159

# Graphene Science Handbook

Print publication date:  April  2016
Online publication date:  April  2016

Print ISBN: 9781466591318
eBook ISBN: 9781466591325

10.1201/b19642-5

#### Abstract

Formation of high-quality electrical and thermal contacts between nanostructured materials such as carbon nanotubes or graphene and metal electrodes is one of the fundamental issues in modern nanoelectronics. The quality of contact can be improved by nonlocal laser annealing at increased power. The improvement of thermal contacts to initially rough metal electrodes is attributed to local melting of the metal surface under laser heating, and increased area of real metal–graphene contact. The accuracy of thermal conductivity measurements for suspended multilayer graphene (MLG) flakes by micro-Raman technique was shown to depend critically on the quality of thermal contacts between the flakes and metal electrodes used as a heat sink. Improvement of the thermal contacts was observed also between MLG and silicon oxide surface, with more efficient heat transfer from graphene as compared with the graphene–metal case.

#### 3.1  Introduction

The extraordinary thermal properties of graphene motivated numerous studies aiming at its applications for heat management in micro- and nanoelectronics [14]. However, on the way to successful applications, many important issues have yet to be addressed, in particular, in the formation of high-quality metal–graphene thermal contacts [2,510]. In many cases, poor contacts may affect not only the electrical transport but also efficiency of heat dissipation in sub-micrometer scale graphene-based devices [6]. Thus, high graphene thermal conductivity and high quality of thermal contacts with metal electrodes are equally important for heat management in such devices. Note that experimental works focused on the thermal properties of graphene–metal contacts are still scarce when compared with theoretical studies [11]. A number of techniques were reported in the literature to measure thermal conductivity of graphene or reduced graphene oxide, including the optothermal micro-Raman method [9,10,1214] that is used in the present research, as well as the thermal bridge [15] and four point probe [16] methods, where sample heating and local temperature measurements are realized indirectly by either optical or electrical means.

Methods to prepare graphene flakes of different thicknesses (single-layer graphene [SLG], few-layer graphene [FLG], and multilayer graphene [MLG]) are summarized in Table 3.1, and the results of recent experimental studies on thermal conductivity in graphene are presented in Table 3.2.

### Table 3.1   Methods Used for Fabrication of Graphene Sheets and Flakes

Method

SLG, FLG, or MLG

Process Conditions

Reference

CVD

SLG, FLG

Large-area sheets, possibility to transfer to large variety of substrates

Hot wall reactor (1000°C)

[17]

Super-short-pulsed laser-induced deposition

FLG, MLG (up to 8 nm thick)

Freestanding; largely covers the whole substrates

Hot wall reactor (1100–1300°C)

[18]

Reduction of MLG oxide

SLG, FLG, or MLG, depending on the starting material

Thickness depends on the starting material

Rapid thermal expansion in hot wall reactor (1050°C)

[19]

Exfoliation through thermal shock

Isolated graphite nanoribbons (MLG)

Mean aspect ratio ~250

Vacuum oven, use of sulfuric and fuming nitric acids

[20]

Acid treatment of expandable graphite

SLG or FLG nanoribbons MLG

Sub-10-nm width; ultrasmooth edges

Heating in forming gas to 1000°C

[21]

Liquid-phase exfoliation

Freestanding, possesses quality of initial bulk graphite

Need to use solvents

[22]

### Table 3.2   Methods to Measure Thermal Conductivity in Graphene (SLG, FLG, MLG—Single-Layer, Few-Layer, and Multilayer Graphene)

Graphene Type/Fabrication Method

Method of Measurements

Configuration of Measurements

Thermal Conductance (W m-1 K-1)

Raman Shift/Temperature Conversion Coefficient

Reference

SLG/CVD

Microelectrothermal system

Suspended samples

1500–1800 (300 K) (increases with length)

[23]

SLG/CVD Isotropically modified

Raman shift (2D)

Circle

2197–4419 (300 K)

6.98–7.31 × 10-2 cm-1/K

[24]

SLG/CVD

Raman shift (2D)

Circle

2.6–3.1 × 103 (350 K)

7.2 × 10-2 (2D), 4.4 × 10-2 cm-1/K (G)

[25]

SLG/exfoliation

Raman shift (2D)

Circle

1800 (325 K) 710 (500 K)

0.072 cm-1/K

[14]

SLG/CVD

Raman shift (G)

Circle

2500 (350 K) 1400 (500 K)

0.0405 cm-1/K

[9]

SLG/CVD

Raman stokes/anti stokes ratio

Circle

600 (295 K)

[10]

SLG/exfoliation

Raman shift (G)

Trench

4840–5300 (300 K)

0.016 cm-1/K

[8]

FLG/exfoliation

Microelectrothermal system

Thermal bridge

1400–1495 (300 K)

[26]

FLG/exfoliation

Thermometer

Trench

560–620 (300 K)

[15]

Nanoribbons of FLG

Electrical

Trench

1100 (300 K)

[27]

MLG/exfoliation

Thermal flash

Platelets

776–2275 (300 K)

[28]

Here, for studies of thermal contacts between FLG and MLG, we used the confocal micro-Raman method at low laser power. The graphene flakes were prepared for natural graphite by sonication and deposited onto metallic electrodes by AC di-electrophoresis technique. By applying increased laser power, it was possible to observe the formation of improved thermal contacts resulting in significantly decreased local temperature of graphene under laser heating.

