2D Materials TOPICAL REVIEW • OPEN ACCESS Recent citations Graphene related materials for thermal - Efficient machine-learning based management interatomic potentialsfor exploring thermal conductivity in two-dimensional materials Bohayra Mortazavi et al To cite this article: Yifeng Fu et al 2020 2D Mater. 7 012001 - Impact of p-Type NiO Pocket and Ultra- Thin Graphene Layer on the RF Performance of -Ga2O3 MOSFET Narendra Yadava et al - The dimensionality effect on phonon View the article online for updates and enhancements. localization in graphene/hexagonal boron nitride superlattices Tengfei Ma et al This content was downloaded from IP address 158.109.11.194 on 29/06/2020 at 14:43 2D Mater. 7 (2020) 012001 https://doi.org/10.1088/2053-1583/ab48d9 OPEN ACCESS TOPICAL REVIEW Graphene related materials for thermal management RECEIVED Yifeng Fu1 , Josef Hansson1 , Ya Liu1,2, Shujing Chen3, Abdelhafid Zehri1, Majid Kabiri Samani1, 13 June 2019 Nan Wang4, Yuxiang Ni5 , Yan Zhang3 , Zhi-Bin Zhang6 , Qianlong Wang7, Mengxiong Li2, Hongbin Lu2, RE VISED 21 August 2019 Marianna Sledzinska8 , Clivia M Sotomayor Torres8,9, Sebastian Volz10, Alexander A Balandin11 , ACCEP TED FOR PUBLICATION Xiangfan Xu12 and Johan Liu1,3 27 September 2019 1 Electronics Materials and Systems Laboratory, Department of Microtechnology and Nanoscience (MC2), PUBLISHED Chalmers University of Technology, SE-412 96 Göteborg, Sweden 2 22 October 2019 State Key Laboratory of Molecular Engineering of Polymers, Department of Macromolecular Science, Collaborative Innovation Center of Polymers and Polymer Composites, Fudan University, 2005 Songhu Road, Shanghai 200433, People’s Republic of China 3 Original content from SMIT Center, School of Mechatronics Engineering and Automation, Shanghai University, Shanghai 200444, People’s Republic of China 4 this work may be used SHT Smart High Tech AB, Kemivägen 6, SE-412 58, Gothenburg, Sweden 5 under the terms of the School of Physical Science and Technology, Southwest Jiaotong University, 610031, Chengdu, People’s Republic of China Creative Commons 6 Division of Solid-State Electronics, Department of Engineering Sciences, Uppsala University, SE-751 21, Uppsala, Sweden Attribution 3.0 licence. 7 Shenzhen Shen Rui Graphene Technology Co., Ltd, Huike Industrial Park, Baoan District, Shenzhen, People’s Republic of China Any further distribution 8 Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, Barcelona, 08193, Spain of this work must 9 maintain attribution ICREA-Institucio Catalana de Recerca i Estudis Avancats, E-08010 Barcelona, Spain 10 to the author(s) and the Laboratory for Integrated Micro-Mechatronic Systems LIMMS/CNRS-IIS(UMI2820), Institute of Industrial Science, title of the work, journal The University of Tokyo, 4-6-1 Komaba, Meguro-ku,Tokyo, 153-8505, Japan citation and DOI. 11 Nano-Device Laboratory, Department of Electrical and Computer Engineering, Materials Science and Engineering Program, University of California, Riverside, California 92521, United States of America 12 Center for Phononics and Thermal Energy Science School of Physics Science and Engineering, Tongji University, Shanghai 200092, People’s Republic of China E-mail: yifeng.fu@chalmers.se, johanliu@shu.edu.cn and xuxiangfan@tongji.edu.cn Keywords: graphene, 2D materials, thermal management, material fabrication, thermal characterization Abstract Almost 15 years have gone ever since the discovery of graphene as a single atom layer. Numerous papers have been published to demonstrate its high electron mobility, excellent thermal and mechanical as well as optical properties. We have recently seen more and more applications towards using graphene in commercial products. This paper is an attempt to review and summarize the current status of the research of the thermal properties of graphene and other 2D based materials including the manufacturing and characterization techniques and their applications, especially in electronics and power modules. It is obvious from the review that graphene has penetrated the market and gets more and more applications in commercial electronics thermal management context. In the paper, we also made a critical analysis of how mature the manufacturing processes are; what are the accuracies and challenges with the various characterization techniques and what are the remaining questions and issues left before we see further more applications in this exciting and fascinating field. Contents 3.1.3. LPE graphene based heat spreader 8 3.2. Graphene enhanced thermal composites 11 1. Introduction 2 3.3. Graphene fibers 13 2. Basic theory of thermal transport 4 3.4. Graphene laminates 13 3. Materials development 4 3.5. Graphene based 3D structures 14 3.1. Graphene based heat spreaders 4 3.5.1. Graphene foam 14 3.1.1. Mono- and few-layer graphene 3.5.2. Vertically aligned graphene sheets 15 based heat spreader 5 3.5.3. Hybrid graphene structures 15 3.1.2. Graphene film as heat spreader 6 3.6. Graphene nanofluids 15 © 2019 IOP Publishing Ltd 2D Mater. 7 (2020) 012001 Y Fu et al 3.7. Other 2D materials 17 2D materials are a group of materials possessing 3.8. Summary 19 layered structures with a thickness of a few atoms. 4. Modeling of thermal transport in graphene 19 The most representative 2D material is graphene, 4.1. Molecular dynamics simulations which was mechanically exfoliated for the first time of interfacial thermal resistance involving by Novoselov et al, using Scotch tape [2]. Graphene graphene20 consists of carbon atoms bonded in a hexagonal lat- 4.1.1. The impact of graphene layer tice and exhibits unique structural, electrical, thermal, number20 mechanical and chemical properties [3–5], therefore it 4.1.2. The effects of interfacial has become one of the hottest research fields for vari- coupling and substrate property 22 ous applications in both academia and industry. For 4.1.3. The effects of doping on instance, a record high electron mobility of 3  ×  107 graphene thermal performance 24 cm2 V−1 s−1 has been theoretically predicted for gra- 4.2. Functionalization of graphene to phene [6] and a mobility of 350 000 cm2 V−1 s−1 has increase heat spreading performances 24 been exper­imentally reported from chemical vapor 5. Thermal characterization 25 deposition (CVD)-grown graphene [7], which could 5.1. Thermal bridge 25 meet the requirement of high-end electronic devices. 5.2. Electron beam self-heating method 26 The extremely strong yet flexible feature of graphene 5.3. Scanning thermal microscopy 27 also holds the promise of many demanding applica- 5.4. Optothermal Raman spectroscopy 28 tions such as sport equipments [8, 9], flexible batteries 5.5. Pulsed photothermal reflectance 29 [10, 11], solar cells [12–14], etc. With the rise of gra- 5.6. Dependence of resistance on temperature 30 phene, other 2D materials also attracted great interest 5.7. Joule heating 30 for potential applications in electronics [15–17]. 5.8. 3ɷ method 31 Among the unique properties of graphene and 5.9. Transient plane source 31 related 2D materials, their high thermal conductivity 5.10. Laser flash 31 [18–25] shows great potential to address the thermal 5.11. Summary 33 management challenge in electronics systems. Taking 6. Current and future potential applications 34 graphene for example, the first measurements of sus- 7. Concluding remarks 34 pended graphene using optothermal Raman technique References35 by Balandin et al (as shown in figure 1) revealed that the thermal conductivity values substantially exceeding 1. Introduction that of the bulk graphite which is ~2000 W m−1 K−1 at room temperature (RT) [18, 19]. Independent follow- Thermal management and heat dissipation are generic up measurements confirmed this conclusion [20, 26, problems that exist in many large power and heat 27]. Ruoff et al used the optothermal method to meas- exchange systems. Intensive heat density has been ure the suspended monolayer graphene with various observed not at least in the electronics systems. The sizes in vacuum and gaseous environments [20, 26], heart of the electronics sector, i.e. the semiconductor and they found that the thermal conductivity values industry has followed Moore’s law since 1965. In the range from (2.6  ±  0.9) to (3.1  ±  1.0)  ×  103 W m−1 past decades, chip manufacturers have been increasing K−1 near 350 K. Yoon et al used the thermal micros- the number of transistors with shrinked size to achieve copy with improved signal-to-noise ratio to measure higher component density and clock frequency. The the thermal conductivity of residue-free graphene pursuing for high performance dramatically increased and obtained thermal conductivity values range from power consumption in integrated circuits, which led 2430  ±  190 to 2100  ±  160 W m−1 K−1 for suspended to great challenge on heat dissipation in electronics graphene bridges at 335–366 K [27]. The intriguing systems. In recent years, Moore’s law has slowed down thermal properties of graphene were explained by the and is expected to hit the wall very soon due to the specifics of the long-wavelength phonon transport in physical limits imposed by quantum effect. Instead 2D crystal lattices [19, 21, 28]. The long-wavelength of further miniaturization of transistors, multi-core phonons in graphene have exceptionally long mean design has been proposed and applied to continue free path which is limited by the size of the sample even the performance evolution. This will release the stress if the thermal transport is diffusive [19, 29]. The lat- on thermal management to some extend but the ter can be explained by noting that the three-phonon problem of non-uniform local over-heating inside Umklapp scattering alone is not suffcient for restora- chips remains unsolved. For instance, heat flux at local tion of the thermal equilibrium in 2D crystal lattice hotspots has exceeded 1000 W cm−2 in insulated gate unlike in 3D crystal lattices [30]. One of the implica- bipolar transistors (IGBT) [1] which is a big threat to tions of this effect is an anomalous dependence of the the reliability of the component and will significantly thermal conductivity of few-layer graphene with the shorten their lifetime. number of atomic planes in the samples [21, 28, 31]. 2 2D Mater. 7 (2020) 012001 Y Fu et al Figure 1. Illustration of the first measurement of the thermal conductivity of graphene using the Raman optothermal method. Reproduced with permission from [19], © Nature Publishing Group. Other interesting features of phonon thermal conduc- be introduced first. After that, various graphene con- tion in graphene include non-monotonic depend­ stellations including its derivatives and related 2D ence on the ribbon width [32], and strong isotope and materials demonstrated for thermal management point-defect scattering [33]. applications will be reviewed and summarized in The exceptional thermal properties of graphene detail. Theor­etical analysis on the performance of the coupled with its flexibility motivated extensive thermal management materials will be compared and research on its derivatives, including graphene oxide, summarized to understand the phonon and thermal graphene films, graphene fibers, graphene foams, gra- transport in the 2D material systems. In addition, dif- phene laminates, graphene thermal interface mat­erials ferent thermal characterization methods applied for (TIMs), etc, for thermal management applications. these mat­erials will be presented and their advantages Various composites in which graphene and its deriva- and limits as well as accuracies will be summarized tives play a role of fillers [34–38] have been developed. and commented. At the end of this review, the chal- A mixture of liquid phase exfoliated (LPE) graphene lenges and opportunities to use graphene and other and few-layer graphene flakes perform excellently as 2D materials for thermal management will be dis- fillers in thermal pastes [34, 35] and thermal phase cussed and commented. change materials [39]. Graphene is a better filler than carbon nanotubes (CNTs) in thermal compos- 2. Basic theory of thermal transport ites owing to its excellent thermal coupling to matrix materials and substantially lower cost. Meter-sized Heat conduction is realized by the collision of graphene films fabricated from exfoliated graphene microscopic particles and movement of heat carriers flakes in suspension exhibited excellent thermal per- in matters. In a material, heat conduction is governed formance and showed great potential as heat spreaders by Fourier’s law, as expressed below: [40–42]. q = −κ · ∇T (1) Another 2D material which is very promising for thermal management is boron nitride (BN), which has where q is the local heat flux with an unit of W m−2, similar lattice to graphene but with boron and nitride κ is thermal conductivity of the material with an atoms alternatively arranged in the hexagon struc- unit of W m−1 K−1, and ∇T is the local temperature ture (hBN). Theoretically, hBN possesses high ther- gradient with an unit of K m−1. The Fourier’s law mal conductivity up to 1700–2000 W m−1 K−1 [43], describes how efficiently heat can be conducted from so it has been used to develop TIMs [44–49] and heat a high temperature region to a low temperature region spreaders [50–52]. More importantly, hBN is an elec- in a material. However, for thermal management in trical-insulating material which makes it a strategically electronics where heat has to be conducted through important and very good complementary to graphene different materials across contact interfaces, thermal and their derivatives where electrical conduction is not resistance is commonly applied to evaluate the allowed. efficiency of thermal transport because it is additive In this paper, we will review the recent progress and convenient to measure. The thermal resistance is on thermal management using graphene based mat­ calculated by: erials as well as other 2D materials such as hBN. The ∆T (2) R= . fundamental heat transfer mechanisms will briefly Q 3 2D Mater. 7 (2020) 012001 Y Fu et al Figure 2. Graphene quilt as heat spreader for AlGaN/GaN HFETs. (a) Optical image of the AlGaN/GaN HFETs before placing the graphene heat spreader. (b) Schematic of the FLG heat spreader placed on the drain contact of the AlGaN/GaN HFET. (c) SEM image of the graphene heat spreader transferred onto the drain contact. (d) Optical image of the graphene quilt overlapping the metal drain contact and the GaN substrate. (e) SEM image of the heat spreader-metal contact region and GaN surface. (f) Schematic of the graphene quilt and the device structure. The scale bars are 100 µm in (a) and (d). The scale bars are 10 µm and 1 µm in (c) and (e), correspondingly. (a)–(f) Are reproduced with permission from [62], © Nature Publishing Group. In equation (2), ∆T is the temperature difference with enhancement of thermal conductivity in (K) between two surfaces and Q is the thermal energy different ways. (W) conducted between these two surfaces. The total thermal resistance R consists of thermal resistance of 3.1. Graphene based heat spreaders the materials along the heat conduction path which is Heat spreader plays a key role in thermal management dependent on the thermal conductivity and thickness in, for instance, electronics systems. It enables much of the materials, and the contact resistance at the bigger surface area than the original surface on interface of two different materials which is dependent components for heat exchange, therefore dramatically on many factors including bonding pressure, surface facilitating the heat dissipation to cool down roughness, surface cleanliness, etc. electronics systems. Traditional heat spreaders are In order to improve the heat dissipation from typically made of metals such as aluminum and copper electronics systems to the ambient, high thermal con- which are quite heavy [55, 56]. The 2D structure and ductivity of materials, small material thickness and huge surface-to-volume ratio make graphene and efficient interaction at material interfaces are desired. related 2D materials ideal candidates as heat spreaders. Different from material thickness and interfacial con- ditions that can be engineered in specific applications, 3.1.1. Mono- and few-layer graphene based heat thermal conductivity is the intrinsic property of a spreader material which is dependent on the transport of elec- The in-plane thermal conductivity of exfoliated and trons and phonons. In 2D materials where free elec- suspended graphene has been reported as high as trons are limited, the heat conduction is dominated by 2000–5300 W m−1 K−1 in the literature [18, 19, 23, phonons. It is also noticed that thermal conductivity 29, 34, 57]. The values are comparable to CNTs [19, in a 2D material varies significantly in different direc- 58, 59], as well as higher than the values reported tions due to their anisotropic atomic structures [53, for graphite [60] and diamond [61]. Balandin et al 54]. In the x-y plane, atoms interact with each other demonstrated the first graphene based heat spreader through covalent bonding so the in-plane thermal using few-layer graphene mechanically exfoliated conductivity is very high, whereas in the z-direction from highly oriented pyrolytic graphite (HOPG) [62]. van der Waals force (which is very weak) governs the The graphene-graphite quilts were firstly exfoliated inter-layer interaction therefore the through-plane and then transferred onto SiC substrates to cool down thermal conductivity of 2D materials is normally very high-power GaN transistors as shown in figure 2. low [19]. Results showed that temperature at the hotspots can be lowered by ~20 °C when the transistor was operating 3. Materials development at ~13 W mm−1 which can be translated into a heat density of about 250 W cm−2. This indicates that the In this section, we will comment and summarize the graphene enhanced structure here as the hotspot state of the art of the graphene based materials in could extend the lifetime of the device by an order- different forms and configurations as they contribute of-magnitude. Further modeling results indicated 4 2D Mater. 