Thermal Transport in Supported Graphene Nanomesh - ACS Applied

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Thermal Transport in Supported Graphene Nanomesh Ze Xiong, Xinyu Wang, Kenneth Hong Kit Lee, Xiaojun Zhan, Yue Chen, and Jinyao Tang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b00097 • Publication Date (Web): 07 Mar 2018 Downloaded from http://pubs.acs.org on March 8, 2018

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ACS Applied Materials & Interfaces

Thermal Transport in Supported Graphene Nanomesh Ze Xiong†, Xinyu Wang||,#, Kenneth Hong Kit Lee †, Xiaojun Zhan†, Yue Chen|| and Jinyao Tang†*

†Department of Chemistry, The University of Hong Kong, Hong Kong 999077, China.

||Department of Mechanical Engineering, The University of Hong Kong, Hong Kong 999077, China.

#Institute of Thermal Science and Technology, Shandong University, Jinan 250061, China.

KEYWORDS. Graphene Nanomesh, Thermal Transport, Back Scattering, Coherent Scattering, Thermoelectrics.

ABSTRACT

Graphene is considered as a promising candidate material to replace silicon for the next generation nanoelectronics due to its superb carrier mobility. To evaluate its thermal dissipation capability as electronic materials, the thermal transport in monolayer graphene was extensively explored over the past decade. However, the 1 ACS Paragon Plus Environment

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supported chemical vapor deposition (CVD) grown monolayer graphene with submicron structures were seldom studied, which is important for practical nanoelectronics. Here we investigate the thermal transport properties in a series of CVD graphene nanomeshes patterned by a hard-template-assisted etching method. The experimental and numerical results uncovered the phonon backscattering at hole boundary (< 100 nm neck width) and its substantial contribution to the thermal conductivity reduction.

Graphene, as the representative 2D material, has been extensively studied for field effect transistor1, photodetector2 as well as sensors3 in the past decade. With its unique band structure, ultra-high carrier mobility, superior mechanical strength, high thermal conductivity, and compatibility with existing semiconductor industry fabrication process, graphene is considered as a promising candidate to replace silicon for the next generation high-performance electronics4. Since the heat dissipation of the high-performance electronics is one of the critical considerations in integrated circuit design, the thermal transport properties of graphene have been extensively studied experimentally5-6 as well as theoretically7-10 in both suspended11-12 and supported form13-14. Notably, for large-scale integrated graphene circuits, the most probable device configuration may be based on chemical vapor deposition (CVD) grown graphene supported on oxide substrate where the high thermal conductivity up to ~ 450 W·m-1·K-1 was recorded13, which promises a better thermal management compared to silicon with thermal conductivity lower than 100 W·m-1·K-1 in thin film form15. However, in practical electronic circuits, the high-density nanopatterned 2 ACS Paragon Plus Environment

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monolayer graphene with an excess amount of graphene edges will be used, which may significantly deteriorate the effective thermal conductivity of graphene layer due to the enhanced phonon boundary scattering16-17. Although the thermal transport in periodic phononic crystal7 and asymmetric nanoribbon structures18 has been examined by numerical simulation previously, the experimental study is still limited19. Therefore, it is essential to investigate the thermal transport properties of the densely patterned graphene layer supported on oxide substrate, laying the foundation for the design of graphene-involved electronic devices and thermal management circuit20.

To obtain the thermal conductivity of nanostructured materials, the most reliable and widely used method is based on the suspended thermal bridge device21, which provides good temperature sensitivity, accurate heat flow measurements, and wide temperature range13-15, 22. In this study, we adopted the thermal bridge device to investigate a series of CVD graphene nanomesh (GNM) fabricated by a hard-template-assisted etching method (HTE). In contrast to the soft block polymer templates, the inorganic HTE can largely rule out the potential organic residue on the graphene surface, which may influence thermal transport properties by introducing additional surface phonon scattering sites23.