#### 3.2  Preparation and Characterization of FLG and MLG

Methods of preparation of FLG and MLG flakes (Table 3.1, see also [6,7,29]) include chemical vapor deposition [17], super-short-pulse laser produced plasma deposition [18], reduction of MLG oxide [19], exfoliation through thermal shock [20], acid treatment of expandable graphite [21], etc. All these methods have certain merits and disadvantages. Some of them are toxic, others are energy-intensive and time consuming, can produce defects in graphene, or cannot be used for large-scale production. In this work, the conventional low-cost liquid-phase exfoliation method [3036] was employed to prepare FLG and MLG. For this, we used natural graphite powder (size of polycrystals 1–3 mm) from Nacional de Grafite Ltda (Brazil). Two types of solvents were used:N,N-dimethylformamide (DMF) and isopropyl alcohol (IPA), both analytical grades. FLG/MLG dispersion was prepared from a mixture of natural graphite flakes (1 mg) in DMF or IPA (1 mL) using ultrasound processing followed by centrifugation. It is known that the surface energy of solvents and solute (Hildebrand solubility parameter) must be very close to each other [22,33,37] for effective process of exfoliation. In our case, Hildebrand parameters for DMF and IPA are 24.86 and 23.58 (MPa)1/2, respectively, and ~23 (MPa)1/2 for graphene [38]. After centrifugation, the supernatant high-density solution (~0.4 mL), containing graphene flakes with lateral sizes from 0.5 to 10 μm (with lateral size-to-thickness ratios up to 200–300 as measured using SEM), were carefully removed by pipette and retained for analysis and further use. Exfoliation of graphite by sonication in a liquid phase is believed to be the result of the action of shock waves and microjets generated in liquid sonication [3941]. A schematic of the exfoliation process is shown in Figure 3.1. Cavitation is a nonlinear phenomenon that concentrates and transforms the low-density elastic wave energy into higher energy densities through rapid formation and collapse of gas bubbles in the liquid. Collapse of bubbles on the solid graphite surface will cause breaking of the solid by the produced shock wave, whereas collapse in the liquid close to the surface causes a microjet of solvent that can hit the solid with a great kinetic energy [42,43]. The energy released is sufficient to remove top graphitic layers after disrupting weak molecular interactions between them, leading to gradual delamination and dispersion of the initial graphite flakes. It is usually assumed that polycrystalline natural graphite starts to exfoliate in the areas containing defects and next at the grain boundaries. Due to complexity of the cavitation process in liquids, many parameters can affect the resulting dimensions of flakes (lateral size and thickness), including the bath temperature, sonication, and centrifugation time, see Reference 39 for more details. Suspensions of graphene sheets have been fabricated in DMF and IPA with different time of sonication (Figure 3.2).

Figure 3.1   A schematic overview of the process of exfoliation of natural graphite in liquid phase. During sonication, bubbles and shock waves are produced, followed by cavitation with delamination graphite.

Figure 3.2   Solutions with FLG in DMF. (a) Mixture of DMF and natural graphite, (b) suspension after 2 min of sonication, and (c) suspension after 240 min of sonication.

For the size characterization, graphene flakes were deposited over holey carbon transmission electrons microscopy (TEM) grids with the mean size of holes near 1 μm. The statistical analysis for large number (hundreds) of sheets was performed to characterize the lateral graphene size distribution. Measured distributions were found to follow the so-called log normal size distribution, that is, the statistics for the particle size logarithms is normal (Gaussian), as first reported by Kolmogorov in 1941 [44], for the case of gold particles obtained by mechanical processing (attrition) of gold-containing rocks (Equation 3.1):

3.1

where

exp(μ) = L c (median size)

L c⟩ = exp(μ + σ2/2) (expected value)

(standard deviation)

This kind of distribution was observed later in many different situations, and can be expected to be valid in our case. To analyze the size distribution, histograms of lateral sizes for graphene sheets deposited over holey TEM grids were first obtained, with the number of measurements always being high enough (>100), see Figure 3.3 for DMF, similar results were obtained for IPA, not shown.

Figure 3.3   SEM images (a,b) of FLG deposited from DMF solution on holey carbon grids, for different sonication times (2 and 240 min, respectively) and (c,d) statistical distribution of graphene lateral sizes and lognormal fitting to the histogram for 2 and 240 min.

With increasing sonication time, the mean size was found to decrease from ~5 μm at 2 min to ~2 μm for 240 min, see Figure 3.4. The thickness of samples was found to vary from less than 2 to 30 nm (decreasing with sonication time), most of the samples being MLG or thin graphite nanoplatelets [39]. The aspect ratio (lateral size/thickness) was estimated roughly using SEM images to vary within a range 50–300 for all cases studied here, depending slightly on the sonication and centrifugation time and the type of solvent. Raman analysis with a micro-Raman spectrometer in confocal configuration (λ = 473 nm and 633 nm), was performed for flakes deposited on the TEM-grids to confirm high quality of graphene, with small full width at half maximum values, usually near 16–18 cm−1 (Figure 3.5). The D/G band ratio, widely used to evaluate the quality of the flakes, was found to vary from near 0 to 0.2 (tending to increase with sonication time), being consistent with small defect-free flakes.

Figure 3.4   Distribution function (after fitting) of graphene sizes for 2 and 240 min of sonication in DMF.

Figure 3.5   Raman spectra of graphene flakes with (a) 60 and (b) 695 min of sonication.

#### 3.3  Deposition of MLG

For the experimental study of the MLG/metal contact formation, linear test structures of W, Ti, and Au (100 nm thick) were prepared by a conventional lift-off technique and metal sputtering (Figure 3.6) [45]. Then, gaps between electrodes (~1 μm wide, ~5 μm deep) were cut by FIB milling to prepare a pair of metallic electrodes [46]. MLG flakes were deposited from liquid solutions between electrodes using an AC-dielectrophoresis method (DEP) with normal process parameters: frequency of 40 MHz, 1–3 V peak-to-peak voltages, and 30–180 s deposition time [47,48]. Electrical contacts between MLG and metal electrodes were further improved with thermal annealing under high-vacuum conditions (10−6 Torr) and the electrical resistances were measured, using a two terminals method. The results of two terminals measurements show that after annealing the contact resistances reduced by orders of magnitude, with values in the range from 0.1 to 10 kΩ μm2 [49,50].