7 (2020) 012001 Y Fu et al Figure 3. Single-crystal monolayer graphene grown on Ge surface [73]. (A) Schematic of single-crystal monolayer graphene grown from unidirectionally aligned multiple seeds. (B) A typical SEM image of graphene seeds at the early stage of growth. (C) A photograph of graphene grown on a 5.08 cm Ge/Si wafer. (D) A HR-TEM image of the single-crystal monolayer graphene. (Inset) Four overlaid SAED patterns. (E) A cross-sectional TEM image demonstrating that the as-grown graphene is monolayer. (Inset) A schematic illustration of the monolayer graphene grown on the H-terminated Ge surface. Reproduced with permission from [73]. that the efficiency of the graphene heat spreader is that the graphene heat spreader can lower the PhC dependent on the device structure and geometry [63]. cavity by 45 K under an optical power of 100 µW. CVD Gao et al used CVD method to grow mono- and few- graphene was also applied by Lee et al to cool down layer graphene as heat spreader [64, 65]. It was found GaAs/InGaAs/InGaP collector-up heterojunction that the hotspot with a heat flux of 430 W cm−2 on Si bipolar transistors, where 30% reduction of thermal chips can be cooled down by ~13 °C (from 121 °C to resistance was observed [68]. 108 °C) using mono-layer graphene as a heat spreader, Compared to the mechanically exfoliated gra- whereas multi-layer graphene can only cool down the phene, the CVD method to grow graphene is becom- hotspot by ~8 °C. This is attributed to the smaller grain ing more and more mature so the CVD graphene size of graphene grown on Ni foils than those grown based heat spreader shows better process scalability on Cu foils, which resulted to more grain boundaries and compatibility [69–71]. On the other hand, gra- and consequently lower thermal performance of the phene synthesized from CVD method contains much graphene material. Bae et al used multi-layer graphene more defects and grain boundaries (i.e. domain size is grown on Ni surface as heat spreaders on flexible much smaller) in its crystalline structure and there- substrates [66]. Results showed that graphene based fore exhibits lower thermal conductivity than their heat spreader brings more uniform temperature mechanically exfoliated counterparts [19]. Lee et al distribution on the substrate compared to gold based reported that thermal conductivity values of sus- heat spreaders. Shih et al used mono-layer graphene pended CVD graphene are around 2660, 1890, and 680 grown from CVD method to cool down a photonic W m−1 K−1 for average grain sizes of 4.1, 2.2, and 0.5 crystal (PhC) cavity [67]. Experimental results showed µm, respectively [72], showing clear dependence of 5 2D Mater. 7 (2020) 012001 Y Fu et al Table 1. Comparison between material fabrication processes and thermal properties of GFs. Thermal Assembled Exfoliation Film formation Heat conductivity structures Raw material /dispersion methods methods treatment (°C) (W m−1 K−1) Ref Graphene film GO Not mentioned Self-assembling 1000 60 [90] Graphene film GO Ultrasonication Vacuum filtration 1200 1043.5 [82] Graphene film GO Ultrasonication Self-assembling 2000 1100 [91] Graphene film Graphene Ball-milling Vacuum filtration 2850 1434 [92] Graphene film Thermally Ultrasonication Electro-spray 2850 1434 [85] exfoliated deposition graphene Graphene film Graphite oxide Not mentioned Self-assembling 3000 1950 [93] Graphene film GO Shear mixing Self-assembling 2850 3214 [40] thermal conductivity on graphene grain size. In addi- amorphous silicon dioxide (SiO2) was found to be tion, fitting data showed that the thermal conductivity ~600 W m−1 K−1 at RT owing to phonon coupling of suspended single-crystal graphene is around 5500 and scattering [23, 84]. Due to this and the limitations W m−1 K−1 which is very close to mechanically exfoli- mentioned above, graphene films (GFs) assembled ated graphene [72]. from chemically or thermally exfoliated graphene The limitation from crystalline defects in CVD sheets were developed as new heat dissipation grown graphene is being addressed by recent advances materials. in material synthesis. In the past few years, great pro- Many different assembly processes have been gress has been achieved on CVD graphene, large grain developed, such as vacuum filtration [82–84], elec- size up to wafer level single crystal graphene has been trospinning [85], wet-spun method [42], dip coating reported. For instance, Lee et al successfully grown [86], inkjet printing [87], and spin coating [88]. The single-crystal mono-layer graphene on Ge substrate assembling mechanisms of graphene or graphene without any wrinkles [73], as shown in figure 3. Due oxide (GO) flakes are based on different physical and to the extremely weak interaction between graphene chemical interactions among flakes, such as Van der and the underlying Ge surface, etch-free dry transfer Waals force and hydrogen bonds. During the flake of the graphene was realized which makes it possible assembly, individual particles can be spontaneously to recycle the Ge substrate for continual graphene or passively aligned to form well-oriented layer struc- growth. This method requires complex preparation of tures. For example, the evaporation of GO suspensions the substrate, for instance the single-crystal Ge under- leads to a phase change of GO from random to liquid layer has to be epitaxially grown on Si substrate prior crystal at gas–liquid interfaces, which provides the to the graphene growth. Recently, fast growth of large driving force to form film structures [89]. single-crystal graphene has been reported [74–79]. The reported thermal performance of GFs varied For instance, Wu et al [74] realized fast growth of inch- widely depending on different fabrication methods sized single-crystal graphene on CuNi alloy substrates, [40, 82–93]. As shown in table 1, the in-plane thermal 1.5-inch large graphene mono-layer can be grown in conductivity values of most fabricated GFs are below 2.5 h using locally feeding carbon precursors at a sin- 1500 W m−1 K−1, which are much lower than that of gle nucleation site. Lin et al also reported the growth of the commercial pyrolytic graphite sheets (PGS) with super-clean graphene with enhanced optical, electrical the highest value of 1950 W m−1 K−1. and thermal properties [80]. The poor thermal conductivity of GF is strongly The progress in CVD technology pushed the gra- related to the structural defects both at atomic level phene heat spreader closer towards practical applica- and microscale. Previous studies have revealed that the tion. However, other challenges such as handling of heat conduction in graphene is essentially governed CVD graphene at industry scale, process compatibility, by phonon transport inside the sp2 bonded hexago- and limited total thermal energy that mono-layer and nal carbon lattice [94–96]. Molecular dynamics (MD) few-layer graphene can conduct are still obstacles to be simulation has shown that the thermal conductiv- removed before CVD graphene can be applied as heat ity of graphene can be reduced by 90% with oxygen spreaders in industry [62, 64]. content of 5% [94]. Therefore, a high crystallinity and large grain size of graphene is critical for achieving 3.1.2. Graphene film as heat spreader GFs with outstanding thermal conductivities along Although the thermal conductivity of suspended the in-plane direction. To restore the crystallinity of graphene is very high at RT, the in-plane thermal graphene, different approaches have been reported, conductivity of graphene decreases significantly when including chemical and thermal reductions to get it is in contact with a substrate [53]. For instance, the rid of oxygen in the materials. For example, GFs were in-plane thermal conductivity of SLG supported on treated by different chemical reducing agents, such 6 2D Mater. 7 (2020) 012001 Y Fu et al Figure 4. Fabrication process of GFs. (a) Sketch of the fabrication process. (b) Optical image of GO flakes with an average size of about 6 µm. (c) AFM image of GO flakes with a thickness of less than 1 nm. (d) SEM image of cross-section of the fabricated GFs. (e) Optical image of the fabricated large-area GFs. (f) In-plane thermal conductivity of GFs before and after pressing after annealing under 2850 °C. Reproduced with permission from [40]. as L-ascorbic acid [97] and hydroiodic acid [98, 99]. decomposition of oxygen groups leads to the forma- Thermal annealing at the carbonization temperature tion of CO2 or CO gases which can increase the layer of 1300 °C [82, 90, 100] and the graphitization temper­ distance and even forms air pockets (as shown in ature of 2200 °C [85] have also been reported for figure 4) that will decrease the alignment of graphene reduction. The quality of GFs varies a lot depending flakes in the film [40]. on the reduction process. It has been widely accepted Currently, the advantages of high temperature that high temperature annealing of GFs above 2000 °C annealed GFs is not obvious as compared to PGS. To enables defect healing and improves the crystallinity in further improve the thermal conductivity of GFs, graphene materials [101, 102]. By careful control of the structural optimization becomes highly essential, such graphitization temperature and pressure, it is possible as improving grain size, achieving good alignment, to achieve similar thermal conductivity of GFs as in fabricating large and smooth structures and reducing PGS [40]. In spite of all the merits of high temperature the interlayer binding energy. A recent study concluded annealing, there are also some issues in the GF anneal- that the increase in grain size from ~200 nm to ~10 ing process that need to be addressed. For instance, the µm leads to an exponentially increased thermal con- 7 2D Mater. 7 (2020) 012001 Y Fu et al Figure 5. Infrared images of the chip surface. (a) Temperature distribution on the bare chip. (b) Temperature distribution on the chip with graphene heat spreader but without FGO. (c) Temperature distribution on the chip with graphene heat spreader and FGO. Reproduced with permission from [110]. ductivity of graphene from ~610 to ~5230 W m−1 K−1 structure and high density of GFs contributes signifi- [103]. A large grain size can greatly benefit the trans- cantly to a much higher thermal conductivity than that fer of low-frequency ballistic phonons inside the grain of PGS when the thickness is more than 25 µm. as well as their good transmittance across the grain The scientific question that still needs to be boundaries, thereby leading to the ultrahigh in-plane addressed is whether we can further increase the ther- thermal conductivity of GF. The thermal conductiv- mal conductivity of graphene film towards even higher ity of GFs is also dependent on the lattice structure of values. Theoretical study indicates that in a perfect graphene layers at the through-plane direction. Pho- and defect-free structure, thermal conductivity of non interfacial scattering among graphene layers is the graphene can reach close to 10 000 W m−1 K−1 [107]. main roadblock to the improvement of thermal con- It seems that careful control of the turbostratic state, ductivity. Previous studies showed that changing the defect and wrinkle free and well aligned structures order of graphite from AB Bernal stacking graphene together with large grain size are the right strategy to to turbostratic-stacking graphene led to an obvious push the thermal conductivity of graphene film even decrease of interlayer binding energy [104], which can higher. significantly decrease the phonon interfacial scattering and benefit the heat transfer at the in-plane direction 3.1.3. LPE graphene based heat spreader [105]. A recent study proved this theory and showed Liquid phase exfoliation (LPE) is a very important that thermal conductivity of GFs had significant complementary to tape assisted mechanical improvement up to 3200 W m−1 K−1 with the presence exfoliation, CVD, and sublimation method to produce of 37% of turbostratic-stacking graphene. graphene in suspension form. The method starts from In addition, the assembling methods of GFs give graphite particles and allows large scale production of more flexibility to design the film structure compared graphene at low cost. Therefore, it holds the promise to the fabrication of PGS. For example, the thickness of of many applications including coating, composites, commercial PGS is limited within 10–100 µm which inks, fibers, heat spreading materials, etc. There are gives fewer choices for customers. For GFs, different two types of LPE process, one is pure mechanical thicknesses from a few hundreds of nanometers up exfoliation in liquid using shear or nominal forces, to millimeters can be realized easily, which can meet e.g. by sonication, to overcome the van der Waals all kinds of requirements from different applications force in graphite to directly produce pristine graphene ranging from microelectronics to military and space flakes. The other involves chemical reaction during exploration. In addition, commercial PGSs have the exfoliation, that means the graphite particles are gradually decreased densities when the film thickness firstly expanded and oxidized and then exfoliated to increases. Previous studies about the polyimide (PI) produce graphene oxide (GO) suspension which can pyrolytic process also reported that the orientation be subsequently reduced to generate so called reduced of graphite layer texture became much worse in the graphene oxide (rGO). Most LPE processes reported case of thick PGS (above 25 µm) due to the increased today are originated from Hummer’s method [108] amount of curvatures and layer misfit [106]. There- with modifications such as using different oxidants fore, the thickness of PGS fabricated in industry is and temperature to make the production process safer usually limited within 25 µm when the film density and more environmental friendly. Compared to the reaches to 2.1 g cm−3 to get a well-oriented graphite pure mechanical exfoliation in liquid, the production layer texture. Different from the PGS, the GFs are pre- of graphene from reduced GO flakes has advantages assembled by individual GO sheets and have much bet- of large lateral size, good dispersibility, and large-scale ter orientations in the horizontal direction. Therefore, industrial productivity but suffers from more defects the thickness increase would not lead to the increase of in the graphene lattice and more impurities in the layer misfit in GFs. The well-oriented graphene layer graphene material. 8 2D Mater. 7 (2020) 012001 Y Fu et al Figure 6. Infrared images of the chip surfaces. (a) Temperature distribution on the conventional LED chip. (b) Temperature distribution on the LED chip with embedded rGO pattern. Reproduced with permission from [110]. Figure 7. (a) Optical image of the pristine epoxy, and epoxy with the loading of 18 vol.% and 19 vol.% of graphene and h-BN fillers, respectively. Note a distinctively black color of graphene composite as opposed to the white color of h-BN composite. (b) Scanning electron microscopy image of the epoxy composite with 45 vol.% of graphene fillers. The microscopy image of the high- loading composites shows clearly the overlapping of graphene fillers inside the epoxy matrix. The overlapping fillers confirmed the formation of the percolation network at this high loading fraction of graphene. Reproduced with permission from [111], © American Chemistry Society. Heat spreaders based on LPE graphene have been and drop coated graphene heat spreader, respectively. demonstrated to cool down hotspots up to 1750 W Finite element method (FEM) modeling revealed that cm−2 [109]. Zhang et al applied both vacuum filtration the alignment of graphene flakes in the heat spreader and drop coating methods to fabricate graphene films and the thermal boundary resistance between gra- as heat spreaders from pure mechanical LPE graphene phene and the chip surface are the key parameters suspension [109]. 