, several 2DLMs have more than one atomic layer in a unit. For example, TMDs have a transition metal layer sandwiched by two chalcogenide atomic layers as shown in Figure 1e and Figure 5b (side view). Among all TMDs, MoS 2 has attracted the most attention for potential Figure 5. Structure characterization of MoS 2 : a) Top view and b) Side view of single layer MoS 2. c) High resolution transmission electron microscope and d) Selected area electron diffraction pattern image of few layer MoS 2. e) Four examples of Raman spectra of suspended, monolayer MoS 2 collected at 100, 180, 260, and 320 K. Spectra offset vertically for clarity. f) Raman peak frequencies of both A 1g (blue squares) and E 1 2g (red circles) modes as a function of temperature. Fitting lines and resulting linear temperature coefficients χ T are shown. The scale bar is 5 nm in (c). c,d) Reproduced with permission. [42] Copyright 2014, American Institute of Physics. e,f) Reproduced with permission. [43] Copyright 2014, American Chemical Society WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com (6 of 17)

7 Figure 6. Thermal conductivity of MoS 2 reported by Jo et al., [42] Sahoo et al., [41] Yan et al., [43] Liu et al. [105] applications in electronic and optoelectronic devices, [99 101] as well as chemical catalysis. [102] It has been shown that as the number of layers reduces, the band gap of MoS 2 turns from an indirect gap of 1.3 ev in bulk MoS 2 into a direct gap of 1.8 ev in a monolayer. [103,104] Additionally, the phonon vibration modes also change with different numbers of layers. [103] The layered structure, which can be seen at the edge of a few layer sample in HRTEM image (Figure 5c) and in the SAED pattern (Figure 5d), is related to the top view honeycomb structure of monolayer MoS 2 in Figure 5a. As a typical layered structure 1 material, the two prominent Raman peaks, i.e., the in-plane E 2g and out-of-plane A 1g mode, which relate to the in-plane opposite vibration between S and Mo atoms and the out-of-plane motion of S atoms, respectively, have been measured in Raman spectra (Figure 5e). [43] The temperature dependence of Raman spectra 1 in monolayer MoS 2 is illustrated in Figure 5e,f. Both the E 2g and A 1g peaks show a clear decreasing trend with temperature. The strong Raman signal of MoS 2 makes it ideal for the optothermal Raman measurement. There have been several theoretical investigations on the thermal transport of MoS 2 nanosheets and nanoribbons [ ] focusing on the basic phonon transport properties, anisotropic properties, and effect of defects and strains. The experimental study of thermal transport in few-layer MoS 2 prepared by chemical vapor deposition method has been reported by Sahoo et al. [41] (Figure 6). The thermal conductivity of an 11-layer sample was measured to be about 52 W m 1 K 1 at room temperature with the first-order temperature coefficient of A 1g peak. Later, a more detailed study of temperature- and laserpower-dependent Raman characterization on monolayer MoS 2 exfoliated from naturally occurring bulk materials yielded a thermal conductivity of 34.5 ± 4 W m 1 K 1[43] at room temperature. Jo et al. [42] used the micro-bridge method to measure the basal-plane thermal conductivity of MoS 2 with 4-layer and 7-layer thicknesses across a wide temperature range. As shown in Figure 6, the measured thermal conductivities of monolayer and few-layer MoS 2 are lower than that of bulk MoS 2. In addition to the suspended sample, a relatively higher thermal conductivity 62 W m 1 K 1 was observed in supported monolayer MoS 2. [114] As to the thickness dependence for thermal conductivity of MoS 2, a theoretical calculation has shown a decreasing trend from monolayer to three layers [115] due to the smaller group velocity for different phonon modes and higher phonon scattering rate induced by the changes of the anharmonic force constants, which can serve as a reference for further experiment studies. Results for other kinds of TMDs can be found in Table 1. A 32 W m 1 K 1 thermal conductivity of monolayer WS 2 has been measured with the optothermal Raman technique, [116] which is comparable to monolayer MoS 2 in Yan s work. [43] The similar phonon and Raman scattering in different kinds of TMDs from monolayer, multilayer, and bulk materials have been discussed earlier. [117] It is believed that other than phonon frequency due to the different mass between Mo and W atom, the general features of 1L-, 2L- and bulk structures in both MoS 2 and WS 2 should be