Figure 3.6   Test structures prepared by conventional lithography (a) and electrodes for FLG deposition prepared by FIB (b).

Examples of samples obtained after DEP depositions over Ti and W electrodes followed by annealing in high vacuum (700°C, 1 h), as well as cross sectioning of the deposited flakes using FIB can be seen in Figures 3.7 and 3.8. For cross sectioning, the MLG flakes deposited over electrodes were protected with a Pt layer deposited by focused electron beam (FEB) (Figure 3.7d), and cross sectioning of contacts between MLG and metal were made by FIB to expose the structure of contacts (Figure 3.7e). The results for Ti indicate very tight contact apparently without diffusion of titanium inside the graphene flake (Figure 3.7f and g). Stronger metal–MLG interaction (due to annealing) can be observed in the case of W electrodes (Figure 3.8b), where an area with intermediate contrast at the metal–graphene interface (20–30 nm thick) is clearly seen, probably due to possible formation of tungsten carbide during high-temperature annealing. After annealing, some samples with one or two MLG flakes deposited between electrodes were selected for contact resistance measurements. For this, the total two terminal resistances were measured, and the resistances of contact leads and MLGs were estimated from the flake dimensions and known electrical resistances for electrode material and graphite. Then contact resistance (R) and resistivity (R.A) values were calculated, where A is the contact area. Values of contact resistance and resistivity for W electrodes (similar data were obtained for Ti) are shown in the Table 3.3 and Figure 3.9. The data indicate a strong reduction of contact resistance/resistivity with increasing annealing temperature.

Figure 3.7   SEM images of MLG and details of border contact (a,b,c). Flakes were protected with an FEB-deposited Pt layer followed by FIB milling, and cross sectioning of MLG/Ti contacts were further performed to expose the structure of contacts (d,e). (f,g) Cross section with larger magnification in the supported part of MLG.

Figure 3.8   SEM images of MLG/W-electrode contact after annealing. (a) Flakes were protected with an FEB-deposited Pt layer followed by cross sectioning of contacts to expose the interface structure. (b) The results indicate strong diffusion for contacts improved with thermal treatment.

Figure 3.9   Resistance of contact area as a function of annealing temperature.

### Table 3.3   Typical Values of Contact Resistivity for W Electrodes versus Annealing Temperature

Temperature of Annealing (°C)

Contact Resistivity (kΩμm2)

500

7.5 ± 2.5

600

2.3 ± 1.0

700

0.4 ± 0.2

#### 3.4  Micro-Raman Method to Measure Thermal Conductivity of MLG

Potential applications of graphene for thermal management in electronic devices are very promising as in-plane thermal conductivity of SLG is extremely high, up to 5.3 × 103 W m−1K−1 [29]. With increasing number N of layers in FLG/MLG, thermal conductivity K of graphene was shown to decrease rapidly, reaching the value for bulk graphite (near 1000 W m−1K−1 at room temperature) for N > 5 [12]. The theoretical studies predict K value for ideal infinite SLG as high as 104 W m−1K−1 [51], however reported experimental values vary widely, from 600 to 5000 W m−1 K−1. This variation can be attributed in part to the difficulties to prepare and transfer high-quality (defect-less) graphene with number of layers known, as well as to uncertainties in the laser absorbed power, finite size of the laser spot, contribution of impurities, and edge effects [24,27]. One more source of uncertainties in K measurements is related to poor thermal contacts between graphene and metal electrodes. Heat transfer through contacts and interfaces between nanostructured materials is an important issue in nanoelectronics, in studies of nanocomposites and thermal interface materials, but it is still poorly understood and the existing models of electrical and thermal (macro) contacts are often inapplicable at the nanoscale [52,53]. In conventional electronic devices, interfaces between two thermally dissimilar materials like metals and semiconductors are assumed to be planar and perfectly matched. In reality, the contact thermal resistance between nanostructured materials is determined by two factors: the overlap of phonon states for two solids and the properties of the interface itself (roughness, adhesion between materials). The heat transfer between two solids in a perfect contact (strong bond) can be calculated using diffusive mismatch model (DMM) or acoustic mismatch model (AMM) [24,54]. The efforts to improve the thermal interface models continue [5557], however, the existing models are based on various simplifying assumptions and often fail to describe real nanoscale systems composed by materials with large differences in mechanical and thermal properties. In particular, graphene materials are characterized by extremely high anisotropy (in-plane/cross-plane) and large vibrational mismatch with most solid materials used in nanoelectronics. The maximum vibrational frequencies in graphene are much higher than those in metals [58,59] (45 THz compared to 7–10 THz in metals), with the difference being smaller for oxides [60,61]. The sp2 bonding in graphene is responsible for high elastic stiffness in a basal plane, while rough metals surfaces can suffer plastic deformation at short length scale (at point contacts) under heating and pressure [62]. The existing models have difficulties also in describing weakly interacting solids with small adhesion energy. This is the case of graphene supported over most metals or oxides like SiO2 that do not form chemical bonds with carbon. Adhesion energy of graphene to amorphous SiO2 has been recently measured to be 0.45 and 0.31 J m−2 for SLG and FLG, respectively [63], being slightly higher for metals like Cu—0.72 J m−2 [64] and Ni (fcc)—0.81 J m−2 [65], respectively. Adhesion between graphene and metals can be calculated using molecular dynamics (MD) simulations [53,65]. MD simulations were shown to be useful also for analyses of the effects of atomistic changes (impurities, defects, strain) on thermal properties of materials and interfaces [66]. Using the modified AMM method, Prasher [56] has shown that reduced adhesion implies significantly lower heat transfer between two materials. It should be noted however, that even low adhesion between two surfaces produces some pressure squeezing the materials against each other, and this is especially important when plastic deformation of contacting materials is possible. The real contact area between rough materials (or between rough and plane materials) can be just a small fraction of the nominal contact area. Then the local pressure due to adhesion at the isolated contact points under heat flow can eventually produce a kind of “welding” between two solid surfaces resulting in a significant increase of the real contact area and decrease of the thermal contact resistance [67,68]. An MLG is essentially a rigid structure with atomically flat surface that cannot conform to rough metal surfaces. Therefore, for the MLG–metal contact improvement, the metal surface must be smoothened. Alternatively, for metals that can interact chemically with carbon forming carbides (like tungsten) stronger thermal contact can be established at high enough annealing temperature [69]. The adhesion energy can be also increased through functionalization of contacting surfaces, substituting a weak van der Waals interaction by stronger covalent bonding [70].

