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Beyond graphene, the layered transition metal dichalcogenides (TMDs) have gained considerable attention due to their unique properties. Herein, we review the lattice dynamic and thermal properties of monolayer TMDs, including their phonon dispersion, relaxation time, mean free path (MFP), and thermal conductivities. In particular, the experimental and theoretical studies reveal that the TMDs have relatively low thermal conductivities due to the short phonon group velocity and MFP, which poses a significant challenge for efficient thermal management of TMDs-based devices. Importantly, recent studies have shown that this issue could be largely addressed by connecting TMDs and other materials (such as metal electrode and graphene) with chemical bonds, and a relatively high interfacial thermal conductance (ITC) could be achieved at the covalent bonded interface. The ITC of MoS2/Au interface with chemical edge contact is more than 10 times higher than that with physical side contact. In this article, we review recent advances in the study of TMD-related ITC. The effects of temperature, interfacial vacancy, contact orientation, and phonon modes on the edge-contacted interface are briefly discussed.
Two-dimensional (2D) material is a rapidly expanding research area. The great success of graphene has ignited intensive interest in other 2D materials. The layered transition metal dichalcogenides (TMDs) is one of the most widely researched classes of 2D materials beyond graphene. The TMDs are normally represented with the formula MX2, where X is a chalcogen atom (S, Se, or Te), and M is a transition metal atom from groups IV–X (such as Ti, Mo, and W), as shown in Fig.
![]() | Fig. 1. (color online) Transition metals and the three chalcogen elements in the TMD layered structures. Reprinted with permission from Ref. [1], copyright (2013) by Macmillan Publishers Limited. |
![]() | Fig. 2. (color online) (a) Structure of monolayer MoS2. Side view (b) and top view (c) of monolayer MoS2. The horizontal orientation is armchair direction, the vertical orientation is zigzag direction. The atoms in purple and yellow color are Mo and S, respectively. Reprinted with permission from Ref. [2], copyright (2013) by the Frontiers of Physics. |
TMDs have gained significant interest due to their unique optical, electronic, mechanical and thermal properties.[3] The monolayers of all the members in this family are semiconducting with bandgaps of around 1–2eV,[4] which makes them prime candidates for electronic devices. Furthermore, unlike the indirect bandgaps for bulk TMDs, the monolayer TMDs has direct bandgaps due to their ultrathin structures (quantum confinement), which induce the changes of electronic structure in monolayer TMDs. The direct bandgap indicates that they are also well suited for optoelectronics. Indeed a wide range of different TMD-based optoelectronic devices have already been successfully fabricated, such as high-performance field-effect and thin film transistors,[5] photovoltaics,[6] and photodetectors.[7] As a member of 2D TMD family, monolayer MoS2, has a large direct bandgap of 1.8 eV. For MoS2 transistor, through various processing techniques, such as improving sample quality, removing absorbates, or depositing atop a high-dielectric layer, its room temperature carrier mobility can be significantly enhanced,[8–11] and close to its theoretically predicted phonon-limited intrinsic value (about
Thermal management is an important issue for the design and application of electronic devices, which even is becoming a limiting factor currently to the device development.[15–29] Owing to the atomic thickness of monolayer TMDs, thermal management is more challenging in TMDs-based electronics. On one hand, highly localized Joule heating in their ultrathin confined space can easily create “hot spots”.[30,31] On the other hand, previous experimental[32–34] and theoretical studies[2,35–40] revealed that the thermal conductivities of monolayer TMDs are 2–3 orders lower than that of graphene. These two limitations cause a crucial bottleneck for efficient thermal management of TMD-based devices. Furthermore, similar to electron scattering at an interface, phonon scattering at an interface also plays a critical role in the nanoscale devices, which is even more crucial than the material itself.[41–43] Thus, low thermal conductivity in monolayer TMDs and thermal conductance at the interface will significantly affect performance and reliability of the TMDs-based devices.
In this article, we review the recent advances in the study of the dynamic and thermal properties of 2D TMDs from both experimental and theoretical points of view. The rest of this article is organized as follows: section
Since phonon energy is essentially the energy of atomic vibrations, to understand the thermal properties of TMDs, it is necessary to firstly inspect the lattice vibrational modes (phonons) of the materials. MoS2 is a typical layered dichalcogenide, and the most studied material in this family. Each MoS2 unit cell contains 3 (1 Mo and 2 S) atoms, which leads to the formation of 3 acoustic (A) and 6 optical (O) phonon modes as shown in Fig.
