Thermal conductivity reduction in three dimensional graphene-based nanofoam

Abstract

This work investigates the thermoelectric properties of a three dimensional nanofoam of few layer graphene (3D-NFG) decorated with holes having diameter of several tens of nanometer. The nanoporous 3D graphene structures were fabricated by a chemical vapor deposition method to ensure high electrical conductivity required for potential applications as thermoelectric materials. The thermal conductivity of the suspended 3D-NFG samples was measured by an optothermal method and found to be 10.8 W m⁻¹ K⁻¹. The substantially reduced values of thermal conductivity were attributed to the small diameter of the pores and their inhomogeneous distribution. Suppression of heat conduction with preserved electrical conductivity is beneficial for the proposed thermoelectric applications.

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Graphene, a two dimensional sheet of sp² bonded carbon atoms, has been proposed as an emerging material for thermoelectrics¹ (TE), as well as for electronics,² solar cells, and supercapacitors,³ due to its high electrical and thermal conductivity. The energy-conversion efficiency of a TE material is evaluated by a dimensionless figure of merit (ZT), defined as ZT = S²σT/κ, where S is the Seebeck coefficient, σ denotes the electrical conductivity, κ is the thermal conductivity, and T is the working temperature.⁴ In order to obtain a high ZT value, it is essential to lower the κ (=κ_ph + κ_el) value while retaining high power factor (S²σ). Theoretical studies have reported⁵ that the reduction of κ_ph can be achieved by boundary scattering on graphene-based antidot lattice (GAL) structures, which are made of a periodic array of holes, which also causes an electronic band gap to open around the Fermi level. However, there has been no experimental report on the thermal properties of fabricated GALs, although electrical conductivity was experimentally controlled by varying the periodicity and number of layers of a synthesized GAL.⁶ To obtain a GAL with high ZT value, a low degree of disorder is desirable since a high degree of disorder may reduce the electrical conductivity and the Seebeck coefficient simultaneously, as well as lowering the thermal conductivity.⁷ The thermoelectric property of materials also varies according to the dimensionality of the structures.^8,9 Three dimensional materials are believed to possess better thermoelectric properties as reported in the case of silicon inverse opals,¹⁰ nanodot superlattices,¹¹ graphene foam,¹² graphene networks¹³ etc. For instance, Wang et al.¹⁴ reported a much reduced thermal conductivity value, in the range of 182–349 W m⁻¹ ​K⁻¹, for a graphene foam with few hundred micron sized pores, as compared to 1300–5800 W m⁻¹ ​K⁻¹ for normal single layer graphene (SLG) or few layer graphene (FLG). Alternatively, a recent report by Dimitris et al. suggested that it may be possible to obtain a strong reduction in thermal conductivity values with graded porous materials having inhomogeneous porosity, compared to that of materials with homogenous porosity.¹⁵ Inhomogeneous porosity denotes random/different pore size throughout the structure. However, it is difficult to experimentally engineer inhomogeneous porous materials.¹⁶ We decided to tackle this issue using chemical vapor deposition (CVD) to grow a 3D-NFG without a template; such a process ensures reasonably good electrical conductivity as well as the presence of a large number of random pores.

The detailed synthesis procedure for obtaining 3D-NFG is reported elsewhere.^17,18 Fig. 1a and b respectively show SEM and TEM images of the 3D-NFGs with pore diameters in the range of 40–180 nm. The size of the samples is 1.5 × 1.5 cm. The magnified TEM image also reveals that the films are folded with many wrinkles: these features may affect phonon propagation. It has been reported¹⁹ that the wrinkles, created by additional stress in the graphene due to the different diffusion rates of carbon atoms on nickel, produce ∼27% lower thermal conductivity than that of unwrinkled graphene.^19,20 Fig. 1c provides the Raman spectra results for the 3D-NFG. The D′ band of 3D-NFG at ∼1620 cm⁻¹ is observed due to the presence of defects in graphene. Our 3D-NFG with an I_D/I_G ratio of 0.63 and I_2D/I_G ratio of 0.99 indicates high quality few-layered graphene. The surface roughness of our ∼150 nm-thick 3D-NFG, as measured by AFM, was found to be ∼41.1 nm, which is higher than the values of 3.2 and 5 nm for single layer²¹ (SLG) and few layer graphene²² (FLG), respectively, indicating the presence of scattering centers due to the rough surfaces, as shown in Fig. 1d.

Fig. 1 (a) SEM image of the 3D-nanofoam of graphene (3D-NFG), (b) TEM image showing pores in 3D-NFG after nickel etching, (c) Raman spectrum and (d) AFM image of 3D-NFG showing the surface roughness.

Fig. 2a and b displays the XPS results of 3D-NFG and the deconvoluted C1s peak, respectively, obtained after fitting the data using a Gaussian distribution function. The major peak at 284.48 eV is due to the non-oxygenated C–C bond (sp² bond). The deconvoluted peaks at binding energy of 285.82, 286.93 and 288.18 eV are correspondingly assigned to C–OH, CO, OC–OH bonds (sp³ bond). The increase in content of C–OH and CO may be due to the etching conditions used, in addition to the structural disorder. It has been reported²³ that multi-layer graphene (MLG) nanowall growth on Si substrates causes sp³ bonds to be present in between the nanowalls. The XPS results correlates well with that of Raman data for 3D-NFG.