The quality of thermal contacts is characterized by thermal contact resistance R th (or thermal boundary conductance G) [66,68] that can be calculated by using the equation:

3.2

where Q is the heat flow through the interface (absorbed laser power), S is the contact area, and ΔT is the temperature drop at the interface. Schmidt et al. [71] obtained experimental values of metal–graphite (HOPG) thermal boundary conductance (TBC) at room temperature (RT) of ~3 × 107 W m−2 K−1 for Au, ~5 × 107 W m−2 K−1 for Cr and Al, and ~108 W m−2 K−1 for Ti. Similar data for Au–HOPG interface were reported by Norris et al. [55]: near 3 × 107 W m−2 K−1 at RT for as-cleaved HOPG surfaces. Much higher values were obtained by Hirotani et al. [72], in a study of thermal interfaces between Au and graphitic layers (c-axis) in ~100 nm diameter multiwalled carbon nanotubes (MWCNTs), varying from 8.6 × 107 W m−2 K−1 to 2.2 × 108 W m−2 K−1.

TBC between SLG or FLG (1.2–3.0 nm thick) and amorphous SiO2 was measured to range from ~0.8 × 108 to ~2 × 108 W m−2 K−1, with no clear dependence on the number of layers by Chen et al. [73]. Different models give values varying from 6 × 107 W m−2 K−1 [40] to 3 × 108 W m−2 K−1 [67] for perfectly flat graphene–amorphous SiO2 interface at RT. Even higher TBC can be expected for graphene interfaces with crystalline oxide materials such as sapphire [74].

For graphene (c-axis) interfaces with metals, the TBC values measured in most studies vary from 3 × 107 W m−2 K−1 to 1 × 108 W m−2 K−1 at room temperature, whereas higher values are measured for silicon oxide, up to 2 × 108 W m−2K−1. It should be emphasized also that experimental methods may give reduced TBC values in particular for metals, as real contact areas for rough metal surfaces are lower than nominal graphene/metal contact areas, while less difference can be expected for graphene/silicon oxide (smooth) surfaces. In practice, the presence of a thermal contact resistance together with a small contact area means that a considerable temperature drop (tens to hundreds K) can appear at interfaces between two dissimilar materials under heat flow. Such high temperatures can result in graphene burning and failure of the nanodevices, and also can affect the accuracy of K measurements.

In principle, high-quality thermal contacts between graphene and metals can be obtained using conventional high-temperature annealing in vacuum. However, as shown in our study [50], this can induce strain in MLG due to the formation of tight mechanical contacts between the graphene and metal electrodes followed by the shrinkage of the electrodes, thus stretching the graphene flake. Therefore, it is desirable to perform annealing by heating the graphene flake and the area of contacts locally, without substantial heating of the electrode bodies. Here, it is proposed to do such annealing by using the same laser resulting in mild “welding” of the graphene to the initially rough metal surface. The micro-Raman method was used here for determination of thermal conductivity along suspended MLG flakes, and the dramatic effect of localized laser thermal annealing for improving of thermal contacts between graphene and metals or silicon oxide, as well on the results of K measurements, was shown.

Experimentally, suspended flakes of graphene were used to study the properties of thermal conductivity in MLG. A 473 nm laser focused on the sample with 100× objective (~400 nm diameter laser spot, max laser power at the sample of 10.5 MW) was used for monitoring of the sample’s temperature, using the optothermal micro-Raman method [29] based on measurements of the frequency downshift ΔωG of a graphene G-line with increasing temperature, with the same laser used for local heating of suspended graphene samples (Figure 3.10) [75]. From the measured ΔωG value, the local graphene temperature rise ΔT above room temperature T RT can be estimated, using conversion coefficient g = ΔωGT [cm−1K−1], obtained in calibration experiments. The coefficients were measured to be −0.016, −0.015, and −0.011 cm−1K−1 for SLG, bilayer graphene, and MLG, respectively [76]. In other studies, values from −0.011 to −0.024 cm−1 K−1 for MLG (or HOPG) were reported [77,78]. The reasons for such a discrepancy are not clear at the moment. This may be attributed to different quality of samples, not perfect thermal contacts between the graphene and heat sink, and different geometries of the experiment. For example, a finite size of the laser spot on a sample can affect the measurement accuracy if it is comparable with the distance between the heating point and heat sink. Here, we accepted the value ΔωG = −0.011 cm−1 K−1. Resuming, from the measured G-peak downshift ΔωG, the local MLG temperature rise ΔT above room temperature T RT was estimated, using a relation ΔT(K) = −ΔωG(cm−1)/0.011 cm−1 K−1. Assuming that a perfect thermal contact is established between a graphene and a heat sink (i.e., room temperature T RT is achieved at the contact point), the temperature gradient ΔT/L = (T hT RT)/L is estimated, where L is the distance between the heating point and heat sink, and T h is the temperature measured at the point of laser heating. As a heat sink, metal electrodes known as good heat conductors are commonly used. Further, using the Fourier equation the K value can be calculated:

3.3

where P abs is the laser power absorbed on the sample and A is the sample cross-sectional area. In Equation 3.3, we consider that heating occurs in the center of the graphene flake and both electrodes contribute equally to heat absorption. Note that heat dissipation onto the underlying substrate occurs within the length scale given by the so-called thermal healing length L H, estimated to be ~0.1–0.2 μm [66]. The L H value should be added to L in Equation 3.3 while calculating K for short samples.