![]() | Fig. 3. (color online) Phonon dispersion and projected PDOS for (a) MoS2, (b) MoSe2, and (c) WS2. Reprinted with permission from Ref. [44], copyright (2016) by the Royal Society of Chemistry. |
The phonon dispersion and density of states (DOS) of MoSe2 and WS2 are also shown in the Figs.
At the low wave vector
![]() | Fig. 4. (color online) Phonon group velocity of acoustic phonon modes along the ![]() |
Phonons have relaxation times as they travel through the materials due to various scattering processes, such as phonon–phonon umklapp scattering, boundary scattering, and defects scattering. Since extrinsic boundary scattering and defects scatting can be removed by improving material quality, the phonon–phonon umklapp scattering is highly associated with the intrinsic phonon relaxation process/time, which can be derived through Klemensʼs time-dependent perturbation theory[48,49]
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![](cpb_27_3_034402/cpb_27_3_034402_ieqn15.gif)
![](cpb_27_3_034402/cpb_27_3_034402_ieqn16.gif)
![]() | Fig. 5. (color online) (a) Relaxation time and (b) mean free path for LA, TA, and ZA modes in monolayer MoS2 with a function of frequency. Reprinted with permission from Ref. [36], copyright (2014) by American Physical Society. |
Phonon mean free path (MFP) is a key quantity for understanding the size-dependent thermal properties. The umklapp scattering limited MFP λ can be obtained, based on the mode relaxation time τ and group velocity v. The phonon MFP for the mode at the
The thermal conductivity κ of monolayer TMDs can be obtained based on Fourierʼs law,
The low thermal conductivities of TMDs have been reported in both theoretical[2,36,44] and experimental[32–34,51] studies. Table
![]() | Table 1.
Summary of the thermal conductivities of different monolayer TMDs at room temperature. . |
![]() | Table 2.
Summary of the interfacial thermal conductances between different monolayer MoS2 and other materials at room temperature. . |
It has been well known that the in-plane thermal conductivity of graphene decreases significantly when it is in contact with a substrate.[47] Similar trends has also been reported for monolayer TMDs due to damping of the flexural acoustic phonon.[55] Using optothermal Raman technique, the measured thermal conductivities of suspended monolayer MoS2 and MoSe2 are 84 and
Monolayer TMDs is promising in electronic and photonic device applications, such as transistors, light-emitters, and photodetectors.[57] With the successful growth of MoS2 on insulating substrates,[14] and the significant improvement in the mobility,[58–60] it is reasonably expected that high-performance field-effect transistors based on monolayer MoS2 will be realized in the near future. Unlike the single transistor, owing to the atomic thickness of 2D materials, thermal management of their integrated devices is becoming vitally important. The Joule heating in the confined ultrathin 2D TMDs can easily create localized hot spots. Unfortunately, previous studies[2,32–35] revealed that the monolayer TMDs have remarkable low thermal conductivity. Furthermore, phonon scattering at an interface also plays a critical role, which hinders the heat transport across the interface.[41–43,61–63] combination of these limitations poses a significant challenge for efficient thermal management of TMDs-based devices, and interfacial thermal conductance (ITC) between TMDs and other (electrode) materials will adversely affect device reliability and performance.
In general, there are two types of interface geometry between TMD sheets and other material surface: side contact and edge contact.[57]
Side contact can be made by contacting the basal plane of TMD sheet with other materials surface. However, the pristine surface of TMD sheet does not tend to form covalent bonds with the other material surface, and the interface across them can only interact via van der Waals forces, thus normally a low ITC is expected at the side contact interface. The ITC for MoS2/graphene interface is
As discussed before, monolayer TMDs have very low in-plane thermal conductivities and interfacial thermal conductance at the side-contacted interface, which hinder the heat dissipation from TMDs-based integrated devices. A probable solution is to construct an edge-contacted interface with covalent bonds by fully utilizing the contacted relative high thermal conducting materials to speed up the heat dissipation of “hot-spot” in TMDs-based devices.