Fig. 2 (a) XPS spectrum of 3D-NFG and (b) deconvoluted C1s spectrum of 3D-NFG.

The thermal conductivity value of the 3D-NFG was measured by the optothermal method based on Raman spectroscopy.^1,24 The schematic diagram of the optothermal measurements are presented in Fig. 3a. To measure the intrinsic thermal conductivity of 3D-NFG, a trench of 300 nm depth and 6 μm width was made using FIB on the substrate. The 3D-NFG samples were transferred onto trench for the measurements and the measurement point is indicated by the red crossbar in Fig. 3b. Fig. 3c shows a characteristic Raman G peak of the tested 3D-NFG film at low and high excitation power. In the following thermal measurement, we intentionally increased the intensity of the excitation laser power so that it could induce local heating of the sample. The Raman peak position of G peak shifted from 1582.8 cm⁻¹ to 1566.6 cm⁻¹ as the power increased from 0.5 mW to 4.0 mW as indicated in Fig. 3c.

Fig. 3 (a) Schematic view of the thermal conductivity measurement on suspended 3D-NFG samples, (b) Raman microscopy image of the 3D-NFG film located on the trench (red crossbar denotes the measurement position, inset image-optical microscopy image of the 3D-NFG on trench), (c) shift in G peak position due to the change in the excited laser power in the suspended 3D-NFG samples, (d) finite element simulation result of temperature distribution in 3D-NFG with the given geometry used to extract the thermal conductivity.

Fig. 3d show the finite element simulation result of the temperature distribution in 3D-NFG with the given geometry when the simulation result matches the experimental data; the thermal conductivity value of suspended 3D-NFG samples was extracted as 10.8 W m⁻¹ K⁻¹, which is lower than the previously reported values.^12,14 The thermal conductivity value of suspended 3D-NFG is attributed to the contribution of phonon flexural (ZA) modes in addition to the LA and TA modes. The flexural modes are blocked by the presence of substrate in case of supported samples and it's also affected by number of layers in case of suspended samples. However, the suspended 3D-NFG has low K values (10.8 W m⁻¹ ​K⁻¹) that are comparable to its amorphous limit of graphene (11.6 W m⁻¹ ​K⁻¹). This drastic reduction can be assigned to (i) the presence of pores that reduce phonon MFP and (ii) the presence of oxygen in the structure that acts as effective scattering centers.

The electrical conductivity value of the 3D-NFG films was measured using the four point probe technique. Table 1 presents the electrical conductivity of two dimensional and three dimensional structures of graphene, showing a large difference between graphene and graphene nanomesh (GNM)/nanoperforated graphene/3D-NFG. The difference is due to band gap opening and defects (edge, surface) in the structure. Compared to a few layers of graphene with high conductivity, the three dimensional graphene architectures have relatively low conductivity due to their unique structure, change in mean free path and interlayer junction resistance between the sheets. Our 3D-NFG films had conductivity of ∼8 S cm⁻¹ at room temperature, which agrees well with the previously reported³¹ conductivity values of graphene foams. We attributed this reasonably high conductivity value of our 3D-NFG, which does not greatly deteriorate the thermoelectric properties, to the CVD growth method. Besides, the electrical properties of graphene depend on defects and impurity doping as well as the growth technique. In conclusion, we experimentally demonstrated a two order-of-magnitude reduction of thermal conductivity in graphene-based nanofoams with nanometer size pores. The thermal conductivity value of suspended 3D-NFG was 10.8 W m⁻¹ ​K⁻¹. The drastic reduction in the thermal conductivity of 3D-NFG can be attributed to the following factors: (i) wrinkles in the structure, (ii) surface roughness of the film, (iii) the presence of pores with appropriate nanosize, (iv) a proper sp²/sp³ ratio of 3.6, and (v) random distribution of pores in 3D-NFG. This result demonstrates the potential of structural control for significantly improving the thermoelectric properties of graphene-based thermoelectric materials.

Table 1 Electrical conductivity values of various graphene based structures

Material	Conductivity
Few layer graphene^25	10^4 S m^−1
Graphene paper^26	50 S cm^−1
Graphene aerogel^27	100 S m^−1
Laser scribed graphene^28	17 S cm^−1
rGO hydrogel^29	5 × 10^−3 S cm^−1
Graphene/PDMS foam^30	0.6–2.0 S cm^−1
Graphene foam^31	10 S cm^−1
3D-NFG (this study)	8 S cm^−1

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Acknowledgements

We thank Prof. Alexander A. Balandin at UCR for help in optothermal measurements and helpful discussions. This work is supported by NRF with the Contract no. NRF-2015-R1A2A2A01005250 and 2015-M2B2A4030502 (National nuclear R&D program, MSIP) and by IBS-R019-D1.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra19130k

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