It is generally assumed that 2.3% of laser power is absorbed by a single graphene layer in a visible spectral range [79], however in the UV region the absorption can be higher [80], and in micro-Raman experiments done by Cai et al., a value of 3.3 ± 1.1% was reported for 532 nm laser wavelength [2]. Uncertainties in optical absorption in graphene (due to defects, impurities, varying number of layers) obviously contribute to errors in estimations of K using the micro-Raman technique. Further, it should be noted that the G-line downshift may depend on the heating mechanism, and heating by electrical current or by laser may result in a partial thermal equilibrium (not all phonon modes are equally excited), in contrast to the full thermal equilibrium reached in hot cells [81]. Therefore, the use of conversion coefficients determined under thermal equilibrium conditions for evaluation of local temperatures for the laser heated graphene may result in additional errors.

Nair et al. [79] has shown that the reflectance of SLG is less than 0.1%. No data are available for reflectance from an FLG, however, the reflectance of bulk graphite at the range of 500 nm was found to be as high as ~30%. For FLG graphene, the reflectance is probably lower, but should approach to 30% for thick samples (>20 nm). We used here the 30% reflectance value for our estimates of absorbed laser power.

Poor electrical or thermal contacts between the graphene surface and substrate could be also due to the presence of the so-called dead layer [1] (the graphene-substrate gap filled by air, water, or other impurities), and also can depend on the way of sample preparation and the roughness of the substrate surface especially in the case of metallic contacts deposited by sputtering. In contrast, the surface of the silicon dioxide has a smooth surface that in some cases (big contact area) can result in a small thermal contact resistance [12,29].

Other sources of uncertainties are related to possible deviations of temperature distribution from the idealized scheme shown in Figure 3.10, due to poor thermal contacts between the graphene flake and metal electrodes. In this case, the real values of ΔT may be lower and L may be larger than shown on Figure 3.10, resulting in underestimated K values.

Figure 3.10   Schematic setup of the experiment. (The source of the material, V. A. Ermakov et al., Nonlocal laser annealing to improve thermal contacts between multi-layer graphene and metals, Nanotechnology, vol. 24, no. 15, p. 155301. Copyright 2013, IOP Publishing Ltd. is acknowledged.)

#### 3.5  Experimental Determination of MLG Thermal Conductivity and Thermal Contact Resistivity

Examples of MLG deposited over various metal (W, Au, Ti) electrodes forming side contacts with the metal are shown in Figure 3.11a through f. As the cuts made by FIB were longer than metal electrodes, in a few cases we also found graphene flakes deposited over the gaps outside the electrodes (over the silicon oxide surface) that allowed us to study the effects of annealing between graphene and silicon oxide (Figure 3.11e). Cuts between electrodes were made with width of 1 μm (±10%), and a tilted image of the cut is shown in Figure 3.11d, where nonvertical cut walls can be seen.

Experiments were performed in air, using a 473 nm wavelength laser beam with a spot of ~400 nm and the maximum power up to 10 MW that was focused at the center of suspended MLG platelets. Most of experiments were performed with 20–30 nm thick (60–90 monolayers) samples, so that practically full laser power (with a correction for reflection) was absorbed by the samples. In other words, in such experiments there is no uncertainty in absorbed laser power. The G-line position was found first to shift linearly with laser power (see Figure 3.12a, black squares) indicating gradual heating of the sample proportional to the absorbed power, as expected. However, with increasing power the shift was found to saturate or even reduce. In the case shown in Figure 3.12a, the saturation occurs at −22 cm−1, in other cases the maximum shift was found to vary between 7 and 23 cm−1 for laser power up to 10.5 MW, depending on the flake dimensions and quality of contact with electrodes, the smallest downshifts were obtained for Au electrodes. Using the conversion coefficient g = −0.011 cm−1 K−1, very high local graphene temperatures (from 600°C to 2000°C) can be estimated. The saturation can be attributed to two different mechanisms. First, improvement of the thermal contact between the MLG and metal electrode can occur during sample heating, then heat losses to the electrodes become stronger and the sample temperature drops. Second, gradual sample thinning due to graphene etching in air and thus reduced laser absorption during the heating process, as the increasing part of the laser power passes through the flake without absorption. Obviously, such strong heating should inevitably result in gradual layer-by-layer graphene etching and thinning by oxygen present in the air [82,83]. However, our results proved this process to be relatively slow, with a maximum rate much less than one monolayer per second for T max ~ 2000 K, as revealed by special thinning experiments, see below. This means that a considerable number of spectra can be acquired during the thinning process before the moment when MLG becomes thin enough to reduce absorption of laser light in the sample. Furthermore, care was taken here to keep the sample expositions at minimum required for the spectra acquisition (typically, ~1 s at T max) leading to minimum sample changes during the exposition.

Figure 3.12   G peak position versus absorbed laser power during the first irradiation (initial laser annealing, black squares) and after annealing (gray open circles) for the same FLG flake on W contacts (a), SiO2 (b), and Au contacts (c). (The source of the material, V. A. Ermakov et al., Nonlocal laser annealing to improve thermal contacts between multi-layer graphene and metals, Nanotechnology, vol. 24, no. 15, p. 155301. Copyright 2013, IOP Publishing Ltd. is acknowledged.)