similar. The thermal conductivity of a 45 nm-thick TaSe 2 sample was measured as 9 W m 1 K 1. [118] Moreover, an ultralow cross-plane thermal conductivity [119] (0.05 W m 1 K 1 ) was observed in disordered, layered WSe 2 sheets by TDTR Table 1. Room temperature thermal conductivity of different kinds of TMDs. Sample Size Method k (W m 1 K 1 ) Comments [43] MoS 2 monolayer Raman 34.5 exfoliated, transferred; suspended [42] MoS 2 4-layer Micro-bridge exfoliated, transferred; suspended 7-layer [41] MoS 2 11-layer Raman 52 CVD, transferred; suspended [114] MoS 2 monolayer Raman 62.2 supported TaSe 2 film [118] 45 nm film Raman 9 exfoliated; suspended [119] WSe 2 62 nm film TDTR 0.05 cross plane; disordered film [120] TiS 2 bulk Parallel thermal conductance method 0.69 organic intercalation WS 2 [116] monolayer Raman 32 CVD; suspended WS 2 [116] bilayer Raman 53 CVD; suspended (7 of 17) wileyonlinelibrary.com 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

8 technique. These results show tremendous opportunities for thermoelectric applications if the electrical properties can be optimized through stacking or combination of 2DLMs Black Phosphorus Black phosphorus (BP) is attracting a lot of attention as one of the emerging 2D semiconductors for potential applications in electronics and optoelectronics. [ ] The structure of monolayer BP is illustrated in Figure 7a,b. The two different geometries in the side view (Figure 7b) represent two different high-symmetry directions, denoted as the zigzag (ZZ) and the armchair (AM) directions. An exfoliated BP specimen characterized by transmission electron microscopy is marked with the two highly symmetric directions (Figure 7c,d). The anisotropic transport properties of BP due to its anisotropic structure have been both theoretically predicted and experimentally demonstrated, which provide opportunities for transport management. While success in exfoliating clean atomically thin layers from bulk BP makes it possible to investigate its property experimentally, BP is also well known for being unstable under the ambient environment. Therefore, passivation and protection processes, [45,127] such as using AlO x coating, have to be employed during the measurement. Similar to many other 2DLMs, a thickness-dependent [128] and strain-controlled [129,130] band gap has been found in few-layer black phosphorus. Unlike the well-explored electrical properties, there are only a few experimental studies of thermal transport in BP. A low thermal conductivity of 10 W m 1 K 1 was found in bulk Figure 7. Structure characterization of black phosphorous: a) Top view and b) Side view of single layer BP. c) High-resolution transmission electron microscopy lattice image of a BP flake. d) Selected area electron diffraction pattern taken from the area shown in (c). e) Four sample Raman spectra taken at 24, 42, 57, and 72 C with armchair-polarized laser. The dashed lines correspond to the peak positions at 24 C. f) The A g 2 Raman shift as a function of temperature for both armchair- and zigzag-polarized laser. The dashed lines show linear fit results. The scale bars are 10 nm 1 and 20 nm 1 in (c) and (d), respectively. c,d) Reproduced with permission. [44] Copyright 2015, Nature Publishing Group. e,f) Reproduced with permission. [46] Copyright 2015, Nature Publishing Group WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com (8 of 17)

9 polycrystalline BP samples. [131] There are many theoretical investigations [ ] on the thermal transport properties of BP, especially its anisotropic properties. Based on first-principles calculations, the Boltzmann transport equation has been used to extract the intrinsic in-plane thermal conductivity in two directions, which gives a relatively high anisotropic ratio of 3.5. For example, Jain and McGaughey [138] predicted values of 110 W m 1 K 1 and 36 W m 1 K 1 along the AM and ZZ directions, respectively, at 300 K. The thermal conductivity of few-layer BP near room temperature has been measured by the optothermal Raman technique and explained with ab initio phonon dispersion calculations. [46] To make a quasi-one-dimensional heat transfer along certain direction, a thin aperture was used to yield ultra-thin focal laser line perpendicular to the suspended BP on a narrow trench. Due to its most significant temperature sensitivity and high Raman intensity (Figure 7e,f), the A 2 g peak was selected as the thermometer from three Raman peaks. The measured AM and ZZ thermal conductivities were about 20 and 40 W m 1 K 