3ɷ measurement showed that the determining the performance of the heat spreader. thermal conductivity of the drop coated graphene film Zhang et al also reported a heat spreader using is around 110 W m−1 K−1 in the in-plane direction, reduced GO films [110]. In order to decrease the ther- which is much lower than the graphene exfoliated by mal boundary resistance, a silane functionalized GO tape due to the defects in the graphene crystal and the (FGO) layer was coated as thermal coupler between huge contact resistance between the graphene flakes. A the heat spreader and the chip. Molecular dynamics temperature drop of 6 °C and 4 °C is detected at the simulation (MDS) showed that thermal conductiv- hotspot using vacuum filtrated graphene heat spreader ity of the graphene heat spreader can be increased by 9 2D Mater. 7 (2020) 012001 Y Fu et al Figure 8. Thermal conductivity enhancement η%  =  100  ×  ((K  −  Km))/Km as a function of filler loading fraction (here Km is the thermal conductivity of the base material and K is the thermal conductivity of resulting composite). The red circles and blue squares are the experimental data points for epoxy with graphene and h-BN fillers, respectively. Graphene filled epoxies outperform h-BN filled epoxies primarily because the intrinsic thermal conductivity of the graphene is higher than that of h-BN. Reproduced with permission from [124], © American Chemistry Society. 15%–56% after functionalization due to the decreased films as heat spreaders from GO suspensions, provided cross-plane phonon scattering between the graphene that the GO flakes turn to graphene of good quality. It heat spreader and the chip. Thermal characterization has been repeatedly reported that complete reduction results showed that the heat spreader with silane FGO and graphene lattice restoration of GO can be real- decreased the hotspot temperature by 12 °C in con- ized by means of super-high temperature annealing, trast to a temperature drop of 6 °C by the graphene i.e. 1700 °C to 3000 °C [114]. A previous study reports heat spreader without silane FGO, as shown in figure 5. thermal conductivity at 1400 W m−1 K−1 was achieved Improved heat dissipation in GaN light-emitting from solution-processed GO films after annealing at diodes (LEDs) was also observed by Han et al using 2850 °C and mechanical pressing which shows great embedded GO pattern [110]. GO dispersion was potential for heat spreading application [115]. firstly coated on sapphire substrate and followed by thermal reduction in hydrogen under 1100 °C. After- 3.2. Graphene enhanced thermal composites wards the rGO was patterned by lithography and The unique heat conduction properties of graphene GaN layer was grown on top by epitaxial growth. Fol- motivated experimental studies of graphene and FLG lowing this step the LED structure was fabricated so in TIM, thermal composites and coatings [20, 24, that the patterned rGO was embedded underneath. 25, 34, 39, 62, 116, 117]. The first studies of graphene Experiment results show that the peak temperature composites found that even a small loading fractions of the chip surface is about 5 °C lower on the rGO of random graphene fillers can result in increased embedded LED compared to the conventional LED, thermal conductivity of epoxy composites [34, 118, as shown in figure 6. 119]. The large variations of the thermal conductivity The thermal performance of LPE graphene heat of graphene thermal composites originates from spreader is dependent on a few factors. Firstly, the pres- differences in the methods of preparation, matrix ence of dispersant and other constituents most of time materials, quality of graphene, lateral sizes and degrades the properties of the thin films. Secondly, the thickness of graphene fillers and other factors [19, arrangement in the individual graphene flakes in a thin 31, 33, 120–123]. Most of the early investigations of film plays an important role in determining the film thermal composites with graphene fillers were limited performance. It has shown that, by means of filtration, to the low loading fractions of fillers, f   <  10 vol.%. The highly aligned graphene films show strong anisotropic situation has changed recently when composites with thermal conductivities, i.e. 120 W m−1 K−1 in in-plane large loading of graphene became available owing to direction versus 0.5–2 W m−1 K−1 in cross-plane direc- the technological developments and substantial cost tion [112]. The final but not the least factor concerns reduction (see figure 7). lateral size of graphene flakes. It was shown that ther- Thermal properties of composites with the high mal conductivity increases linearly with the increase loading fraction of graphene or FLG fillers is inter- of flake size which indicates that heat conduction is esting from both fundamental science and practical mainly limited by flake boundaries [113]. Therefore, applications points of view. The high loading results it is possible to prepare high performance graphene in achieving the thermal percolation in the compos- 10 2D Mater. 7 (2020) 012001 Y Fu et al Figure 9. Mechanism of wet-fusing assembly and morphology of as-prepared graphene oxide fiber fabrics (GOFFs) and graphene fiber fabrics (GFFs). (a) Optical microscopy (OM) and (b) polarized-light optical microscopy (POM) images of GO fibers. (c) Wet-fusing of GO fibers. (d) A piece of thin GOFF (0.05 mm). (e) A piece of thick GOFF (3 mm). (f) A thermally annealed GFF with porous feature. (g) GOFF (left) and GFF (right), indicating the slight shrinkage of lateral dimension and color change. (h) A stripe of GFF coiled around a glass rod. (i) Four GFFs of different sizes and thicknesses. Scale bars, (a) and (b) 500 µm, (c) 150 µm, (d), (f), (h) and (i) 20 mm. Reproduced with permission from [163]. ites [125–132]. The thermal percolation is less under- [144, 145]. There have been significant progress in the stood phenomenon that the electrical percolation methods of reduction of graphene oxide (GO) [139, [133–140]. The electrical percolation is described by 146–148]. These developments made graphene fillers t the scaling law σ ∼ ( f − fE ) , where σ is the electrical practical even for the composites with the high loading conductivity of the composite, f is the filler loading fraction. A recent study reported thermal properties of volume fraction, fE is the filler loading fraction at the composites with the high loading (up to f   =  45 vol.%) electrical percolation threshold, and t is the critical of graphene and h-BN [124]. The electrically insulat- exponent. Unlike the electrical conductivity, in most of ing h-BN was used for comparison with graphene in cases, the thermal conductivity of composites does not order to establish the general trends in thermal con- reveal such noticeable changes as the loading fraction ductivity of composites with 2D filler materials (see increases. Controlling electrical and thermal percola- figure 8). It was found that the thermal percolation tion in composites with graphene using filler optim­ happens at higher loading than the electrical percola- ization and perhaps combining graphene with other tion in graphene composites. The thermal conductiv- electrically insulating 2D fillers such as hexagonal ity of graphene epoxy composites exceeded ~12.5 W boron nitride (h-BN) remains an important challenge m−1 K−1, which is higher than that of commercially for further development of graphene thermal compos- available TIMs [124, 149]. ites. Besides, graphene composite material also showed There is a strong practical motivation for research great potential as a heat sink material. Conventional of composites with the high loading of graphene for heat sinks are made of metals, such as copper or alu- instance for better TIMs for heat removal in electron- minum, with fins to increase its surface area. How- ics [22, 141–143]. Commercially available TIMs with ever, carbon based heat sink attracts lot of interests the bulk thermal conductivity below 5 W m−1 K−1 no due to its light weight, anisotropic and high thermal longer meet the industry requirements. Composites conductivity. Graphite has a long history of being with the high loading of graphene have the potential to considered as material for heat sink. In 2003, Norley deliver high thermal conductivity. Recent technologi- et al proposed to make graphite-based heat sinks with cal developments demonstrated that the LPE graphene controllable isotropy [150]. In their design, flat and can be produced in large quantities inexpensively well oriented graphite sheet was bonded together to 11 2D Mater. 7 (2020) 012001 Y Fu et al Figure 10. (a)–(c) Images and thermal conductivity of graphene/PEI laminate. Reproduced with permission from [113]; (d) and (e) images and thermal conductivity of graphene/copper laminate. Reproduced with permission from [116]; (f) constructed molecular models of graphene for the thermal transfer performance valuation. Reproduced with permission from [171]; (g) a typical developed 3D representative volume element of graphene laminate constructed in Abaqus/Standard. Reproduced with permission from [171]; (h) multiscale results for effective thermal conductivity of graphene and h-BN laminates as a function of flake size. Reproduced with permission from [171]. make a graphite heat sink. It was found that the ther- performance. Moreover, graphene/graphite based mal conductivity of this graphite heat sink in the hori- heat sink is able to control the thermal conductivity in zontal direction is higher than the vertical direction. different directions, which provides the possibility of In the next year, Getz et al fabricated a heat sink made preferentially heat transport. from different size of graphite sheets based on simi- lar concept [151]. Recently, heat sink performance 3.3. Graphene fibers of graphene and its composites has been studied. Wu Graphene fibers are, similarly to graphene films, et al used Cu nanoparticle coated graphene sheets to macroscopic assembled structures of interlocking fabricate a composite film with thermal conductivity layers of reduced graphene oxide flakes. They have up to 1912 W m−1 K−1 at 50 °C. Simulation revealed so far mainly been studied for their mechanical and that the graphene/Cu composite film exhibits more electrical properties [157], for replacing carbon efficient thermal transport ability compared to Cu fibers and application within smart textiles. However, and graphene film [152]. Wai et al developed a facile they also hold great promise for use in thermal mechanical cleavage method to synthesize graphene applications [158]. nanosheets and graphene nanosheets/Cu (GN/Cu) Graphene oxide (GO) fibers can be fabricated composite film. Heat sink made from this GN/Cu through wet-spinning of liquid crystal GO disper- composite film reached a thermal conductivity as sions into a coagulant bath [157]. The assembled GO high as 2142 W m−1 K−1, showing an increase of 26% fibers are then reduced to form graphene fibers, and compared to the graphene sheet heat sink [153]. Lu possibly annealed as well. The process has a pleth- et al coated 1900 nm graphene sheets on aluminum ora of param­eters, both within the GO dispersion, heat sink to obtain a 7 °C temper­ature decrease com- coagulant bath, spinning setup, reduction process pared to uncoated heat sink under a heat flux of 1.8 and annealing, This enables a very high variability in W cm−1 [154]. In recent years, patents based on gra- graphene fiber properties, and the possibility to fur- phene enhanced heat sinks have been filed [155, 156] ther optimize the properties. For instance, Xin et al due to the advantages of light weight and high thermal [158] showed how an optim­ized mixture of small 12 2D Mater. 7 (2020) 012001 Y Fu et al Figure 11. (a) Flexible graphene film was folded into a frog; (b) graphene/Cu laminate in the status of bending; (c) TEM image of a graphene sheet; (d) optical microscopy image and (inset in (d)) corresponding size distributions of graphene sheets; (e) optical image of building bricks; (f) diagrammatic sketch and schematic diagram (the inset) of graphene/Cu laminate surface; (g) SEM image of the surface of graphene film with many granular bubbles and microfolds and (h) graphene/Cu laminate, the insets are schematic diagram of heat conduction from heat resource through graphene film and graphene/Cu laminate, respectively. Reproduced with permission from [175]. and large GO flakes leads to an improvement in ther- sheets are combined by binders or Van der Waals force. mal ­conductivity (1290 W m−1 K−1) and mechanical Until now, a few simple fabrication techniques for strength compared to only large flakes. Xu et al [159] graphene laminates have been developed, including systematically eliminated defects at all levels to achieve CVD [169], drop-casting, spin-coating, spray-coating a Young’s modulus of up to 282 GPa [159], strength of and dip-coating [170]. 1.45 GPa which was recently improved even further Improvement of thermal conductivity up to 600 by Xin et al [160] which used microfluidics to control times for plastic substrate and 24% for Cu film has the flake orientation during the spinning process. This been achieved by coating graphene to fabricate the resulted in, rather than circular fibers, belt-like struc- laminate structure (figures 10(d) and (e)) [113, 116]. tures with a record high thermal conductivity of 1575 Except for the extremely high thermal conductivity W m−1 K−1, Young’s modulus of 309 GPa and tensile of pristine graphene, reduced surface roughness and strength of 1.9 GPa. While the best mechanical prop- improved grain size on the substrate also contributed erties of graphene fibers were still not on par with the to the thermal performance of metal based graphene strongest carbon fibers [161], the thermal conductiv- laminate [171]. Moreover, it is widely believed that ity has surpassed carbon fibers that have undergone the alignment and flake size of graphene influence the similar thermal annealing [162]. thermal conductivity more than the density of gra- The wet-spinning fabrication route is highly scal- phene fillers in a graphene laminate. After compressed able, with possible spinning speeds of kilometers with large flake-size graphene, linear improvement per hour [159] per nozzle, opening the possibility of of thermal conductivity from 40 to 90 W m−1 K−1 large-scale application as filler in polymer matrices, was achieved by Balandin et al for graphene laminate or as freestanding structures within flexible electron- [113], as seen in figures 10(a)–(c). In particular, mul- ics or textiles. Toward these applications, Li et al [163] tiscale modeling of heat conduction in graphene lam- demonstrated a flexible and porous non-woven fab- inates demonstrated that flake size is one of the main ric of fused graphene fibers, with an in-plane thermal factors affecting the thermal conductivity of graphene conductivity of 301.5 W m−1 K−1 at a density of 0.22 g laminates (figures 10(f)–(h)) [171]. For the small gra- cm−3, as shown in figure 9. phene flakes, inter-flake contact resistance makes a big difference to the thermal conductivity. Consequently, 3.4. Graphene laminates increasing graphene flake size [57], building covalent Graphene laminates have been demonstrated for bonds between graphene flakes [172, 173] and ori- surface protective, water desalination [164], gas entating graphene sheets [54] are effective routes to impermeable barrier [165] and electromagnetic further improve the thermal conductivity of graphene interference shielding [166]. But applying graphene laminates. laminates for thermal coating applications is becoming So far, the volume fraction of graphene in the gra- more and more popular. Generally, in a graphene phene laminates is very low, therefore many research- laminate, graphene is deposited on various substrates, ers are trying to increase the percentage of graphene including polymers (polyethylene terephthalate in the laminates to improve their thermal conductiv- (PET)) [113] and metals (copper [167, 168], ity. However, the surface of graphene film is chemi- Aluminum [154]). In a graphene laminate, graphene cally inert and it is difficult to combine the graphene 13 2D Mater. 