In the thinning experiments, designed to determine the MLG etching rate at the maximum laser power, we deposited MLG flakes onto a crystalline Si substrate covered by thermally grown 300 nm thick SiO2 layers. We applied a method to measure the thickness of FLG over Si, recently proposed by Han et al. [82] and Koh et al. [83], to monitor the changes in the flake thickness during the sample annealing in air. The method is based on comparison between the integrated intensities of the Raman lines of graphene (G-line) and first-order optical phonon peak from underlying Si (520 cm−1). The MLG thickness, before and after the thinning experiment, was also measured using atomic force microscopy that allowed an independent evaluation of the thickness changes. Due to much lower cross-layer heat conductivity of graphitic materials [66,80], absorption of the laser light in the flake leads to strong heating mostly of the upper layers and their layer-by-layer etching due to interaction with oxygen and the formation of volatile products such as CO or CO2. The MLG flakes chosen for such experiments were thin enough (usually, thinner than 10 nm) to detect the characteristic Si-line (520 cm−1) from the substrate. Continuous detection of the I(G)/I(Si) ratio allowed us to track the flake thinning while the G-line downshift provided the information about the local temperature. Note that the method is suitable for reliable measurements of the number of layers N up to ~10. For thicker flakes the relation between the I(G)/I(Si) ratio and the N number becomes nonlinear affecting the measurements accuracy, however semiquantitative information on the sample thickness evolution still can be obtained. For these measurements, only flakes with lateral dimensions exceeding 1.5–2.0 μm were used, to avoid a parasitic contribution from the bulk Si signal collected from the area around the flake (i.e., without absorption by the flake). Typical temporal evolution of the I(G)/I(Si) ratio and temperature is shown in Figure 3.13. The process of thinning (reduction of the I(G)/I(Si) ratio) was accompanied by gradual decrease of the sample temperature (G-line downshift) due to decreasing absorption in the flake. In Figure 3.13, the ratio changes from 0.8 to 0.25, that translates in evolution of N from ~10 to ~4, following the calibration given in Reference 83 for approximately the same conditions. The thinning process was relatively fast for T as high as 1500–2000 K, when ~4 monolayers were etched out during the first 60 s under laser irradiation with power of 10 MW. Further, under the present conditions the thinning process was always found to stop when the temperature reduced to ~850–900 K, when monolayer graphene was not reached yet, see Figure 3.13. AFM measurements were performed to find that the minimum thickness obtained in our experiments was limited to ~1.5–2.0 nm, compatible with the estimates of N min near five layers (see an example in Figure 3.14). The temperature when the graphene etching stops (near 600°C) is comparable with the results of TGA analysis by Han et al. [82] for graphene and Pang et al. [84] for nanotubes (slightly lower T values were obtained for graphite). Interestingly, at the final stage of thinning (T < 1000 K) it was possible to observe step-like changes of the I(G)/I(Si) ratio and thus the number of layers (see inset for Figure 3.13b), indicating basically a layer-by-layer character of the MLG thinning, where a fast layer removal is followed by very long periods (up to 700–1000 s) of small changes in the I(G)/I(Si) ratio.

Figure 3.13   (a) Layer-by-layer thinning process for FLG deposited onto oxidized Si substrate—I(G)/I(Si) ratio and temperature of the flake, +—temperature, open circles—I(G)/I(Si) ratio. The inset shows the signals evolution during first 500 s. (b) Dependence of thinning rate versus temperature (dots—derived from experimental data, line—smoothed curve). The inset in (b) shows evolution of the number of layers at the final stage of thinning. (The source of the material, V. A. Ermakov et al., Nonlocal laser annealing to improve thermal contacts between multi-layer graphene and metals, Nanotechnology, vol. 24, no. 15, p. 155301. Copyright 2013, IOP Publishing Ltd. is acknowledged.)

Figure 3.14   AFM measurements of MLG thickness before and after laser thinning. Note that the minimum thickness of the flake after the thinning process is ~2 nm. (The source of the material, V. A. Ermakov et al., Nonlocal laser annealing to improve thermal contacts between multi-layer graphene and metals, Nanotechnology, vol. 24, no. 15, p. 155301. Copyright 2013, IOP Publishing Ltd. is acknowledged.)

Further, the quality of graphene flakes apparently did not change during annealing, as G-line FWHM and I(D)/I(G) ratios remained at the same level (in some case, even a small reduction of the ratio was detected). In Figure 3.15a, one example of Raman spectra taken before and after annealing in the thinning experiment is shown for the flake with the G-line FWHM and I(D)/I(G) ratio of ~15 cm−1 and ~0.05, respectively. In general, the I(D)/I(G) ratio was found to vary from ~0.01 to 0.05 for different samples (in Figure 3.15b, a spectrum with a small D line is shown; such samples were mostly used for K measurements). This is much smaller than observed in other studies with narrower graphene nanoribbons [66,85], indicating very low density of defects and relatively large average size of graphene crystallites in our samples. Following the approach developed by Cançado et al [86] (see also [13,85]), the average crystallite size L a in graphene can be found using the formula: L a ~ 560 [I(D)/I(G)]−1/E L 4, where E L is the laser photon energy in eV. For I(D)/I(G) = 0.05, L a ~ 280 nm can be estimated, being higher for smaller ratios. The fact that an increase of I(D)/I(G) ratio was not observed during annealing indicates that no additional defects (or average crystallites size reduction) were induced by laser processing under the present conditions, characterized by very short exposures (<1s) by laser light.

Figure 3.15   Raman spectra of different FLG: (a) the same sample before and after laser annealing, at laser power of 0.29 MW, 1 s; (b) another sample, spectrum obtained at laser power of 2 MW, 5 s. (The source of the material, V. A. Ermakov et al., Nonlocal laser annealing to improve thermal contacts between multi-layer graphene and metals, Nanotechnology, vol. 24, no. 15, p. 155301. Copyright 2013, IOP Publishing Ltd. is acknowledged.)