1, respectively, for BP films thicker than 15 nm, showing a significant anisotropy. Meanwhile, another work using the micro-bridge method [44] for BP nanoribbons reported similar results. By micro-patterning exfoliated BP flakes with electron beam lithography (EBL) in a selected direction, anisotropic thermal transport at temperatures higher than 100 K was observed. In addition, the thickness and temperature dependence of the BP thermal conductivity has also been observed (Figure 8a) and the peak value of a 170 nm-thick BP nanoribbon reaches about 24 W m 1 K 1 and 21 W m 1 K 1 at 100 K and 150 K, respectively. Relatively thick exfoliated BP flakes with thickness ranging from 138 to 552 nm have been measured with the TDTR technique by Jang et al. [45] They extracted both cross-plane and in-plane thermal conductivity with the conventional and beam-offset TDTR technique, and observed strongly anisotropic in-plane thermal conductivities of 86 ± 8 and 34 ± 4 W m 1 K 1 along the zigzag and the armchair directions, respectively. Zhu et al. revealed 3D anisotropic thermal conductivities of black phosphorus and explained the results with the structural asymmetry-induced group velocity variation along different crystalline orientations by first-principles calculation. [139] By comparing differences between atomically flat plane (graphene) with the wave-like layer in MoS 2 and BP, the role the out-of-plane acoustic (ZA) mode played in the in-plane thermal transport is revealed and used to explain the thickness-dependent behavior. [45] For BP-like 2D materials with non-planar structures, the contribution of ZA mode for in-plane thermal conductivity is relatively low and the surface scattering is considered to be the dominating mechanism. [138] However, in graphene-like flat plane structures, the ZA mode dominates and will be suppressed in a few-layer structure and supported sample. [36] Therefore, the in-plane thermal conductivity decreases with increasing thickness in few-layer graphene-like materials, while the opposite trend exists in BP-like materials. The thickness-dependent in-plane thermal conductivity of BP is summarized in Figure 8b. In addition to the intrinsic thermal conductivity for BP, the promising performance for thermoelectrics has been studied in monolayer BP. [134,140] Theoretical calculation [141] has revealed that the prominent electrical and thermal conducting directions are orthogonal to one another. Therefore, it is expected Thermal conductivity(wm -1 K -1 ) b Thermal conductivity(wm -1 K -1 ) a Jang et al. Lee et al. Luo et al. Temperature(K) ZZ AM Temperature(K) Figure 8. a) Temperature-dependent thermal conductivity of BP flake (170 nm) in two directions. [44] b) Thickness-dependent thermal conductivity reported by Jang et al., [45] Lee et al., [44] and Luo et al. [46] Black, red, and blue symbols represent AM, ZZ, and cross-plane directions, repectively. that with proper doping levels, high ZT (= S 2 σ T/k) values can be obtained, due to the high electrical conductivity and low thermal conductivity in the AM direction. [141] With the advances in the micro-bridge method mentioned previously, Lee et al. [44] also measured thermoelectric properties (Seebeck coefficient and electrical conductivity) for BP nanoribbons. A higher power factor near room temperature is observed in AM nanoribbon (t = 170 nm), which originates from a Seebeck coefficient of 320 µv K 1 and an electrical conductivity of about 1500 S m 1. The relatively low ZT value (ZT = ), smaller than the theoretically predicted value for monolayer BP, is attributed to the low σ in the undoped sample and high k in thick BP ribbons. In addition, electrical and thermoelectric transports have also been investigated in thin black phosphorus devices with gated electric fields, giving a Seebeck coefficient of about 0.4 mv K 1 at room temperature. [46] Following these experimental works (9 of 17) wileyonlinelibrary.com 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