The experiments started with CVD grown monolayer graphene on the copper film, which was transferred to an oxidized silicon substrate after removal of the copper foil. The as-transferred graphene was annealed under ambient pressure with a mixed flow of Ar (300 sccm) and H2 (30 sccm) at 300 °C for 1h to remove possible

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polymer residue. Then a piece of anodic aluminum oxide thin film (AAO) with quasi-hexagonally packed through holes was transferred onto the graphene surface (Fig. 1a) and served as a hard etching mask for reactive-ion etching (RIE) treatment (Fig. S1). After the oxygen RIE etching, the GNM was generated, and the AAO thin film was removed by immersing in 1 wt.% tetramethylammonium hydroxide (TMAH) aqueous solution and rinsed clean by DI water (Fig. 1b). Then a SiO2 supported GNM ribbon bridged between two isolated SiO2 thermal islands was defined by electron beam lithography. After depositing the corresponding platinum heater and temperature sensor by sputtering, the SiO2 and underneath silicon surrounding the thermal islands was selectively removed by CHF3 RIE and gas phase XeF2 etching, respectively (Fig. 1c). The final device can be seen from Fig. 1d, in which the GNM supported by SiO2 is ~ 20 µm in length and ~ 5 µm in width.

Since the phonon transport is strongly determined by the detailed nanostructure of graphene11,

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, a series of GNMs with different pitch size were

prepared by using several AAO thin films as the etching mask (Fig. S2). After the oxygen RIE etching, the obtained GNM is examined with transmission electron microscope (TEM) and scanning electron microscope (SEM) as shown in Fig. 2 and Fig. S3. The pitch size (LP) and neck width (LN) of our GNM are extracted from the images for later analysis. It is noteworthy that for the GNM with large pitch value, although its neck width simultaneously rises, the suspended long GNM stripe is prone to fracture, leaving only limited structure units for TEM measurement. As a result, the geometrical parameters of small pitch (65 nm and 125 nm) GNMs were extracted 4 ACS Paragon Plus Environment

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based on their TEM images, whereas the SEM image was used for large pitch (450 nm) GNM statistics (Fig. S4 and Table S1).

The thermal conductance (G) of the SiO2 bridge with and without supported graphene sample is obtained with two consecutive measurements under vacuum with the same device before and after oxygen plasma removal of GNM (Fig. 3a-d). The thermal conductance of graphene (∆G) layer is calculated by subtracting the measured thermal conductance of bare SiO2 bridge from SiO2 bridge supported GNM14. Then the thermal conductivity κ of graphene can be calculated using the expression ∆GL/(wt)=κ, where L and w are the length (20 µm) and width (5 µm) of the graphene sample, t is the thickness of graphene (0.34 nm). We adopted the standard four-point resistant method for the thermal conductance measurement, which has uncertainty level ~ 1 nW·K-1

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and shown as error bar in Fig. 3a-d. The temperature dependent

thermal conductivity of GNM with different pitch size is presented and compared to that of pristine graphene in Fig. 3e. The thermal conductivity of pristine CVD graphene is measured as 477 ± 31 W·m-1·K-1 at room temperature, which is comparable to previously reported thermal conductivity of the supported polycrystalline CVD graphene13. With the holes involved in the graphene, the thermal conductivity of GNM is systematically reduced, and no obvious Umklapp peak can be observed within measurement temperature range. Resembling the observation in nanostructured silicon thin film15, 24, the incorporated holes strongly enhanced the boundary scattering which leads to strong diffusive behavior in phonon transport and the phonon mean free path dominated by the boundary scattering. Because the 5 ACS Paragon Plus Environment


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phonons with mean free path longer than 100 nm in graphene accounted for more than 80% of the accumulated thermal conductivity25 and can be strongly scattered by the densely packed holes with similar neck width, the size-dependent thermal conductivity reduction can be clearly observed in our GNM samples. The electronic properties of our GNM were also examined by fabricating field effect transistor with similar procedure reported previously2. Compared to pristine graphene, the electrical conductivity of GNM is suppressed from 3.21×105 S/m to 6.57×104 S/m at 0 V gate bias while no obvious gate voltage dependence is observed in our GNM transistor device (Fig. S5b). Particularly, the thermal power of GNM is constantly positive and not strongly modulated by the gate bias as can be seen in pristine graphene (Fig. S5c), which implies that the GNM is p-type doped by the edge oxidation in the oxygen plasma treatment process.