The saturation of the G-line position downshift with increasing power (Figure 3.12) therefore can be attributed mostly to the gradual annealing of the graphene–metal contact, resulting in improving heat transfer through the contact and thus reduced graphene heating. This is confirmed by results obtained in the second run (performed immediately after the first one), when much lower G-line downshifts are detected for the same laser powers, with the curve slope of −8 × 103 cm−1 W−1, as compared with −2.2 × 104 cm−1 W−1 for the first irradiation (Figure 3.12a). Heat losses from the graphene surface due to thermal contact with air (~105 W m−2 K−1) [87] and by radiation are estimated to be much smaller than the absorbed laser power (~0.1 and 10−8 MW, respectively). Thus, under the present conditions the main mechanism of heat losses is due to heat transfer through the graphene–metal contacts, and the reduced sample heating during the second run clearly indicates the improved thermal conductivity of the graphene–metal contact after annealing occurred during the first irradiation. The thermal contact improvement is likely due to the partial melting of the metal surface in contact with the graphene, reducing of the initially high metal surface roughness under the graphene, and corresponding increase of the contact area and adhesion between surfaces. This is possible because of distinctly different mechanical properties of two contacting materials: (i) MLG with a perfectly flat surface, characterized by high in-plane elastic stiffness and high cross-plane hardness, and (ii) rough metal surface that is subject to plastic deformation at nanoscale length under pressure (due to adhesion) and heat flow.

Interestingly, much weaker graphene heating was observed for samples deposited over SiO2 (Figure 3.11d), both before and after the annealing (G-line downshift −1.6 × 103 cm−1 W−1 and −8 × 102 cm−1 W−1, respectively). Note that the contact annealing in this case was possible only for higher powers (>5 MW) and lower G-line downshift (−7 cm−1) corresponding to T max ~ 600°C, see Figure 3.12b. This is a clear indication of initially better thermal contacts between the graphene and thermal oxide surface that is much flatter (roughness ~0.1 nm) compared with metals (W and Au). Note that for the oxide substrate, the maximum sample heating does not exceed ~600°C, when no sample burning and thinning can be expected, thus the significant reduction of the sample heating can be attributed only to the improvement of thermal contacts.

Note that the Raman measurements provide only local values of temperature (ΔT 1 and ΔT 2), before and after annealing (Figure 3.16) while temperature drops at the graphene–substrate interface (ΔT i1 and ΔT i2), are unknown. This leads to underestimated values of K as real values of the temperature change along the graphene (ΔT g) are smaller than those measured by the micro-Raman method. Assuming that annealing changes only the interface properties (reducing ΔT i1 due to the contact area increase) and the temperature change along the MLG remains the same (ΔT g), one can get: ΔT 1 = ΔT g + ΔT i1, ΔT 2 = ΔT g + ΔT i2, where ΔT i1 = P abs/(S 1 G) and ΔT i2 = P abs/(S 2 G), S 1 and S 2 are real contact areas before and after annealing, and ΔT g is determined by Equation 3.2: ΔT g = −P abs L/(2KA). Further, assuming that after annealing the contact area becomes close to the nominal contact area S nom (S 1S 2S nom), estimates of the temperature drop at the interface after annealing can be made using the literature data on the thermal boundary conductance G: ΔT i2 = P abs/(S nom G). Further, the temperature change along the graphene can be calculated using the results after annealing: ΔT g = ΔT 2 − ΔT i2 ≈ ΔT 2P abs/(S nom G). Then, the temperature drop at the interface before annealing and the contact area increase due to annealing can be estimated: ΔT i1 = ΔT 1 − ΔT g ≈ ΔT 1 − ΔT 2 + ΔT i2 = P abs/(S 1 G) and S 2/S 1 = ΔT i1T i2, respectively. Finally, estimates were made to show that corrections to ΔT g in our experiments after annealing (due to ΔT i2) can vary from ~10 K (for SiO2) to 100–150 K (for metals). These corrections result in considerable increase (that can reach 30%–40% or even more) of the calculated K values for metal electrodes, with smaller corrections for SiO2. Note also that if the annealing is not complete (S nom > S 2), the ΔT i2 is in fact higher and the ΔT g value is then overestimated, thus K is still underestimated.

Figure 3.16   Scheme showing improvement of thermal contacts between FLG and metal contacts during laser annealing, and the resulting changes of temperature distribution over the sample. (The source of the material, V. A. Ermakov et al., Nonlocal laser annealing to improve thermal contacts between multi-layer graphene and metals, Nanotechnology, vol. 24, no. 15, p. 155301. Copyright 2013, IOP Publishing Ltd. is acknowledged.)

Using the approach described here and determined above ΔT i1 values, estimations gave G near (2.5–3) × 106 W m−2 K−1 for W and Au and 6 × 107 W m−2 K−1 for SiO2 before annealing, and contact areas as low as 6%–8% for metals and 30% for SiO2 (see Table 3.4). The thermal boundary conductance strongly increased as a result of laser annealing, and the highest TBC was observed for SiO2. This finding proves that heat transfer by phonons from graphene to silicon oxide can be even more efficient than to metals, see also [71,73]. Based on these observations, two important conclusions can be made: (i) high-temperature (T ≥ 1000°C) local annealing is necessary to achieve reasonable quality of contacts with metal surfaces that are usually relatively rough (although the degree of roughness may depend on the metal deposition method), (ii) high-quality thermal contacts between two nearly atomically flat surfaces (MLG and silicon oxide) can be achieved at lower temperatures (T ~ 600°C). The improvement of contact in the latter case can be attributed to removal of air pockets, solvent traces, and other possible impurities.

### Table 3.4   Estimates of Thermal Boundary Conductance between MLG and Metals (W, Au) and SiO2

G (W m-2 K-1)

Conditions

W

Au

SiO2

Before annealing

3 × 106

2.5 × 106

6 × 107

(6%)

(8%)

(30%)

After annealing a

5 × 107

3 × 107

2 × 108

Source: The source of the material, R. R. Nair et al., Fine structure constant defines visual transparency of graphene, Science, vol. 320, no. 5881, p. 1308, 2008. Copyright 2013 IOP Publishing Ltd. is acknowledged.

Notes:

a  Assuming perfect contact after annealing, data from References 71 and 73.

Further, using Equation 3.3 and corrections as discussed above, the thermal conductivity values were estimated for a number of MLG samples before and after annealing. For example, the values obtained were K ~ 340 W m−1 K−1 and 560 W m−1 K−1 for the samples shown in Figure 3.11a,b (400 nm and 1 μm wide, respectively, both ~20 nm thick), near room temperature. In calculations of K using Equation 3.3, thermal healing length L H of 0.1 μm was added to L value, as discussed above. It is important to note that much lower values (not exceeding 150 W m−1 K−1) were obtained for samples before laser annealing. The obtained data (after annealing) are comparable with other reported results for narrow graphene samples where K is reduced due to a strong effect of phonon scattering at the edges [66,84,88]. For instance, for narrow SLG nanoribbons supported over SiO2 [50] K median values were measured to be ~80 W m−1K−1 for samples 20–60 nm wide being much smaller than measured for graphene of larger size (≫0.3 μm) under the same conditions. The same trend was observed for FLG (3–5 layers) by Wang et al. [88], where K values were found to be much smaller for narrow samples, for both supported and suspended graphene, decreasing from 1250 W m−1K−1 for 5 μm wide sample to 150 W m−1 K−1 (supported) or 170 W m−1K−1 (suspended) for 1 μm wide samples. These data show the strong effect of the sample width on graphene thermal conductivity.

Figure 3.11   MLG flakes deposited over metal electrodes: W (a), Au (b), Ti (c), and SiO2 layer (e). (f) An overview of electrodes with several FLG flakes deposited over the gap, (a,c,e,f) are top images and (d) is a tilted image (52°). The scale bar corresponds to 1 μm. (The source of the material, V. A. Ermakov et al., Nonlocal laser annealing to improve thermal contacts between multi-layer graphene and metals, Nanotechnology, vol. 24, no. 15, p. 155301. Copyright 2013, IOP Publishing Ltd. is acknowledged.)

It is important to emphasize again that the main point of this study is to show the importance of good thermal contacts on the K measurements accuracy (that is frequently overlooked in the experiments).

In addition, we performed similar experiments with MWCNTs (diameters in the range of 20–30 nm, where the number of graphitic layers is about the same as in the experiments with MLG described above) deposited under the same conditions over metal (Au, W) electrodes with 1 μm gaps, followed by the same laser annealing procedure. Similar effect of thermal contacts improvement was observed, and K values up to ~1000 W m−1 K−1 were estimated after annealing, in good agreement with data reported for MWCNTs of 20–30 nm diameter by Fujii et al. [89], where K was found to decrease fast for increasing nanotube diameter, from K ~ 2000 W m−1 K−1 to K ~ 500 W m−1 K−1 at 10 nm and 28 nm diameter, respectively. The main difference between nanotubes and MLG in such measurements consists in the absence of edges for nanotubes where enhanced phonon scattering occurs. This comparison strengthens the hypothesis that the main reason for relatively small K values obtained here can be attributed mostly to the small size of flakes, rather than to other factors such as contaminants and graphene quality.

Finally, electrical two-terminal measurements performed before and after laser annealing, showed some reduction of the resistance for most of samples, with lowest electrical contact resistivity estimated to be at the order of ~1 kΩ μm2 or higher after annealing [50]. However, in most cases this electrical contact reduction was much smaller as compared with the improvement obtained here for thermal contact resistance (up to an order of magnitude). This can be probably attributed to the fact that annealing was performed in air, resulting likely in the notable oxidation of metal (W and Ti) electrodes.

#### 3.6  Conclusions

The formation of thermal contacts between MLG flakes and different metals (W, Ti, and Au) as well as with silicon oxide surfaces was studied here using confocal Raman spectroscopy. It was demonstrated that the accuracy of thermal conductivity measurements for suspended MLG flakes by an optothermal micro-Raman technique depends critically on the quality of thermal contacts between the flake and initially rough metal electrode surface. The same laser at higher power was used for the contacts improvement by annealing that occurs usually at temperatures above 900°C. After very short laser exposures (~1 s, with just a few mJ of laser energy deposited at a spot), compared with much longer periods of conventional thermal annealing (~1 h), considerable reduction of the sample heating by laser was observed. After improvement of the thermal contacts achieved by the laser annealing, we were able to perform more precise measurements of MLG thermal conductivity. The maximum values obtained for narrow MLG samples used here are close to 600 W m−1 K−1 (consistent with the literature data for flakes with submicron lateral dimensions) compared with much lower values <150 W m−1 K−1 obtained without annealing. This finding shows the importance of establishing good thermal contacts between graphene and metals. The improvement of thermal contacts to initially rough metal electrodes was attributed to local melting of the metal surface under laser heating (heat flow through the contact area) and increasing area of real contact and enhanced adhesion. Note that for the graphene–metal contact improvement, the localized heating by laser occurs in another (suspended) part of graphene, so that the contact annealing can be called remote or nonlocal. It is also interesting to note that improvement of thermal contacts was observed also between MLG and FLG with silicon oxide surface, for the latter the graphene–substrate heat transfer was found to be much higher, with the thermal boundary conductance estimated to be ~200 MWm−2 K−1 as compared to the metals such as Au and W used in the present work (~30–50 MW m−2 K−1).

#### Acknowledgments

The authors thank CNPq, FAPESP, and INCT NAMITEC for financial support, CCS-UNICAMP staff for technical assistance, and CTI Renato Archer, R. Savu (CCS-UNICAMP) and A. L. Gobbi (LNNano) for help in the preparation of samples.

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