10 and insights, a high anisotropy ratio in thermal conductivity and improved thermoelectric properties are expected in atomically thin BP Bismuth Telluride Another type of 2DLMs that draws significant attention is the group V VI materials, such as Bi 2 Te 3, Bi 2 Se 3, and Sb 2 Te 3. As illustrated in Figure 9ab, these materials consist of van der Waals connected quintuple layers, in which five atomic layers are covalently bonded in plane. This group of materials is attracting a lot of attention mainly because of two reasons. First, materials like Bi 2 Te 3 have been known as some of the most important thermoelectric materials. Moreover, some members like Bi 2 Te 3, Bi 2 Se 3, and Sb 2 Te 3 have recently been identified as topological insulators (TI) with topologically protected conducting surface states. [ ] In the past few years, there have been many efforts to build the correlation between topological insulator behavior and the superior thermoelectric performance [146,147] or to take advantage of these surface states to further improve the thermoelectric performance, [ ] but so far no widely accepted consensus has been reached in the community. A theoretical calculation, based on molecular dynamics, predicted a more detailed trend for in-plane lattice thermal conductivity (k l ) in few-layer Bi 2 Te 3 at room temperature. [153] It is predicted that k l will demonstrate a non-monotonous trend with first a decrease from 12 to 3 quintuple layers and then an increase as the quintuple layers further reduces from 3 to 1. As such, a minimum value of 1.1 W m 1 K 1 is expected at 3 quintuple layers due to the interplay between phonon Umklapp scattering and boundary scattering. BiSbTe bulk alloy demonstrated an enhanced peak ZT value of up to 1.4 at a temperature of about 100 C, [154] which was mainly attributed to the reduced thermal conductivity. Via vacuum vapor phase deposition [ ] and mechanical exfoliation, [10,158] atomically thin 2D nanoplates and ultrathin films with maximum lateral sizes of up to 20 µm can be obtained. The as-synthesized Bi 2 Te 3 nanoplates (Figure 9c) with high crystal quality (Figure 9d) have been used for measuring thermoelectric properties through the micro-bridge method (Figure 9e). [47] Thermal conductivity results with selected thicknesses, 9.2 nm (black rectangle), 13.1 nm (red circle) and 20.9 nm (green diamond), were plotted in Figure 10a. Obviously, a reduced k can be observed when the thickness of Bi 2 Te 3 is reduced below 20 nm compared with the bulk value (2 3 W m 1 K 1 ) in basal-plane. Another result is used as comparison (Figure 10a), in which in-plane (purple) or cross-plane (pink) thermal conductivity was measured in stacked Bi 2 Te 3 thin films. [10] A further reduction of thermal conductivity below 1 W m 1 K 1 in both directions was observed due to the phonon interface scattering between thin films. Figure 10b shows the experimental thickness-dependent thermal conductivity in comparison with the theoretical lattice thermal conductivity of one quintuple layer. Figure 9. Structure characterizations of Bi 2 Te 3 : a) Side view of several quintuple layer and b) Top view of one quintuple layer. c) Bi 2 Te 3 NPs protruding out of a SiO 2 substrate and d) transferred onto a microbridge device (25.2 nm thick NP). e) Selected area electron diffraction pattern from a 4.25 µm diameter suspended section of the 17.8 nm thick NP showing transport is along the 1120 direction in the single crystal (arrow). The scale bars are 10 µm, 2 nm, and 0.5 Å 1, respectively. c e) Reproduced with permission. [47] Copyright 2013, American Chemical Society. 4. Applications 4.1. Thermoelectrics Compared to bulk and other low-dimensional material systems, the unique layer-dependent and anisotropic transport properties in 2DLMs make them promising for transport management. Due to the huge surface-area-to-volume ratio, surface states may dominate the transport properties, which have been investigated in 2D TIs for enhanced thermoelectric performance. [159] Although these advantages in 2DLMs and obtained improved thermoelectric performance in nanostructured BiSbTe alloys [154,160] suggest better thermoelectric properties of the group V VI 2DLMs, investigation of the thermoelectric property of Bi 2 Te 3 nanoplates yielded reduced seebeck coefficient and limited ZT (below 0.25). [47] This significant reduction in the ZT value is attributed to the surface band bending effect induced by exposure of samples to ambient conditions. Most recent work demonstrates that such surface band bending in TI could modify the band structure, tune the Fermi level, and 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com (10 of 17)