As a typical example, MoS2 field effect transistor (FET), it has been reported that there exists a large contact resistance at the interface between the MoS2 sheet and metal electrode with the side contact due to the van der Waals gap, which drastically restrains the drain current.[57] However, for the edge contact, strong overlapping of electronic orbitals exists between the MoS2 and metal electrode, which leads to a remarkable reduction in tunnel barrier and a significant increase in electrical current. The ITC has been significantly increased from
Although the thermal conductivity of monolayer MoS2 is 2–3 orders lower than that of graphene, it is interesting to find that the covalent bonds formed at the MoS2/metal interface enables its ITC to be comparable with that of graphene-metal interface. As shown in Fig.
![]() | Fig. 6. (color online) Dependence of interfacial thermal conductance on Au crystal surfaces and contact directions. Reprinted with permission from Ref. [61], copyright (2016) by the Springer. |
Furthermore, the ITC is found temperature-dependent. Figure
![]() | Fig. 7. (color online) (a) Interfacial thermal conductance of MoS2/Au interface as a function of temperature; (b) interfacial temperature jump and heat flux as a function of temperature. Reprinted with permission from Ref. [61], copyright (2016) by the Springer. |
Since phonon energy is essentially the energy of atomic vibrations, the analyses of energy transfer across interfaces can also be carried out in the frequency domain. From lattice dynamic point of view, the key factor that determines the phonon transport across two connecting materials is the overlapping of phonon PDOS between them.[62,63,73–75] The overlapping/similarity of PDOS two connecting materials can be quantitatively analyzed using cosine similarity measure[74]
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![](cpb_27_3_034402/cpb_27_3_034402_ieqn43.gif)
![](cpb_27_3_034402/cpb_27_3_034402_ieqn44.gif)
![]() | Fig. 8. (color online) Phonon density of states of Au and MoS2 with different S vacancy concentration in the central region of MoS2. Reprinted with permission from Ref. [61], copyright (2016) by the Springer. |
Besides MoS2/metal edge contact, edge contact between TMDs and other 2D materials is also an interesting and important issue. For example, unlike low thermal conducting MoS2, another 2D counterpart, graphene, has ultra-high thermal conductivity.[76–79] Naturally, it is expected to construct edge-contacted MoS2/graphene interface to speed up the heat transport. Figure
![]() | Fig. 9. (color online) In-plane MoS2/graphene covalent-bonded heterostructure with hot and cold baths at the ends. Reprinted with permission from Ref. [63], copyright (2017) by the Springer. |
According to the molecular dynamics simulation, it is found that each covalent bond at the interface serves as an independent channel for thermal conduction, which enables the ITC to be tuned linearly by adjusting the interfacial bond density.
The efficiency of different phonon modes transferring across the interface can be quantified by energy transmission coefficient α using the phonon wave packet method.[81,82] The energy transmission coefficient α can be obtained by
![]() | Fig. 10. (color online) Snapshots of a phonon wave packet travelling across the MoS2/graphene interface. The travelling direction is indicated by blue arrows, and brown dashed lines denote the interface. (a) LA, ![]() ![]() ![]() ![]() |
![]() | Fig. 11. (color online) Energy transmission coefficient α of a phonon wave packet as a function of frequency. The inset displays the phonon dispersion of graphene and MoS2. The MoS2 phonon dispersion is adopted from Ref. [36] by first principle calculations. Reprinted with permission from Ref. [63], copyright (2017) by the Springer. |
Meanwhile, the rapid development in materials synthesis techniques has made many novel edge-contacted in-plane 2D heterostructures possible. For example, recently, 2D graphene/h-BN in-plane heterostructures were successfully synthesized.[82] In particular, it is now possible to grow atomically sharp interfaces between graphene and h-BN domains using combined atmospheric pressure chemical vapor deposition (CVD) and reactive ion etching.[83] These fascinating advances in the synthesis of 2D heterostructures have laid a promising foundation for realizing such edge-contacted interfaces.
This article presents an overview of the thermal properties of TMDs in both experimental and theoretical perspectives. The lattice dynamics and thermodynamic properties of TMDs have been summarized. The experimental and theoretical studies reveal that the TMDs have relatively low thermal conductivities, which are 2–3 orders lower than that of graphene. The low thermal conductivities pose a significant challenge for efficient thermal management of TMDs-based devices. In the context of TMDs-based electro devices, heat dissipation from the devices and interconnects is primarily limited by their low thermal conductivities and the relatively weak van der Waals interfaces. The recent studies have suggested that this issue could be largely addressed by connecting TMDs and other materials with covalent bonds, and the interfacial thermal conductance of the covalent bonded interface could be highly tunable.
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