To provide an in-depth understanding of the thermal transport in GNMs, the experimental thermal conductivities were compared with the molecular dynamics (MD) simulation results taken from a series unsupported GNM structures with different LP and LN (Fig. 3f). Since the thermal conductivity variation between supported and unsupported GNMs, after normalized by the thermal conductivity of corresponding pristine graphene, was found negligible in our simulation (Fig. S9), the unsupported graphene was simulated to save computational resources. It is worth mentioning that the GNM can be regarded as an interconnected graphene nanoribbon networks with semi-periodic hexagonal structure. Previously, the thermal conductivity of graphene nanoribbon with ribbon width of ~ 15 nm was measured to be ~ 80 6 ACS Paragon Plus Environment

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W·m-1·K-1, which is considerably higher than our 65 nm pitch GNM (23 ± 17 W·m-1·K-1) albeit the wider neck width in our GNM than the nanoribbon26. This fact raised the question, whether this additional thermal conductivity suppression is resulting from the coherent phonon scattering due to the phononic crystal effect27-28 or the more traditional phonon backscattering at the boundaries15, 24.

To address this issue, we investigate the temperature distribution across GNM via the molecular dynamics simulation, where a heat source is set as 350 K and a heat sink is maintained at 250 K across the 196 nm simulation domain. The temperature contour of a typical GNM with a pitch size of 50 nm and neck width of 25 nm is presented in Fig. 4a. The normalized temperature profiles along X-axis denoted by the dash lines in Fig. 4a are displayed in Fig. 4b. Since the neck width of GNM is much smaller than the intrinsic phonon mean-free-path, the phonon transport ballistically between two adjacent holes and backscattered at the graphene boundaries. This effect can be identified from a locally overheated region close to the left edge of the hole due to the backscattered phonons from the edge. Analogously, a locally cooled region is shown near the right edge of the hole as the phonon transport is shadowed by the hole. This peculiar inverted temperature distribution leads to an additional thermal resistance similar to the observation in porous silicon by the Monte Carlo simulation29, which may be accounted for the lower thermal conductivity of GNMs compared to graphene nanoribbons. For 65 nm and 125 nm GNMs, the neck widths LN of the submicron mesh structures are all around 20 nm, which is far smaller than the intrinsic mean free path of supported graphene (~ 100 nm) but larger than the 7 ACS Paragon Plus Environment


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dominant phonon wavelength (~ 2 nm)25. Therefore, the phonon transport within the neck is ballistic while the backscattering on the graphene edges may be the primary root for the reduction of thermal conductivity in these two GNMs17, which has been previously predicted in theoretical calculation9. In contrast, the neck widths LN of 450 nm GNM is around 155 nm which is larger than the intrinsic phonon mean free path. As a result, the diffusive phonon transport induced by Umklapp scattering will be enhanced and the thermal conductivity suppression due to the phonon backscattering is of less significance. On the other hand, it has been extensively debated whether the coherent phonon transport can play a significant role in the periodic nanomesh structure, particularly in silicon nanomesh24, 27. To enable the coherent interference of phonons within a periodic nanoporous thin film, it requires: 1) a significant portion of the phonons transport ballistically between adjacent holes; 2) the nature of the phonon scattering at the material boundary is more specular rather than diffusive30. Since the intrinsic phonon mean free path in supported graphene is comparable with that in silicon, the coherence of the phonon in small pitch samples can be expected, which makes the GNMs a good candidate for high-temperature phononic material.

Regarding the nature of the phonon scattering at the graphene boundaries, since high-frequency phonons with a wavelength shorter than 5 nm contributed the majority (91%) of accumulated thermal conductivity in graphene25, high-frequency edge disorder with the large wavevector (q >2π/ 5 nm) may lead to the decoherence of phonons due to diffusive scattering, while the contribution of low-frequency edge disorder is negligible. From the transmission electron microscope images, the 8 ACS Paragon Plus Environment

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as-etched graphene edges are quite smooth with root-mean-square edge roughness < 0.4 nm after filtering out the low frequency (q

Thermal Transport in Supported Graphene Nanomesh - ACS Applied

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