11 Figure 10. a) Temperature-dependent thermal conductivity of Bi 2 Te 3 nanoplates and films (9.2 nm black rectangle, 13.1 nm red circle, and 20.9 nm green diamond). b) Thickness-dependent property of 2D Bi 2 Te 3 : calculated single layer [153] and measured few layer. [47] therefore could significantly alter the Seebeck coefficient and electrical conductivity. [161] As an example of TMDs for flexible thermoelectric application, the organic intercalation of TiS 2 [120] showed a low thermal conductivity of 0.69 W m 1 K 1. In addition, attractive thermoelectric properties in inorganic/ organic hybrid 2D superlattices with enhanced electrical mobility and reduced thermal conductivity are also reported. [120] A room temperature ZT of about 0.13 in SnS 2 (16 nm thick) has been reported, which represents a high value in a thin layer and at high temperature. [162] Additionally, a high power factor [163] has been measured for bi-layer MoS 2, and a high Seebeck coefficient was found in thick BP materials and devices. [164] Besides the in-plane transport properties, thermoelectric transport across 2D heterostructures has been investigated in the graphene/h-bn/graphene system, [165] with the thermoelectric voltage generated at the interface giving a Seebeck coefficient of about 99.3 µv K 1. Furthermore, the lower thermal conductivity in the cross-plane direction due to weak van der Waals interaction is favorable for thermoelectric applications. For example, the ultralow value of cross-plan thermal conductivity in random-stacked WSe 2 [119] may help to improve ZT Thermal Interface Material The high thermal conductivities observed in 2DLMs such as graphene and few-layer h-bn provide opportunities to improve heat transfer at the interface, [166] even though it should be noted that heat dissipation in 2DLMs supported on a substrate is quite different from the intrinsic in-plane thermal transport in suspended 2DLMs. [36,73,167,168] Recent data [165] have shown a thermal interface conductance of about W m 2 K 1 at the graphene/h-bn heterojunction, which is lower than that of the common metal/graphene/substrate combination due to the different interface quality. It is expected that with a high quality interface enabling high in-plane thermal conductivity, 2DLMs can play a critical role in the next generation of electronic and optoelectronic devices. [169,170] Additionally, due to the high basal-plane thermal conductivity, few-layer graphene and graphite have been used as thermal interface material [171] to enhance thermal conductivity in a poor thermal conductive medium. Balandin et al. introduced applications in thermal interface materials by using hybrid-graphene composites. [172,173] As part of the efforts to achieve energy sustainability in heating and cooling applications, researchers have pursued using phase-change materials (PCM) for energy harvesting. Thermal interface materials have been applied to enhance the ultralow thermal conductivity (<1 W m 1 K 1 ) of common PCMs. More recently, attentions have been focused on a graphene-based supported foam. The ultrathin graphene foam (UGF) has been used as a supported architecture (Figure 11a c) and is easily combined with PCMs. With the designed structure, a higher k in UGF composites is reported (Figure 11d). [ ] The progress in the growth and assembly of 2DLMs [177] and the theoretical analysis [ ] of thermal transport in heterostructures enables the combination of 2DLMs with various thermal properties for advanced functions and applications. With tremendous potential demonstrated, there are also several challenges before widespread applications can be realized. First, to date, most of the thermal measurement results concern the thermal properties of graphene and its hybrid structures. The relevent studies of other 2D materials and novel heterogeneous structures [183,177] remain limited. Second, unclear interfacial thermal conductance at the interface between 2DLMs and other materials makes it challenging to produce a well-defined and uniform thermal contact, which is crticial for the thermal management performance on the chip-scale devices. [184,185] One particular issue worth special attention in the application of 2DLMs is their highly anisotropic thermal properties, [105] which stem from their unique crystalline structures. Because of the much weaker van der Waals interactions between different atomic layers as compared to the much stronger covalent bonds within each atomic layer, the thermal conductivity along the cross-plane direction is much lower. Interestingly, different from the more traditional view that the low thermal conductivity corresponds to a short phonon MFP, [186,187] the MFP (11 of 17) wileyonlinelibrary.com 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