7 (2020) 012001 Y Fu et al Figure 12. Macroscale Ni-templated (a) 3D graphene foam, (b) h-BN foam, (c) SEM image of graphene foam cross-section. Reproduced with permission from [176]. film with metal. Initially, graphene/metal laminates or attractive for TIM applications. Graphene foams graphite/metal laminates were fabricated by vacuum are primarily synthesized through graphene CVD hot pressing [174]. Owing to the rough surface of the on Ni foams and the subsequent etching of the Ni graphene films and metals, the contact resistance at template, leaving a free-standing graphene structure. the bonding interface is typically very high [175]. In [179]. A similar structure can also be formed using order to reduce the contact resistance, interfacial mat­ freeze casting of or hydrothermal reduction of GO erials, such as indium, thermal conductive adhesive suspensions [180, 181]. As free standing structures, (TCA) and commercial double-side tape, were used to both graphene foam and a graphene/CNT aerogel assemble graphene films and Cu foils (figure 11) [175]. has been demonstrated for TIM applications, with Results showed that the thermal conductivity of gra- thermal conductivity of around 88 W m−1 K−1 for phene/Cu laminates can be 3 times higher than that compressed graphene foam (figure 12) [176, 181] and of Cu after the optimization at the interface [175]. On low thermal interface resistances at very low pressures the other hand, the thickness of interfacial materials is [179]. Similar structures have also been demonstrated difficult to control which will lower the performance using h-BN [176, 182], with a cross-plane thermal of the laminates. To further improve the thermal con- conductivity of up to 62 W m−1 K−1 for compressed ductivity of the laminates, Cu thin layer (about 1 µm h-BN foam [176]. Both graphene and h-BN foams thick) was sputtered on the surface of graphene films can be infiltrated to form polymer composites [182, [175]. Similar to the interlock system within building 183]. An et al created a vertically aligned graphene blocks, granular bubbles and microfolds on the sur- foam epoxy composite with a through-plane thermal face of graphene film make it tightly anchored on the conductivity of 35.5 W m−1 K−1 at a graphene loading coated Cu layer. Since the large flake size in graphene fraction of 19 vol%, significantly higher than randomly can reduce the number of contacts and the introduc- dispersed graphene enhanced composites. Recently, tion of Cu makes the heat capacity of the laminate Zhamu et al, synthesized a highly elastic and resilient higher than pristine graphene film, this graphene/Cu graphene foam by a chemical-free method. This laminate has high thermal conductivity up to 1932 W graphene-carbon hybrid foam showed super effective m−1 K−1 [175]. potential application as a heat sink [184]. 3.5. Graphene based 3D structures 3.5.2. Vertically aligned graphene sheets In addition to the previously mentioned graphene Graphene sheets have excellent in-plane thermal structures, there are a number of graphene based 3D conductivity, but is normally limited to heat spreading structures that have been proposed for use in thermal application due to the low through-plane thermal management. conductivity. A potential solution to this limitation is to stack multiple graphene sheets to form a bulk 3.5.1. Graphene foam material which can be used for TIM and other Graphene foam consists of graphene assembled in a thermal applications. Liang et al [185] introduced porous macroscale foam-like structure. The porosity the concept, creating a material with a through-plane of the foam makes the effective thermal conductivity of thermal conductivity of 112 W m−1 K−1. Graphene graphene foam very low, with a thermal conductivity films are stacked and bonded together with solder of 0.26 to 1.7 W m−1 K−1 at a solid concentration of or polymer, and then cut perpendicular to the heat around 0.45 vol% [177]. Nonetheless, graphene conducting axis into thin slices applicable as TIM. The foams exhibit a thermal conductivity close to that of concept has further been improved and optimized by metal foams, at an order of magnitude higher degree Zhang et al [186] and by Wang et al [187, 188], with a of porosity [178]. In addition, graphene foams have thermal conductivity of 615 W m−1 K−1 and 1379 W a very high degree of compressibility, making them m−1 K−1 respectively. The exceptionally high thermal 14 2D Mater. 7 (2020) 012001 Y Fu et al conductivity compared to conventional TIM, and concentration of graphene nanosheets [201, 202]. even higher than heat sink materials, eliminates the Functionalized graphene exhibited more pronounced normal drawbacks for TIM with a thick bond line. increase in the heat transfer of water-based nanofluids Instead, the thermal contact resistances between TIM (i.e. up to 171 increase in heat transfer coefficient at and joining surfaces are the limiting factors rather than 0.01% loading) [203]. Ghozatloo et al [201] showed the thermal conductivity. Indeed, as seen by Wang et al an increase of 31.83% in the thermal conductivity of [188], the overall performance depends mainly on the deionized water used in heat exchanger at 0.075 wt% contacts, and through bonding with a thin indium of Potassium persulfate (KPS) oxidized graphene layer the performance rivals that of thin solder joints, with an increase in the heat transfer coefficient with while retaining good flexibility and thickness which is the concentration of the loading. When used in heat crucial for gap filling applications. pipe, the graphene could improve the heat transfer by increasing the surface wettability between the fluid 3.5.3. Hybrid graphene structures and solid surface of the pipe [204], while an increase in The unique properties of 2D materials can be further the dynamic viscosity has to be considered [205]. The taken advantage of together with other materials in addition of up to 0.3 vol.% graphene nanoplatelets hybrid combinations. Normally, the through-plane resulted in a decrease of the contact angle of the thermal conductivity of graphene structures is a nanofluid than that of the distilled water by 20% [206]. limitation. A possible way to increase the Z-direction A thermal resistance reduction of 48.4% was obtained thermal conductivity is to introduce more thermal as the deposition of the graphene nanoplatelets that paths through covalent bonding of graphene layers formed a coating on the wick surfaces and improved using an intermediary material. This has been the surface wettability [204]. Study on the effect of demonstrated using carbon nanorings [189] and more graphene presence on the viscosity behaviour of the recently using in situ grown vertically aligned SiC base fluid suggested a Newtonian behaviour, where the nanorods [190]. By this approach, the through-plane thermal conductivity, dynamic viscosity and density thermal conductivity was increased from 4 to 17 W were found to increase [207]. The temperature was m−1 K−1 in a TIM application. also reported to have an effect on the dynamic viscosity Another application of hybrid graphene structures and density but not on the thermal conductivity is together with CNTs. CNT arrays have been widely under turbulent conditions. Meanwhile, some study investigated for use as TIMs [191], but are severely lim- exhibited a non-Newtonian behaviour of distilled ited by the thermal contact resistance between CNT water nanofluids with functionalized hydrogen- and substrate. However, simulations suggests that exfoliated graphene [208]. The lack of temperature CNTs covalently bonded to graphene has the potential dependency in theoretical formulation neglected for a significantly lower resistance [192–195]. Real- particle-particle interactions [209], where a viscosity izing this structure experimentally has proven dif- increase of over 30 times was reported as the particle- ficult, but has been demonstrated using novel CVD particle interaction was taken into consideration, approaches [196, 197]. Furthermore, Sun et al [198] together with a maximum enhancement of showed that covalent anchoring of CNTs to graphene thermal conductivity by 1.43 times at 1.5% volume could lower the thermal contact resistance by several fractions in external flows in laminar regime. The orders of magnitude. Hybrid graphene/CNT struc- particle-particle interaction was also emphasized tures with CNT arrays grown on graphene films can be by Anoop et al [210], and the particle aggregation used for efficient heat dissipation [198] or novel TIM and the electroviscous effect at the particle-fluid structures [199]. interface were also non-negligible. An increase in the thermal conductivity and specific heat capacity 3.6. Graphene nanofluids of up to 48% and 18%, respectively, was reported by Nanofluids attract increasing research interest due to Rodríguez-Laguna et al [211]. As for the case of high their advanced heat transfer properties compared to boiling point organic solvent, the resulted thermal conventional fluids. The benchmark study on the effect conductivity was attributed to a long-range effect of of nanoparticles on the thermal conductivity of fluids the dispersed graphene on the solvent molecules and showed positive correlations between nanoparticles a local orientation of the solvent molecules parallel and thermal conductivity of fluids [200] that was to the graphene sheet. Studies regarding graphene stipulated by classical theory. Graphene, with its high nanomaterial have shown a positive correlation thermal conductivity, has also been studied in the effort between the thermal properties and the graphene aiming at integrating graphene as fillers in heat transfer loading in the carrier medium. fluids for a large spectrum of applications. Graphene The improvement of the thermo-physical prop- suspensions were found to effectively enhance the erties of the nanofluid can be expected by the aid of thermal properties of the host fluids. For example, the graphene additives. At the meantime, challenges graphene nanofluid showed an enhancement in the raise from the complex phenomenon at the gra- thermal conductivity at more than 36% compared phene-liquid interface and the understanding of the to the pure fluid, and the effect increases with the mechanism of graphene contribution to the ther- 15 2D Mater. 7 (2020) 012001 Y Fu et al Figure 13. Schematic representation of thermal wall–fluid interactions. Reproduced with permission from [215]. Figure 14. (a) Proposed model of AgNP–BNNSs for thermal conducting paths. (b) TEM images of a slice of the BNNSs. (c) TEM image of AgNP–BNNSs. Reproduced with permission from [229]. mal transport. Extensive investigations are needed on the fluid velocity and state [215–217]. The resist­ to understand how the graphene increased the sta- ance at the solid–liquid interface of a nanochannel bility of the liquid [212]. When applying graphene coated by graphene layers was studied, and results nanofluids in heat dissipation, the thermal resistance showed that an influence of fluid-wall interface at the interface is a key issue in the heat transport. strength on the interfacial thermal resistance [218]. Modelling and simulations have been carried out to Computational fluid dynamics (CFD) methods study the interfacial thermal resistance. The acous- were also available in investigations on the thermohy- tic mismatch model (AMM) attributed the thermal draulic performance of nanofluids. Both single-phase resistance to phonon radiation and acoustic imped- and two-phase models were developed for nanofluids ance [213], and the diffuse mismatch model (DMM) consist of nano-sized additives and the base fluid [219, focused on the phonon density mismatch [214]. 220]. Simulation results showed that the graphene Molecular dynamics simulations (MDS) provided nanoplatelet enhanced the transport properties at tur- insights into the thermal transport across the inter- bulent convection heat transfer [221], while there was faces. Kim et al studied the thermal resistance at the no advantage of the nanofluid at low concentration solid–liquid interface, as shown in figure 13, and sug- in laminar convective heat transfer. Reproduced with gested the dependence of interface thermal resistance permission from [222]. 16 2D Mater. 7 (2020) 012001 Y Fu et al 3.7. Other 2D materials conductivity of monolayer hBN was still over 100 In addition to graphene and its derivatives, hexagonal W m−1 K−1 [225]. They also applied spray-assisted BN (hBN) is another 2D material possessing spherical hBN platelets [226] and hot-pressed BN interesting electrical and thermal properties therefore [227, 228] to enhance the polymer composites, and shows great potential as heat spreaders and composite a thermal conductivity of 2.3 W m−1 K−1 and 23.1 W fillers. Theoretical calculation shows that the thermal m−1 K−1 was realized, respectively. It was reported conductivity of hBN nano-ribbons is as high as that the hot-pressing induced orientation of the BN 1700–2000 W m−1 K−1 [43]. In addition, hBN is an contributed significantly to the thermal performance electrically insulating material with a bandgap of of the composites [227, 228]. In order to decrease the ~5.955 eV [223]. This allows hBN to directly contact interfacial thermal resistance between the BN flakes, with devices and circuits when it is applied as a heat nanoscale silver particles were added to bridge the spreader, therefore dramatically decreases the thermal BN flakes and an in-plane thermal conductivity of boundary resistance and improve the heat spreading 65.7 W m−1 K−1 was achieved, as shown in figure 14 performance. [229]. Shen et al used polydopamine (PDA) coated Sun et al used LPE method to synthesis hBN flakes hBN as fillers in the composite and achieved in-plane and followed by the fabrication of hBN films as heat thermal conductivity of 5.4 W m−1 K−1 [230]. Wat- spreaders to cool down hotspots with a heat flux of tanakul et al also used hBN to formulate the thermal 600 W cm−2 [50]. Thermal characterization showed composite, but the hBN material was not functional- that the temperature at the hotspot was decreased by ized and a maximum thermal conductivity of 1.97 W 20 °C. Since the hBN flakes are too fragile to form a m−1 K−1 was demonstrated [48]. free-standing film, acetate cellulose solution was used Hydrogen boride is a 2D material with hydro- to improve the mechanical strength of the hBN heat gen atoms bridging the hexagonal boron network. spreader. Bao et al used drop-coated few-layer hBN Recently, He et al calculated the thermal conductance as heat spreaders [51]. Experimental results showed of 2D hydrogen boride [231]. It was found that the that the hBN heat spreader can decrease the hotspot lattice thermal conductance in hydrogen boride was temper­ature by 3.8 °C under 1000 W cm−2. If the hBN comparable as in graphene (4.07 nW K−1 nm2 versus film is enhanced by graphene, the hotspot temperature 4.1 nW K−1 nm2), but electron thermal conductance can be lowered by 9.2 °C under the same heat flux. Liu in hydrogen boride (3.6 nW K−1 nm2) was almost ten et al used plasma enhanced CVD method without cat- times that of graphene. Therefore, the total thermal alyst to grow poly-crystalline hBN on SiO2/Si, quartz, conductance of hydrogen boride could be two-fold sapphire and silicon substrates [224]. Owing to the of graphene, which is the highest value in all reported direct growth and conformal interface between hBN materials. But this needs further confirmation by and the substrates, the interfacial thermal resistance experimental measurement. has been decreased and much higher saturated power 2D transition metal dichalcogenides (TMDs) are density on the field effect transistors can be achieved. also a member of the 2D material family. Generally, Choi et al used 35 nm and 80 nm thick hBN films to TMDs are atomically thin semiconductors typically cool down hotspots on Si substrates. They achieved a in the form of MX2, in which M is a transition metal factor of 4.1 and 2.2 reduction of hotspot temperature, atom (Mo, W, etc) and X is a chalcogen atom (S, Se, respectively [52]. or Te). Theoretical predictions based on the phonon Similar to graphene and their derivatives, hBN Boltzmann transport equation have found that mono­ has also been used as composite fillers to develop layer MS2 is able to achieve thermal conductivity as TIMs. Jang et al used silane coupling agents to modify high as 142 W m−1 K−1 at RT, then followed by MoS2 the BN surface to improve its dispersibility in epoxy (103 W m−1 K−1) and MoSe2 (54 W m−1 K−1) [232]. [44]. They found that longer carbon chain in the However, the measurement results are not in line with coupling agent can lead to better interfacial adhesion the theoretical calculation so far. Lee et al measured the between BN and epoxy in the composite, which con- in-plane thermal conductivity of monolayer, bilayer sequently improved the thermal conductivity of the and multilayer MoS2 by a non-invasive Raman spectr­ composite to about 3.5 W m−1 K−1, i.e. an increase of oscopy method. Their results show that the in-plane 45.4% compared to pure BN enhanced thermal com- thermal conductivities for the monolayer, bilayer, posite. The effect of the coupling agent is also verified and multilayer MoS2 are 13.3  ±  1.4, 15.6  ±  1.5, and by Wang et al who applied hBN, cubic BN (cBN) and 43.4  ±  9.1 W m−1 K−1, respectively. Reduced phonon conglomerated hBN as fillers in the composites [45]. boundary scattering was used to explain the increase The highest thermal conductivity of 10.1 W m−1 K−1 in thermal conductivity with the increased number of was obtained from the hBN based composite, and MoS2 layers [233]. It has been reported that a 4-layer- this can be further improved to 12.3 W m−1 K−1 by thick MoS2 exhibited a thermal conductivity of 44–50 adding AlN particles to fill in the space between the W m−1 K−1 at RT, while a 7-layer-thick MoS2 exhib- BN flakes. Wong and Sun’s group theoretically inves- ited 48–52 W m−1 K−1 as reported by Shi et al [234]. tigated the functionalization of hBN by -OH and Therefore, various phonon properties such as intera- -O(CH2)4CH3 groups and found that the thermal tomic bonding and anharmonic vibrations, and their 17 2D Mater. 7 (2020) 012001 Y Fu et al Table 2. Different forms of 2D materials for thermal management applications. Materials/structures Application area Thermal conductivity (W m−1 K−1) Heat transport direction Mono- and few layer Heat spreader (micro-scale) >2000 (suspended) [18, 19, 23] In-plane graphene 600 (attached) [23, 81] Graphene films Heat spreader 1000–3000 [40, 82, 85, 90–93] In-plane LPE graphene Heat spreader 120 [112] In-plane h-BN films Heat spreader 390 [248] In-plane Graphene foam TIM <2 (pristine) [177] Isotropic 90 (compressed) [176, 181] h-BN foam TIM 60 (compressed) [176] Vertically aligned TIM 100–600 [185, 186] Through-plane, graphene in-plane unidirectional Graphene enhanced TIM, thermal composites, 3–15 [25, 34, 39] Isotropic composite coatings h-BN enhanced TIM, thermal composites, 1–6 [44, 45, 124, 249] Isotropic composite coatings Graphene fibers Flexible heat spreader, 1200–1600 (single fiber) [158, 160] Unidirectional smart textiles Figure 15. (a) Simulated heat flux in the sample. Scale bar corresponds to 30 nm. (b) Temperature distribution in the sample. Scale bar is 30 nm. Inset: detail of the marked region. (c) Thermal conductivity as a function of the average grain size assuming two values of single-crystalline thermal conductivity of MoS2: 100 W m−1 K−1 (full circles) and 34 W m−1 K−1 (open squares). Reproduced with permission from [235]. roles in heat transport, still need further investigation single-crystalline MoS2, as shown in figure 15. In the to understand the thermal performance of TMDs. small grain size limit (below 100 nm) the grain bound- Heat conduction in 2D materials can be effectively aries play the major role in the heat transport and the engineered by means of controlling nanoscale grain both assumptions lead to similar values of the effec- structure. It was experimentally shown that 5 nm- tive thermal conductivity. Only by increasing the grain thick polycrystalline MoS2 with grains of about 5 nm sizes, the effect of the grain on thermal conductivity size the thermal conductivity decreased to below 1 W increases and the predictions start to differ. m−1 K−1 [235]. Finite element method simulations on The importance of grain boundaries in heat trans- a sample resembling the experimental one has shown port was also shown for polycrystalline MoS2 in which that the grain boundary conductance was the limiting thermal conductivity of 0.27 W m−1 K−1, was obtained factor for the heat transfer. In the polycrystalline sam- in a sample formed by a combination of horizontally ple the significant temperature changes occur across and vertically oriented grains in similar proportion. the grain boundaries and the majority of the heat flux Analysis by means of molecular dynamics and finite is conveyed by the large grains that are percolating element method simulations confirmed that such a together. Consequently, the heat-flux is mainly trans- grain arrangement leads to the lowest grain boundary ferred along percolation paths, which minimizes the conductance [236]. crossing with grain boundaries. The calculation yields MXenes are another class of 2D materials con- an effective grain boundary conductance of 87.5  ±  1.5 sisting of few-atom thick of transition metal car- MW m−2 K−1 for the polycrystalline MoS2 films [235]. bides, nitrides, or carbonitrides. Until now, the In the same work [235] thermal conductivity as research on MXenes for thermal management is a function of grainsize was calculated, assuming two still limited. Ananthakumar et al added 2D Ti3SiC2 values of the thermal conductivities of 100 W m−1 MXene nanosheets into fluid to improve the ther- K−1 (full circle) or 34.5 W m−1 K−1 (full square) for mal conductivity to 0.276 W m−1 K−1, an increase 18 2D Mater. 7 (2020) 012001 Y Fu et al of 45% with a loading of 0.25 Vol% MAXene [237]. tic quality improvement of the graphene film is needed. Lin et al measured the effective thermal conductiv- Promising avenues are increased grain size and reduc- ity of Ti3C2Tx MXene films and results showed that ing interlayer binding energy, as well as a combination the effective thermal conductivity of Ti3C2Tx MXene of various concepts of graphene alignment structures. films increased from 1.26 W m−1 K−1 at 80 K to 2.84 For TIM applications, the two main tracks are gra- W m−1 K−1 at 290 K [238]. phene and h-BN enhanced composites and pure 2D Theoretical calculations have been performed to based monolithic structures. Graphene enhances com- investigate the thermal properties of silicene by Green- posites are advantageous in that the polymer matrix Kubo method, non-quilibrium MD and first-principle can reduce the thermal contact resistance and can be approach, and thermal conductivity values of 20 W m−1 created with a variety of form factors, as with most cur­ K−1 [239], 14.6–65 W m−1 K−1 [240–243], and 9.4 W rently commercially available TIMs. Composites with m−1 K−1 [244], were predicted respectively. First-prin- a high loading of graphene can have a higher thermal ciple method has also been applied by Peng et al and conductivity than commercial alternatives, although it Zaveh et al to investigate stanene and a thermal conduc- is overall much lower than for pure graphene mat­erials. tivity of 11.6 W m−1 K−1 was reported [245, 246]. MD Graphene monolithic structures such as graphene simulations have been performed by Balatero et al to foam or vertically aligned graphene can achieve sig- investigate Germanene nanoribbons with armchair and nificantly higher thermal conductivity, but are limited zigzag chirality, and length dependent thermal conduc- by the thermal contact resistance in TIM applications. tivity values ranging from 14 to 52 W m−1 K−1 have been Nonetheless, both tracks offer significant improvement found [247]. Experimental measurements are yet to be over existing TIM within certain applications. performed to verify these theor­etical calculations. In addition to these main application areas, there are additional application areas where graphene and 3.8. Summary 2D-materials may play a role. For instance, graphene The different graphene, graphene derivatives and and h-BN enhanced composites may find application other 2D materials for thermal applications are in coating or other thermal composites, and graphene summarized in table 2, and compared in terms of fibers may be interesting for smart textiles. thermal conductivity, heat transfer direction and application areas. The main application areas for 4. Modeling of thermal transport in these materials within thermal management is graphene heat spreading and TIM. In table 2, we can see that the thermal conductivity of mono- and few-layer Carbon being one of the most studied element and graphene approaches to the theoretical maximum taking a central part in key domains such as life or value, but their performance drops quickly when energy, the modeling of graphene is not a recent story, attached onto a substrate surface. In addition, the especially if considered as a brick element of graphite. low thickness of mono- and few-layer graphene heat Tight binding models and then density functional spreaders means that the total heat transfer may be theory computations can be traced back to several relatively small despite of a high thermal conductivity. decades [250]. Those quantum descriptions are able Nonetheless, we may see use in specific applications to qualify structure, electronic properties and their owing to the small size and the possibility of placing it derivatives as well as chemical combinations. But they extremely close to the heat source. remain limited to the zero temperature condition and Macro-scale graphene heat spreaders can transfer include a small number of atoms. heat at a scale relevant for many applications, such as More recently, with the uprising of fullerenes mobile phone cooling. Compared to graphene films, and then graphene, several teams from nanophysics LPE graphene offers closer adherence to substrates, but have investigated the thermal properties of graphene suffer in terms of thermal conductivity. Although it is by using Molecular Dynamic technique. Molecu- possible to improve the thermal conductivity through lar Dynamics is a classical description of the atomic high-temperature annealing and pressing, such meth- motion based on a fair description of the force field. In ods will be incompatible with most substrates. On the graphene, interatomic forces have to involve the fifth other hand, graphene films can be treated separately neighbor, to describe phonons, which are the main from the substrate, which gives potential processing heat carriers. possibilities that lead very high thermal conductivity. This method allows for the simulation of sys- Nonetheless, graphene films may be the first appli- tems of millions of thermally active atoms. However, cation area where graphene based materials reaches a its classical nature forbids it to predict behaviors at widespread commercial use, for instance, in the mobile temper­ature below the third of the Debye temperature. of Mate 20. Here, the graphene assembled film is used This condition is challenging when considering the sp2 for a quick heat spreading from the battery, RF and CPU hybridized bonded orbitals of graphene, generating modules to the casing. The efficient heat spreading can extremely stiff links between atoms. This stiff bond is bring down the perceived temperature of the casing in a at the origin of the extremely high, and maybe diverg- hand. In order to decrease the temperature further, dras- ing, thermal conductivity of graphene [18]. Conse- 19 2D Mater. 7 (2020) 012001 Y Fu et al Figure 16. The calculated inter-FLG thermal resistance as a function of layer number at 300 K. Reproduced with permission from [252]. quently, Debye temperature of graphene is larger than simulations such as molecular dynamics simulations 1000 K. However, the flexural (ZA) modes are the pre- provide an accurate and fast way for such tasks. dominant phonon modes involved in heat transport and those are characterized by low frequencies and can 4.1.1.1.Layer number dependent inter-layer thermal be considered safely as classical [30]. resistance in few layer graphene Covering a substrate with graphene or few layer By using non-equilibrium molecular dynamics graphene has been proven to efficiently spread heat (NEMD) simulations, Wei et al [251] calculated [62]. Thermal management of nanodevices can hence the layer number dependent interfacial thermal be efficiently performed by the adequate integration of resistance between two neighboring graphene layers. graphene based multilayers or composites. In this sec- The interfacial thermal resistance Rinter was obtained tion, thermal properties of graphene and few layer gra- according to the following formula phene will be investigated when in direct contact with a N ·L substrate and then when the contact is functionalized. (N − 1) · Rinter = κC 4.1. Molecular dynamics simulations of interfacial where L is the layer thickness (i.e. 0.34 nm), N is the thermal resistance involving graphene layer number and κc is the effective cross-plane thermal Understanding and controlling the interfacial thermal conductivity of multilayer graphene. The value of the resistance involving graphene and few layer graphene interfacial thermal resistance for N  =  48 is almost (FLG) are crucial to the development and performance one order magnitude smaller than that for N  =  6. The of FLG-based films in thermal management. Several decreasing trend for the interfacial thermal resistance factors govern the interfacial thermal resistance with the layer number was explained by the size effects. It involving graphene, including but not limited to is the hot and cold reservoirs that limit the phonon mean the layer number, the substrate property, and the free path, which causes the interfacial thermal resistance interfacial coupling. In this section, we review the decreases almost linearly with the layer number. advances in the molecular dynamics simulations of To eliminate the size effect in NEMD, Ni et al [252, interfacial thermal resistance involving graphene, 253] adopted an approach based on equilibrium aiming to provide a clear picture of how these important molecular dynamics (EMD) simulations. The thermal factors affect the interfacial thermal property. resistance Rint between two systems with temperature difference ∆T could be calculated by the following equation proposed by Volz et al [254]: 4.1.1. The impact of graphene layer number ∞ Å ã The layer number of graphene has large impact on the T (0) ∆T (t) 1 1 ˆ Rint kB = ¨ ∂ dt + , inter-layer thermal resistance of few layer graphene 0 T(0) 2 N1 N2 (FLG), as well as the resistance between FLG and the substrate. Due to the experimental inaccuracy, it is where kB is the Boltzmann constant, N1 and N2 difficult to measure the layer number-induced thermal refer to the number of degrees of freedom of the resistance variation directly from conventional two subsystems in interaction. This method is not experimental approaches. Fortunately, computer constrained by the thermal reservoirs and allows for 20 2D Mater. 7 (2020) 012001 Y Fu et al Figure 17. Contact resistance between FLG and SiO2 substrate versus layer number at 300 K: a comparison between MD simulations and measurements. Reproduced with permission from [257]. The red dashed line is the averaged value of the experimental results. Reproduced with permission from [256]. Figure 18. In-plane thermal conductivity (red circles) of the graphene based film and its associated thermal resistance R (blue rectangles) with the functionalized graphene substrate as a function of the number of molecules and the equivalent molecule number density in the functionalized graphene substrate. Reproduced with permission from [110]. the calculation of the thermal resistance between two FLG either by increasing the graphene layer number or single layers of graphene. The calculated resistances by adding a substrate. from different methods shown in figure 16 agree in that the interfacial resistance decreases as the number 4.1.1.2.Layer number dependent interfacial thermal of FLG increases. The interfacial resistance finally resistance between few layer graphene and a substrate reaches the graphite limit at large layer numbers. The thermal contact between graphene and the Unlike in suspended FLG, no significant layer substrate is known to be impeded by the weak Van der dependence is found for Rint in supported FLG SiO2 Waals interactions at play. Despite a large number of substrate [255], indicating that it is less sensitive to the studies on the SLG-substrate and FLG-substrate contact layer number due to the existence of the substrate. At resistances, the latter has always been considered as small layer numbers, Rint in supported FLG is much independent to the layer number, since no correlation lower than that in the suspended configuration. These between resistance and layer number could be observed results suggest that one can reduce Rint in suspended due to experimental inaccuracy. However, equilibrium 21 2D Mater. 7 (2020) 012001 Y Fu et al Figure 19. Comparison of the effects of defect and doping on thermal transport properties of graphene. Reproduced with permission from [268]. molecular dynamics calculations reveal that the graphene/graphite-polymer systems. They found that contact resistance between FLG and SiO2 decreases long wavelength phonons in graphene play important with layer number and converges for six graphene roles in thermal transport across the graphene- layers [256]. Figure 17 shows that the MD data are in polymer interfaces. The existence of the low frequency satisfactory agreement with the experimental values modes (2–16 THz), due to out-of-plane motions, [257], especially for FLGs with layer number from enables strong coupling between graphene spectra and 1 to 4. When the layer number is larger than 4, the polymer spectra and thus facilitates interfacial thermal measurement gave a range of the resistances due to the transport. Using MD simulations, Chen et al [261] limited experimental accuracy, but the averaged value found that thermal conductivity of supported FLG of 2 × 10−8 m2 KW−1 (red dashed line) is quite close to increases rapidly with the layer thickness, reaching the MD data 1.7 × 10−8 m2 KW−1. about 90% of that of the bulk graphite limit at 6 layers, and eventually saturates at the thickness of 13.4 nm (40 4.1.2. The effects of interfacial coupling and substrate layers). property Phonon transmission through graphene inter- The interfacial thermal resistance (Rint) between faces is affected not only by the atomic interactions graphene/FLG and the substrate is a crucial limiting but also by the structure of substrate. In traditional factor to their thermal performance in devices. understanding, amorphous solids transport heat far Covalent functionalization has been proved to slower than its crystalline forms due to the short pho- efficiently promote heat transfer between interfaces by non mean free path. However, when it comes to the introducing additional thermal pathways through the interfacial thermal transport where the intrinsic pho- functionalizing molecule. Zhang [110] and Han [258] non mean free path of one component at the interface et al studied the thermal performance of a supported does not dominate the thermal conductance, the situ- graphene-based film with the addition of silane- ation can be different. With NEMD simulations, Li functionalized molecules. Their molecular dynamics et al [262] studied the effect of the crystallinity of SiC simulations show that both the thermal conductivity substrate, and found that the Rint across amorphous and Rint decrease with respect to the number density interface is smaller than crystalline interfaces. This of the silane-based molecules (figure 18). Wang et al phenomenon is presumably due to rough surface fea- [259] reported that the interfacial thermal transfer ture of amorphous solids and the wide phonon chan- can be engineered by intercalating guest atoms such nels opened by the smooth phonon density of states as argon, which modulates the interfacial thermal of amorphous SiC. Nevertheless, Zhang et al [263] conductivity, and insulates the supported graphene reported that the heat removal ability in 2D transis- sheet electronically. Luo et al [260] used steady-state tors does rely heavily on the thermal conductivity of NEMD to calculate interfacial thermal resistance of the substrate, and it is difficult to largely reduce the 22 2D Mater. 7 (2020) 012001 Y Fu et al Figure 20. (a) Sketch of the chemical bonds of the silane molecule. (b) Schematic of a graphene film on different supports. Left: conventional silica substrate. Right: the proposed silica/FGO substrate. Reproduced with permission from [62]. Figure 21. (a) Molecular dynamics simulation results of in-plane thermal conductivity k of the graphene film and (b) interfacial thermal resistance R between the FGO substrate and the graphene film versus the graphene layer number lG in the film. The molecule density is r  =  0.081 nm−2. Reproduced with permission from [258]. hot-spot temperature by tuning the 2D material– be affected by doping. Using NEMD, the interfacial substrate interface resistance. thermal resistance and thermal rectification of nitrogen- Apart from the above mentioned factors, the ther- doped zigzag graphene (NDZG) are investigated by mal property of graphene can also be affected by other Shi et al [267]. It is found that the interfacial thermal means, such as strain engineering [264], and by creat- resistance at the location of nitrogen-doping causes ing phononic crystal structures [265]. severe reduction in thermal conductivity of the NDZG. Thermal rectification of the triangular single-nitrogen- 4.1.3. The effects of doping on graphene thermal doped graphene (SNDG) decreases with increasing performance temperature. Chen et al investigated the effects of Doping is the most feasible method to open a sizeable defect and isotopic doping with different ratios on the and well-tuned bandgap in graphene. The B and N thermal conductivity of graphene by NEMD [268, atoms are the natural candidates for doping in graphene 269], as shown in figure 19. The spectral phonon because of their similar atomic size as that of C and of relaxation time and normalized accumulation thermal their hole acceptor and electron donor characters for conductivity with respect to the phonon mean free substitutional B- and N-doping, respectively [266]. path (MFP) reveal that the long-MFP phonon modes However, the thermal performance of graphene can are strongly suppressed in the defected and doped 23 2D Mater. 7 (2020) 012001 Y Fu et al Figure 22. (a) SEM image of suspended MEMS devices, the rectangle in red color is the 2D materials ready to be measured, the scale bar is 20 µm. Insert: schematic of a prefabricated suspended thermal bridge device. (b) Schematic of the thermal contact resistance Rc and the intrinsic thermal resistance Rint; Rc comes from the contacting point between sample and suspended membranes. (c) Length-dependent thermal resistance of suspended few-layer MoS2, from which Rc can be extracted. (d) Temperature profile crossing the Sensor (Finite Element Simulations: COMSOL Multiphysics 5.2)). (e) Picture of the measurement stage (Electron- beam self-heating method) and chip carrier adapted on the SEM sample holder. (f) Schematic of high-energy electron beam pathing though sample. (g) Schematic diagram of the focused electron-beam self-heating technique. (h) The equivalent thermal resistance circuit for the electron-beam self-heating method, showing the Ri(x) from the left sensor to the local heat spot, the thermal contact resistance (RCL and RCR), temperature rise of the left (ΔTL) and right (ΔTR) sensor. Reproduced with permission from [95, 273]. graphene, resulting in the suppressed size dependence The microscopic origin of the thermal conduc- and the weaker temperature dependence of the thermal tivity k enhancement in the graphene film was inves- conductivity compared to the pristine graphene. tigated by probing the mode-wise phonon relaxation time. By inserting the APTES molecule, the relaxa- 4.2. Functionalization of graphene to increase heat tion time of the acoustic flexural modes ZA largely spreading performances increase at low frequencies, whereas the longitudinal Graphene in-plane heat conduction can be increased and transverse modes undergo a slight decrease. The by intercalating chemical bonding between graphene notable increase for the ZA modes accounts for the and substrate. Accordingly, thermal management enhancement in k of the graphene film bonded to the of a micro heater can be considerably improved via substrate since the ZA modes contribute considerably introducing alternative heat-spreading channels to k as much as 77% at 300 K [30]. implemented with graphene assembled film (GF) The cross-plane heat conduction between the top bonded to functionalized graphene oxide (FGO) graphene films and the lower FGO layers is governed through amino-silane molecules. A GF bonded to the by the competing effects of (i) the intercalation of the FGO substrate through silane molecules is shown in molecules that tends to weaken the interlayer coupling figures 20(a) and (b). 3-Aminopropyltriethoxysilane of graphene therefore increasing the cross-plane ther- (APTES) has three –Si–O– groups and one –NH2 mal resistance and (ii) the additional heat channels end, as shown in figure 4(a). Owing to the simple introduced by the molecules covalently bonding the chemistry of APTES, it can easily bind two different graphene sheets that tend to facilitate the cross-plane substrates. The –Si–O end of APTES binds to the GO thermal coupling. substrate. The crosslinked Si–O structure acts as a Molecular dynamics simulations and ab initio strong bonding layer between the substrate and GFs. calcul­ations reveal that the functionalization con- On the other hand, the –NH2 end of APTES binds onto strains the cross-plane scattering of low-frequency carboxyl groups on the functionalized graphene film. phonons, which in turn enhances in-plane heat con- To explore the effect of functional APTES mol- duction of the bonded graphene film by recovering the ecules on the in-plane thermal conductance of the long flexural phonon lifetime. Those results provide graphene film, molecular dynamics simulations were evidence that a graphene film deposited on a FGO sub- implemented to study a nanoscale molecular junction strate provides a very attractive platform for thermal between two stacks of multilayer graphene nanoflakes. management applications. The in-plane thermal conductivity k of the film and its interfacial thermal resistance R with the FGO sub- 5. Thermal characterization strate is plotted as a function of the graphene layer num- ber lG in the film in figures 21(a) and (b), respectively. There are various thermal characterization methods. It is clearly seen from figure 21(a) that the critical Each method can give very different results even for layer number for the in-plane thermal conductivity the same material. This puts the characterization switch is lc  =  2. into a central and critical role as graphene based 24 2D Mater. 7 (2020) 012001 Y Fu et al Figure 23. Illustration of the optothermal Raman technique. The first experimental study of thermal conductivity of graphene was made possible with an optothermal Raman technique (panel (a)). The heating power ΔP was provided by a laser light focused on a suspended graphene layer connected to heat sinks at its ends. Scanning electron microscopy image shows bilayer graphene of rectangular shape suspended across a 3 µm-wide trench in a Si wafer (panel (b)). Temperature rise, ΔT, in response to changing excitation power, ΔP, is determined with a micro-Raman spectrometer. The G peak in graphene’s Raman spectrum exhibits strong temperature dependence (panel (c)). The inset shows that the optical absorption in graphene is a function of the light wavelength. The calibration of the spectral position of the G peak with temperature is performed by changing the sample temperature while using very low laser power to avoid local heating. The optothermal Raman technique has been extended to other suspended films (panel (d)). The images are reproduced with permission from the Nature Publishing Group. materials for real use often exists in micro-thick Thermal bridge method was firstly used by Xu dimensions. Below is a summary of the state-of the art et al to measure the thermal conductivity and thermal of the thermal measurement techniques used for the power of suspended single layer graphene [31, 95, 274]. graphene and other 2D materials. Figure 22(a) is the scanning electron microscope image of a typical MEMS device. The MEMS consists of two 5.1. Thermal bridge 25 µm  ×  20 µm low-strain SiNx membranes, each is The thermal bridge method was firstly introduced/ suspended by six 400 µm to 600 µm long beams. A invented by Kim et al to measure the thermal platinum or gold resistive coil is prepatterned on top of conductivity of individual multi-walled CNTs in each SiNx membranes and beams, which serves as both year 2001, before which time thermal conductivity heater (Rh) and temperature sensor (Rs), depending on of nanotubes/nanowires were measured in the form the direction of heat flow. The suspended single layer of pallet or bundles using one-heater two-sensors graphene thermally connects these two membranes method and the measured thermal conductivity and is electrically isolated from the resistive coil. The in not intrinsic due to the dominated inter-tube device should be mounted in chamber with vacuum scatterings [270]. Complex electron beam lithography condition better than 1  ×  10−5 pa, to eliminate back- was introduced to fabricate microdevices suitable ground gas convection and thermal radiation between for thermal measurement, in which two suspended membranes. An AC current (usually with amplitude microelectromechanical system (MEMS) were of 100 nA to few µA and frequency of few thousand fabricated and used to suspend low-dimensional hertz) with a biased DC voltage is applied to the heater, samples and detect temperature changes at microscale. and another AC current with the same amplitude/fre- This thermal bridge method is considered to be one quency is applied to the sensor. The DC current (I) is the most successful techniques in measuring thermal used to apply micro-watt Joule heat into heater and conductivity and thermopower of nanotubes, increase its temperature (Th) and the AC current is nanowires and 2D materials [271, 272]. used to measure the resistance of Rh/Rs, corre­sponding 25 2D Mater. 7 (2020) 012001 Y Fu et al to Th/Ts since resistive coil can be used as temperature could introduce further measurement uncertainty monitor. The Joule heat at the heater Rh will partly or thermal rectification [288]; (b) background ther- dissipate through the six beams. The rest of them will mal radiation between membranes should be fur- dissipate through sample which connecting the two ther measured and substracted when sample hold membranes, gradually increases the temper­ature Ts extremely low thermal conductance [289]; (c) the at sensor Rs. In the steady state, the thermal conduc- absorbed particles, in particular the polymer residues, tion of sample σs and the suspended SiNx beams σl, can reduce the thermal conductivity of suspended 2D can be obtained from σl  =  (Qh  +  Ql)/(ΔTh  +  ΔTs) materials to be at a comparable level to that in sup- and σs  =  ΔTsσl/(ΔTh  −  ΔTs), where Qh, Ql, ΔTh, and ported ones, which obscures the intrinsic thermal ΔTs are heating power on heater, heating power on one conduction of the 2D phonons [275]. SiNx beam, temperature rise at Rh and Rs, respective. Improved thermal bridge (ITB) method can be The thermal conductivity κ of sample can be obtained used to measure much thicker materials. Instead of by κ  =  L  ×  σs/S  =  L/(R  ×  S), where L, S and R are the placing mono- to few-layer 2D materials on the micro- sample length, cross-section area and total thermal fabricated heaters and temperature sensors, thick 2D resistance. material strips can be suspended between two home- Thermal bridge method is commonly used in made resistors to measure the in-plane thermal con- measuring thermal conductivity of suspended single ductivity of the target material [40]. or multiple layer 2D materials including graphene [31, 95, 275–277], boron nitride [248, 278, 279], black 5.2. Electron beam self-heating method phosphorus [280–282], transition-metal dichalcoge- Electron-beam self-heating method provides a direct nides [273, 283–285] and etc. However, there are many measurement of thermal contact resistance, and problems and challenges. For example, thermal con- therefore the intrinsic thermal conductivity [273, 276, ductivity of graphene and MoS2 scatters several folds 287]. This method is modified based on the thermal randomly, leaving the intrinsic thermal conductivity bridge method and the sample is mounted inside unsolved with hot debate and disagreement persisting the SEM chamber for measurement (figure 22(e)). [31, 95, 273, 275–277, 283–285]. Different from thermal bridge method where Rh acts The primary challenge lies in the thermal con- as heating source and Rs as temperature sensor, the two tact resistance Rc at the two ends of samples, which membranes are both regarded as temperature sensor contributes unavoidably to the total measured ther- and the electron beam is used as the heating source. mal resist­ance R, i.e. R  =  Rint  +  2Rc, where Rint is the During measurement, the electron beam is scanned intrinsic thermal resistance of sample (figure 22(b)). along the length of sample, during which the energy of To reduce the influence from the Rc, Xu et al deposited electrons is absorbed and therefore heats the local spot metal bars at two ends of graphene to create additional (figures 22(f) and (g)). heat path, however the length-dependent thermal The local heat generated by absorbed electrons resistance of suspended graphene shows that the con- flows towards the two membranes and increases their tact cannot be eliminated to below the negligible level temperature. The measured thermal resistance (Ri(x)) [31]. Therefore, systematic measurement of length- from one membrane to the heating spot is given by: dependent thermal resistance is always required to î −α (x) ó extract the Rc at every temperature measured (figure Ri (x) = Rl α1+α 0 i i (x) ∆TL0 , α0 = ∆T R0 and αi = ∆T ∆TL R , 22(c)) [283, 286]. Alternatively, Liu et al and Adil et al where Rl is the equivalent thermal resistance of the sup- used a brand-new method, i.e. electron-beam self- porting beams, x is the distance from one membrane heating technique, to measure the Rc directly, which to heating spot. ΔTL0 and ΔTR0 are the temperature will be discussed in details later in this manuscript rises of the left and right membranes measured by (section 5.2) [276, 287]. thermal bridged method. ΔTL and ΔTR are corre­ The secondary challenge is related to the uneven sponding temperature rise when the focused electron temperature distribution inside the SiNx membrane. beam is scanned along the length of the samples. The The measured Th and Ts, corresponding to Rh and Rs, thermal conductivity of the samples is calculated by: 1 are the averaged temperature of membranes, however κ = (dRi /dx)·A , where A is the cross-section area of the the temperature at contact point between sample and samples (figure 22(h)). membrane are required to calculate thermal conduc- Electron-beam self-heating method is consid- tivity. This mismatch obscures the intrinsic thermal ered to be the rare techniques which can measure the conductivity especially at the situation when σs and σl thermal contact resistance and interfacial thermal are in the same order of magnitude. To solve this prob- resistance of heterostructure directly. However, this lem, a finite element simulation is required to simulate technique is still quite challenging. The primary chal- the exact temperature rise at the contact point (figure lenge lies in the difficulty in fabricating clean and sus- 22(d)) [277, 278]. pended sample suitable for the measurement, since Some other minor challenges are: (a) the geo- any polymer residue, defects, rough edges etc could metric asymmetry of heater and sensor beams, due affect the path of high-energy electrons and results to electron beam lithography and etching processes, in fluctuation in Ri(x) curves. More importantly, this 26 2D Mater. 7 (2020) 012001 Y Fu et al Figure 24. (a) Schematic diagram of the pulsed photothermal reflectance technique. (b) Top view of the graphene film. (c) Cross-section of the graphene film. (d) Schematic of the functionalization interface. (e) Hotspot structure. (f) Normalized surface temperature of PPR measurmenet of the thermal interface resistance at the Au-Cr/FGO/GF and Au-Cr/GO/GF samples. (g) Normalized surface temperature of PPR measurmenet of the thermal interface resistance at the Au-Cr/FGO/SiO2 and Au-Cr/GO/ SiO2 samples. Reproduced with permission from [258]. technique is limited to thick samples in which there are gle-layer graphene membranes with radius between relatively long path for the focused electron beam to 150 nm and 1.6 µm were measured in a high-vacuum go through and more atoms and electrons to interact SThM with 17 nm thermal spatial resolution. The with each other, introducing more heat in sample and dependence on the thermal contact resistance between increasing the signal to noise ratio [273]. This is prob- tip and graphene as a function of the membrane radius ably the reason that the extension of such a technique was obtained, with values between 1.15 and 1.52  ×  108 to suspended single-layer 2D materials has not been KW−1 [294]. reported yet. For the samples with radius below 775 nm the vari- ation of the contact resistance was explained in terms 5.3. Scanning thermal microscopy of ballistic phonon transport, while in the larger sam- Scanning thermal microscopy (SThM), modified from ples a transition from ballistic to diffusive thermal atomic force microscopy (AFM), is a type of scanning transport was observed. This study also emphasized probe microscopy that maps the local temperature the role of the surface quality of the graphene sample with nanoscale resolution and the thermal conduction and the thermal resistance between the graphene and of the samples. Instead of a sharp probe in AFM, a the substrate on thermal transport. thermal resistance probe or thermocouple probe is used to detect the local temperature. This technique has 5.4. Optothermal Raman spectroscopy been used to measure heat dissipation, local heat spot, The optothermal Raman spectroscopy technique grain boundaries of graphene and other 2D materials for measurements of the thermal conductivity has electronic devices [52, 224, 290–293]. However, directly been developed and popularized by Balandin and co- measuring thermal conductivity of 2D materials or workers in the context of graphene research [18, 19, other nanomaterial is nearly impossible due to the 21, 22, 28, 57, 295–297]. This steady-state technique unknown heat loss from cantilever, air conduction/ was first used to measure the thermal conductivity convection, tip-sample interfacial thermal resistance, of the suspended graphene flakes, and later extended heat radius and etc [271]. to a range of other 2D materials and macroscopic Recently a crossover from ballistic to diffusive ther- thin films. In the optothermal Raman technique, the mal transport in suspended graphene membranes was excitation laser acts simultaneously as a local heat measured using the SThM technique. Suspended sin- source and temperature sensor [18, 19, 21, 22, 295, 27 2D Mater. 7 (2020) 012001 Y Fu et al Figure 25. (a) Schematic diagram of the DRT method for the measurement of thermal conductivity. (b) 3D graphene based foam architecture. (c) Effective electrical resistivity of the graphene based foam. (d) Solid electrical resistivity of the FLG and ultrathin graphite within the graphene based foam. (e) Measured effective thermal conductivity of the graphene based foam. (f) Solid thermal conductivity of FLG and ultrathin graphite. Images (b)–(f) are reproduced with permission from [177]. 296]. The method requires the material under study Since the development of this technique by Balan- to have a pronounced phonon Raman peak. As the din and co-workers [18], this non-contact technique first step, one establishes the temperature dependence has been used for measuring thermal conductivity of the Raman peak. It is done using the low power of various graphene based films [19, 20, 26, 121, 298] laser excitation to avoid local heating of the sample and a wide range of other 2D materials [299–303]. The with the laser. The sample temperature is controlled application of this technique is not limited to quasi- externally by placing the sample to the cold-hot cell. 2D materials, and has been extended to relatively thick The temperature dependence of the Raman peaks films [90, 113]. More details of the technique can be constitutes the calibration characteristic, which found in a few dedicated reviews [19, 96, 295, 304]. can be used for determining the local temperature. Recently, a variation of the Raman based tech- As the second step, one starts to increase the power nique, namely two-laser Raman thermometry was of the excitation laser in order to produce local introduced [305]. The basic idea of this method is to heating on the sample. The resulting temperature use two lasers: one high power laser fixed in the centre is calculated from the shift in the Raman peak of the membrane, which serves as a steady state heater position and known calibration characteristic. The (405 nm wavelength), and another, low power, probing measurement procedure also requires the knowledge laser (488 nm wavelength), which probes the Raman of the dissipated power in the sample. In the original shift on the sample. For both heating and probe laser experiments by the Balandin and co-workers for the absorbed power is measured, and the probing laser investigation of the thermal conductivity of graphene, power is kept to the minimum to avoid sample heating. the dissipated power was determined by comparing Either temperature profiles or the full temperature the measured integrated Raman intensity of the G maps of suspended samples can be obtained with this peak of graphene and graphite [18]. In the follow up technique, allowing for the direct solution of the Fou- works, whenever the sample geometry allowed, the rier heat equation. This is an improvement compared methods was modified to measure the transmitted to the techniques based on one laser, were only the power by a detector placed under the sample [19]. It temperature of the hotspot is probed. The technique is important to determine the absorbed power of the has been succesfully applied for measuring the thermal laser light under the conditions of the experiment. For conductivity of 2D materials, such as MoS2 [235]. example, the optical absorption of graphene can be higher than 2.3% per atomic plane at higher photon 5.5. Pulsed photothermal reflectance energies (shorter wavelength), and be affected by Figure 24 shows the schematic diagram of pulsed the surface contaminations, sample bending and photothermal reflectance (PPR) experimental setup. near-field optical effects due to reflectance from the In this approach, thermal conductivity of the materials substrates [19, 295]. Figure 23 illustrates Balandin´s (bulk or film) is characterized in nanosecond regime method of measuring the thermal conductivity using by thermoreflectance technique. Keading et al were the Raman spectroscopy on the example of graphene and first to apply the PPR technique to measure the thermal macroscopic thin film. conductivity of SiO2 thin films [306]. This technique is 28 2D Mater. 7 (2020) 012001 Y Fu et al Figure 26. (a) Sketch of the Joule heating set-up. (b) Suspended graphene enhanced conductive adhesives measured by the Joule heating method. (c) Temperature profiles of the graphene based conductive adhesives as shown in (b). Reproduced with permission from [313]. Figure 27. (a) Schematic diagram of conductive wire deposited on top of the surface for thermal conductivity measurement of bulk materials. This wire acts as a heater and thermometer. (b) Heat flow for a low thermal conductivity film on high thermal conductivity substrate. In this case Kf  Ks and df  2b. (c) Sample fabrication using 3ω method to measure the thermal contact resistance between graphene and SiO2 substrate. Reproduced with permission from [322]. (d) Experimental measurements of the thermal contact resistance between graphene and SiO2, for four samples of different thicknesses. Reproduced with permission from [322]. an optical and noncontact method consisting a pump time. The heated surface induces a change in refrac- laser and a probe laser. Before the measurement of tive index on the surface [307]. The probe laser is a 1 thermal conductivity, a metal film, preferably gold is mW He–Ne laser focused at the center of the pump deposited on top of the sample surface for the purpose spot with a 20 µm spot size to monitor the changes in of enhancing heat absorption and capturing surface the beam reflected from the gold surface. The temper­ temperature by thermoreflectance technique. ature excursion of metal surface is measured through Han et al applied the PPR method to measure the the temperature dependence of metal’s reflectivity. interfacial thermal resistance between rGO films (with Since for most metals, the ­thermo-reflectance coeffi- and without chemical functionalization) and the sup- cient Ctr  =  ΔR/(R0ΔT) where R0 and T are a reference porting substrate [258]. They used a Nd:YAG laser reflectivity and the metal temperature respectively) pulse with a full width at half maximum of 7 ns, pulse is about constant [307], the intensity of reflected repetition rate of 10 Hz, and pulse energy of 5 mJ. The probe beam is inversely proportional to the gold measurement started with the pump laser pulse with surface temperature. Temperature excursion profile spot size of 3 mm incident on the sample surface that depends on the thermal properties of the underlying induces the sample’s surface temperature change over layers and thermal resistance between the layers. By 29 2D Mater. 7 (2020) 012001 Y Fu et al solving the heat diffusion equation analytically, the profile along the film will reach a steady state within thermal properties of a film can be extracted from several micro-seconds after heating. All the experi- its thermal response captured by the PPR technique ments were conducted in an airtight testing environ­ [198, 308, 309]. ment in order to prevent the effect of airflow. During the measurement heat sink temperature was main- 5.6. Dependence of resistance on temperature tained in constant temperature TL/2  =  T−L/2  =  To. In this method, the suspended sample is heated by Temperature profile of the target material is distrib- running the alternating current (AC) and DC current uted symmetrically with respect to the center of the through the sample and temperature of the sample sample. was measured by dependence of the resistance on the The maximum temperature TM was achieved in temperature (DRT) of the sample. In this case, the the center of the sample. By considering the temper­ temperature coefficient of resistance of the sample was ature at the edge (T0) and middle point (TM) of the measured as well. The film was suspended between two sample, the thermal conductivity of the target material copper heat sinks and placed in a vacuum chamber and is defined by the following equation: electrodes were attached in a four-point differential VIL/2 resistance configuration. The sample has to be cut k = (3) . 4wt(TM − T0 ) into slices with the ratio of length/width less than 0.1. Therefore, the heat conduction along the GF can be Where k is the in-plane thermal conductivity of target considered as 1D heat transfer. Figure 25(a) shows the material. By measuring the temperature at the edge schematic diagram of the self-heating (DRT) method. and center of the material by IR detector, together In the AC method, a iac,rms  =  1 mA current with a with the voltage across the sample and applied current frequency of 2000 Hz coupled with the DC current and the dimensions of the sample, the thermal was run into the sample, raising its temperature conductivity can be calculated. For instance, Wang through Joule heating. Then the resistance of the et al used the Joule heating method to measure the sample at different values of IDC is obtained by thermal conductivity of graphene enhanced thermal Rsample(IDC)  =  vac,rms/iac,rms where vac,rms is the first conductive adhesives and they found that the thermal harmonic voltage drop across the sample measured conductivity of conductive adhesive with 3 wt% by lock-in amplifier. During self-electrical-heating graphene is 8 W m−1 K−1, which is about 4 times of the sample, the change in electrical resistance of higher than the reference conductive adhesive without the UGF was measured and used to determine the graphene [313]. The IR image and temperature profile average temperature rise. The thermal conductivity of of the graphene enhanced conductive adhesive sample the sample is then obtained by using the applied Joule is shown in figures 26(b) and (c). heating power and corresponding average temperature rise as inputs to a combined heat conduction [40, 177, 5.8. 3ɷ method 310]. Figures 25(b)–(f) shows an example of using the Corbino [314, 315] in 1911 noticed that when a DRT method to measure the thermal conductivity of current at frequency ω runs through a resistor, in 3D graphene based foam architecture. addition to a voltage across the resistor at frequency ω, the third-harmonic voltage (3ω) appears in the 5.7. Joule heating resistor. This effect is a consequence of the temperature Nanomaterials such as graphene and CNTs show clear dependence of resistivity. Later, it was found that the temperature dependent Joule heating effect [311, third-harmonic voltage has a practical application to 312]. In this method, the suspended graphene films measure the thermal properties of solids and liquids are heated by running a direct current (DC) and the [316]. In this technique, a thin metal wire is used to temperature rise of the sample is measured by inferred heat the specimen indirectly and the same wire serves radiation (IR). The sketch of the Joule heating set-up both as a heater and thermometer. The 3ω technique, and samples are shown in figure 26(a). was developed by Cahill and Pohl in 1987 [317] During the measurement, the material is sus- and now it is a widely used technique for thermal pended and fixed across two electrodes. A DC current conductivity measurement on bulk and thin film [109, will be run through the material and the temperature 318–320]. The method used is based on heat diffusion of the material would correspondingly change. The in a semi-infinite solid as shown in figure 27(a). A DC current is adjusted to have a temperature rise of thin electrically conductive wire is deposited on top less than 10 °C on the target material so that the radia- of solid-state specimen whose thermal conductivity tion and convection loss can be neglected. The volu- needs to be measured. Figure 27(b) shows the cross metric heat generation due to Joule heating, Q  =  VI/ section of the heat flow in a typical thin film sample. (Lwt), is uniform, where w, t and L are the width, thick- In most thermal conductivity measurement tech- ness and length of the sample, and V, I are the voltage niques, heat is applied at a known rate and the temper­ across the contacts and the current, respectively. ature is monitored to deduct the thermal conductivity. Due to the difference in the heat capacity of the In the 3ω method, the deposited wire acts as a heater target material and the heat sink, the temperature and thermometer simultaneously when a sinusoidal 30 2D Mater. 7 (2020) 012001 Y Fu et al current at frequency (ω) is running in the wire. The has been used to characterized graphene filled compos- heater frequency is adjusted in such a way that the pen- ites [325, 326]. etration depth of heat is smaller than the thickness of In the case of measuring highly thermal conductive the solid. graphite/graphene thin-film structures, there are some There are two ways to measure thermal conductiv- limitations that need to be addressed carefully. For ity of thin film on substrate. One is the slope method example: the sample size might have to be very large and the other one is the differential method [321]. (up to 120 mm for graphite) in order to increase the In both methods, heat conduction across the film is time of the transient. The thickness of the testing sam- assumed to be 1D. To satisfy this assumption, several ple is also preferred to be larger than the radius of hot requirements have to be established as follow: disk sensor to achieve high accuracy. Moreover, many important parameters, like heating power, measuring • Wire width should be larger than the film thickness, time, and radius of disk, must be selected carefully in but should be smaller than the thermal penetration order to obtain reasonable results. depth for line heat source approximation. • Substrate’s thermal conductivity should be higher 5.10. Laser flash than that of the thin film. The Laser Flash technique is a widely used method • Heating frequency should be adjusted in such a way to measure the thermal diffusivity and thermal that thermal penetration depth is much larger than conductivity of materials due to a few important the thickness of the film. features, such as high precision and reproducibility, short measurement times, and well-defined testing Chen et al used the differential 3ω method to meas- atmospheres. The laser flash technique determines the ure the contact thermal resistance between graphene through-plane thermal diffusivity of millimeter thin and SiO2 substrate over a temperature range from 42 K plane samples [327]. During a measurement, the lower to 310 K [322]. As shown in figure 27(c), they firstly surface of the sample is firstly heated by a short laser deposited mechanically-exfoliated graphene on oxi- pulse. The resulting temperature change on the upper dized Si wafer, and then the graphene samples were surface of the sample is then measured by an infrared annealed at 400 °C for 1 h to get rid of the residues. detector. In its most simple adiabatic configuration, Afterwards a thin SiO2 insulating layer was covered on the thermal diffusivity a of the sample is related to graphene so that the heating elements can be depos- the thickness l and the time to half of the maximum ited on top. Finally Ar ion beam was used to pattern temperature t50 rise according to [327]: the graphene sample to ensure 1D heat flow through l2 the graphene flake. The measurement results (figure a = 0.1388 . t50 27(d)) showed that the contact thermal resistance between graphene and the underneath SiO2 layer is in More complicated models allows for corrections due the range of 5.6  ×  10−9–1.2  ×  10−8 m2 K W−1 at RT, to finite pulse lengths and heat losses [328, 329]. It and the contact thermal resistance is independent of is also possible to measure multilayer structures of the graphene thickness. either three layers [330] or two layers with a contact resistance between [331], as long as the properties 5.9. Transient plane source of all but one layer is known beforehand. Such a The transient plane source (TPS) technique is hot non-contact method of Laser Flash benefits on wire based transient method, first developed by S eliminating the effect of contact thermal resistance E Gustafsson [323]. The TPS method consists of a and shows directly about the material’s bulk thermal thin spiral circuit sandwiched between thin polymer properties. To measure in-plane thermal properties, substrates, which is placed in a sandwich structure a special in-plane sample holder is designed so that between two surfaces of a bulk material to be tested. the position for the energy input on the bottom side The spiral acts as both heater and sensor for the of the sample and the position for measuring the measurement. A current through the circuit heats temperature increase on the top side of the sample the sample, and the transient temperature response is (energy output) are located at different lateral measured through a resistance change in the circuit. positions [332]. Thus, the measured temperature The method can be used to extract both thermal increase of the sample shows the thermal diffusivity conductivity and specific heat capacity. in a horizontal direction (in-plane). In spite of all In its basic configuration, the TPS method relies merits of Laser Flash technique, there are some on the assumption that the material to be tested can be potential limitations when measuring highly thermal modeled as infinite, i.e. that the thickness of the mat­ conductive graphene/graphite thin film structures. erial is larger than the penetration depth of the transient For example, the testing samples must always be heating pulse. However, adaptations of the technique coated by a layer of graphite with a thickness of a few has allowed for the measurement of thinner samples micrometers in order to enhance the absorption of [324]. Due to these limitations however, the method is laser energy and the emission of IR radiation to the primarily suited to measurement of bulk samples, and detector. The thinner testing samples are, the greater 31 Table 3. Summary of different thermal measurement methods. 2D Mater. 7 (2020) 012001 Method Material geometry Material size (lateral) Material preparation Measurement Advantages Limitations/challenges Thermal bridge Suspended single- ~Few µm—tens 2D material flakes In-plane thermal conductivity High accuracy, being able to measure thin Complex sample preparation and in- layer to thin film of 2D of µm suspended on of 2D materials film down to single atomic layer fluence of contact thermal resistance materials micro-fabricated heaters from sample to contact electrodes and temperature sensors Electron beam self-heating Suspended few-layer ~Few µm—tens Modified from thermal In-plane thermal High accuracy Difficult to fabricate clean and to membrane of 2D of µm bridge method, mat­erial conductivity, contact thermal suspended sample suitable for the materials mounted in SEM chamber resistance, interfacial thermal measurement and limited to relatively resistance in heterostructures thick samples Scanning thermal microscopy Single-layer to thin ~Few µm—tens 2D material flakes placed Heat dissipation, local heat Easy sample preparation, nanoscale Extremely difficult to measure film of 2D material of µm on insulating substrate spot, grain boundaries of 2D mapping of local temperature and heat thermal conductivity due to unknown flakes materials, extremely difficult to conduction heat loss from cantilever, air measure thermal conductivity conduction/convention, tip-sample interfacial thermal resistance, heat 32 radius and etc Optothermal Raman Suspended single-layer ~Few µm—few cm Materials suspended In-plane thermal conductivity Easy sample preparation, high accuracy, Complex sample preparation for spectroscopy 2D materials up to between two electrodes of materials freedom in material size atomically thin materials thick films Pulsed photothermal Nanoscale thin film up Millimeter size Thin metal film Cross plane thermal Easy sample preparation, high accuracy, Not possible to measure in-plane reflectance to bulk 2D materials deposited on target conductivity and contact freedom in material size thermal conductivity material on substrate thermal resistance Dependence of resistance on Suspended thin strips Millimeter size Material length/width In-plane thermal Low cost, easy sample preparation Only applicable to conductive temperature up to bulk 2D ratio  <0.1 conductivity, temperature coef- materials, measurement must be mat­erials ficient of resistance performed in vacuum Joule heating-IR Suspended thin strips Millimeter size Material length/width In-plane thermal conductivity Low cost, easy sample preparation Only applicable to conductive mat­erials up to bulk 2D ratio  <0.1 mat­erials 3ω Nanoscale thin film Millimeter size Thin metal film In-plane and cross-plane Low cost, high accuracy For thin film measurement the up to microscale 2D deposited on target thermal conductivity substrate’s thermal conductivity should materials material be higher than that of the thin film Transient plane source Microscale up to bulk Millimeter size Materials with flat surface In-plane and cross-plane Fast, easy sample preparation Unproven measurement of very thin, 2D materials thermal conductivity, thermal small-sized and very high-thermal diffusivity, specific heat capacity conductivity materials Laser flash Microscale up to bulk Millimeter size Materials with flat surface In-plane and cross-plane Easy sample preparation Not possible to measure very thin and Y Fu et al 2D materials thermal conductivity small-sized materials 2D Mater. 7 (2020) 012001 Y Fu et al Figure 28. Diagram of thermal characterization methods used for measurement of 2D materials with different thicknesses. influence of graphite coating layer will be. Therefore, However, ITB method is also very attractive and is samples with a thickness less than 10 µm are hard based on the same idea as ASTM 5470 standard, but it to be measured accurately by laser flash equipment. requires tedious time for setting up the experiments. In addition, the time resolution of input laser and However, it can give quite good accuracy, often in the detector also has strong effect to the accuracy of range of 10%–20% [40]. Electron beam self-heating the testing results, especially for ultra-high thermal method requires similar sample fabrication as the conductive materials (above than 1000 mm2 s−1). thermal bridge method. Additionally, it utilizes the Various graphene based composite films measured electron beam in SEM chamber to heat up the sam- by Laser Flash method have been reported [325, ple for thermal measurement. Although the setup is 333–337]. very complex, the method offers direct measurement of contact thermal resistance. Optothermal Raman 5.11. Summary spectr­oscopy needs information of calibration coef- As presented above, there are many different methods ficient in different temperatures which can be very that can be used to evaluate the thermal performance ­different to obtain with high accuracy, therefore affect- of 2D materials. Depending on the geometry and ing its trustiness of the data produced. PPR or Time required properties of the materials, the method has domain time reflectance method is recommended for to be carefully selected so that the measurement can the measurement of cross-plane thermal conductiv- be performed by the simplest method with reasonable ity and interfacial contact thermal resistance of 2D accuracy. Table 3 shows a summary of all methods with materials and combined structures with thickness of remarks on their advantages and limitations. 10 nm to 10 mm, but materials/structures with a few A diagram for different thermal characterization nanometer thickness is still possible to be measured methods used for different thickness of materials is by this method, as it becomes much more difficult to shown in figure 28. Generally speaking, it is difficult prepare the sample with such a small thickness. With to point out which method should be used to get best 3ω method for the 2D materials of graphene, it needs accuracy and most exact value regarding the thermal to create an insulation layer between the graphene and performance. Every method has accuracy issues which substrate adding on additional sample preparation are related to intrinsic, equipment set up and geomet- effort and cost. Transient plane source is a convenient ric factors. Scanning Thermal Microscopy method method to quickly measure various thermal proper- cannot generate direct values of thermal conductivity ties of 2D materials, but it is limited to relatively thick but rather give the temperature distribution/gradient, and big-sized samples. Laser flash is very useful for often in submicron length scale, for instance across a generic purpose of the thermal measurement as it the grain boundary, thus providing very useful infor- does not require specific sample preparation, but it is mation when studying thermal transport properties. not useful for sample thickness less than for instance Thermal bridging method often requests MEMS 10 µm. Joule heating method offers simple and quick based technology with clean room skills. Therefore, it measurement based on Fourier’s Law and it gives rea- is not very commonly used for engineering purposes. sonable accuracy with less than 20% in most cases. The 33 2D Mater. 7 (2020) 012001 Y Fu et al key issue is here, to determine the emissivity ­factor as Acknowledgments function of temperature for the sample measured. The DRT method, especially carried out in vacuum, YF, JH, YL, AZ, MK and JL acknowledge the financial is interesting but it takes quite long time for the sam- support from The Swedish National Science Foundation ple preparation. To conclude, it seems that Joule heat- (VR under the contract No 621-2007-4660), The ing is the most versatile and easy-to-use method for Swedish Foundation for Strategic Research (SSF) quick screening purpose of graphene based films with under contract (No SE13-0061), the Swedish Board for different thicknesses from a few micrometers up to innovation under the Siografen program and from the millimeters. Production Area of Advance at Chalmers University of Technology, Sweden. SC, YZ and JL acknowledge 6. Current and future potential the financial support by the Key R&D Development applications Program from the Ministry of Science and Technology of China with the contract No: 2017YFB040600 and Up to date, a few applications have been demonstrated the National Natural Science Foundation of China to use graphene and related 2D materials for thermal (No. 51872182). XX is supported the National Natural management on commercial products. For example, Science Foundation of China (No. 11674245 & No. graphene was used to coat LED filaments and it 11890703). MS and CMST acknowledge financial was claimed that graphene can facilitate the heat support from the CERCA programme/Generalitat de dissipation in the LED bulb, therefore extending the Catalunya, the Severo Ochoa Centres of Excellence lifetime and improving the efficiency of the LEDs programme, funded by the Spanish Research Agency [338]. Graphene based heat spreader can be supplied (AEI, Grant No. SEV-2017-0706). with different thicknesses varying from 20 µm to 100 µm with thermal conductivity up to 3200 W ORCID iDs m−1 K−1 [339–341]. In addition, vertically aligned graphene based TIM is available to offer thermal Yifeng Fu https://orcid.org/0000-0001-7783-8766 conductivity up to 1000 W m−1 K−1 in the Z direction Josef Hansson https://orcid.org/0000-0003-1278- [341]. Furthermore, it is claimed that graphene based 946X thermal grease with thermal conductivity  >10 W m−1 Yuxiang Ni https://orcid.org/0000-0001-8567-6998 K−1 can be provided [342]. Yan Zhang https://orcid.org/0000-0002-2461-060X A real commercial application of graphene film Zhi-Bin Zhang https://orcid.org/0000-0003-0244- seems to be in the mobile of Mate 20. It seems that the 8565 graphene assembled film can bring down the percep- Marianna Sledzinska https://orcid.org/0000-0001- tion temperature efficiently. In order to decrease the 8592-1121 temperature further, drastic quality improvement of Alexander A Balandin https://orcid.org/0000-0002- the graphene film is needed. 9944-7894 Xiangfan Xu https://orcid.org/0000-0001-7163- 7. Concluding remarks 4957 Johan Liu https://orcid.org/0000-0001-9931-1439 The large-scale production of high quality 2D materials has been considered as the major obstacle for their industrial application. Thanks to the very strong References interest in graphene and related 2D materials, great [1] Manno M, Yang B, Khanna S, McCluskey P and Bar-Cohen A progress has been achieved to produce 2D materials 2015 Microcontact-enhanced thermoelectric cooling of over the past years. Roll-to-roll system has been ultrahigh heat flux hotspots IEEE Trans. Compon. Packag. Manuf. Technol. 5 1775–83 developed to fabricate continuous large-area graphene [2] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, by CVD method. 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