12 Figure 11. (a) Scanning electron microscopy images of the strut walls of freestanding graphene-based foam (GF) samples. b) Low resolution and c) High resolution transmission electron microscopy. d) Measured thermal conductivity of unfilled UGFs, k foam, (open circles) and UGF PCM composites, k comp, (filled circles) at near room temperature. Shown for comparison are results from the rule of mixtures calculations. Scale bars are 50 µm for (a), 1 µm for (b), 5 nm for (c), and 1 nm for inset in (c). a c) Reproduced with permission. [174] Copyright 2012, American Chemical Society. d) Reproduced with permission. [175] Copyright 2014, Royal Society of Chemistry. along the c-axis can in fact be quite long. For example, it has been recently realized that for graphite, the c-axis MFP could be 200 nm long, nearly two orders of magnitude larger than the traditionally believed value of just a few nanometers. [ ] While we are not aware of any experimental data for thermal conductivity of 2D heterostructures along the cross-plane direction, it would be extremely interesting to see whether these structures lead to coherent phonon transport as new monolithic materials with reconstructed phonon spectra, or these structures simply behave as many interfaces that scatter phonons. One important implication of the potentially very long phonon MFP along the c-axis of 2DLMs in their application as thermal interfacial materials is that if a layer of 2DLMs of thickness less than the phonon MFP is used, then phonons could be bounced back and forth between the two boundaries. Only when phonons experience three phonon scattering within the 2DLM can they be converted into phonons that can be transported along the in-plane directions and dissipate heat along the basal plane. Even though this has not been directly verified in 2DLMs, this conclusion can be drawn from the experimental observation that the contact area-normalized contact thermal conductance between individual multi-wall carbon nanotubes is still approximately linearly proportional to the tube diameter or number of walls in each tube. [188] It is worth noting that structure anisotropy could also lead to very different thermal conductivities within the basal plane, which has been predicted by theoretical or numerical studies. [111,132,192] However, to date, besides the reported results in BP, [44 46] experimental demonstration of anisotropic thermal conductivity along different directions within the basal plane of 2DLMs has been lacking. As such, it will be very interesting to experimentally verify whether strong anisotropy exists along different directions in the basal plane. In fact, enhanced thermoelectric performance has been predicted by taking advantage 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim wileyonlinelibrary.com (12 of 17)

13 of the strong anisotropy of thermal transport in the basal plane of phosphorene. [141] 5. Conclusion and Outlook In summary, in the past few years quite a few 2DLMs have been fabricated into atomically thin samples, and studied for their thermal transport properties, with special attention paid to the effects of sample size and temperature dependence. Optothermal Raman technique can extract thermal conductivity efficiently, while the suspended micro-bridge method can also simultaneously obtain thermoelectric parameters. Using these two methods, attractive in-plane thermal conductivity and thermoelectric properties have been revealed in graphene, h-bn, MoS 2, BP and Bi 2 Te 3, respectively. While a graphene-like flat plane structure enables ultrahigh thermal conductivity, [79] intrinsic phonon-phonon scattering due to lattice anharmonicity and stronger phonon-isotope scattering limit its value in h-bn. [97] In the case of sandwiched structures of monolayer TMDs (such as MoS 2 ), the non-planar structures with much weaker interatomic bonds result in quite different phonon dispersions (group velocities and Grüneisen parameters), [103,107,117] which result in remarkably lower thermal conductivities. In addition to the interatomic bonds, differences may also arise from interlayer coupling strength. As an example, a recent theoretical investigation reveals a correlation between thermal resistance and interface coupling strength at graphene/h-bn interface. [178] Anisotropic interlayer coupling in BP [130] and tunable thermal conductivity at van der Waals interfaces in BN ribbons [193] also indicate the dependence of thermal transport on interlayer bonds. It is generally recognized that enhanced interlayer coupling directly reduces interfacial thermal resistance and that phonon coupling will affect basal plane thermal transport. [178,193] These fully account for the general and distinct thermal transport properties in 2DLMs and their hybrid structures. The unique and exciting properties provide challenges and opportunities for further understanding of fundamental phonon transport mechanisms and broader applications in fields involving thermal transport fields. Nanoscale devices based on these 2DLMs are emerging in thermoelectric conversion and comprehensive heat management fields. Despite these great progresses in 2D thermal transport, there are still questions remaining to be answered. Measurements of monolayer structures (except for graphene and MoS 2 ) are still a challenge and are needed for a thorough understanding of the intrinsic thermal properties of other 2DLMs. In several aspects, the reported experimental results are not consistent with theoretical analysis. For example, different thickness-dependent thermal conductivity was shown with some controversies. Except for a series of experimental results in graphene, there is not yet a complete size-dependent thermal conductivity measurement using the same technique in other 2DLMs. Different measurement methods and diverse sample quality, as well as the uncertain thermal interface resistance have led to scattered data among different experiments. Another point that must be noted is that, according to the theoretical predictions [91,194] and the experimental measurement, [44] the thermal conductivity of 2DLMs may vary significantly with sample length while keeping the width constant. As such, data from different experiments may not be strictly comparable due to their different lateral scales. More accurate measurements, more unique properties, and broader applications in these intriguing 2D systems attract us to go further. In order to get more accurate thermal conductivity, we may need to build novel measurement setups that can reduce the errors, such as those from the thermal contact resistance in the experiments. Moreover, further investigation can be expected in new 2D systems. For example, most recent reports in PtS 2 [195] and the MoS 2 /WS 2 heterostructure [196] have aroused huge interest in strong interlayer interaction, which may cause different transport property compared to the weak van der Waals interactions in conventional 2DLMs. Although several theoretical analyses have been reported for hybrid 2D materials, more experimental results are in demand for an intensive understanding. Additionally, ultralow thermal conductivity and high figure of merit in single-crystal bulk SnSe [197,198] and the recently reported negative correlation between electrical and thermal conductivity in SnS 2 [162] could be beneficial for thermoelectric applications. Along with several experimental results of heat rectification in 1D system, [69,199] thermal diodes in 2D systems have not been explored intensively in experiment either, though a theoretical analysis has been made. [200] In addition, the development and the construction of new 2DLMs also open tremendous opportunities. For example, 2DLMs, consisting of a covalently bonded, dangling-bond-free lattice and weakly bound (by van der Waals interactions) neighboring layers, can serve as building blocks for constructing a wide range of interesting structures, such as mosaics and van der Waals heterostructures (vdwhs), without the constraints of lattice matching and processing compatibility. It is expected that this will provide a new playground for exploring materials and structures with novel thermal properties and developing their thermal related applications. Acknowledgements This work is jointly supported by the State Key Program for Basic Research of China (No. 2015CB659300), National Natural Science Foundation of China (NSFC No and No ), Natural Science Foundation of Jiangsu Province (No. BK ), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and the Fundamental Research Funds for the Central Universities. The authors thank Mr. Matthew D. Gerboth for his careful proofreading of the manuscript. Received: August 11, 2016 Revised: November 8, 2016 Published online: January 6, 2017 [1] K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, A. K. Geim, Proc. Natl. Acad. Sci. USA 2005, 102, [2] M. Xu, T. Liang, M. Shi, H. Chen, Chem. Rev. 2013, 113, [3] S. Z. Butler, S. M. Hollen, L. Cao, Y. Cui, J. A. Gupta, H. R. Gutie, T. F. Heinz, S. S. Hong, J. Huang, A. F. Ismach, (13 of 17) wileyonlinelibrary.com 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim